ULTRAFAST NONRADIATIVE DECAY AND EXCITATION ENERGY TRANSFER BY
CAROTENOIDS IN PHOTOSYNTETIC LIGHT-HARVESTING PROTEINS
By
Soumen Ghosh

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Chemistry – Doctor of Philosophy
2017

ABSTRACT
ULTRAFAST NONRADIATIVE DECAY AND EXCITATION ENERGY TRANSFER BY
CAROTENOIDS IN PHOTOSYNTETIC LIGHT HARVESTING PROTEINS
By
Soumen Ghosh
This dissertation investigates the photophysical and structural dynamics that allow
carotenoids to serve as efficient excitation energy transfer donor to chlorophyll acceptors in
photosynthetic light harvesting proteins. Femtosecond transient grating spectroscopy with optical
heterodyne detection is employed to follow the nonradiative decay pathways of carotenoids and
excitation energy transfer to chlorophylls. It was found that the optically prepared S2 (11Bu+)
state of β-carotene decays in 12 fs fs to populate an intermediate electronic state, Sx, which then
decays nonradiatively to the S1 state. The ultrafast rise of the dispersion component of the
heterodyne transient grating signal reports the formation of Sx intermediate since the rise of the
dispersion signal is controlled by the loss of stimulated emission from the S2 state. These
findings were extended to studies of peridinin, a carbonyl substituted carotenoid that serves as a
photosynthetic light-harvesting chromophore in dinoflagellates. Numerical simulations using
nonlinear response formalism and the multimode Brownian oscillator model assigned the Sx
intermediate to a torsionally distorted structure evolving on the S2 potential surface. The decay of
the Sx state is promoted by large amplitude out-of-plane torsional motions and is significantly
retarded by solvent friction owing to the development of an intramolecular charge transfer
character in peridinin. The slowing of the nonradiative decay allows the Sx state to transfer
significant portion of the excitation energy to chlorophyll a acceptors in the peridinin–
chlorophyll a protein. The results of heterodyne transient grating study on peridinin–chlorophyll
a protein suggests two distinct energy transfer channels from peridinin to chlorophyll a: a 30 fs

process involving quantum coherence and delocalized peridinin–Chl states and an incoherent,
2.5 ps process involving the distorted S2 state of peridinin. The torsional evolution on the S2 state
is accompanied by the formation of an ICT character and dynamic exciton localization, which
controls the mechanism of excitation energy transfer to chlorophyll a acceptors in the peridinin–
chlorophyll a protein.

Copyright by
SOUMEN GHOSH
2017

To my parents

v

ACKNOWLEDGEMENTS

It has been an incredible journey so far. I started my journey in a small village Kamra, state
West Bengal in India. The meager financial resources never became a limiting factor in my
higher studies because of many kind-hearted individuals. They helped me along the way though
their support, inspiration and encouragement and thereby, shaped my carrier. My journey
towards a Ph.D. would have been impossible without their help. I am so greatly indebted to all of
them.
I would like to thank my graduate advisor Professor Warren F. Beck for his constant
motivation, guidance and support. You nurtured me in my early days of graduate school and
helped me blossom into a scientist. Thank you for giving me the intellectual freedom and
training me for academia. Being a teaching assistant to your undergraduate courses has
influenced my teaching philosophy and has changed the way I teach a subject now. Thank you. I
have been fortunate to have you as my advisor.
I would also like to thank my senior colleagues Dr. Michael Bishop and Dr. Jenny Jo Mueller
for training me on 2D-photon echo techniques and for all their contributions to this work. Dan
(Jerome Roscioli), it has been a real pleasure to work with you. I have learnt a lot from you, both
about science and life in general. Thank you for your friendship. Jason and Ryan, I wish you the
best for your graduate carrier and for carrying the research forward in new exciting directions. I
am also thankful to my committee members, Professors James McCusker, Marcos Dantus and
Benjamin Levine for asking insightful questions and for helping me with recommendation letters
during my postdoctoral search.

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My friends in the Chemistry and Engineering departments of MSU have been an integral part
of this Spartan experience. Without my Spartan Family, this journey would have been difficult. I
will always cherish the occasional get-togethers, gossips and great foods that made this place a
home away from home. Though it would be difficult to list everyone’s name, I owe special
thanks to Dr. Arkaprabha Konar and Dr. Shreya Nad for their love, advice and encouragement.
You both have been great role models for me during my Ph.D. years. I am thankful to my college
friends from IIT Kanpur and Belur days for being a breadth of fresh air amidst the hectic
schedule of graduate life.
I am fortunate to come across many great teachers during my high school and college days.
They inspired the little me to strive for the best and work hard to achieve my goals. I owe much
of my academic aspirations to my teachers. A special thanks to my Master’s thesis advisor
professor Pratik Sen at IIT Kanpur for sparking my interest in ultrafast spectroscopy.
I am lucky to have an awesome family. Thank you Maa and Baba for giving me the freedom
to fly. All what I am today is because of you. Without your love, encouragement and sacrifice, I
would not have made this far. I am really thankful to have lovely and caring sisters in my life.
Thank you for looking after our parents. Finally, a very special thanks to Maitreyee Rej for
accepting me the way I am. Thank you for your love and for being a part of this journey. I hope
that I have made all of you proud.

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TABLE OF CONTENTS

LIST OF TABLES………………………………………………………………………………...x
LIST OF FIGURES……………………………………………………………………………....xi
KEY TO ABBREVIATIONS………………………………………………………………….xxiv
OVERVIEW OF THE DISSERTATION………………………………………………………....1
Chapter 1: Introduction to Photosynthetic Light Harvesting by Carotenoids................................. 3
1.1 Photosynthesis: An Overview ............................................................................................... 3
1.2 Architecture of the Light Harvesting Antenna...................................................................... 4
1.3 Energy Transfer Mechanisms in Light-Harvesting Proteins ................................................ 6
1.3.1 Incoherent Energy Transfer ........................................................................................... 7
1.3.2 Coherent Energy Transfer .............................................................................................. 8
1.4 Carotenoids as Light Harvesting Chromophores: Ultrafast Photophysics ........................... 9
1.4.1 Dark Intermediate States in Carotenoids ..................................................................... 11
1.4.2 Intramolecular Charge Transfer in Carotenoids .......................................................... 13
1.5 Light Harvesting in the Peridinin–Chlorophyll a Protein ................................................... 15
1.6 Hypotheses and Proposed Work ......................................................................................... 20
1.6.1 Conformational Dynamics of Conjugated Polyenes .................................................... 20
1.6.2 Approach: Heterodyne Detected Transient Grating Spectroscopy .............................. 23
REFERENCES ......................................................................................................................... 26
Chapter 2: Nonradiative Decay of the S2 (11Bu+) State of β-Carotene: Contributions from Dark
Intermediates and Double Quantum Coherences .......................................................................... 33
2.1 Introduction ......................................................................................................................... 34
2.2 Experimental Section .......................................................................................................... 38
2.2.1 Sample Preparation ...................................................................................................... 38
2.2.2 Linear Spectroscopy..................................................................................................... 38
2.2.3 Nonlinear Spectroscopy ............................................................................................... 38
2.3 Experimental Results .......................................................................................................... 40
2.3.1 Linear Spectroscopy and Laser Excitation Spectrum .................................................. 40
2.3.2 β-carotene transient grating signals ............................................................................. 41
2.4 Numerical Simulation of Linear and Nonlinear Response .................................................. 49
2.4.1 Numerical Simulation of Absorption Spectrum .......................................................... 52
2.4.2 Numerical Simulation of Transient Grating Signal ..................................................... 54
2.4.2.1 Simulation of Transient Grating Signal Without Sx .............................................. 62
2.4.2.2 Simulation of Transient Grating Signal Without Sx .............................................. 70
2.4.2.3 Contributions of Double-Quantum Coherence Pathways ...................................... 77
2.5 Discussion ........................................................................................................................... 79
2.6 Conclusions ......................................................................................................................... 88
APPENDIX ............................................................................................................................... 91

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REFERENCES ......................................................................................................................... 96
Chapter 3: Nonradiative Deactivation of the S2 (11Bu+) State of Peridinin: Detection and
Spectroscopic Assignment of an Intermediate in the Decay Pathway ........................................ 102
3.1 Introduction ....................................................................................................................... 103
3.2 Experimental Section ........................................................................................................ 108
3.2.1 Sample Preparation .................................................................................................... 108
3.2.2 Linear and Nonlinear Spectroscopy ........................................................................... 109
3.3 Experimental Results ........................................................................................................ 109
3.3.1 Linear Spectroscopy and Laser Excitation Spectrum. ............................................... 109
3.3.2 Heterodyne Transient Grating Signal of Peridinin .................................................... 110
3.4 Numerical Simulations...................................................................................................... 117
3.4.2 Simulation of the Absorption Spectrum. ................................................................... 119
3.4.3 Simulation of the Heterodyne Transient Grating Signals .......................................... 120
3.5 Discussion ......................................................................................................................... 125
3.6 Conclusion ........................................................................................................................ 130
APPENDIX ............................................................................................................................. 133
REFERENCES ....................................................................................................................... 140
Chapter 4: Torsional Dynamics and Intramolecular Charge Transfer in the S2 (11Bu+) Excited
State of Peridinin: A Mechanism for Enhanced Mid-Visible Light Harvesting ......................... 146
4.1 Introduction ....................................................................................................................... 147
4.2 Experimental Methods ...................................................................................................... 148
4.2.1 Sample Preparation .................................................................................................... 148
4.2.2 Femtosecond Spectroscopy........................................................................................ 148
4.3 Results and Discussions .................................................................................................... 149
APPENDIX ............................................................................................................................. 159
REFERENCES ....................................................................................................................... 175
Chapter 5: Excitation Transfer by Coherent and Incoherent Mechanisms in the Peridinin–
Chlorophyll a Protein.................................................................................................................. 180
5.1 Introduction ....................................................................................................................... 181
5.2 Experimental Methods ...................................................................................................... 183
5.2.1 Sample Preparation. ................................................................................................... 183
5.2.2 Femtosecond Spectroscopy........................................................................................ 183
APPENDIX ............................................................................................................................. 194
REFERENCES ....................................................................................................................... 203
Chapter 6: Conclusions and Future Directions ........................................................................... 207
REFERENCES ....................................................................................................................... 210	

ix

LIST OF TABLES

Table 2.1 MBO model parametersa for the simulation of the β-carotene S 0 → S 2 absorption
spectrum in benzonitrile at 295 K. ........................................................................................ 54
Table 2.2 Transition frequencies ( ω ij ) and relative transition dipole strengths ( µ ij ) used in
the simulation of the transient-grating signal from β-carotene without inclusion of the Sx
state (see Figure 2.9). ............................................................................................................ 65
Table 2.3 MBO model parametersa for the S1 → S n1 ESA transition of β-carotene in
benzonitrile at 295 K. ............................................................................................................ 66
Table 2.4 Transition frequencies ( ω ij ) and relative transition dipole strengths ( µ ij ) used in
the simulation of the transient-grating signal from β-carotene with inclusion of the Sx state
(see Figure 2.9). .................................................................................................................... 72
Table 3.1 MBO model parametersa for the simulation of the peridinin S0→S2 absorption
spectrum in methanol at 295 K (Figure 3.1). ...................................................................... 120
Table 3.2 Transition frequencies ( ω ij ) and relative transition dipole strengths ( µ ij ) used in
the simulation of the transient-grating signal from peridinin shown in Figures 3.11–3.13.121
Table A3.1 Transition frequencies ( ω ij ) and relative transition dipole strengths ( µ ij ) used
in the simulation of the transient-grating signal from peridinin in which the identity of the
state Sx is equated with the S1 state but with an initially higher energy due to vibrational
excitation, here about two quanta for C–C or C=C modes of the conjugate polyene
backbone (+2590 cm−1)....................................................................................................... 136
Table 4.1 Lifetime of the Sx state of peridinin, as obtained from the global target models of
the absorption and dispersion components of the transient grating signal in four solvents 152
Table A4.1 Lifetimes of the S2, Sx, and S1 states, as obtained from the global models of the
transient grating signal from peridinin in four solventsa .................................................... 173
Table A5.1 Transition frequencies ( ω ij ) and relative transition dipole strengths ( µ ij ) used
in the simulation of the transient-grating signal from PCP................................................. 199	

x

LIST OF FIGURES

Figure 1.1 Schematic description of light harvesting and energy transfer to reaction centers
in photosynthetic organism. From reference 1. Copyright (2014) John Wiley & Sons, Ltd,
used with permission............................................................................................................... 4
Figure 1.2 The nonameric structure of the peripheral light harvesting complex (LH2) from
Rhodopseudomonas acidophila.(1NKZ.pdb)5 From reference 1. Copyright (2014) John
Wiley & Sons, Ltd, used with permission. (a) and (b) views perpendicular to the membrane
plane with and without the protein scaffold. (c) and (d) views parallel to the membrane
plane with and without the protein scaffold. B800 ring is shown in red and B850 ring is
shown in blue. The ι polypeptide is colored yellow and the β polypeptide is colored green.
Carotenoids are shown in orange. ........................................................................................... 5
Figure 1.3 Nonradiative decay pathways in carotenoids. From reference 19. Copyright
(2010) American Chemical Society, used with permission. Internal conversion processes are
denoted by blue and red arrows; black arrows denote vibrational relaxation. Absorption
spectra (top right) of LH2 (purple), PCP (orange), and LHCII (green). The range of energies
of carotenoid S2 and S1 transitions are also shown by the orange and red bars beneath the
spectra. Structure of different carotenoids are shown at the bottom..................................... 10
Figure 1.4 Three different models for the nature of the ICT state in peridinin and other
carbonyl-containing carotenoids dissolved in polar solvents. From reference 57. Copyright
(2013) Biophysical Society, used with permission. (left) S1 and ICT strongly quantum
mechanically mixed (S1/ICT); (middle) ICT as a separate (diabatic) electronic state from S1
(S1 + ICT); and (right) S1 and the ICT state being one and the same state (S1(ICT)). Solid
lines represent radiative transitions. The dashed line represents internal conversion from S2
to S1; a is absorption; f is fluorescence. ................................................................................ 14
Figure 1.5 Structure of the trimeric peridinin–chlorophyll a protein (PCP) from
Amphidinium carterae (1PPR.pdb) as determined by Hofmann et al.60 ............................... 16
Figure 1.6 Energy levels and pathways for nonradiative decay in carotenoids and for
excitation energy transfer from carotenoids to (B)Chls in photosynthetic light-harvesting
proteins. After Beck et al. from 71. ...................................................................................... 17
Figure 1.7 Structure and conformation of the chromophores in a monomeric unit of PCP.
From reference 56. Copyright (2003) American Chemical Society, used with permission. (a)
arrangement of four distinct peridinins (Per) and two distinct chlorophylls (Chl)in each
domain and numbered as in the X-ray crystal structure. (1PPR.pdb) (b) Comparison of the
conformations of the peridinins showing the distinctive distortions of the symmetry in the
PCP. Peridinins are oriented for maximal overlap in the polyene backbone (c) median
structure of the peridinins. (d) lowest-energy vacuum structure of peridinin based on
B3LYP/6-31G(d) density functional calculation. ................................................................. 19

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Figure 1.8 Potential energy surfaces near the Franck–Condon structure for short cyanines,
short PSBs, and for longer cyanines and PSBs. From reference 75. Copyright (2000)
American Chemical Society, used with permission. The black lines indicate minimumenergy trajectory along the stretching and torsion coordinates towards a conical intersection
region. ................................................................................................................................... 21
Figure 1.9 Contour representations of the spectrally resolved components of the heterodyne
transient grating signal from Rhodamine 6G in methanol at room temperature (22 °C). (a)
absorption component; (b) dispersion component. For the absorption component, the yellow
end of the color bar corresponds to net ground state bleaching and/or stimulated emission;
the dark blue end indicates excited state absorption. ............................................................ 24
Figure 1.10 Spectrally integrated absorption (red) and dispersion (blue) components of the
transient grating signals from rhodamine 6G in methanol at room temperature (22 °C). .... 25
Figure 2.1 Pathways for nonradiative decay in carotenoids and for excitation energy
transfer from carotenoids to (B)Chls in photosynthetic light-harvesting proteins. The onephoton transitions transitions between states of the same symmetry or pseudoparity are
electric-dipole forbidden.5,6 Nonradiative decay from the S2 and S1 (21Ag−) states is
indicated with wavy arrows. Energy transfer pathways from the carotenoid S2 and S1 states
to the (B)Chl Qx and Qy states, are indicated with filled arrows. ......................................... 35
Figure 2.1 Structure of β-carotene. ...................................................................................... 37
Figure 2.3 Room-temperature absorption spectrum of β-carotene in benzonitrile solvent.
Superimposed is the spectrum of the OPA signal-beam output (520 nm center wavelength),
as tuned for the heterodyne transient-grating experiments. .................................................. 40
Figure 2.4 Real (absorption) component of the heterodyne transient grating signal from βcarotene in benzonitrile solvent at room temperature (22 °C). The yellow end of the color
bar corresponds to net ground-state bleaching or stimulated emission; the dark blue end
indicates excited state absorption.......................................................................................... 44
Figure 2.5 Imaginary (dispersion) component of the heterodyne transient grating signal
from β-carotene in benzonitrile solvent at room temperature (22 °C). The phasing of the
color bar is consistent with that used in Figure 2.4 for the absorption component. At 520
nm, the yellow contours correspond to the net ESA signal from the S1 state....................... 45
Figure 2.6 Evolution-associated and decay-associated spectra (EAS and DAS, respectively)
from a global analysis of the absorption component of the heterodyne transient-grating
signal (Figure 2.4) from β-carotene in benzonitrile over the -100 fs–12 ps delay range. The
DAS (bottom panel) characterize the spectral changes associated with a parallel decay of
the three spectra; black: 12 fs decay; red: 142 fs decay; blue: 11.6 ps decay back to the
ground state. The EAS (top panel) assume a sequential process: black: instantaneously
formed initial species, 12 fs decay; red: first intermediate species, 12 fs rise, 142 fs decay;
blue: second intermediate component, 142 fs rise, 11.6 ps decay back to the ground state.

xii

The inset shows the time evolution of the populations for the three components in the
sequential model against a linear–logarithmic time axis split at 1 ps. The global model
includes a convolution with a 60 fs Gaussian-shaped instrument response function centered
at the zero of the probe delay axis. ....................................................................................... 46
Figure 2.7 Evolution-associated and decay-associated spectra (EAS and DAS, respectively)
from a global analysis of the dispersion component of the heterodyne transient-grating
signal (Figure 2.5) from β-carotene in benzonitrile over the -100 fs–12 ps delay range. The
DAS (bottom panel) characterize the spectral changes associated with a parallel decay of
the three spectra; black: 12 fs decay; red: 142 fs decay; blue: 10.2 ps decay back to the
ground state. The EAS (top panel) assume a sequential process: black: instantaneously
formed initial species, 12 fs decay; red: first intermediate species, 12 fs rise, 142 fs decay;
blue: second intermediate component, 142 fs rise, 10.2 ps decay back to the ground state.
The inset shows the time evolution of the populations for the three components in the
sequential model against a linear–logarithmic time axis split at 1 ps. The global model
includes a convolution with a 60 fs Gaussian-shaped instrument response function centered
at the zero of the probe delay axis. ....................................................................................... 47
Figure 2.8 Time evolution of the absorption (red) and dispersion (blue) components of the
heterodyne transient grating signals from β-carotene in benzonitrile solvent at 520 nm, as
plotted against a linear–logarithmic time axis split at 1 ps. Both signals are superimposed
with the fitted global models described in Figures 2.6 and 2.7, respectively. ...................... 48
Figure 2.9 Schematic energy-level diagram for β-carotene, as used in the simulations of the
heterodyne transient grating signal from β-carotene. Solid green arrows indicate groundstate and excited-state absorption transitions. Blue wavy arrows mark internal conversion
transitions. Double-headed arrows show the detuning ( Δ ) between the center of the laser
spectrum and the vertical energy of an electronic transition. Note that in some of the
simulations that follow, the Sx manifold is omitted; in that case, the S2 state decays
nonradiatively directly to the S1 state. .................................................................................. 50
Figure 2.10 Comparison of the room temperature S0→S2 absorption spectrum of β-carotene
in benzonitrile (dark blue curve) with a simulation (red dash-dotted curve) obtained using
the MBO model (Equations 2.6-2.8) and the parameters listed in Table 2.1. ...................... 54
Figure 2.11 Excitation pulse sequence for third-order nonlinear spectroscopies, including
transient grating spectroscopy, after Brixner et al.22 and Sugisaki et al.40 Three excitation
pulses with wavevectors k 1 , k 2 , and k 3 are centered at times −T − τ , −T , and 0,
respectively. The time intervals t1 , t 2 , and t3 are between the interactions with the electric
fields from the three pulses. The interactions can occur at any time inside the pulse
envelope. P (3) (t) denotes the resulting third-order nonlinear polarization at time t . ......... 55
Figure 2.12 Double-sided Feynman diagrams for pathways contributing to the third order
nonlinear optical response of β-carotene based on the energy-level scheme shown in
Figure 2.9 and the assumption of detection along the k s = −k 1 + k 2 + k 3 direction. The solid

xiii

arrows indicate field–matter interactions on the ket (left) and bra (right) side of the density
matrix. The curly arrow denotes the emission event in the phase-matched direction arising
from the coherence created by the third field–matter interaction. The dashed lines indicate
relaxation of population between states. Time increases as one goes from the bottom to the
top in each diagram. .............................................................................................................. 57
Figure 2.13 Wave-mixing energy level (WMEL) diagrams47 and the corresponding doublesided Feynman diagrams for the double quantum coherence pathways in β-carotene given
the assumption of detection along the k s = −k 1 + k 2 + k 3 direction. In the WMEL diagrams,
time is ordered from left to right. The solid and dotted arrows in the WMEL diagrams
indicate interactions from the ket and bra sides of the density matrix, respectively. The
wavy line indicates the final emission of the signal. ............................................................ 60
Figure 2.14 Numerical simulation of the absorption component of the transient grating
signal from β-carotene, with the Sx state omitted from the energy level scheme shown in
Figure 2.9. The parameters used in the calculation are listed in Table 2.1–2.3 and in the text.
The yellow end of the color bar corresponds to net ground-state bleaching or stimulated
emission; the dark blue end indicates excited state absorption............................................. 63
Figure 2.15. Numerical simulation of the dispersion component of the transient grating
signal from β-carotene, with the Sx state omitted from the energy level scheme shown in
Figure 9. The parameters used in the calculation are listed in Table 2.1–2.3 and in the text.
At 520 nm, the yellow contours correspond to the net ESA signal from the S1 state........... 64
Figure 2.16 Comparison of the experimental and calculated absorption components of the
transient grating signal from β-carotene. The calculation omits the Sx state from the energy
level scheme shown in Figure 2.9. The experimental (Figure 2.4) and calculated signals
(Figure 2.14) were integrated over the laser frequency axis and normalized at the 500 fs
delay point. Top Panel: Absorption components from the experimental transient (data
points) and from the simulation (solid line). Bottom Panel: Absorption components
calculated from individual Feynman pathways: Orange, GSB; Red, SE from the S2 state;
Blue, S 2 → S n2 ESA; Green, DQC; Black, S1 → S n1 ESA.................................................. 67
Figure 2.17 Comparison of the experimental and calculated dispersion components of the
transient grating signal from β-carotene. The calculation omits the Sx state from the energy
level scheme shown in Figure 2.9. The experimental (Figure 5) and calculated signals
(Figure 2.15) were integrated over the laser frequency axis and normalized at the 500 fs
delay point. Top Panel: Dispersion components from the experimental transient (data
points) and from the simulation (solid line). Bottom Panel: Dispersion components
calculated from individual Feynman pathways: Orange, GSB; Red, SE from the S2 state;
Blue, S 2 → S n2 ESA; Green, DQC; Black, S1 → S n1 ESA.................................................. 68
Figure 2.18 Numerical simulation of the absorption component of the transient grating
signal from β-carotene, with the Sx state included in the energy level scheme shown in
Figure 2.9. The parameters used in the calculation are listed in Table 2.1, 2.2, and 2.4 and in

xiv

the text. The yellow end of the color bar corresponds to net ground-state bleaching or
stimulated emission; the dark blue end indicates excited state absorption. .......................... 71
Figure 2.19 Numerical simulation of the dispersion component of the transient grating
signal from β-carotene, with the Sx state included in the energy level scheme shown in
Figure 2.9. The parameters used in the calculation are listed in Table 2.1, 2.2, and 2.4 and in
the text. The phasing of the color bar is consistent with that used in Figure 2.18 for the
absorption component. At 520 nm, the yellow contours correspond to the net ESA signal
from the S1 state. ................................................................................................................... 71
Figure 2.20. Comparison of the experimental and calculated absorption components of the
transient grating signal from β-carotene. The calculation includes the Sx state in the energy
level scheme shown in Figure 2.9. The experimental (Figure 2.4) and calculated signals
(Figure 2.18) were integrated over the laser frequency axis and normalized at the 500 fs
delay point. Top Panel: Absorption components from the experimental transient (data
points) and from the simulation (solid line). Bottom Panel: Absorption components
calculated from individual Feynman pathways: Orange, GSB; Red, SE from the S2 state;
Blue, S 2 → S n2 ESA; Green, DQC; Black, S1 → S n1 ESA.................................................. 73
Figure 2.21 Comparison of the experimental and calculated dispersion components of the
transient grating signal from β-carotene. The calculation includes the Sx state in the energy
level scheme shown in Figure 2.9. The experimental (Figure 2.5) and calculated signals
(Figure 2.19) were integrated over the laser frequency axis and normalized at the 500 fs
delay point. Top Panel: Dispersion components from the experimental transient (data
points) and from the simulation (solid line). Bottom Panel: Dispersion components
calculated from individual Feynman pathways: Orange, GSB; Red, SE from the S2 state;
Blue, S 2 → S n2 ESA; Green, DQC; Black, S1 → S n1 ESA.................................................. 74
Figure 2.22. Comparison of the experimental and calculated dispersion components of the
transient grating signal from β-carotene. The calculation includes the Sx state in the energy
level shown in Figure 2.9 but employs the Sx–Snx energy gap in the visible region (~22000
cm-1) used in the calculations by Sugisaki et al.37 The experimental (Figure 2.5) and
calculated signals were integrated over the laser frequency axis and normalized at the 500 fs
delay point. Top Panel: Absorption components from the experimental transient (data
points) and from the simulation (solid line). Bottom Panel: Dispersion components from the
experimental transient (data points) and from the simulation (solid line). ........................... 77
Figure 2.23 Absorption component of the heterodyne transient grating signal from βcarotene in benzonitrile measured with a range of negative coherence delays, τ < 0 . The
signals are normalized at the population delay T = 500 fs, where only population signals
contribute. ............................................................................................................................. 79
Figure 2.24 Diabatic energy curves for all-trans polyenes with respect to a generalized
bond length alternation coordinate. The diagram includes a dark intermediate state (Sx) in
the transfer of population from the bright S2 (11Bu+) state to the dark S1 (21Ag−) state. ....... 83

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Figure 2.25 Proposed scheme for radiationless decay of carotenoids after optical
preparation of the S2 state; after similar diagrams in Sanchez-Galvez et al.67 and Beck et
al.17 The states that apply to planar structures are indicated by symmetry labels. Key points
along the radiationless path from the Franck–Condon S2 state structure are labeled with
ethylenic structures, which depict the Sx and X dark states as structures near the S2
transition state and along the torsional gradient, respectively. ............................................. 84
Figure A2.1 Frequency integrated transient grating signal from neat benzonitrile at room
temperature under the same measurement conditions used for β-carotene in Figures 2.4 and
2.5: (a) absorption component; (b) dispersion component; (c) complex modulus. .............. 92
Figure A2.2 Complex modulus of the heterodyne transient-grating signals from β-carotene
in benzonitrile at three solute optical densities: (a) A = 0.26, as in Figures 4 and 5;
(b) A = 0.13; and (c) A = 0.07. ............................................................................................. 93
Figure 3.1 Structure of peridinin ........................................................................................ 105
Figure 3.2 Room-temperature absorption spectrum of peridinin in methanol solvent.
Superimposed is the spectrum of the OPA signal-beam output (520 nm center wavelength),
as tuned for the heterodyne transient-grating experiments. ................................................ 109
Figure 3.3 Real (absorption) component of the heterodyne transient grating signal from
peridinin in methanol solvent at room temperature (22 °C). The yellow end of the color bar
corresponds to net ground-state bleaching or stimulated emission; the dark blue end
indicates excited state absorption........................................................................................ 111
Figure 3.4 Imaginary (dispersion) component of the heterodyne transient grating signal
from peridinin in methanol solvent at room temperature (22 °C). The phasing of the color
bar is consistent with that used in Figure 3.3 for the absorption component. At 520 nm, the
yellow contours correspond to a net ESA signal. ............................................................... 111
Figure 3.5 Time evolution of the populations for the three species in a global analysis of the
heterodyne transient grating signal (Figures 3.3 and 3.4) from peridinin in methanol over
the −100 fs–12 ps delay range, as plotted against a linear–logarithmic time axis split at 1 ps:
black: instantaneously formed species, 12 Âą 4 fs decay; red: first intermediate species,
12 Âą 4 fs rise, 900 Âą 100 fs decay; blue: second intermediate species in the absorption
component, 900 Âą 100 fs rise, 9.9 Âą 0.5 ps decay back to the ground state; dashed blue:
second intermediate species in the dispersion component, 900 Âą 100 fs rise , 7.5 Âą 0.5 ps
decay. .................................................................................................................................. 113
Figure 3.6 EAS from a global analysis of the absorption component of the heterodyne
transient grating signal (Figure 3.3) from peridinin in methanol over the −100 fs–12 ps
delay range. ......................................................................................................................... 113
Figure 3.7 Evolution associated spectra (EAS) from a global analysis of the dispersion
component of the heterodyne transient-grating signal (Figure 3.4) from peridinin in

xvi

methanol over the −100 fs–12 ps delay range. The EAS assume a sequential pathway from
the optically prepared S2 state (black) through two intermediates (red, then blue) back to the
ground state. ........................................................................................................................ 114
Figure 3.8 Time evolution of the absorption (red) and dispersion (blue) components of the
heterodyne transient grating signals from peridinin in methanol solvent at 520 nm, as
plotted against a linear–logarithmic time axis split at 1 ps. Both signals are superimposed
with the fitted global models described in Figures 3.5–3.7, respectively. .......................... 114
Figure 3.9 Schematic energy-level diagram for peridinin, as used in the simulations of the
heterodyne transient grating signal from peridinin and as used previously with β-carotene.10
Solid green arrows indicate ground state and excited-state absorption transitions. Blue wavy
arrows mark internal conversion transitions. Double-headed arrows show the detuning (Δ)
between the center of the laser spectrum and the vertical energy of an electronic transition.
The laser tuning for the present experiments is at the red onset of the S0 → S2 absorption
spectrum, so a negative detuning from the absorption maximum is indicated in the
diagram. .............................................................................................................................. 118
Figure 3.10 Comparison of the room temperature S0→S2 absorption spectrum of peridinin
in methanol (dark blue curve) with a simulation (red dash-dotted curve) obtained using the
MBO model and the parameters listed in Table 3.1. .......................................................... 120
Figure 3.11 Numerical simulation of the absorption component of the transient grating
signal from peridinin calculated according to the energy level scheme shown in Figure 3.9.
The parameters used in the calculation are listed in Tables 3.1 and 3.2 and in the text. The
yellow end of the color bar corresponds to net ground–state bleaching or stimulated
emission; the dark blue end indicates excited state absorption........................................... 122
Figure 3.12 Numerical simulation of the dispersion component of the transient grating
signal from peridinin	 calculated according to the energy level scheme shown in Figure 3.9.
The parameters used in the calculation are listed in Tables 3.1 and 3.2 and in the text. The
phasing of the color bar is consistent with that used in Figure 3.11 for the absorption
component. At 520 nm, the yellow contours correspond to the net ESA signal from the S1
state. .................................................................................................................................... 123
Figure 3.13 Comparison of the experimental and calculated absorption components of the
transient grating signal from peridinin. The experimental (Figure 3.3) and calculated
signals (Figure 3.11) were integrated over the laser frequency axis and normalized at the 1
ps delay point. Top Panel: Absorption component from the experimental transient grating
signal (data points) superimposed with those from the numerical simulation (solid line).
Bottom Panel: Absorption components calculated from individual Feynman pathways:
Orange, GSB; Red, SE from the S2 state; Blue, S 2 → S n2 ESA; Green, DQC; Violet,
S x → S nx ESA, Black, S1 → S n1 ESA. ................................................................................ 124
Figure 3.14 Comparison of the experimental and calculated dispersion components of the
transient grating signal from peridinin. Top Panel: Dispersion component from the

xvii

experimental transient grating signal (data points) and superimposed with those from the
numerical simulation (solid line). Bottom Panel: Dispersion components calculated from
individual Feynman pathways: Orange, GSB; Red, SE from the S2 state; Blue, S 2 → S n2
ESA; Green, DQC; Violet, S x → S nx ESA, Black, S1 → S n1 ESA. .................................... 125
Figure 3.15 Proposed scheme for radiationless decay of peridinin after optical preparation
of the S2 state; after similar diagrams in Sanchez-Galvez et al.72 and Beck et al.9 The states
that apply to planar structures are indicated by symmetry labels. Key points along the
radiationless path from the Franck–Condon S2 state structure are labeled with ethylenic
structures, which depict the Sx and X76 dark states as structures near the S2 transition state
and along the torsional gradient, respectively..................................................................... 128
Figure A3.1 Comparison of the experimental and simulated dispersion rise of peridinin in
methanol for models employing S2 lifetime ranging from 6–56 fs. The dotted curve
indicates the experimental data. The black curve, for 12 fs, is from the model reported in the
main text.............................................................................................................................. 135
Figure A3.2 Numerical simulation of the absorption component of the transient grating
signal from peridinin calculated by treating Sx as vibrationally excited S1 state. The
parameters used in the calculation are listed in Tables 3.1 and A3.1 and in the text. The
yellow end of the color bar corresponds to net ground–state bleaching or stimulated
emission; the blue end indicates excited state absorption. .................................................. 137
Figure A3.3 Numerical simulation of the dispersion component of the transient grating
signal from peridinin	 calculated by treating Sx as a vibrationally excited S1 state. The
parameters used in the calculation are listed in Tables 3.1 and A3.1 and in the text. At 520
nm, the yellow contours correspond to the net ESA signal from the S1 state..................... 137
Figure A3.4 Comparison of the experimental and calculated absorption components of the
transient grating signal from peridinin calculated by treating Sx as vibrationally excited S1
state. The parameters used in the calculation are listed in Tables 3.1 and A3.1 and in the
text. The experimental (Figure 3.3) and calculated signals (Figure 3.11) were integrated
over the laser frequency axis and normalized at the 1 ps delay point. Top Panel: Absorption
components from the experimental transient (data points) and from the simulation (solid
line). Bottom Panel: Absorption components calculated from individual Feynman
pathways: Orange, GSB; Red, SE from the S2 state; Blue, S 2 → S n2 ESA; Green, DQC;
Violet, S x → S nx ESA, Black, S1 → S n1 ESA. .................................................................... 138
Figure A3.5 Comparison of the experimental and calculated dispersion components of the
transient grating signal from peridinin calculated by treating Sx as vibrationally excited S1
state. The parameters used in the calculation are listed in Tables 3.1 and A3.1 and in the
text. The experimental (Figure 3.4) and calculated signals (Figure 3.12) were integrated
over the laser frequency axis and normalized at the 1 ps delay point. Top Panel: Dispersion
components from the experimental transient (data points) and from the simulation (solid
line). Bottom Panel: Dispersion components calculated from individual Feynman pathways:

xviii

Orange, GSB; Red, SE from the S2 state; Blue, S 2 → S n2 ESA; Green, DQC; Violet,
S x → S nx ESA, Black, S1 → S n1 ESA. ................................................................................ 139
Figure 4.1 Structures of peridinin (1) and β–carotene (2) ................................................. 147
Figure 4.2 Contour representations of the spectrally resolved absorption component of the
heterodyne transient grating signal from peridinin at room temperature (22 °C) in: (a)
acetonitrile; (b) ethyl acetate; (c) methanol; and (d) 2-propanol. The corresponding
dispersion components are shown in the Appendix. The yellow end of the color bar
corresponds to net ground state bleaching or stimulated emission; the dark blue end
indicates excited state absorption. The black dotted lines indicate the wavelengths for the
single-wavelength slices plotted in Figure 4.3. ................................................................... 150
Figure 4.3 Single-wavelength slices of the absorption component of the heterodyne
transient grating signal from peridinin (see Figure 4.2), as fitted by a global target model: in
(a) acetonitrile, at 507 nm; (b) ethyl acetate, at 507 nm; (c) methanol, at 520 nm; and
(d) 2-propanol, at 520 nm. The lower panels for each solvent show the relative population in
the three states in the fitted model: black, Franck–Condon S2 state; red, Sx intermediate
state; blue, S1 state. ............................................................................................................. 151
Figure 4.4 Power-law dependencies of Sx lifetime, τ Sx on solvent properties: (a)
τ Sx = a + bη α with respect to the solvent viscosity, η, with a = − 0.57 , b = 1.7 and
α = 0.4 .(b) τ Sx = a + bτ α avg with respect to the average polar solvation time, τ avg , with

a = 0.18 , b = 0.41 and Îą = 0.4 . ..................................................................................... 153
Figure 4.5 Proposed scheme for the radiationless decay of the S2 state of carotenoids.13,25
The ethylenic structures shown depict the Sx and X3 states as torsionally distorted S2
structures near the transition state barrier (‡) and further along the torsional gradient,
respectively. ........................................................................................................................ 155
Figure A4.1 Room-temperature (22 °C) absorption spectrum of peridinin in acetonitrile
solvent. Superimposed is the spectrum of the OPA signal-beam output (505 nm center
wavelength), as tuned for the heterodyne transient-grating experiments. .......................... 162
Figure A4.2 Real (absorption) component of the heterodyne transient grating signal from
peridinin in acetonitrile solvent at room temperature (22 °C). The yellow end of the color
bar	 corresponds to net ground state bleaching or stimulated emission; the dark blue end
indicates excited state absorption. This figure is shown in panel (a) of Figure 4.2. ........... 162
Figure A4.3 Imaginary (dispersion) component of the heterodyne transient grating signal
from peridinin in acetonitrile solvent at room temperature (22 °C). The phasing of the color
bar is consistent with that used in Figure A4.2 for the absorption component. At 505 nm, the
yellow contours correspond to a net ESA signal. ............................................................... 163

xix

Figure A4.4 Time evolution of the populations for the three species in a global analysis of
the heterodyne transient grating signal (Figures A4.2 and A4.3) from peridinin in
acetonitrile over the −100 fs–10 ps delay range, as plotted against a linear–logarithmic time
axis split at 1 ps: black: instantaneously formed species, 12 Âą 4 fs decay; red: first
intermediate species, 12 Âą 4 fs rise, 0.39 Âą 0.14 ps decay; blue: second intermediate species
in the absorption component, 0.39 Âą 0.14 ps rise, 8.6 Âą 0.3 ps decay back to the ground
state; dashed blue: second intermediate species in the dispersion component, 0.39 Âą 0.14 ps
rise , 8.1 Âą 0.5 ps decay. ...................................................................................................... 163
Figure A4.5 Evolution-associated spectra (EAS) from a global analysis of the absorption
component of the heterodyne transient grating signal (Figure A4.2) from peridinin in
acetonitrile over the −100 fs–10 ps delay range. The EAS assume a sequential pathway
from the optically prepared S2 state (black) through two intermediates (red, then blue) back
to the ground state. .............................................................................................................. 164
Figure A4.6 Evolution associated spectra (EAS) from a global analysis of the dispersion
component of the heterodyne transient-grating signal (Figure A4.3) from peridinin in
acetonitrile over the −100 fs–10 ps delay range. ................................................................ 164
Figure A4.7 Time evolution of the absorption (red) and dispersion (blue) components of the
heterodyne transient grating signals from peridinin in acetonitrile solvent at 507 nm, as
plotted against a linear–logarithmic time axis split at 1 ps. Both signals are superimposed
with the fitted global models described in Figures A4.4–A4.6, respectively. .................... 165
Figure A4.8 Room-temperature (22 °C) absorption spectrum of peridinin in ethyl acetate
solvent. Superimposed is the spectrum of the OPA signal-beam output (505 nm center
wavelength), as tuned for the heterodyne transient-grating experiments. .......................... 165
Figure A4.9 Real (absorption) component of the heterodyne transient grating signal from
peridinin in ethyl acetate solvent at room temperature (22 °C). The yellow end of the color
bar corresponds to net ground state bleaching or stimulated emission; the dark blue end
indicates excited state absorption. This figure is shown in panel (b) of Figure 4.2............ 166
Figure A4.10 Imaginary (dispersion) component of the heterodyne transient grating signal
from peridinin in ethyl acetate solvent at room temperature (22 °C). The phasing of the
color bar is consistent with that used in Figure A4.9 for the absorption component. At 505
nm, the yellow contours correspond to a net ESA signal. .................................................. 166
Figure A4.11 Time evolution of the populations for the three species in a global analysis of
the heterodyne transient grating signal (Figures A4.9 and A4.10) from peridinin in ethyl
acetate over the −100 fs–100 ps delay range, as plotted against a linear–logarithmic time
axis split at 1 ps: black: instantaneously formed species, 12 Âą 4 fs decay; red: first
intermediate species, 12 Âą 4 fs rise, 0.64 Âą 0.14 ps decay; blue: second intermediate species
in the absorption component, 0.64 Âą 0.14 ps rise, 130 Âą 3.5 ps decay back to the ground
state; dashed blue: second intermediate species in the dispersion component, 0.64 Âą 0.14 fs
rise, 83 Âą 10 ps decay. ......................................................................................................... 167	

xx

Figure A4.12 Evolution-associated spectra (EAS) from a global analysis of the absorption
component of the heterodyne transient grating signal (Figure A4.9) from peridinin in ethyl
acetate over the −100 fs–100 ps delay range. The EAS assume a sequential pathway from
the optically prepared S2 state (black) through two intermediates (red, then blue) back to the
ground state. ........................................................................................................................ 168
Figure A4.13 Evolution associated spectra (EAS) from a global analysis of the dispersion
component of the heterodyne transient-grating signal (Figure A4.10) from peridinin in ethyl
acetate over the −100 fs–100 ps delay range. The EAS assume a sequential pathway from
the optically prepared S2 state (black) through two intermediates (red, then blue) back to the
ground state. ........................................................................................................................ 169
Figure A4.14 Time evolution of the absorption (red) and dispersion (blue) components of
the heterodyne transient grating signals from peridinin in ethyl acetate solvent at 507 nm, as
plotted against a linear–logarithmic time axis split at 1 ps. Both signals are superimposed
with the fitted global models described in Figures A4.11–A4.13, respectively. ................ 169
Figure A4.15 Room-temperature (22 °C) absorption spectrum of peridinin in 2-propanol
solvent. Superimposed is the spectrum of the OPA signal-beam output (520 nm center
wavelength), as tuned for the heterodyne transient-grating experiments. .......................... 170
Figure A4.16 Real (absorption) component of the heterodyne transient grating signal from
peridinin in 2-propanol solvent at room temperature (22 °C). The yellow end of the color
bar corresponds to net ground state bleaching or stimulated emission; the dark blue end
indicates excited state absorption. This figure is shown in panel (d) of Figure 4.2............ 170
Figure A4.17 Imaginary (dispersion) component of the heterodyne transient grating signal
from peridinin in 2-propanol solvent at room temperature (22 °C). The phasing of the color
bar is consistent with that used in Figure A4.16 for the absorption component. At 520 nm,
the yellow contours correspond to a net ESA signal. ......................................................... 171
Figure A4.18 Time evolution of the populations for the three species in a global analysis of
the heterodyne transient grating signal (Figures A4.16 and A4.17) from peridinin in 2propanol over the −100 fs–48 ps delay range, as plotted against a linear–logarithmic time
axis split at 1 ps: black: instantaneously formed species, 12 Âą 4 fs decay; red: first
intermediate species, 12 Âą 4 fs rise, 1.7Âą 0.13 ps decay; blue: second intermediate species in
the absorption component, 1.7Âą 0.13 ps rise, 47 Âą 1.6 ps decay back to the ground state;
dashed blue: second intermediate species in the dispersion component, 1.7Âą 0.13 ps rise,
32 Âą 3 ps decay. .................................................................................................................. 171
Figure A4.19 EAS from a global analysis of the absorption component of the heterodyne
transient grating signal (Figure A4.16) from peridinin in 2-propanol over the −100 fs–48 ps
delay range. The EAS assume a sequential pathway from the optically prepared S2 state
(black) through two intermediates (red, then blue) back to the ground state. .................... 172	

xxi

Figure A4.20 EAS from a global analysis of the dispersion component of the heterodyne
transient-grating signal (Figure A4.17) from peridinin in 2-propanol over the −100 fs–48 ps
delay range. ......................................................................................................................... 172
Figure A4.21 Time evolution of the absorption (red) and dispersion (blue) components of
the heterodyne transient grating signals from peridinin in 2-propanol at 520 nm, as plotted
against a linear–logarithmic time axis split at 1 ps. Both signals are superimposed with the
fitted global models described in Figures A4.18–A4.20, respectively. .............................. 173
Figure 5.1 Peridinin and Chl a chromophores in the X-ray crystal structure of PCP from
Amphidinium carterae.6 (a) Space-filling rendering of the chromophore cluster from a
single subunit of PCP, with the peridinin (white) and Chl a (blue) chromophores numbered
with residue numbers from 1PPR.pdb. (b) Ground-state absorption spectrum for the S0 →
S2 transition from PCP at room temperature (22 °C), with the spectrum from the 520 nm (40
fs) laser excitation pulses superimposed and marked with the wavelengths for the 0–0
vibronic transition for the peridinin chromophores, as estimated in reference 16: 1, for
peridinins 612 and 622; 2, for peridinins 613 and 623; 3, for peridinins 611 and 621; and 4,
for peridinins 614 and 624. ................................................................................................. 182
Figure 5.3 Kinetic scheme for the radiationless decay and excitation transfer pathway in
PCP, as used in the numerical model (Figures 5.4 and A5.6–A5.7) for the heterodyne
transient grating signal (Figure 5.2). ................................................................................... 186
Figure 5.4 Comparison of the absolute intensity and time evolution of the absorption and
dispersion components of the heterodyne transient grating signals from PCP (red) and from
peridinin in 2-propanol (blue), as plotted with respect to a linear–logarithmic time axis split
at 1 ps. The plotted absorption and dispersion transients were obtained by integrating over
the laser frequency axis. The plotted data points for PCP are shown superimposed with
fitted profiles from the numerical model for the transient grating signal (Figures A5.6–
A5.7), as obtained with the radiationless decay and excitation transfer pathways shown in
Scheme 5.1 and the MBO model parameters reported in Tables A5.1–A5.2. The time
profiles for peridinin in 2-propanol were obtained from the global model reported in
reference 18. The bottom panel plots the time evolution of the populations in the S2 (red), Sx
(blue), and S1 (green) states from the model for the signal from PCP................................ 187
Figure 5.5 Schematic potential energy curves for peridinin in the PCP complex based on
those suggested in previous work for peridinin in solution.17,18,20,21 The potentials are plotted
with respect to a split reaction coordinate that describes the structural displacements along
bond-length alternation and torsional (ϕ) coordinates; a low barrier (‡) divides planar and
twisted structures. The dashed segments show the profiles for peridinin in solution......... 190
Figure A5.4. Schematic energy-level diagram for peridinin. Solid green arrows indicate
ground state and excited-state absorption transitions. Blue wavy arrows mark internal
conversion transitions. Double-headed arrows show the detuning (∆) between the center of
the laser spectrum and the vertical energy of an electronic transition. ............................... 198	

xxii

Figure A5.5 Comparison of the room temperature S0→S2 absorption spectrum PCP (dark
blue curve) with a simulation (red dash-dotted curve) of the peridinin spectrum obtained
using the MBO model and the parameters listed in Table A5.1-A5.2. ............................... 200	

xxiii

KEY TO ABBREVIATIONS

ATP

adenosine triphosphate

BChl

bacteriochlorophyll

CCD

charge-coupled device

Chl

chlorophyll

ESA

excited-state absorption

FC

Franck–Condon

ICT

intramolecular charge-transfer

LHCII

light-harvesting complex II

LO

local oscillator

N

conjugation length

NADPH+

reduced nicotinamide adenine dinucleotide phosphate

NPQ

nonphotochemical quenching

OPA

optical parametric amplifier

PCP

peridinin–chlorophyll a protein

PSB

protonated Schiff base

SE

stimulated emission

TPM

triphenylmethane

xxiv

OVERVIEW OF THE DISSERTATION

The goal of this dissertation is to determine the structural and photochemical mechanism that
control and optimize excitation energy transfer from carotenoids to chlorophyll (Chl) acceptors
in a light-harvesting protein. The dynamics of nonradiative decay and excitation energy transfer
ot chlorophylls have been studied using transient grating spectroscopy with optical heterodyne
detection. The heterodyne detection allows a complete characterization of the third-order
nonlinear optical signal emitted by a sample in terms of two components in quadrature, the
absorption and dispersion components. As discussed in the dissertation, the ultrafast rise of the
dispersion signal and detection of different ground state recovery timescales observed in the
absorption and dispersion channels provide direct evidence for the formation of conformationally
distorted intermediates in the nonradiative decay pathway of carotenoids. The experimental
findings are corroborated by numerical simulations using nonlinear response function theory and
the multimode Brownian oscillator model. The rest of the dissertation is organized as follows:
Chapter 1 presents a brief overview of light harvesting by carotenoids. The design principle
of light harvesting antenna complexes and the mechanisms of energy transfer are introduced
first. The complexity in understanding carotenoid photophysics and energy transfer pathways in
the peridinin–chlorophyll a protein are discussed next. A hypothesis based on conformational
dynamics of the conjugated polyene is presented, which could answer many outstanding
questions about carotenoid photophysics and energy transfer pathways in light-harvesting
proteins. This chapter concludes with a brief discussion of heterodyne transient grating technique
that has been employed to address these questions.

1

Chapter 2 reports results from heterodyne transient grating spectroscopic studies on βcarotene in benzonitrile. We show that a simultaneous modeling of the absorption and dispersion
components of the heterodyne transient grating signals leads to an unambiguous detection of the
Sx intermediate in the S2→S1 decay pathway. Our results also rule out any contributions from the
double quantum coherence to the observed signal.
Chapter 3 reports the detection and assignment of a similar Sx intermediate in case of
peridinin in methanol. Numerical simulation of the heterodyne transient grating signals using
nonlinear response theory and multimode Brownian oscillator model rules out the possibility of
Sx being a vibrationally excited or hot S1 state. Rather the Sx state is best assigned to a twisted
conformation of the S2 state.
Chapter 4 discusses the results of heterodyne transient grating studies of peridinin in a series
of polar solvents. It is found that the ICT character in peridinin is developed by out-of-plane
torsional motions of the conjugated polyene backbone. The decay of the Sx state is substantially
slowed by solvent friction due to the formation of an ICT character as twisting happens.
Chapter 5 focusses on the energy transfer mechanisms in the peridinin–chlorophyll a protein.
The results from heterodyne transient grating suggests that the S2 state of peridinin serves as the
donor for two channels of energy transfer to chlorophyll a acceptors: a 30 fs process involving
quantum coherence and delocalized peridinin–Chl states and an incoherent, 2.5 ps process
involving the Sx intermediate state. The coherent to incoherent transition is promoted by
torsional motions which lead to dynamic exciton localization.
Chapter 6 summarizes the overall impact of the dissertation, and future prospects are
discussed.

2

Chapter 1: Introduction to Photosynthetic Light Harvesting by Carotenoids

1.1 Photosynthesis: An Overview
Photosynthesis is the fundamental biological process that can harness the power of sun.
Organisms like plants, bacteria and algae employ photosynthesis to capture and store solar
energy into chemical bonds, which is essential to power life.1 Though photosynthetic organism
varies widely in terms of their habitat, they have similar basic constituents for the photosynthetic
apparatus. They all use a light harvesting antenna system that is coupled to a photosynthetic
reaction center. Solar energy is absorbed by an array of pigment protein complexes in the lightharvesting antenna and then transferred over hundreds of Ångströms to the photosynthetic
reaction center. After receiving the excitation, an electron transfer is initiated in the reaction
center and the absorbed energy is harvested as stable charges across a cell membrane. This
generates a trans-membrane electrochemical gradient, which is used in the formation of energy
storage molecules like adenosine triphosphate (ATP) and/or reduced nicotinamide adenine
dinucleotide phosphate (NADPH+).
An efficient light-harvesting process is crucial to the success of photosynthesis. Absorption
of solar photons by the antenna complex excites the pigment molecules from their ground state
to an excited electronic state. Before various radiative and nonradiative processes quench the
excited states, excitation energy must be harvested. This is ensured by the ultrafast timescales of
the energy transfer and charge separation. Excitations migrate through different pigment-protein
complexes and reach the reaction center in just 10–100 ps. The primary charge separation takes
place in about 3 ps. The overall quantum efficiency of light-to-charge separation is >90 %.2 The

3

design principles that makes photosynthetic light harvesting so efficient, however, remain to be
elucidated.

Figure 1.1 Schematic description of light harvesting and energy transfer to reaction centers in
photosynthetic organism. From reference 1. Copyright (2014) John Wiley & Sons, Ltd, used
with permission.

1.2 Architecture of the Light Harvesting Antenna
The availability of high-resolution X-ray crystal structures has allowed us to determine the
structural organization of the light-harvesting antenna complexes surrounding a reaction center.
Figure 1.2 shows the structure of main light-harvesting protein found in purple bacteria, LightHarvesting 2 (LH2) complex3,4 from Rhodopseudomonas acidophila. The LH2 consists of nine
circular arrays of ιβ-heterodimers, with each subunit binding three bacteriochlorophyll a (BChl)
molecules and one carotenoid. The BChls are arranged in two concentric ring-like structures in
LH2. Based on the position of the characteristic Qy band of bacteriochlorophylls, the rings are
denoted as B800 and B850. The B800 pigments are approximately 21 Å apart from each other
and are weakly coupled. In contrast, the distance between individual BChls in the B850 ring is

4

9 Å. As a result, the excited states of the BChls are strongly coupled and delocalized over the
B850 ring forming an exciton manifold. Carotenoids in the LH2 complex are also found to be in

Figure 1.2 The nonameric structure of the peripheral light harvesting complex (LH2) from
Rhodopseudomonas acidophila.(1NKZ.pdb)5 From reference 1. Copyright (2014) John Wiley &
Sons, Ltd, used with permission. (a) and (b) views perpendicular to the membrane plane with and
without the protein scaffold. (c) and (d) views parallel to the membrane plane with and without
the protein scaffold. B800 ring is shown in red and B850 ring is shown in blue. The Îą
polypeptide is colored yellow and the β polypeptide is colored green. Carotenoids are shown in
orange.
close proximity (3.4–3.7	Å) to both the B800 and B850 pigments Carotenoid which plays the
role of an accessory pigment, absorb in the blue-green part of the solar spectrum and transfer

5

energy to BChls. As a result, energy flows downhill from higher energy carotenoids to lower
energy bacteriochlorophylls and is delivered irreversibly into the reaction center, the so-called
energy funnel.1
The use of an energy funneling antenna system becomes critical at low-light conditions due
to the low photon flux density of sunlight. As a result, less than one excited states are generated
per second. The photosynthetic reaction center, however, requires multiple excitations for a
biochemical activity to take place. Accumulating photons at multiple sites and then funneling it
to a single reaction center allows the light intensity to concentrate. Moreover, by employing
different chromophores, light harvesting complexes can absorb at different parts of the solar
spectrum and allows better utilization of the solar spectrum than ever possible by the reaction
center alone.6 Because of their wide range of absorption, the chromophores need to share the
excitation energy amongst themselves so that it can reach the reaction center even from the
farthest absorbing chromophores. This is ensured by the protein scaffold, which holds the
chromophores in proper orientation and distances and thereby, facilitates excitation energy
transfer. The structural arrangement of the chromophores and interactions between them and the
protein environment often determine the spectral properties and energy transfer mechanisms in
the light-harvesting complex.

1.3 Energy Transfer Mechanisms in Light-Harvesting Proteins
The mechanism of energy transfer involves coupling of chromophores via electric dipoledipole interaction, which depends on the relative orientation and distance between the
chromophores. The rate of excitation energy transfer is governed by the Fermi golden rule
expression

6

k DA =

2
1
V DA J DA
2
! c

(1.1)

where k DA is the rate of energy transfer from the donor (D) to acceptor (A). V DA denotes the
electronic coupling strength between the chromophores. Here J DA is the overlap integral
between the emission spectrum of the donor and absorption spectrum of the acceptor molecule
and ensures conservation of energy. Depending on the relative coupling between the pigments
themselves and with the surrounding environment, the mechanism of excitation energy transfer
can be either be incoherent or coherent types.
1.3.1 Incoherent Energy Transfer
Incoherent type energy transfer happens in the weak-coupling limit in which the dipoledipole coupling between the chromophores are weaker than their coupling to the environment. In
this scenario, the excitation essentially gets localized prior to energy transfer. As a result,
excitation energy transfer occurs by hoping from one chromophore to another. In this scenario,
the Fermi golden rule takes the form of FĂśrster theory and the incoherent hopping rate is given
by7

k DA ∝

Îş2
τ D R6

∍f

D

(ν )ξ A (ν )

dν
ν4

(1.2)

where Îş is the mutual orientation factor of the transition dipoles, R is the distance between them
and τ D is the radiative lifetime of the donor. The integral includes spectral overlap between the
emission spectrum of the donor f D and the absorption spectrum of the acceptor Îľ A . The
incoherent Forster energy transfer rate, therefore, strongly depends on the transition dipole

7

strength of the donor. The FĂśrster theory, however, is inadequate to describe excitation energy
transfer in photosynthetic systems because of close-packed packing of the chromophores within
the light-harvesting proteins.
1.3.2 Coherent Energy Transfer
The close proximity of the chromophores in the light harvesting proteins results in relatively
strong coupling amongst themselves and the coupling strength varies from several tens to several
hundred wavenumbers. If the electronic couplings between the chromophores are stronger than
their coupling to the surrounding bath, then the excitations are delocalized over the excited state
of the chromophores. Formation of such delocalized excited states or excitons allow rapid
transfer of energy not limited by the Forster rate.8
Indeed, the protein has the ability to tune the electronic couplings amongst the chromophores
by changing their electronic properties of the chromophores and thereby determines influence the
mechanism of excitation energy transfer.8 Experiments by Fleming et al.9,10 have suggested that
relatively long lived electronic coherences, delocalized excited states spanning several
chromophores, may enhance the quantum efficiency of light harvesting. These and other
results11–14 suggest that the energy-transfer and nonradiative channels determining the fate of a
captured photon in a light-harvesting protein are exquisitely balanced by the microscopic details
of the electronic interactions between light-harvesting chromophores and by the structure and
dynamics of the surrounding protein and solvent medium. A proper understanding of carotenoidto-chlorophyll energy transfer, therefore, requires a detailed knowledge of the excited state
photophysics that carotenoids undergo after light absorption.

8

1.4 Carotenoids as Light Harvesting Chromophores: Ultrafast Photophysics
Carotenoids are one of the most abundant pigments found in nature. In addition to their role
in light harvesting, carotenoids are involved in photoprotection by quenching the excited states
of (bacterio)-chlorophylls in excess sunlight. This is an example of triplet-triplet energy transfer
and is known as nonphotochemical quenching (NPQ).15 Carotenoids also help scavenging
harmful singlet oxygen15,16 and other reactive species, and therefore provides protection
mechanisms against deceases like cancer, arteriosclerosis and macular degeneration in human
retina.17 All these functional properties of are intimately related to the ultrafast photophysics of
carotenoids.
Carotenoids belong to the class of conjugated polyenes and they are generally treated as a
three electronic levels system. The electronic energy levels of carotenoids are shown in
Figure 1.3. Since linear polyenes belong to the C2h point group, the ground electronic state S0 of
carotenoids has 11Ag− symmetry. The first excited state S1 has 21Ag− symmetry. Because of its
symmetry property, one-photon optical transition from the ground state to the S1 state is dipoleforbidden. The S1 state is therefore formally referred to as an optically dark state. The lowest
energy symmetry-allowed transition occurs from the S0 state to the S2 (11Bu+) state and is
responsible for the absorption band of carotenoids. The vibronic structure observed in the
absorption spectrum (See Figure 1.3) of a carotenoid arises due to the stretching vibrational
modes of the C–C (1150 cm-1) and C=C (1600 cm-1) bonds of its polyene backbone and
combinations thereof. In accordance with the behavior of a particle in a box, both the S0–S2 and
S1–S0 electronic energy gaps decrease with increasing conjugation length.18

9

Figure 1.3 Nonradiative decay pathways in carotenoids. From reference 19. Copyright (2010)
American Chemical Society, used with permission. Internal conversion processes are denoted by
blue and red arrows; black arrows denote vibrational relaxation. Absorption spectra (top right) of
LH2 (purple), PCP (orange), and LHCII (green). The range of energies of carotenoid S2 and
S1 transitions are also shown by the orange and red bars beneath the spectra. Structure of
different carotenoids are shown at the bottom.
Fluorescence up-conversion experiments determined that the lifetime of the S2 state is less
than 300 fs20,21 and undergoes quick nonradiative decay to the S1 state. Formation of the S1 state
can be identified using time-resolved transient absorption technique in which a prominent band
arises in the 500–600 nm range due to the S1→Sn excited state absorption.22 The lifetime of the
S1 state varies from several picoseconds to couple of hundreds of picosecond depending on the
conjugation length of the carotenoid. The decay of the S1 state back to the ground state follows
the energy-gap law.23–25

10

1.4.1 Dark Intermediate States in Carotenoids
The above-mentioned three-level description of carotenoid photophysics is probably
oversimplified and cannot account for many of its spectroscopic observations. For example, the
S2→S1 nonradiative decay rate does not follow the energy gap law. With increasing conjugation
length of carotenoids, the S2–S1 energy gap decreases but the lifetime of the S2 state gets
shorter.24,26 This anomalous dependence on the conjugation length could be explained if an
intermediate electronic state, denoted as Sx, mediates the S2→S1 nonradiative decay. Similarly,
hot vibrational spectral feature is observed in transient absorption experiments and is thought to
be due to the formation of a dark S* state. The presence of such dark states makes the carotenoid
photophysics extremely difficult to understand and their assignment and role are still a topic of
significant controversy.27
The presence of a dark electronic state with 11Bu– symmetry within the S2–S1 gap was first
predicted by Tavan and Schulten in 1987 based on electronic structure calculations on polyenes
with N ≥ 9.28 The first experimental support for this state came in 1999 from the resonance
Raman experiments on all-trans-spheroidene by the Koyama group.29 Subsequent transient
absorption measurements on neurosporene from the same group assigned a near-IR band (800–
950 nm) as excited state absorption from the 11Bu– state. Later, transient absorption experiments
on β-carotene and lutein performed with 15 fs pulses by Cerullo et al. showed that the S2 state
decays in 12 fs to produce a distinct electronic state Sx with excited state absorption feature in
the 800–900 range. Similar to the previous works, this was identified as the 11Bu– state.30
The presence of 11Bu- state was subsequently investigated employing a variety of four wave
mixing techniques. Femtosecond Stimulated Raman spectroscopy experiments by McCamant et
al. on β-carotene in cyclohexane31 found that rise of the C=C stretch frequency of the S1 state

11

follows the decay of the C–C stretch mode of the S2 state implying that no intermediate state is
needed to explain the observation. This was supported by the pump degenerate four wave mixing
experiments which suggested that the transient Raman bands previously attributed to the
intermediate state can be explained as a vibrational dynamics of the C=C stretching mode in the
S1 manifold. Christensson et al.32 performed three-pulse photon echo peak shift (3PEPS)
experiment on β-carotene and astaxanthin and found that the ground state bleach along with the
excited state absorptions corresponding to S2→Sn2 and S1→Sn1 electronic transitions were suffice
to model the experimental data. They didn’t find evidence for the Sx intermediate, but rather
proposed that the S2→S1 nonradiative decay might proceed through conical intersections.
Another dark intermediate, denoted as the S* state, is identified as a shoulder on the shortwavelength side of the ESA spectrum from the S1 state.33 The shoulder becomes more
pronounced when the carotenoid is bound to proteins than in solution. The S* state can serve as
acts as a precursor to the triplet state in carotenoids and can transfer energy to the BChl Qy state
in the purple bacterial LH1 and LH2 complexes.34,35 All these spectroscopic observation led to
the suggestion that the S* represents a separate electronic state positioned near the S1 state and
populated via nonradiative relaxation from the S2 state. This assignment, however, was
challenged based on the results from pump-dump-probe experiments.36,37 Depletion of S2 state
population by the dump-pulse was found to selectively affect the transient absorption signal only
from the S1 state; the S* feature remained unaffected. This led to the suggestion that the S* state
is hot ground state populated by impulsive stimulated Raman scattering from the S2 state. In an
alternative hypothesis, Frank et al. proposed that the S* state is a twisted conformation of the S1
state based on electronic structure calculations and temperature and solvent dependence of the S*

12

signal.38–40 In this model, the upon excitation the S2 state undergoes conformational changes
prior to decaying to the S1 and S* states.
1.4.2 Intramolecular Charge Transfer in Carotenoids
In addition to the above-mentioned electronic states, carotenoids like peridinin and
fucoxanthin are known to possess an additional intramolecular chare transfer (ICT) states. These
carotenoids contain carbonyl groups in conjugation with the extended π-electron system of the
polyene backbone and show unusual solvent dependence on excited state properties. This
behavior is highly unusual for carotenoids; in general, the spectral properties and lifetimes of the
S1 state of carotenoids are independent of the solvent environment. The lifetime of the lowest
excited singlet state of peridinin, however, changes from 7 ps in the highly polar solvent,
trifluoroethanol, to 172 ps in two nonpolar solvents, cyclohexane and benzene.41,42 The
wavelengths of emission maxima, the quantum yields of fluorescence, and the transient
absorption spectra were also affected by the solvent polarity. The solvent sensitivity of peridinin
has been attributed by Frank and coworkers to the presence of an ICT state,41,42 and this idea has
been supported by both theoretical computations43 and experiments on numerous other carbonylcontaining carotenoids and polyenals.44–53
Despite many studies, how the ICT character develops in the S1 state is not understood.
Three hypotheses have been proposed. Two of the possible hypotheses (Figure1.4) suggest that
the excited-state dynamics in the S1-state manifold propagate along an intramolecular chargetransfer coordinate that links diabatic (S1 + ICT) states41,43,49,54 or quantum-mechanically mixed
(S1/ICT) states.46,55 A third hypothesis suggests that the S1 and ICT states are the same state; the
ICT character in this case is derived from a quantum-mechanical mixing of the S1 and S2 states

13

(S1(ICT)). This mechanism increases the dipole strength of the mixed state by borrowing

Optimization
intensity
from the S2 state.56of

S1 Energy-Transfer Efficiency


via Intramolecular Charge-Transfer (ICT) Character
S1/ICT

S1+ICT

S1(ICT)

Bautista
et al.,
J. Phys.models
Chem.for
A the
1999,
103,of2267
andstate
103,in8751.

Figure
1.4 Three
different
nature
the ICT
peridinin and other carbonylZigmantas
et al. J. Phys.
Chem.
2003,solvents.
107, 5339.

containing
carotenoids
dissolved
in Bpolar
From reference 57. Copyright (2013)
Shima
et
al.,
J.
Phys.
Chem.
A
2003,
107,
8052.

Biophysical Society, used with permission. (left) S1 and ICT strongly quantum mechanically
Vaswani
et al.,
J. Phys.
Chem.
B 2003, (diabatic)
107, 7940.electronic state from S (S + ICT); and
mixed
(S1/ICT);
(middle)
ICT
as a separate
1
1
(right) S1 and the ICT state being one and the same state (S1(ICT)). Solid lines represent
radiative transitions. The dashed line represents internal conversion from S2 to S1; a is
absorption; f is fluorescence.

From the above discussions, it is clear that the nonradiative decay pathways of carotenoids
are extremely complicated due to the presence of possible dark electronic intermediate states.
Detection and establishing the nature of these dark states is crucial to understand the light
harvesting function of carotenoids. Understanding how the ICT character is developed in
carbonyl-containing carotenoids is crucial to understand its role in the light-harvesting
mechanisms of carotenoids.

14

1.5 Light Harvesting in the Peridinin–Chlorophyll a Protein
A perfect model system to study light harvesting strategy is the peridinin–chlorophyll a
protein (PCP) from marine dinoflagellate Amphidinium carterae. The carotenoid peridinins serve
as the main light harvester in PCP, unlike other light-harvesting complexes in purple bacteria and
green plants where carotenoids serve as accessory light harvesting pigments. Peridinin captures
mid-visible (470–570 nm) solar photons and delivers the excitation energy to Chl a acceptors
very high (~90%) quantum efficiency.58,59 The X-ray crystal structure (Figure 1.5) of trimeric
PCP shows that in each subunit eight peridinin carotenoids and two Chl a chromophores are
bound together in dense cluster by a basket of Îą helices in a C2-symmetric, two-domain
assembly. The distance between two Chl a molecules in the two domains are approximately
17 Å. In contrast, the four peridinins in each domain are effectively in van der Waals contact (3.3
to 3.8 Å separation) with a central Chl a acceptor.60 Moreover, PCP has a well-characterized
crystal

structure60

and

amenable

to

single-point

mutation

and

reconstitution

with

chlorophylls.61,62 This feature offers us the unique opportunity to vary experimentally the singletstate energy gaps that control the various energy-transfer and nonradiative photophysical
processes that arise from the structural interaction of Chls and carotenoids without significantly
perturbing the structure.63–65

15

Figure 1.5 Structure of the trimeric peridinin–chlorophyll a protein (PCP) from Amphidinium
carterae (1PPR.pdb) as determined by Hofmann et al.60
Figure 1.6 shows the general scheme that applies to carotenoid–to–(B)Chl energy transfer in
photosynthetic light harvesting proteins. Strong, electric-dipole-allowed transitions from the
carotenoid ground state, S0 (11Ag−), to the S2 (11Bu+) excited state are followed by downhill
energy transfer to the Qx or Qy singlet states of chlorophylls (Chls) over short distances.27,66
Because the carotenoid S2 state lies above that of the Qx excited state of Chl or BChl, S2→Qx
excitation energy transfer via the Förster resonant dipole–dipole mechanism7,67 is energetically
favored. This pathway competes with fast S2→S1 nonradiative decay, however, so only a fraction
of the total energy-transfer yield typically involves the S2 state. Given that there is very little
dipole strength for the S1→S0 transition, one might expect that the yield of Förster energy
transfer to the Chl Qy state would be very small. This expectation prompts the suggestion of a
Dexter-type, orbital-overlap, electron exchange-mediated energy-transfer mechanism,68but

16

calculations suggest that energy transfer by the dipole–dipole mechanism can still be more
favorable in light-harvesting proteins.59,69,70

Carotenoids
S2

11Bu+

S1

21Ag–

(B)Chls
Qx
Qy

S0

11Ag–

S0

Figure 1.6 Energy levels and pathways for nonradiative decay in carotenoids and for excitation
energy transfer from carotenoids to (B)Chls in photosynthetic light-harvesting proteins. After
Beck et al. from 71.
In the LH2 complex from Rhodopseudomonas acidophila, it is known that that 85% of the
energy-transfer yield between a carotenoid, rhodopin glucoside, and BChl a in the B800–B820
system from occurs in ~90 fs via the S2-state channel; only 15% of the yield goes through the S1state channel using the dipole-dipole mechanism despite the short distance to the BChl a
acceptor.69 The total energy-transfer yield is only 70%. The S1 state of rhodopin glucoside in this
system has relatively low dipole strength and a short lifetime, so energy transfer competes
unfavorably with nonradiative decay of the S1 state. In contrast, the currently accepted picture in
PCP is that nearly two thirds of the 90% total energy transfer yield involves coupling of the
carotenoid S1 state to the Chl Qy state via production of an ICT state, which lies below the S1
state in polar solvents.41 Despite having all of this structural information at hand, the mechanisms
that mediate energy transfer from peridinin to Chl a via the S2 and S1 states are incompletely

17

understood. It remains to be established how the dark S1 state of the peridinins is coupled to that
of the Chls so that energy transfer is efficient.
The enhanced light harvesting function in PCP is thought to be the result of two structural
adaptations. The first is that peridinin adds an allene group and a lactone ring in conjugation with
the extended π-electron system of the carotenoid polyene. These structures contribute to
intramolecular charge-transfer (ICT) character that leads to significantly enhanced energytransfer coupling to Chl a. Energy transfer from the S1 state is also optimized in light-harvesting
proteins by placing the carotenoid nearly in van der Waals contact with an adjacent Chl so that
the Coulomb coupling between them is as large as possible.7,59,69,72 The conclusion that the four
peridinin carotenoids in a single domain of PCP interact in the strong electronic coupling limit is
supported by circular dichroism spectroscopy73 and by calculations,59 but it remains an open
question whether coherent energy transfer mechanisms are operative in PCP or not.
The intramolecular charge transfer and light harvesting function of PCP is further optimized
by the imposition of conformational strain on peridinins by the surrounding binding sites. As
shown in Figure 1.7, the average structure of peridinin found in the X-ray crystal structure is
significantly distorted from the minimum energy, ground-state structure determined by density
functional calculations. The allene end of the molecule is bent away from the mostly linear
projection of the conjugated polyene backbone, but most importantly the length of the
conjugated region is compressed by more than 0.2 Å and the pattern of bond-length alternation
of the C–C and C=C bonds is partially inverted. These distortions are likely to enhance the
energy transfer yield by mixing the dark S1 state with the bright S2 state.56,57

18

Photochemical Properties of Peridinin

J. Phys. Chem. A, Vol. 10

Minus states are “covalent” in character,
bond description involving a linear co
structures that have small amounts of
contrast, “+” states are ionic in charact
a first approximation in terms of the addi
excitations. Thus, “+” states are often
additive properties of the participating
states are typically stabilized by a polar
covalent states are relatively unaffected
polyene chain or environment.35 In many
of the excited states are determined m
versus “covalent” (-) properties than th
unsymmetric (u) labels. The positions a
both the1Ag*--like and 1Bu*+-like state
the absorption properties are typically do
the photochemical properties are do
challenge is to assign the energetic an
the S1 state, because it is optically forbid
can often be observed in fluorescen
deduced from an analysis of the fluo
emission profile, the emission takes
excited-state geometry. The Franck-C
S1 state are therefore not well-establish
possible to assign the location of the
recent investigations have suggested th
carotenoids possess other electronic st
state, between S2 (11Bu*+ ) and S1 (21A
and two-photon absorption into 1Bu*- st
and in linear polyenes, the 1Bu*- state is
in both one and two photon spectroscopy
shown, however, that this state becom
when there are cis-linkages or polar
chain.34

Figure 1. Structure of the pigments associated with one-third of the
trimeric minimal unit comprising the PCP complex is shown in A based
Figure 1.7 Structure and onconformation
the chromophores
in Sharples,
a monomeric
unit of PCP. From
PDB entry 1PPRof
(Hofmann,
E.; Wrench, P. M.;
F. P.;
Hiller, R. G.; Welte, W.; Diederichs, K. Science 1996, 272, 1788). The
reference 56. Copyright
(2003)
American
Society,
with permission.
peridinin
molecules
are colored toChemical
reflect the pseudo
2-fold axisused
that
runs vertically through the center of the protein. The peridinin molecules
(a) arrangement of four transfer
distinct
peridinins
(Per) and
two
distinct
chlorophylls
(Chl)in each
energy
to the Chl-a molecules
shown
in light
green. Insert
B
shows the structures of all of the peridinin molecules oriented for
domain and numbered as
in the X-ray crystal structure. (1PPR.pdb) (b) Comparison
ofa the
Peridinin is
highly substituted caro
maximal overlap in the polyene chain. A median structure of the
peridinin
molecules
within
the
crystal
is
shown
in
C
and
compared
to
the
Peridiniales
group
conformations of the peridinins showing the distinctive distortions of the symmetry in the PCP. of dinoflagellates
the lowest-energy vacuum structure based on density functional methods
the molecule displays an atypical C3
in D. in the polyene backbone (c) mediancarotenoids
Peridinins are oriented for[B3LYP/6-31G(d)]
maximal overlap
structureand
of possesses
the
an allene gro

conjugationdensity
with the π-electron conjuga
features
of the complex
withofitsperidinin
spectroscopic
properties
and
peridinins. (d) lowest-energy
vacuum
structure
based
on B3LYP/6-31G(d)
labeled the carbon atoms along the
attempting to rationalize its exceptionally high efficiency of
simplified numbering scheme to facil
functional calculation. energy transfer between peridinin and Chl a.14-30
The photochemical behavior of carotenoids and long-chain
polyenes is dominated by the properties of the two lowest-lying
excited singlet states. Because the properties of these states in
low-symmetry, highly substituted polyenes can be understood
by reference to the corresponding states observed under rigorous
C2h symmetry, it is common to use the C2h symmetry labels for
reference.31-33 The lowest excited singlet state in long-chain
linear polyenes, S1, has 1Ag*--like symmetry and is optically
forbidden under one-photon selection rules because the closed
shell ground state has identical symmetry. The second excited
singlet state in these polyenes, S2, has 1Bu*+-like symmetry and
is strongly allowed under one-photon selection rules. This state
is responsible for the strong Îťmax absorption band observed in
carotenoids. The superscript 19
“+” and “-” labels refer to the
configurational properties of the states with reference to the
addition or subtraction of component excitations.34 Minus states,
such as the 1Ag*- state, are described to a first approximation

conformers. Note that the carbonyl grou
also part of the polyene conjugated netw
addition to epoxy and acetate function
suggest no symmetry at all. Yet, the stea
fluorescence spectra of peridinin in non
similar to those usually observed in car
a strong absorption band in the visible re
energy with increasing solvent polariza
identifies this band with the strong di
1B *+-like transition. The fluorescence
u
is significantly red-shifted from its abso
ing that the emission originates from a lo
which is consistent with a 1Ag*--like sta
is typical of carotenoids and polyenes
but less than nine carbon-carbon double
of the S1 state and the S1 f Sn transie
of peridinin are not typical of caroteno

1.6 Hypotheses and Proposed Work
The observation that many carotenoids have distorted geometry in PCP and in other lightharvesting proteins including LH25 led us to hypothesize that the conformational motion of the
conjugated polyene backbone of a carotenoid may play important roles in its excited state
photophysics and energy transfer mechanism. The role of conformational dynamics in carotenoid
photophysics has been described in detail in reference 71, in which Beck et al. proposed a new
model for the mechanism of the nonradiative decay of carotenoids that explicitly involves largeamplitude out-of-plane motions. The central argument of the hypothesis is based on current
theories74–79 for nonradiative decay in polyenes and related systems.
1.6.1 Conformational Dynamics of Conjugated Polyenes
A two-state-two-mode picture is generally employed to explain the photophysics of a
conjugated polyene.74,75 A particular feature of this model is that the nonradiative decay of a
conjugated polyene proceeds along the two orthogonal coordinates; the bond length alternation
and torsional modes. The stretching and compression motions which are directed from the
Franck–Condon region, effectively reverses the bond order in the conjugated part of the
molecule and initiates a nonradiative relaxation.33,80–82 The initial momentum along the C=C and
C–C bond stretching-compression coordinate is subsequently converted into motions of the
torsional coordinates. Relaxation along the torsional gradient brings the molecules at 90° twisted
minimum energy structure near the conical intersection with the ground state potential energy
surface. Nonradiative relaxation through the conical intersection to the ground state then yields
the original configuration or a photoisomerized configuration.

20

Figure 1.8 Potential energy surfaces near the Franck–Condon structure for short cyanines, short
PSBs, and for longer cyanines and PSBs. From reference 75. Copyright (2000) American
Chemical Society, used with permission. The black lines indicate minimum-energy trajectory
along the stretching and torsion coordinates towards a conical intersection region.
Figure 1.8 shows the two-state-two-mode model that is usually invoked to explain the
photophysics of short cyanines and protonated Schiff bases (PSBs); the two orthogonal modes
being the bond-length alternation and the torsional coordinates.74,75 Depending on the energy
barrier between the planar and twisted conformations of the molecule, the photoisomerization
dynamics can involve a barrier or become barrierless. The height of the barrier and hence the
gradients of the potential energy surface near the Franck–Condon geometry are controlled by the
effective conjugation length.75 For molecules with small conjugation lengths such as shorter
cyanines, the photoisomerization dynamics is barrierless and the potential energy surface looks
ridge-like. In such topology the system evolves from Franck–Condon region along the stretching
coordinate and the strongly-coupled torsional motions at the same time. For short PSBs, the
excited state topology looks valley-ridge like and few stretching vibrations takes place prior to
the coupling of stretching-torsional motions. In contrast, the topology of the excited state
surfaces for the longer cyanines and PSBs is valley-like and involves an energy barrier. The

21

Franck–Condon geometry lies at a local planar minimum with respect to the torsional
coordinates and the initial evolution occurs considerably along the bond stretching coordinate.
After several vibrations, a trajectory along the torsional coordinate is launched which overcomes
the energy barrier and promotes a descent towards the conical intersection region.83
Unlike the cyanines and PSBs, the model that is used to describe the nonradiative decay of
carotenoids invokes a barrierless picture. The S2→S1 nonradiative decay of carotenoids has been
explained in terms of progression along the C=C and C–C bond stretching-compression
coordinate. The role of out-of-plane torsional coordinate has been hardly considered. As we will
establish later in the dissertation, that the nonradiative decay of carotenoids can be explained in
terms of conformational motions of its polyene backbone, including the presence of dark
electronic states and formation of an intramolecular charge transfer which enhances the light
harvesting function of carotenoids. The selection rules that govern the photophysics of linear
polyene molecules are often relaxed for carotenoids with distorted conformations. As argued by
Beck et al.,71 owing to the properties of the conjugated polyene backbone, it is likely that the
bent and twisted carotenoid structures further enhance the energy-transfer yield by increasing the
transition dipole strength of formally dark electronic states and formation of an ICT state. The
main questions that have been addressed in this dissertation are:
1. Whether the dark electronic state, Sx mediates the S2→S1 nonradiative relaxation in
carotenoids or not? If it does, what is the nature of the Sx state?
2. What is the mechanism of ICT formation in carotenoids containing carbonyl groups?
3. How does the ICT character enhance the light harvesting function of the peridinin–
chlorophyll a protein?

22

In order to answer the above-mentioned questions, we have employed femtosecond transient
grating technique with optical heterodyne detection.84–86

1.6.2 Approach: Heterodyne Detected Transient Grating Spectroscopy
The experimental implementation of heterodyne transient grating technique was first reported
in the works of Miller and coworkers84,85 and Fleming and coworkers.86–89 The heterodyne
detection allows complete characterization of the signal electric field emitted from the sample in
terms of the two components in quadrature, real (absorption) and dispersion (imaginary)
components.85,90–93 The dispersion component is not detected in the conventional femtosecond
pump–probe spectroscopy, which provides information only about the real, absorptive of the
third-order signal; the absorption and dispersion components are combined as the sum of their
squares in homodyne detected transient grating or photon echo experiments.
Figure 1.9 shows the contour representation of the absorption and dispersion components of
the transient signal of rhodamine 6G in methanol obtained with 40 fs laser pulses centered at
520 nm wavelength. For a two-level system like rhodamine, both the absorption and dispersion
components are dominated by the contributions from ground state bleach and stimulated
emission signal. Figure 1.10 shows the time evolution of the integrated absorption and dispersion
signals as function of delay between the pump and probe pulse. Both the components exhibit
similar time profiles and contain no additional dynamics information than what is available from
a pump-probe technique.

23

A
540

Wavelength (nm)

520

500
B
540

520

500
0

200

400

Delay (fs)
Figure 1.9 Contour representations of the spectrally resolved components of the heterodyne
transient grating signal from Rhodamine 6G in methanol at room temperature (22 °C).
(a) absorption component; (b) dispersion component. For the absorption component, the yellow
end of the color bar corresponds to net ground state bleaching and/or stimulated emission; the
dark blue end indicates excited state absorption.

24

Re[ES] and Im[ES]
0

500

1000

Delay (fs)

Figure 1.10 Spectrally integrated absorption (red) and dispersion (blue) components of the
transient grating signals from rhodamine 6G in methanol at room temperature (22 °C).
For Molecules which undergo excited state photoisomerization, such as cyanines and crystal
violet, Xu et al. found that the absorption and dispersion components exhibit different
dynamics.87–89 They established that this behavior arises due to the formation of a hot ground
state conformer which has shifted photoinduced absorption compared to the laser spectrum and
hence contributes differently in the absorption and dispersion channel. This particular sensitivity
towards spectral detuning makes heterodyne transient grating a suitable technique for
investigating intermediate electronic states and conformational motions that accompanies a
nonradiative decay processes. As we will show in subsequent chapters, when applied to
carotenoids, this technique leads to considerable simplifications of their nonradiative decay
channel and energy transfer pathways, which can be understood in terms of the conformational
dynamics of their polyene backbone.

25

REFERENCES

26

REFERENCES

(1)

Blankenship, R. E. Molecular mechanisms of photosynthesis; John Wiley & Sons: 2013.

(2)

van Grondelle, R.; Dekker, J. P.; Gillbro, T.; Sundstrom, V. Biochimica et Biophysica Acta
(BBA) - Bioenergetics 1994, 1187, 1-65.

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32

Chapter 2: Nonradiative Decay of the S2 (11Bu+) State of β-Carotene:
Contributions from Dark Intermediates and Double Quantum Coherences

Femtosecond transient grating spectroscopy with heterodyne detection was employed to
characterize the nonradiative decay pathway in β-carotene from the S2 (11Bu+) state to the S1
(21Ag−) state in benzonitrile solution. The results indicate definitively that the S2 state populates
an intermediate state, Sx, on an ultrafast timescale prior to nonradiative decay to the S1 state. The
requirement for inclusion of the Sx state in the nonradiative decay pathway is the observed fast
rise time of the dispersion component, which is predominantly controlled by the decay of the
stimulated emission signal from the optically prepared S2 state. The finding that the excited-state
absorption spectrum from the Sx state is significantly red shifted from that of S2 and S1 leads to a
new assignment for the spectroscopic origin of the Sx state. Rather than assigning Sx to a discrete
electronic state, such as the 1Bu− state suggested in previous work, it is proposed that the Sx state
corresponds to a transition state structure on the S2 potential surface. In this hypothesis, the 12 fs
time constant for the decay of the S2 state corresponds to a vibrational displacement of the C–C
and C=C bond-length alternation coordinates of the conjugated polyene backbone from the
optically prepared, Franck–Condon structure to a potential energy barrier on the S2 surface that
divides planar and torsionally displaced structures. The lifetime of the Sx state would be
associated with a subsequent relaxation along torsional coordinates over a steep potential energy
gradient towards a conical intersection with the S1 state.

The work presented in this chapter has been adapted from J. Phys. Chem. B 2015, 119, 1490514924. Copyright (2015) American Chemical Society.

33

2.1 Introduction
The light-harvesting function of carotenoids in photosynthesis1–4 is initiated by optical
preparation of the second excited singlet state, S2 (11Bu+), which decays nonradiatively to yield
the first excited singlet state, S1 (21Ag−). Both states can serve as excitation energy donors to the
Q-band singlet states of (bacterio)chlorophyll ((B)Chl) molecules in light-harvesting complexes
(Figure 2.1). The mechanism that enables the S1 state to function efficiently in energy transfer to
(B)Chls is of considerable interest because only the S2 state can be directly populated by optical
transitions; the S1 state is a dark state, lacking electric dipole-allowed one-photon transitions to
or from the ground state, S0 (11Ag−). The bulk of the quantum yield of energy transfer is
nevertheless carried by the S1 state, however, because the lifetime of the S2 state is very short,
typically 150 fs. The rate of excitation energy transfer in light-harvesting proteins is optimized
structurally by placing the carotenoid donor nearly in van der Waals contact with the (B)Chl
acceptor. Additionally, it is likely that an intramolecular charge-transfer (ICT) character
develops in carbonyl-containing carotenoids, such as peridinin and fucoxanthin, during the
nonradiative decay process from the S2 state to the S1 state.
Whether the S2 state undergoes an ultrafast nonradiative decay process to populate one or
more dark intermediates prior to populating the S1 state remains indeterminate despite extensive
debate in the literature. PolĂ­vka and SundstrĂśm4 have reviewed the considerable body of
evidence both for and against the existence of the state denoted Sx, which is detected in
femtosecond pump–probe experiments in terms of an excited-state absorption (ESA) band in the
near-IR in <20 fs after optical preparation of the S2 state.7–11 Koyama and coworkers7 assigned Sx
to the 11Bu− state, which was predicted by Tavan and Schulten12 to lie below the S2 state. More
recently, Ikuta et al.13 proposed that the S2 state yields the 31Ag− state prior to populating the

34

11Bu− state; it is notable that Shreve et al.14 assigned the unusually large polarizability of the S2
state to strong coupling to an Ag− state nearby.

Carotenoids
S2 (11B u+)

Chlorophylls
Qx

Energy

150 fs

S1 (21 Ag – )

Qy

S0 (11 Ag – )

S0

hν
10 ps

Figure 2.1 Pathways for nonradiative decay in carotenoids and for excitation energy transfer
from carotenoids to (B)Chls in photosynthetic light-harvesting proteins. The one-photon
transitions transitions between states of the same symmetry or pseudoparity are electric-dipole
forbidden.5,6 Nonradiative decay from the S2 and S1 (21Ag−) states is indicated with wavy arrows.
Energy transfer pathways from the carotenoid S2 and S1 states to the (B)Chl Qx and Qy states, are
indicated with filled arrows.
An additional dark intermediate state, X, was recently identified by Scholes and
coworkers15,16 in two-dimensional electronic spectra (2DES). An off-diagonal cross peak
assigned to the X state was observed in solutions of sphaeroidene or rhodopin glucoside and in
preparations of the LH2 complex at short delays after optical preparation of the S2 state. The
cross peak implicates the X state as an intermediate between the S2 and S1 states. In LH2, where
BChl acceptors are present, cross peaks were also observed that connect X to the BChl Qx state.
These results indicate directly that the X state can serve as an excitation energy donor to the
BChl Qx state. Because the ESA spectrum from the Sx state is significantly red shifted compared
to that from the X state, it seems likely that Sx and X states should be regarded as distinct
states.17 The 2DES spectra provide some relief from the overlapping ESA and stimulated
emission (SE) signals that complicate analyses of the kinetic profiles of intermediates along the
35

S2 → S1 nonradiative decay pathway in conventional one-dimensional pump–probe spectra. At
this point a definitive determination of the nature of the process that apparently yields the Sx and
X states has not yet been made nor is there even a consensus that they exist.
Further complicating the interpretation of the nonradiative decay pathways of carotenoids is
the presence of an upper singlet state, Sn2, which is populated directly from the S2 state by ESA
transitions.18,19 Because the energy gap between the S2 and Sn2 states is almost the same as that
between the S0 and S2 states, optical preparation of an Sn2–S0 electronic coherence via a doublequantum pathway competes with pathways that yield population in the S2 state. In conventional
two-beam pump–probe spectroscopy, the free-induction decay signals generated by the action of
a delayed probe pulse on the Sn2–S0 double-quantum coherence are radiated in the same direction
and are superimposed spectrally and temporally on the population signals derived from
population in the S2 state.20 The dephasing time of the Sn2–S0 double-quantum coherence would
be expected to be very short, perhaps comparable to the pure dephasing time for the S0–S2
coherence, so its decay would be expected to accompany the decay of population from the S2
state into the Sx state.
In this contribution, we show for the first time that femtosecond transient grating
spectroscopy with optical heterodyne detection provides crucial information on the nonradiative
decay of the S2 state of carotenoids that is not available from conventional pump–probe
spectroscopy. In comparison to pump–probe spectroscopy, heterodyne transient grating
spectroscopy offers two distinct advantages in studies of carotenoids. First, the heterodyne
detection scheme allows a full characterization of the complex third-order nonlinear optical
signal by resolving its real (absorption) and imaginary (dispersion) components, the latter not
being observed at all in pump–probe signals. These components interfere with each other in

36

transient-grating spectroscopy with homodyne detection, where only the total signal amplitude
(the complex modulus) is detected directly by a square-law detector. Second, the doublequantum coherence and population signals occur in different time delay regions; the time
orderings of the field-matter interactions that yield the two types of signals are restricted by
detection of the signal in a particular phase-matched direction, as determined by the outgoing
wavevectors of the three excitation pulses. As we demonstrate here, both advantages lead to a
considerable simplification of the interpretation of the transient-grating signal from β-carotene.

Figure 2.1 Structure of β-carotene.
The results show that the dispersion component enables an unambiguous detection of the
nonradiative decay of the S2 state of β-carotene in benzonitile to a dark intermediate state in <20
fs. Numerical simulations of the absorption and dispersion components of the transient grating
signal with an internally consistent model lead to an assignment of the intermediate to the Sx
state with models that incorporate lineshape parameters consistent with the near-IR ESA
spectrum obtained by Cerullo et al.9 This finding places some restrictions on the nature of the
vibrational dynamics that follow optical preparation of the S2 state. We suggest that results are
consistent with the hypothesis17 that Sx state should be assigned to a transition state structure at
the activation-energy barrier between planar and twisted structures on the S2 potential energy
surface rather than being assigned to a discrete electronic state of a planar conformation. This
hypothesis leads to a natural explanation for some of the properties of carotenoids in
photosynthetic light-harvesting proteins.

37

2.2 Experimental Section
2.2.1 Sample Preparation
β-carotene was obtained from Sigma-Aldrich (catalog number C-9750) and was purified by
high-performance liquid chromatography (HPLC) using a Waters 600E/600S multisolvent
delivery system equipped with a 2996 photodiode array detector, as described previously.21 The
column was a Waters Atlantis Prep T3 OBD 5 Âľm column (19 x 100 mm). Acetonitrile was
delivered isocratically at a flow rate of 7.0 mL/min. Samples collected from the HPLC were
dried under nitrogen gas and stored at −20°C until further use. For femtosecond spectroscopy,
solutions of purified β-carotene were dissolved in benzonitrile and then spun in a desktop
microcentrifuge to pellet any insoluble material or debris. The absorbance was then adjusted to
0.3 or less for a 1 mm path at the center of the laser spectrum, 520 nm, by adding neat
benzonitrile. The samples were held in a 1 mm quartz cuvette at room temperature (295 K).
2.2.2 Linear Spectroscopy
Linear absorption spectra were acquired with a Hitachi U-4001 spectrophotometer.
2.2.3 Nonlinear Spectroscopy
Femtosecond transient-grating signals were acquired at room temperature (295 K) with
optical heterodyne detection using a passively phase-stabilized photon-echo spectrometer and
Fourier-transform spectral interferometry. The experiments were performed with 520-nm
excitation pulses obtained from an optical parametric amplifier (OPA, Coherent OPA 9400),
which was pumped by a 250-kHz amplified Ti:sapphire laser (Coherent Mira-Seed oscillator and
RegA 9050 regenerative amplifier). The pulse durations were estimated as having ≥40 fs

38

durations from measurements of the typically 60 fs width of the third-order dispersion signal
from neat methanol solvent, but the simulations that follow indicate that the effective pulse
duration with group-velocity dispersion from the sample cell's contents included was 45 fs.
The photon-echo spectrometer built for use in these experiments follows aspects of the
designs previously discussed by Brixner et al.22 and Moran and Scherer.23 Four laser pulses were
obtained by splitting an incident pump–probe pulse pair with a transmission diffractive optic. A
sequence of two spherical mirrors with 20 cm focal lengths was used to collimate and focus the
four pulses onto the sample in the forward boxcars configuration. The pump–probe population
delay was controlled using a time-of-flight delay driven by a Nanomover actuator (Melles Griot)
prior to the diffractive optic; a second Nanomover actuator controlled the lateral translation of
wedge-shaped prisms in the pump beams to control the coherence delay, which was set to zero
for transient-grating experiments. The time delays were calibrated by spectral interferometry
with a pinhole aperture at the sample position.22,24 The three measurement pulses each carried <1
nJ/pulse; the local oscillator pulse was further attenuated by 3.5 O.D. using fused-silica neutral
density filters.
The spatially overlapped third-order signal and local oscillator were spatially filtered after the
sample using a series of iris diaphragms and then collimated and focused into a spectrograph
(Spex 270m, 1200 gr/mm grating) by a pair of spherical lenses. The spectral interferogram from
the signal and local oscillator was detected using a back-illuminated, liquid nitrogen-cooled CCD
detector (Princeton Instruments VersArray 1300B, 700 × 1300 pixels, 100-ms integration
time/spectrum). Scattered light was removed using the beam-shuttering protocol outlined by
Brixner et al.22 The spectrometer was controlled by LabVIEW (National Instruments) programs.

39

2.3 Experimental Results
2.3.1 Linear Spectroscopy and Laser Excitation Spectrum
Figure 2.3 shows the linear absorption spectrum corresponding to the S0 (11Ag−) →
S2 (11Bu+) transition of β-carotene in benzonitrile solvent at room temperature (295 K). For the
transient-grating experiments discussed in this paper, the spectrum of the signal-beam output of
the OPA was tuned to 520 nm. The pulse durations were estimated as 40 fs fwhm, Gaussian
pulses assumed, from the 60 fs fwhm width of the dispersion component of the transient grating
signal from neat methanol that was measured with these pulses. The OPA spectrum is centered
on the red onset of the absorption spectrum and near to the wavelength of the 0–0 vibronic
transition. This tuning photoselects the lowest energy conformers25 from the ground-state

Absorption

ensemble and prepares the S2 state with minimal excess vibrational excitation.

0
350

400

450

500

550

600

Wavelength (nm)

Figure 2.3 Room-temperature absorption spectrum of β-carotene in benzonitrile solvent.
Superimposed is the spectrum of the OPA signal-beam output (520 nm center wavelength), as
tuned for the heterodyne transient-grating experiments.

40

2.3.2 β-carotene transient grating signals
Transient-grating signals from β-carotene in benzonitrile were acquired with heterodyne
detection and Fourier-transform spectral interferometry. The heterodyne detection scheme used
in this work followed the general approach described by Jonas and coworkers26 and several
techniques implemented by Brixner et al.22 The processing and interpretation of third-order
nonlinear optical signals was previously outlined by Moran, Scherer, and coworkers,23,27 and the
following summary adopts their notation.
In the transient-grating experiment, two pump pulses arrive synchronously (with coherence
time interval τ = 0 ) at the sample position and directed along wavevectors k 1 and k 2 . After a
population (or waiting) interval T , , the probe pulse arrives along wavevector k 3 . The sample
then emits a signal (frequency ω t , with emission time t > 0 with respect to the probe pulse). In
our experimental configuration, the signal is detected along the k s = −k 1 + k 2 + k 3 direction by
using the forward boxcars configuration for the pump and probe wavevectors; signals are also
emitted along other combinations of the input wavevectors, but they are not detected in our
experiment. When optical heterodyne detection is employed, a weak local oscillator pulse arrives
at the sample prior to the probe pulse along the k s wavevector so as to interfere with the
outgoing third-order signal; in our experiment the local oscillator and probe pulses are spaced by
~800 fs. The population-time dependence of the third-order signal is recorded by scanning the
population time T to carry the probe pulse from negative to positive delays with respect to the
pump pulses. The data acquisition and data processing procedures described by Brixner et al.22
were implemented to acquire a spectral interferogram that carries the third-order signal and lacks
background scattering by alternately shuttering beams 1 and 3 and taking differences.

41

The third-order signal field, Es(3) (t,T ,τ ) , is the sum of the fields from the nonresonant
solvent and resonant solute and is related to their third-order polarizations, P (3) (t,T ,τ ) , by

i2π lω t (3)
(3)
Psolvent (t,T ,τ ) + Psolute
(t,T ,τ )
n(ω t )c

(

Es(3) (t,T ,τ ) =

)

(2.1)

where l is the length of the sample cell, n(ω t ) is the refractive index as a function of the signal
frequency, c is the speed of light, and T and τ are the interpulse delays that specify the threepulse program. P (3) (t,T ,τ ) is determined by the three successive actions of the electric fields
from the three pulses, Es(3) (t,T ,τ ) that define a particular Feynman pathway.23,28 Optical
heterodyne detection obtains the spectral interferogram I tot (ω t ,T ,τ ,τ LO ) as23
I tot (ω t ,T ,τ ,τ LO ) =

∍

∞

−∞

(

d t Es(3) (t,T ,τ ) + E LO (t − τ LO )exp(iω t t)

)

2

(2.2)

where E LO (t − τ LO ) is the electric field of the local oscillator and τ LO is the time delay between
the local oscillator and probe pulses. The third-order signal is isolated by a Fourier-transform
algorithm22,26 as a complex cross term

I het (ω t ,T ,τ ,τ LO ;ϕ LO (ω t )) = I s (ω t ,T ,τ ) I LO (ω t ) exp ⎡⎣ i(ϕ s (ω t ) − ϕ LO (ω t ) − ω tτ LO ) ⎤⎦

(2.3)

where I s (ω t ,T ,τ ) is the signal intensity, I LO (ω t ) is the intensity of the local oscillator, and

ϕ s (ω t ) and ϕ LO (ω t ) are the phases of the signal and local oscillator, respectively. The phase
ϕ LO (ω t ) was determined experimentally in this work as described previously by Xu et al.29 and
by Moran et al23 from the purely dispersive signal from neat solvent, which was measured in the
same sample cuvette used for the solute β-carotene sample and with kinematic replacement in the

42

cuvette holder. The I LO (ω t ) term in equation 2.3 is canceled by dividing the signal with the
2

square root of a separately acquired spectrum of the local oscillator, I LO (ω t ) , which isolates
the signal field as

Es(3) (ω t ,T ,τ ) = ξˆs (ω t ,T ,τ )exp ⎡⎣ −iϕ s (ω t ) ⎤⎦

(2.4)

where ξˆs (ω t ,T ,τ ) denoted the electric field amplitude. The real and imaginary parts of

Es(3) (ω t ,T ,τ ) obtain the absorption and dispersion components, respectively. The sum of their
squares obtains the modulus (or power spectrum),
2

2

Es(3) (ω t ,T ,τ ) ≡ Re ⎡⎣ Es(3) (ω t ,T ,τ ) ⎤⎦ + Im ⎡⎣ Es(3) (ω t ,T ,τ ) ⎤⎦

2

(2.5)

which is proportional to the homodyne signal collected by a square-law detector along the k s
wavevector in the absence of a local oscillator field.
Figures 2.4 and 2.5 show the absorption and dispersion components of the heterodyne
transient grating signal from β-carotene in benzonitrile at room temperature over the 0–500 fs
range for the population delay T. Both components were obtained with a consistent choice of
signal phase, ϕ s (ω t ) that projects the ground state bleaching (GSB) and stimulated emission
(SE) pathways for the resonant β-carotene solute in the absorption component as positive-going
signals (increasing emission intensity). This choice of phase obtains negative-going signals for
the dispersion component obtained from neat solvent.
The absorption component of the β-carotene signal exhibits a biphasic transient, with a
prompt rise and an initial decay yielding a net excited-state absorption (ESA) signal in <100 fs.
In contrast, the β-carotene dispersion signal is essentially monophasic; after a very short delay,

43

<20 fs, it exhibits a rising profile; as explained below, the rising signal has principal
contributions from GSB and ESA. The negative-going peak observed near the zero of time
comes from the dispersion signal from the benzonitrile solvent (Figure A2.1 in the Appendix).
The weak, derivative shaped signal from benzonitrile in the absorption component arises from
self-phase modulation due to the passage of the femtosecond excitation pulses. A β-carotene
solute concentration series (Figure A2.2) shows that the contribution of benzonitrile to the
modulus signal is small but not negligible at the 0.3 O.D. conditions used in Figures 2.4 and 2.5.
At lower solute concentrations, the dispersion signal from the solvent is dominant near the zero
of time; at higher solute concentrations, the signal/noise ratio decreases and distortions of the
signal can be discerned, especially in 2DES signals.30

Figure 2.4 Real (absorption) component of the heterodyne transient grating signal from βcarotene in benzonitrile solvent at room temperature (22 °C). The yellow end of the color bar
corresponds to net ground-state bleaching or stimulated emission; the dark blue end indicates
excited state absorption.

44

Figure 2.5 Imaginary (dispersion) component of the heterodyne transient grating signal from βcarotene in benzonitrile solvent at room temperature (22 °C). The phasing of the color bar is
consistent with that used in Figure 2.4 for the absorption component. At 520 nm, the yellow
contours correspond to the net ESA signal from the S1 state.
In order to establish the principal time constants and lineshapes for the evolution of the
transient grating spectrum, the absorption and dispersion transient grating data sets from the βcarotene transient grating signal over the -100 fs–12 ps range were subjected to a global target
analysis.31–33 The absorption and dispersion components are expressed in the global model as a
set of spectral components and associated kinetic time constants with convolution with the
instrument-response function, as defined by the electric field profiles of the pump and probe
laser pulses. A preliminary singular value decomposition analysis indicated that the models for
the absorption and dispersion components required at least three kinetic components. Figures 2.6
and 2.7 show the decay-associated spectra (DAS) and evolution-associated spectra (EAS) for the
absorption and dispersion signals corresponding to a three component global model with
common timescales. Figure 2.8 shows a slice through the data sets and fitted models at a probe
wavelength of 520 nm, the center of the laser spectrum.

45

0.8

EAS

0.6
0.4
0.2
0
1.0
Population

0.8

DAS

0.6
0.4

0.8
0.6
0.4
0.2
0
0

1
Time (ps)

0.2

10

0

510

520

530

540

Wavelength (nm)

Figure 2.6 Evolution-associated and decay-associated spectra (EAS and DAS, respectively)
from a global analysis of the absorption component of the heterodyne transient-grating signal
(Figure 2.4) from β-carotene in benzonitrile over the -100 fs–12 ps delay range. The DAS
(bottom panel) characterize the spectral changes associated with a parallel decay of the three
spectra; black: 12 fs decay; red: 142 fs decay; blue: 11.6 ps decay back to the ground state. The
EAS (top panel) assume a sequential process: black: instantaneously formed initial species, 12 fs
decay; red: first intermediate species, 12 fs rise, 142 fs decay; blue: second intermediate
component, 142 fs rise, 11.6 ps decay back to the ground state. The inset shows the time
evolution of the populations for the three components in the sequential model against a linear–
logarithmic time axis split at 1 ps. The global model includes a convolution with a 60 fs
Gaussian-shaped instrument response function centered at the zero of the probe delay axis.

46

EAS

0.2
0
1.0
Population

−0.2
−0.4

0.8
0.6
0.4
0.2
0

0.2

0

1
Time (ps)

10

DAS

0
−0.2
−0.4

510

520

530

540

Wavelength (nm)

Figure 2.7 Evolution-associated and decay-associated spectra (EAS and DAS, respectively)
from a global analysis of the dispersion component of the heterodyne transient-grating signal
(Figure 2.5) from β-carotene in benzonitrile over the -100 fs–12 ps delay range. The DAS
(bottom panel) characterize the spectral changes associated with a parallel decay of the three
spectra; black: 12 fs decay; red: 142 fs decay; blue: 10.2 ps decay back to the ground state. The
EAS (top panel) assume a sequential process: black: instantaneously formed initial species, 12 fs
decay; red: first intermediate species, 12 fs rise, 142 fs decay; blue: second intermediate
component, 142 fs rise, 10.2 ps decay back to the ground state. The inset shows the time
evolution of the populations for the three components in the sequential model against a linear–
logarithmic time axis split at 1 ps. The global model includes a convolution with a 60 fs
Gaussian-shaped instrument response function centered at the zero of the probe delay axis.

47

Re[Es] and Im[Es]

0

0

1

10

Time (ps)

Figure 2.8 Time evolution of the absorption (red) and dispersion (blue) components of the
heterodyne transient grating signals from β-carotene in benzonitrile solvent at 520 nm, as plotted
against a linear–logarithmic time axis split at 1 ps. Both signals are superimposed with the fitted
global models described in Figures 2.6 and 2.7, respectively.
The EAS describe the transient-grating signal in terms of a sequential model corresponding
to the decay of the instantaneously formed S2 state through two intermediates back to the ground
state. The <500 fs parts of the absorption and dispersion components were well described with
common decay time constants: 12 fs and 142 fs. Because the 12 fs decay involves kinetics that
are shorter in timescale than the instrument-response width, as determined by the 40 fs pulses
used in these experiments, this time constant is estimated with considerable indeterminacy. Both
time constants are comparable to those determined for the decay of the S2 and Sx states
determined in the Cerullo et al.9 pump–probe experiments with β-carotene in cyclohexane
solvent. The EAS spectrum of the first intermediate, presumably that corresponding to the Sx
state, is much weaker and is slightly red shifted compared to that of the instantaneously formed,
S2 state. Further, note that the dispersion spectrum of the S2 state is biphasic, whereas the
dispersion spectrum of the first intermediate is monophasic. As discussed in the simulations that

48

follow, these aspects provide some clues about the spectroscopic nature of the Sx state and the
line-broadening dynamics that accompany optical excitation of the S2 state.
The global models for the absorption and dispersion signals, however, have significantly
different time constants for the decay of the third spectrum, from the second intermediate state in
the global model: 11.6 ps in the absorption signal and 10.2 ps in the dispersion signal. These
decays correspond to nonradiative recovery back to the ground state, S0, from the S1 state. The
different time constants indicate that the ground-state recovery process from the S1 state yields
initially a conformationally displaced ground-state intermediate prior to relaxation to the initial,
photoselected ground-state conformational distribution. This aspect of the nonradiative decay
process will be examined in a separate contribution, which will include numerical simulations of
the transient spectra that accompany the relaxation process on the ground-state potential surface.
2.4 Numerical Simulation of Linear and Nonlinear Response
In order to understand the time evolution of the absorption and dispersion components of the
heterodyne transient grating signal from b-carotene, we performed numerical simulations using
the nonlinear optical response function formalism. This approach has been extensively used in
combination with the multimode Brownian oscillator model (MBO),28 which is used to treat the
interactions of electronic chromophores with the surrounding solvent medium and
thermodynamic bath.34–36 The numerical simulations presented here follow the approach
implemented by Brixner et al.22 for a three-level system and as expanded by Christensson et al.19
for simulations of carotenoids. The effects of the finite pulse durations and bandwidths of the
excitation laser pulses are included so that the results can be explicitly compared with the
experimental results in the frequency and time domains. Simulations of the homodyne transient
grating signals of b-carotene in tetrahydrofuran were discussed previously by Hashimoto and

49

coworkers.37–40 Christensson et al.18,41 reported simulations of the photon echo and doublequantum coherence signals from b-carotene in benzonitrile. To our knowledge, the present work
includes the first simulations of the heterodyne transient grating signal from a carotenoid system
that employ simultaneous modeling of the absorption and dispersion components.

ΔS2

Sn2

ΔSx

ΔS1

Energy

Snx
Sn1
S2

ΔS0

Sx
S1

S0

Figure 2.9 Schematic energy-level diagram for β-carotene, as used in the simulations of the
heterodyne transient grating signal from β-carotene. Solid green arrows indicate ground-state and
excited-state absorption transitions. Blue wavy arrows mark internal conversion transitions.
Double-headed arrows show the detuning ( Δ ) between the center of the laser spectrum and the
vertical energy of an electronic transition. Note that in some of the simulations that follow, the Sx
manifold is omitted; in that case, the S2 state decays nonradiatively directly to the S1 state.
Figure 2.9 shows the energy level scheme of b-carotene that was employed in the simulations
we performed. After optical preparation of the S2 state, an intermediate electronic state, here
labeled Sx, mediates nonradiative decay to the S1 state. Broadband pump-probe experiments have
previously identified ESA transitions from S2 and Sx.9 The S1 state is known to exhibit a strong
ESA signal in the visible region. Therefore, along with the S 2 → S0 stimulated emission (SE)
and S0 → S 2 ground state bleaching (GSB) transitions, ESA transitions from S2, Sx, and S1 to
higher lying singlet states with the appropriate symmetry need to be included in the simulation.

50

Internal conversion pathways from the Sx state to the S0 state are not included in the simulation;
further, no optical transitions from S0 to Sx have been observed, so the transition dipole moment
for optical transitions between the S0 and Sx states is considered negligible.37
In order to determine whether the presence of the Sx state is indicated by the heterodyne
transient grating signals we observed with β-carotene, in the following simulations we have
compared the results obtained with two energy-level schemes, one with the Sx manifold included
as shown in Figure 9 and the other without. The simulations performed by Christensson et al.41
did not include an intermediate state between S2 and S1.The homodyne transient grating signals
from β-carotene and related carotenoids obtained by Hashimoto and coworkers37–40 were best
described with simulations that included an intermediate state. The goal of our simulations is to
find a set of suitable parameters that fit the absorption and dispersion components of the transient
grating signal at the same time. In each simulation, the parameters were varied first to find the
best fit for the absorption component and then the same set of parameters were used to simulate
the dispersion component.
In the MBO model, an energy-gap time-correlation function, M (t) is used to describe the
fluctuations of the energy levels of a molecular system. It is constructed from the sum of terms
associated with each type of Brownian mode: a Gaussian (G) inertial solvation term,42,43
exponential (E) terms for diffusive solvation, and a series of cosinusoids for underdamped
intramolecular vibrational modes (v)28,34

M(t) = λ G exp ⎡⎣ −(t / τ G ) 2 ⎤⎦ + ∑ λ E,i exp(−t / τ E ,i )
i

⎛
⎞
⎛ γ v, j ⎞
+ ∑ λ v, j exp(−γ v, j t / 2) ⎜ cos(Ω v, j t) + ⎜
sin(Ω v, j t)⎟
⎟
⎝ 2Ί v, j ⎠
⎝
⎠
j

51

(2.6)

1/2

where Ω v = ⎡⎣(ω v ) 2 − (γ v / 2) 2 ⎤⎦ . Here, λ and τ denote the reorganization energy and dephasing
time of a specific Brownian mode. The inverse damping time of a vibrational mode with a
natural frequency ω v is denoted by γ v = 1/ τ v .
The time evolution of the time-correlation function can then be represented by a linebroadening function, g(t)

t

t1

t

0

0

0

g(t) = Δ 2 ∫ d t1 ∫ d t 2 M(t 2 ) + iλ ∫ d t1 M(t1 )

(2.7)

where Δ represents the total coupling strength, which tells how strongly the gap between energy
levels is modulated by the Brownian modes, and Îť stands for the total solvation reorganization
energy.

M (t) can be directly estimated from a measurement of the three-pulse stimulated photonecho peak shift (3PEPS),44 but a simulation of the ground-state absorption spectrum is usually
performed to obtain several of the parameters in Equation 2.6. Once M (t) is determined and

g(t) is calculated from it, all the linear and nonlinear optical responses of a system can be
calculated with internal consistency using the Condon approximation and a second-order
cumulant expansion.28
2.4.1 Numerical Simulation of Absorption Spectrum
In general, the ground-state absorption spectrum can be determined using the line-broadening
function as28

σ A (ω ) ∝ ω Re ∫ d t exp ( i(ω − ωeg )t ) exp ( −g(t))
∞

0

52

(2.8)

where ω eg = ω 0–0 + λ is the vertical transition frequency,19 which corresponds to the energy gap
between the e and g potential surfaces at the ground-state structure; ω 0−0 denotes the frequency
for the 0–0 vibronic transition. When applied to β-carotene, e and g correspond to the resonant S2
and ground state S0, respectively.
Figure 2.10 compares the S 0 → S 2 absorption spectrum from β-carotene with a calculated
spectrum determined using equations 2.6–2.8; the model parameters for different Brownian
modes are listed in Table 2.1. The experimental and calculated spectra exhibit nearly identical
profiles from the low-frequency onset to the peak absorbance and then the 0–2 vibronic satellite;
while the vibrational structure is well modeled past that point to higher frequencies, the two
spectra increasingly deviate on the blue side of the spectrum where twisted conformations (with
somewhat different lineshape parameters) may make a contribution to the experimental profile.
The optimized value for ω eg is 21550 cm−1. The width of the absorption spectrum is determined
by the sum of the coupling strengths of the Brownian modes. Two high frequency underdamped
vibrational modes are included in the calculation, 1150 cm-1 and 1520 cm-1, which are the
ground-state frequencies of the totally symmetric, resonance Raman active, C–C and C=C bonds
in the conjugated polyene backbone of β-carotene.45 These modes produce the vibronic
progression that is visible in the absorption spectrum. The reorganization energies and
vibrational dephasing times included in M (t) are similar to those employed by Christensson et
al.41 in their simulations. The exponential component in M (t) with a 1 ps time constant roughly
corresponds to the line-broadening timescale observed in the time evolution of the pump-probe
spectrum of b-carotene.46

53

Absorbance

18000

20000
22000
-1
Wavenumber (cm )

24000

26000

Figure 2.10 Comparison of the room temperature S0→S2 absorption spectrum of β-carotene in
benzonitrile (dark blue curve) with a simulation (red dash-dotted curve) obtained using the MBO
model (Equations 2.6-2.8) and the parameters listed in Table 2.1.
Table 2.1 MBO model parametersa for the simulation of the β-carotene S 0 → S 2 absorption
spectrum in benzonitrile at 295 K.

ω v (cm−1)

Mode

λ (cm−1)

τ (fs)

Gaussian

100

10

—

Exponential 1

300

500

—

Exponential 2

450

1000

—

Vibration 1

520

2200

1150

Vibration 2

1120

2200

1520

See Equations 2.6-2.8. For a given term in M (t) , λ is the reorganization energy and τ denotes the
damping time constant; ω v is the frequency for a vibrational mode.
a

2.4.2 Numerical Simulation of Transient Grating Signal
In heterodyne transient grating spectroscopy, a sequential interaction with three laser pulses
induces a third-order polarization in the sample. In the boxcar geometry, as implemented in our
transient-grating spectrometer, the resulting signal field is detected in the phase-matched

54

k s = −k 1 + k 2 + k 3 direction, where k i stands for the wavevector of the ith pulse. The pulse
sequence and the time variables are shown in Figure 2.11.

Pulse 1

Pulse 3

Pulse 2

τ

T

k1

k2

Signal

k3
P(3)(t)

-T-τ

-T

t1

t2

0

t3

t

Figure 2.11 Excitation pulse sequence for third-order nonlinear spectroscopies, including
transient grating spectroscopy, after Brixner et al.22 and Sugisaki et al.40 Three excitation pulses
with wavevectors k 1 , k 2 , and k 3 are centered at times −T − τ , −T , and 0, respectively. The
time intervals t1 , t 2 , and t3 are between the interactions with the electric fields from the three
pulses. The interactions can occur at any time inside the pulse envelope. P (3) (t) denotes the
resulting third-order nonlinear polarization at time t .
The third-order polarization, P (3) (τ ,T ,t) , can be written as a convolution of the system
response and the electric fields of the three laser pulses as

P (3) (τ ,T ,t) =

∞

∞

∞

0

0

0

∍ ∍ ∍

dt1 dt 2 dt3 S (3) (t1 ,t 2 ,t3 ) E3 (t − t3 )E2 (t + Τ − t3 − t 2 )

(2.9)

× E1(t + τ + T − t3 − t 2 − t1 )

where S (3) (t1 ,t 2 ,t3 ) is the system response determined by the sum of the relevant third-order
Feynman pathways, as discussed below, Ei are the electric fields of the laser pulses, and t i are
the time intervals between the field–matter interactions. Assuming the weak-field limit and the
and the rotating wave approximation, and assuming that only the terms that contribute in the
phase-matched direction are included, P (3) (τ ,T ,t) , can be expressed as22

55

P (3) (τ ,T ,t) = exp(−iω 0 t + iω 0τ ) ∫

{

∞
0

∞

∞

0

0

∍ ∍

dt1 dt 2 dt3

× SR ⎡⎣ A1* (t + τ + T − t1 − t 2 − t3 ) A2 (t + T − t 2 − t3 ) A3 (t − t3 )
+ A1* (t + τ + T − t1 − t 2 − t3 ) A3 (t − t 2 − t3 ) A2 (t + T − t3 )⎤⎦
+SNR ⎡⎣ A2 (t + T − t1 − t 2 − t3 ) A1* (t + τ + T − t 2 − t3 ) A3 (t − t3 )

(2.10)

+ A3 (t − t1 − t 2 − t3 ) A1* (t + τ + T − t 2 − t3 ) A2 (t + T − t3 )⎤⎦
+SDQC ⎡⎣ A2 (t + T − t1 − t 2 − t3 ) A3 (t − t 2 − t3 ) A1* (t + τ + T − t3 )
+ A3 (t − t1 − t 2 − t3 ) A2 (t + T − t 2 − t3 ) A1* (t + T + τ − t3 )⎤⎦

}

Equation 2.10 is expressed in terms of the electric field envelope function for the ith pulse, Ai (t) ,
which scales the electromagnetic wave 	Ei (t) = Ai (t)exp(−iω 0 t + ik i ⋅ r) , where 	k i is the wave
vector of the electric field and ω 0 is the carrier frequency. The times t1 , t 2 , and t3 indicate the
time intervals between the electric field interactions, τ is the time delay between the first and
second pulses (the coherence delay), and T is the time delay between the second and third pulses
(the population delay). Given that the laser pulses have finite pulse durations, all of the possible
time orderings for the three field–matter interactions have to be taken into account. The system
response terms SR, SNR, and SDQC represent the sums of the several responses contributing to the
rephasing (R), nonrephasing (NR) and DQC Feynman pathways, respectively. The detailed
expressions for these pathways depend on the particular model (Figure 2.9) under consideration.
Once the polarization P (3) (τ ,T ,t) has been calculated, the signal field can be obtained using
Equation 2.1, and then the absorption (real) and dispersion (imaginary) components of the
transient grating signal can be calculated.

56

ks

S0 S0
S2 S 0

ks
k3

S2 S 0

S2 S2
S2 S 0

k2

ks

k1

k2

S0 S0

R1,g

R2,g

S2 S2

S2 S2

k2

S 0 S2
S0 S0

ks
k3

k1

k2

ks

Sx Sx

k3

k2
k1

k3
k2

S0 S0
S2 S 0
S0 S0
R4,g

R3,g

S n2 S2

S n2 S2

k1

S2 S 0

S2 S2

S n2 S 0

ks

k1

S0 S0

k1

S n2 S 0

k3

S2 S 0

k3

S2 S 0

k2

S0 S0

k2

S0 S0
R4,f

R*3,f

ks

Sx Sx

S1 S1

ks

S n1 S1

k3

Sx Sx

S2 S 0

RSx,R

S0 S0

S2 S 0

S0 S0

S 0 S2

k2

k1

ks

S2 S2

k1

S2 S 0

S0 S0

S2 S2

S2 S2

S0 S0

ks

S0 S0

k1

S nx S x

Sx Sx

S0 S0

S 0 S2

R*2,f

S nx S x

k2

k3

S2 S2

S2 S 0

R*1,f

k3

k3

S 0 S2

S0 S0

k3

ks

S2 S2

S n2 S2

ks

S0 S0

k2

k1

S1 S1
S n1 S1

S1 S1

k3

S1 S1

S2 S2

S2 S2

S 0 S2

S2 S 0

S0 S0

S0 S0

RSx,NR

RS

1,R

k1

k2

S0 S0
R S1,NR

Figure 2.12 Double-sided Feynman diagrams for pathways contributing to the third order
nonlinear optical response of β-carotene based on the energy-level scheme shown in Figure 2.9
and the assumption of detection along the k s = −k 1 + k 2 + k 3 direction. The solid arrows indicate
field–matter interactions on the ket (left) and bra (right) side of the density matrix. The curly
arrow denotes the emission event in the phase-matched direction arising from the coherence
created by the third field–matter interaction. The dashed lines indicate relaxation of population
between states. Time increases as one goes from the bottom to the top in each diagram.
Figure 2.12 shows double-sided Feynman diagrams for all the pathways needed to calculate
the transient grating signals for the case where the Sx state is included given the assumption of
detection along the k s = −k 1 + k 2 + k 3 direction. For a simulation without inclusion of the Sx
state, the Feynman diagrams associated with ESA transitions from the Sx state are omitted from
the calculation, and nonradiative decay from S2 populates S1 directly. This effectively removes

57

k1

the Sx manifold from Figure 2.9. SE transitions from Sx are not included in the model because of
the narrow probe bandwidth used in the present experiments.
The labels for the Feynman diagrams and the associated response functions shown in Figure
2.12 are as used in the previous work for a three-level system by Brixner et al.,22 but we have
added the diagrams required to handle the additional states included in Figure 2.9. The response
functions R1,g – R4,g describe SE and GSB pathways for transitions between the ground state S0
(g) and the resonant S2 state, (e). R1,* f and R2,* f indicate the ESA pathways from the S2 state to
the Sn2 (f) state. R3,* f and R4, f are the DQC pathways. The pathways labeled RS x and RS1 are for
the rephasing (R) and nonrephasing (NR) pathways involving ESA from the Sx and S1 states,
respectively.
The DQC diagrams deserve additional explanation. The Feynman pathways that contribute to
the DQC signals are shown in Figure 2.13 along with the corresponding wave-mixing energy
level (WMEL) diagrams.47 The first field–matter interaction creates a coherence between the
ground state S0 and the resonant excited state S2. Rather than creating a population in the S2 or S0
states, the second field–matter interaction results in a coherence between the ground state and the
double-quantum excited state, Sn2. This is called a DQC, and it emits light via a free-induction
decay with a frequency corresponding to the S0–Sn2 energy gap, approximately twice the
frequency of the S0–S2 absorption that was initially pumped. The third field–matter interaction
drives an ESA-like transition that prepares a S2– Sn2 coherence ( R3,* f ), or it drives a SE-like
transition yielding a S0 – S2 coherence ( R4, f ). Both of these coherences oscillate at frequencies
near to the S0–S2 absorption band so they can be detected experimentally in a one-color
experiment. Depending on the relative transition dipole strengths for the third field–matter

58

interaction in the two pathways, the total contribution of DQC pathways to the third-order signal
can be positive (increasing light emission) or negative (decreasing light emission).
Note that the (2,3,1) time ordering shown in the DQC diagrams corresponds to a negative
coherence time τ (pulse 2 arrives prior to pulse 1) and to negative population delays T (pulse 3
arrives prior to pulse 1). This sequence of interactions is required if the signal is to be detected
along the k s = −k 1 + k 2 + k 3 direction used in the present experiments. In pump–probe
experiments, where the pump pulse accounts for the first two field–matter interactions ( k 1 = k 2 )
and the detected signal has to be emitted along the direction of the delayed probe pulse

(k s = k 3 ), additional DQC pathways, corresponding to all possible time orderings for the three
field–matter interactions, contribute to the signal.18,20 Thus, the transient grating experiment

(τ = 0) restricts the DQC pathways to a subset of the possible time orderings; it confines the
DQC signal to the width of the excitation pulses symmetric with the zero of time ( T = 0 ).
Further, as shown below, the transient grating experiment can be conducted with different small
and negative coherence delays ( τ < 0 ) in order to project out the DQC contribution relative to
the population-dependent pathways.
For use in nonlinear optical simulations, the third-order response functions associated with
the Feynman pathways shown in Figure 2.12 and Figure 2.13 are expressed in terms of linebroadening functions, g(t) . These functions have been listed elsewhere,19,22,28 but they are
reproduced in the Appendix for completeness and employ a consistent notation. In the following
simulations, it is assumed that population relaxation between states results in vibrational
decoherence; the phase for the underdamped vibrational terms in M (t) is randomized by the
conversion from one state by the conversion from one state to another.48 Accordingly, all the
response functions that include nonradiative decay between states during the interval between the

59

second and third field–matter interactions have to be scaled by Markovian population
kinetics.48,49 Note that the validity of this assumption will be revisited in the Discussion section.
For now, consider that the use of 40 fs pulses in the present experiments limits us to an impulsive
spectral bandwidth that is much narrower than required to observe coherent wavepacket motions
in the high-frequency, bond-length alternation coordinates included in M (t) .

ks

S n2

S n2 S2

3

S n2 S 0

S2
1

2

S2 S2

S0

k3
k2

S2 S 0

ks

S0 S0

k1

S2 S 0

k1

S0 S0

R* 3,f

S n2
3

1

S n2 S 0

S2
2

S0

k3

S2 S 0

k2

S0 S0

R 4,f

Figure 2.13 Wave-mixing energy level (WMEL) diagrams47 and the corresponding double-sided
Feynman diagrams for the double quantum coherence pathways in β-carotene given the
assumption of detection along the k s = −k 1 + k 2 + k 3 direction. In the WMEL diagrams, time is
ordered from left to right. The solid and dotted arrows in the WMEL diagrams indicate
interactions from the ket and bra sides of the density matrix, respectively. The wavy line
indicates the final emission of the signal.
The kinetic scheme is different for the two types of models used in the simulation that
follow. For models omitting Sx, the expression for SR, SNR and SDQC in Equation 2.10 are:

60

⎡ −ΓS1
⎤
ΓS2
SR = R3,g ⎢
exp ( −ΓS2 t 2 ) +
exp ( −ΓS1 t 2 ) ⎥
( ΓS2 − ΓS1 )
⎢⎣ ( ΓS2 − ΓS1 )
⎥⎦
⎡ −ΓS2
⎤
ΓS2
− RS1 ,R ⎢
exp ( −ΓS2 t 2 ) +
exp ( −ΓS1 t 2 ) ⎥
( ΓS2 − ΓS1 )
⎢⎣ ( ΓS2 − ΓS1 )
⎥⎦
+ R2,g − R1,* f exp ( −ΓS2 t 2 )

(

(2.11)

)

⎡ −ΓS1
⎤
ΓS2
S NR = R4,g ⎢
exp ( −ΓS2 t 2 ) +
exp ( −ΓS1 t 2 ) ⎥
( ΓS2 − ΓS1 )
⎢⎣ ( ΓS2 − ΓS1 )
⎥⎦
⎡ −ΓS2
⎤
ΓS2
− RS1 ,NR ⎢
exp ( −ΓS2 t 2 ) +
exp ( −ΓS1 t 2 ) ⎥
( ΓS2 − ΓS1 )
⎢⎣ ( ΓS2 − ΓS1 )
⎥⎦

(

(2.12)

)

+ R1,g − R2,* f exp ( −ΓS2 t 2 )
SDQC = R4, f − R3,* f

(2.13)

Whereas for the model with the intermediate, the expressions for SR, SNR and SDQC in
Equation (2.10) are determined as

⎡
ΓS2 ΓS x
SR = R3,g ⎢
exp ( −ΓS1 t 2 )
⎢⎣ ( ΓS2 − ΓS1 ) ( ΓS x − ΓS1 )
−

⎤
ΓS2 ΓS1
ΓS1 ΓS x
exp ( −ΓS x t 2 ) +
exp ( −ΓS2 t 2 ) ⎥
( ΓS2 − ΓSx )( ΓSx − ΓS1 )
( ΓS2 − ΓSx )( ΓS2 − ΓS1 )
⎥⎦

⎡
ΓS2
− RS x ,R ⎢
⎢⎣ ( ΓS2 − ΓS x

⎤

− exp −Γ t ) + exp ( −Γ t )} ⎥
){ (
⎥
S2

2

Sx

2

⎦

⎡
ΓS2 ΓS x
− RS1 ,R ⎢
exp ( −ΓS1 t 2 )
⎢⎣ ( ΓS2 − ΓS1 ) ( ΓS x − ΓS1 )
−

⎤
ΓS2 ΓS x
ΓS2 ΓS x
exp ( −ΓS x t 2 ) +
exp ( −ΓS2 t 2 ) ⎥
( ΓS2 − ΓSx )( ΓSx − ΓS1 )
( ΓS2 − ΓSx )( ΓS2 − ΓS1 )
⎥⎦

(

)

+ R2,g − R1,* f exp ( −ΓS2 t 2 )

61

(2.14)

⎡
ΓS2 ΓS x
S NR = R4,g ⎢
exp ( −ΓS1 t 2 )
⎢⎣ ( ΓS2 − ΓS1 ) ( ΓS x − ΓS1 )
−

⎤
ΓS2 ΓS1
ΓS1 ΓS x
exp ( −ΓS x t 2 ) +
exp ( −ΓS2 t 2 ) ⎥
( ΓS2 − ΓSx )( ΓSx − ΓS1 )
( ΓS2 − ΓSx )( ΓS2 − ΓS1 )
⎥⎦

⎡
ΓS2
− RS x ,NR ⎢
⎢⎣ ( ΓS2 − ΓS x

⎤

− exp −Γ t ) + exp ( −Γ t )} ⎥
){ (
⎥
S2

2

Sx

2

⎦

(2.15)

⎡
ΓS2 ΓS x
− RS1 ,NR ⎢
exp ( −ΓS1 t 2 )
⎢⎣ ( ΓS2 − ΓS1 ) ( ΓS x − ΓS1 )
−

⎤
ΓS2 ΓS x
ΓS2 ΓS x
exp ( −ΓS x t 2 ) +
exp ( −ΓS2 t 2 ) ⎥
( ΓS2 − ΓSx )( ΓSx − ΓS1 )
( ΓS2 − ΓSx )( ΓS2 − ΓS1 )
⎥⎦

(

)

+ R1,g − R2,* f exp ( −ΓS2 t 2 )
SDQC = R4, f − R3,* f

(2.16)

In equations 2.11–2.16, Γi denotes the inverse lifetime 1/ τ i for a given state i.
2.4.2.1 Simulation of Transient Grating Signal Without Sx
Using the theory discussed above, we simulated the transient grating signal from β-carotene
in benzonitrile assuming first that the Sx manifold is omitted from Figure 2.9, so the radiationless
decay proceeds directly from S2 to S1. The absorption and dispersion components calculated with
an optimized set of parameters are shown in Figures 2.14 and 2.15.The simulations employ a
laser spectrum centered at 19230 cm−1 and a pulse duration of 45 fs. The lifetime for the S2 state
is set here to 150 fs. The S1 state is assigned an 11.6 ps lifetime, to match the decay time constant
exhibited by the absorption component in the global model. These simulations are intended,
however, to describe only the <500 fs population time range, so no attempt is made here to
handle the spectroscopic origin of the different ground-state recovery time constants observed in

62

the global model for the absorption and dispersion components. As we will discuss in a separate
contribution with a more detailed model for that part of the response, the different kinetics
observed in the two components arises from an initial production of a conformationally displaced
structure on the S0 potential surface.

Figure 2.14 Numerical simulation of the absorption component of the transient grating signal
from β-carotene, with the Sx state omitted from the energy level scheme shown in Figure 2.9.
The parameters used in the calculation are listed in Table 2.1–2.3 and in the text. The yellow end
of the color bar corresponds to net ground-state bleaching or stimulated emission; the dark blue
end indicates excited state absorption.

63

Figure 2.15. Numerical simulation of the dispersion component of the transient grating signal
from β-carotene, with the Sx state omitted from the energy level scheme shown in Figure 9. The
parameters used in the calculation are listed in Table 2.1–2.3 and in the text. At 520 nm, the
yellow contours correspond to the net ESA signal from the S1 state.
Table 2.2 gives the energy gaps and relative transition dipole moment strengths for the
relevant spectroscopic transitions obtained after optimization of the model. These parameters are
dependent on the reorganization energies used in the model and therefore they differ somewhat
from the values employed by Christensson et al.41 The lineshape parameters for the S 0 → S 2
transition were taken from the model for the absorption spectrum simulation, as discussed above
and listed in Table 2.1. The ESA transition from S 2 → S n2 was modeled with an identical set of
line-broadening parameters. This choice results in an ESA lineshape for S2 that is similar to that
observed by Cerullo et al,9 but the simulations and DQC results discussed below require it to be
shifted farther to the blue. The optimized model sets the S 2 → S n2 energy gap to 17000 cm−1, as
listed in Table 2.2. A similar value was obtained by Christensson et al.19. Also as specified by
Christensson et al.,19 the lineshape parameters for the off-diagonal functions22 associated with the

64

S 2 → S n2 transitions were assumed to have the same temporal dependence but half the
reorganization energy of the ground state bleaching transition.
Table 2.2 Transition frequencies ( ω ij ) and relative transition dipole strengths ( µ ij ) used in the
simulation of the transient-grating signal from β-carotene without inclusion of the Sx state (see
Figure 2.9).
Transition

ω ij (cm−1)

Âľ ij (Debye)

S0 → S 2

21550

1

S 2 → S n2

17000

0.35

S1 → S n1

17850

1.70

Lastly, the lineshape parameters for the S1 → S n1 ESA transition were chosen such that the
simulated spectrum has the same shape as the pump-probe spectrum observed at long population
delays.9 The MBO parameters are listed in Table 2.3; as in previous work41 an additional
vibrational mode of 1820 cm-1 is added to better simulate the vibronic structure observed in the
ESA from the S1 state. As determined in femtosecond stimulated Raman experiments,50,51 this
mode has a similar intensity as the 1520 cm-1 mode in the S1 state and therefore needs to be
included in the simulation.

65

Table 2.3 MBO model parametersa for the S1 → S n1 ESA transition of β-carotene in benzonitrile
at 295 K.
Mode

λ (cm−1)

τ (fs)

Gaussian

100

10

—

Exponential 1

300

500

—

Exponential 2

450

1000

—

Vibration 1

200

200

1150

Vibration 2

250

200

1520

Vibration 3

300

200

1820

ω v (cm−1)

See Equations 2.7–2.10. For a given term in M (t) , λ is the reorganization energy and τ denotes the
damping time constant; ω v is the frequency for a vibrational mode.
a

The simulated transient grating response shown in Figures 2.14 and 2.15 does not provide an
acceptable description of both components of the experimentally observed transient grating
signal even though a visual comparison with Figures 2.4 and 2.5, respectively, might initially
suggest a reasonable concordance. In order to allow an easily visualized, quantitative comparison
of the calculated and observed signals, Figure 2.16 and Figure 2.17 show plots of the absorption
and dispersion components, respectively, as their integrals over the signal frequency axis with
respect to the population delay T. These plots are comparable in appearance to the 520-nm
experimental transients shown in Figure 2.8. The experimental and calculated signals are
normalized at T = 500 fs, where the chief contribution to the signal is from ESA from the
population in the S1 state.

66

Intensity
Intensity
−100

0

100

200

300

400

500

Delay (fs)

Figure 2.16 Comparison of the experimental and calculated absorption components of the
transient grating signal from β-carotene. The calculation omits the Sx state from the energy level
scheme shown in Figure 2.9. The experimental (Figure 2.4) and calculated signals (Figure 2.14)
were integrated over the laser frequency axis and normalized at the 500 fs delay point. Top
Panel: Absorption components from the experimental transient (data points) and from the
simulation (solid line). Bottom Panel: Absorption components calculated from individual
Feynman pathways: Orange, GSB; Red, SE from the S2 state; Blue, S 2 → S n2 ESA; Green,
DQC; Black, S1 → S n1 ESA.

67

Intensity
Intensity
−100

0

100

200

300

400

500

Delay (fs)

Figure 2.17 Comparison of the experimental and calculated dispersion components of the
transient grating signal from β-carotene. The calculation omits the Sx state from the energy level
scheme shown in Figure 2.9. The experimental (Figure 5) and calculated signals (Figure 2.15)
were integrated over the laser frequency axis and normalized at the 500 fs delay point. Top
Panel: Dispersion components from the experimental transient (data points) and from the
simulation (solid line). Bottom Panel: Dispersion components calculated from individual
Feynman pathways: Orange, GSB; Red, SE from the S2 state; Blue, S 2 → S n2 ESA; Green,
DQC; Black, S1 → S n1 ESA.
With the parameters chosen, the rise and decay of the experimental and simulated absorption
transients match reasonably well (Figure 2.16), but keep in mind that the absorption component
was used as the target for the simulation. The rapid initial decay, which exhibits a 12 fs time
constant in the global model, mostly arises from line broadening of the GSB. The decay of the
SE from the S2 state with a 150 fs time constant is accompanied by a concurrent rise of negative
going ESA from the S1 state. Because the S2 and S1 states share the same ground state, the GSB
is essentially nondecaying after the initial line broadening. The DQC pathways contribute a
relatively small contribution to the overall absorption signal with a Gaussian shape coinciding

68

with the zero of the delay T axis. A larger contribution arises from the ESA signal from the S2
state, which decays with a 150 fs time constant; owing to detuning of the laser spectrum from its
energy gap, the S2 ESA signal is smaller that one might have expected just considering the
relative transition dipole strengths of the ESA and GSB contributions.
Using the same model parameters, however, the simulated dispersion component very poorly
matches the experimental signal because it rises too slowly (Figure 2.17). Note that the
dispersion signal has a significant negative going contribution near the zero of time from the
benzonitrile solvent (Figure A2.1), which is not included in the calculated response.
Nevertheless, over the 50–500-fs range, the calculated dispersion signal is well below that of the
experiment. The calculated dispersion signal catches up with the experimental signal only at the
500 fs delay point, where the two transients are normalized.
The origin of the problem with the rise of the calculated dispersion signal is made clear upon
examination of the time dependence of the contributions from the different Feynman pathways.
Recall that the dispersion and absorption components are related by the Kramers–Kronig
relationship,29,52,53 so the signs of the different contributions to the dispersion signal depend
sensitively on the lineshape for each contribution and on the detuning of the laser spectrum.
Owing to spectral diffusion, the probe laser spectrum used in the present experiments is
effectively detuned to the red side of the GSB signal that is present at long delay times T. In
contrast, the probe spectrum is on the blue side of the ESA signal from the S1 state. Accordingly,
both the GSB and ESA signals contribute positive going signals to the dispersion component.
The GSB contributes a prompt rising signal that is synchronized with the arrival of the pump
pulses, but the rise of the S1 ESA signal is slower, as it is determined in this model by the rate at
which S2 decays. The DQC and S2 ESA signals also contribute prompt positive signals to the

69

dispersion, so they contribute to the rising character of the dispersion component, but as in the
absorption component their contributions are relatively weak. Thus, the problem is with the SE
signal from the S2 state. Because it is shifted to the red of the laser spectrum, as was observed in
the work by de Weerd et al.,54 it contributes a negative-going signal to the dispersion component.
The overall rise of the calculated dispersion signal is significantly slower than that for the
experimental transient because the SE signal decays with a 150 fs time constant. This
comparison indicates directly that the SE signal is actually decaying much more rapidly than
calculated with the model lacking the Sx state.
2.4.2.2 Simulation of Transient Grating Signal Without Sx
We obtained much better results in simulations that included the Sx state as an intermediate
along the radiationless decay pathway between S2 and S1 state, as indicated in Figure 2.9. The
absorption and dispersion components calculated with an optimized set of parameters are shown
in Figures 2.18 and 2.19. Figures 2.20 and 2.21 compare the experimental and calculated
frequency integrated absorption and dispersion transients, respectively. In these simulations, the
lifetimes of S2 and Sx states were set to be 12 fs and 142 fs respectively, as determined from the
global model (Figures 2.6–2.8).

70

Figure 2.18 Numerical simulation of the absorption component of the transient grating signal
from β-carotene, with the Sx state included in the energy level scheme shown in Figure 2.9. The
parameters used in the calculation are listed in Table 2.1, 2.2, and 2.4 and in the text. The yellow
end of the color bar corresponds to net ground-state bleaching or stimulated emission; the dark
blue end indicates excited state absorption.

Figure 2.19 Numerical simulation of the dispersion component of the transient grating signal
from β-carotene, with the Sx state included in the energy level scheme shown in Figure 2.9. The
parameters used in the calculation are listed in Table 2.1, 2.2, and 2.4 and in the text. The
phasing of the color bar is consistent with that used in Figure 2.18 for the absorption component.
At 520 nm, the yellow contours correspond to the net ESA signal from the S1 state.

71

The transition dipole moment for optical transitions between the S0 and Sx states is set to
zero,37 so in this model Sx contributes only an S x → S nx ESA pathway, as shown in Figure 2.9,
to the system response. The model parameters for the ESA transition are not well defined owing
to the probe detuning in the present experiments. A guess for the energy gap (11200 cm−1, Table
4) was obtained by fitting the ESA lineshape assigned to Sx that Cerullo et al.9 observed in their
broadband pump–probe experiments. The lineshape parameters and relative transition dipole
strength applied for the Sx ESA transition are the same as used for the GSB. The lineshape
parameters used for the S1 state are the same as used above for the model omitting the Sx state.
Note that the transition dipole strengths of the S 2 → S n2 ESA and S1 → S n1 ESA transitions had
to be altered from those used above (Table 2.2) to obtain a better agreement between the
experimental and simulated absorption transient; in particular, the transition dipole strength for
the ESA transition from the S2 state was strengthened by more than a factor of 2.
Table 2.4 Transition frequencies ( ω ij ) and relative transition dipole strengths ( µ ij ) used in the
simulation of the transient-grating signal from β-carotene with inclusion of the Sx state (see
Figure 2.9).
Transition

ω ij (cm-1)

Âľ ij (Debye)

S0 → S 2

21550

1

S 2 → S n2

17000

0.75

S x → S nx

11200

1

S1 → S n1

17850

1.54

72

Intensity
Intensity
−100

0

100

200

300

400

500

Delay (fs)

Figure 2.20 Comparison of the experimental and calculated absorption components of the
transient grating signal from β-carotene. The calculation includes the Sx state in the energy level
scheme shown in Figure 2.9. The experimental (Figure 2.4) and calculated signals (Figure 2.18)
were integrated over the laser frequency axis and normalized at the 500 fs delay point. Top
Panel: Absorption components from the experimental transient (data points) and from the
simulation (solid line). Bottom Panel: Absorption components calculated from individual
Feynman pathways: Orange, GSB; Red, SE from the S2 state; Blue, S 2 → S n2 ESA; Green,
DQC; Black, S1 → S n1 ESA.

73

Intensity
Intensity
−100

0

100

200

300

400

500

Delay (fs)

Figure 2.21 Comparison of the experimental and calculated dispersion components of the
transient grating signal from β-carotene. The calculation includes the Sx state in the energy level
scheme shown in Figure 2.9. The experimental (Figure 2.5) and calculated signals (Figure 2.19)
were integrated over the laser frequency axis and normalized at the 500 fs delay point. Top
Panel: Dispersion components from the experimental transient (data points) and from the
simulation (solid line). Bottom Panel: Dispersion components calculated from individual
Feynman pathways: Orange, GSB; Red, SE from the S2 state; Blue, S 2 → S n2 ESA; Green,
DQC; Black, S1 → S n1 ESA.
The optimized parameters in this model again result in a good match of the simulated
absorption component with experiment. The ability to model the absorption component equally
well with or without Sx included in the energy level scheme shows that detuning of the probe
bandwidth is large compared to the absorption bandwidth. The observed 12 fs decay is
accordingly assigned again predominantly to line broadening of the GSB contribution. Again, the
GSB does not recover after the initial line broadening because Sx shares the same ground state
with S2 and S1. The 142 fs decay observed in the absorption component mainly reflects the rise
of the S1 ESA. The contributions of the SE and ESA from the S2 are comparable in this model

74

owing to the strengthening of the transition dipole moment for the S2 ESA transition, which also
strengthens the DQC contribution.
A comparison of the experimental and calculated dispersion components, both as contour
figures (Figures 2.5 and 2.19) and as frequency integrated transients (Figure 2.21), however,
shows that inclusion of the Sx state in the model provides a much better description of the
experimental results. The model follows the experimental dispersion signal very well at delays
>100 fs. The difference between the experimental and simulated dispersion transient now mainly
arises from the negative going contribution from the benzonitrile solvent (Figure A2.1),
especially near the zero of time. As in the absorption component, the ESA signal of the Sx state
makes only a very small contribution to the overall signal because the detuning of the probe
bandwidth is large compared to the width of the ESA lineshape. This means that the Sx state
behaves kinetically as a "dark" state overall, with no strong contributions on resonance with the
probe bandwidth, that effectively quenches the signals from the optically prepared S2 state. The
rising trend over the 100–500-fs period is now much better simulated because the negative going
SE contribution from the S2 state decays much more rapidly. In fact, this is the most important
conclusion from the simulations: the fast rise of the dispersion component is associated with the
decay of the SE component from the resonant S2 state as the Sx state is populated. The dispersion
component makes it possible to discern separately the contributions of spectral diffusion from
the relaxation of population from S2.
A similar conclusion was made by Sugisaki et al.,37 who showed that no recurrent excitedstate wavepacket motions contribute to the homodyne transient grating signal, at least as probed
in the region of the S0–S2 absorption band. Their results require that nonradiative decay of the S2
state to the Sx state occurs with a time constant that is shorter than the period of the high-

75

frequency, C–C and C=C stretching frequencies. The model used by Sugisaki et al., however,
includes an ESA lineshape from the Sx state that overlaps with the S0 → S2 ground state
absorption region of the spectrum. Figure 2.22 shows, however, that use of the Sugisaki et al. Sx–
Snx energy gap in the model results in a poorer description of the present experimental results.
The Sx ESA now makes a stronger contribution to the absorption component, so the calculated
signal decays much more rapidly than we observe experimentally. The dispersion component is
not as strongly affected because its lineshape has a zero crossing in the probed region, but the
detuning to the blue results in an overall negative contribution to the dispersion that results in a
poorer fit to the experimental signal. As the Sx–Snx energy gap is scanned, the simulations
indicate differential effects on the absorption and dispersion components that are inconsistent
with the observed results unless it is tuned far enough to the red of the probed energy gap with
respect to the width of the ESA lineshape. These results show that despite the "dark" character of
the Sx state, we can reasonably conclude that the ESA spectrum from the Sx state has parameters
like that observed in the Cerullo et al.9 pump–probe experiments. Note also that this conclusion
argues against the assignment by Kosumi et al.55 of the Sx ESA spectrum to a nonresonant, twophoton absorption pathway.

76

Intensity
Intensity
−100

0

100

200

300

400

500

Delay (fs)

Figure 2.22 Comparison of the experimental and calculated dispersion components of the
transient grating signal from β-carotene. The calculation includes the Sx state in the energy level
shown in Figure 2.9 but employs the Sx–Snx energy gap in the visible region (~22000 cm-1) used
in the calculations by Sugisaki et al.37 The experimental (Figure 2.5) and calculated signals were
integrated over the laser frequency axis and normalized at the 500 fs delay point. Top Panel:
Absorption components from the experimental transient (data points) and from the simulation
(solid line). Bottom Panel: Dispersion components from the experimental transient (data points)
and from the simulation (solid line).
2.4.2.3 Contributions of Double-Quantum Coherence Pathways
In both simulations, with and without inclusion of Sx in the nonradiative decay pathway, the
DQC contribution to the transient grating signal is relatively small compared to the contributions
from population-dependent pathways. The heterodyne transient grating experiment makes the
number of DQC pathways that contribute to the signal smaller than in pump–probe spectroscopy
because, as explained above, only certain time orderings for the field–matter interactions are
detected. With Sx included in the model, however, the DQC signals are more intense because the

77

transition dipole strength for the ESA from the S2 had to be increased from that used in the
model without Sx.
In order to experimentally test the parameters that affect the DQC pathways, we performed a
series of heterodyne transient grating experiments with the coherence delay τ scanned to
negative values, as described in the work by Joo and coworkers.56,57 The analysis of the field–
matter time orderings that follows from the DQC Feynman diagrams (Figure 2.13) indicates that
when τ < 0 , the DQC pathways are enhanced in probability but that the DQC signal itself is
limited to population delays T < 0 . When τ = 0 , as in the conventional transient grating
experiments discussed above, the DQC signal decays at population delays T > 0 following the
intensity profile of the laser pulses.
Figure 23 shows the absorption component from a series of transient grating experiments in
which τ was scanned from 0 fs to −15 fs. The transient grating signals are normalized at the
population decay T = 500 fs, where only population signals contribute, in order to project out
the DQC-dependent parts of the signal. The rise of the signal moves to increasingly negative T
values, as expected, as τ is scanned to negative values. The peak intensity is largest for

τ = 10 fs, and the signal is about 20% larger than with τ = 0 . Qualitatively, these results
indicate that the effective dephasing time for the S n2 S0 DQC is ~10 fs; as τ is scanned to more
negative delays, the peak signal intensity decays because the S n2 S0 DQC has to wait longer for
the last pulse in the (2,3,1) sequence to arrive. Further, the relative strength of the DQC signals
estimated in the simulations above including Sx (Figures 2.18–2.21) is approximately correct;
DQC pathways are contributing a minor fraction compared to the τ -invariant population signals
measured at T = 0 in the τ = 0 experiments.

78

Intensity

−10 fs
−15 fs
−5 fs
0 fs

−100

0

100

200

300

400

500

Delay (fs)

Figure 2.23 Absorption component of the heterodyne transient grating signal from β-carotene in
benzonitrile measured with a range of negative coherence delays, τ < 0 . The signals are
normalized at the population delay T = 500 fs, where only population signals contribute.
These findings allow a clear assessment of the contributions of DQC pathways to the
observed signals under our conditions. Owing to being confined to the T < 0 region in the
heterodyne transient grating experiments, the impact of DQCs where Sx contributes to the time
evolution of the signal is non-zero but minimal, especially at T > 20 fs, as controlled by the 40
fs pulses used in the present experiments. Because they are included in both simulations, the
DQC pathways do not have an impact on the decision about whether Sx needs to be included in
the nonradiative decay pathway from S2.

2.5 Discussion
The absorption and dispersion components of the heterodyne transient-grating signal from βcarotene in benzonitrile, Figures 2.4 and 2.5, respectively, exhibit large changes in intensity and
lineshape during the 12 fs kinetic component of the global model (Figures 2.6–2.8). To
determine what causes these changes, we performed a set of numerical simulations employing
the nonlinear optical response function formalism and the MBO model. Pathways for the

79

populations and DQCs that follow excitation of the S0 to S2 transition were included in the
models we tested.
The results of the simulations show that the time evolution of the transient-grating signal
includes significant contributions from three processes with similar effective timescales: spectral
diffusion and dynamic solvation, DQCs, and nonradiative decay from the S2 state to the Sx
intermediate state. The distinct temporal profiles exhibited by the absorption and dispersion
components, however, are principally determined by the S2 to Sx nonradiative decay process. The
simulations indicate that good simultaneous fits of the absorption and dispersion components of
the transient grating signal of β-carotene cannot be obtained unless the Sx state is included in the
model as an intermediate state between S2 and S1. The key observation is an ultrafast rise of the
dispersion component, which is controlled primarily by the decay of the SE from S2. If Sx is not
included in the model, the dispersion exhibits a much slower rise that is controlled by the rise of
the ESA signal from the S1 state. As we will explain in the following, it is significant that the Sx
ESA spectrum is well red shifted from the S0–S2 energy gap because it impacts the choice of
hypotheses for the nature of the Sx intermediate and for the mechanism for its formation after
optical preparation of the S2 state.
As observed in the work by Xu and Fleming,29,53,58 with excitation pulses on resonance with
a strong electronic transition, the absorption and dispersion components of a nonlinear optical
signal exhibit distinct time profiles when an intermediate state is populated on the nonradiative
decay pathway from the initially prepared state to the ground state. This feature of heterodyne
transient grating spectroscopy allows us to determine several of the properties of the Sx state
despite being limited by the probe bandwidth to a narrow spectral range. Owing to the Kramers–
Kronig relation between the absorption and dispersion components for any response pathway,

80

the shape of the temporal response for each component depends quite sensitively on how far the
laser spectrum is tuned to the red or blue of the energy gap between the levels being driven in a
particular pathway.
The energy gap and lineshape parameters we obtained for the Sx ESA signal from the
simulations of the transient grating signals are actually quite consistent with the near-IR ESA
spectrum observed by Cerullo et al.9 for β-carotene at a pump–probe delay of 50 fs, which
maximally populates the Sx state. This finding is inconsistent with the conclusion by Kosumi et
al.55,59 that the near-IR ESA signal from Sx is predominantly due to excitation of nonresonant,
two-photon absorption pathways. The direct contribution of the Sx state to the absorption and
dispersion signals with 520 nm probing is very weak due to the detuning to the blue, but the flow
of population through Sx has a big impact on the temporal response because the decay from S2 to
Sx effectively quenches the SE and ESA signals of the S2 state.
The conclusion that the S2 state is rapidly depopulated by nonradiative decay, much more
rapidly than is consistent with the 150 fs rise time of the S1 state, is consistent with the finding by
Sugisaki et al.37 that the vibrational coherence observed in β-carotene solutions with probe light
tuned into the S2 state absorption region is due to stimulated Raman transitions to the ground
state manifold. If the S2 state lived as long as 150 fs, then there would be enough time prior to a
nonradiative crossing to the S1 state potential surface for several vibrations of the highfrequency, C–C and C=C bond-length alternation coordinates of the conjugated polyene
backbone.60,61 That these motions are not observed in the Sugisaki et al. experiments means that
wavepacket motion is not recurrent to the Franck–Condon region of the S2 state potential
surface. This conclusion is consistent with an ultrafast surface-crossing event to the Sx state.

81

With a broadband continuum reaching into the near-IR, however, Liebel et al.62 observed
excited state wavepacket motions with a damping time of 140 fs when probed at energy gaps
well to the red of that for the S0–S2 transition. Their observations are consistent, then, with an
assignment to coherent wavepacket motions after formation of the Sx state. If this assignment is
correct, the vibrational phase is retained during the ultrafast surface-crossing event from the S2
state to the Sx state. The present simulations, which employed a simple Markov population
transfer model, assume that vibrational decoherence accompanies the conversion of S2 to Sx.
Owing to our use of 40 fs pulses, however, it would not have been possible to observe excitedstate vibrational coherence in modes with frequencies above about 400 cm−1.
Simulations employing an ESA spectrum for Sx set to the blue of that from S2, as in the work
by Sugisaki et al.,37 result in simulated absorption and dispersion transients that do not match the
observed signal very well (Figure 2.22). A blue shifted ESA spectrum for Sx would be more
consistent with a conventional hypothesis for the vibrational dynamics that accompany
radiationless decay from S2 to S1. As shown in Figure 24, displacements along the bond-length
alternation coordinates would promote a crossing of the S2 and Sx potential surfaces, the latter at
slightly lower energy. The Sx surface would then serve as a bridge to the S1 state. Such a scheme
would in principle account for a deviation from the energy-gap law of the S2 to S1 nonradiative
decay rate.63–65 It would also account for the observations of Maiuri et al.,11 who observed that a
crossing from the S2 state to the Sx state does not occur for sphaeroidene dissolved in the highly
polarizable solvent CS2. The observation of electronic quantum beats with excitation near the
peak of the S0–S2 absorption spectrum by Ostroumov et al.,66 however, indicates that the S2 state
interacts fairly strongly with an adjacent state at higher energies than the Franck–Condon energy
gap, not at lower energies as proposed in the figure. This idea is compatible with the

82

aforementioned work by Shreve et al.,14 who detected a strong coupling of the S2 state to a
nearby state with g symmetry.

Potential Energy

S2 (11Bu+)

Sx

S1 (21Ag−)

S0 (11Ag−)

Bond Length Alternation

Figure 2.24 Diabatic energy curves for all-trans polyenes with respect to a generalized bond
length alternation coordinate. The diagram includes a dark intermediate state (Sx) in the transfer
of population from the bright S2 (11Bu+) state to the dark S1 (21Ag−) state.
As an alternative hypothesis, we suggest that a red-shifted ESA spectrum from Sx can be
better explained by vibrational dynamics involving a strong coupling of displaced bond-length
alternation coordinates with torsional coordinates of the conjugated polyene backbone. This idea
is based on the scheme shown in Figure 2.25, which describes the general nature of the potential
energy surface for conjugated polyenes, cyanines, and protonated Schiff bases of intermediate
lengths;67 it has several features in common with that suggested previously for carotenoids by de
Weerd et al.54 We previously discussed in detail the theoretical background for this scheme and
outlined some of its implications for the nature of the dark intermediate states that are

83

encountered in the nonradiative decay of carotenoids in solution and in photosynthetic lightharvesting proteins.17

x1Ag−

planar

twisted

Sn

11Bu+
Sx

Potential Energy

φ
X

S2

21Ag−
S1

11Ag−

S0

trans

‡

φ = 90°

cis

Reaction Coordinate

Figure 2.25 Proposed scheme for radiationless decay of carotenoids after optical preparation of
the S2 state; after similar diagrams in Sanchez-Galvez et al.67 and Beck et al.17 The states that
apply to planar structures are indicated by symmetry labels. Key points along the radiationless
path from the Franck–Condon S2 state structure are labeled with ethylenic structures, which
depict the Sx and X dark states as structures near the S2 transition state and along the torsional
gradient, respectively.
Figure 2.25 schematically represents the potential energy surfaces of carotenoids in terms of
a reaction coordinate principally composed of sequential motions along two generalized
vibrational coordinates, the bond-length alternation coordinates and torsional coordinates with
respect to one of the C=C bonds of the conjugated polyene backbone. Based on the calculations
discussed by Olivucci et al. for molecules with intermediate to long conjugation lengths,67 the
forces that act on the S2 state Franck–Condon structure are predominantly along the bond-length

84

alternation coordinates. A coupling to torsional modes, however, occurs with displacement from
the Franck–Condon structure and leads to the formation of a local activation barrier, which
divides planar and twisted conformations. The transition state structure at the barrier would be
expected to exhibit a red-shifted ESA spectrum; the energy gap between the S2 state and the Sn2
state narrows there because the barrier height will decrease as the π* character increases and the
two states are displaced with respect to each other along the bond-length-alternation coordinates.
The scheme shown in Figure 2.25 identifies Sx as a transition-state structure on the S2 surface
rather than as a discrete electronic state. The ultrashort time constant for the formation of Sx
corresponds to the time it takes for the bond-length-alternation modes to undergo nearly a full
excursion from the Franck–Condon structure, about one-half of a vibrational period. The
molecule is acted upon then by a steep torsional gradient that directs the structure towards a
conical intersection, where the S2, S1, and S0 surfaces would be expected to converge. The
torsional motions are not resonance Raman active, so the key event in the nonradiative decay
process amounts to an intramolecular conversion of the initial momentum of the Franck-Condon
structure from the bond-length alternation coordinates into the torsional coordinates. This idea
has been discussed previously in theoretical and experimental work on PSBs in rhodopsins68,69
and in cyanines in solution.70
The 142 fs lifetime of the Sx state determined in the present results, then, would correspond
to the time it takes for a wavepacket to propagate down the S2 torsional gradient until it crosses
through a seam with the S1 state potential surface.71 It follows that the X state observed in 2DES
by Ostroumov et al.15,16 in terms of cross peaks should be assigned to a twisted S2 structure. This
assignment accounts for the longer timescale they associate with formation of the X state
compared to that observed here for the Sx state. The simple model used in our simulations treats

85

Sx just as an intermediate state between S2 and S1; the kinetics are determined only by the loss of
the S2 SE signal and the appearance of the S1 ESA signal. The intervening dynamics after the
formation of Sx are hidden from us due to the narrow probe bandwidth we used in the present
experiments.
Once the torsional motions begin as the Sx transition state structure is reached, the increasing
displacement that follows along torsional coordinates of the conjugated polyene will naturally
lead to an ICT character and a resultant frictional coupling to the surrounding solvent.72,73 An
interpretation of the aforementioned results of Liebel et al.62 is that underdamped coherent
wavepacket motions occur beyond the transition state on the S2 surface at least with respect to
the high frequency, bond-length alternation coordinates. The minimum-energy path on the S2
potential surface would not necessarily be expected to exhibit strong oscillations with respect to
the torsional or other out-of-plane normal coordinates, however, because these motions are likely
to be increasingly diffusive in character as the displacement past the transition state increases if
the solvent friction is significant. The ICT character may be of considerable importance in the
energy-transfer function of carotenoids in photosynthetic light-harvesting proteins because it
would increase the Coulomb coupling to the (B)Chl acceptor.
Given that the trans–cis photoisomerization quantum yield for longer polyenes is much less
than unity, it is likely that an irreversible crossing through a seam to the S1 state occurs far from
the 90° torsional geometry of the conical intersection.74 The S1 state is produced with a
considerable excess vibrational excitation, which leads to the observed blue shifting and
sharpening of the ESA bandwidth at delays >500 fs as this population cools owing to
intramolecular vibrational redistribution and vibrational relaxation.75

86

This hypothesis naturally accounts for the behavior of the broad ESA spectrum observed by
Cerullo et al. for the S2, Sx, and S1 states;9 it should evolve initially due to displacement with
respect to the bond-length alternation coordinates and then along the torsional coordinates, where
spreading of the wavepacket would reflect the action of solvent friction. The observed ESA
spectrum moves initially very rapidly to the red after optical preparation of the S2 state as the
transition state (Sx) is reached, and then the ESA spectrum moves to the blue, which is consistent
with relaxation down the torsional gradient. The blue-shifting ESA spectrum would be expected
to be inhomogeneous and be strongly overlapped with a red-shifting SE signal, so parts of this
response are likely to be obscured in conventional, one-dimensional spectra.17
We will treat the time evolution of the heterodyne transient grating signal from β-carotene
over the >500 fs range in a separate contribution, but an important point to make now is that
Figure 25 anticipates that a conformationally displaced ground state structure is expected to be
the initial product of the S1 to S0 nonradiative decay event. Simulations can be used to show how
the conformational relaxation process on the S0 surface back to the originally photoselected
ground state structure accounts for the distinct time constants that we observed for the recovery
of the absorption and dispersion components of the transient grating signal. Further, because the
twisted structures would have an ICT character, as noted above, the S1 to S0 decay would be
anticipated to have a reverse charge transfer character and an associated strong solvent
coupling.17 This feature would cause the conformational relaxation to be slower in some cases
than a conventional vibrational cooling process. In carbonyl-substituted carotenoids, such as
peridinin76–79 and fucoxanthin,80 the time constants for the S1 to S0 and ground-state
conformational relaxation for this process would be expected to have an unusual and distinctive
dependence on the solvent polarity and polarizability.

87

2.6 Conclusions
We report in this contribution the first femtosecond transient grating experiments on βcarotene that employ optical heterodyne detection with spectral interferometry. In addition to
providing the information required to assess several important controversies in the carotenoid
literature, this work supports a structural hypothesis that accounts for the timescales and
dynamics that depopulate the resonant S2 state. The detection scheme we employed is critically
important because it limits the order with respect to time with which the three field–matter
interactions produce coherences and populations and because it provides information on the linebroadening dynamics that is ordinarily hidden from conventional pump–probe experiments,
especially when narrow band probe spectra are employed.
A global target analysis establishes the key time constants and principal spectra that describe
the time evolution of the absorption and dispersion components of the transient grating signal.
But as in previous work in the ultrafast regime where coherences contribute to the signal, a
proper interpretation of the system response requires the use of numerical simulations of the
detected signals. The simulations establish how the relevant third-order Feynman pathways
involving populations and double quantum coherences contribute to the response. For the first
time to our knowledge for a carotenoid, these simulations simultaneously describe the absorption
and dispersion components of the signal using a consistent set of parameters that effectively fit
the observed response.
The results of this work establish clearly that the S2 state of β-carotene undergoes a
radiationless decay pathway involving an ultrafast (12 fs) depopulation of the initial optically
prepared state. The simulations show that the SE contribution to the signal decays due to
population of a spectroscopic intermediate state, Sx, that is effectively dark with respect to the

88

probe bandwidth used in the present experiments. This is an important conclusion because it
argues against previous suggestions55,59 that a nonresonant two-photon absorption process rather
than an intermediate state accounts for the ESA signals from the Sx state. Further, the
contribution of DQCs to the transient grating signal were demonstrated experimentally and in the
simulations not to be a significant determining factor in making the conclusion that the S2 state
decays rapidly to Sx rather than going directly to S1.
The model parameters that fit the experimental signals best are consistent with the previous
observation by Cerullo et al.9 of an near-IR ESA spectrum for the Sx state. Rather than
supporting assignment of the Sx state to the 1Bu− state of Tavan and Schulten, as previously
suggested, the parameters favor a structural hypothesis for the deactivation of the S2 state
involving a coupling between displaced high-frequency, bond-length alternation coordinates and
torsional coordinates of the conjugated polyene backbone. In this hypothesis, the Sx state is a
transition state structure, at the peak of the activation energy barrier that divides planar and
twisted structures on the S2 potential surface. It is produced by the prompt excursion from the
Franck–Condon structure along the bond-length alternation coordinates; the timescale for the
formation of the transition state corresponds to less than a vibrational period for a C=C stretching
mode.
Once activated, the conjugated backbone would then undergo a torsional relaxation from the
Sx structure. This establishes the lifetime of the Sx state, 142 fs, as the time it takes a wavepacket
to diffuse down the steep torsional gradient on the S2 surface and cross through a seam to the S1
surface, and it further suggests that the X state detected previously in 2DES experiments15,16
arises from a twisted structure along the way. The proposed mechanism naturally suggests that
an ICT character develops as the twisting occurs and that solvent friction retards the decay to the

89

S1 state. An important additional suggestion is that the structures that are operative in excitation
energy transfer to carotenoids in photosynthetic light-harvesting proteins involve twisted
structures with ICT character, which will be expected to exhibit improved donor–acceptor
couplings and transition dipole strengths for energy transfer to adjacent (B)Chls.

90

APPENDIX

91

APPENDIX

A2.1 Supporting Results

Re [Es]

A

Im [Es]

B

|Es|2

C

−100

0

100

200

300

400

500

Delay (fs)

Figure A2.1 Frequency integrated transient grating signal from neat benzonitrile at room
temperature under the same measurement conditions used for β-carotene in Figures 2.4 and 2.5:
(a) absorption component; (b) dispersion component; (c) complex modulus.

92

A

|Es|2

B

C

0

200

400

600

800

1000

Delay (fs)

Figure A2.2 Complex modulus of the heterodyne transient-grating signals from β-carotene in
benzonitrile at three solute optical densities: (a) A = 0.26, as in Figures 4 and 5; (b) A = 0.13;
and (c) A = 0.07.
For use in simulations of nonlinear optical signals, the third-order response functions
associated with the Feynman pathways shown in Figures 2.12 and 2.13 are usually expressed in
terms of line broadening functions, g(t) . These functions have been listed elsewhere19,22,28 but
they are reproduced in the following for completeness and employ a consistent notation.
For a three level system, the ground state and the first and second excited states are denoted
as g, e and f, respectively. The line broadening function that is used to simulate the absorption
spectrum is represented by g ee (t) . The line broadening function for the ESA transition from the
S2 state is given by g ff (t) . The off-diagonal line broadening function g ef (t) and g fe (t) depend
on the cross-correlation between the GSB and ESA transitions from the S2 state and they are
assumed to be the same. The line broadening functions g S xS x (t) and g S1S1 (t) are related to the
fluctuations of the ESA transitions from the Sx and S1 states, respectively.

93

In the expressions that follow, the detunings (Figure 2.9) between the laser and the vertical
transition energies are determined as

ΔS0 = ω 0 − ω S0→S2
Δ S2 = ω 0 + ω s2→sn 2
Δ S x = ω 0 − ω sx→snx
Δ S1 = ω 0 − ω s1→sn1
Here ω 0 is the center frequency of the laser spectrum and ω i→ j indicates the frequency of a
particular transition.

Using the notations introduced above, and letting Âľ ij stand for the transition dipole moment for a
given transition, the expression for the response functions reads
2

2

R1,g (t1 ,t 2 ,t3 ) = µ eg µ eg exp(iΔ S0 t1 + iΔ S0 t3 )
× exp ⎡⎣ −g ee* (t3 ) − g ee (t1 ) − g ee* (t 2 ) + g ee* (t 2 + t3 ) + g ee (t1 + t 2 ) − g ee (t1 + t 2 + t3 ) ⎤⎦
2

2

R2,g (t1 ,t 2 ,t3 ) = µ eg µ eg exp(−iΔ S0 t1 + iΔ S0 t3 )
× exp ⎡⎣ −g ee* (t3 ) − g ee* (t1 ) + g ee (t 2 ) − g ee (t 2 + t3 ) − g ee* (t1 + t 2 ) + g ee* (t1 + t 2 + t3 ) ⎤⎦
2

2

R3,g (t1 ,t 2 ,t3 ) = µ eg µ eg exp(−iΔ S0 t1 + iΔ S0 t3 )
× exp ⎡⎣ −g ee (t3 ) − g ee* (t1 ) + g ee* (t 2 ) − g ee* (t 2 + t3 ) − g ee* (t1 + t 2 ) + g ee* (t1 + t 2 + t3 ) ⎤⎦
2

2

R4,g (t1 ,t 2 ,t3 ) = µ eg µ eg exp(iΔ S0 t1 + iΔ S0 t3 )
× exp ⎡⎣ −g ee (t3 ) − g ee (t1 ) − g ee (t 2 ) + g ee (t 2 + t3 ) + g ee (t1 + t 2 ) − g ee (t1 + t 2 + t3 ) ⎤⎦

94

2

2

R1,* f (t1 ,t 2 ,t3 ) = µ eg µ ef exp(−iΔ S0 t1 + iΔ S2 t3 )
× exp ⎡⎣ −g ee* (t1 ) − g ee (t 2 ) + g ef (t 2 ) − g ee (t3 ) + 2g ef (t3 ) − g ff (t3 ) + g ee* (t1 + t 2 )
−g ef* (t1 + t 2 ) + g ee (t 2 + t3 ) − g ef (t 2 + t3 ) − g ee* (t1 + t 2 + t3 ) + g ef* (t1 + t 2 + t3 )⎤⎦
2

2

R2,* f (t1 ,t 2 ,t3 ) = µ eg µ ef exp(iΔ S0 t1 + iΔ S2 t3 )
× exp ⎡⎣ −g ee (t1 ) + g ee* (t 2 ) − g ef* (t 2 ) − g ee (t3 ) + 2g ef (t3 ) − g ff (t3 ) − g ee (t1 + t 2 )
+g ef (t1 + t 2 ) − g ee* (t 2 + t3 ) + g ef* (t 2 + t3 ) + g ee (t1 + t 2 + t3 ) − g ef (t1 + t 2 + t3 )⎤⎦
2

2

R3,* f (t1 ,t 2 ,t3 ) = µ eg µ ef exp ⎡⎣ iΔ S0 t1 + i (Δ S0 + Δ S2 )t 2 + iΔ S2 t3 ⎤⎦
× exp ⎡⎣ −g ee (t1 ) + g ef (t1 ) + g ee (t 2 ) − g ef (t 2 ) − g ee* (t3 ) + g ef* (t3 ) − g ee (t1 + t 2 )
−g ee (t 2 + t3 ) + 2g ef (t 2 + t3 ) − g ff (t 2 + t3 ) + g ee (t1 + t 2 + t3 ) − g ef (t1 + t 2 + t3 )⎤⎦
2

2

R4, f (t 1 ,t 2 ,t 3 ) = µ eg µ ef exp ⎡⎣iΔ S0t 1 + i (Δ S0 + Δ S2 )t 2 + iΔ S2t 3 ⎤⎦
× exp ⎡⎣ − gee (t 1 ) + gef (t 1 )− gee (t 2 )+ 2gef (t 2 )− g ff (t 2 )− gee (t 3 )+ gef (t 3 )
	

+ gee (t 1 +t 2 )− gef (t 1 +t 2 )+ gee (t 2 +t 3 )− gef (t 2 +t 3 )− gee (t 1 +t 2 +t 3 ) ⎤⎦
2

2

RS x ,R (t1 ,t 2 ,t3 ) = µ eg µS x exp ⎡⎣ −iΔ S0 t1 + iΔ S x t3 ⎤⎦ exp ⎡⎣ −g ee* (t1 ) − g S xS x (t3 ) ⎤⎦
2

2

RS x ,NR (t1 ,t 2 ,t3 ) = µ eg µS x exp ⎡⎣ iΔ S0 t1 + iΔ S x t3 ⎤⎦ exp ⎡⎣ −g ee (t1 ) − g S xS x (t3 ) ⎤⎦
2

2

RS1 ,R (t1 ,t 2 ,t3 ) = µ eg µS1 exp ⎡⎣ −iΔ S0 t1 + iΔ S1t3 ⎤⎦ exp ⎡⎣ −g ee* (t1 ) − g S1S1 (t3 ) ⎤⎦
2

2

RS1 ,NR (t1 ,t 2 ,t3 ) = µ eg µS1 exp ⎡⎣ iΔ S0 t1 + iΔ S1t3 ⎤⎦ exp ⎡⎣ −g ee (t1 ) − g S1S1 (t3 ) ⎤⎦

95

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96

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Chapter 3: Nonradiative Deactivation of the S2 (11Bu+) State of Peridinin:
Detection and Spectroscopic Assignment of an Intermediate in the Decay
Pathway

Femtosecond heterodyne transient grating spectroscopy was employed to investigate the
nonradiative decay pathway from the S2 (11Bu+) state to the S1 (21Ag−) state of peridinin in
methanol solution. Just as previously observed by this laboratory for β-carotene in benzonitrile,
the real (absorption) and imaginary (dispersion) components of peridinin exhibit ultrafast
responses indicating that S2 state decays in 12 fs to produce an intermediate state, Sx. The excited
state absorption spectrum from the Sx state of peridinin, however, is found to be markedly blue
shifted from that of β-carotene because it makes a substantial contribution to the signal observed
with 40 fs, 520 nm pulses. The results of a global target analysis and numerical simulations using
nonlinear response functions and the multimode Brownian oscillator model support the
assignment of Sx to a displaced conformation of the S2 state rather than to a vibrationally excited
(or hot) S1 state. The Sx state in peridinin is assigned to a structure with a distorted conjugated
polyene backbone moving past an activation-energy barrier between planar and twisted
structures on the S2 potential surface. The lengthened lifetime of the Sx state of peridinin in
methanol, 900 Âą 100 fs, much longer than that typically observed for carotenoids lacking
carbonyl substituents, ~150 fs, can be attributed to the slowing of torsional motions by solvent
friction. In peridinin, the system–bath coupling is significantly enhanced over that in β-carotene
solution most likely due to the intrinsic intramolecular charge transfer character it derives from
the electron withdrawing nature of the carbonyl substituent.
The work presented in this chapter has been adapted from J. Phys. Chem. B 2016, 120, 3601–
3614. Copyright (2016) American Chemical Society.

102

3.1 Introduction
Carotenoids perform several essential functions in photosynthetic organisms,1,2 including
photoprotection3 and light harvesting in the blue-green (450-550 nm) part of the solar spectrum
where (bacterio)chlorophyll ((B)Chl) absorbs inefficiently.3,4 The mechanisms that allow
efficient excitation energy transfer between carotenoids and (B)Chl in light-harvesting proteins
have yet to be fully elucidated owing to the complexity of the nonradiative decay pathways and
the production of dark intermediate states5 following optical excitation of carotenoids in solution
and in proteins.
This contribution deals with the earliest dynamics that follow optical preparation of the
S2 (11Bu+) state of peridinin, the principal light-harvesting chromophore in the peridinin–
chlorophyll a protein (PCP).6–8 This work is motivated by our recent proposal9 that the S2 state in
carotenoids naturally obtains an intramolecular charge-transfer (ICT) character by undergoing
activated torsional motions of the conjugated polyene backbone. In recent work on β-carotene,10
we suggested that structures near an activation energy barrier on the S2 potential surface dividing
planar and twisted structures account for the formation in <20 fs of an intermediate state
generally denoted as Sx, which has been the focus of considerable controversy.5 A similar
nonradiative decay intermediate has not yet been detected for peridinin, but as discussed below,
knowledge of its presence and of the mechanism for its formation would aid an understanding of
how peridinin can function efficiently as a light-harvesting chromophore. The idea that excitedstate twisting motions contribute to the ICT character of peridinin was considered early on by
Bautista et al.,11 and the possibility that the especially large transition dipole moment for the S1
state of peridinin in the peridinin–chlorophyll a protein arises from twisted structures was raised
previously by Krueger et al.7

103

Because of the nominal C2h symmetry of carotenoids, strong one-photon optical transitions
occur from the ground state S0 (11Ag−) to the S2 (11Bu+) state, whereas transitions to the S1
(21Ag−) state are symmetry forbidden. Some carotenoids, particularly those with fewer than ten
carbon–carbon bonds, exhibit a very weak fluorescence from the S1 state, so the dipole strength
of the S1 state in these cases is very small.12,13 Because the carotenoid S2 state lies above that of
the Qx excited state of Chl or BChl, S2→Qx excitation energy transfer via the Förster resonant
mechanism14,15 would be generally favored. This pathway competes with ultrafast S2→S1
nonradiative decay,16 however, so only a fraction of the total energy-transfer yield from peridinin
involves the S2 state. In PCP, two-thirds of the total energy transfer yield (~90%) is currently
thought to occur via energy transfer from the carotenoid S1 state to the Chl Qy state.6,8,17
Given that the S1→S0 transition has very little oscillator strength, one might expect that the
yield of energy transfer from peridinin to the Chl Qy state would be very small. But as
exemplified in the X-ray crystal structures of carotenoid-containing light-harvesting proteins,18,19
including that of PCP,20,21 the efficiency of excitation energy transfer from a carotenoid to a
B(Chl) is apparently enhanced by placing the donor and acceptor molecules nearly in van der
Waals contact.17 This observation initially prompts the suggestion of a Dexter-type, orbitaloverlap, electron exchange-mediated energy-transfer mechanism,22 but calculations suggest that
energy transfer by the FĂśrster mechanism are more favorable in light-harvesting proteins because
of a relatively strong Coulomb coupling of the transition dipoles of the donor carotenoid and
acceptor (B)Chl.17,23–25
It is evident also that the efficiency of excitation energy transfer from carotenoids to (B)Chls
can be further improved by chemical substituents that alter the distribution of π electrons along
the conjugated polyene backbone. Peridinin (Figure 3.1) is an example of a carotenoid with a

104

carbonyl group in conjugation with the extended conjugated polyene backbone; its electron
withdrawing character combined with the electron releasing properties of the allene group on the
other end of the molecule contributes to a very large change in permanent dipole moment
accompanying the vertical S0 to S2 transition.26,27

HO

OCOCH3

O
O

15
O

11

•

15'

11'

HO

Figure 3.1 Structure of peridinin
An excited-state intramolecular redistribution of π-electron density in peridinin is further
indicated by the strong solvent dependence of the S1 state lifetime, as shown by Frank and
coworkers,11,28 and this idea has been supported by both theoretical computations25 and
experiments on numerous other carbonyl-containing carotenoids and polyenals.8,16,29–36 The
lifetime of the S1 state of peridinin directly correlates with solvent polarity, ranging from 7 ps in
a highly polar solvent, trifluoroethanol, to 172 ps in two nonpolar solvents, cyclohexane and
benzene. The fluorescence emission maximum, the quantum yield of fluorescence, and the
excited-state absorption (ESA) line shape from the S1 state are also affected by the choice of
solvent. This behavior is considered highly unusual for carotenoids; in general, the spectral
properties and lifetimes of the S1 state of carotenoids are independent of the solvent
environment. Frank and coworkers attributed the solvent sensitivity of the S1 state of peridinin to
the nonradiative formation of an ICT state, and subsequent work in several laboratories has
indicated that other carbonyl-substituted carotenoids exhibit similar properties.37,38 Owing to the
ICT character, the energy transfer pathways in PCP would be expected to be much more

105

sensitive to the reaction field arising from the polarity and polarizability of the surrounding
protein and chromophore medium.26,27,39
Despite the experimental and theoretical studies reviewed above, how the ICT character
develops in the S1 state of peridinin remains unclear. Four hypotheses have been proposed in
previous work.40 Two of the possible hypotheses suggest that a redistribution of charge follows
formation of the S1 state due to propagation along an intramolecular charge-transfer coordinate
that connects locally excited and ICT states, either in the weak coupling or nonadiabatic
regime11,25,32,41 or in the strong coupling or adiabatic regime.16,42 A third hypothesis suggests that
the S1 state obtains oscillator strength and an intrinsic ICT character from a strong quantummechanical mixing of the S1 and S2 states.43 A more recent hypothesis, based on electronic
structure calculations and a consideration of the role of the solvent, suggests that the ICT state is
formed upon optical preparation of the S2 state via bond-order reversal and configurational
mixing of the S1 and S2 states,40,43 which accompanies the large vertical change in permanent
dipole moment.26,27 The S1 and S2 states would be further mixed by torsional motions of the
conjugated polyene backbone. In our hypothesis,9 an instantaneous displacement along the
resonance Raman-active C–C and C=C coordinates that contribute to the bond-length alternation
of the conjugated polyene backbone44 promotes formation in <20 fs of a transition-state structure
at a barrier dividing planar and twisted structures on the S2 state potential surface. The torsional
motions that accompany relaxation from the transition state promote the formation of a
biradicaloid electronic structure and the development of additional ICT character.45–48 The ICT
character would be considerably enhanced by out-of-plane (pyramidal) distortions of the
conjugated polyene backbone accompanying the torsional displacement.45,46

106

In this contribution, we report the first observations and numerical modeling of the
femtosecond transient grating signal from peridinin obtained with heterodyne detection. The
results represent a full characterization of the evolution of the third-order nonlinear optical signal
after optical preparation of the S2 state in terms of its real (absorption) and imaginary
(dispersion) signal components. As shown in our recent work on β-carotene,10 the dispersion
component provides information that is crucial in the detection of dark intermediate states. For a
given pair of states, the absorption and dispersion line shapes are defined by the Kramers–Kronig
relation. Because the dispersion line shape is bipolar, however, the sign of the detected
dispersion signal is sensitive to the detuning of the probe laser spectrum. Accordingly, when
nonradiative decay yields intermediate structures along the pathway back to the ground state, the
absorption and dispersion components exhibit distinct time profiles that turn out to be extremely
selective for the model parameters for a particular multilevel scheme. This approach had been
previously used by Xu et al. to study the excited-state conformational dynamics of crystal violet
and Rhodamine 640.49,50
The results show that the nonradiative decay of the S2 state of peridinin in methanol follows a
pathway very much like that of β-carotene. Global target analyses51 and numerical simulations
using nonlinear response function theory52 show that the S2 state of peridinin decays in 12 fs to
form an intermediate state well prior to the formation of the S1 state. Just as in β-carotene, we
attribute the intermediate, Sx, to a twisted form of the S2 state. The ESA spectrum from the Sx
state in peridinin, however, is found to be markedly blue shifted from that of β-carotene because
it makes a substantial contribution to the signal observed with 40 fs, 520 nm pulses. These results
are best interpreted in terms of a substantial stabilization of the twisted region of the S2 potential
surface of peridinin due to the presence of a substantial ICT character. The relatively long

107

lifetime of the Sx state, 900 fs, suggests that it could serve as the principal excitation energy
transfer donor to Chl a in PCP.

3.2 Experimental Section
3.2.1 Sample Preparation
Peridinin was isolated53 from laboratory-grown Amphidinium carterae (National Center for
Marine Alga and Microbiota, strain CCMP121). Cells were disrupted by adding 20 mL of
acetone to an equal volume of loosely packed cell pellet and gently shaking. Two hundred mL of
a 1:1 mixture (v/v) of hexane and methyl tert-butyl ether were added and the mixture was
transferred to a 250 mL volumetric flask. The lower phase containing cellular debris, Chl, and
residual growth media was separated and discarded. The pigmented hyperphase was washed with
an additional 9 mL of water, and collected, combined, and dried using a rotary evaporator. The
sample was then redissolved in 10 mL of acetonitrile. In order to remove Chl, ~2 mL aliquots
were filtered through a Waters Sep-Pak 12cc C18 cartridge (Waters Corp., WAT036915).
Samples were additionally purified by high-performance liquid chromatography (HPLC) which
removed other carotenoid pigments and the remaining Chl. This was performed using a Waters
600E/600S multi-solvent delivery system equipped with a 2996 photodiode array detector and a
Waters Atlantis Prep T3 OBD 5 Âľm column (19 x 100 mm).54 Acetonitrile was delivered
isocratically at a flow rate of 7.0 mL/ min. Samples collected from the HPLC were dried using
nitrogen gas and stored at −20°C. All solvents were purchased from Fisher Scientific (Waltham,
MA). For femtosecond spectroscopic experiments, peridinin was dissolved in methanol to obtain
an optical density of 0.3 for at the center of the laser spectrum (520 nm) in a cuvette with a 1 mm
optical path length.

108

3.2.2 Linear and Nonlinear Spectroscopy
Linear absorption spectra were recorded at room temperature with a Hitachi U-4001
spectrophotometer. The experimental setup and techniques used for heterodyne transient grating
spectroscopy were described in detail in the previous chapter.

3.3 Experimental Results
3.3.1 Linear Spectroscopy and Laser Excitation Spectrum.
The continuous-wave absorption spectrum of peridinin in methanol at room temperature
(295 K) is shown in Figure 3.2. The broad, structureless band spanning the 350–550-nm region
arises from the electric-dipole-allowed S0 → S2	 transition. The laser spectrum was tuned to the
red onset near the 0–0 vibronic transition to prepare the S2 state with minimal excess vibrational

Absorbance

energy. This tuning also selects the lowest energy ground-state conformers.37

0
350

400

450

500

550

600

Wavelength (nm)

Figure 3.2 Room-temperature absorption spectrum of peridinin in methanol solvent.
Superimposed is the spectrum of the OPA signal-beam output (520 nm center wavelength), as
tuned for the heterodyne transient-grating experiments.

109

3.3.2 Heterodyne Transient Grating Signal of Peridinin
Figures 3.3 and 3.4 shows the experimental real (absorption) and imaginary (dispersion)
components of the heterodyne transient grating signals of peridinin in methanol at room
temperature. As plotted, the purely dispersive nonresonant signal from neat solvent is a
negatively going signal. In the absorption component for the resonant peridinin solute, the
ground-state photobleaching (GSB) and stimulated emission (SE) contributions to the absorption
component are positive signals, and excited state absorption (ESA) contributes a negative
signal.10
The absorption component of the peridinin transient grating signal in methanol is a biphasic
transient. Near time zero a strong positive (yellow in the figure) signal centered around 515 nm
is observed due to an instrument-limited rise of the GSB and SE contributions. The signal decays
very rapidly, in <50 fs, to yield a negative going signal (blue in the figure) centered around 525
nm mainly due to the loss of SE and formation of strong ESA. In contrast, the dispersion
component is monophasic and positive going throughout the experimental delay time. At 520
nm, where the dispersion signal is strongest, the signal corresponds predominantly to the rise of
an ESA contribution. The pattern of intensity changes exhibited by both components of the
transient grating signal from peridinin is very similar to that observed previously in our
laboratory for β-carotene in benzonitrile solution.10

110

Figure 3.3 Real (absorption) component of the heterodyne transient grating signal from peridinin
in methanol solvent at room temperature (22 °C). The yellow end of the color bar corresponds to
net ground-state bleaching or stimulated emission; the dark blue end indicates excited state
absorption.

Figure 3.4 Imaginary (dispersion) component of the heterodyne transient grating signal from
peridinin in methanol solvent at room temperature (22 °C). The phasing of the color bar is
consistent with that used in Figure 3.3 for the absorption component. At 520 nm, the yellow
contours correspond to a net ESA signal.

111

In order to estimate the lineshapes and timescales that contribute to the absorption and
dispersion components of the heterodyne transient grating signal from peridinin, a global target
analysis51 using the Glotaran/TIMP package55,56 was performed over the −100 fs–12 ps delay
range. This analysis obtains a set of principal spectral components and their associated kinetic
timescales; a 60 fs Gaussian instrument response function was included in the model. The global
model reported in Figures 3.5–3.8 corresponds to a sequential decay of three species, the
minimum number indicated by a preliminary singular value decomposition (SVD) analysis.
Figure 3.5 shows the time profile of the populations for the three species, the instantaneously
formed S2 state and two sequentially populated intermediates. The lifetimes and confidence
intervals for the three species, as listed in the caption to Figure 3.5 and discussed in the
following, were obtained from the global analysis. The confidence intervals were determined to
be consistent with the fit parameters obtained from analyses of additional data sets. Figures 3.6
and 3.7 show the evolution associated spectra for each species, as obtained for the global models
of the absorption and dispersion components, respectively. Figure 3.8 shows a slice across the
data set at a central probe wavelength of 520 nm that compares the time evolution of the
experimental absorption and dispersion signals with the fitted model.

112

Population

0.8

0.6

0.4

0.2

0
0

1

10

Time (ps)

Figure 3.5 Time evolution of the populations for the three species in a global analysis of the
heterodyne transient grating signal (Figures 3.3 and 3.4) from peridinin in methanol over the
−100 fs–12 ps delay range, as plotted against a linear–logarithmic time axis split at 1 ps: black:
instantaneously formed species, 12 Âą 4 fs decay; red: first intermediate species, 12 Âą 4 fs rise,
900 Âą 100 fs decay; blue: second intermediate species in the absorption component, 900 Âą 100 fs
rise, 9.9 Âą 0.5 ps decay back to the ground state; dashed blue: second intermediate species in the
dispersion component, 900 Âą 100 fs rise , 7.5 Âą 0.5 ps decay.

0.4

EAS

0.3
0.2
0.1
0

1.0

normEAS

0.5
0
−0.5
−1.0
500

510

520

530

540

Wavelength (nm)

Figure 3.6 EAS from a global analysis of the absorption component of the heterodyne transient
grating signal (Figure 3.3) from peridinin in methanol over the −100 fs–12 ps delay range.
113

EAS

0.1

0

−0.1

1.0

normEAS

0.5
0
−0.5
−1.0
500

510

520

530

540

Wavelength (nm)

Re[Es] and Im[Es]

Figure 3.7 Evolution associated spectra (EAS) from a global analysis of the dispersion
component of the heterodyne transient-grating signal (Figure 3.4) from peridinin in methanol
over the −100 fs–12 ps delay range. The EAS assume a sequential pathway from the optically
prepared S2 state (black) through two intermediates (red, then blue) back to the ground state.

0

0

1

10

Time (ps)

Figure 3.8 Time evolution of the absorption (red) and dispersion (blue) components of the
heterodyne transient grating signals from peridinin in methanol solvent at 520 nm, as plotted
against a linear–logarithmic time axis split at 1 ps. Both signals are superimposed with the fitted
global models described in Figures 3.5–3.7, respectively.

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Over the <1 ps delay range, the absorption and dispersion components of the heterodyne
transient signal from peridinin in methanol are satisfactorily modeled with the same time
constants for the decay of the first two kinetic components: 12 Âą 4 fs and 900 Âą 100 fs. The
indeterminacy for the 12 fs component is proportionally large because of the larger width of the
instrument-response function. As discussed below, an additional determination of the lifetime of
the S2 state and the associated confidence interval is obtained from numerical simulations. The
lifetime of the intermediate species, 900 Âą 100 fs, is considerably longer than the 142 Âą 20 fs
lifetime of the intermediate in β-carotene, as determined using the same measurement conditions
and with the same analysis techniques. The confidence interval for the intermediate is
predominantly determined by covariance with the fitted lifetime of the S2 state.
The instantaneously formed spectrum from the S2 state of peridinin exhibits an absorption
spectrum with net GSB/SE character (Figure 3.6) over the entire probe bandwidth; the first
intermediate yielded by its decay exhibits a spectrum dominated by ESA, with only a narrow
region in the blue, <515 nm range showing net GSB character. The dispersion spectrum (Figure
3.7) for the initial, S2 component is bipolar, with a central positive going region flanked by two
negative regions. The dispersion lineshapes for the subsequent spectra are positive over the entire
probe bandwidth, which is consistent with the ultrafast formation of a red-shifted and linebroadened spectrum from an initially narrow, hole-burned spectrum. As in β-carotene, the time
evolution of the transient grating spectrum from peridinin is dominated at short delays by
spectral line-broadening and solvation processes.
The first intermediate then decays to yield a second intermediate exhibiting in the absorption
component a spectrum with predominantly ESA character (Figure 3.6). This spectrum is
assigned to the S1 state.11,29 It is apparent that the narrow probe spectrum used in these

115

experiments limits detection of the ESA signals especially on the red side of the plotted range, so
the band shape should not be overinterpreted; it is known that the S1 and ICT states of peridinin
exhibit overlapping ESA lineshapes, with the broad ICT band extending at least to 725 nm in
methanol from a maximum near 590 nm.11 The net GSB character observed to the blue of 515
nm in the spectrum of the first intermediate has decayed and the apparent ESA minimum has
shifted only 2 nm to the blue. In the dispersion component, the spectrum of the second
intermediate (Figure 3.7) exhibits a similar small shift to the blue but mainly on the red edge.
Following the Kramers–Kronig relationship, because the dispersion line shape is significantly
broader than that of the absorption component, spectral shifts are accordingly less obvious in the
dispersion component.
The Kramers–Kronig relationship also comes into play in the interpretation of the groundstate recovery time constants in the absorption and dispersion components of the peridinin
transient grating signal, 9.9 Âą 0.5 ps and 7.5 Âą 0.5 ps, respectively (Figure 3.5). A somewhat
smaller difference in time constant for the ground-state recovery components was observed in βcarotene.10 These time constants should be regarded as effective, tail limited estimates. The
ground-state recovery portions of the absorption and dispersion signals are multiexponential
waveforms due to the initial production of conformationally displaced structures upon
nonradiative decay from S1 to S0.10,50 The longer time constant estimated for the decay of the
absorption component includes the time required for the originally photoselected ground-state
distribution of conformers to be recovered. Because its line shape is broader than that of the
absorption component, the dispersion component predominantly senses the time constant for
nonradiative decay from S1 to S0; it is less sensitive than the absorption component to the blue

116

shift and narrowing of the photoinduced absorption spectrum from the displaced S0 conformers
that accompanies their relaxation.

3.4 Numerical Simulations
In order to assign the ultrafast intermediate observed in peridinin in 12 fs after optical
preparation of the S2 state, we have performed numerical simulations of the transient grating
signal using the nonlinear response function formalism and the multimode Brownian oscillator
model (MBO).52 The theory used in these simulations is exactly as described in detail in our
previous work on β-carotene, which extends the treatments provided by Brixner et al.57 and of
Christensson et al.58
Figure 3.9 shows the energy level scheme for peridinin that was applied in the simulations.
After optical preparation of the S2 state, population decays nonradiatively to the S1 state by
passing through an intermediate state, here labeled Sx as in the model for β-carotene, but the
nature of this state in peridinin remains to be determined from the results of the simulations. As
noted above, the narrow probe spectral bandwidth used in the present experiments precludes
detection of the red-shifted ESA band from the ICT state,6 so the scheme shown in Figure 3.8
only includes a generic S1 state serving as the kinetics compartment that receives population
from the Sx intermediate. As discussed previously,10 the calculations assume that population
transfer from one state to other results in vibrational decoherence, so the population transfers are
handled with Markovian population kinetics.59,60 This assumption impacts primarily whether or
not coherent wavepacket motions modulate the SE and ESA contributions to the transient grating
signal, and here our use of nominally 40 fs pulses precludes detection of high-frequency modes,
especially those of the C–C and C=C bond-length alternation coordinates of the conjugated

117

polyene. Along with the GSB and SE transitions associated with the S0 and S2 states, ESA
transitions from the S2, Sx and S1 states to higher lying Sn states are included in the simulation.
SE transitions from the Sx and S1 states are not included in the model, again due to the narrow
probe spectral bandwidth used in the experiments; SE from the ICT state is anticipated in the
near-IR, >900 nm region of the spectrum.8,29,61 Since we are mainly interested here in the
population dynamics on the <1 ps timescale, the separate ground-state recovery time constants
for the absorption and dispersion components are not treated explicitly in the model; modeling of
this aspect of the results would require the addition of a conformationally displaced S0 species.
The lifetimes of the S2, Sx and S1 states are taken to be 12 fs, 900 fs, and 9.9 ps, as obtained from
the global analysis of the absorption component of the transient grating signal.

ΔS2

Sn2

ΔSx

ΔS1

Energy

Snx
Sn1
S2

ΔS0

Sx
S1

S0

Figure 3.9 Schematic energy-level diagram for peridinin, as used in the simulations of the
heterodyne transient grating signal from peridinin and as used previously with β-carotene.10
Solid green arrows indicate ground state and excited-state absorption transitions. Blue wavy
arrows mark internal conversion transitions. Double-headed arrows show the detuning ( Δ )
between the center of the laser spectrum and the vertical energy of an electronic transition. The
laser tuning for the present experiments is at the red onset of the S0 → S2 absorption spectrum, so
a negative detuning from the absorption maximum is indicated in the diagram.

118

3.4.2 Simulation of the Absorption Spectrum.
Figure 3.10 compares the experimentally observed ground-state absorption spectrum for
peridinin in methanol with a simulated spectrum obtained using the MBO model. The line
broadening parameters used in the simulations are listed in Table 3.1. The optimized value of the
vertical transition energy for the peridinin S0 to S2 transition in methanol is 21670 cm−1. Two
high frequency vibrational modes, corresponding to the totally symmetric C–C and C=C
stretching modes of the conjugated polyene backbone,62 are included in the simulation. Most of
the model parameters are quite similar to those used for β-carotene in benzonitrile, but the total
reorganization energy, 𝜆, for the Gaussian and exponential Brownian modes is much larger for
peridinin. The reorganization energies and dephasing times of the vibrational modes used here in
the model for the absorption spectrum are similar to those employed by Christensson et al.63
These parameters indicate that the system–bath coupling is stronger for peridinin than βcarotene. The origin of the stronger interaction with the solvent in peridinin is the presence of
hydrogen-bonding interactions of solvent molecules with the carbonyl substituent. The increased
system–bath coupling causes the underlying vibrational structure from the two underdamped
high-frequency modes in the model to be unresolved in the absorption spectrum. As was also
observed with β-carotene,10 the simulation describes the absorption spectrum very well from the
red onset to just past the maximum, but the observed spectrum exhibits additional intensity
beyond the maximum that may have contributions from higher-energy conformers.

119

Absorbance

18000

20000
22000
-1
Wavenumber (cm )

24000

26000

Figure 3.10 Comparison of the room temperature S0→S2 absorption spectrum of peridinin in
methanol (dark blue curve) with a simulation (red dash-dotted curve) obtained using the MBO
model and the parameters listed in Table 3.1.
Table 3.1 MBO model parametersa for the simulation of the peridinin S0→S2 absorption
spectrum in methanol at 295 K (Figure 3.1).
Mode

λ (cm−1)

τ (fs)

Gaussian

300

10

—

Exponential 1

700

150

—

Exponential 2

1500

1000

—

Vibration 1

460

2200

1150

Vibration 2

1060

2200

1520

ω ν (cm−1)

For each mode, λ is the reorganization energy and τ denotes the damping time constant; ω ν is the
frequency for a vibrational mode.
a

3.4.3 Simulation of the Heterodyne Transient Grating Signals
Table 3.2 gives the energy gaps and relative dipole strengths of the electronic transitions for
the scheme shown in Figure 3.9, as obtained after optimization of the numerical simulation. The
energy gap and the MBO lineshape parameters for the S0→S2 GSB and S0→S2 SE transitions are
obtained from those used to fit the absorption spectrum. The energy gaps for the S2→Sn2 and

120

S1→Sn1 ESA transitions are set to 14800 cm-1 and 17390 cm−1, respectively, as determined from
published pump–continuum-probe spectra from peridinin in methanol.11,29 The lineshape
parameters for the ESA transitions are assumed to be the same as for the S0→S2 transition. This
choice results in a S1→Sn1 ESA lineshape that is similar to that observed in the pump-probe
spectrum from peridinin in methanol.11,29 The transition dipole strength for the S1 ESA transition
was adjusted to describe the transient grating signal at delays T >5 ps, where only the S1 state
contributes significantly. The energy gap and dipole strength of the Sx→Snx transition were
optimized to fit both the absorption and dispersion components simultaneously.
Table 3.2 Transition frequencies ( ω ij ) and relative transition dipole strengths ( µ ij ) used in the
simulation of the transient-grating signal from peridinin shown in Figures 3.11–3.13.
Transition

ω ij (cm−1)

Âľ ij (Debye)

S0 → S 2

21670

1

S 2 → S n2

14800

0.35a

S x → S nx

17300

1.58

S1 → S n1

17390

1.65

a

The ESA transition for the S2 state is well to the red of the probe bandwidth, so it makes no
contribution to the signals calculated for the bandwidth probed with 520 nm pulses. The value
indicated for the transition dipole strength for this ESA transition is the same as that used previously
for β-carotene in benzonitrile,10 and it is not optimized for peridinin in methanol.

The absorption and dispersion components of the transient grating signal calculated with
these parameters are shown in Figures 3.11 and 3.12 with the assumption of excitation pulses
centered at 520 nm and 45 fs pulse durations. In order to permit an easily visualized and
quantitative comparison of the experimental results with the simulations, Figures 3.13 and 3.14
compare the calculated models with the experimental absorption and dispersion signals, as
integrated over the signal emission frequency axis. As in our previous simulations of the

121

transient grating signal from β-carotene in benzonitrile,10 there are discrepancies at short probe
delays particularly in the rise of the absorption component. The simulations employed 45 fs
pulse durations, which are somewhat broader than estimated from the width of the dispersion
component in neat methanol solvent. This choice was made to obtain a better simulation of the
shape of the rise of the dispersion component. A 45 fs effective pulse width was also required in
the previously reported simulations of the transient grating signal from β-carotene, which were
obtained under the same measurement conditions.10 The rise of the absorption component is also
affected by the lack of inclusion of low- to mid-frequency vibrational components in the MBO
model, which make negative-going contributions at short delays.64

Figure 3.11 Numerical simulation of the absorption component of the transient grating signal
from peridinin calculated according to the energy level scheme shown in Figure 3.9. The
parameters used in the calculation are listed in Tables 3.1 and 3.2 and in the text. The yellow end
of the color bar corresponds to net ground–state bleaching or stimulated emission; the dark blue
end indicates excited state absorption.

122

Figure 3.12 Numerical simulation of the dispersion component of the transient grating signal
from peridinin	 calculated according to the energy level scheme shown in Figure 3.9. The
parameters used in the calculation are listed in Tables 3.1 and 3.2 and in the text. The phasing of
the color bar is consistent with that used in Figure 3.11 for the absorption component. At 520
nm, the yellow contours correspond to the net ESA signal from the S1 state.
As was also observed for β-carotene in benzonitrile, the ultrafast rise of the dispersion
component of the transient grating signal provides the strongest evidence that the S2 state has a
very short lifetime. Owing to the inner filter effect,65,66 the dispersion signal from the methanol
solvent is effectively negligible under the 0.3 OD resonant solute conditions used in this
experiment. This is quite different from the situation for β-carotene in benzonitrile, where the
solvent makes a significant dispersion signal owing to its much higher polarizability. The fast
rise in the dispersion signal from peridinin is predominantly controlled by the decay of the SE
signal from the S2 state, but the rise in ESA from the Sx signal also makes a significant
contribution to the response. The confidence interval for the lifetime of the S2 state was tested in
a series of calculations in which the lifetime of the S2 state was varied from 6 fs to 56 fs (Figure
A3.1 in the Appendix). The rise of the dispersion component is evidently consistent with the Âą 4

123

fs interval obtained from the global modeling, and it is clear that the lifetime cannot be as long as
20 fs because of significant negative deviations from the experiment at probe delays >25 fs.
Also, as also observed and demonstrated explicitly in the previous work on β-carotene,10
simulations (not shown) were performed using models that omit the Sx manifold of states shown
in Figure 3.9. The calculated transient grating signal exhibits a much slower rise in the dispersion
owing to the slow decay of the SE from the S2 state and the concomitant slow rise of the

Intensity

Intensity

contribution by ESA from the S1 state.

0

200

400

600

800

1000

Delay (fs)

Figure 3.13 Comparison of the experimental and calculated absorption components of the
transient grating signal from peridinin. The experimental (Figure 3.3) and calculated signals
(Figure 3.11) were integrated over the laser frequency axis and normalized at the 1 ps delay
point. Top Panel: Absorption component from the experimental transient grating signal (data
points) superimposed with those from the numerical simulation (solid line). Bottom Panel:
Absorption components calculated from individual Feynman pathways: Orange, GSB; Red, SE
from the S2 state; Blue, S 2 → S n2 ESA; Green, DQC; Violet, S x → S nx ESA, Black, S1 → S n1
ESA.

124

Intensity
Intensity

0

200

400

600

800

1000

Delay (fs)

Figure 3.14 Comparison of the experimental and calculated dispersion components of the
transient grating signal from peridinin. Top Panel: Dispersion component from the experimental
transient grating signal (data points) and superimposed with those from the numerical simulation
(solid line). Bottom Panel: Dispersion components calculated from individual Feynman
pathways: Orange, GSB; Red, SE from the S2 state; Blue, S 2 → S n2 ESA; Green, DQC; Violet,
S x → S nx ESA, Black, S1 → S n1 ESA.

3.5 Discussion
The global target analysis shown in Figures 3.3 and 3.4 indicate that the heterodyne transient
grating signal from peridinin in methanol undergoes very rapid changes in intensity and
lineshape after optical preparation of the S2 state with 40 fs pulses at 520 nm. In order to
understand better the dynamics underlying these changes, we performed an extensive series of
numerical simulations using nonlinear optical response functions and the MBO model.67,68 The
simple nonradiative decay scheme used in the simulations (Figure 3.9) is the same as that used
previously for β-carotene,10 where it was determined that the intermediate state called Sx is
formed in only 12 fs after optical preparation of the S2 state. The experimental results and
125

simulations reported in this paper indicate that a similar nonradiative decay intermediate is also
produced in peridinin. The global model and numerical simulations provide strong evidence for
the conclusion that the decay of the S2 state of peridinin occurs with a 12 Âą 4 fs time constant,
which is much shorter than the previous estimate of 56 fs16 and indistinguishable from the values
we determined for β-carotene in benzonitrile10 or by Cerullo et al. in hexane.69

The

spectroscopic assignment of the intermediate state produced by the decay of S2	 and the nature of
the relaxation process that produces it in peridinin, however, require further discussion. The case
for not assigning the intermediate to a vibrationally excited S1 state needs to be outlined first.
The 900 fs lifetime of the intermediate state determined in the global model and used in the
numerical simulations of the transient grating signal from peridinin in methanol is in the regime
generally associated with vibrational cooling in carotenoids,70,71 so it is reasonable to suggest that
the intermediate we detect upon decay of the S2 state is a vibrationally excited S1 state. This was
the assignment proposed in a number of previous studies using femtosecond pump–probe
spectroscopy.8,16,29,32,39 But as indicated by the studies of radiationless decay in crystal violet and
malachite green by Xu et al.,50 vibrational cooling would be accompanied by a significant blue–
shifting and narrowing of a photoinduced absorption or ESA line shape. The very small change
in lineshape retrieved by the global model for the Sx to S1 decay over the narrow probe
bandwidth of the 520 nm pulses used in the present experiments is not obviously consistent with
this expectation. Further, the finding that the same time constant can be used to fit the decay of
the intermediate satisfactorily in both the absorption and dispersion component is inconsistent
with a significant shift or narrowing of the spectrum; vibrational cooling would have been
expected to contribute a longer time constant in the absorption component. Lastly, the strongest
argument against a conclusion that the intermediate is

126

a vibrationally excited S1 state is

indicated by simulations of the transient grating signal. Figures A3.2–A3.5 in the Appendix
present a simulation showing the impact of replacing the Sx state in Figure 3.9 with an excited
vibrational level in the S1 manifold. The decay of the S2 state in this simulation results in a much
more pronounced biexponentiality in the decay of the absorption component or in the rise of the
dispersion component than is observed experimentally.
Instead, we suggest that the decay of the S2 state detected in the transient grating experiment
is better explained in terms of a prompt vibronic displacement on the S2 potential surface that
results in a distorted conformation. We recently proposed a general nonradiative decay model9
for carotenoids that involves vibrational displacements in the C–C and C=C bond-length
alternation coordinates followed by torsional and out-of-plane coordinates of the conjugated
polyene backbone. This scheme was constructed from a consideration of the potential energy
surfaces of conjugated polyenes, cyanines, and protonated Schiff bases of intermediate
lengths.47,72 The extent of coupling between the stretching and torsional motions of the
conjugated polyene backbone depends on several factors, including the conjugation length and
the nature of the surrounding medium (solvent and/or protein derived). For molecules with
intermediate to long conjugation lengths, such as β-carotene and peridinin, the Franck-Condon S2
geometry would be expected to lie at a potential minimum with respect to the torsional
coordinates. This results in a local activation barrier that separates planar and twisted regions of
the S2 potential energy surface (Figure 3.15). The forces that act on the Franck–Condon S2
structure are chiefly along the bond-length alternation coordinates, which accordingly exhibit
strong resonance Raman activity. In this picture, the 12 fs lifetime of the S2 state in β-carotene
and peridinin corresponds approximately to a half period of the bond-length alternation
coordinates. The Sx state would be produced by a coherent displacement from the Franck-

127

Condon geometry to the activation barrier region, where a torsional gradient on the S2 potential
surface would be encountered for the first time. In this model, the Sx state corresponds to
transition-state-like structures near the barrier that have just begun to twist with respect to one or
more of the C=C bonds. The system would then start a decent along a steep torsional gradient
leading towards a conical intersection, where the S2, S1, and S0 surfaces would converge.

x1Ag

planar

twisted

Sn

11Bu+

Potential Energy

Sx
X

21Ag

S2

S1

S0
1

1 Ag

trans

‡

= 90°

cis

Reaction Coordinate

Figure 3.15 Proposed scheme for radiationless decay of peridinin after optical preparation of the
S2 state; after similar diagrams in Sanchez-Galvez et al.72 and Beck et al.9 The states that apply to
planar structures are indicated by symmetry labels. Key points along the radiationless path from
the Franck–Condon S2 state structure are labeled with ethylenic structures, which depict the Sx
and X76 dark states as structures near the S2 transition state and along the torsional gradient,
respectively.
The formation of the twisted structures we assign to the Sx state accounts for the rapid and
irreversible loss of SE from the S2 state in the region of the spectrum probed near the Franck–
Condon energy gap, as in the present experiments. This is the main origin of the ultrafast rise
component in the dispersion channel observed in β-carotene and peridinin. Nonradiative decay

128

from the twisted part of the S2 surface to the S1 state requires propagation along the torsional
gradient from the barrier region to reach a seam between the two surfaces,47 most likely well
before a π/2 twist occurs.73,74 In peridinin, given the restraint to out-of-plane motions of the
conjugated polyene backbone by the Îł-lactone ring, the twisted region of the molecule would be
anticipated on the opposite end of the molecule, producing a twist or pyramidalization45,46 (or
kink75) in the backbone9 before before the allene moiety.
As torsional motions and out-of-plane motions are initiated in the Sx state near the barrier on
the twisted part of the S2 potential energy surface of a carotenoid, an ICT character and a
stronger frictional coupling to the surrounding solvent would be expected to arise naturally as the
conjugated polyene backbone is distorted.9,45,46,48 In general, because the carotenoids exhibit
singlet excited states with extensive delocalization of the π* character, the separation of charge
would be expected to be distributed over much of the length of the conjugated polyene backbone
on either side of the point where the twisting distortion begins. In the case of peridinin, the
enhanced system–bath coupling and the large change in permanent dipole moment that
accompanies optical preparation of the S2 state26,27 will dramatically enhance the additional ICT
character obtained from torsional displacements over that for carotenoids lacking carbonyl
substitution. This idea accounts both for the blue shifted Sx ESA spectrum we detect in the
simulations and for the dramatically enhanced Sx state lifetime of peridinin (900 fs) in methanol
compared to that for β-carotene in benzonitrile (140 fs). Given the near coincidence of the S0–S2
energy gaps of β-carotene in benzonitrile and for peridinin in methanol, which effectively
normalizes the solvent shifts for the S2 planar structures, one can infer from the blue-shifted ESA
spectrum that the potential energy region for the Sx intermediate for peridinin in methanol near
the barrier is substantially stabilized. The longer lifetime of the Sx state in peridinin would then

129

be associated with slowing by solvent friction of the torsional decent to the seam leading to the
S1 state. Vibrational equilibration in the S1 vibrational manifold would only then be expected to
follow on the 0.5–1 ps timescale, as detected in previous work with broader probe spectral
coverage.70,71,77–81 Note that this model anticipates that in some solvents the decay of the Sx state
will be so slowed by solvent friction that the rate of vibrational energy dissipation will be much
faster than the torsional relaxation; the decay of Sx will be rate limited by the polar solvation
timescale due to the coupling to the ICT character and/or the viscosity of the solvent medium due
to the involvement of large-amplitude torsional motions.

3.6 Conclusion
This contribution discusses new details of the nonradiative decay pathway from the
S2 (11Bu+) state to the S1 (21Ag−) state of peridinin in methanol solution, obtained for the first
time with heterodyne transient grating spectroscopy. As was also observed in the previous study
from this laboratory on β-carotene in benzonitrile, detection of the real (absorption) and
imaginary (dispersion) components of the transient grating signal from peridinin provides a more
precise measurement of the lifetime of the S2 state compared to previous work using pump–
probe spectroscopy employing longer excitation pulses. The results provide some new insight
into the nature of the dynamics that are associated with the decay of the S2 state. The time
evolution of the transient grating signal establishes that the S2 state decays in only 12 fs to
produce an intermediate state, Sx. Numerical modeling using the response function formalism
and the MBO model establishes that a simultaneous description of the ultrafast decay and rise of
the absorption and dispersion components of the transient grating signal, respectively, requires a
nonradiative process that quenches the SE contribution from the S2 state. The modeling further

130

indicates that the intermediate state cannot be satisfactorily assigned to a vibrationally excited S1
state.
The observation that the excited state absorption spectrum from the Sx state of peridinin is
significantly blue shifted from that of β-carotene supports the radiationless decay model we
proposed recently for carotenoids; the Sx state in peridinin is assigned to a transition-state-like
structure near an activation-energy barrier between planar and twisted structures on the S2
potential surface. The short lifetime for the S2 state is associated with a nonrecurrent vibrational
displacement from the Franck–Condon geometry along the C–C and C=C bond-length
alternation coordinates of the conjugated polyene backbone to the region of the barrier, where a
gradient along torsional coordinates is encountered. Due to the intrinsic redistribution of πelectron density obtained from the electron withdrawing character of the carbonyl substituent of
peridinin, the barrier and the twisted region of the S2 potential surface are substantially stabilized
compared to β-carotene and other carotenoids lacking carbonyl substitution. The ICT character
that results upon further relaxation on the torsional gradient on the S2 potential surface after the
barrier is passed accounts for the lengthening of the lifetime of the Sx state of peridinin over that
observed in β-carotene; the resulting increase in the solvent friction would slow the passage from
the S2 surface through a seam to the S1 surface.47
The finding that the lifetime of the S2 state is much shorter than previously estimated and the
suggestion that the decay of the resulting Sx state is significantly slowed by solvent friction has
significant implications in understanding the mechanism of excitation energy transfer from
peridinin to Chl a in PCP. Based on fluorescence excitation experiments,11 the overall energy
transfer efficiency from peridinin to Chl a after optical preparation of the S2 state is found to be
~90%, of which 25% is thought to occur nearly instantaneously between the peridinin S2 state to

131

the Chl a Qx state; the remaining 75% of the energy transfer yield is currently thought to involve
energy transfer from the S1/ICT state to Qy with a 3 ps time constant.8,23 The present results
suggest, in contrast, that it may actually be the Sx state that serves as the excitation energy donor
to either of the Chl a excited states. The structure of peridinin in PCP is somewhat compressed
along the conjugated polyene and bent near the allene moiety at the opposite end of the
conjugated polyene in a manner that promotes a partial inversion of the bond-length alternation
pattern compared to that in the planar, all-trans ground state obtained as a energy minimum in
electronic structure calculations. It is proposed that this distortion results in a strong mixing of
the characters of the S2 and S1 states and a large enhancement of the energy transfer yield to the
Chl a acceptor.40,43 We suggest that the ground-state conformation favored in PCP results in an
Sx-like conformation immediately upon optical preparation of the S2 state. This conformation
would be expected to relax further along torsional or out-of-plane coordinates in the protein to
assume an even larger ICT character and a larger Förster transition-dipole–transition-dipole
coupling to the Chl a acceptor. The result is a distorted donor state that should have some
correspondence to that of the X intermediate (Figure 3.15) reported by Ostroumov et al.76,82 in
two-dimensional electronic spectra recorded from the LH2 complex from purple bacteria.

132

APPENDIX

133

APPENDIX

A3.1 Lifetime of the S2 State
As discussed in the main text, the 12 fs lifetime of the S2 state is determined with
considerable indeterminacy due to the relatively longer, 40 fs pulses used in the experiment. To
place some additional restrictions on the lifetime of the S2 state, we performed additional
numerical simulations of the heterodyne transient grating signal in which the lifetime of the S2
state was varied from 6 to 56 fs. All of the other parameters in the simulation were fixed to the
optimum values used with the 12 fs model; as in the main simulation shown in the text, the
effective pulse duration was set to 45 fs. The results of these simulations clearly indicate that the
previously estimated S2 lifetime of 56 fs16 is much too long because it makes the rise of the
dispersion signal poorly match that of the experimentally determined signal. The results indicate
that S2 lifetime is definitely shorter than 20 fs. The confidence interval range indicated by the
global model, 12 Âą 4 fs, evidently provides a reasonable estimate of the actual lifetime of the S2
state.

134

Intensity

τ1=6 fs
τ1=12 fs
τ1=15 fs
τ1=20 fs
τ1=30 fs
τ1=40 fs
τ1=56 fs

−100

0

100

200

300

400

500

Delay (fs)

Figure A3.1 Comparison of the experimental and simulated dispersion rise of peridinin in
methanol for models employing S2 lifetime ranging from 6–56 fs. The dotted curve indicates the
experimental data. The black curve, for 12 fs, is from the model reported in the main text.
A3.2 Assignment of Sx to a Vibrationally Excited S1 State
A range of simulations was performed in which the Sx manifold shown in Figure 3.9
represents an excited vibrational state of S1. The energy level scheme for these calculations is the
same as shown in Figure 3.9, but now the manifold of states for the Sx intermediate corresponds
to that for the S1 state. Due to the initial vibrational excitation in the S1 manifold obtained from
the nonradiative transfer from the S2 state, the energy gap to the Snx (= Sn1) state is narrower than
for the relaxed S1 state manifold. Further, because by hypothesis the vibrationally excited S1
intermediate and the relaxed S1 state have the same electronic configuration, the transition dipole
strengths for their ESA transitions are set to the same values (Table A3.1). All other parameters
are the same as the those used in the calculation presented in Figures 3.11–3.14.
Table A3.1 gives the energy gaps and relative dipole strengths of the electronic transitions.
The absorption and dispersion signals determined with the above parameter sets are shown in
Figure A3.2 and A3.3 with the assumption of excitation pulses at 520 nm and 45 fs durations.

135

Figures A3.4 and A3.5 compare the experimental absorption and dispersion signals with models
as integrated over the emission frequency axis.
The red shift for the ESA spectrum arising from the assumption of the vibrational excitation
of the intermediate has a large effect on the calculated absorption component. Figure A3.2–A3.6
show the impact of a 2590 cm−1 excitation, which corresponds to about two quanta for a C–C or
C=C mode of the conjugated polyene backbone. If the initial vibrational excitation is even 400
cm−1 above the 0–0 level of the S1 state, the ESA transition from the intermediate is shifted
completely out of the probe's bandwidth, and the calculated absorption component then exhibits
a more pronounced biexponential decay to net ESA character. A large deviation from the
experimental trace is observed chiefly in the amplitude of the slower, 900 fs portion. The
corresponding defect in the calculated dispersion component is in the slower, 900 fs part of the
rising transient. To get a good fit to the experimental results, one has to set the initial vibrational
excitation for the intermediate above the 0–0 energy of the S1 state to a much smaller value.
Table A3.1 Transition frequencies ( ω ij ) and relative transition dipole strengths ( µ ij ) used in the
simulation of the transient-grating signal from peridinin in which the identity of the state Sx is
equated with the S1 state but with an initially higher energy due to vibrational excitation, here
about two quanta for C–C or C=C modes of the conjugate polyene backbone (+2590 cm−1).
Transition

ω ij (cm-1)

Âľ ij (Debye)

S0 → S 2

21670

1

S 2 → S n2

14800

0.35a

S x → S nx

14800

1.65

S1 → S n1

17390

1.65

a

The ESA transition for the S2 state is well to the red of the probe bandwidth, so it makes no
contribution to the signals calculated for 45 fs, 520 nm pulses. The value indicated for the transition
dipole strength here is the same as that used previously for β-carotene in benzonitrile10 and is not
optimized for peridinin.

136

Figure A3.2 Numerical simulation of the absorption component of the transient grating signal
from peridinin calculated by treating Sx as vibrationally excited S1 state. The parameters used in
the calculation are listed in Tables 3.1 and A3.1 and in the text. The yellow end of the color bar
corresponds to net ground–state bleaching or stimulated emission; the blue end indicates excited
state absorption.

Figure A3.3. Numerical simulation of the dispersion component of the transient grating signal
from peridinin	 calculated by treating Sx as a vibrationally excited S1 state. The parameters used
in the calculation are listed in Tables 3.1 and A3.1 and in the text. At 520 nm, the yellow
contours correspond to the net ESA signal from the S1 state.

137

Intensity
Intensity

0

200

400

600

800

1000

Delay (fs)

Figure A3.4 Comparison of the experimental and calculated absorption components of the
transient grating signal from peridinin calculated by treating Sx as vibrationally excited S1 state.
The parameters used in the calculation are listed in Tables 3.1 and A3.1 and in the text. The
experimental (Figure 3.3) and calculated signals (Figure 3.11) were integrated over the laser
frequency axis and normalized at the 1 ps delay point. Top Panel: Absorption components from
the experimental transient (data points) and from the simulation (solid line). Bottom Panel:
Absorption components calculated from individual Feynman pathways: Orange, GSB; Red, SE
from the S2 state; Blue, S 2 → S n2 ESA; Green, DQC; Violet, S x → S nx ESA, Black, S1 → S n1
ESA.

138

Intensity
Intensity

0

200

400

600

800

1000

Delay (fs)

Figure A3.5 Comparison of the experimental and calculated dispersion components of the
transient grating signal from peridinin calculated by treating Sx as vibrationally excited S1 state.
The parameters used in the calculation are listed in Tables 3.1 and A3.1 and in the text. The
experimental (Figure 3.4) and calculated signals (Figure 3.12) were integrated over the laser
frequency axis and normalized at the 1 ps delay point. Top Panel: Dispersion components from
the experimental transient (data points) and from the simulation (solid line). Bottom Panel:
Dispersion components calculated from individual Feynman pathways: Orange, GSB; Red, SE
from the S2 state; Blue, S 2 → S n2 ESA; Green, DQC; Violet, S x → S nx ESA, Black, S1 → S n1
ESA.

139

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140

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145

Chapter 4: Torsional Dynamics and Intramolecular Charge Transfer in the
S2 (11Bu+) Excited State of Peridinin: A Mechanism for Enhanced Mid-Visible
Light Harvesting

Of the carotenoids known in photosynthetic organisms, peridinin exhibits one of the highest
quantum efficiencies for excitation energy transfer to chlorophyll (Chl) a acceptors. The
mechanism for this enhanced performance involves an order-of-magnitude slowing of the
S2 (11Bu+) → S1 (21Ag−) nonradiative decay pathway compared to carotenoids lacking carbonyl
substitution. Using femtosecond transient grating spectroscopy with optical heterodyne
detection, we have obtained the first evidence that the nonradiative decay of the S2 state of
peridinin is promoted by large-amplitude torsional motions. The decay of an intermediate state
termed Sx, which we assign to a twisted form of the S2 state, is substantially slowed by solvent
friction in peridinin due to its intramolecular charge transfer (ICT) character.

The work presented in this chapter has been adapted from J. Phys. Chem. Lett., 2016, 7, 3621–
3626. Copyright (2016) American Chemical Society.
146

4.1 Introduction
Obtaining photochemically robust chromophores with strong absorption in the mid-visible
portion of the spectrum and efficient pathways of excitation energy transfer for use in lightharvesting materials is a particularly challenging problem that photosynthetic organisms have
solved by inclusion of carotenoids in light-harvesting complexes.1–3 Peridinin (1), the principal
light absorber in the peridinin–chlorophyll a protein (PCP) in dinoflagellates,4 exhibits one of the
highest known efficiencies (~90%) for excitation energy transfer from a carotenoid to Chl
acceptors.5,6 The structural mechanism that enhances this energy transfer function involves the
presence of an unusual carbonyl substituted Îł-lactone ring in conjugation with the polyene
backbone. The electron-withdrawing tendency of the carbonyl group contributes to a
redistribution of π-electron density and an ICT character.7

HO

O
O

OCOCH3

•

O
HO

1

2

Figure 4.1 Structures of peridinin (1) and β–carotene (2)
The light-harvesting function of carotenoids employs strong absorption bands in the midvisible part of the spectrum arising from the electric-dipole allowed S0 (11Ag−) → S2 (11Bu+)
transition.8 Energy transfer between the S2 state and a Chl acceptor is accordingly favorable
through the FĂśrster mechanism,9 which relies on the strong oscillator strength of the donor
carotenoid for the downward S2 → S0 transition that accompanies excitation of the Chl Qx or Qy

147

transitions. The energy-transfer yield, however, is usually constrained by the very short (<150 fs)
lifetime of the S2 state due to nonradiative decay to the S1 (21Ag−) state. From a Förster
perspective, energy transfer from the S1 state would be expected to be less efficient than from the
S2 state because the S1 → S0 transition is effectively forbidden.10,11 Birge, Frank, and coworkers
have proposed that peridinin performs better than non-carbonyl substituted carotenoids in energy
transfer to Chls because the S2 and S1 states are mixed as a result of the partial C–C/C=C
excited-state bond-order reversal that accompanies the carbonyl-induced ICT character.12 The
results of the present contribution, however, indicate that the carbonyl substitution in peridinin
also markedly improves the ability of the S2 state to serve as an efficient energy transfer donor
by substantially lengthening its lifetime. We can now show that decay from the S2 state to the S1
state is promoted by large-amplitude torsional motions, which are strongly retarded by solvent
friction because of the enhanced ICT character peridinin obtains as it twists.

4.2 Experimental Methods
4.2.1 Sample Preparation
Peridinin from laboratory-grown Amphidinium carterae (strain CCMP121) was isolated as
described in detail previously and purified by high-performance liquid chromatography.13 For the
femtosecond spectroscopic experiments, peridinin was dissolved in a given solvent to obtain an
optical density of 0.3 at the center of the laser spectrum in a fused silica cuvette with a 1 mm
optical path length.
4.2.2 Femtosecond Spectroscopy
Transient grating signals were obtained at 22 °C as described in detail previously.13,14 40 fs
excitation pulses were obtained from an optical parametric amplifier (OPA, Coherent OPA
148

9450), which was pumped by a 250 kHz amplified Ti:sapphire laser (Coherent Mira Seed
oscillator and RegA 9050 amplifier). The transient grating signals were recorded with a
diffractive-optic based, passively phase stabilized, photon echo spectrometer.15,16

4.3 Results and Discussions
We studied the nonradiative decay of the S2 state of peridinin in four polar solvents with
femtosecond transient grating spectroscopy and optical heterodyne detection17 using a passively
phase-stabilized, diffractive optic based spectrometer.15,16 The S0 → S2 transition was excited
with 40 fs laser pulses tuned to the red edge of the absorption spectrum of peridinin near the
wavenumber of the 0–0 vibronic transition in a given solvent. The absorption spectrum and the
tuning of the laser in each solvent are shown in the Appendix.
Figure 4.2 shows contour representations of the spectrally resolved absorption component of
the transient grating spectrum of peridinin in four polar solvents over the 0–500 fs probe delay
range. The time evolution of both components of the transient grating spectrum is well described
by a sequential pathway from the instantaneously formed (Franck–Condon) S2 state through two
intermediate states, Sx and S1, prior to recovery to the ground state, S0. The evolution-associated
spectra (EAS) and the formation and decay time constants (Table A4.1) obtained for each state
by fitting the absorption and dispersion components of the transient grating signal in each solvent
using a sequential global target model18 are presented in the Appendix. Assignments for the
nonlinear optical pathways that contribute to the EAS from each state were made using the
previously published numerical simulations of the transient grating signal from peridinin in
methanol, which were performed using the response function formalism and the multimode
Brownian oscillator model.13

149

520

525 A

B
0.5

Wavelength (nm)

505
505

0

490

490

540 C

540 D

520

520

500

0

200

400

500

−0.5

0

200

400

Delay (fs)
Figure 4.2 Contour representations of the spectrally resolved absorption component of the
heterodyne transient grating signal from peridinin at room temperature (22 °C) in: (a)
acetonitrile; (b) ethyl acetate; (c) methanol; and (d) 2-propanol. The corresponding dispersion
components are shown in the Appendix. The yellow end of the color bar corresponds to net
ground state bleaching or stimulated emission; the dark blue end indicates excited state
absorption. The black dotted lines indicate the wavelengths for the single-wavelength slices
plotted in Figure 4.3.
Figure 4.3 compares examples of single-wavelength slices of the absorption component of
the transient grating signal that show how the populations of the three states in the nonradiative
decay pathway control the shape of the response in the four solvents. The Franck–Condon S2
state species decays almost instantaneously (<16 fs) in each case. The spectrum from S2 consists
mainly of ground-state depletion and stimulated emission (SE) signals over the probed
bandwidth; a net excited-state absorption (ESA) spectrum appears upon formation of the first
intermediate state, Sx, which is apparently comparable13 to the intermediate state observed with
similar kinetics after optical preparation of the S2 state in other carotenoids.2,14 The numerical
150

simulations show that the ultrafast kinetics for the formation of Sx in β-carotene and peridinin
can be clearly discerned especially in the rising ESA kinetics of the dispersion component.13,14
Nonradiative decay of Sx then yields a net ESA spectrum from the S1 state, which is somewhat
more intense and only slightly blue shifted from that of Sx as probed here. It should be noted that
the limited probe bandwidth used in these experiments precludes detection of the red shifted,
solvent dependent ESA band in the 600 nm region of the spectrum that is usually assigned to an
ICT (or S1/ICT) state in polar solutions of peridinin,7,19,20 so the use of an generic compartment for
the S1 state is appropriate in the present global models.

B

Population

Intensity

A

0

1

10

0

1

10

D

Population

Intensity

C

0

1

10

0

1

10

Delay (ps)
Figure 4.3 Single-wavelength slices of the absorption component of the heterodyne transient
grating signal from peridinin (see Figure 4.2), as fitted by a global target model: in (a)
acetonitrile, at 507 nm; (b) ethyl acetate, at 507 nm; (c) methanol, at 520 nm; and (d) 2-propanol,
at 520 nm. The lower panels for each solvent show the relative population in the three states in
the fitted model: black, Franck–Condon S2 state; red, Sx intermediate state; blue, S1 state.

151

Table 4.1 Lifetime of the Sx state of peridinin, as obtained from the global target models of the
absorption and dispersion components of the transient grating signal in four solvents.
Solvent

a

Sx lifetime (ps)	 η(cP)a 𝜏avg(ps)b

Acetonitrile

0.39 Âą 0.14

0.345

0.26

Ethyl acetate

0.64 Âą 0.14

0.45

0.86

Methanol

0.90 Âą 0.10

0.597

5

2-propanol

1.70 Âą 0.13

2.4

26

Solvent viscosity, from reference 23. bAverage polar solvation time, from Table 3 of reference 24.

While the conversion of the S2 state to the Sx intermediate occurs at the same ultrafast rate in
all of the solvents (see Table A4.1), the lifetime of Sx is more than quadrupled by moving from
acetonitrile to 2-propanol. Table 4.1 reports the lifetimes for the Sx state in comparison with two
properties of the solvent, the viscosity and the average polar solvation time. Figure 4.4 shows
that the lifetime of Sx increases monotonically with respect to both properties and tends towards
saturation in the most viscous or slow solvent, 2-propanol. In contrast, Figure A4.29 shows that
the lifetime of the Sx state is not monotonically dependent on the solvent polarity. This behavior
makes it clear that the Sx state has a distinct electronic configuration from the S1 state, which
exhibits a strong, essentially linear dependence on the solvent polarity (Table A4.1 and Figure
A4.31), as was observed previously by Frank and coworkers.7 It was proposed previously20,21
that a vibrationally excited level of the S1 state is formed in peridinin directly upon nonradiative
decay of the S2 state on the ~50 fs time scale, but as discussed in detail in the previous work on
the transient grating signal from peridinin in methanol,13 numerical simulations of the vibrational
cooling of such a "hot" S1 intermediate yield multiexponential absorption and dispersion decays
that are markedly different from those observed experimentally. Further, the wide range of
lifetimes observed for Sx over the range of solvents studied here is inconsistent with the weak

152

dependence on the structure of the solvent that would be expected for a vibrational cooling
process.22

2.0

A

1.5

Sx Lifetime (ps)

1.0
0.5
0
0

2.0

0.5

1.0
1.5
Viscosity (cP)

2.0

2.5

B

1.5
1.0
0.5
0
0

5
10
15
20
25
Average Polar Solvation Time (ps)

Figure 4.4 Power-law dependencies of Sx lifetime, τ Sx on solvent properties: (a) τ Sx = a + bη α
with respect to the solvent viscosity, η, with a = − 0.57 , b = 1.7 and α = 0.4 .(b)
τ Sx = a + bτ α avg with respect to the average polar solvation time, τ avg , with a = 0.18 , b = 0.41
and Îą = 0.4 .
Instead, as proposed previously,13,14,25 the Sx state is best assigned to a twisted form of the S2
state. The time evolution of the high-frequency, C=C bond stretching bands recently observed
using transient IR and stimulated Raman spectroscopy by Di Donato et al.26 supports the
previous conclusion from pump–probe and pump–dump–probe spectroscopy by Zigmantas et
al.20 and Papagiannakis et al.,27 respectively, that distortions of the conjugated polyene backbone
of peridinin occur after optical preparation of the S2 state. The viscosity dependence reported
here for the lifetime of the Sx state, however, establishes for the first time that large-amplitude
torsional motions promote nonradiative decay from Sx to S1. As is also observed for the decay of
excited states in triphenylmethane (TPM) dyes28 and cyanines,

153

29

the lifetime of the Sx state

follows a power law function with respect to the solvent viscosity (Figure 4.4a), which indicates
that solvent friction retards progress along torsional coordinates towards a position-sensitive
sink30 (or seam13,14,31) leading to the S1 state. But a better correlation of the lifetime of Sx is
obtained with respect to the average polar solvation time (Figure 4.4b), which suggests that the
friction that slows the decay from Sx to S1 includes a solvent reorganization 32in response to the
net transfer of charge that accompanies the twisting and pyramidalization of a C=C bond.33–35 A
comparable lifetime dependence was observed in the dye LDS–821, which exhibits a twisted
intramolecular charge-transfer (TICT) excited state.36
The present results strongly support our previous hypothesis that the structure of peridinin in
the S2 state undergoes a two-step structural evolution prior to decaying to the S1 state. This
hypothesis is framed by the potential energy surfaces depicted schematically in Figure 4.5, which
are based on aspects of the potential energy surfaces of conjugated polyenes, cyanines, and
protonated Schiff bases (PSBs) of intermediate conjugation lengths.31,37 The literature
background and the implications of this scheme, with application to the nonradiative decay and
nonlinear spectroscopic properties of carotenoids in solution and in light-harvesting proteins, was
discussed in detail previously.13,14,25 The key feature of Figure 4.5 is that the π* excited state
potential surfaces are divided by a low transition state barrier between planar and twisted
conformations of the conjugated polyene backbone.25,37 After optical preparation of the S2 state
from the planar minimum of the ground state, the first step in the nonradiative decay process is a
solvent-independent displacement from the planar Franck–Condon structure along the resonance
Raman-active C–C and C=C stretching coordinates of the conjugated polyene. In no more than
half a vibration of these high-frequency coordinates, the system passes the transition-state barrier
to form the Sx state, which is assigned to S2 structures in which the conjugated polyene backbone

154

has just begun distortions with respect to torsional coordinates. Because the Îł-lactone ring
inhibits out-of-plane motions, the distortion of the conjugated polyene backbone of peridinin
would be expected to occur along the intervening length prior to the allene moiety. Vertical
excitations of conformationally distorted ground state structures directly to the twisted part of the
S2 potential surface might contribute to the increased excited-state ICT character of peridinin
detected in previous work with excitation in the red tail of the S0 → S2 absorption spectrum.20,26

Figure 4.5 Proposed scheme for the radiationless decay of the S2 state of carotenoids.13,25 The
ethylenic structures shown depict the Sx and X3 states as torsionally distorted S2 structures near
the transition state barrier (‡) and further along the torsional gradient, respectively.
The second step in the nonradiative decay of the S2 state involves further torsional
distortions of the conjugated polyene backbone accompanying a descent of the steep potential
energy gradient from the transition state barrier towards a convergence of the energies of the S2,
S1 and S0 states. The rate at which evolution occurs along the torsional coordinates controls the

155

lifetime of the Sx state, and here friction from the surrounding solvent makes a strong
contribution to the dynamics. Nonradiative decay from Sx would occur by passage through a
seam to the S1 state, probably well before a 90° twist, given that photoisomerization to the cis
conformation is not observed.
The torsional and/or pyramidal distortions that peridinin undergoes on the >20 fs timescale
during relaxation of the Sx state and subsequently upon nonradiative decay to the S1 state in polar
solution result in an enhanced ICT character and an unusual sensitivity to the polarity of the
solvent medium, as observed previously in extensive studies of the characteristic ICT ESA band
in the 600 nm region of the spectrum.7 The net SE signal observed in the near-IR (950 nm)
region of the spectrum19,38,39 may include contributions from torsionally displaced structures on
the S2 potential surface near the seam to the S1 state and/or from the vibrationally excited
structures produced after passage to the S1 state; the rise time of the SE signal is comparable to
that associated with the decay of Sx measured in the present work but there is an additional
sensitivity to the solvent polarity.19 A similar net SE signal has been observed in distorted
PSBs.40 As discussed previously,13,25 an additional redistribution of π-electron density along the
distorted conjugated polyene backbone and further out-of-plane distortion would be expected to
accompany a search of the S1 potential surface as vibrational cooling occurs on the >0.5 ps
timescale. This cooling process is not detected in the present experiments due to the limited
probe bandwidth, but experiments with broadband continuum probing have detected it in
peridinin39 and in other carotenoids.41,42
The mechanism shown in Figure 4.5 should also apply to carotenoids lacking carbonyl
substitution. In general, an ICT character and a frictional coupling to the surrounding solvent
would be expected to develop as a carotenoid relaxes along torsional coordinates in the S2 state.25

156

Owing to extensive delocalization of the π* character, the separation of charge in the S2 state
would be distributed over much of the length of the conjugated polyene backbone on either side
of the twisting distortion.13 For peridinin, the ICT character is especially large because of the
contribution of the carbonyl substituent, which results in a very large permanent dipole moment
increase upon photoexcitation to the S2 state.43,44 The ICT character is then further enhanced in
peridinin by distortion of the conjugated polyene backbone.26,45 As a result, the solvent friction in
the S2 state of peridinin is much larger than for β–carotene and retinal, where the excited state
lifetimes are essentially independent of the solvent.46,47 The lifetime detected previously for the
Sx state of β-carotene, 150 fs,2,14 is accordingly significantly shorter than observed for peridinin
even in the fastest solvent, acetonitrile.
We suggest that these results have important implications in understanding the mechanism of
excitation energy transfer from carotenoids to Chl acceptors in photosynthetic light-harvesting
proteins. Because it strongly enhances the solvent friction suffered by torsional motions in the S2
state, the carbonyl substitutent of peridinin causes the lifetime of the Sx state to be extended into
the >1 ps regime, well over that observed for carotenoids lacking carbonyl substitution like βcarotene (150 fs). Such a long lifetime allows the Sx to serve as an efficient energy transfer donor
to Chl acceptors in PCP. Current estimates hold that 75% of the total ~90% excitation energy
transfer yield is mediated in PCP by the Förster mechanism with a time constant of 2.5–3.0 ps;
the remaining 25% of the yield is carried by a very fast energy transfer channel that may involve
electronic coherence or delocalized excited states.5,6,48 The solvent environment of peridinin due
to the surrounding protein and chromophores in PCP is roughly comparable in viscosity and
polarity to ethylene glycol, as gauged by a comparison of the linebreadth, absence of resolved
vibronic structure, and shift of the ground-state absorption spectra in the two environments.6 The

157

power law models for the lifetime of Sx as a function of viscosity and average solvation time
(Figures 4.4a and 4.4b) predict an intrinsic lifetime for Sx in ethylene glycol in the range from
1.4 ps (from the solvation time, τ avg = 15.3 ps24) to 5 ps (from the viscosity, η = 19.9 cP23).
These lifetimes are certainly long enough to allow the Sx state of peridinin to make a significant
contribution in PCP as an energy transfer donor state because Sx would be expected to retain
much of the oscillator strength of the Franck–Condon S2 state. This prediction should be
compared to the presently accepted picture for the FĂśrster energy transfer channel in PCP, which
holds that the S1 state of peridinin effectively borrows oscillator strength from the "bright" S2
state via the ICT character it obtains from the carbonyl substitution.12,49 An additional
enhancement in PCP is the selection by the peridinin-binding sites of distorted ground-state
conformations,49 which would be expected to lengthen the effective lifetime of Sx even more by
optimizing the carbonyl-induced ICT character and the resultant frictional coupling to the
environment immediately upon excitation to the S2 state. Note that a distorted carotenoid S2
structure (X, Figure 4.5) is also implicated in energy transfer pathways to bacteriochlorophyll a
detected in two-dimensional electronic spectra from the LH2 complex of purple bacteria,3 but in
our picture the energy transfer yield in this case is not as large as in PCP partly owing to the
shorter lifetime of the S2 state.

158

APPENDIX

159

APPENDIX

A 4.1 Supporting Results
Heterodyne transient grating signals were obtained with 40 fs excitation pulses for peridinin
dissolved in the following solvents: acetonitrile, ethyl acetate, methanol, and 2-propanol. As
shown in the absorption spectra for each case, the laser was tuned to maintain a ~50% detuning
to the red from the absorption maximum, which places the excitation near the wavenumber of the
0–0 vibronic transition for the S0 (11Ag−) to S2 (11Bu+) transition. The optical density of the
samples at the center of the laser spectrum was 0.3 across the 1 mm cuvette.
For each solvent, we present in the following contour representations of the absorption (real)
and dispersion (imaginary) components of the transient grating signal, as determined using
Fourier transform spectral interferometry.15 A global target analysis18 using the Glotaran and
TIMP programs50,51 was employed to fit both components of the transient grating signal to a
sequential decay model involving three kinetic components: the S2 state prepared by the laser
pulse, an Sx intermediate state, and the S1 state, which then yields the ground state, S0. A
preliminary singular value decomposition (SVD) analysis indicated the contributions of three
spectrokinetic components in all the solvents studied. The spectral time evolution in the
sequential decay model is described by the evolution-associated spectra (EAS). The nature of the
time evolution of the EAS has been discussed in detail for β-carotene14 and peridinin13 in
previous publications with support from a comprehensive set of numerical simulations using the
response function formalism and the multimode Brownian oscillator model. Note that this work

160

considered a range of alternative models and considered especially the possible assignment of
the Sx state in peridinin to a vibrationally excited energy level of S1.
The lifetimes and associated confidence intervals for each of the states in the model in the
four solvents were determined from the global target analysis, and the confidence intervals were
found to be consistent with those obtained from the set of lifetimes from replicate runs. As noted
previously,13 the lifetime of the S2 state is determined with considerable indeterminacy in these
experiments due to the use of 40 fs excitation pulses. We found, however, that a better estimate
of the lifetime of S2 for peridinin in methanol was obtained from numerical simulations of the
transient grating signal; in particular the rise time of the dispersion signal provides a bracketing
of the lifetime of the S2 state between 8 fs and 16 fs. The indeterminacy for the lifetime of the S2
state in the other three solvents is similar to that in methanol.
As discussed previously,13,14 the lifetimes for the S1 state returned by the models for the
absorption and dispersion components are significantly different because of differential detection
of a contribution from a conformationally displaced ground state species, which is produced
upon nonradiative decay of the S1 state. The longer S1 lifetime observed in the absorption signal
reflects the additional time required for conformational relaxation to occur on the ground-state
potential surface to recover the original, photoselected ground-state conformation. The
dispersion is less sensitive to the blue shift of the photoinduced absorption spectrum because the
dispersion lineshapes are much broader than the absorption lineshapes. This phenomenon is
comparable to that previously observed by Xu et al. in heterodyne transient grating studies of the
triphenylmethane dye crystal violet.52 The global models do not include this part of the dynamics
because the narrow probe spectra range obtained from the 40 fs pulses does not provide enough
spectral coverage of the ground-state photoinduced absorption spectrum.

161

Absorbance

Acetonitrile

0
350

400

450

500

550

600

Wavelength (nm)

Figure A4.1 Room-temperature (22 °C) absorption spectrum of peridinin in acetonitrile solvent.
Superimposed is the spectrum of the OPA signal-beam output (505 nm center wavelength), as
tuned for the heterodyne transient-grating experiments.

Figure A4.2 Real (absorption) component of the heterodyne transient grating signal from
peridinin in acetonitrile solvent at room temperature (22 °C). The yellow end of the color bar	
corresponds to net ground state bleaching or stimulated emission; the dark blue end indicates
excited state absorption. This figure is shown in panel (a) of Figure 4.2.

162

Figure A4.3 Imaginary (dispersion) component of the heterodyne transient grating signal from
peridinin in acetonitrile solvent at room temperature (22 °C). The phasing of the color bar is
consistent with that used in Figure A4.2 for the absorption component. At 505 nm, the yellow
contours correspond to a net ESA signal.	

Population

0.8

0.6

0.4

0.2

0
0

1

10

Time (ps)

Figure A4.4 Time evolution of the populations for the three species in a global analysis of the
heterodyne transient grating signal (Figures A4.2 and A4.3) from peridinin in acetonitrile over
the −100 fs–10 ps delay range, as plotted against a linear–logarithmic time axis split at 1 ps:
black: instantaneously formed species, 12 Âą 4 fs decay; red: first intermediate species,
12 Âą 4 fs rise, 0.39 Âą 0.14 ps decay; blue: second intermediate species in the absorption
component, 0.39 Âą 0.14 ps rise, 8.6 Âą 0.3 ps decay back to the ground state; dashed blue: second
intermediate species in the dispersion component, 0.39 Âą 0.14 ps rise , 8.1 Âą 0.5 ps decay.

163

EAS

0.2

0.1

0

1.0

normEAS

0.5
0
−0.5
−1.0
490

500

510

520

530

Wavelength (nm)

Figure A4.5 Evolution-associated spectra (EAS) from a global analysis of the absorption
component of the heterodyne transient grating signal (Figure A4.2) from peridinin in acetonitrile
over the −100 fs–10 ps delay range. The EAS assume a sequential pathway from the optically
prepared S2 state (black) through two intermediates (red, then blue) back to the ground state.
0.2

EAS

0.1

0

normEAS

1.0

0.5

0

490

500

510

520

530

Wavelength (nm)

Figure A4.6 Evolution associated spectra (EAS) from a global analysis of the dispersion
component of the heterodyne transient-grating signal (Figure A4.3) from peridinin in acetonitrile
over the −100 fs–10 ps delay range.

164

Re[Es] and Im[Es]

0

0

1

10

Time (ps)

Figure A4.7 Time evolution of the absorption (red) and dispersion (blue) components of the
heterodyne transient grating signals from peridinin in acetonitrile solvent at 507 nm, as plotted
against a linear–logarithmic time axis split at 1 ps. Both signals are superimposed with the fitted
global models described in Figures A4.4–A4.6, respectively.

Absorbance

Ethyl Acetate

0
350

400

450

500

550

600

Wavelength (nm)

Figure A4.8 Room-temperature (22 °C) absorption spectrum of peridinin in ethyl acetate
solvent. Superimposed is the spectrum of the OPA signal-beam output (505 nm center
wavelength), as tuned for the heterodyne transient-grating experiments.

165

Figure A4.9 Real (absorption) component of the heterodyne transient grating signal from
peridinin in ethyl acetate solvent at room temperature (22 °C). The yellow end of the color bar
corresponds to net ground state bleaching or stimulated emission; the dark blue end indicates
excited state absorption. This figure is shown in panel (b) of Figure 4.2.

Figure A4.10 Imaginary (dispersion) component of the heterodyne transient grating signal from
peridinin in ethyl acetate solvent at room temperature (22 °C). The phasing of the color bar is
consistent with that used in Figure A4.9 for the absorption component. At 505 nm, the yellow
contours correspond to a net ESA signal.

166

1.0

Population

0.8
0.6
0.4
0.2
0
0

1

10

100

Time (ps)

Figure A4.11 Time evolution of the populations for the three species in a global analysis of the
heterodyne transient grating signal (Figures A4.9 and A4.10) from peridinin in ethyl acetate over
the −100 fs–100 ps delay range, as plotted against a linear–logarithmic time axis split at 1 ps:
black: instantaneously formed species, 12 Âą 4 fs decay; red: first intermediate species, 12 Âą 4 fs
rise, 0.64 Âą 0.14 ps decay; blue: second intermediate species in the absorption component,
0.64 Âą 0.14 ps rise, 130 Âą 3.5 ps decay back to the ground state; dashed blue: second
intermediate species in the dispersion component, 0.64 Âą 0.14 fs rise, 83 Âą 10 ps decay.

167

EAS

0.15
0.10
0.05
0

1.0

normEAS

0.5
0
−0.5
−1.0
490

500

510

520

530

Wavelength (nm)

Figure A4.12 Evolution-associated spectra (EAS) from a global analysis of the absorption
component of the heterodyne transient grating signal (Figure A4.9) from peridinin in ethyl
acetate over the −100 fs–100 ps delay range. The EAS assume a sequential pathway from the
optically prepared S2 state (black) through two intermediates (red, then blue) back to the ground
state.

168

EAS

0.10
0.05
0

−0.05

1.0

normEAS

0.5

0

−0.5
490

500

510

520

530

Wavelength (nm)

Re[Es] and Im[Es]

Figure A4.13 Evolution associated spectra (EAS) from a global analysis of the dispersion
component of the heterodyne transient-grating signal (Figure A4.10) from peridinin in ethyl
acetate over the −100 fs–100 ps delay range. The EAS assume a sequential pathway from the
optically prepared S2 state (black) through two intermediates (red, then blue) back to the ground
state.

0

0

1

10

100

Time (ps)

Figure A4.14 Time evolution of the absorption (red) and dispersion (blue) components of the
heterodyne transient grating signals from peridinin in ethyl acetate solvent at 507 nm, as plotted
against a linear–logarithmic time axis split at 1 ps. Both signals are superimposed with the fitted
global models described in Figures A4.11–A4.13, respectively.

169

Absorbance

2-Propanol

0
350

400

450

500

550

600

Wavelength (nm)

Figure A4.15 Room-temperature (22 °C) absorption spectrum of peridinin in 2-propanol solvent.
Superimposed is the spectrum of the OPA signal-beam output (520 nm center wavelength), as
tuned for the heterodyne transient-grating experiments.

Figure A4.16 Real (absorption) component of the heterodyne transient grating signal from
peridinin in 2-propanol solvent at room temperature (22 °C). The yellow end of the color bar
corresponds to net ground state bleaching or stimulated emission; the dark blue end indicates
excited state absorption. This figure is shown in panel (d) of Figure 4.2.

170

Figure A4.17 Imaginary (dispersion) component of the heterodyne transient grating signal from
peridinin in 2-propanol solvent at room temperature (22 °C). The phasing of the color bar is
consistent with that used in Figure A4.16 for the absorption component. At 520 nm, the yellow
contours correspond to a net ESA signal.
1.0

Population

0.8

0.6

0.4

0.2

0
0

1

10

Time (ps)

Figure A4.18 Time evolution of the populations for the three species in a global analysis of the
heterodyne transient grating signal (Figures A4.16 and A4.17) from peridinin in 2-propanol over
the −100 fs–48 ps delay range, as plotted against a linear–logarithmic time axis split at 1 ps:
black: instantaneously formed species, 12 Âą 4 fs decay; red: first intermediate species, 12 Âą 4 fs
rise, 1.7Âą 0.13 ps decay; blue: second intermediate species in the absorption component,
1.7Âą 0.13 ps rise, 47 Âą 1.6 ps decay back to the ground state; dashed blue: second intermediate
species in the dispersion component, 1.7Âą 0.13 ps rise, 32 Âą 3 ps decay.

171

0.8

EAS

0.6
0.4
0.2
0
1.0

normEAS

0.5
0
−0.5
−1.0
500

510

520

530

540

Wavelength (nm)

Figure A4.19 EAS from a global analysis of the absorption component of the heterodyne
transient grating signal (Figure A4.16) from peridinin in 2-propanol over the −100 fs–48 ps delay
range. The EAS assume a sequential pathway from the optically prepared S2 state (black)
through two intermediates (red, then blue) back to the ground state.

EAS

0.4
0.2
0
−0.2

normEAS

1.0

0.5

0

−0.5
500

510

520

530

540

Wavelength (nm)

Figure A4.20 EAS from a global analysis of the dispersion component of the heterodyne
transient-grating signal (Figure A4.17) from peridinin in 2-propanol over the −100 fs–48 ps
delay range.

172

Re[Es] and Im[Es]

0

0

1

10

Time (ps)

Figure A4.21 Time evolution of the absorption (red) and dispersion (blue) components of the
heterodyne transient grating signals from peridinin in 2-propanol at 520 nm, as plotted against a
linear–logarithmic time axis split at 1 ps. Both signals are superimposed with the fitted global
models described in Figures A4.18–A4.20, respectively.

Solvent Dependence of the Global Model Parameters
Table A4.1 Lifetimes of the S2, Sx, and S1 states, as obtained from the global models of the
transient grating signal from peridinin in four solventsa
Solvent

Polarityc

Polarizabilityd

8.6 Âą 0.3/8.1 Âą 0.5

0.921

0.210

0.64 Âą 0.14

126 Âą 4/83 Âą 10

0.626

0.226

12 Âą 4

0.90 Âą 0.10

9.9 Âą 0.5/7.5 Âą 0.5

0.913

0.202

10 Âą 2

1.70 Âą 0.13

46.5 Âą 1.6/32.3 Âą 2.9

0.852

0.230

S2 lifetime
(fs)

Sx lifetime

S1 lifetime (ps)

(ps)

(absp/disp) 	

Acetonitrile

12 Âą 4

0.39 Âą 0.14

Ethylacetate

12 Âą 4

Methanol
2-propanol
a

Solvent parameters are taken from Table 4.2 of reference 7;
Lifetimes for S1 as obtained from the absorption (absp) and dispersion (disp) components;
c
Polarity P(Îľ ) as calculated from the dielectric constant
d
Polarizability , as calculated from the index of refraction
b

173

Sx lifetime (ps)

2.0

1.5

1.0

0.5

0.6

0.7

0.8

0.9

Polarity

Figure A4.22 Lifetime of the Sx state plotted as a function of solvent polarity.

Sx lifetime (ps)

2.0

1.5

1.0

0.5

0.20

0.21

0.22

0.23

Polarizabilty

S1 lifetime (ps)

Figure A4.23 Lifetime of the Sx state plotted as a function of solvent polarizability.

100

50

0
0.6

0.7

0.8

0.9

Polarity

Figure A4.24 Lifetime of the S1 state in the absorption component plotted as a function of
solvent polarity.

174

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175

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Chapter 5: Excitation Transfer by Coherent and Incoherent Mechanisms in
the Peridinin–Chlorophyll a Protein

Excitation transfer from peridinin to chlorophyll (Chl) a acceptors is unusually efficient in
the peridinin–chlorophyll a protein (PCP) from dinoflagellates. We can show for the first time
that this enhanced performance arises from the long intrinsic lifetime obtained for the S2 (11Bu+)
state of peridinin that is obtained in PCP, 4.4 ps, due to the presence of its carbonyl substituent.
Results from heterodyne transient grating spectroscopy show that the S2 state serves as the donor
state for two channels of excitation transfer: a 30 fs process involving quantum coherence and
mixed peridinin–Chl states, and an incoherent, 2.5 ps process that is initiated by dynamic
localization, which accompanies the formation of a conformationally distorted S2 state structure
in 45 fs. The distorted S2 state has a long lifetime in PCP due to its intramolecular charge transfer
(ICT) character and enhanced system–bath coupling, which retards the torsional motions that
promote nonradiative decay to the S1 (21Ag−) state. The observed lifetime of the S1 state, 18.9 ps,
precludes a significant contribution to excitation transfer, but a role in nonphotochemical
quenching remains a possibility.

The work presented in this chapter has been adapted from J. Phys. Chem. Lett., 2017, 8, 463–
469. Copyright (2017) American Chemical Society.

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5.1 Introduction
Of the known photosynthetic light-harvesting complexes that employ carotenoids as midvisible antenna chromophores,1 the peridinin–chlorophyll a protein (PCP) from marine
dinoflagellates is noted for its very high (~90%) quantum efficiency for excitation energy
transfer from the carotenoid peridinin to Chl a acceptors.2–5 Each subunit of PCP binds a dense
cluster of eight peridinin carotenoids and two Chl a chromophores in a C2-symmetric, twodomain assembly (Figure 5.1a) inside a basket of Îą helices. The four peridinins in each domain
are nearly in van der Waals contact (3.3 to 3.8 Å separation) with a central Chl a acceptor.6 The
structure of PCP indicates an elegant interplay between the electronic effects of carbonyl
substitution of the conjugated polyene of peridinin7 and of the strained conformations imposed
on the peridinins by the binding sites in PCP.8
The states and mechanisms that mediate excitation transfer from peridinin to Chl a have been
investigated by several laboratories using femtosecond spectroscopy.2–5,9 The scheme that
emerges from this work involves two excitation transfer channels. The S2 (11Bu+) state of
peridinin is assigned a very short lifetime, ~50 fs, which limits the yield of an ultrafast excitation
transfer process involving it as the donor state. The nature of this process remains in question
because it has not yet been observed directly. The product of the nonradiative decay of the S2
state is usually identified as a vibrationally excited (or "hot") S1 (21Ag−) state species. During and
after vibrational cooling on the <1 ps timescale, the S1 state then serves as the donor state for a
2.5–3 ps excitation transfer channel involving the Förster mechanism10,11 that carries as much as
two-thirds of the overall yield. This part of the scheme is intriguing because the S1 state of
peridinin is known to be effectively a "dark" state, lacking very much oscillator strength for
transitions to and from the ground state, S0 (11Ag−).12,13 In addition, the low energy ICT state2,7,14

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arising from peridinin's carbonyl substituent that accompanies or is formed from the S1 state is
thought to have poor spectral overlap in PCP with the Qx or Qy transitions of the Chl a
acceptors,15 so its role as a donor state is questionable.

622

A

612

621

611

623

613
C602

624

B

C601

614

1

Absorbance

2
3
4

400

500

600

700

Wavelength (nm)

Figure 5.1 Peridinin and Chl a chromophores in the X-ray crystal structure of PCP from
Amphidinium carterae.6 (a) Space-filling rendering of the chromophore cluster from a single
subunit of PCP, with the peridinin (white) and Chl a (blue) chromophores numbered with residue
numbers from 1PPR.pdb. (b) Ground-state absorption spectrum for the S0 → S2 transition from
PCP at room temperature (22 °C), with the spectrum from the 520 nm (40 fs) laser excitation
pulses superimposed and marked with the wavelengths for the 0–0 vibronic transition for the
peridinin chromophores, as estimated in reference 16: 1, for peridinins 612 and 622; 2, for
peridinins 613 and 623; 3, for peridinins 611 and 621; and 4, for peridinins 614 and 624.
In an effort to resolve this paradox, we report in this contribution some new results from
femtosecond heterodyne transient grating studies that show that more than half of the optically

182

prepared S2 state population is quenched by excitation transfer to Chl a via an ultrafast process
that very likely involves mixed peridinin–Chl a exciton states and a quantum coherent
mechanism. Then, rather than involving the S1 state as a donor, the remaining minor fraction of
the excitation transfer yield is mediated by the FĂśrster mechanism and a conformationally
distorted form of the S2 state, Sx, which we identified in previous work on peridinin in polar
solution.17,18 The results indicate that dynamic localization of the optically prepared exciton
states accompanies the ultrafast conformational displacement that prepares the Sx state from the
Franck–Condon S2 state.

5.2 Experimental Methods
5.2.1 Sample Preparation.
PCP was isolated from Amphidinium carterae cells in the laboratory of Roger Hiller
(Macquarie University) according to previously published methods.19 For femtosecond
spectroscopic experiments, PCP samples were suspended in a buffer solution containing 50 mM
tricine-NaOH, 20 mM KCl, pH 7.5 to obtain an optical density of 0.3 for at the center of the laser
spectrum (520 nm) in a cuvette with a 1 mm optical path length.
5.2.2 Femtosecond Spectroscopy.
Transient grating signals were obtained at 22 °C as described in detail previously using a
250 kHz amplified Ti:sapphire laser and optical parametric amplifier (Coherent RegA 9040 and
OPA 9450) and a diffractive-optic based, passively phase stabilized, photon-echo spectrometer.20
Following the experimental procedures and theory outlined in our previous work on βcarotene and peridinin in polar solvents,17,18,20we characterized excitation transfer and
nonradiative decay processes in PCP complexes from Amphidinium carterae at room
183

temperature using a passively phase-stabilized, diffractive optic based spectrometer that employs
spectral interferometric detection. Pump and probe pulses (40 fs duration) were centered at 520
nm, halfway up the red onset of the peridinin ground state absorption band of PCP. As shown in
Figure 5.1b, this laser spectrum predominantly selects the S0 → S2 absorption transition of
peridinins in PCP; absorption by Chl a in this region of the spectrum is negligible.5 A similar
detuning relative to the absorption maximum was used in the previous work on peridinin in
several polar solvents in order to excite the 0–0 vibronic transition.18 In PCP, the four peridinins
in each domain have distinct site energies; the laser spectrum overlaps with the 0–0 regions for
three of the four peridinins (2–4 in Figure 1b).
Figure 5.2 shows contour representations of the spectrally resolved absorption and dispersion
components of the transient grating spectrum of PCP over the 0–500 fs probe delay range. The
transient grating spectrum's appearance and time evolution is quite similar to that observed from
peridinin in polar solvents under the same measurement conditions.17,18 Both components of the
signal are well described by a global target model (see the Appendix) defined by contributions
only from three spectrokinetic species in a sequential pathway (Scheme 5.1): the S2 state, which
decays in 18Âą4 fs; an intermediate, Sx, with a 1.6Âą0.1 ps lifetime, and the S1 state, which
recovers to the ground state, S0 (11Ag−), in 18.9±0.4 ps. Contributions to the signal from Chl a
are negligible in the probed region, so only peridinin species were included in the model. Also,
as noted previously,17,18 the probed bandwidth is not broad enough to detect the excited-state
absorption band near 600 nm that is observed from the S1/ICT state of peridinin in polar
solvents, so a generic compartment for the S1 state is also appropriate in the current model for
PCP. The Sx state is assigned to a distorted conformation of the S2 state, which is generated from
the Franck–Condon S2 state via displacements along torsional and/or other out-of-plane

184

(pyramidal) coordinates of the conjugated polyene backbone. The rationale for not assigning the
Sx species to a vibrationally excited S1 state was extensively discussed in previous work on the
bases of numerical simulations17 and the distinct solvent dependences of the Sx and S1 states.18

Figure 5.2 Contour representations of the heterodyne transient grating signal from peridinin at
room temperature (22 °C): (a) absorption component; (b) dispersion component. For the
absorption component, the yellow end of the color bar corresponds to net ground state bleaching
and/or stimulated emission; the dark blue end indicates excited state absorption. For the
dispersion component, the phasing of the color bar is consistent with that used for the absorption
component. At 525 nm, the yellow contours correspond to a net excited-state absorption signal.

185

Spectroscopic parameters for the three species that contribute to the transient grating
spectrum from PCP were then determined from numerical simulations of the ground state
absorption spectrum and of both components of the transient grating signal. The simulations
were performed using the response function formalism and the multimode Brownian oscillator
(MBO) model, as described previously,17,18,20 but excitation transfer pathways from S2 and Sx to
Chl a acceptors were added (Figure 5.3) to account for the quenching of peridinin excited states.
Excitation transfer processes between the peridinins are not included in the model, so the
parameters describe a population weighted average. The model parameters are tabulated in the
Appendix.
S2

k2x

k2C

Sx

kx1

S1

k10

S0

kxC

Chl a

Figure 5.3 Kinetic scheme for the radiationless decay and excitation transfer pathway in PCP, as
used in the numerical model (Figures 5.4 and A5.6–A5.7) for the heterodyne transient grating
signal (Figure 5.2).
Although the time evolution of the transient grating signals from peridinin in solution and in
PCP indicate the involvement of the same spectrokinetic intermediates, the numerical model for
PCP shows that the S2 and Sx states of peridinin are quenched due to excitation transfer to Chl a
but with time constants that are almost three orders of magnitude apart. Figure 5.4 compares with
absolute intensity scaling the absorption and dispersion components of the frequency integrated
transient grating signal from PCP with those of peridinin in 2-propanol. A direct comparison of
the signals from the two samples can be made because the tuning of the laser spectrum relative to
the absorption maximum, the pulse durations and energies, and the optical density at the center
of the laser spectrum are all well matched. The signal from peridinin in 2-propanol is used here
as an example because the Sx lifetime in 2-propanol is similar to that observed in PCP.18
186

Absorption
Dispersion

0

Population

0
0.3

0

0

0.5

1

10

Delay (ps)

Figure 5.4 Comparison of the absolute intensity and time evolution of the absorption and
dispersion components of the heterodyne transient grating signals from PCP (red) and from
peridinin in 2-propanol (blue), as plotted with respect to a linear–logarithmic time axis split at 1
ps. The plotted absorption and dispersion transients were obtained by integrating over the laser
frequency axis. The plotted data points for PCP are shown superimposed with fitted profiles
from the numerical model for the transient grating signal (Figures A5.6–A5.7), as obtained with
the radiationless decay and excitation transfer pathways shown in Scheme 5.1 and the MBO
model parameters reported in Tables A5.1–A5.2. The time profiles for peridinin in 2-propanol
were obtained from the global model reported in reference 18. The bottom panel plots the time
evolution of the populations in the S2 (red), Sx (blue), and S1 (green) states from the model for
the signal from PCP.
The reduced peak intensity for the transient grating signal from PCP in Figure 5.4 can be
explained only by quenching of the Franck–Condon S2 state via an ultrafast energy transfer
pathway to Chl a acceptors on a timescale comparable to the instrument response function's
width. From Scheme 5.1, the overall rate constant for the conversion of S2 to Sx obtained in the
global model is the sum of the rate constants for nonradiative decay to Sx and for excitation

187

transfer to Chl a, k 2 x + k 2c = (18 ± 4fs) −1 . A choice of 1 k 2c = 30 ± 4fs and 1 k 2 x = 45 ± 8fs for
the time constants for excitation transfer and nonradiative decay, respectively, accounts for the
reduced signal intensity in PCP. These time constants determine that 60% (+6%, −8%) of the
optically prepared peridinin S2 state is transferred to Chl a; in other words, the yield of the Sx
state in PCP is only about 40% (+8%, −6%) of that in peridinin solution. The intrinsic lifetime of
the S2 state in the absence of excitation transfer, 45 fs, is more than three times as long as that
estimated previously for peridinin in solution.18
Similarly, the decay of the transient grating signal in PCP over the 50 fs–5 ps range is
consistent with quenching of the Sx state by Chl a. As noted earlier, excitation transfer to Chl a
during this part of the response has been detected in previous studies to occur with a 2.5–3 ps
time constant; an exponentially rising Chl a GSB signal is detected at 670 nm in pump–probe
experiments with >100 fs pulses.2–4 From Figure 5.3, with k x1 + (k 2c ≡ (2.5ps) −1 ) = (1.6 ± 0.1ps) −1 ,
one obtains 1 k x1 = 4.4 Âą 0.9 ps. From the model for the transient grating signal (Figure 5.3), the
integrated yield of the Sx to Chl a excitation transfer process is 57%, which indicates an overall
quantum yield of 23% (+4%, −4%) starting from the 40% (+8%, −6%) yield of the Sx state.
The total quantum yield for excitation transfer from peridinin to Chl a obtained from the sum
of the yields from S2 and Sx is 83% (+10%, −12%). Although it should be regarded as a crude
estimate, this yield fully accounts for the 90% yield previously estimated from a comparison of
the absorption and fluorescence excitation spectra2–4 and does not involve the S1 state as an
excitation donor. The yield is probably somewhat underestimated owing to the use of relatively
long excitation pulses in the present experiments and the fast nonradiative decay and excitation
transfer processes that deactivate S2. Further, the long lifetime observed for the S1 state
compartment in the global model essentially rules out its being quenched by excitation transfer to

188

Chl a. No excitation transfer processes with time constants longer than 2.5 ps have been detected
in PCP, and the 18.9Âą0.4 ps lifetime determined in this work for S1 would require that the rate be
very slow indeed compared to that from Sx.
The slowing by almost three orders of magnitude of the excitation transfer rate that
accompanies nonradiative decay of S2 to Sx in PCP can be readily explained by a decrease in the
oscillator strength and a concomitant increase in the system–bath coupling or reorganization
energy upon formation of the Sx state. Both effects are caused by large-amplitude conformational
distortions of the conjugated polyene backbone of peridinin.
Figure 5.5 shows a schematic representation of the potential energy surfaces that account for
the time evolution of the third order signals from peridinin in solution and in PCP. The potential
energy curves describe a reaction coordinate for the structural displacements that follow optical
preparation of the S2 state of carotenoids, with displacements first along the resonance Ramanactive C–C/C=C bond stretching coordinates that determine the bond-length alternation of the
conjugated polyene backbone and then along torsional and other out-of-plane coordinates that
lead towards a convergence of the energies of the S2, S1, and S0 states at a conical
intersection.17,18,20,21Because optical excitations of peridinins in PCP occur from strained groundstate conformations,8 vertical transitions to the S2 state occur near to or perhaps even past the
transition state barrier that divides planar and twisted conformations. Immediate displacements
then occur along the bond-length alternation and torsional coordinates to yield the twisted
structures associated with the Sx state, and further evolution along the torsional gradient
promotes nonradiative decay to the S1 state.17,18 The excitations of peridinins in PCP are likely to
be analogous to those that occur in the red tail of the ground-state absorption spectrum of
peridinin in solution, which result upon formation of the S2 state in very large changes of the

189

permanent dipole moment,22,23 an enhanced ICT character,24–26 and a concomitant increase in the
system–bath coupling.17,18 The observation that formation of Sx and S1 in PCP is markedly
slower than for peridinin in solution indicates that the friction that retards the twisting or
pyramidalization of the conjugated polyene backbone of peridinin is apparently much stronger in
PCP. Further, using the observed power-law dependences of the Sx lifetime for peridinin in polar
solution, we estimated previously that the lifetime of Sx in PCP would be expected to fall in the
range from 1.4 to 5 ps.18 The intrinsic lifetime determined in the present work for Sx, 4.4 ps, is at
the top of this range. This finding shows that large-amplitude conformational distortions are
indeed involved in nonradiative decay for peridinins in PCP despite their being bound and
conformationally strained by their protein and chromophore-derived surroundings.

x1Ag−

planar

twisted

Sn

Potential Energy

11Bu+

S2
1

2 Ag

−

S1

11Ag−

S0

trans

‡

φ = 90°

cis

Reaction Coordinate

Figure 5.5 Schematic potential energy curves for peridinin in the PCP complex based on those
suggested in previous work for peridinin in solution.17,18,20,21 The potentials are plotted with
respect to a split reaction coordinate that describes the structural displacements along bondlength alternation and torsional (ϕ) coordinates; a low barrier (‡) divides planar and twisted
structures. The dashed segments show the profiles for peridinin in solution.
190

The 30 fs excitation transfer process that occurs from the S2 state is consistent with a
quantum coherent27 mechanism involving peridinin-Chl a exciton states. In this hypothesis, the
electronic interaction between peridinins and between peridinins and Chl a initially lies in the
intermediate to strong coupling regime, in which the electronic coupling strengths determined by
the oscillator strengths, 𝐽, are larger than the system–bath reorganization energies, 𝜆.28 That a
manifold of exciton states actually exists in the PCP system rather than just a set of isolated
(weak coupling regime) peridinin or Chl states has been repeatedly argued in analyses of the
circular dichroism spectrum.29–32 Downward transfer of population in this manifold of exciton
states is a non-FĂśrster type of excitation transfer; the excited state probability density moves
predominantly from peridinin to Chl as nonradiative relaxation occurs to the lowest energy
states. Analogous exciton relaxation processes and very similar timescales have been previously
identified in systems falling in the intermediate to strong electronic coupling regime, such as in
allophycocyanin trimer complexes,33–35 LH1,36 and in diacetylene-bridged perylenediimide
dimer.37
Note that the 30 fs excitation transfer process accounts for the well documented but
otherwise unexplained finding that the Qy transition from Chl a in PCP is instantaneously
bleached in pump-probe spectra.2,3,5 As an example, the initial spectrum obtained from a global
model for the time evolution of the pump–probe spectrum of PCP by van Stokkum et al.5
includes a Chl a bleaching or stimulated emission lineshape at 670 nm riding on a much broader
excited-state absorption band from the peridinin S2 state. It accounts for about 70% of the final
Chl a signal intensity; the FĂśrster 2.5 ps excitation process accounts for an increase of 30%.
Considering that the excitation pulses were not short enough to resolve the ultrafast and FĂśrster
excitation transfer processes, the 70/30 ratio for the instantaneous and final intensities for the Chl

191

a signal is fully consistent with our estimate that two-thirds of the excitation transfer yield comes
from the exciton states that are initially populated optically.
Effectively competing with the 30 fs exciton relaxation process, however, is the prompt
conformational distortion of the peridinins that produces the Sx state and subsequent twisted S2
structures. As the conjugated polyene backbone is distorted, the J couplings between peridinins
and between peridinins and Chl a will decrease rapidly because the oscillator strength drops as
the bright S2 state is increasingly mixed with the dark S1 state.8 At the same time, the
reorganization energies λ increase markedly owing to the additional ICT character and systembath coupling that develops as the conjugated polyene backbone twists.18,38–40 This combination
of decreasing J and increasing Îť esults in dynamic exciton localization, an irreversible collapse
of the initially delocalized excited state wavefunctions onto single chromophores.11,28,33,35,41,42
This process initiates the slower excitation transfer process from the Sx state of peridinin to Chl a
acceptors via the FĂśrster mechanism.
Thus, the enhanced excitation transfer yield obtained by peridinin in PCP compared to other
carotenoid-containing light-harvesting complexes is correctly attributed to the carbonyl
substituent, but the mechanism for this enhancement is evidently quite different from that
envisioned in prior work in which the S1 state was implicated as a donor state. The results
indicate that the lifetime of the Sx state controls the minor fraction of the yield of excitation
transfer to Chl a acceptors involving the FĂśrster mechanism. Because the lifetime of the Sx state
for carotenoids lacking carbonyl substitution is usually more than an order of magnitude shorter
than observed in peridinin,18 the excitation transfer yield involving Sx as a donor would be
expected to be limited. This is apparently the situation in the LH2 complex, where a distorted S2
state structure serves as an excitation donor to bacteriochlorophyll a.43 The residual fraction of

192

peridinin excited states that decay nonradiatively to the S1 state in PCP may actually play a role
in a nonphotochemical quenching mechanism, as suggested early on by Bautista et al,7 especially
given that the S1 state is accompanied by a red shifted ICT state that has a poor FĂśrster overlap
with Chl a acceptors.15 A great deal of control over the overall excitation transfer yield is
accordingly possible in the PCP complex in vivo through protein conformational changes,
especially those that alter the solvent exposure and binding sites for the peridinin chromophores
when it is associated as a trimeric complex to the thylakoid membrane.

193

APPENDIX

194

APPENDIX

A5.1 Global and Target Analysis
Heterodyne transient grating signals from PCP were obtained at room temperature with 40 fs
excitation pulses centered around 520 nm; the tuning of the OPA is shown in Figure 5.1b.
Fourier transform spectral interferometry44 was employed to separate out the absorption (real)
and dispersion (imaginary) components of the transient grating signal. A global target analysis45
using the Glotaran and TIMP programs46,47 was then employed to fit both components of the
transient grating signal to a sequential decay model involving contributions from three
spectrokinetic species in a sequential pathway (Scheme 5.1): the S2 state, which decays in
18Âą4 fs, an intermediate, Sx, with a 1.6Âą0.1 ps lifetime; and the S1 state, which recovers to the
ground state, S0 (11Ag−), in 18.9±0.4 ps. A preliminary singular value decomposition (SVD)
analysis indicated the contributions of only three spectrokinetic components. Note that only a
generic compartment is included for the S1 state; the probe bandwidth available in these
experiments is not broad enough to probe the broad excited-state absorption spectrum that is
observed from the ICT state of peridinin near 600 nm.2,7 The lifetimes for each of the states in
the model were as determined from the global target analysis, which gives confidence intervals
that are consistent with analyses of multiple runs. As noted previously,17 the lifetime of the S2
state is determined with considerable indeterminacy in these experiments due to the use of 40 fs
excitation pulses. We found, as in the previous work on β-carotene20 and peridinin,17,18 that a
better estimate of the S2 lifetime was obtained from the rise time of the dispersion signal and
through numerical simulations of both components of the transient grating spectrum.

195

The spectral time evolution in the global model is described by the evolution-associated
spectra (EAS), which are shown in Figures A5.2 and A5.3. The spectral line shapes of the three
spectrokinetic species are quite similar to those for peridinin solution, which were described
previously.17,18

Population

0.8

0.6

0.4

0.2

0
0

1

10

Time (ps)

Figure A5.1. Time evolution of the populations for the three species in a global analysis of the
heterodyne transient grating signal (Figure 5.2) from PCP over the −100 fs–12 ps delay range, as
plotted against a linear–logarithmic time axis split at 1 ps: black: instantaneously formed species,
18 fs decay; red: first intermediate species, 18 fs rise, 1.6 ps decay; blue: second intermediate
species in the absorption component, 1.6 ps rise, 18.9 ps decay back to the ground state.

196

0.3

EAS

0.2
0.1
0

1.0

normEAS

0.5
0
−0.5
−1.0
510

520

530

540

Wavelength (nm)

Figure A5.2 EAS from a global analysis of the absorption component of the heterodyne transient
grating signal (Figure 5.2) from PCP over the −100 fs–12 ps delay range. The EAS assume a
sequential pathway from the optically prepared S2 state (black) through two intermediates (red,
then blue) back to the ground state.
0.2

EAS

0.1

0

−0.1

normEAS

1.0

0.5

0

−0.5
510

520

530

540

Wavelength (nm)

Figure A5.3 Evolution associated spectra (EAS) from a global analysis of the dispersion
component of the heterodyne transient-grating signal (Figure 5.2) from PCP over the −100 fs–12
ps delay range. The EAS assume a sequential pathway from the optically prepared S2 state
(black) through two intermediates (red, then blue) back to the ground state.
197

A 5.2 Numerical Simulation
We simulated the experimental absorption spectrum and heterodyne transient grating signals
from PCP using nonlinear response function theory and the multimode Brownian oscillator
(MBO) model.48 The protocol we followed is exactly as used previously for the simulations of
the signals from β–carotene and peridinin in methanol.17,20
Figure A5.4 shows the energy level scheme for the excited state nonradiative decay of
peridinin, as used previously.17,18 The vertical transition energies and the dipole strengths
associated with the transitions are listed in Table A5.1.

ΔS2

Sn2

ΔSx

ΔS1

Energy

Snx
Sn1
S2

ΔS0

Sx
S1

S0

Figure A5.4 Schematic energy-level diagram for peridinin. Solid green arrows indicate ground
state and excited-state absorption transitions. Blue wavy arrows mark internal conversion
transitions. Double-headed arrows show the detuning (∆) between the center of the laser
spectrum and the vertical energy of an electronic transition.

198

Table A5.1 Transition frequencies ( ω ij ) and relative transition dipole strengths ( µ ij ) used in the
simulation of the transient-grating signal from PCP.
Transition

ω ij (cm−1)

Âľ ij (Debye)

!S0 → S2

21200

1

!S2 → Sn2

14800

0.35

!S x → Snx

17750

1.3

!S1 → Sn1

18500

1.23

Table A5.2 MBO model parametersa for the simulation of the peridinin S0→S2 absorption
spectrum of peridinin in PCP at 295 K (Figure A5.5).
Mode

λ (cm−1)	

τ 	(fs)

ω υ (cm−1)	

Gaussian

800

10

—

Exponential 1

700

150

—

Exponential 2

1000

20000

—

Vibration 1

460

2200

1150

Vibration 2

1060

2200

1520

For each mode, λ is the reorganization energy and τ denotes the damping time constant; ω υ is the
frequency for a vibrational mode.
a

199

Absorbance

350

400

450

500
550
600
Wavelength (nm)

650

700

Figure A5.5 Comparison of the room temperature S0→S2 absorption spectrum PCP (dark blue
curve) with a simulation (red dash-dotted curve) of the peridinin spectrum obtained using the
MBO model and the parameters listed in Table A5.1-A5.2.
Figures A5.6 and A5.7 show the simulated absorption and dispersion components of the
transient grating signal from peridinin in PCP. In the optimized model, the excited-state
absorption (ESA) transition energy from the Sx state in PCP (Figure A5.4) is shifted to the blue
by 450 cm−1 compared to that for peridinin in methanol. Additionally, the vertical transition
energy for the S1 state was adjusted (blue-shifted by 1110 cm−1) to obtain a comparable fit of the
absorption and dispersion transient grating signals at long delay times. The transition dipole
strengths for the ESA transitions from Sx and S1 were also slightly smaller than determined in the
simulations of the signal from peridinin in methanol. This finding is consistent with
photoselection of distorted ground state conformers in PCP.

200

Figure A5.6. Numerical simulation of the absorption component of the transient grating signal
from PCP.	The parameters used in the calculation are listed in Tables A5.1 and Table A5.2.

Figure A5.7. Numerical simulation of the dispersion component of the transient grating signal
from PCP. The parameters used in the calculation are listed in Tables A5.1 and A5.2 and in the
text.
These signals were integrated across the emission (signal) spectrum to obtain the time
profiles plotted in Figure 5.4. The kinetic scheme used in the model was as used previously for
β-carotene and peridinin in solution but with the addition of two channels of energy transfer from

201

S2 and Sx, as shown in Scheme 5.1. The overall lifetimes for S2, Sx, and S1 were as obtained from
the global model. The intrinsic lifetime of S2, 1 k 2 x , and the energy transfer time constant 1 k 2c
were varied while maintaining the overall 18 fs decay time constant determined by the global
model to match of the integrated intensity of the absorption and dispersion components with
those from the global model for peridinin in 2-propanol,18 as plotted in Figure 5.4. A 2.5 ps time
constant was assumed for 1 k xc , so a 4.4 ps intrinsic lifetime was chosen for 1 k x1 to maintain
the overall lifetime for Sx, 1.6 ps, as determined by the global model.

202

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206

Chapter 6: Conclusions and Future Directions

In this dissertation, the mechanisms of nonradiative decay and excitation energy transfer by
carotenoids were investigated using femtosecond heterodyne transient grating spectroscopy. The
specific goal was to determine the role of intermediate electronic states and conformational
motions in the mechanisms that mediate carotenoid to chlorophyll energy transfer. The
experimental findings were corroborated by numerical simulations using nonlinear response
function formalism and the multimode Brownian oscillator model.
The controversy regarding the possible presence of an intermediate electronic state (Sx)
mediating the S2–S1 nonradiative decay pathway of carotenoids was addressed. In β-carotene, the
ultrafast rise of the dispersion signal and detection of different ground state recovery timescales
observed in the absorption and dispersion channels have provided direct evidence for the
formation of conformationally distorted intermediates. The dark intermediate labelled Sx in
previous work is assigned to a torsionally distorted structure evolving on the S2 (11Bu+) potential
surface. These findings were extended to studies of peridinin. Nonradiative decay of the Sx state
in peridinin is hindered by solvent friction owing to the development of an ICT character. This
work identifies the role of torsional dynamics of the conjugated backbone in promoting
nonradiative decay and ICT character in carotenoids. In the peridinin–chlorophyll a protein, the
torsional evolution on the S2 state is accompanied by the formation of ICT character and
dynamic exciton localization, which controls the mechanism of excitation energy transfer to
chlorophyll a acceptors.
The results presented in this thesis have raised several important questions that need further
investigation. In our work on the peridinin–chlorophyll a protein, we found that the S2 to Chl a

207

pathway accounts for a significant fraction of the quantum yield for energy transfer. This
pathway, however, has never been observed directly due to the very short lifetime of the S2 state.
The present work suggests that the lifetime of the S2 state of peridinin in methanol is only 12 fs,
which is much shorter than the previously estimated value of 50 fs.1,2 The near instantaneous rise
of the bleaching signal from the Qx state of Chl a observed upon excitation of peridinin
chromophores led Zigmantas et al.2 led us to propose that a coherent energy transfer process is
responsible for the majority of the energy transfer yield. The ultrafast timescale of energy
transfer from the S2 state (<30 fs) in our work also points to this mechanism.
In future work, broadband two-dimensional electronic spectroscopy could be employed to
determine if coherent energy transfer is involved in PCP. An incoherent FĂśrster type downhill
energy transfer process manifests itself as a single cross peak in the two-dimensional electronic
spectrum, whereas coherent energy transfer would be manifested as cross peaks above and below
the diagonal.3,4 These cross peaks would be expected to oscillate at frequencies corresponding to
the strength of the electronic interaction between the donor and acceptor.5–7
Our finding that out-of-plane torsional motions promote nonradiative decay and formation of
an intramolecular charge transfer character in carotenoids may have important implications in
understanding the photoactivation and nonphotochemical quenching mechanism in the orange
carotenoid protein (OCP) from cyanobacteria.8–13 The OCP employs a carbonyl-substituted
carotenoid, 3'-hydroxyechinenone14,15 or canthaxanthin as a sensor for incident light levels and as
a quencher of bilin excited states in the phycobilisome. The NPQ mechanism involving the OCP
works under high light conditions by switching from a dark, orange state (OCPO) to an active,
red state (OCPR); binding of OCPR to the phycobilisome results in a reduction of the rate of
excitation energy transfer to the PSII reaction center.16 How the carotenoid in OCPO senses

208

ambient light levels with its strong absorption feature to the S2 state and then decays
nonradiatively to trigger the photoactivation response is not yet understood. It has been proposed
that an ICT state serves as a low lying quenching electronic state that is crucial to the
photoprotection function.17,18 It is reasonable to suggest, however, that OCPO undergoes a
nonradiative decay pathway after optical excitation starting from a twisted S2 structure having
some of the properties suggested for the Sx or X states in the potential-energy scheme as
discussed in the previous chapters. The key event would be the relaxation pathway from the S1
state to the ground state, S0, and the preparation of a conformationally displaced protein
structure. Whether or not a photoactivation reaction trajectory is launched or not would be
determined by which side of the twisted (ϕ=π/2) S0 maximum that the system lands upon
nonradiative decay. Most of the time, the system would be expected to relax by returning to the
originally photoselected ground state. A minor fraction of events, however, would involve
relaxation to an alternate ground-state conformation, which would begin the process of
photoactivation. These ideas could also be explored using transient grating spectroscopy or twodimensional electronic spectroscopy.
To conclude, the work presented in this dissertation has definitively established the role of
conformational dynamics and intermediate electronic states in the photosynthetic light harvesting
function of carotenoids. The new picture of carotenoid photophysics that has emerged from this
work is likely to be useful in understanding the photoprotection mechanism of carotenoids. The
new insights about light harvesting obtained from this work will provide the necessary guiding
principles for designing an efficient chromophore for mid-visible solar harvesting.

209

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