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dissertation entitled

VIBRATIONAL COHERENCE IN ZINC PORPHYRINS IN
POLAR SOLUTIONS AND IN PROTEINS: VAN DER WAALS
INTERACTIONS WITH SURROUNDING GROUPS IN THE
FIRST SOLVATION SHELL

presented by

Kevin Lawrence Dillman

has been accepted towards fulﬁllment
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Ph.D. degree in Chemistry

 

 

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VIBRATIONAL COHERENCE IN ZINC PORPHYRINS IN
POLAR SOLUTIONS AND IN PROTEINS: VAN DER WAALS
INTERACTIONS WITH SURROUNDING GROUPS IN THE
FIRST SOLVATION SHELL

By

Kevin Lawrence Dillman

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Chemistry

2009

ABSTRACT

VIBRATIONAL COHERENCE IN ZINC PORPHYRIN S IN
POLAR SOLUTIONS AND IN PROTEINS: VAN DER WAALS
INTERACTIONS WITH SURROUNDING GROUPS IN THE
FIRST SOLVATION SHELL

By

Kevin Lawrence Dillman

We have employed femtosecond dynamic-absorption spectroscopy to monitor the
low-frequency vibrational coherence from ZnII tetralds(N-methylpyridyl)porphyrin
(ZnTMPyP) in polar solutions and ZnH-substituted cytochrome c (ZnCytc). The
ground-state vibrational coherence from ZnTMPyP is dominated by rapidly damped
components whose intensities are perhaps an order of magnitude stronger than the
more slowly damped components that arise from the skeletal normal modes of the
porphyrin macrocycle. The mean frequencies of the rapidly damped features exhibit
a solvent-dependent shift. The shift is consistent with a van der Waals potential dom-
inated by London-dispersion interactions. In the excited-state vibrational coherence,
these components exhibit an increase in frequency that suggests the potential is al-
tered by the presence of charges. These components are assigned to intermolecular
vibrational modes between the porphyrin and clustered, ﬁrst-shell solvent molecules.
The vibrational coherence from ZnCytc in the native state is exhibits similar behav-
ior. Low-frequency metal-doming modes contribute ~10 and ~30 cm‘l oscillatory
features, but the strongest component in the vibrational coherence is a very rapidly
damped (damping time y<150 fs) contribution centered at 79 cm‘l. This feature

is assigned to van der Waals interactions between the porphyrin chromophore and

nearby nonpolar amino-acid residues in the surrounding protein medium. The vibra-
tional coherence from the molten-globule state of ZnCytc does not exhibit the rapidly
damped feature. Its resonance Raman activity is effectively quenched owing to ex-
pansion of the hydrophobic core and randomization of the surrounding structure.
The results strongly suggest that the van der Waals modes gain resonance Raman ac-
tivity through a direct attack of the solvent or neighboring groups on the Tr-electron
density of the porphyrin chromophore. These findings provide the first structural ac-
counting for the rate-controlling, low-frequency vibrational motions that are coupled

to the electron-transfer reactions in photosynthesis.

ACKNOWLEDGMENTS

The research presented in this dissertation could not have been performed with-
out the support of many other individuals. First and foremost is that of my advisor,
Professor Warren Beck. I thank him for his invaluable guidance and his mentorship.
Without him and the effort he has put into teaching me, this work would have been
impossible. I thank my committee members, Professor Marcos Dantus, Professor
James McCusker and Professor Lynmarie Posey for their time and input.

I thank Dr. Kathrine Shelly and Dr. Sanela Lampa-Pastirk for their patience and
instruction. They taught me almost everything I know about how to perform fem-
tosecond spectroscopy. I also thank my fellow graduate student Jagnyaseni Tripathi.
Her curiosity and questions have led me to a better understanding of my own work.
I have been fortunate to work with several talented undergraduate students, and I
particularly wish to acknowledge Kenneth Barnes, Aaron Dame and Steven Miller.

I must also thank my entire family, who have provided me with endless encour-
agement. Speciﬁcally, I must thank my parents, Tom and Ellen Dillman, who have
always been there to support me, and my brother, Peter, for his excellent friendship.

I thank the Department of Chemistry at Michigan State University for a Teach-
ing Assistantship (2005-2009). This research was supported by the National Sci-
ence Foundation Biomolecular Systems Cluster/Molecular Biophysics program un-
der grants MCB-009120 and MCB-OSZOOOZ. Additional support for instrumentation
was provided by the Michigan Structural Biology Center at Michigan State University,

which is supported by the Michigan Life Sciences Corridor.

iv

TABLE OF CONTENTS

LIST OF TABLES vii
LIST OF FIGURES viii
LIST OF ABBREVIATIONS xii
1 Introduction 1
2 Vibrational Coherence and Photosynthetic Electron Transfer 4
2.1 Electron Transfer in Photosynthesis ....................... 5
2.2 Vibrational Coherence and Wavepackets .................... 9
2.3 Dynamic-Absorption Spectroscopy ........................ 1 1
2.4 Vibrational Coherence in the Purple-Bacterial Photosynthetic Reaction
Center ......................................... 14
2.5 Vibrational Coherence from Myoglobin and Cytochrome c ......... 19

2.6 Vibraﬂ'onal Coherence in Bacteriochlorophyll Solutions and Proteins . . 25
2.6.1 Vibrational Coherence in Bacteriochlorophyll a in Polar solution . 25

2.6.2 Intermolecular Vibrational Coherence From B777 and B820 . . . . 30
2.7 Proposed Experiments ............................... 32
3 Ground-state vibrational coherence in polar solutions of Zn“ tetrakis(N-
methylpyridyl)porphyrin with Soret-band excitation 38
3.1 Summary ........................................ 38
3.2 Introduction ...................................... 39
3.3 Experimental ..................................... 44
3.3.1 Sample Preparation ............................. 44
3.3.2 Continuous-Wave Absorption and Fluorescence Spectroscopy . . 44
3.3.3 Femtosecond Spectroscopy ........................ 45
3.4 Results ......................................... 49
3.5 Discussion ....................................... 68
3.5.1 Conclusions .................................. 81

4 Excited-state vibrational coherence in methanol solution of Zn“ tetrakis(N-

methylpyridyl)porphyrin 83
4.1 Summary ........................................ 83
4.2 Introduction ...................................... 84
4.3 Experimental ..................................... 87

4.3.1 Sample Preparation ............................. 87

4.3.2 Continuous-Wave Absorption and Fluorescence Spectroscopy . . 87

4.3.3 Femtosecond spectroscopy ........................ 88
4.4 Results ......................................... 89
4.5 Discussion ....................................... 97

4.5.1 Conclusions .................................. 101

5 Vibrational coherence in the native and molten-globule states of Zn“-

substituted cytochrome c 105
5.1 Summary ........................................ 105
5.2 Introduction ...................................... 106
5.3 Experimental ..................................... 108
5.3.1 Sample Preparation ............................. 108
5.3.2 Continuous-Wave Absorption and Fluorescence spectroscopy . . 1 1 1
5.3.3 Femtosecond Spectroscopy ........................ 1 1 1
5.4 Results ......................................... 1 12
5.5 Discussion ....................................... 1 1 7
5.5.1 Conclusions .................................. 129
BIBLIOGRAPHY 131

3.1

3.2

3.3

3.4

3.5

4.1

4.2

4.3

5.1

5.2

LIST OF TABLES

Model parameters for the exponential decays in the pump—probe tran-
sients in ZnTMPyP solutions at 22 °C. .....................

Solvent dependence of the asymmetric Gaussian lineshape parameters
for the rapidly damped components observed in the vibrational coher-
ence from ZnTMPyP. ................................

Gaussian lineshape parameters for the slowly damped modulation com-
ponents observed in ZnTMPyP pump—probe transients. ..........

Comparison of Gaussian linewidths and effective exponential damping
times for the modulation components observed in the vibrational co-
herence from ZnTMPyP in CH3 OH. .......................

Parameters for the model ZnTMPyP-CH3OH intermolecular potentials
shown in Figure 3.12 ................................

Gaussian lineshape parameters for the slowly damped modulation
components obtained from the 62 5-nm pump—probe transient from
ZnTMPyP in methanol (see Figure 4.2). .....................

Gaussian lineshape parameters and effective exponential damping
times for the rapidly damped modulation components obtained from
the 625-nm pump—probe transient of ZnTMPyP in methanol (see Fig-
ure 4.2). ........................................

Parameters for ZnTMPyP—CH3OH intermolecular potentials (see Fig-
ure 4.4) ........................................

Gaussian lineshape parameters for the modulation components ob-
tained from the pump-probe transient of ZnCytc in the native state (see
Figure 5.3). ......................................

Gaussian lineshape parameters for the modulation components ob-
tained from the pump—probe transient of ZnCytc in the molten-globule
state (see Figure 5.4). ................................

77

94

120

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

2.10

2.11

2.12

2.13

2.14

LIST OF FIGURES

Temperature dependence of the primary electron transfer rate constant
in the reaction center of Blastochloris viridis. ................. 6

Driving force A130 and reorganization energy An for a model pair of
non-adiabatic potential energy surfaces, Ea and E b .............. 8

Excited-state and ground-state coherent wavepacket motion in the
dynamic-absorption experiment .......................... 10

Femtosecond dynamic-absorption transients of bacteriorhodopsin. . . . 12

Fourier-transform spectra and model calculations of the oscillatory part
of the pump-probe transients obtained from bacteriorhodopsin ...... 13

Dynamic-absorption transient from the reaction centers of Rhodobacter
sphaeroides R-26 at 100 K. ............................. 1 5

Dynamic-absorption transients at various temperatures of reaction cen—
ters of Rhodobacter sphaeroides R-26 at 100 K, 10 K, and 293 K. ..... 16

Fourier-transform spectra of the oscillatory parts of the pump-probe
signals of the dynamic absorption transients of Rhodobacter sphaeroides. 18

Open band femtosecond dynamic-absorption spectroscopy measure-
ments on MbNO samples. ............................. 22

Sequence of dynamic-absorption transients using the open band detec-

tion scheme on FeCytc ................................ 23
Femtosecond dynamic-absorption transients of deoxyMb. ......... 24
Dynamic-absorption transient from BChl a in pyridine ............ 26

Model of the rapidly damped vibrational coherence observed in BChl or
solutions as a distribution of damped cosinusoids, £(w). ......... 27

Solvent dependence of the mean frequency (w) of the rapidly damped
vibrational coherence observed in BChl a solutions in a range of polar
solvents on the solvent dipole moment. .................... 28

f .

2.15

2.16

2.17

2.18

3.1

3.2

3.3

3.4

3.5

3.6

3.7

The Hu and Schulten model for the B820 subunit in LH1 from Rhodobac-
ter sphaeroides, showing the pair of BChl macrocycles and the trans-
membrane or helices in ribbon and surface renderings. ........... 31

Expanded view of the rapidly damped oscillation observed in the
dynamic-absorption transient from BChl a in acetone. ........... 33

Expanded view of the rapidly damped oscillation observed in the
dynamic-absorption transient from B777. ................... 34

Expanded View of the rapidly damped oscillation observed in the
dynamic-absorption transient from B820. ................... 3 5

Optimized structure of ZnII meso—tetrakis(N-methylpyridyl)porphyrin
(ZnTMPyP) complexed with a single methanol molecule as an axial lig-
and to the Zn11 ion. ................................. 43

Femtosecond pump-probe spectrometer, consisting of a prism-pair
pulse compressor (PC), second-harmonic generator (SHG), and a mod-
ified Mach-Zehnder interferometer. ....................... 46

Soret (v > 20000 cm‘l) and Q-band region of the continuous-wave
absorption (solid curve) and ﬂuorescence (dotted curve) spectra from
ZnTMPyP in CH3OH at room temperature (23 °C), plotted as the dipole
strength, A/v and F/v3, respectively, and normalized to unit area with
respect to the ﬂuorescence spectrum and Q band ............... 50

Soret-band absorption absorption dipole-strength (A / v) spectra from
ZnTMPyP in (a) CH30H, (b) DMF, (c) CH3 CN, and (d) DMSO. ........ 5 1

Femtosecond pump—probe dynamic-absorption transients detected at
422 nm (0.5-nm bandpass) with ZnTMPyP solutions in (a) CH3OH, (b)
CD30D, (c) DMF, (d) CH3CN, and (e) DMSO. .................. 53

Oscillatory signals obtained from the pump—probe transients from
ZnTMPyP solutions (see Figure 3.5) as the difference between the nor-
malized signal and the ﬁtted exponential decay functions: in (a) CH30H,
(b) CD30D, (c) DMF, (d) CH3CN, and (e) DMSO. ................ 55

Fourier transform magnitude spectra from the oscillatory residuals (see
Figure 3.6) of the pump-probe signals from ZnTMPyP solutions in (a)
CH30H, (b) CD30D, (c) DMF, (d) CH3CN, and (e) DMSO. ........... 59

3.8

3.9

3.10

3.11

3.12

4.1

4.2

4.3

4.4

5.1

Comparison of the Gaussian waveforms (thick curves) obtained for the
3, 38, and 215-cm‘1 components in the oscillatory signals observed
from ZnTMPyP in CH30H solution with fitted exponentially damped
waveforms (thin curves, see Equation 3.4) .................... 64

Frequency domain representation of the time-domain models of the os-
cillatory signals (see Figure 3.6) observed in ZnTMPyP solution: in (a)
CH30H, (b) CD30D, (c) DMF, (d) CH3CN, and (e) DMSO. ........... 65

Time-domain representation of the rapidly damped oscillatory compo-
nents (see Figures 3.6 and 3.9) in the pump-probe signals from ZnTMPyP
solutions in (a) CH30H, (b) CD30D, (c) DMF, (d) CH3CN, and (e) DMSO. . 66

Dependence of the mean frequency of the rapidly damped oscillatory
components (see Figures 3.6 and 3.9) observed in the pump-probe sig-
nals from ZnTMPyP solutions in CH30H, DMF, CH3 CN, and DMSO. . . . . 69

Model potential-energy curves for the ZnTMPyP-CH3OH complex calcu-
lated using Equation 3.1 1 and the experimentally observed mean inter-
molecular mode frequency, 79 cm‘1 (see Table 3.2): (a) Q = 0; (b) Q = 1;
and (c) the attractive, charge-dependent terms for Q = 1. ......... 76

Soret (v>20000 cm‘l) and Q-band region of the continuous-wave ab-
sorption (solid curve) and ﬂuorescence (dotted curve) spectra from
ZnTMPyP in methanol at room temperature (23 °C), plotted as the dipole
strength, A(v)/v and F(v)/v3, respectively, and normalized to unit

area for the ﬂuorescence spectrum and Q band. ............... 90
Femtosecond pump—probe dynamic absorption transient detected at
632 nm (4-nm bandpass) with ZnTMPyP in methanol. ............ 91

Comparison of the intensities and lineshapes observed in the excited-
state and ground-state vibrational coherence from ZnTMPyP in methanol. 93

Model potential-energy curves for the ZnTMPyP-CH30H van der Waals
complex as a function of the charge Q on the ZnTMPyP moiety: (a) Q =
0; (b) Q = 1; (c) the attractive, charge-dependent terms for Q = 1;
((1) Q = 2 and (e) the attractive, charge-dependent terms for Q = 2. . . . 102

Ribbon (left) and surface (right) renderings of the X-ray crystal structure
of horse-heart ferricytochrome c (1hrc.pdb) ................... 110

5.2

5.3

5.4

5.5

5.6

Soret (v> 23000 cm’l) and Q-band regions of the continuous-wave ab-
sorption spectrum of ZnCytc in the native (solid curves) and molten-
globule (circles) states. ............................... 1 13

Soret-band (420-nm) pump—probe transient from the native state of Zn-
Cytc. .......................................... 1 1 5

Soret-band (420-nm) pump—probe transient from the molten-globule
state of ZnCytc. The signal points (circles) are superimposed on a model
consisting of the sum of an exponential decay and two oscillatory com—
ponents. ........................................ 1 16

Frequency-domain representations of oscillatory components of the fit-
ted models of the vibrational coherence obtained from the (a) native
state and (b) molten globule state of ZnCytc. ................. 118
Detail of the X-ray crystal structure of ferricytochrome c (1hrc.pdb) ex-
amining possible interactions of the protein with the n-electron density
of the porphyrin .................................... 126

LIST OF ABBREVIATIONS

B777, monomeric subunit protein of B820
B820, dimeric subunit protein of the LH1 light-harvesting complex

BChl, bacteriochlorophyll

BPheL, primary electron acceptor in the photosynthetic reaction center

CD3 OD, perdeuturated methanol
CH3 OH, methanol

CH3 CN, acetonitrile

DMF, N,N-dimethylformamide
DMSO, dimethylsulfoxide

ESA, excited-state absorption
FeCytc, FeIII cytochrome c

fwhm, full width at half maximum
K, lysene

Mb, myoglobin

N, asparagine

P, primary electron donor in the photosynthetic reaction center
PB, photobleaching

Qa, primary quinone electron acceptor in the photosynthetic
ter

reaction cen-

Qb, secondary quinone electron acceptor in the photosynthetic reaction cen-
ter

RISRS, resonant impulsive stimulated Raman scattering
SE, stimulated emission

T, threonine

W, tryptophan

Y, tyrosene

ZnCytc, ZnII cytochrome c

ZnTMPyP, ZnII mesatetrakis(N-methylpyridyl)porphyrin

ZnT'PP, ZnII tetraphenylporphyrin

CHAPTER 1

Introduction

The electron-transfer reactions in the purple-bacterial photosynthetic reaction center
are nearly barrierless.l Low-frequency vibrational modes that couple to the reaction
account for the majority of the reorganization energy that matches the driving force
in the Marcus theory for condensed-phase electron-transfer ratesz‘4 and contribute
to the barrierless reaction kinetics. The structural origin of these modes has not
been previously determined. This dissertation provides the first detailed structural
accounting for the vibrational motions that are coupled to the electron-transfer re-
actions in photosynthesis. The findings suggest that the relevant vibrational modes
are intermolecular in nature. They arise from van der Waals interactions between the
chromophore and nearby amino-acid residues in the surrounding protein medium.

This dissertation is organized as follows:

Chapter 2 introduces some of the previous contributions that have led to the prin-
cipal work covered in this dissertation. We brieﬂy cover the nature of the electron-
transfer reactions in the photosynthetic reaction center, and we discuss the nature
of the dynamic-absorption experiment. We examine the results of some of the early
vibrational coherence measurements on the reaction center and the results of simi-

lar experiments on myoglobin and cytochrome c. We finish by discussing previous

work from this laboratory. Femtosecond dynamic-absorption spectroscopy on bacte-
riochlorophyll (BChl) in polar solution, and on the light—harvesting subunit proteins
B777 and 8820 reveal that the low-frequency vibrational coherence is dominated by
rapidly damped components that are assigned to intermolecular vibrational modes.
These modes exhibit a dependence on the dipole moment of the solvent. These re-
sults inspire the experiments discussed in the subsequent chapters.

In Chapter 3, we examine the origin of the rapidly damped vibrational coherence
from ZnII tetrakis(N-methylpyridyl)porphyrin (ZnTMPyP) with Soret-band excitation.
ZnTMPyP has a high degree of symmetry, so it has a much smaller dipole moment
than BChl. We discuss the effect this should have on the rapidly damped mode. We
discuss how the dependence of the mean frequency of the intermolecular mode on
the solvent dipole moment is consistent with a van der Waals intermolecular poten-
tial with the strongest terms coming from London-dispersion interactions. We show
evidence of a isotope-dependent shift in the frequency of the intermolecular mode
from methanol and perdeuturated methanol. We conclude that the rapidly damped
vibrational modes arise from intermolecular modes with clustered, ﬁrst—shell solvent
molecules.

Chapter 4 discusses the intermolecular vibrational coherence from ZnTMPyP with
Q-band excitation. The vibrational coherence observed in these experiments arises
from wavepacket motion on the $1 excited state. We observe that the intermolecular
mode is shifted to substantially higher frequencies than previously obtained from
ground-state vibrational coherence of ZnTMPyP. In the excited state of ZnTMPyP,
the n-electron density extends over the N-methylpyridyl rings, so charge terms are
added to the van der Waals intermolecular potential. We discuss how these terms
dominate the potential and change its character relative to the neutral potential. We

conclude with a brief discussion of how the formation of charged species in electron-

transfer reactions in the photosynthetic reaction center can trap the charged species
and contribute to their high quantum efficiency.

Chapter 5 concludes this dissertation with a discussion of the van der Waals inter-
action in ZnH-substituted cytochrome c (ZnCytc). We compare the vibrational coher-
ence from the native and molten-globule states of ZnCytc In a protein environment,
the van der Waals mode arises from interactions with nearby amino-acid residues.
We examine how the potential is dominated by London-dispersion interactions, and
how the absence of nearby polar or charged residues in the native state leads to inho-
mogeneous linebroadening of the van der Waals mode. In the molten-globule state,
the protein core expands and the interactions are randomized. These factors effec-
tively quench the van der Waals mode in the molten globule. We discuss how this
result suggests that the van der Waals modes gain resonance Raman activity through
direct attack of the nearby groups on the Tr-electron density of the chromophore. We
conclude that the addition of charged or polar groups could tune the frequency of
the van der Waals mode, and that similar interactions are likely candidates for the

rate-controlling interactions in the photosynthetic reaction center.

CHAPTER 2

Vibrational Coherence and

Photosynthetic Electron Transfer

Over the last 25 years, there has been an effort to design light-harvesting and
electron-transfer molecular donor-acceptor systems for use in solar energy conver-
sion applications.5'17 A central design principle in this work has been to mimic
various aspects of the structure and function of natural photosynthetic reaction cen-
ters, such as that from the purple non-sulfur bacteria.8v10 The quantum efficiency
of man-made systems falls far short of the essentially unity efficiency of the natural
reaction center.18’ 19 It is quite likely that what has not been mimicked so far is the
structure and dynamics of the surrounding protein medium;

This dissertation describes an experimental study of how solvent structures
around porphyrins in polar solutions and in a small redox protein are coupled to
electronic transitions. The experiments employ a time-domain version of resonance
Raman spectroscopy, dynamic-absorption spectroscopy. These studies provide the
first detailed structural accounting for the vibrational motions that are coupled to
the electron-transfer reactions in photosynthesis. In order to provide an introduc-

tion to these questions, the structure of electron transfer in photosynthesis is re-

Viewed. Vibrational coherence and wavepacket generation are then discussed, and
the dynamic-absorption pump-probe experiment is introduced. Observations of vi-
brational coherence ﬁrst in the photosynthetic reaction center and then in myoglobin
and cytochrome c will be reviewed. This chapter concludes with a review of the
vibrational coherence observed from bacteriochlorophyll in polar solutions and in

proteins.

2.1 Electron Transfer in Photosynthesis

The electron-transfer rate for the primary and secondary charge-separation reactions
in the purple-bacterial photosynthetic reaction center is almost completely indepen-
dent of temperature},20 Figure 2.1 shows the rate constant as a function of tem-
perature for the primary electron-transfer rate in the reaction center of Blastochlo-
ris viridis. The ﬁgure indicates that as the temperature increases, the reaction rate
decreases: at room temperature, the primary electron transfer event takes approx-
imately 3 ps, while at 10 K, the reaction time decreases to ~700 fs. This behavior
deﬁes the typical temperature dependence expected from the Arrhenius equation,
k = Ae‘Ea/RT, where the rate k decreases as the temperature T increases.21 This
fact suggests that the electron-transfer reaction in the photosynthetic reaction center
is nearly barrierless, so Ea is approximately 0. This both accounts for the rate behav-
ior and for the long lifetimes of the non-neutral products: if the barrier is zero for
the charge-separation reaction, then provided the reaction is enthalpically favored,
the barrier for the charge-recombination reaction is high. Bixon and Jortner exam-
ined the case where vibrational modes of the solvent coupled to the electron transfer
reaction.1'22v23 In particular, for the case where the reaction is truly barrierless, or

Ea = 0, the reaction rate k can be expressed as1

2111/2 (ehw/kBT— 1)1/2

= 2.
h2w(2p)1/2 ehw/kBT+1 ( 1)

 

 

5

 

1(98)

k (1011 sec")

 

 

 

I J __ I
o 100 200 300
T (K)

 

Figure 2.1. Temperature dependence of the primary electron transfer rate constant
in the reaction center of Blastochloris viridis. (Adapted from reference 1.)

where V is the electronic coupling, 00 is the vibrational frequency, h is Planck’s con-

stant divided by 211‘ and k3 is Boltzmann’s constant.

From the Marcus theory for condensed-phase electron-transfer rates?“4 the ac-
tivation energy for the electron-transfer reaction depends on both the driving force,
the Gibbs free energy difference between the reactant and product AGO, and the re-
organization energy A, the energy required by the reactant to assume the geometry
of the product state. Under the Born-Oppenheimer approximation,21 the reactant
must reorganize before the electron transfer can occur. Figure 2.2 shows the re-
organization energy for a model pair of non-adiabatic potential energy surfaces. A
spontaneous reaction (for which AGO is negative) has a positive driving force. The

activation energy is given by
Ed = hw(p — 5)2/45 (2.2)

Here, p = AGO/ha), and S = A/hw. Since the rate constant is inversely proportional
to the activation energy, it is clear from Equation 2.2 that for a given spontaneous
reaction with a ﬁxed AGO<0, the reaction rate will increase as the reorganization
energy It increases between 0 and AGO. This is the so-called ‘normal regime’ in the
Marcus theory.4 As the reorganization increases beyond the driving force, the ‘in-
verted regime’, the reaction rate decreases. However, if the reorganization energy
exactly matches the driving force, then the (p — S)2 term in Equation 2.2 will become
zero, so the reaction barrier will vanish. Bixon and Jortner observed that the relevant
vibrational modes coupled to the electron transfer reaction that provided the bulk of
the reorganization energy needed to match the driving force were in the ~ 100 cm‘1
regimeLZO'22 The structural origin of these low-frequency modes, however, was
indeterminate.

The next section discusses how femtosecond spectroscopy can be used to moni-

tor wavepacket motion on a potential energy surface. It also reviews the phenomenon

Energy

 

 

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i.

I'.

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l

:

I I

l l

I I

I I

I I

I I

I I

:<—>:
D
'0

 

 

Qn,a Qn b
Vibrational Displacement

Figure 2.2. Driving force A150 and reorganization energy An for a model pair of non-
adiabatic potential energy surfaces, Ea and Eb. The driving force corresponds to the
Gibbs free energy difference between the minimum of the potential wells between the
reactant (Qma) and product (@133) states. The reorganization energy is the difference
between the minimum of the the potential well for the reactant and the energy of the
reactant surface at the geometry of the product minimum.

of vibrational coherence. These two concepts form the basis of the femtosecond

dynamic-absorption experiment, which is discussed later.

2.2 Vibrational Coherence and Wavepackets

Vibrational coherence arises from coherent wavepacket oscillation on a vibronic po-
tential energy surface.24'26 When a coherent pulse of light that is resonant with a
vibronic transition hits a sample, it launches a wavepacket provided that the pulse is
impulsive (i.e., the duration of the pulse is shorter than the period of the vibrational
mode).27 The ﬁrst and second actions of the electric ﬁeld of the pump with the mat-
ter in the sample prepare a population in either the ground state or some resonant
excited state.25'26 Figure 2.3 shows the formation and motion of a wavepacket in
the dynamic—absorption experiment. The excited-state potential energy surface le)
is displaced from the ground-state surface lg) in Figure 2.3. Because the two sur-
faces are displaced along the vibronic reaction coordinate, the potential is sloped
in the Franck-Condon region. The slope of the potential surface generates a force
on the wavepacket. This imparts momentum to the wavepacket, which will begin to
move away from the Franck-Condom regionZS-zgr29 on either the ground or excited
state. For the case of a ground-state wavepacket, this mechanism is analogous to
resonance-Raman scattering”, 25- ”‘33

Following its formation, the wavepacket oscillates in the potential well. For a
ground-state wavepacket, the duration of the pump pulse controls the displacement
and momentum of the wavepacket. For a particular vibrational mode, the optimum
pulse duration is approximately one-third of the mode’s period. If the pulse is sig-
niﬁcantly shorter than the optimum duration, then the displacement away from the
Franck-Condon region is small, and the experimentally detectable modulation by the

wavepacket of a probe pulse is weak. If the pump pulse is too long, then it is no

 

 

Energy

 

 

 

 

0 ya 0
O O
I I
rg re

Vibrational Displacement

Figure 2.3. Excited-state and ground-state coherent wavepacket motion in the
dynamic-absorption experiment. The excited-state (Ie)) and ground-state (I g))
potential-energy surfaces are drawn as parabolas that are displaced with respect to a
generalized multimode coordinate; 1'9 and re mark the equilibrium ground-state and
excited-state geometries, respectively. Thick arrows represent the resonant pump-
laser ﬁeld; thin arrows show the direction that the wavepackets evolve during the
ﬁrst passage on the two surfaces. The numbers indicate event times, starting with
the ground-state probability density (t = 0), creation of the excited-state wavepacket
by the pump ﬁeld (t = 1), creation of the ground-state wavepacket by the pump ﬁeld
(t = 2), and evolution during the ﬁrst vibration (t = 3). The turning-point regions,
where a wavepacket narrows and reverses its direction of motion, are marked on
both surfaces with diamonds; white (unﬁlled) diamonds mark the turning points that
conuibute to the interference pattern in the dynamic absorption spectrum. (From
reference 29.)

10

longer impulsive, so this too decreases the modulation intensity.33 For an excited-
state wavepacket, the intensity patterns are different. As long as the excited state is
displaced from the ground state, the excited-state wavepacket will gain momentum if
the pulse is impulsive. The strongest modulations will be those modes with the low-
est frequency. The momentum of the wavepacket also trivially depends on the dis-
placement of the excited state relative to the ground state. Not all modes are equally
displaced; modes with a larger displacement will impart a greater momentum to the
wavepacket than modes with a smaller displacement. The experimentally detectable
modulation of a probe pulse will be greater for modes with larger displacements.
The next section discusses the femtosecond dynamic-absorption pump—probe exper-
iment, which can be used to monitor wavepacket motion and can generate informa-

tion about the vibrational modes.

2.3 Dynamic-Absorption Spectroscopy

Vibrational coherence can be detected using the dynamic-absorption tech-
nique.?-6’32-35‘37 As the wavepacket oscillates back and forth in the potential well,
changes in the transmitted intensity of a variably delayed probe pulse can be mea-
sured. As the wavepacket oscillates, it is only resonant with the probe pulse at a
particular geometry of the vibronic displacement along the reaction coordinate. As
the wavepacket moves on- and off-resonance with the probe bandwidth, the inten-
sity of the transmitted probe pulse is modulated with the probe delay. When the
wavepacket is on-resonance, the absorption of the sample increases, and the intensity
of the transmitted probe beam decreases. When the wavepacket is off-resonance, the
transmitted intensity increases. The dynamic-absorption pump—probe experiment
monitors the intensity of the transmitted probe beam as a function of the variable

probe delay. The resonant transitions generate an oscillatory signal in the time do-

11

 

 

 

 

 

 

 

 

 

  

0.02

0.01

0

-0.01

'0'02-02 Tojode i i ' 1Z4 ' 1.8 i 2.2 2.6
Ielay(ps)

 

- -_‘__. -._- _._“ ‘
‘ A - w j'u v'v

 

 

 

Figure 2.4. Femtosecond dynamic-absorption transients of bacteriorhodopsin. The
laser spectrum was monitored at (a) 568 nm, (b) 620 nm, and (c) 656 nm probe

wavelengths. (Adapted from reference 32.)

12

 

 

 

 

 

 

 

 

MEL.

800A 1000 1200 1400 1600

 

Figure 2.5. Fourier-transform spectra and model calculations of the oscillatory part
of the pump-probe transients obtained from bacteriorhodopsin (see Figure 2.4).
Panel a shows the spectrum obtained with a 568 nm probe wavelength and the
580 nm calculated spectrum. Panel b shows experimental and spectra at 620 nm.
Panel c shows 656 nm experimental and 650 nm calculated spectra. The calculations
used to generate the models are detailed in references 32, 33 and 34. (Adapted from
reference 32.)

13

main that can be analyzed in the frequency domain to produce peaks corresponding

to the coupled vibrational modes.

Early use of this technique included characterization of torsional motions
in retinal that are associated with formation of the photoisomerization prod-
uct state in bacteriorhodopsin and rhodopsin by Shank, Mathies and cowork-
ers.31'33' 36, 38“” Figure 2.4 shows the dynamic-absorption transients obtained from
bacteriorhodopsin using 12 fs excitation pulses by Shank and co-workers.32 Follow-
ing excitation by the pump-pulse, each transient exhibits a pattern of oscillations
over at least the ﬁrst picosecond. These oscillations correspond to the motions of
the wavepacket described above. Fourier-transform spectra corresponding to the
dynamic-absorption transients are shown in Figure 2.5. These spectra show peaks
at 1010, 1160, 1200 and 1525 cm‘l. Below each experimental spectrum in the ﬁg-
ure is a calculated model spectrum. The models exhibit good agreement with the
experimental spectra. The peaks correspond to vibrational modes at those frequen-
cies. The results are signiﬁcant because they reveal the particular vibrational modes
that are coupled to vibronic transition. This methodology is equally applicable to
the vibrational modes coupled to the electron transfer reaction in the photosynthetic

reaction center.

2.4 Vibrational Coherence in the Purple-Bacterial
Photosynthetic Reaction Center

Vos, Martin and co-workers observed vibrational coherence in the photosynthetic re-
action center of Rhodobacter sphaeroides R-26 following impulsive excitation of the
primary electron donor, P. The vibrational coherence in the stimulated emission
signal following excitation of the primary electron donor is primarily modulated pri-

marily by low-frequency oscillations. The damping time of the vibrational coherence

14

 

    

oscillatory part (x3)

0.05 -

100 K
probe 796 nm

 

 

 

 

 

 

0 1 , 2 3
Time (ps)

Figure 2.6. Dynamic-absorption transient from the reaction centers of Rhodobacter
sphaeroides R-26 at 100 K. The oscillatory part of the signal is shown magniﬁed x3
above the transient. (From reference 43.)

15

 

   
  

probe 930 nm

 

«3.232333%?
0.1
10 K
W02. ............
‘ 293 K

 

 

l l I 1 l a I l l

0 2 4 6 8
Time (ps)

 

Figure 2.7. Dynamic-absorption transients at various temperatures of reaction cen-
ters of Rhodobacter sphaeroides R-26 at 100 K, 10 K, and 293 K. The oscillatory

portions of the signals are shown magniﬁed x3 (normalized to the maximum signal
at 100 K). (From reference 43.)

16

(<1 ps at 10 K) was on the same time scale as the primary electron transfer reaction.
Moreover, the frequencies of these modes were in the 30-100 cm‘1 regime.“‘51 A
sample dynamic absorption transient from their early experiments43 is presented
in Figure 2.6. At 100 K, the strongest contribution to the oscillatory portion of the
signal is a low-frequency mode with a period greater than 500 fs. At lower tem-
peratures, the low-frequency components provide greater contributions to the over-
all vibrational coherence signal than at room temperature, as shown in Figure 2.7.
The low-frequency components are perhaps an order of magnitude larger than any
higher-frequency contributions. The low-frequency components are damped almost
completely within the ﬁrst two picoseconds. Vos, Martin and co-workers assigned
these low-frequency vibrations to global modes of the protein medium“!52 These
low-frequency modes are likely candidates for the modes that account for the major-
ity of the reorganization energy in the charge-separation reactions in photosynthesis.

Subsequent experiments revealed strong components between 80 and 1 50 cm’l,
in addition to low frequency (15-80 cm’l) modes.47 The Fourier-transform spec-
trum from these experiments is shown in Figure 2.8 The top panel shows two strong
features at 84 and 145 cm“1, and a slightly weaker one at 192 cm'l. The bottom
panel shows a strong 30 cm‘1 mode. The linewidths of these components are rela-
tively broad, perhaps 50 cm"1 full-width at half—maximum (fwhm) for the 30-cm‘1
and 145-cm"1 peaks. The low-frequency features were once again assigned to mo-
tions of the protein“,48 In particular, it was suggested that these low-frequency
~30 cm'1 modes were phonon-like in character, involving collective motions of the
entire protein.48'SO However, the frequency of these modes are much lower than the
~100 cm‘1 modes that Bixon and Jortner suggested were coupled to the primary
electron-transfer reaction},22 However, Figure 2.8A also suggests the possible pres-

ence of a very broad (>100 cm"1 fwhm) component centered near 125 cm‘l. This

feature was not discussed by the authors. The nature of the broad lineshape com-

17

145

 

1L ........ I

0 100 200 300 400 500

30 B

0 100 200 300 400 500
Frequency (cm'1)

Figure 2.8. Fourier-transform spectra of the oscillatory parts of the pump—probe
signals of the dynamic absorption transients of Rhodobacter sphaeroides. The pump—
probe signals were obtained with pump pulses of 30 fs (A, solid curve) and 100 fs (B).
For comparison, the same analysis for the data at 10 K (30-fs pump pulses) is shown
(A, curve). (Adapted from reference 47.)

18

ponents in ZnII porphyrins in polar solutions and in proteins is discussed heavily in
Chapters 3-5. If the modes are not global motions of the protein, as suggested by
Vos, Martin and co-workers, then the structural origin of the coupled modes is still

indeterminate.

2 . 5 Vibrational Coherence from Myoglobin and

Cytochrome c

Although they do not directly address the questions raised in the previous section,
the pump-probe vibrational coherence experiments performed by Champion and co-
workers are discussed here. Their experiments probe the vibrational coherence of
the proteins cytochrome c (Cytc) and myoglobin (Mb). Both of these proteins con-
tain a heme group,53 similarly to bacteriochlorophyll, although the proteins stud-
ied by Champion typically contained iron as the metal ion bound to the porphyrin
rather than magnesium. The ZnH-substituted form of cytochrome c (ZnCytc), how-
ever shares some additional similarities to the magnesium-containing heme in bac-
teriochlorophyll. We examine the the vibrational coherence from ZnCytc in Chap-
ter 5, and it grants crucial insight into the nature of the modes that are relevant to
the electron-transfer reactions. The instrumental setup used by Champion and co-
workers implements some novel design elements. We take advantage of similar tech-
niques in our experiments discussed in Chapters 3-5. The results found by Cham-
pion and co-workers that are reviewed in this section revealed several low-frequency
vibrational modes of the heme that provide a basis to which we later compare the
results of the ZnCytc experiments in Chapter 5 These results are also signiﬁcant be-
cause they demonstrate that skeletal normal modes of the porphyrin can be observed

in the vibrational coherence.

19

The experiments by Champion and co-workers were performed using a
Tizsapphire laser to generate 45-120 fs pulses between 700 and 960 nm.53‘S7 These
pulses were frequency-doubled by a BBQ crystal to generate blue pulses that could
probe the Soret absorption band of the samples. A particularly novel approach used
in these experiments was the use of spatially selective detection techniques that al-
lowed a narrow region of the probe bandwidth to be analyzed.“56 This method
could be used to selectively enhance the intensity of components in the vibrational
coherence signals over certain ranges of frequencies compared to experiments where
the entire probe bandwidth was integrated.“56 The narrow probe bandwidth en-
hances the modulation depth of the transmitted probe, which increases the signal
quality and also enhances the detected intensity of certain modes. Data analysis
was performed using linear predictive singular value decomposition (LPSVD) meth-
odssg‘60 to analyze the resulting pump—probe transients.S3 The LPSVD algorithm
was used to generate frequency and damping time information for the various com-
ponents from the overall vibrational coherence signal.

The most prominent vibrational modes consistently observed in the dynamic ab-
sorption signals, such as those shown in Figures 2.9 and 2.10, were near 40 and
80 cm'1.54'56' 57,51162 Figure 2.9 shows the dynamic-absorption transients and cor-
responding LPSVD spectra from MbNO. The most intense components in the spectra
are the low-frequency oscillations. They are up to an order of magnitude stronger
than any of the high-frequency components. Figure 2.10 shows the transients and
LPSVD spectra from ferrous cytochrome c (FeCytc). Similarly to MbNO, the most in-
tense components are the from the low-frequency ~40-cm’1 and ~80-cm‘1 modes.
The observed frequencies are somewhat higher in FeCytc than in MbNO. The 40-cm‘1
mode was assigned to doming motions of the central metal ion in the heme, while
the 80-cm'l mode was assigned to an overtone of the doming mode.57 A relatively

high-frequency mode near 220 cm'1 was also reported. This mode was assigned to a

20

 

metal-doming mode involving the metal ion and one of its axial ligands.57 In partic-
ular, for the case of FeCytc, this mode was assigned to the stretch between the metal
ion and its axial His-18 ligand.S4 While typically weaker than the doming modes,
this mode was consistently observed in both myoglobin and cytochrome c.5415“;1
These results are important for comparison to our later experiments on ZnII meso-
tetrakis(N-methylpyridyl)porphyrin (ZnTMPyP) in Chapters 3 and 4 and also in par-
ticular to our experiments on ZnCytc in Chapter 5.

While the results reported by Champion and co-workers give very good results
for the slowly damped features in the vibrational coherence, they do not address
any rapidly damped features. The focus of the experiments was on the origin of the
low-frequency components near 40 cm‘l, but additional features in the vibrational
coherence can be observed. In particular, a direct comparison of a Fourier-transform
spectrum and LPSVD ﬁt of a pump-probe transient obtained from deoxymyoglobin
reveals a broad component near 300 cm‘1 in the Fourier-transform spectrum and
LPSVD analysis,53 as shown in Figure 2.11 that is not directly addressed by the
authors. Figure 2.11 shows the dynamic-absorption transient of deoxyMB; Panel b
reveals a broad background centered near 300 cm“1 that underlies the narrower
components. This lineshape is similar to that discussed earlier from the vibrational
coherence from the reaction center of Rhodobacter sphaeroides (see Figure 2.8). Simi-
lar features can be seen in Figures 2.9 and 2.10. In each case, the broad portion of the
broad background has superimposed narrower components. The broad lineshape is
characteristic of a rapidly damped feature in the time domain. The vibrational modes
corresponding to these features likely play a critical role in the previously discussed

electron transfer reactions in the photosynthetic reaction center.

21

AT (a.u.)

-1

-1

0.0

 

Residual

Fe-His
437 nm

Residual

Fe-His

439 nm

Residual

Fe-His
442 nm

Residual

F -H'
e ls 445nm

1.5 2.0 2.5 3.0

Time (ps)

22

Intensity (a.u.)

 

 

C?

-L

 

O

—L

 

 

Fe-His

167

 

 

0
0

100 200 300 400
Frequency (cm'1)

Figure 2.9. Open band femtosecond dynamic-absorption spectroscopy measure-
ments on MbNO samples. The left panels present the oscillatory parts of the the
pump-probe signals (circles) with their LPSVD ﬁts (solid line). The 40 cm‘1 com-
ponent (dashed line) is superimposed on the oscillatory signal and the 220 cm—1
mode shown is shifted for clarity (thin solid line). The right panels show the LPSVD-
generated power spectra. (Adapted from reference 54.)

Ferrous cytochrome c

 

 

 

 

 

 

45
’3
, \W 91
, . V_ 4 158
43
87 168
:i A 43
«ii =3
V G
9 s
C C
3 -1. E 91
E _
45
92
169
-1.

 

 

 

 

 

 

45 W

o. / 1
45 .
W 91 - o 1 2

 

 

 

 

 

 

 

 

 

 

-1. / _________ 91m? ..........
0.0 035 1.0 135 2:0 25 3:0 3.5 0 160 260 300
Time (ps) Frequency (and)

Figure 2.10. Sequence of dynamic-absorption transients using the open band detec-
tion scheme on FeCytc. The left panels present the oscillatory part of the signal, and
the right panels show the corresponding power spectra. The ~45 cm‘1 oscillation
(solid line and the ~91 nw oscillation (dashed line) used in the ﬁt are shown displaced
from the data. The inset in the lower-right panel displays the Morse potential used
in the simulation. (Adapted from reference 57.)

23

 

  
   
   

(b)

deoxyMb
12:1.76 ps

lllll;l l4lllllLJlll

 

 

Relative Intensity

 

 

 

 

 

1411'] l—Ll l l_LLl l 114. I l lllllllllllleJnlllLlilL
0.5 1.0 1.5 100 200 300 400
t (m) '17 (cm")

Figure 2.11. Femtosecond dynamic-absorption transients of deoxyMb. The signal (a)
is shown along with the LPSVD ﬁt (solid line). The discrete Fourier transform ampli-
tudes (dotted line) and the power spectrum derived from the LPSVD analysis (upper
solid line) (b) are compared with the resonance Raman spectrum (lower solid line).
The low frequency residual (c) is superimposed with the LPSVD ﬁt that describes its
oscillation and decay. (From reference 53.)

24

2.6 Vibrational Coherence in Bacteriochlorophyll
Solutions and Proteins

The experiments that will be discussed in Chapters 3-5 were inspired by work from
this laboratory on bacteriochlorophyll a (BChl) that suggested a new interpretation
for the structural origin of the ~100 cm“1 modes coupled to the electron trans-
fer reactions in the photosynthetic reaction center. The results of the experiments
suggested that these modes arise from intermolecular interactions between the chro-
mophore and the solvent or surrounding protein medium. Experiments on BChl a in
polar solutions revealed that the vibrational coherence was dominated by rapidly
damped modes. These modes exhibited a shift in frequency with a greater than
quadratic dependence on the solvent dipole moment. This behavior was consis-
tent with a van der Waals intermolecular potential.63 Additional experiments on
the light-harvesting subunit proteins B777 and B820 revealed that direct attack on
the n-electron density of the chromophore by the solvent appeared to be necessary
for the intermolecular mode to gain resonance Raman activity. Although the later
experimental chapters cover this work In more detail, in the following the main ideas

are reviewed.

2.6. l Vibrational Coherence in Bacteriochlorophyll a in

Polar solution

Pump-probe experiments with Q-band excitation on BChl a in pyridine solution
revealed two distinct types of components in the low-frequency vibrational coher-
ence.64 The ﬁrst were a set of slowly damped components that persisted out to 8 ps.
These components had frequencies over a range of 11—206 cm‘l; their damping
times y ranged from 800 fs to 1.7 ps. In addition to these components, a very strong,

rapidly damped feature was also observed. This component had a much shorter

25

 

 

 

 

 

 

x3
19‘ 3'
'E
:3
OJ
.2 2-
E .
(D
J: L 1 ps
I— 1-
I—
<
o
I l I l l I
0 2 4 6 8 10
Probe Delay (ps)

Figure 2.12. Dynamic-absorption transient from BChl a in pyridine. The inset shows
a magniﬁed View of the ﬁrst picosecond of the signal. (From reference 63.)

26

[1((0) I (t) \

A, II

 

 

 

 

 

 

2ps

 

 

 

Figure 2.13. Model of the rapidly damped vibrational coherence observed in BChl
a solutions as a distribution of damped cosinusoids, £(w). A log-normal disuibu-
tion L (a), deﬁned by its center frequency (00, width Aw and asymmetry (or skew)
p, sampled over its full width. Each sample Lorentzian lineshape has its own center
frequency 000,-, and corresponds in the time domain to an exponentially damped cos-
inusoid in the time domain (b) with an intrinsic damping time y. Summing the set of
Lorentzians obtained by sampling over the full width of the log-normal distribution
£(w) (c) results in a superposition whose rapidly damped waveform (d) resembles
the vibrational coherence observed in BChl solutions. (Adapted from reference 63.)

27

 

 
 
   
  

 

 

200 -
acetone
175 .
'5
Q 150 _
’3‘ pyridine
125 .. 1-propanol
100 A
' I ' l I

 

Dipole Moment, D

Figure 2.14. Solvent dependence of the mean frequency (00) of the rapidly damped
vibrational coherence observed in BChl (1 solutions in a range of polar solvents on the
solvent dipole moment. The data points are superimposed on a model curve derived
from an expression for the natural frequency for a 6-12 intermolecular potential for
the BChl-solvent mode. The expressions for the intermolecular potential and natural
frequency are detailed in reference 63 and in Chapters 3-5 (From reference 63.)

28

damping time (200 fs), and dominated the early-time portion of the transient absorp-
tion signal. It was suggested that this 155 cm‘1 mode was due to an intermolecular
interaction between BChl and a pyridine molecule in the ﬁrst solvation shell.
Subsequent experiments were performed by Katherine Shelly on BChl a in a se-
ries of polar solvents."33 The observed vibrational coherence was again dominated
by rapidly damped components (see Figure 2.12). The ﬁgure shows the dynamic-
absorption transient from BChl a in pyridine solution. By far the strongest feature
in the vibrational coherence is a rapidly damped component, which is shown in the
inset of Figure 2.12. This feature is almost completely damped within the ﬁrst 500 fs,
but it is at least an order of magnitude larger than any other oscillatory component.
The lineshapes corresponding to the rapidly damped components exhibited behavior
consistent with the superposition of several Lorentzian lineshapes with a distribution
of frequencies (see Figure 2.13). In such a picture, the overall lognormal distribution
shown in Figure 2.13a arises from the sum of individual Lorentzian lineshapes. This
behavior is consistent with a picture where the rapid damping times are due to inho-
mogeneous line broadening. The individual Lorentzians correspond to the lineshape
generated by a single molecule. The local variations between different molecules in
the ensemble generate slightly different frequencies. The time-domain superposition
of these individual waveforms is a rapidly damped oscillation. The rapidly damped
components also exhibited a solvent-dependent frequency shift. The shift followed
a trend consistent with a van der Waals intermolecular potential between the chro-
mophore and a nearby solvent molecule (see Figure 2.14). The van der Waals potential
is discussed in detail in the experimental chapters 3-5. The frequency of the rapidly
damped mode increased with a greater than quadratic dependence on the dipole mo-
ment of the solvent. The intermolecular potential was dominated by dipole-dipole
interactions. In the nonpolar solvent limit, the mean frequency of the rapidly damped

vibrational coherence was extrapolated to be ~100 cm‘l. The results further sug-

29

 

gested that interactions between the chromophore and clustered, ﬁrst-shell solvent
molecules dominated the low-frequency vibrational coherence. This conclusion pro-

vides the movitvation for much of the work that follows in this dissertation.

2.6.2 Intermolecular Vibrational Coherence From B777 and B820

Additional experiments on the light-harvesting subunit proteins B777 and B820
yielded similar results.65 B820 is a dimer containing a pair of BChl macrocycles (see
Figure 2.15). In the purple-bacterial LH1 light—harvesting complex, 15 B820 subunits
combine to form a ring around the photosynthetic reaction center.66 The monomer
that pairs to form B820 is known as B77767"71 In B777, a single BChl macrocy-
cle binds to an or helix by coordinating the Mg11 ion to a histidine residue.“72 In
the monomeric form, the BChl is directly exposed to the solvent. In B820, the BChl
macrocycles form a van der Waals complex. Figure 2.15 shows that in the complex,
the BChl macrocycles directly face each other. In this conﬁguration, the macrocyles
resemble the special pair in the primary electron donor P in the photosynthetic reac-
tion center.65' 73' 74

In B777, the vibrational coherence strongly resembled that of BChl in acetone
from the earlier experiments (see Figures 2.16 and 2.17). The rapidly damped por-
tion of the signal was much more intense than the more slowly damped oscilla-
tions. The rapidly damped feature could be modeled as the sum of two compo-
nents. These components were assigned to hindered translational and rotational
(librations) modes between the porphyrin chromophore and one of the surrounding
solvent molecules.“65 In B820, the vibrational coherence, while still dominated by
rapidly damped components, was signiﬁcantly weaker (see Figure 2.18) than in B777.
The frequencies of the rapidly damped components were also lowered. These results
were consistent with an assignment of the rapidly damped vibrational coherence to

intermolecular vibrational modes. In the monomeric B777 direct attack on the rt—

30

 

Figure 2.15. The Hu and Schulten75 model for the B820 subunit in LH1 from
Rhodobacter sphaeroides, showing the pair of BChl macrocycles and the transmem-
brane or helices in ribbon and surface renderings. (From reference 65.)

31

electron density of the chromophore is possible. The B820 dimer, however, shields
the chromophore because the BChl macrocycles are paired. As a result, the strength
of the intermolecular interaction is signiﬁcantly attenuated. Additional interactions
between the BChl macrocycle and a nearby tryptophan residue and BChl-BChl inter-
actions were also observed in B820. The results further advanced the hypothesis that
the intermolecular vibrational modes are the dominant ones in the low-frequency vi-
brational coherence. They also suggested a mechanism for gaining resonance Raman

activity: direct attack on the n-electron density of the chromophore.

2.7 Proposed Experiments

The results from this work on BChl a, B777 and B820 suggest further experiments
to clarify the nature of this intermolecular vibrational mode. These results suggest
that the vibrational coherence from BChl is dominated by intermolecular modes with
a clustered, ﬁrst-shell solvent molecules that attack the Tr-electron density of the
BChl macrocycle. This result should be generalizable to other tr-electron containing
systems, such as a porphyrin. It is not clear, however, that the intermolecular mode
from BChl in polar solution is fully understood; the vibrational coherence lacks nor-
mal intramolecular (skeletal) vibrational modes of the porphyrin chromophore. The
relative resonance Raman activities of the intramolecular and intermolecular modes
cannot be directly compared. In order to compare the two types of modes, both must
be present in the vibrational coherence. By varying the solvent environment, the in-
termolecular van der Waals modes can be distinguished. The Soret-band excitation
experiments performed by Champion and co-workers on myoglobin and cytochrome
c revealed the presence of several skeletal modes in the vibrational coherence,53'S7
so they suggest that other porphyrins or porphyrin-containing proteins might make

good candidates for further study.

32

103x AT/T

 

 

 

 

 

 

I l I T I
200 300 400 500 600
Probe Delay (fs)
CD
'0
3
'E
U)
(U
2
(D
.2
<15
(I)
0: 0
I I I I I
0 100 200 300 400 500

Frequency (cm")

Figure 2.16. Expanded view of the rapidly damped oscillation observed in the
dynamic—absorption transient from BChl a in acetone. The signal is superimposed
with a model deﬁned by the sum of two independent log-normal distributions £(w)
of damped cosinusoids. The scaling of the ordinate is relative to the magnitude of the
pump-probe ground-state depletion signal. Bottom: Plots of £(w) for the two com-
ponents observed in acetone and their sum .’M(w) (thick curve). (From reference 63.)

33

 

 

80 —
I'-
\
l- 40 —
G
X
m 0 '—
o
T'
-40 _
I I I I I
200 300 400 500 600
Probe Delay (fs)
0
.o
B
'E
O)
(O
2
0)
..>_
E
G)
D: 0

 

 

 

 

0 100 200 300 400 500
Frequency (cm'I)

Figure 2.17. Expanded View of the rapidly damped oscillation observed in the
dynamic-absorption transient from B777. The signal is superimposed with a model
deﬁned by the sum of two independent log-normal distributions £(w) of damped
cosinusoids. The scaling of the ordinate is relative to the magnitude of the pump-
probe ground-state depletion signal. Bottom: Plots of [(00) for the two components
observed in B777 and their sum 5mm) (thick curve). (From reference 65.)

34

 

 

 

 

 

l- 4-

\

l- _

<1 0

X

m ’4'—

o

‘-

-8-
I I I I I I I I I
400 600 800 1000 1200 1400 1600 1800 2000
Probe Delay (fs)

(D

'0

3

'E

U)

(U

2

(D

.2

E

SE 0

I I I I

0 50 100 150 200

Frequency (cm'I)

Figure 2.18. Expanded view of the rapidly damped oscillation observed in the
dynamic-absorption transient from B820. The signal is superimposed with a model
defined by the sum of two independent log-normal distributions £(w) of damped
cosinusoids. The scaling of the ordinate is relative to the magnitude of the pump-
probe ground-state depletion signal. Bottom: Plots of £(w) for the two components
observed in B820 and their sum .’M(00) (thick curve). (From reference 65.)

We can examine the vibrational coherence from ZnII mesa-tetrakis(N-
methylpyridyl)porphyrin (ZnTMPyP) in a series of polar solutions. These experiments
use Soret-band excitation, so they monitor the ground-state vibrational coherence of
ZnTMPyP in analogy to the experiments on BChl. By varying the dipole moment of
the solvent, we can look for changes in the mean frequency of the rapidly damped
mode. We can also compare the vibrational coherence from ZnTMPyP in methanol
and perdeuturated methanol solutions to search for evidence of an isotpe effect.
ZnTMPyP has a small permanent dipole moment compared to BChl, so the frequency
of the rapidly damped mode should be smaller than that observed in the vibrational
coherence from BChl solution. The rapidly damped vibrational coherence should
still exhibit a solvent dependent shift, and it should be more intense than the slowly
damped skeletal modes.

The stimulated-emission experiments by Vos, Martin and co-workers on pho-
tosynthetic reaction centers monitored vibrational coherence from the excited
state.45’48' 50' 51' 76 By tuning the laser Q-band of the absorption spectrum, the vibra-
tional coherence from the excited state ZnTMPyP can be similarly monitored. In the
excited state, the Tr-electron density of ZnTMPyP extends over the N-methylpyridyl
rings, so the van der Waals intermolecular potential senses charges on the porphyrin.
The addition of charges to the intermolecular potential should have a signiﬁcant ef-
fect on the frequency of the intermolecular mode.

We cannot fully characterize the behavior of the van der Waals mode in a protein
environment from the B777 and B820 experiments. In B777, the BChl macrocycle
is directly exposed to the solvent, while in B820 the BChl forms a dimer to provide
shelter from the solvent. A monomeric porphyrin in the interior of a protein may
behave differently. The issue of which amino-acid residues in the protein couple to
the TI —>Tr* transition of the porphyrin macrocycle must be considered. In a protein

such as ZnII cytochrome c (ZnCytc), we can compare the vibrational coherence from

36

the native and molten-globule states to test the response of the van der Waals mode
to a change in the local environment of the porphyrin. The following chapters will

address these issues.

37

CHAPTER 3

Ground-state vibrational coherence in

‘6‘“ m-«P-ﬁ

polar solutions of
ZnII tetrakis(N-methylpyridyl)porphyrin

with Soret-band excitation

3.1 Summary

Ground-state coherent wavepacket motions arising from intermolecular modes
with clustered, ﬁrst-shell solvent molecules were observed using the femtosec-
ond dynamic absorption technique in polar solutions of Zn11 mesa-tetrakis(N-
methylpyridyl)porphyrin (ZnTMPyP) with excitation in the Soret absorption band. As
was observed previously in bacteriochlorophyll a solution, the pump-probe tran-
sients in ZnTMPyP solutions are weakly modulated by slowly damped (effective
damping time y > 1 ps) features that are assigned to intramolecular modes, the skele-
tal normal modes of vibration of the porphyrin. The 40-cm‘1 and 215-cm"1 modes

from the metal-doming and metal—solvent-ligand modes, respectively, are members

38

of this set of modulation components. A slowly damped 2-4-cm‘1 component is
assigned to the internal rotation of the N-methylpyridyl rings with respect to the
porphyrin macrocycle; this mode obtains strong resonance Raman intensity enhance-
ment from an extensive delocalization of rt-electron density from the porphyrin in
the ground state onto the rings in the n* excited states. The dominant features
observed in the pump-probe transients are a pair of rapidly damped (y < 250 fs)
modulation components arising from intermolecular modes with solvent molecules.
This structural assignment is supported by an isotope shift of the average mode
frequencies in methanol and perdeuterated methanol. The solvent dependence of
the mean intermolecular mode frequency is consistent with a van der Waals inter-
molecular potential that has signiﬁcant contributions only from the London disper-
sion and induction interactions; ion-dipole or ion-induced-dipole terms do not make
large contributions because the Tr-electron density is not extensively delocalized onto
the N-methylpyridyl rings. The modulation depth associated with the intermolecu-
lar modes exhibits a marked dependence on the electronic structure of the solvent
that is probably related to the degree of covalency; the strongest modulations are
observed in acetonitrile and dimethylsulfoxide. The results strongly support a struc-
tural assignment of the low-frequency modes that are coupled to the primary and
secondary electron-transfer reactions in photosynthetic reaction centers to inter-
molecular modes between the redox-active chromophores and ﬁrst-solvation shell
groups from the surrounding protein, and an important additional function of the

intermolecular modes in the stabilization of charged intermediates is suggested.

3.2 Introduction

In the purple-bacterial photosynthetic reaction center, the primary and sec-

ondary charge-separation reactions exhibit effectively activationless dynamics ow-

39

ing to coupling to low-frequency vibrational modes in the 100-cm'1 regirne.1'20’22
The main components detected in the vibrational coherence observed in pump-
probe43“16"“3’51’76 and ﬂuorescence upconversion77 transients following impulsive
excitation of the primary electron donor, P, are modes with frequencies in the 30—
100-cm‘1 range. The possibility that the modes observed in the vibrational coher-
ence are the ones that are coupled to the electron-transfer reaction coordinate has
been discussed,4gv 78‘“ but their structural origin remains indeterminate. Bixon and
Jortnerlrzoi 27- attributed the coupled modes to the protein medium, and Vos, Martin,
and coworkers suggested that the modes that are active in the vibrational coherence
are delocalized or phonon-like in character.“ 50

In recent work, the Beck laboratory has advanced an alternative hypothesis that
the vibrational modes that control the electron-transfer dynamics in reaction cen-
ters are intermolecular in origin, between the redox-active chromophores and groups
in the first-solvation shell from the surrounding protein medium. This hypothesis
is supported by our observations using femtosecond pump-probe spectroscopy of
the rapidly damped low-frequency vibrational coherence from bacteriochlorophyll a
(BChl) in polar solution“!64 and in the light-harvesting subunit proteins B777 and
B820.65 In solution, BChl exhibits a slowly damped set of modulations over the 100—
8000-fs probe delay range; these components exhibit damping times in the >1-ps
regime and mode frequencies ranging from 10-220-cm‘1. The magnitude spectrum
obtained by Fourier transformation is comparable to the low-frequency region of
the conventional resonance Raman spectrum from BChl in solution, in ﬁlms, and in
the reaction center,85'86 so these slowly damped features are assigned to the low-
frequency skeletal modes of the BChl macrocycle.64 By far the strongest features in
the vibrational coherence from BChl solutions, however, are a very rapidly damped
set of modulation components in the sub-ps time scale. These features are well de-

scribed by time-domain models that correspond in the frequency domain to inhomo-

40

geneously broadened lineshapes with very broad, asymmetric Gaussian proﬁles. The
mean frequency of the rapidly damped vibrational coherence exhibits a greater than
quadratic dependence on the gas-phase dipole moment of the solvent. This trend
is consistent with a van der Waals intermolecular potential in which the London-
dispersion and dipole—dipole interactions make large contributions; the extrapolated
100-cm‘1 frequency in the nonpolar limit arises predominantly from the London-
dispersion term.63 The rapidly damped vibrational coherence observed in the B777
system is comparable to that observed with BChl in acetone solution because the BChl
macrocycles are exposed to the polar head groups of the surrounding nonionic de-
tergent. In the paired BChl system called B820 that forms when two B777 monomers
associate, however, the supporting or helices sterically protect the BChl macrocycles
from direct attack by the surrounding detergent. The vibrational coherence then re-
veals weaker and more slowly damped components at 28 cm"1 and 46 cm‘1 that are
assigned to BChl—tryptophan and BChl—BChl intermolecular modes.65

The intermolecular modes that contribute to the vibrational coherence in
BChl-containing systems modulate the pump-probe ground-state depletion sig-
nal owing to the resonant impulsive stimulated Raman scattering (RISRS) mecha-
nism.24‘26'30'32'3"3 It was suggested that these modes are resonance Raman active
because molecules in the ﬁrst solvation shell make a direct attack on the Tr-electron
density above and below the macrocycle and are displaced by the Tr—>1T* transi-
tion.63v65 This hypothesis suggests that the spatial organization of the n-electron
density in the ground state selects the ﬁrst-shell solvent molecules that contribute
to the vibrational coherence. As a test of these ideas, we discuss in this chapter the
low-frequency ground-state vibrational coherence in polar solutions of ZnII meso-
tetrakis(N-methylpyridyl)porphyrin (ZnTMPyP, see Figure 3.1). Owing to the nominal
C4 symmetry axis normal to the macrocycle, ZnTMPyP has a small net dipole mo-

ment; with a single methanol (CH3OH) axially ligated to the ZnII ion, the calculated

41

dipole moment is only 0.66 D (see Figure 3.1). ZnTMPyP is nevertheless soluble in
a range of polar solvents because the peripheral N-methylpyridyl rings each carry a
positive charge. Because the Tr-electron density in the ground state (see Figure 3.1a) is
mostly conﬁned to the region of the porphyrin, however, the resonance Raman active
solvent molecules are effectively held at some distance from the peripheral charges,
so charge-dependent terms will make only a small contribution to the intermolecular
potential. In short, the ground-state intermolecular mode frequency in ZnTMPyP so-
lution should be smaller than detected in the same solvents in BChl solution because
the only terms in the intermolecular potential that will make large contributions are
those that depend on the polarizability of the porphyrin: the London-dispersion and
solvent-dipole-induced-dipole terms.

The results show that the vibrational coherence from ZnTMPyP detected with
Soret-band excitation contains dominant contributions from rapidly damped features
arising from intermolecular modes with clustered solvent molecules. The compo-
nents arising from intramolecular modes, from the porphyrin macrocycle proper or
from the metal-axial-ligand interaction, can be distinguished from the intermolec—
ular modes because they exhibit long damping times and narrow lineshapes. The
intermolecular mode frequency follows the expected dependence on the solvent’s
dipole moment; the 70-cm'1 frequency in the nonpolar limit and the observation
of a isotope shift in perdeuterated methanol are consistent with the hypothesis dis-
cussed above. In addition to supporting a structural assignment of the low-frequency
modes that are coupled to the electron-transfer reactions in photosynthetic reaction
centers, the results have additional signiﬁcance because they suggest a role for in-
termolecular modes in the stabilization of charged intermediates in redox catalysis
in proteins. The results described in this chapter were previously published in the

Journal of Physical Chemistry (see reference 88.)

42

 

Figure 3.1. Optimized structure of Zn11 meso—tetrakis(N-methylpyridyl)porphyrin
(ZnTMPyP) complexed with a single methanol molecule as an axial ligand to the Zn11
ion. The structure was obtained from a B3LYP hybrid density functional electronic
structure calculation with Gaussian 0387 at the 6-31G level of theory. The ball-and-
stick structures are shown superimposed with density surfaces for (a) the highest
occupied molecular orbital (HOMO) and for (b) the lowest unoccupied molecular or-
bital (LUMO).

43

3.3 Experimental

3.3. 1 Sample Preparation

ZnTMPyP (CAS 28850-44-4) was used as received from Sigma-Aldrich. CH3OH
(spectrophotometric grade) and CD3OD (99.8 atom %D) were obtained from Sigma-
Aldrich. CH3OD (99 atom %D) was obtained from Cambridge Isotope Labs. Ace-
tonitrile (CH3CN, from Mallinkrodt, spectrophotometric grade), dimethylsulfoxide
(DMSO, from EMD, ACS grade), and N,N-dimethylformamide (DMF, from Jade Sci-
entiﬁc, reagent ACS grade) were used as received.

For use in the femtosecond pump-probe experiments, solutions of ZnTMPyP were
prepared by dissolving the dry ZnTMPyP powder in the indicated solvent to obtain
an absorbance of 0.4 for a path length of 1.0 mm at the center of the laser spectrum
at 420 nm, as detailed below; with the methanols and DMSO, the solution was passed
through a 0.22-pm microﬁlter prior to checking the absorbance. The samples were
held in the femtosecond pump-probe spectrometer at room temperature (23 °C) in
a fused-silica ﬂow cuvette (0.5-mm path length). A peristaltic pump was used to
circulate a 10-mL reservoir of sample solution through the cuvette at 2.75 mL/min.
The sample’s absorption spectrum was monitored during the experiment for changes
arising from photochemistry or permanent photobleaching. The sample reservoir

Was exchanged with fresh solution several times during each run.

3.3.2 Continuous-Wave Absorption and Fluorescence Spectroscopy

Absorption spectra were obtained at 23 °C with a Hitachi U—2000 spectrophotometer
(2-nm band pass). Fluorescence spectra were acquired at 23 °C with a Hitachi F-4500
spectroﬂuorimeter (5-nm band pass for the excitation and emission monochroma-

tors). As presented as a function of wavenumber, the ﬂuorescence intensities are

44

multiplied by the square of the wavelength in order to compensate for the ﬁxed (in

wavelength units) spectral bandpass of the emission spectrometer.89

3.3.3 Femtosecond Spectrosc0py

Femtosecond pump-probe transients with impulsive excitation were recorded using
the dynamic-absorption technique26v32'35'37 with a pump—probe spectrometer (see
Figure 3.2) consisting of a frequency doubled, self-mode-locked Ti:sapphire oscil-
lator (Coherent Mira-F oscillator and Verdi V5 (5 W) NszVO4 pump laser, Coher-
ent/Inrad 5-050 second-harmonic generator), a SFlO Brewster prism-pair pulse com-
pressor, and a rapid-scanning, modiﬁed Mach-Zehnder interferometer with confocal
sample and autocorrelation-crystal positions. The present experiments employ 50-fs
pulses with intensity spectra centered at 420 nm (4-nm FWHM, as measured with an
Ocean Optics USE-2000 spectrometer/CCU detector with a 0.5-nm bandpass), and a
fairly narrow bandpass (0.5 nm) of the transmitted probe beam. This approach cor-
responds to that used by Champion and coworkers in their studies of low-frequency
vibrational coherence in heme proteins”, 55162

The apparatus and methodology used in this work is largely that described in
our recent study of rapidly damped vibrational coherence in BChl solutions with Q-
band (780-nm) excitation,63 but a number of changes were required to permit work
in the blue part of the spectrum. A 76-MHz train of 840-nm pulses is generated by
a Coherent Mira 900E Ti:sapphire oscillator equipped with Coherent’s X-wave broad-
tuning-range (690-1020-nm) cavity optics; the oscillator is pumped by a Coherent
Verdi pump laser (S-W output). As shown in Figure 3.2, these red pulses ﬁrst enter
a pulse-compression system composed of a double-passed pair of SFlO Brewster-
angled prisms and an adjustable interprism path length. The output pulses are di-

rected to a Coherent/Inrad 5-050 second-harmonic generator, which is ﬁtted with a

45

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46

type I B-barium borate (BBO) second—harmonic generation (SHG) crystal (l-mm path
length).

The co-propagating 420 and 840-nm output beams that radiate from the BBQ
crystal are then directed to a modiﬁed Mach-Zehnder pump-probe interferometer.
For this work, the interferometer was redesigned to support a dichroic mode of oper-
ation that allows us to control and characterize pump-probe pairs of blue pulses in
the 350—500-nm region of the spectrum. The interferometer employs a femtosecond
autocorrelator beamsplitter (CV1 Laser, FABS-800-4SS) to split the input beam into
pump and delayed probe pulses; as speciﬁed, the 800-nm beamsplitter divides the
s-polarized 840-nm light evenly into two beams, but the p-polarized 420-nm light
is divided by the beamsplitter into two beams with a 3:1 pump:probe intensity ratio.
The pump-probe delay is scanned continuously by a galvanometer-driven retroreﬂec-
tor (Clark-MXR, ODL-150) mounted in the probe beam’s arm of the interferometer.
The pump beam’s intensity is modulated at 100 kHz by a A/2-retarding (at 420 nm)
photoelastic modulator (Hinds Instruments) and a calcite polarizer (Karl Lambrecht),
in series.90 Because the planes of polarization of the 420-nm and 840-nm compo-
nents are orthogonal as they enter the photoelastic modulator owing to the use of
the Type I SHG crystal, the 420-nm and 840-nm beams that emerge from the calcite
polarizer exhibit amplitude-modulation envelopes that are 90° out-of-phase with re-
spect to each other, but no their planes of polarization are parallel, as analyzed by
the polarizer. The compensating calcite polarizer in the probe beam is oriented 45°
with respect to the pump-beam’s polarizer, so the two orthogonally polarized colors
are analyzed equivalently, and the output planes of polarization are parallel.

Finally, a single dichroic beamsplitter removed from the Coherent/Inrad 5-050
SHG unit is mounted to separate the 420-nm and 840-nm light in the pump and
probe beams, which propagate along parallel paths on the optical table as they exit

the delay arms of the Mach-Zehnder interferometer. A fused-silica singlet lens (5-

47

 

cm focal length) is employed to focus the 420-nm pump and probe beams onto the
sample; the 840-nm pump and probe beams are focused onto a thin (100nm thick-
ness) BBO autocorrelation crystal by a matching lens. After it emerges from the
sample, the probe beam is analyzed by a calcite polarizer oriented at 90° with re—
spect to the pump-beam’s plane of polarization, and then the residual probe light
enters an Acton-Research SP-150 monochromator. An ampliﬁed photodiode (Thor-
labs PDA55) and a lock-in ampliﬁer (SRS, SR8 50) referenced to the pump-modulation
frequency are used to detect the pump—probe signal from a 0.5-nm bandpass of the
probe beam. A photomultiplier (1P28, in a Clark-MXR housing) and a lock-in am-
plifier (Femto, LIA-MV-200H) are used to detect the background-free autocorrelation
signal that is generated by the 840-nm pump-probe beams incident upon the BBQ
autocorrelation crystal. The pump-probe and autocorrelation signals are recorded
and averaged simultaneously by a sample-and-hold ampliﬁer and transient recording
system, as described previously.29 In the present work, the probe delay is linearly
scanned at 1.0 Hz over the -3 to +27 ps range. The pump-probe and autocorrelation
signals are sampled at 17 kHz, and there are 13000 points in each scan; the effective
dwell time during data acquisition is 2.3 fs/point.

The autocorrelation signal obtained from the 840-nm pump and probe beams is
used in the characterization of the group-delay dispersion of the entire apparatus.
The effective instrument-response function for the 420-nm pump and probe pulses
is minimized by adjusting the distance between the pair of Brewster prisms; the
width of the 840-nm autocorrelation and the pump-probe photobleaching rise time
obtained with the 420-nm pulses are monitored simultaneously. The autocorrelation
signal is also used as a reference timing pulse for the transient recorder29 that is used
to acquire simultaneously the autocorrelation signal and the pump—probe signal. The
autocorrelation pulse is precisely correlated on the probe-delay axis with the zero of

time, where the 420-nm pump and probe pulses overlap temporally in the sample,

48

so its timing is used to cancel the temperature-induced drift in the dimensions of
the pump and probe arms of the interferometer and to compensate for jitter in the
scanning of the probe-delay line. The use of the fundamental (red) pulses in the
autocorrelation arm of the instrument permits us to operate this instrument with the
blue pump and probe pulses tuned well into the ultraviolet. If the blue pulses were
used directly to obtain the autocorrelation, the 200-nm transmission cutoff of the
BBQ crystal would not permit tuning of the pump and probe pulses below 400 nm.
Each dynamic-absorption transient that is presented here and in the subsequent
chapters is the result of averaging together several scans. For each probe delay point,
the mean and standard deviation from the set of individual scans were recorded.
Statistical filtering was used to reject outlying points. The transients effectively rep-
resent the result of several days worth of repeated experiments for each type of

sample.

3.4 Results

Figure 3.3 shows continuous-wave absorption and ﬂuorescence spectra from
ZnTMPyP in methanol (CH3OH) at 23 °C. The spectra are plotted as relative dipole
strengthsggvgli92 as a function of wavenumber v, A(v) /v and F (v) /v3, respectively.
The absorption spectrum features two bands, the Soret (or B) band and the Q band,
in the blue and red parts of the spectrum, respectively. The ﬂuorescence spectrum
extends to the red of the Q band. Figure 3.4 shows the solvent dependence of the
Soret-band region from solutions of ZnTMPyP in CH3 OH, dimethylformamide (DMF),
acetonitrile (CH3CN), and dimethylsulfoxide (DMSO) at 23°C. Also shown in Figure 3
is the output spectrum from the frequency doubled Ti:sapphire oscillator as it was
tuned for the dynamic-absorption experiments to 420 nm. The detected probe band-

pass was obtained from the red side of the laser spectrum (422 nm).

49

 

 

Relative Dipole Strength

 

 

Frequency (103 cm")

Figure 3.3. Soret (v > 20000 cm‘l) and Q-band region of the continuous-wave
absorption (solid curve) and ﬂuorescence (dotted curve) spectra from ZnTMPyP in
CH3OH at room temperature (23 °C), plotted as the dipole strength, A / v and F/v3,
respectively, and normalized to unit area with respect to the ﬂuorescence spectrum

and Q band.

50

 

 

k

20 22 24 26
Frequency (103 cm“)

Relative Dipole Strength
C.’
ggg

 

 

 

 

 

Figure 3.4. Soret-band absorption dipole-strength (A/v) spectra from ZnTMPyP in
(a) CH3OH, (b) DMF, (c) CH3CN, and (d) DMSO. Superimposed with arbitrary scaling
on (a) is the intensity spectrum of the 420-nm, 50-fs pulses used in all of the pump—
probe experiments.

51

The dynamic-absorption transients obtained from the ZnTMPyP solutions under
these experimental conditions are shown in Figure 3.5. Following an intense coher-
ence spike that goes off the plotted scale,93'95 the transients exhibit a pattern of
cosinusoidal modulations nearly all the way to the end of the 25-ps recording that
is superimposed upon a single or double exponential decay function. The modu-
lation pattern includes a strong very low-frequency component with positive-going
recurrences at ~2 ps and ~18 ps; this oscillation carries a less intense set of higher
frequency modulations that are even more slowly damped. Lastly, a very rapidly
damped modulation contributes primarily to the 250-600-fs region of the transient.
This portion of the signal is similar in character to the rapidly damped vibrational
coherence observed in polar solutions of BChl, where the slowly damped portion of
the signal is perhaps ten times weaker than observed in the ZnTMPyP transient.63

The dynamic-absorption signals from ZnTMPyP were ﬁt in the time domain to a
model consisting of a single- or double-exponential decay and an oscillatory portion
containing slowly and rapidly damped parts. The models used previously with the
signals observed in BChl solution and in the B820 or B777 systems were intended to
handle only the rapidly damped components in the modulation pattern.63'65 After
truncation of the signal prior to the 250-fs delay point in order to avoid contributions
from the tail of the coherence spike and from nonresonant background signals,95
the oscillatory part was isolated by subtracting a ﬁtted single- or double-exponential
function:

I(t) = A0(1 +A1e-t/T1+A2e-t/T2) (3.1)
The ﬁt parameters are listed in Table 3.1. The transients and ﬁts were normalized by
dividing by A0 in order to compare the amplitude of the modulation components to

the intensity of the pump-induced ground-state depletion signal, which is effectively

constant on the 0—25-ps time scale.

52

 

/

x3

 

 

 

 

 

 

 

 

 

 

AT/T
m A ca 00
O
0 Z,
01- f
i

10 15 20
Time (ps)

Figure 3.5. Femtosecond pump—probe dynamic-absorption transients detected at
422 nm (0.5-nm bandpass) with ZnTMPyP solutions in (a) CH3OH, (b) CD30D, (c)
DMF, (d) CH3CN, and (e) DMSO. The >250—fs portion of the signal in CH3OH-is also
shown in a x3 expanded View. The signal traces are shown superimposed on single-
or double-exponential ﬁt functions of the form A0(1 + A1 e't/ T1 + Aze‘t/TZ) for the
250-fs-25-ps range. The ﬁt parameters are provided in Table 3.1. As plotted, the
signals are normalized by dividing by the non-decaying fraction, A0.

53

Table 3.1. Model parametersa for the exponential decays in the
pump-probe transientsb in ZnTMPyP solutions at 22 °C.

 

 

Solvent A1 T1 (ps) A2 T2 (ps)
CH3OH 0.194 1 4 — —
CD3OD 0.260 2.5 — —
DMF 2.32 2.4 — —
CH3CN 0.160 1 2 0.293 1.4
DMSO 1.64 0 8 5.78 3.2

 

a I(t) = A0(1 +A1e‘t/Tl +A2e‘t/72); A0 is a normalization con-
stant.
b See Figure 3.5.

54

AT/T

 

 

 

1 l

 

1%
>
1
I
>
>
I
I

 

99 93.055.09.09

00 N-L-‘OOO—t

ON OO’IOU‘IOU‘IO
l

4

MAKAA/lll ,‘Iin A II\ AAAAAAAAALI

 

 

  

‘ ‘ UV VWUWVVVWWVWV’VVVHW

 

 

1000 2000 3000 4000 5000
Time (fs)

Figure 3.6. Oscillatory signals obtained from the pump—probe transients from
ZnTMPyP solutions (see Figure 3.5) as the difference between the normalized sig-
nal and the ﬁtted exponential decay functions: in (a) CH30H, (b) CD30D, (c) DMF,
(d) CH3CN, and (e) DMSO. The data points are shown superimposed on a time-
domain model composed of slowly damped and rapidly damped components (see
Equations 3.2-3.6). The model parameters are listed in Tables 3.2 and 3.3.

55

The oscillatory residuals, the difference between the normalized signal and the
ﬁtted decay function, were then ﬁt by a multicomponent model that contains both
slowly damped and rapidly damped oscillatory components (see Figure 3.6). The
slowly damped part was modeled over the 250—7000-fs range as a sum of damped

cosinusoids of the form
_ 2 2
Ii“) = Aie t 0i /2 cos(w0it — (bi) /\/21T (3.2)

with each modulation component i having a center frequency 000,- and phase (1),.

These waveforms correspond to Gaussian lineshapes in the frequency domain,
_ _ . 2 2
1,-(w) = A,- e (w “’01) “2‘5 ’ / (aidzn) (3.3)

where the linewidth is controlled by the standard deviation, 0,- = Awi / 2m, with
Awi representing the full width at half maximum. Equations 3.2 and 3.3 are nor-
malized so that the amplitude Ai corresponds to the area of the lineshape in the
frequency domain and to the intensity of the signal in the time domain; Equation
3.2 corresponds to the Fourier transform of Equation 3.3. As discussed below, an
approximate description of the signal can be obtained with components described

by exponentially damped cosinusoids,
Ii(t) = Ai e‘t/yi cos(w0it — (1),) (3.4)

which correspond to Lorentzians in the frequency domain, but a poorer ﬁt to the
signal was obtained especially at long delays t; the model walks out-of-phase with
respect to the experimental signal, and the time dependence of the amplitude is
poorly described.

The rapidly damped part of the oscillatory residuals (Figure 3.6) was modeled in
the time domain as the sum of two inhomogeneously broadened components with
asymmetric Gaussian lineshapes. It was previously shown that such a model pro-

vides a good description of the rapidly damped vibrational coherence from BChl in

56

polar solution;63'64 the reader is directed to that work for a detailed discussion and
for tests of the model. The two rapidly damped components are assigned, in order
of frequency, to the hindered translational and librational (hindered rotational) inter-
molecular modes between the porphyrin or chlorophyll macrocycle and its clustered,
first-solvation-shell solvent molecules.63v 96, 97

In the work on BChl solutions, each rapidly damped component was described
in the time domain by an integral over a distribution of exponentially damped cos-
inusoids with an intrinsic (or homogeneous) damping time y; the intensities of the

cosinusoids are scaled by a lognormal lineshape,98 £(w):
II”) = I0 dw£(w) cos(wt — (1),) e’t/l’ (3.5)

£(w) is parameterized by its area, At, its center frequency, wot, its width , Awi, and
an asymmetry (or skew) parameter, pi.

In the present work, the £(w) distribution function was approximated with the
piecewise sum of two half-Gaussian lineshapes, 6010,14,, 000,-, 0,, pi), and the integral
is replaced by a sum over an evenly spaced set of sub-Gaussian components I j(t) of
width 03/ 4 spaced by (Ti/2:

22
1,-(t) = Z 6(w0j = 000,- + (j — 8)oj,Ai,w0i,oi,pi)IJ-(t,woj,oj = oi/4) (3.6)
j=0
The j sub-Gaussians are expressed in the time and frequency domain by expressions
analogous to Equations 3.2 and 3.3; in the sum, they are scaled by the intensity of
6(a)) sampled at their center frequencies, woj. The right- and left-side widths ”ml
of 6(a)) are determined by the overall width of the distribution 0,- and its asymmetry
Pi as

O'i= (O'l-l-0'r)/2=0'l(1+pi)/2 (3.7)

The widths or and o; are related by p,- = 07/01; the left- (I) and right-hand (r) half-

Gaussians are deﬁned by Equation 3.3 over 00 < (001' and w 2. 000,, respectively. Note

57

that the choice of the width and spacing of the sub-Gaussians determines the num-
ber required (here, 23) to obtain a smooth approximation of a lognormal distribution.
The sum in Equation 3.6 was truncated at 0 cm’l, if necessary, in order to avoid the
addition of negative frequencies to the waveform, and it was normalized so that the
area of the lineshape in the frequency domain was set to the amplitude parame-
ter At. The resulting rapidly damped waveform and lineshape are indistinguishable
from those obtained in the previous work for a given set of parameters, but the
nonlinear optimization program runs perhaps two orders of magnitude faster than
before because the lognormal lineshape function itself98 is avoided and the number
of sub-Gaussians in the sum is small. A further beneﬁt is that no assumption of the
intrinsic damping time y is required—a Raman echo experiment would be required
to obtain a discrete measurement of the homogeneous linebroadening”, 100

The slowly and rapidly damped portions of the signal were modeled separately
in order to simplify the optimization procedure. The slowly damped part of the
residual oscillatory signal was modeled ﬁrst using a set of components constrained
to have narrow lineshapes (Awi < 10 cm‘l). Starting frequencies and widths for
these components were obtained from a Hanning-windowed Fourier-transform spec—
trum (see Figure 3.7); the window function attenuates the rapidly damped portion
of the signal.92 The twelve most intense components in the Fourier-transform spec-
trum were included in the slowly damped part of the model. The converged model
produced a Hanning-windowed Fourier transform spectrum that matched the exper-
imental spectrum; the frequencies, widths, and relative amplitudes are particularly
well deﬁned because the linewidths are narrow. The rapidly damped model discussed
above was then constrained during the second phase of the optimization process to
return only broad lineshapes (Awi > 10 cm‘l). In all the solvents studied, the sum of
two rapidly damped asymmetric Gaussian components provided a good description

of the rapidly damped residual function.

58

 

801
A

60-

40-

201 x8

40- B

30~

20- x4

10-

1204 C

30i x14

0
r

 

Relative Magnitude

_. -b
01 o o
I l J

0.

801 E
60‘

40_ x1.75
20-

 

 

 

 

0 100 200 300 400
Frequency (cm“)

Figure 3.7. Fourier transform magnitude spectra from the oscillatory residuals (see
Figure 3.6) of the pump-probe signals from ZnTMPyP solutions in (a) CH30H, (b)
CD3OD, (c) DMF, (d) CH3CN, and (e) DMSO. The Fourier transform was applied to the
oscillatory input signals after a Hanning window was applied over the 250-7000-fs
range.

Table 3.2. Solvent dependence of the asymmetric Gaussian lineshape pa-
rameters for the rapidly damped components observed in the vibrational
coherence from ZnTMPyP.

 

 

 

 

 

Solvent
Component Parametera CH3 OH CD30D DMF CH3 CN DMSO

1 (00, cm-1 68 63 82 80 100
Aw, cm-1 49 55 59 50 48

Ab 9.81 10.1 7.67 69.8 62.2

p 1.18 1.17 1.45 1.21 1.17

2 000, cm-1 81 73 94 119 124
Aw, cm-1 59 45 50 59 56

Ab 15.1 17.2 8.10 82.3 125

p 1.18 1.18 1.29 1.15 1.55

Sum (w), cm-1 79 74 95 106 125
z,- A, 24.9 27.3 15.8 152 187

 

3‘ See Equations 3.2-3.6 and the text.
b Normalized to the intensity of the ~215-cm'1 slowly damped compo-
nent in each solvent.

60

.Am.m 588$ 88 82888 888.888 88:88.8: 8 $538 w 828888 .8“ 88:88 and n
.w 888988 h8 88
.3 88:88.88 55 3.. 8882988 55. .88 58 85 o.mim.m 88888.”— 88 83.1786 83d £188 .93 a

 

 

 

588 8:8 888 Sod Sod 53..
88 .88 .38 :8 .88 88 88 .8 3. .88 88 .88 .28 88 .488 8:. 88
28.88.88 88.24.58 28.88.88 83.88.88 88.88.88 2
88 .488. 88 Ed .88 .88 88 .88 888 88 .88 88 a. o .88 .88 8
88 .88 .88 88 .588 .28 :8 88 8 .28 88 888 .88 88 .88 .88 a
8 .8888 o. . 8888 3 88888 on. 8.38 on. 8. 88 w
E .88 88 :8 83. 88 Sod 888 88 88 888. .2: 8o .88 .2: a
E .88 8: :3 88 8: 88 .88 .4: 88 .88 8: 8o .88 8: m
88. 8883 88.8882 68.88.42 8888882 no.6. 882 m
88 82. .8 Rd .88 .8 8.8 8:. .8 88 888 .8 88 88 8 .8 u.
88 .88 .8 88 888 .5. 888 .28 .8 88 888 88 88 .88 88 8
33888.2 88.2.8 48888.8 888.888 88.8. .8 8

88 .38 8. 88 .88 8 K 8.8 8 88 .45 8 88 5.8 8 8

828 2688 8,8 888 888 88888

acmZOm

 

8888.88 58.81888 88ng
8 88588 8858388 8088888 8888 >387. 55 .8..— 8855888 5888:: 886880 .m.m 532.

61

The sum of the rapidly damped and slowly damped models is superimposed on
the data points in Figure 3.6. Both the slowly damped and rapidly damped portions
of the model were found to be robust with respect to the starting parameters used
in both parts of the nonlinear optimization procedure. The final fitted amplitudes
Ai have estimated conﬁdence intervals that are no worse than 255%, and the center
frequencies 000i are known with confidence intervals of i 2 cm’ 1. The parameters for
the optimized time-domain models shown in Figure 3.6 are tabulated in Tables 3.2
and 3.3. The tabulated amplitudes A, are normalized with respect to the intensity of
the ground-state depletion part of the signal (see the ordinate scaling for Figure 3.5)
and to the amplitude for the ~2ZlS-cm‘1 component, the strongest slowly-damped,
high-frequency (000i > 100 cm”1) component in all of the solvents but DMSO, where
the 195-cm‘1 component is the strongest.

Effective exponential damping times for the Gaussian or asymmetric Gaussian
modulation components were estimated by ﬁtting an exponentially damped cosinu-
soid (see Equation 3.4) to the Gaussian waveform for each component in the model.
This exercise corresponds in the frequency domain to optimizing a Lorentzian
lineshape to the corresponding Gaussian lineshape. As an example, the Gaussian
linewidths, A000, and the exponential damping times, y, are compared for ZnTMPyP
in CH3 OH in Table 3.4; similar results (not shown) are obtained in the other solvents.
Figure 3.8 compares the Gaussian and ﬁtted Lorentzian waveforms for the 3, 38, and
215-cm‘1 components. The Lorentzian waveforms were optimized over the 250—
7000-fs range, as in Figure 3.6, but the results are comparable when the entire 150-
ZSOOO-fs range shown in Figure 3.8 is fit. In general, the fitted Lorentzian waveform
is more intense than Gaussian waveform at the beginning and end of the waveform;
if the Lorentzian waveform is constrained to fit the Gaussian waveform at the end of
the modulation pattern, the resulting damping time is longer. This issue is especially

important for the slowly damped 3-cm‘1 asymmetric Gaussian component, which

62

Table 3.4. Comparison of Gaussian linewidths and effective exponential
damping timesa for the modulation components observed in the vibra-
tional coherence from ZnTMPyP in CH3OH.

 

 

000,cm'1 Aw, cm‘1 y, ps
3 3.47 2.941).C

21 8.88 1.36
38 2.03 6.71C
68d 49 0.223
81cl 59 0.182
89 2.39 5.64
138 2.78 4.85
177 2.96 4.57
191 2.78 4.87
215 1.67 8.14c
244 1.90 7.16
264 3.62 3.58
284 3.16 4.11
312 3.24 4.16

 

a See Equation 3.4 and Figure 3.8.

b Lower limit; an upper limit of y = 21.6 ps is obtained by fitting to
the t > 15 ps portion of the signal.

C See Figure 3.8.

d Rapidly damped component, see Equation 3.6 and the text.

63

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Relative Magnitude
O

 

 

 

 

I 1 I l

1 5 20 25

OH
01
—L
C

Time (ps)

Figure 3.8. Comparison of the Gaussian waveforms (thick curves) obtained for the
3, 38, and 215-cm‘1 components in the oscillatory signals observed from ZnTMPyP
in CH30H solution with fitted exponentially damped waveforms (thin curves, see
Equation 3.4). The Gaussian linewidths and damping times are listed in Table 3.4.

64

 

 

 

 

 

 

Relative Magnitude

 

 

 

 

1
0 100 200 300 400
Frequency (cm'l)

 

 

Figure 3.9. Frequency domain representation of the time-domain models of the os-
cillatory signals (see Figure 3.6) observed in ZnTMPyP solution: in (a) CH30H, (b)
CD30D, (c) DMF, (d) CH3CN, and (e) DMSO. The broad features in the SO—ZOO-cm‘1
regime are shown superimposed with the spectra (dotted lines) of their underlying
components; in (d) and (e) these features are attenuated in order to keep them on
scale. The spectrum from the 2—4-cm‘1 slowly damped component in (a)-(d) is also
attenuated.

65

 

 

 

AT/T

 

 

 

 

 

 

 

0 200 400 600 800 1000 1200 1400
Time (is)

Figure 3.10. Time-domain representation of the rapidly damped oscillatory compo-
nents (see Figures 3.6 and 3.9) in the pump-probe signals from ZnTMPyP solutions
in (a) CH30H, (b) CD30D, (c) DMF, (d) CH3CN, and (e) DMSO. The dotted portion of
the signal is extrapolated from the ﬁtted region of time (see Figure 3.6).

66

exhibits a 2.94-ps damping time if the overall waveform is fitted, but if the fit is con-
strained to the >10-ps region, a 21.6 ps damping time is obtained. As mentioned
above, we find that Lorentzian waveforms result in a poor overall model for the os-
cillatory residuals even if constrained over the 250-6000-fs region, so the damping
times in Table 3.4 have to be regarded as crude lower-limit estimates of the damping
time. Given that Gaussian lineshapes are observed, and that these lineshapes inher-
ently report inhomogeneous broadening, the true homogeneous damping times may
be signiﬁcantly longer.

Figure 3.9 shows the frequency domain representation of the overall time-domain
model for the oscillatory residuals shown in Figure 3.6. The spectra are dominated
by the broad lineshapes from the rapidly damped components over the SO--200-cm‘1
region. The slowly damped component whose lineshape is centered at 2—4 cm“1 is,
however, comparable in intensity to the sum of the two rapidly damped components
(see Tables 3.2 and 3.3). The other slowly damped components are an order of mag-
nitude less intense.

Figure 3.10 shows a time-domain representation of the summed rapidly damped
components from the models shown in Figure 3.6. Because the effective damping
time for both of the rapidly damped components is <250 fs in all of the solvents,
a great deal of the amplitude of this component lies in the early-time truncated
portion of the pump—probe transient (see Figures 3.5 and 3.6). As extrapolated in
Figure 3.10, the waveforms in CH30H and CD3OD are very similar to the rapidly
damped vibrational coherence observed previously in polar solutions of BChl, where
the intramolecular, slowly damped vibrational coherence is comparatively weak.63' 64
The strong positive-going recurrence at ~200 fs for the waveform in CH30H is only
partially observed in the analyzed time region of the residual; a weaker second re-
currence at ~600 fs is followed by a broad negative-going trough at ~900 fs that

recovers to the baseline over the 1000—1 SOO-fs range. As the solvent is varied, the

67

extent in time of the rapidly damped waveform contracts as the mean frequency,
((0), increases (see Figure 3.10). From the sum of the two underlining component
lineshapes (see Figure 3.9), .’M(w) = 11(w) + 12(w), the mean frequency obtained
using a normalized mean-value relation,

__ 16°de(00)«)
- J6°dwN(w)

 

(w) (3.8)

shifts over the 79—125-cm"1 range as the solvent is varied (see Table 3.2 and Fig-
ure 3.11). As compared to those observed in CH30H, the spectra of the two rapidly
damped components in CD30D (see Figure 3.9) are downshifted by S and 8 cm’1

and the mean frequency is downshifted by S cm‘1 (see Table 3.2).

3.5 Discussion

The femtosecond pump-probe, dynamic-absorption transients obtained with Soret-
band excitation of polar solutions of ZnTMPyP (see Figure 3.5) exhibit a complex
modulated signal superimposed on an exponential or double-exponential decay func-
tion with a ~2-ps time constant leading to a non-decaying offset over the O-ZS-ps
time range. Similar decay components and time constants are attributed to the
$2 —> 51 internal-conversion process in pump—probe or ﬂuorescence-upconversion ex-
periments with ZnII tetraphenylporphyrin (ZnTPP) in nonpolar solvents,101'102 but
for ZnTMPyP in polar solvents the decays arise from vibrational relaxation and vibra-
tional energy transfer to the solvent in the 81 state following an ultrafast (Ts lOO-fs)
intemal-conversion process. In femtosecond transient-absorption experiments em-
ploying continuum probe pulses and 1 SO-fs pump pulses in the Soret band at 404 nm,
Fontaine-Aupart and co-workers103 failed to detect an Sg-state stimulated-emission
band from ZnTMPyP in aqueous solution, so the Sz-state population relaxes to the
Sl-state vibronic manifold almost as rapidly as it is prepared by the pump pulse.

In contrast, a distinct stimulated-emission band was observed for ZnTPP under the

68

130+

DMSO 0
120 -

1104

     
    

Acetonitrile
100 -

90-

Mean Frequency (cm")

80 -
Methanol

 

 

70-

2 3 4
Dipole Moment (D)

Cd
_L

Figure 3.11. Dependence of the mean frequency of the rapidly damped oscilla-
tory components (see Figures 3.6 and 3.9) observed in the pump-probe signals from
ZnTMPyP solutions in CH30H, DMF, CH3 CN, and DMSO. The data points are shown
superimposed with a trend fitted to Equation 3.12.

69

same optical conditions; the intensity of the stimulated emission decays with a 2-ps
time constant as the Sz-state population relaxes to the Sl-state. In ZnTMPyP, pop-
ulation deposited in excited vibronic levels of the Sl-state manifold by the $2 —>Sl
internal-conversion process is detected in terms of excited-state absorption (ESA)
transitions to vibronic levels in the Soret band (states Sn). The time-resolved pump—
probe spectra observed by Fontaine-Aupart and co-workers exhibit a broad-region
of long-lived (> 5 ps) excited-state absorption at wavelengths above 450 nm; the rel-
atively sharp, ground-state depletion band that lies to the blue has a maximum at
435 nm and extends to ~ 405 nm.103 At wavelengths below 435 nm, however, it is
likely that the ground-state depletion and BSA bands overlap extensively. Thus, in
our experiments, the net ground-state depletion signal decreases in intensity as the
Sl-state population cools on the ps time scale because the ESA band shifts to the
blue and overlaps more strongly with the static ground-state depletion band at the
42 2-nm probe bandpass.

The intensity of the decays we observe in the ZnTMPyP pump-probe signals are
solvent dependent, and the decay in two of the solvents (CH3 CN and DMSO) is biexpo-
nential. The decays observed for ZnTMPyP in DMSO and CH3OH are not significantly
altered (not shown) when the laser is tuned to 425 nm, closer to the Soret band’s max-
imum but still on the blue side. These observations show that the observed dynamics
are less dependent on the initial vibronic state prepared in the Sz-state manifold than
they are on the nature of the solvent. Given that dynamic solvation does not con-
tribute to the signal because the 82 state persists for such a short period following
absorption of the pump pulse, the rate at which the excess vibrational energy of the
S] state is dissipated is solvent dependent. Biexponentiality would arise in this case
from the presence of two ensembles of ZnTMPyP with different first-solvation shell
structures. A similar explanation was invoked by Zewaﬂ and coworkers to account

for the biexponential internal conversion for ZnTPP in methylene chloride.101

70

The conclusion that the 82 state of ZnTMPyP decays to the 81 state via an intemal-
conversion process on the s 100-fs time scale is especially significant with respect
to the present work because it restricts assignment of the modulation components
observed in the pump—probe signals to coherent wavepacket motions on the ground-
state potential-energy surface. Table 3.4 shows that all of the slowly damped modu—
lation components have effective damping times that are > 1 ps; even the two rapidly
damped components have effective damping times that are >150 fs. It is unlikely
that the ESA transitions that overlap with the probed region of the spectrum con—
tribute to the modulated signal; the Sg—>Sl intemal-conversion process would be
expected to be incoherent with respect to the initial vibrational phase prepared by
the pump pulses.104

Except for the 2-4-cm‘ 1 component, the modulation components with the largest
amplitudes Ai are observed in the ZOO-cm‘1 region of the spectrum. This pattern
of amplitudes is consistent with an assignment to coherent wavepacket motions on
the ground-state potential energy surface because these experiments employed SO-fs
pump pulses. If the ground- and excited-state potential-energy surfaces of the system
are displaced with respect to the coordinate of a normal mode of vibration, moving
wavepackets on the ground- and excited-state potential surfaces are generated by
two successive actions of the the pump field.24'26'33 The ground-state wavepacket
is created by a process that directly corresponds to resonance Raman scattering.
The duration of the pump pulse controls the displacement and momentum of the
ground-state wavepacket because it places a limit on the time interval between the
ﬁrst action of the pump field that prepares the ground—excited-state polarization
and the second action that materializes the wavepacket on the ground-state surface.
The pump—probe signal is modulated optimally by ground-state wavepacket motion
when the pump-pulse duration is about one-third of the mode’s period; with pulses

that are shorter than the optimum, the wavepacket is not displaced very far away

71

from the Franck-Condon geometry, so only a small modulation of the transmitted
probe signal results. Of course, the depth of modulation of the pump—probe signal
decreases as the pump-pulse duration increases beyond the optimum duration to-
wards the mode’s period.33 With the SO-fs pulses used in the present experiments,
the optimum mode frequency is 222 cm‘l; the relative strength of the ~215-cm’1
component observed in each solvent is probably due to the close matching of the
pump—pulse duration with the mode frequency. Even though the measured ampli-
tude of the 312—cm“1 mode is only about one-ﬁfth that of the 215-cm‘1 mode (see
Table 3.3), the relative resonance Raman activities of the two modes are compara-
ble if one considers that the optimum pulse duration that would drive a 312-cm“1
wavepacket is ~32 fs.

The unusually large amplitude of the very low frequency, 2—4-cm‘1 modula-
tion component would seem to be in conﬂict with an assignment to a ground-state
wavepacket motion. The modulation depth that would be expected with SO-fs pump
pulses would be close to zero for such a low frequency mode unless it is charac-
terized by an unusually large excited-state displacement. Most of the intramolec-
ular vibrational modes of ZnTMPyP would be expected to exhibit comparable dis-
placements, with the strongest modes associated with the n-electron density in the
porphyrin macrocycle, so the rule-of-thumb about the optimum pulse duration dis-
cussed above would reasonably apply.33 An exception might be anticipated for the
internal rotation of the peripheral N-methylpyridyl rings (see Figure 3.1). In the
ground state, the rings are rotated well away from the the plane of the porphyrin; in
the excited state, owing to the ﬂow of the Tr-electron density from the porphyrin re-
gion, the minimum-energy geometry would extend the conjugated region by making
the rings and porphyrin coplanar. Thus, an internal rotation of the rings is launched
in the excited state by resonant excitation of the Soret band because the Sg-state

potential-energy surface is sloped in the Franck-Condon region along that coordi-

72

nate; the internal rotation would obtain signiﬁcant momentum prior to preparation
of the ground-state wavepacket on the ground—state surface, where the rotation is
bound only owing to the poor delocalization of the n-electron density and owing to
steric hindrance. This assignment of the 2—4-cm‘1 mode is also prompted by its
signiﬁcant solvent dependence (see Table 3.3); the highest frequency (4 cm‘l) is ob-
served in the most viscous solvent (DMSO), and perhaps the large amplitude in DMF
relates to a specific clustering around the rings.

The frequencies, linewidths, and relative intensities of the the other slowly
damped modulation components are relatively insensitive to the choice of solvent
(see Table 3.3). These components are well modeled (see Figure 3.6) by relatively
narrow Gaussian components (Equation 3.2). The solvent independence of the mod-
ulation frequencies supports a structural assignment of all of these features to
the intramolecular, skeletal modes of the ZnH-porphyrin macrocycle. Normal-mode
calculations using the B3LYP hybrid density functional for the ZnTMPyP-methanol
complex (see Figure 3.1) are consistent with an assignment of the ~40-cm"1 and
~21 S—cm‘1 components to the metal-doming and ZnH—axial-ligand stretching modes,
respectively; somewhat higher frequencies are assigned to these modes in Fe“—
porphyrins.105 Of these, the former is evidently more solvent sensitive, but it should
be kept in mind that the frequencies and intensities of the very lowest frequency
components in the slowly damped set of features are known with less confidence
than for the higher-frequency or more rapidly damped features. As compared to the
amplitude of the rapidly damped components, the slowly damped components are
much stronger in ZnTMPyP with Soret-band excitation than observed with Q-band
excitation of BChl solution; the resonance Raman intensities of the intramolecular
modes of porphyrins are strongly enhanced by excitation in the Soret band.106

The rapidly damped (y < 1 ps) part of the vibrational coherence observed in

ZnTMPyP solution exhibits solvent-dependent time-domain waveforms that are very

73

similar to those observed in BChl solution. In the frequency domain, the two rapidly
damped components present inhomogeneously broadened lineshapes that are anal-
ogous to the ones assigned to the hindered translational and librational modes in
instantaneous normal mode analyses of molecular dynamics simulations of polar
liquids.96'97i107 A structural assignment of these components to intermolecular
modes between the Zn-porphyrin and the clustered solvent molecules in the ﬁrst sol-
vation shell is directly supported by the observation of an isotope shift in methanol
and perdeuterated methanol solution (see Table 3.2 and Figure 3.9) of approximately
the right magnitude. The mean frequency observed in CH30H is 79 cm'l; in the
harmonic-oscillator limit, if the mode involves an intermolecular mode between a sin—
gle CH3 OH molecule and the ZnTMPyP molecule, the mode should exhibit a downth
to 74.7 cm“1 using the to D = wH(uH/pp)0'5 relationship108 between the frequency
w D of the deuterated species and the frequency w H of the protonated species and
their reduced masses up and pH, respectively. The observation of a slightly lower
mean frequency, 74 cm’l, might indicate the presence of some higher molecular
weight species, perhaps from hydrogen-bonded chains,109‘1 12 but the conﬁdence in-
terval (:2 cm‘l) is larger than this discrepancy. Consistent with the intermolecular
mode assignment, a smaller isotope shift was observed in the presence of CH30D
than in CH30H (results not shown); the observed mean frequency of 76 cm"1 in
CH3OD is within the conﬁdence interval of the expected value of 77.9 cm-l.

As noted in the Introduction, the solvent dependence of the rapidly damped com-
ponents (see Table 3.2 and Figure 3.9) provides a test of the form of the van der

Waals potential introduced in the previous work on BChl solutions,63

2 2 2 2
V = 12 _ Clull lu2| 0(2lﬂ1l + 0‘1IH2I 2 6 .
0(r) a/r (19011012 + (4ns0)2 + 47T80 D r (3 9)

 

 

74

A relation for the natural frequency of the intermolecular mode in the limit of small

displacements from the equilibrium structure,

7/6
Clullzluzl2 0(2|l11|2+0¢1|112|2 7/3 1/2
_ _ + NB
(ba1a2+ (4 so)? 4 £0 2 u

 

 

(3.10)
is obtained from a Taylor series expansion of Equation 3.9. Both expressions con—
tain a series of terms arising from the physical components of the interaction: the
constant at scales the Pauli exchange interaction, the London-dispersion interaction
is scaled by the constant [9 = 31112/ 2(11 + I2), with [1,2 representing the ionization
potentials for the two molecules, c = 2/3kBT scales the dipole-dipole interaction,
and the 0(2IM1 I2 and 0:1 lugl2 terms arise from the solute-dipole and solvent-dipole
induced-dipole interactions, respectively.113'116 In these equations, Hi and ori cor-
respond to the dipole moment and polarizability for the solute (subscript 1) and
solvent (subscript 2); r is the distance between the two molecules, [,1 is the reduced
mass for the intermolecular oscillator, D represents the dielectric constant for the
solvent, and £0 relates the permittivity of free space.

If the solute chromophore is charged, the intermolecular potential gains two ad-

ditional terms, for the ion-dipole and ion—induced dipole interactions:

_ __ «211le2 erZ 2 4
VQ(r) — V0 ((4Tl'50)2 + 41r50)/2D r (3.11)

The ion-dipole term depends linearly on the charge Q of the solute and on the square
of the solvent’s dipole moment, pg; the ion—induced-dipole term contains the polar-
izability 042 of the solvent and the square of the charge, Q2. Both terms depend on
7‘4, so they decay much less rapidly with increasing distance than the rest of the
terms in the intermolecular potential. The mode frequency expression that follows
from Equation 3.1 1 is too lengthy to be included here, but it predicts that the charge-
dependent terms signiﬁcantly increase the mode frequency over that predicted by

Equation 3.10.

75

 

 

 

Potential Energy (cm'1)

 

 

 

 

I

r
2.5 3.0

‘ I
1.5 2.0
Intermolecular Distance (A)

Figure 3.12. Model potential-energy curves for the ZnTMPyP-CH30H complex cal-
culated using Equation 3.11 and the experimentally observed mean intermolecular
mode frequency, 79 cm'1 (see Table 3.2): (a) Q = O; (b) Q = 1; and (c) the attrac-
tive, charge-dependent terms for Q = 1. Table 3.5 lists the other parameters for the
potential curves and compares req and me for curves (a) and (b).

76

Table 3.5. Parameters for the model ZnTMPyP-CHgOH intermolecular potentials

shown in Figure 3.12

 

 

 

Parametera Value
exchange (Pauli) interaction coefficient, a 76.2 eV A12
London-dispersion interaction coefﬁcient, 19 = 3I112 /2(I1 + 12) 9.35 eVb'C
ZnTMPyP dipole moment, lull 0.663 Db
CH3 OH dipole moment, Iﬂzl 1.70 DC
ZnTMPyP polarizability, a1 109.8 A313
CH30H polarizability, a2 3.29 A3C
ZnTMPyP-CH3OH reduced mass, (.1 30.7 Da
CH3OH dielectric constant, D 33C
req (Q = 0) 1.90 A
me (Q = 0) 286 cm-1
Teq (Q = 1) 1.83 A
Vmin(Q= 1) 510 cm‘1

 

‘3 See Equations 3.9 and 3.11 and the text.
b From B3LYP 6-31G electronic structure calculation.

C From reference 1 l 7.

77

Figure 3.12 shows a pair of model potentials for the ZnTMPyP-CH3 OH intermolec-
ular mode that illustrates the effect of turning on the charge-dependent terms in
Equation 3.11 and of changing the intermolecular distance. The only parameter in
the intermolecular potential that is not known from the literature, from a calculation,
or from experiment is that for the exchange interaction, a, but it can be estimated
given an experimental measurement of the mode frequency and an initial assump-
tion of Q = 0 so that the charge-dependent terms are inactive. Combination of
Equations 3.9 and 3.10 and the observed mean frequency of 79 cm'1 (see Table 3.2)
returns a value for a of 76.2 eV A12; the rest of the parameters used in Figure 3.12
are listed in Table 3.5 along with estimates for the equilibrium bond distance, Teq,
and the bond-dissociation energy, me, with Q = O and Q = 1. If a is held constant,
the effect of changing Q from 0 to 1 is a sharpening of the potential near the mini-
mum, which indicates an increased mode frequency, almost a doubling of me, and
a modest 0.07 A reduction in req (compare curves (a) and (b) in Figure 3.12). Curve (c)
in Figure 3.12 shows the magnitude of the charge-dependent terms in Equation 3.1 1,
as calculated for the Q = 1 potential. This curve can be used to gauge the contribu-
tion of the charged terms to the stabilization and mode frequency when the charges
are located at some distance from the clustered solvent molecules. The ones that
interact with the n-electron density in the ground state are those that contribute to
the ground-state vibrational coherence, and on average these solvent molecules are
constrained to be more than 2.5 A from the charges on the N-methylpyridyl rings.
This distance estimate is based on the assumption that the charge is localized on
the nearest carbon atom of the N -methylpyridyl ring and that the solvent molecule is
ﬁxed at Teq for the Q = 0 case normal to the porphyrin ring above the adjacent meso
carbon atom, to which the N-methylpyridyl rings are attached. At this distance, the
charge-dependent terms account for a 70-cm‘1 stabilization, about 25% of me for

Q = 0. Given that the charge is actually delocalized over the N-methylpyridyl ring in

78

 

the ground state, the integrated interaction energy will be considerably smaller than
this worst-case estimate. We conclude that it is a good approximation to neglect the
charge-dependent terms in the ground-state intermolecular potential. In the excited
state, because the n-electron density is extensively delocalized from the porphyrin
region onto the N-methylpyridyl rings, the intermolecular mode frequency should be
signiﬁcantly increased from that in the ground state owing to a larger contribution
of the charge-dependent terms in Equation 3.1 1.

The expression for the intermolecular mode frequency in the absence of charge-
dependent terms, Equation 3.10, can be simpliﬁed to give a relation for the depen-

dence on the dipole moment of the solvent as
v = (C1 + C2|u2|2)7/6 (3.12)

where C1 and C2 are constants. This expression follows directly from Equation 3.10
with the assumption that all of the parameters other than the dipole moment of
the solvent molecule are ﬁxed; a simpler, approximate form was used in the previ-
ous work on BChl solutions.63 Figure 3.11 plots the mean frequency of the rapidly
damped components observed in the ZnTMPyP solutions as a function of the gas-
phase dipole moment of the solvent. The mode frequency increases as the dipole
moment increases in a manner that is consistent with the form of Equation 3.12. The
ﬁt of the mode frequencies to Equation 3.12 extrapolates to a mode frequency near
70 cm“1 in the nonpolar limit. As anticipated in the Introduction, this y-intercept
value is signiﬁcantly lower than the value of ~100 cm“1 observed in BChl solution.
ZnTMPyP’s four-fold symmetry results in a dipole moment of zero in the plane of
the porphyrin; the out-of-plane doming of the ZnII ion due to the axial coordination
of a solvent ligand results in a small dipole-moment component orthogonal to the
plane of the porphyrin (0.66 D, as obtained from the B3LYP 6-31G electronic struc-
ture calculation for the methanol complex, see Figure 3.1). The dipole moment of

BChl is signiﬁcantly larger (3.6 D,118 so the 0(2IM1 I2 induction‘term in Equations 3.9

79

 

and 3.10 that contributes to the y-intercept constant C1 in Equation 3.12 is more
than 25 times smaller for ZnTMPyP since this term scales as the square of the dipole
moment. The remaining term in Equations 3.9 and 3.10 that contributes to the y-
intercept term of Equation 3.12 is the London-dispersion term, boq 0:2. Thus, a great
deal of the residual 70 cm‘1 of the y-intercept value obtained for ZnTMPyP is due
to the London-dispersion term. This conclusion is consistent with the general ob-
servation that the dipole—dipole and London-dispersion terms in the intermolecular
potential are perhaps 10 times larger than either of the induction terms.113‘116
Some of the molecular details of the interaction between ZnTMPyP and the sur-
rounding solvent are suggested by deviations from the ﬁtted curve shown in Fig-
ure 3.11 and by the dependence of the resonance Raman activity for the intermolec-
ular mode on the solvent. The reduction of Equation 3.10 to Equation 3.12 requires
that the polarizability 012 for the solvent molecule is constant as the dipole moment
ug varies. The dispersion of the points for the solvents DMSO, CH3CN, and DMF
from the ﬁtted curve in Figure 3.11 suggests a possible contribution of the solvent
polarizability in the strength of the intermolecular interaction with the ZnTMPyP so-
lute. These solvents have similar dipole moments, yet the mean frequency of the
intermolecular mode varies in them over the 95-125-cm‘1 range, a span of about
one-ﬁfth of the mean value. The increase of the mean frequency from that observed
in methanol (a2 = 3.29 A3 117), 79 cm‘l, to that for acetonitrile (0:2 = 4.4 A3 117),
106 cm’l, depends mostly on the induction term 011 |ﬂ2|2 since the dipole—dipole
term C|M1 [2 lug |2 is relatively small owing to the small dipole moment of ZnTMPyP.
The induction term is relatively large in porphyrin and BChl solutions because of
the large polarizabilities (0(1) of these solutes. The difference between the mean fre-
quency observed in acetonitrile and DMSO (0:2 = 8.87 A3 119), however, probably
arises largely from the enhanced polarizability of the sulfonyl group over that of the

carbonyl. Further, the decreased mean frequency in DMF (a2 = 7.81 A3 117) has

80

 

to be attributed to a speciﬁc solvent effect that decreases the strength of the inter-
molecular interaction given that the polarizability of DMF is almost as large as that
of DMSO.

The solvent dependence of the amplitude of the rapidly damped modulation com-
ponents (see Table 3.2) suggests that the resonance Raman intensity enhancement
for the intermolecular mode partly depends on the covalency of the interaction, the
degree to which the Tr-electron density of the solute chromophore is mixed with that
of the clustered solvent molecule. The use of a van der Waals potential to follow
trends in the mode frequency invokes a purely electrostatic picture, of course, but
some involvement of covalency is suggested by the observation that the strongest
modulation amplitudes occur in CH3CN and DMSO, which feature cyanide/nitrile and
sulfonyl groups, respectively. This observation follows the same trend observed with
Q-band excitation of polar solutions of BChl; the amplitude of the intermolecular vi-
brational coherence was strongest by far in pyridine solution.63 As mentioned above,
DMF seems to be an outlier; the intermolecular modes in DMF and CH3 OH have com-
parable amplitudes even though the former contains delocalized n-electron density
over the amide group. It follows that both the Albrecht A- and B-termslzov121 con—
tribute to the resonance Raman intensity. The A-term would primarily include effects
from the change of shape and extent of the n-electron density that yield a gradient
in the excited-state potential-energy surface in the Franck-Condon region, whereas
the B-term would include couplings of the excited state to nearby states. The part
of the A-term enhancement that arises from the redistribution of n-electron den-
sity in ZnTMPyP’s excited state (see Figure 3.1) is likely to be small given that the
intermolecular modes are easily observed in BChl, which lacks a comparable ground-

to-excited-state displacement of electron density.

81

 

3.5.1 Conclusions

The results discussed in this chapter support the hypothesis that intermolecular
modes between porphyrin or chlorophyll macrocycles and clustered molecules in the
ﬁrst shell of solvent contribute the most intense components to the low-frequency
(0-300-cm‘1) vibrational coherence in polar media. The corresponding mode fre-
quencies fall in the right range to account for the modes that dominate the Marcus
reorganization energy for electron-transfer reactions in photosynthetic reaction cen-
ters. In comparison to the intermolecular modes, the intramolecular modes from
the porphyrin or chlorophyll macrocycle account for features in the vibrational co-
herence that are at least an order of magnitude weaker. Further, an analysis of the
electronic structure of ZnTMPyP suggests that there should be a signiﬁcant ground-
to-excited-state change in the mode frequency and stabilization of the intermolecular
modes owing to the change in shape of the Tr-electron density. The contribution of
ion-dipole and ion-induced-dipole terms to the intermolecular potential in the ex-
cited state of ZnTMPyP should result in a signiﬁcantly higher intermolecular mode
frequency. These projections suggest an important role for intermolecular modes
between the prosthetic groups and their ﬁrst-solvation-shell surroundings in the sta-
bilization of the charged intermediate and product species that occur in proteins

during redox catalysis.

82

CHAPTER 4

Excited-state Vibrational coherence in
methanol solution of

ZnII tetrakis(N-methylpyridyl)porphyrin

4.1 Summary

We have employed femtosecond dynamic-absorption spectroscopy to observe
excited-state wavepacket motions in ZnII meso-tetrakis(N-methylpyridyl)porphyrin
(ZnTMPyP) in methanol solution. The pump-probe transients observed in ZnTMPyP
solution with Q-band excitation exhibit a net excited-state absorption character. The
signals are weakly modulated by slowly damped (effective damping time y>1.5 ps)
components that correspond to skeletal normal modes of the porphyrin macrocycle,
but by far the dominant modulation features are a pair of rapidly damped (y<400 fs)
components arising from intermolecular modes with ﬁrst-shell solvent molecules.
The 256 cm‘1 mean frequency of the rapidly damped components is signiﬁcantly
higher than observed previously in the ground state, 79 cm‘l. This increase in fre-

quency arises from an extensive delocalization of the n-electron density from the

83

porphyrin region to the singly charged N-methylpyridyl rings. In the excited state,
the van der Waals intermolecular potential accordingly obtains large ion-dipole and
ion—induced-dipole terms that account for the increased mode frequency and result
in a signiﬁcant stabilization of the equilibrium structure. These results suggest an
especially important functional role for the intermolecular modes between the re-
dox chromophores and the surrounding protein medium in photosynthetic reaction

centers that involves trapping of charged intermediates.

4.2 Introduction

The observation of vibrational coherence in femtosecond pump—probe ex-
periments with impulsive excitation of electronic chromophores in solu-
tion” 26' 29. 33' 35' 122' 123 is usually associated with resonance Raman activity arising
from an excited-state displacement of a small number of skeletal normal modes of
the chromophore. In several classes of proteins where light-induced chemistry oc-
curs, vibrational coherence in the skeletal modes of a prosthetic group is associated
with the reaction coordinate. Shank, Mathies, and coworkers characterized coher-
ent wavepacket motion in retinal’s torsional modes associated with formation of the
photoisomerization product state in bacteriorhodopsin and rhodopsin.26' 32' 35' 3942
Champion and coworkers observed an analogous reaction-driven vibrational co-
herence in the ground-state out-of—plane porphyrin modes in myoglobin and cy-
tochrome c following photodissociation of axial ligands.53'55-61 Martin, Vos, and
coworker8124 have observed vibrational coherence in cytochrome c oxidase aa3 upon
photolysis and transfer of carbon monoxide from heme £13 to CuB. The excited-state
vibrational coherence observed by Vos and Martin from the primary electron donor,
P, in the purple-bacterial photosynthetic reaction center,4 3'51 however, is likely to in-

volve modes that are derived from the surrounding protein mediumlv 22 rather than

84

just from the paired bacteriochlorophyll (BChl) chromophore itself.73'125'126 Be-
cause of their low frequencies, the modes would be expected to be delocalized over
the protein structure spanning the reaction center’s chromophores just as phonons
are in molecular crystals.43v45’ 50

In the previous chapters, we discussed how the ground-state vibra-
tional coherence observed in solutions of BChl and of Zn“ mesa-tetrakis(N-
methylpyridyl)porphyrin (ZnTMPyP) suggest, in contrast, that by far the strongest
contributions to the vibrational coherence in the 100-cm‘1 regime arise from local-
ized intermolecular modes with clustered, ﬁrst-shell solvent molecules.63‘65v 88 The
pump—probe signals observed with Q-band excitation of BChl in polar solvents are
modulated by rapidly damped (time constant y<200 fs) components that shift to
higher frequencies as the dipole moment of the solvent increases. The mean fre-
quency of these modulation components follows the natural frequency of a van
der Waals intermolecular potential that contains dominant contributions from the
London-dispersion and dipole-dipole interactions.63 The slowly damped (3122000 fs)
modulation components that arise from the skeletal modes of the BChl macrocycle
are perhaps ten times less intense than those from the solvent modes.54 Similar as-
signments were made for the ground-state vibrational coherence observed in polar
solutions of ZnTMPyP with Soret—band (420-nm) excitation. The normal modes of
the porphyrin macrocycle and its single solvent-derived axial ligand contribute very
slowly damped features to the vibrational coherence, some of which persist even to
the 20-ps delay point. The rapidly damped, solvent-dependent modes again account
for the dominant features. The dependence of the mean frequency of the rapidly
damped components follows an intermolecular potential that exhibits a lower mode
frequency in the nonpolar limit than observed in BChl (70 cm"1 and 120 cm‘l,
respectively), and an isotope-dependent shift was observed when the signals from

methanol and perdeuterated methanol were compared. The magnitude of the shift

85

indicates that the intermolecular modes arise in methanol solution predominantly
from 1:1 complexes with the porphyrin solute.88

The intermolecular potential used in the discussion of the ground-state vibra-
tional coherence in BChl and ZnTMPyP solutions includes only the terms that arise
from the polarizability and dipole moment of the neutral solute and solvent. In
ZnTMPyP, the Tr-electron density in the ground state is conﬁned to the porphyrin
macrocycle (see Figure 3.1a), so an attacking solvent molecule does not strongly sense
the positive charges on the peripheral N-methylpyridyl rings. In the 11* excited states
(see Figure 3.1b), however, the Tr-electron density is extensively delocalized from
the porphyrin over two of the N-methylpyridyl rings, so the intermolecular potential
between ZnTMPyP and clustered solvents should gain ion-dipole and ion—induced-
dipole terms. These charge-dependent terms would be expected to contribute to a
signiﬁcant shift to higher frequency for the intermolecular oscillator. We have put
these ideas to the test in this chapter. We show that pump-probe signals obtained
with Q-band excitation of ZnTMPyP monitor excited-state wavepacket motions owing
to detection of a net excited-state absorption signal. As expected, the rapidly damped
portion of the vibrational coherence shifts to a much higher frequency than observed
in the ground-state vibrational coherence observed with Soret-band excitation. These
results advance the hypothesis that resonance Raman-active intermolecular modes
with ﬁrst-solvation-shell components contribute dominantly to the low-frequency vi-
brational coherence in porphyrin and BChl systems. We conclude with a brief discus-
sion of how the charge-dependent terms in the intermolecular potential should play
an important role in the trapping of charge-separated intermediates in the photosyn-

thetic reaction center.

86

4.3 Experimental

4.3. 1 Sample Preparation

ZnTMPyP (CAS 28850-44-4) was used as received from Frontier Scientiﬁc. Methanol
(CH3OH, spectrophotometric grade) was obtained from Sigma-Aldrich. For use in
femtosecond pump-probe experiments, solutions of ZnTMPyP were prepared by dis-
solving the dry ZnTMPyP powder in methanol to obtain an absorbance of 0.4 for a
path length of 1.0 mm at the center of the laser spectrum at 625 nm, as detailed
below. The solution was passed through a 0.22-m ﬁlter prior to checking the ab-
sorbance. The samples were held in the femtosecond pump-probe spectrometer at
room temperature (23 °C) in a fused-silica ﬂow cuvette (0.5-mm path length). A peri-
staltic pump was used to circulate a 10-mL reservoir of sample solution through the
cuvette at 2.70 mL/min. The sample’s absorption spectrum was monitored during
the experiment for changes arising from photochemistry or permanent photobleach-
ing. The sample reservoir was exchanged with fresh solution several times during

each run.

4.3.2 Continuous-Wave Absorption and Fluorescence Spectroscopy

Absorption spectra were obtained at 23 °C with a Hitachi U-2000 spectrophotometer
(2-nm bandpass). Fluorescence spectra were acquired at 23 °C with a Hitachi F-4SOO
spectroﬂuorimeter (S-nm bandpass for the excitation and emission monochroma-
tors). As presented as a function of wavenumber, the ﬂuorescence intensities are
multiplied by the square of the wavelength in order to compensate for the ﬁxed (in

wavelength units) spectral bandpass of the emission spectrometer.89

87

4.3.3 Femtosecond spectroscopy

Femtosecond pump-probe transients with impulsive excitation were recorded using
the dynamic—absorption technique, in which the probe beam is dispersed in a grating
monochromator after passing through the sample.32v 33’ 35‘37 Most of the instrumen-
tation and methodology is similar to that described in the previous work on ZnTMPyP
solutions with Soret-band excitation.88 In this work, however, the pump and probe
pulses were obtained from the signal-beam output of an optical parametric ampliﬁer
(Coherent CPA 9450), which was pumped by an ampliﬁed Ti:sapphire laser (Coher-
ent Mira-seed oscillator and a modiﬁed Coherent RegA 9050 regenerative ampliﬁer,
with Coherent Verdi V5 and V10 pump lasers, respectively). The laser was operated
at a repetition rate of 250 kHz. The experiments were conducted with 13-nJ, 45-fs
pump and 7.2-nJ probe pulses centered at 625 nm (15 nm fwhm, as measured with
an Ocean Optics USB-2000 spectrometer/CCD detector with a 0.5-nm bandpass).
The pump and probe pulses were corrected for group-delay dispersion on the way
to the sample by a SF 10 Brewster prism-pair pulse compressor. The pump-probe
time delay was scanned using a rapid-scanning delay stage (Clark-MXR, ODL-150) in
a modiﬁed Mach-Zehnder interferometer with confocal sample and autocorrelation-
crystal positions. Calcite polarizers and A/2-retarding wave plates in the pump and
probe beams set their planes of polarization at 90°; after passing through the sample,
the probe beam was analyzed by another calcite polarizer oriented 90° relative to the
pump-beam’s plane of polarization, and then it was passed through a monochroma-
tor (Spex 270M, 4-nm bandpass) and detected by an ampliﬁed photodiode (Thorlabs
PDA55). The monochromator’s slits were adjusted to obtain a fairly narrow band-
pass (4 nm) compared to the width of the laser’s spectrum; the monochromator’s
grating was detuned from the laser’s intensity maximum to the ~ 50% intensity point.
This approach is similar to that used by Champion and co-workers in their studies

of low-frequency vibrational coherence in heme proteins.53’55’61 The pump—probe

88

signal was obtained from the photodiode signal using a lock-in ampliﬁer (Femto LIA-
MV-200-H); the pump beam was modulated at 50 kHz by a A/4-retarding photoelastic
modulator (Hinds Instrumentation) with A/4-retarding and A/2-retarding waveplates

and a calcite polarizer in series.

4.4 Results

Figure 4.1 shows continuous-wave absorption and ﬂuorescence spectra from
ZnTMPyP in methanol at 23 °C. The spectra are plotted as relative dipole
strengths89'91'92 as a function of wavenumber v, A(v) /v and F(v) /v3 respectively.
The ﬂuorescence spectrum extends to the red from the 0-0 peak of the Q band, the
absorption feature that corresponds to the ﬁrst excited singlet (81) state. Also shown
in Figure 4.1 is the output spectrum from the OPA as it was tuned to 625 nm for
the dynamic-absorption experiments. Because we wanted to detect vibrational co-
herence from coherent wavepacket motion on the 81 state’s potential-energy surface,
the OPA was tuned as far to the red in the Q band as possible so that the probe
bandpass would detect a large stimulated-emission signal. As estimated from the
dipole-strength spectra, at the 632-nm center of the probe bandpass the stimulated-
emission (SE) signal is ﬁve times larger than the photobleaching (PB) signal.

The dynarnic-absorpn'on transient obtained from ZnTMPyP in methanol under
these experimental conditions is shown in Figure 4.2. Following an intense bipolar
spike that goes off the plotted scale near the pump-probe zero-delay point,93‘95 the
transient exhibits a pattern of cosinusoidal modulations superimposed on a rising
transient of net excited-state absorption (ESA) character. The oscillatory residual ob-
tained by subtracting a ﬁtted biexponential trend consists of a very rapidly damped
portion over the 100-600-fs range followed by a more slowly damped part that per-

sists at least to the 2000-f8 range. This damping character is similar to that observed

89

 

A/v

 

 

 

Relative Magnitude

 

 

 

 

l I I I

I I
12 14 16 18 20 22 24 26
Frequency (103 cm")

Figure 4.1. Soret (v>20000 cm‘l) and Q-band region of the continuous-wave absorp-
tion (solid curve) and ﬂuorescence (dotted curve) spectra from ZnTMPyP in methanol
at room temperature (23 °C), plotted as the dipole strength, A(v)/v and F(v)/v3,
respectively, and normalized to unit area for the ﬂuorescence spectrum and Q band.
Superimposed with arbitrary scaling is the intensity spectrum of the 62 5-nm, 45-fs
pulses used in the pump-probe experiment.

90

 

-O.8 -

 

—1.0-

I r l l l
-300 0 300 600 900 1200 1500 1800
Time (is)

 

 

 

 

Figure 4.2. Femtosecond pump—probe dynamic absorption transient detected at 632
nm (4-nm bandpass) with ZnTMPyP in methanol. The pump-induced change in trans-
mission signal (AT /T) is shown superimposed on a double-exponential ﬁt function
(dashed curve) over the > 100-fs delay range of the form A0(1 +A1e‘t/Tl +A2e“/T2 ),
with A0 = 3.00 x 10—3, A1 = 0.204, T1 = 98 fs, A2 = 0.272, and 72 = 1.8 ps. As
plotted, the signal is normalized by dividing by the nondecaying fraction, A0. The
oscillatory residual, the difference between the signal and the ﬁt function, is shown
above the signal superimposed on a model composed of slowly and rapidly damped
oscillatory components (see Figure 4.3 and Tables 4.1 and 4.2).

91

in polar solutions of BChl and in polar solutions of ZnTMPyP with Soret-band excita-
tion.63'88

After truncation of the <100-fs portion to avoid consideration of the spike near
time zero,95 the oscillatory residual was ﬁt in the time domain to a model consisting

of a sum of damped cosinusoids of the form
_ 2 2
Ii(t) = Aie t 01' /2 cos(w0it — 49,-) /\/21‘r (4.1)

with each component 1' having a center frequency (00,- and phase 43,-. These wave-

forms correspond to Gaussian line shapes in the frequency domain,
_ _ . 2 2
1,-(00) = Aie (w (”01) “201' ) Hap/217) (4.2)

where the linewidth is controlled by the standard deviation, 0,- = Awi/ 2m, with
Awi representing the full width at half maximum. Equations 4.1 and 4.2 are nor-
malized so that the amplitude Ai corresponds to the area of the lineshape in the
frequency domain and to the intensity of the signal in the time domain. Except as
noted in the following, the ﬁtting procedure was described-in detail in the chapter
on the ground-state vibrational coherence from ZnTMPyP.88 The ﬁt is shown super-
imposed on the residual’s data points in Figure 4.2. '

Starting parameters for the slowly damped components (Aw<10 cm‘l) were ob-
tained from a Hanning-windowed Fourier-transform spectrum (see Figure 4.3a). The
window function suppresses the rapidly damped portion of the signal and applies
linebroadening to the slowly damped components. The twelve most intense peaks in
the Fourier-transform spectrum were included in the model. The ﬁt parameters for
the slowly damped components are listed in Table 4.1.

The remaining, rapidly damped (Aw>10 cm‘l) part of the oscillatory residual
was then modeled as the sum of two broad Gaussian components. The ﬁt was

not improved by inclusion in the lineshape of an asymmetry or skew parameter,

92

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A
o ..
B
8 0 -
B
'E C
8
2
a)
.2
c_"6 0
6‘6
D
E
I ' ] I | ' I ' I '
0 100 200 300 400 500

Frequency (cm'1)

Figure 4.3. Comparison of the intensities and lineshapes observed in the excited-
state and ground-state vibrational coherence from ZnTMPyP in methanol. Ex-
cited state, from the 62 5-nm pump—probe signal, see Figure 4.2: (a) Hanning-
windowed, Fourier-transform magnitude spectrum; spectra for (b) the slowly damped
(Aw<10 cm‘l) and (c) the rapidly damped (Aw>10 cm‘l) components from the
time-domain model. Ground state, from the 420-nm pump—probe signal, from ref-
erence 88): spectra for (d) the slowly damped (Aw<10 cm'l) and (e) the rapidly
damped (Aw> 10 cm‘l) components from the time-domain model. In (c) and (e), the
sum of the two rapidly damped components (dotted lines) is shown as the solid trace.
The scaling factor for (d) and (e) is 1.6 times smaller than that for (b) and (c).

93

Table 4.1. Gaussian lineshape parameters for the slowly damped modula-
tion components obtained from the 62 S-nm pump-probe transient from
ZnTMPyP in methanol (see Figure 4.2).

 

 

Component wo (cm—1) Aw (cm‘l) Amplitudea
1 15 2.55 2.84
2 37 2.36 1.00
3 63 2.35 0.507
4 94 9.41 0.776
5 112 9.41 0.761
6 157 2.77 1.42
7 172 2.35 0.597
8 195 4.61 0.597
9 216 2.35 0.313
10 255 2.35 0.373
11 313 4.66 0.358
12 346 9.04 2.54

 

3‘ Normalized relative to component 2, which has an amplitude of 6.72 x
10'3 relative to the ﬁtted nondecaying fraction, A0 (see Figure 4.2).

94

Table 4.2. Gaussian lineshape parameters and effective exponential damping times
for the rapidly damped modulation components obtained from the 62 S-nm pump-
probe transient of ZnTMPyP in methanol (see Figure 4.2).

 

 

Component wo (cm‘ 1) Aw (cm‘ 1) y (fs)a AmplitudeID
l 220 44.0 309 1 7.9
2 285 70.8 193 22.4

 

a Damping time of best-ﬁt exponentially damped cosinusoid (see Equation 4.3).
b Normalized relative to the 37-cm‘1 slowly damped component (see Table 4.1).

95

as was previously required in the modeling of the rapidly damped ground-state com-
ponents.88 The two components are assigned, in order of frequency, to the hindered
translational and librational (hindered rotational) intermolecular modes between the
porphyrin macrocycle and its clustered, ﬁrst-solvation-shell solvent molecules.63'88
The ﬁt parameters for these components are listed in Table 4.2. Also included in Ta-
ble 4.2 are effective damping times y for a best-ﬁt exponentially damped cosinusoid
of the form

Ii(t) = Ai e‘t/yi cos(w0,-t — 4),) (4.3)

which corresponds in the frequency domain to a Lorentzian line shape. The tabulated
values of )7 were obtained as previously described by ﬁtting each Gaussian compo-
nent in the model individually to Equation 4.3. This procedure provides a rough
estimate of the lower limit for the damping time.88

Figures 4.3b and c show frequency domain representations of the slowly and
rapidly damped portions of the optimized model. These spectra should be com-
pared to Figures 4.3d and e, which show spectra for the slowly and rapidly damped
components in the ground-state vibrational coherence.88 The rapidly damped com-
ponents in Figure 4.3c are clearly shifted to a much higher frequency from those in
Figure 4.3c. From the sum of the two underlining component lineshapes (see Fig-
ure 4.3c and e), Mu») = I1(w) + 12(w), the mean frequency was obtained using a

normalized mean-value relation,

_ 16° dw .’M(w)w

(w) _ 16° dwjmw)

(4.4)

 

The mean frequency of the sum of the two rapidly damped components shown in
Figure 4.3c is 256 cm‘l, whereas the mean frequency for those in Figure 4.3e is

79 cm-l.

96

 

4.5 Discussion

The pump-probe signal from ZnTMPyP with Q—band excitation at 625 nm is modu-
lated primarily by coherent wavepacket motions on the 31 -state potential-energy sur-
face. This assignment is based on the tuning of the laser spectrum, the choice of the
detected probe bandwidth (see Figure 4.1), and the observation of a rising net ESA sig-
nal that persists to the end of the recording. This result is consistent with the obser-
vations of Fontaine-Aupart and coworkers,103 who observed a long-lived ESA signal
at probe wavelengths above 575 nm in their pump-continuum-probe time-resolved
spectra. The laser was tuned so that the red side of the laser spectrum, where the
probe bandpass was selected, overlaps favorably with the stimulated-emission spec-
trum (see Figure 4.1). Owing to the 5:1 SEzPB ratio, as judged from the ratio of the
continuous-wave ﬂuorescence and absorption dipole strengths centered at the de-
tected probe bandpass, respectively, and because the strength of the ESA part of the
signal is larger than of the sum of the photobleaching and stimulated-emission parts,
we estimate that ground-state wavepacket motions make less than a 10% contribu-
tion to the pump—probe signal. The SE and BSA signals are synchronously modulated
by the Sl-state wavepacket.

The pattern of modulation intensities observed in Figure 4.3a and b is fully consis-
tent with an assignment to excited-state coherent wavepacket motions. These slowly
damped (y> 1.5 ps, Aw <10 cm’l) features are assigned to the skeletal normal modes
of the ZnTMPyP molecule. In systems where the ground- and excited-state potential-
energy surfaces are displaced with respect to the coordinate of the vibrational mode,
moving wavepackets on the ground- and excited-state potential surfaces are launched
by two successive actions of the pump ﬁeld.24'26t 33 The ground-state wavepacket is
created by a process that directly corresponds to resonance Raman scattering. The
pump-probe signal is modulated optimally by ground-state wavepacket motion when

the pump-pulse duration is about one-third of the mode’s period.26 As we explained

97

previously, the ~222-cm‘1 maximum observed in the intensity proﬁle of the slowly
damped features detected with Soret-band excitation (see Figure 4.3d) is consistent
with an assignment to ground-state wavepacket motions because of our use of 50-fs
pump pulses in that experiment.88 In contrast, for excited-state wavepacket motion,
the amplitudes are expected to increase monotonically as the frequency decreases.26
The intensity proﬁle indicated by Figure 4.3b is obviously consistent with this trend.

The main exception to the expectation that the intensities for the excited-state
wavepacket motions should decrease smoothly with increasing mode frequency is
the relatively intense 346-cm"1 peak, which is assigned to an an out-of—plane defor-
mation mode localized on the N-methylpyridyl rings based on assignments of peaks
at similar frequencies in continuous-wave resonance Raman spectra of ZnTMPyP and
other N-methylpyridyl porphyrins.127 The strength of the 346-cm‘1 peak is es-
pecially notable considering our use of 45-fs pump and probe pulses, which lack
enough impulsive bandwidth to make observation of modulation features above
300 cm"1 facile. Note also that the relatively intense 3-cm'l component observed in
the ground state vibrational coherence (Figure 4.3d) but apparently absent from the
excited-state vibrational coherence (Figure 4.3b) arises from internal rotation of the
N-methylpyridyl rings with respect to the porphyrin. In the ground state, this motion
is relatively unhindered because the n-electron density is conﬁned to the porphyrin
region (see Figure 3.1a); in the excited state, the n-electron density is extensively
delocalized from the porphyrin to the rings (see Figure 3.1b), so the resulting partial
double-bond character strongly clamps internal rotation.

Except for the 3-cm‘1 and 346.cm'1 peaks discussed above, the frequencies of
the components observed in the slowly damped excited-state vibrational coherence
(Figure 4.3b) correlate well with those observed in the ground-state vibrational co-
herence signal (Figure 4.3d). Most of these modes arise from out-of-plane defor-

mations of the porphyrin macrocycle. The 37-cm‘1 and 216-cm‘1 components are

98

 

assigned to the metal-doming and Znn-axial-ligand stretching modes, respectively.
The excited-state mode frequencies for these components differ by less than one
cm‘1 from the frequencies observed in the ground state.88

The rapidly damped (y<400 fs, Aw>15 cm‘l) features shown in Figure 4.3d
and e correspond to the intermolecular modes between the ZnTMPyP molecule and
ﬁrst-shell solvent molecules. In the excited state, the mean frequency of the summed
intensity of these features is 256 cm‘l. This frequency is substantially higher than
the ground-state mean frequency of 79 cm’l. This increase is consistent with the
van der Waals intermolecular potential we introduced previously in our discussion
of the trend of the ground-state frequency as a function of the dipole-moment of the
solvent molecule.88 In the ground state of ZnTMPyP, because the 1t-electron density
is conﬁned to the porphyrin ring (see Figure 3.1), the intermolecular potential can be

expressed as

2 2 2 2
= 12_ Clull |u2| 0(2IM1I +0t1|u2| 2 6
V0(r) a/r (bail 0:2 + (41TEo)2 + 4Tf€0 D r (4.5)

 

 

As shown previously,63 a Taylor series expansion of Equation 4.5 around the equi-
librium geometry gives an expression for the natural frequency of the intermolecular

mode,

 

 

7/6
3 Clll1|2|uz|2 “2111112 +0(1|I12|2 7/3 1/2
= __ b 4.6
v (2a)2/3( 011012+ (411.50)2 + 41r£0 2WD l1 ( )

In the above equations, the constant a scales the Pauli exchange interaction, 19 scales
the London-dispersion interaction, c = 2 / 3 kBT scales the dipole—dipole interactions,
and the (x2 llll |2 and a1|u2|2 terms correspond to dipole-induced-dipole interac-
tions (see Table 4.3).113‘116 In these equations, [1,- and 01,- correspond to the dipole
moment and polarizability for the solute (subscript 1) and solvent (subscript 2); r is
the distance between the two molecules, 11 is the reduced mass for the intermolecular
oscillator, D represents the dielectric constant for the solvent, and £0 relates the per-

mittivity of free space. As expressed above, the dipole-dependent terms apply to the

99

 

high-temperature limit, where k ET is much greater than the well depth, so the inter-
action is averaged over all orientations.115 Since the well depth for ZnTMPyP—CH3 OH
in the ground state (see Table 4.3 and reference 88) is 286 cm‘1 at T=298 K, the as-
sumption that it is appropriate to average the interaction energy over all orientations
may not be valid.

In the excited state, the Tr-electron density is extensively delocalized from the
porphyrin region to the N-methylpyridyl rings (see Figure 3.1), so the formal charges
on the rings are also delocalized. As noted previously,88 the intermolecular potential
should be expanded to include two additional solute-charge-dependent terms corre-

sponding to the ion-dipole and ion-induced dipole interactions with the charge Q:

_ CQIMZI2 0'szZ 2 4
VQm _ v0 —- (--———-( 41160)2 + ——4mo) / 21) r (4.7)

Both of the new terms are attractive; the ion-dipole term depends linearly on the
charge Q of the solute and on the square of the solvent’s dipole moment, [12; the ion—
induced-dipole term contains the polarizability 012 of the solvent and the square of
the charge, Q2. Both terms depend on r‘4, so the potential expands to much larger
intermolecular distances than does the neutral potential (Equation 4.5). Thus, inclu-
sion of the charge-dependent terms causes the potential to extend to much greater
intermolecular distances than does the neutral potential. The relation for the nat-
ural mode frequency that follows from Equation 4.7 is not shown here owing to its
length, but it predicts that the mode frequency should signiﬁcantly increase over that
predicted by Equations 4.5 and 4.6. Equation 4.7 also predicts that the depth of the
potential well will increase signiﬁcantly over that predicted from the neutral potential
(Equation 4.5), so the assumption of orientational averaging made for the uncharged
case is no longer valid, and the result would be an even more stable structure for the
porphyrin-solvent van der Waals complex.

Figure 4.4 shows three model curves for the ZnT'MPyP—CH3OH intermolecular

mode to illustrate the effect of adding charges to the intermolecular potential. Most

100

 

of the parameters in Figure 4.5 and 4.7 are obtained from the literature (see Ta-
ble 4.3). The coefficient of the exchange interaction, a, can be estimated given the
experimental measurement of the ground-state mode frequency (79 cm'l) and the
assumption that Q = 0 in the ground state so that the charge-dependent terms do
not contribute to the intermolecular potential. In the excited state, the Tr-electron
density extends over two of the N-methylpyridyl rings, so it is reasonable to sup-
pose that two charges are introduced. As Q increases from 0 to 2, the potential-well
depth me increases by almost a factor of ﬁve but the equilibrium bond length req
experiences only a ten percent contraction (0.18 A). The potential well sharpens sig-
niﬁcantly as Q increases, so the intermolecular mode will accordingly increase in
frequency. The predicted mode frequency for the Q = 2 case obtained from Equa-
tion 4.7 is 168 cm"1, which is about two-thirds of the mean frequency determined
from the rapidly damped components shown in Figure 4.3c, 256 cm‘l. A better
prediction of the excited-state mode frequency would be obtained from a improved
potential that includes explicitly the excited-state charge distribution and employs a
molecular dynamics simulation to gauge the distribution of solvent-solute interac-

tion distances and orientations.

4.5.1 Conclusions

The ground-to-excited-state increase in the frequency of the intermolecular mode
between ZnTMPyP and its ﬁrst-shell solvent molecules allows ﬁrm conclusions about
the nature of the intermolecular potential and the nature of the coupling of the mode
to the 17 —> 17* transition. First, the magnitude of the increase in the mode frequency
shows the importance of charge-dependent terms in the intermolecular potential rel-
ative to the nonpolar dipole-dependent terms. The effective absence of the charge-
dependent terms in the intermolecular potential detected in the ground state further

suggests that the solvent molecules that contribute to the detected intermolecular

101

 

 

 

 

 

 

 

 

 

 

250-
A 0
E, —250 4
3
oh) "500 -' C ’0'...
c .4"
E —750 4
g, —1000 J
c?
—1250 .-
—1500 — ,
1.5 2.0 2.5 3.0

Intermolecular Distance (A)

Figure 4.4. Model potential-energy curves for the ZnTMPyP-CH3OH van der Waals
complex as a function of the charge Q on the ZnTMPyP moiety: (a) Q = 0; (b) Q = 1;
(c) the attractive, charge-dependent terms for Q = 1; (d) Q = 2 and (e) the attrac-
tive, charge-dependent terms for Q = 2. The curves were calculated using Equa-
tion 3.10 and the experimentally observed ground-state intermolecular mode fre-
quency, 79 cm"1 (see reference 88). Table 4.3 lists the parameters and compares req
and me for curves (a), (b), and (d).

102

Table 4.3. Parameters for ZnTMPyP-CH30H intermolecular potentials (see Fig-

 

 

 

ure 4.4)
Parametersa Symbol Value
exchange (Pauli) interaction coefﬁcient a 76.2 eV A12
London-dispersion interaction coefficient 17 9.35 eVb'C
ZnTMPyP dipole moment in 0.663 Db
CH3OH dipole moment 112 1.70ID
ZnTMPyP polarizability 0(1 109.8 A3 b
CH3OH polarizability ‘ 012 3.29 A3 C
CH3OH dielectric constant D 33C
Equilibrium geometry with Q = 0 Teq 1.90 A
me 286 cm‘1
Equilibrium geometry with Q = 1 req 1.83 A
me 510 cm-1
Equilibrium geometry with Q = 2 req 1.72 A
vmm 1336 cm-1

 

a See Equations 4.5-4.7 and the text.

b From B3LYP/6-31G calculation (see reference 88).

C From reference 1 1 7.

103

 

mode are those that directly contact the n-electron density. In the ground state, the
Tr-electron density is essentially conﬁned to the porphyrin region, so the charges on
the N-methylpyridyl rings are not sensed by the solvent molecules that interact with
the n-electron density. The extensive excited-state delocalization of the Tr-electron
density over the N—methylpyridyl rings then turns on the charge-dependent terms
that control the intermolecular mode frequency. These observations allow us to con-
clude further that the displacement of the intermolecular potential in the excited
state that underlies the ground-state and excited-state wavepacket motions arises at
least in part from the excited-state change of extent of the Tr-electron density; the
expansion of the Tl' electrons pushes the solvent molecules away from the frame of
the porphyrin and launches the wavepacket motions.

These conclusions are signiﬁcant because they imply that substantially increased
activation and reorganization energies will be encountered for electron-transfer re-
actions in polar solution owing to the trapping of net charges by the intermolecular
modes with the surrounding medium. A particular impact would be expected on the
well depths of the intermolecular modes with ﬁrst-shell groups that we suggest make
dominant contributions to the reorganization energies for the electron-transfer reac-
tions in photosynthetic reaction centers. The rate of the secondary electron-transfer
reaction that shuttles the negative charge from BPhef to QA in the purple-bacterial
photosynthetic reaction center would be maximized by locating the BPheL acceptor in
a nonpolar region, as far as possible from polar or charged side chains. In contrast,
the barriers for charge-recombination reactions are raised by placing the primary
electron-donor P and the quinones QA and QB in polar regions of the reaction cen-
ter. These structural features73'125-126 clearly enhance the quantum efficiency of the
two-step, transmembrane charge-transfer/energy-storage mechanism in the reaction

CEI'IIEI'.

104

CHAPTER 5

Vibrational coherence in the native and
molten-globule states of ZnH-substituted

cytochrome c

5.1 Summary

A crucial feature of the long-distance electron-transfer reactions in the purple-
bacterial photosynthetic reaction center is that they exhibit activationless dynamics.
In the previous chapters, we have advanced the hypothesis that van der Waals inter-
actions between the redox-active chromophores and adjacent groups in the protein-
derived medium account for the majority of the reorganization energy in these reac-
tions and accordingly control the activation energy. In this chapter, we test several
aspects of this hypothesis by characterizing the ground-state low-frequency vibra-
tional coherence from ZnH-substituted cytochrome c (ZnCytc) in the native and acid-
induced molten-globule states using femtosecond dynamic-absorption spectroscopy.
The vibrational coherence observed from the native state exhibits two types of com-

ponents. The ﬁrst type is a pair of slowly damped (damping time y>1.5 ps) com-

105

ponents with frequencies of ~10 and ~30 cm‘l that are assigned to metal-doming
modes with the M80 and H18 axial ligands. The second type is a strong, very rapidly
damped (y<150 fs) 79-cm‘l component that is assigned to van der Waals inter-
actions with nonpolar groups from the surrounding protein. The resonance Raman
activity of this set of modes is effectively quenched in the molten-globule state owing
to the expansion of the hydrophobic core and to the randomization of the surround-
ing structure. These ﬁndings show that the van der Waals modes obtain resonance
Raman activity through a direct attack of the neighboring groups upon the Tr-electron
density of the ZnII porphyrin. Similar interactions are likely candidates for the rate-

controlling interactions in the photosynthetic reaction center.

5.2 Introduction

Perhaps the key feature that allows the purple bacterial photosynthetic reaction cen-
ter to perform efficient conversion of solar photons into transmembrane chemical
potential is that the electron-transfer reactions are optimized by the protein struc-
ture so that they occur with activationless dynamics. The rate of electron transfer
is effectively independent of temperature in the theory of Bixon and Jortner because
the reactions are coupled to displacements along vibrational modes of the interven-
ing protein medium that supports the redox-active chromophores}, 22 The tempera-
ture dependence of the rate constant for the primary electron transfer reaction, from
the paired bacteriochlorophyll primary electron donor, P, to the bacteriopheophytin
acceptor, BPheL, is modeled adequately when the mean frequency of the protein-
derived modes lies in the 80-100 cm‘1 regime.20 The observation of vibrational
coherence in the stimulated emission from P* in this frequency range by Vos, Mar-

tin, and co-workers43‘46'48‘51- 76 is probably consistent with the expectations of the

106

Bixon and Jortner theory but the structural assignment of the active modes has re-
mained indeterminate.

Vos and Martin suggest that the modes that appear in the vibrational coherence
in the reaction center are like the phonons of molecular crystals in being delocal-
ized over the protein structure spanning the redox chromophores.43'45v50 In the
previous chapters, we raise an alternative hypothesis that the modes arise from van
der Waals interactions: from localized, formally nonbonding interactions between
the chromophores and groups in the ﬁrst-solvation shell.63‘65v88 We have explic-
itly compared the interactions that occur in polar liquids to those of the solvent
molecules that are coordinated in gas-phase clusters.128 The vibrational modes aris-
ing from these intermolecular interactions contribute rapidly damped features to
the ground-state and excited-state vibrational coherence observed in polar solutions
of bacteriochlorophyll (BChl) and of Zn11 porphyrins. In comparison to the compo-
nents arising from the slowly damped intramolecular (or skeletal) normal modes of
vibration of the chromophores in the < BOO-cm“1 regime, the intermolecular modes
exhibit perhaps ten times the resonance Raman activity.63‘65’88

The broad lineshapes observed in solution for the van der Waals modes arise pre-
dominantly from the inhomogeneously broaded ensemble of chromophore—solvent
interactions in the ﬁrst shell.63'88 In a folded protein structure, the interactions
between a chromophore and the neighboring protein-derived groups are formally
analogous to the those observed in polar solution but are likely to be more highly
ordered. Thus, the lineshape of a particular chromophore-protein interaction should
exhibit a narrower lineshape. In this chapter, in order to test these hypotheses, we
have characterized the ground-state vibrational coherence from ZnH-substituted cy-
tochrome c (ZnCytc) in the native state and in the molten-globule state. The structure
of cytochrome c surrounds the intrinsic metalloporphyrin with an essentially nonpo-

lar environment. The closest polar amino-acid residue lies at a distance of about 3 A.

107

f

This arrangement suggests that the low-frequency vibrational coherence from the na-
tive state should be dominated by London-dispersion interactions with the nonpolar
residues that are at closer range. In the molten-globule state, however, the loss of or-
der and the expansion of the hydrophobic core should turn off the resonance Raman
activity of the modes that contribute to the vibrational coherence in the native state.

The results allow a comparison of the spectrum of the vibrational coherence in
the native and molten-globule states of ZnCytc with that observed from ZnII por-
phyrins in polar solution. The main ﬁnding is that the rapidly damped component
that dominates the vibrational coherence in the native state is completely absent
in the vibrational coherence from the molten-globule state. We conclude that the
protein-dependent changes in lineshape and intensity are consistent with the form
of the van der Waals potential and the mechanism of resonance Raman activity we
introduced previously.63v65'88 The present results strongly support a structural as-
signment of the low-frequency modes that are active in photosynthetic reaction cen-
ters to van der Waals interactions, and we discuss brieﬂy how the mean frequency of
these interactions can be tuned by the introduction of polar residues to the environ-

ment of the redox-active chromophores.

5.3 Experimental

5.3.1 Sample Preparation

ZnCytc was prepared from horse-heart ferricytochrome FeCytc (see Figure 5.1) us-
ing the procedure developed in the Vanderkooi laboratory.129 liquid anhydrous hy-
drogen ﬂuoride (Iinde) was employed as the demetalating agent; the reaction was
run on a home-built gas-handling system in Teﬂon reaction vessels. Metal recon-
stitution of the free-base Cytc product with ZnII was performed in the presence of

a lO-fold molar excess of zinc acetate (Sigma 379786-5G, 99.999%). The extent of

108

demetalation and metal-reconstitution reactions was monitored spectrophotometri-
cally; the starting and product species are easily distinguished from each other in
terms of the number and position of bands in the Q-band region of the absorption
spectrum. ZnCytc product solutions were subsequently worked up using methods
derived from those of Winkler and co-workers130 and Kostic and co-workers.131 Af-
ter desalting, the protein was isolated by cation-exchange chromatography, ﬁrst on
a Whatrnan CM-S2 column and optionally then on a Mono-S 4.6/100 PE FPLC colunm
(GE Healthcare Life Sciences). Fractions corresponding to ZnCytc were equﬂibrated
with a 25-mM sodium phosphate buffer solution at pH 6.9 by repeated concentra-
tion using an Amicon ultraﬁlter and dﬂution with the buffer solution. After a ﬁnal
ultraﬁltration step, the product was analyzed on a Superdex 75 FPLC gel-ﬁltration
column (GE Healthcare Life Sciences). The eluent was monitored simultaneously at
280 and 420 nm. The gel-ﬁltration column was calibrated using a solution of low-
molecular-weight protein standards (GE Healthcare Life Sciences, LMW standards kit).
The chromatograms (not shown) indicate that the porphyrin binding fractions corre-
spond exclusively to monomeric cytochrome c species and that the samples are free
of low-molecular-weight peptide fragments.

Solutions of the acid-induced molten-globule state of ZnCytc were prepared ac-
cording to the methods developed by Goto and co-workers132 and described by
Kostic and co-workers.133 For use in the femtosecond pump-probe experiments,
solutions of ZnCytc in the native or molten-globule states were prepared by dilut-
ing the stock protein solution with pH 7.0 SO-mM sodium phosphate buffer solution
to obtain an absorbance of 0.8 for a path length of 1.0 mm at the center of the laser
spectrum at 420 nm for the native-state samples or at 418 nm for the molten-globule-
state samples.

The samples were held in the femtosecond pump-probe spectrometer at room

temperature (23 °C) in a fused-silica ﬂow cuvette (0.5-mm path length). A peristaltic

109

 

Figure 5.1. Ribbon (left) and surface-(right) renderings of the X-ray crystal structure
of horse-heart ferricytochrome c (1hrc.pdb). The porphyrin and the axial ligands to
the FenI ion, M80 and H18, are shown as stick representations in the ribbon picture,
and space-ﬁlling representations in the surface picture.

110

pump was used to circulate a IO-mL reservoir of sample solution through the cuvette
at 2.70 mL/rnin. The sample’s absorption spectrum was monitored during the exper-
iment for changes arising from photochemistry or permanent photobleaching. The

sample reservoir was exchanged with fresh solution several times during each run.

5.3.2 Continuous-Wave Absorption and Fluorescence spectroscopy

Absorption spectra were obtained at 23 °C with a Hitachi U-2000 spectrophotometer
(2-nm band pass). Fluorescence spectra were acquired at 23 °C with a Hitachi F-4500
spectroﬂuorimeter (S-nm band pass for the excitation and emission monochroma-
tors). As presented as a function of wavenumber, the ﬂuorescence intensities are
multiplied by the square of the wavelength in order to compensate for the ﬁxed (in

wavelength units) spectral bandpass of the emission spectrometer.89

5.3.3 Femtosecond Spectroscopy

Femtosecond pump—probe transients with impulsive excitation were recorded using
the dynamic-absorption technique in which the probe beam is dispersed in a grating
monochromator after passing through the sample.26i32i35'37 The present experi-
ments were conducted with 50-fs pulses with intensity spectra centered at 420 nm
for the native state and 418 nm for the molten-globule state (both 4 nm FWHM, as
measured with an Ocean Optics USE-2000 spectrometer/CCD detector with a 0.5-nm
bandpass) and a fairly narrow bandpass (1 nm) of the transmitted probe beam. This
approach is similar to that used by Champion and co-workers in their studies of
low-frequency vibrational coherence of heme proteins.53i 55,62

The pump—probe spectrometer used in this work consists of a frequency dou-
bled, self-mode-locked Ti:sapphire oscillator (Coherent Mira-F oscillator and Verdi
V5 (5 W) NszVO4 pump laser, Coherent/Inrad 5-050 second-harmonic generator), a

111

SFIO Brewster prism-pair pulse compressor, and a rapid-scanning, modiﬁed Mach—
Zehnder interferometer with confocal sample and autocorrelation-crystal positions.
The planes of polarization of the pump and probe beams were set to be 45° apart
using calcite polarizers and A/2-retarding wave plates. After passing through the
sample, the probe beam was analyzed by another calcite polarizer oriented 90° rel-
ative to the pump-beam’s plane of polarization, and then it was passed through a
monochromator (Acton Research SP-150) and was detected by an ampliﬁed photo-
diode (Thorlabs PDAS). The pump-probe signal was obtained from the photodiode
signal using a lock-in ampliﬁer (Femto LIA-MV-200-H); the pump beam was modu-
lated at 100 kHz by a A/ 2-retarding photoelastic modulator (Hinds Instrumentation)
and a calcite polarizer. The instrumentation and methodology is identical to that

described in Chapter 3.

5.4 Results

Figure 5.2 shows continuous-wave absorption and ﬂuorescence spectra from the
native state of ZnCytc at 23 °C. The spectra are plotted as relative dipole
strength889'91’92 as a function of wavenumber v, A(v) /v and 1-"(v)/v3 respectively.
The absorption spectrum features two bands, the Soret (or B) band and the Q band,
in the blue and red parts of the spectrum, respectively. The ﬂuorescence spectrum
extends to the red from the 0-0 peak of the Q band. Also shown in Figure 5.2 is
the absorption spectrum from the molten-globule state of ZnCytc. The absorption
spectrum of the molten-globule sample is blue shifted relative to that of the native
state sample.

The dynamic-absorption transients obtained for the native and molten-globule
states are shown in Figures 5.3 and 5.4, respectively. Each transient exhibits an in-

tense biphasic spike near the zero of time that goes off the plotted scale.93‘95 The

112

 

 

+12

 

 

F/v3

 

 

Relative Dipole Strength

0
O
O
O
O
0
O
0
O
O
O
O
O
O
O
o
0
O
O
O
O
O

J .

I I I
15 17 19 21 23 25
Frequency (103 cm")

 

 

   

 

 

 

O
J

 

Figure 5.2. Soret (v> 23000 cm’l) and Q-band regions of the continuous-wave ab-
sorption spectrum of ZnCytc in the native (solid curves) and molten-globule (circles)
states. The ﬂuorescence spectrum of the native state of ZnCytc at room temperature
(23 °C) is shown overlapping and extending to the red of the absorption spectrum.
The spectra are normalized to unit area with respect to the ﬂuorescence spectrum

and Q band.

113

native-state transient (see Figure 5.3) then exhibits a very rapidly damped oscillation
over the early-time portion of the signal. The signal drops almost to the baseline
and is then followed by a positive-going recurrence at the 170-fs delay point. The
oscillation appears to be largely damped within the next 600 fs. The transient from
the molten-globule state (see Figure 5.4) does not exhibit this oscillation. The signal
exhibits a smooth transition from the positive side of the spike to a positive offset at
the ~150 fs point. Both transients then exhibit a pattern of slowly damped cosinu-
soidal oscillations superimposed on an exponential decay that extends to the ~4 ps
delay point. The most intense oscillations have periods longer than 1 ps.

Following truncation of the < IOO-fs portion,95 the transients were ﬁt in the time
domain to the sum of an exponential decay and multiple oscillatory components of
the form

2 2
Ii(t) = Aie-t 0i /2 cos(w0it — (bi) /x/2F (5.1)

with each component i having a center frequency (00; and phase (bi. These wave-

forms correspond to Gaussian lineshapes in the frequency domain,
_ _ . 2 2
1,-(w) = A,- e (w “’01) “201' ’ / (0,7211) (5.2)

where the line width is controlled by the standard deviation, ai=Awi mm, with
Awi standing for the full width at half maximum. Equations 5.1 and 5.2 are nor-
malized so that the amplitude A,- corresponds to the area of the lineshape in the
frequency domain and to the intensity of the signal in the time domain. Except as
noted in the following, the modeling procedure was as described in detaﬂ in previ—
ous work on the ground-state vibrational coherence from ZnTMPyP.88 The models are
shown superimposed on the data points of the transient in Figures 5.3 and 5.4. The
two strongest slowly damped components observed below 100 cm“1 in a Hanning-
windowed Fourier-transform spectrum (not shown) were included in the model. The

Fourier-transform spectra from both samples exhibit higher-frequency peaks near

114

 

1.5

 

 

 

 

 

 

 

1.0 4
':
’21 0.5 .-
0.0 ..
I I I I I
0 1000 2000 3000 4000
Time (is)

Figure 5.3. Soret-band (420-nm) pump-probe transient from the native state of Zn-
Cytc. The signal points (circles) are superimposed on a model consisting of the sum
of an exponential decay and two oscillatory components. The exponential has a time
constant of 1.8 ps; the plotted signal is normalized to the exponential’s intensity.
The parameters for the oscillatory components are listed in Table 5.1.

115

 

1.5

 

 

 

 

 

 

 

1.0 - ‘f
‘
':
'2 0 5 7
0.0
I I l l I
O 1000 2000 3000 4000
Time (is)

Figure 5.4. Soret-band (420-nm) pump-probe transient from the molten-globule state
of ZnCytc. The signal points (circles) are superimposed on a model consisting of
the sum of an exponential decay and two oscillatory components. The exponential
has a time constant of 1.8 ps; the plotted signal is normalized to the exponential’s
intensity. The parameters for the oscillatory components are listed in Table 5.2.

116

120 cm‘1 and 220 cm‘l, but these features are comparable in intensity to the
noise level. Similar features were observed by Champion and co-workers in ferri-
cytochrome c and myoglobin.“57 The relative weakness of the higher-frequency
modulation components is consistent with the tuning of the pump spectrum to the
center of the absorption spectrumssi 56

Frequency-domain representations of the models obtained for the oscillatory part
of the native and molten-globule signals are shown in Figure 5.5a and b, respectively.
The parameters for these models are listed in Tables 5.1 and 5.2. The model for the
native-state signal includes two slowly damped features, at 10 and 31 cm‘l, and a
single rapidly damped feature centered at 79 cm’l. The slowly damped components
probably arise from metal-doming modes in sites having axial-ligand interactions to
the ZnII ion with the M80 and H18 side chains, respectively. Comparable features
appear at 1 1 and 26 cm"1 in the molten-globule spectrum, but they are less intense
and narrower in lineshape than those observed in the native state. The broad feature
(A00= 106 cm‘l) at 79 cm‘1 that appears only in the native-state model is assigned to
van der Waals modes with the surrounding protein. It is several times more intense

than the slowly clamped, metal-doming features.

5.5 Discussion

The main ﬁnding of this chapter is that the vibrational coherence observed in the
molten-globule state of ZnCytc lacks the strong, rapidly damped modulation compo-
nent from van der Waals interactions with nearby protein residues that is observed
in the native state. This observation suggests that the expanded hydrophobic core
and the randomization of the local structural order that accompanies the formation
of the molten-globule state destroys the coupling of the ZnII porphyrin’s 1r—>Tr*

transition to the surrounding protein. In the following, we account for this conclu-

117

 

 

 

 

 

 

 

 

ii A
an
.0
3
'E
or
<0
'2' J
m .........
.2 0 -
E
SE
B
o _
I I I I
0 50 100 150 200 250

Frequency (cm'1)

Figure 5.5. Frequency-domain representations of oscillatory components of the ﬁtted
models of the vibrational coherence obtained from the (a) native state and (b) molten
globule state of ZnCytc. The model parameters are listed in Tables 5.1 and 5.2.

118

Table 5.1. Gaussian lineshape parameters for the modulation components
obtained from the pump—probe transient of ZnCytc in the native state (see
Figure 5.3).

 

 

Component 000 (cm'l) Aw (cm'l) Amplitudea
1 10 8.02 0.809
2 3 l 3.25 0.1 77
3 79 106 2.84

 

3 Normalized relative to the amplitude of the exponential decay of the
transient (see Figure 5.3).

119

 

Table 5.2. Gaussian lineshape parameters for the modulation components
obtained from the pump-probe transient of ZnCytc in the molten-globule
state (see Figure 5.4).

 

 

Component wo (cm'l) Aw (cm‘l) Amplitudea
1 1 1 7.76 0.1 57
2 26 0.575 7.08 x 10-2

 

3‘ Normalized relative to the amplitude of the exponential decay of the
transient (see Figure 5.4).

120

sion ﬁrst by considering the spectroscopic origin of the vibrational coherence that we
observe in both samples and then by considering the nature of the change in struc-
ture that modulates the resonance Raman activity and possibly also the lineshape of
the van der Waals modes. We conclude with a brief discussion of the signiﬁcance
of these ﬁndings with respect to the function of the van der Waals interactions in
purple-bacterial reaction centers and how the frequency of these interactions can be
tuned by changing the structure of the protein around the chromophore.

The pump-probe signals obtained with Soret-band excitation of ZnCytc in the na—
tive and molten-globule states are modulated primarily by ground-state vibrational
coherence. Both signals exhibit a net ground-state depletion character over the 4-ps
experimental window, but there is a ~2-ps exponential decay that returns the sig-
nal to the baseline level at the end of the recording (see Figures 5.3 and 5.4). This
behavior is just like that observed previously with ZnTMPyP.88 The exponential de-
cay, then, most likely arises from vibrational cooling in the Sl-state manifold follow-
ing an ultrafast (t<100 fs) internal conversion of the Sz-state population prepared
by the pump pulse.103 Given that the impulsive character of the excitation is not
retained following the Sg—>Sl nonradiative process, the modulations observed in
the pump-probe signals have to be assigned to coherent wavepacket motions on the
ground-state potential energy surface. These motions are launched along the coor-
dinates of the normal modes that are displaced by the 1t—>1T* transition, assuming
the Albrecht A-term mechanism for resonance Raman activity;120'121 the amplitudes
of the associated modulation components that appear in the pump-probe signal are
analogous to relative resonance Raman activities.24‘26' 30' 32’ 33' 121 The intramolecu-
lar or skeletal modes of the ZnII porphyrin obtain resonance Raman activity owing to
the changes in the electronic structure that accompany the Tr—>Tr* transition. The
van der Waals modes between the Zn11 porphyrin and groups that pack around its

rt-electron density obtain resonance Raman activity because they are reoriented or

121

 

displaced by the changes in shape or extent of the n-electron density that accompany
the Tr->Tr* transition.

The slowly damped modulation components (y> 1.5 ps, Aw < 10 cm‘l) correspond
to intramolecular modes, from the porphyrin macrocycle and the axial ligands to
the ZnII ion.65'88 The two modulation features that were modeled in the native
and molten-globule signals are very likely to correspond to metal-doming motions.
In their studies of myoglobin and ferricytochrome 6, Champion and co-workers ob-
served low-frequency modes near 40 cm‘1 that were assigned to the metal-doming
mode.57 In ZnII porphyrins, however, the central metal ion is not as strongly co-
ordinated by the porphyrin, so a decrease in the metal-doming frequency might be
expected. Previous studies have shown that the ZnII ion in porphyrin complexes in
solution prefers a ﬁve-coordinate crystal ﬁeld, so only a single axial ligand is likely
to be bound in ZnCytc.134‘137 Six-coordinate ZnII porphyrins are observed in crys-
tals, but the porphyrin is distorted by crystal-packing forces.133‘140 In ZnCytc, the
resonance Raman spectra obtained by Kostic and co-workers suggest that an ortho-
dox six-coordinate conﬁguration for the ZnII ion is not present.131 The picosecond
time-resolved ﬂuorescence results obtained previously in this laboratory, however,
show that there are two phases of axial-ligand photodissociation with Q-band exci-
tation.141 We suggested in that work that the folded native structure might impose
a six-coordinate structure on the Zn11 ion owing to packing forces from the folded
protein in analogy to those in crystals.

The present work shows that two slowly damped modulation features, at 10 and
30 cm‘l, are present in the signals from the native and molten-globule states of
ZnCytc. We suggest that both of these features arise from the metal-doming mode
of the ZnII porphyrin in two different ﬁve-coordinate conﬁgurations. The lower fre-
quency feature, at 10 and 11 cm‘1 in the native and molten-globule states, respec-

tively, probably arises from the sub-ensemble of molecules in which the Zn11 ion is

122

domed so that an axial-ligand interaction can be made to the side chain of the me-
thionine residue M80. The higher-frequency feature, at 31 and 26 cm"1 in the native
and molten-globule states, would then arise from the sub-ensemble with the ZnII ion
domed so that the axial-ligand interaction is made to the side chain of the histidine
residue H18. The two structures would be distinct because of the signiﬁcant activa-
tion required for the ZnII ion to move across the plane of the porphyrin. The lower
frequency and broader width of the 10-cm‘1 feature probably arises from the weaker
ligand-metal bond formed between the ZnII ion and the thioether side chain of the
methionine residue. The observation that the both the 10-cm‘1 and 30-cm‘1 fea-
tures are signiﬁcantly weaker in modulation amplitude in the molten-globule state
than observed in the native state (see Figure 5.5 and Tables 5.1 and 5.2) suggests
that a smaller fraction of the overall ensemble of molecules coordinates either of the
two amino acids to the ZnII ion at a given instant in time.

Several aspects of the change in protein structure that accompanies the forma-
tion of the molten-globule state account for the disappearance of the rapidly damped
modulation feature that apparently arises from van der Waals interactions in the
native state. The molten-globule state of cytochrome c has been extensively stud-
ied.132-133’142'148 It is characterized by the loss of the ordered interactions be-
tween neighboring groups that characterizes the native structure, but most of the
secondary structural content of the native state is retained.143 The protein structure
adopts an expanded conﬁguration that rapidly samples a range of internal organi-
zations. X-ray light-scattering experiments show that the Stokes radius of the cavity
that surrounds the porphyrin in the molten-globule state is between four and ﬁf-
teen percent larger than that of the native state.142i143 The blue—shifted absorption
spectrum of the molten-globule state (see Figure 5.2) probably results from the low-
ered average polarizability of the protein-derived surroundings that results from the

expanded cavity. Such an expansion would be expected to attenuate strongly the res-

123

 

onance Raman activities of the van der Waals modes because on average the distance
between the adjacent groups and the rt-electron density of the Zn“ porphyrin would
be increased and the associated sensing of the ground-to-excited-state changes in
the n-electron density would be concomitantly decreased. The rapid sampling of
different internal conﬁgurations would be expected to broaden the range of conﬁgu-
rations that contribute to the inhomogeneously broadened ensemble, with a broad-
ened lineshape the likely result. In the time domain, in a pump-probe experiment,
the especially rapid damping of such a component would mitigate further against its
detection.

The relatively low mean frequency of the van der Waals modes observed in the
native state of ZnCytc is consistent with the structure of the FeCytc because there
are no nearby polar residues that are close enough to the n-electron density of the
porphyrin to obtain strong coupling to the 1r—-n* transition and high mode fre-
quencies. In the following, we analyze the range of possible interactions in terms of
the X-ray crystal structure and in terms of the known behavior of the van der Waals
potential.

The frequency of the van der Waals modes can be understood in terms of the
potential that was discussed in the previous chapters. When there are no nearby
charges present, the potential can be expressed as the sum of a repulsive, exchange

term scaled by 7‘12 and a series of attractive terms scaled by 7’6:

2 2 2 2
V 1. =61 1.12_ b +Clull |u2| +0t2|u1| +0t1|ﬂ2| 2 6 53
0( ) / ( Otlotz (41Tfo)2 41T£0 D 1’ ( )

 

 

As shown previously,63 a Taylor series expansion of Equation 5.3 around the equi-
librium geometry gives an expression for the natural frequency of the van der Waals

mode,

 

7/6
3 clullzluzl2 Otzlml2 + 0<1|M2|2 7/3 1/2
v = —— bar or + -
(2a)2/3 ( 1 2 (41750)2 + 4TT£0 2WD [1 (5 4)

124

In both equations, the constant a scales the Pauli (exchange) interaction, 17 scales the
London-dispersion interaction, c = 2 / 3k3T scales the dipole—dipole interactions,
and the (xiu 1,2 terms correspond to dipole-induced-dipole interactions; pi and 0:,-
correspond to the dipole moment and polarizability of the choromphore solute and
solvent (subscripts 1 and 2, respectively). Lastly, r is the distance between the two
molecules, u is the reduced mass of the oscillator, D is the dielectric constant of
the medium, and so is the permittivity of free space.113‘116 As expressed above,
the dipole-dependent terms apply to the high-temperature limit, where kBT is much
greater than the well depth, so the interaction is averaged over all orientations.115 If
the potential well depth is greater than k3 T, the assumption that it is appropriate to
average the interaction energy over all orientations may not be valid.

When the solute or solvent has a charge Q12, the potential gains attractive terms

corresponding to the ion-dipole and ion—induced-dipole interactions:

2 2 2 + 2
VQ(1’) = V0 - (CQIIHZI + CQZIMII + 0‘qu 0(1Q2) /2D21’4 (5.5)

 

 

(41T€0)2 41T£0

This form of the potential is similar to that introduced in Chapters 3 and 4, ex-
cept that we now explicitly account for any charges that may be located either on
the solute or solvent. The ion—dipole term depends linearly on the charge and the
square of the dipole moment pi, and the ion—induced-dipole term depends on the
polarizability (x,- and exhibits quadratic charge dependence. Additionally, the charge-
containing terms have an r'4 dependence on the solute-solvent distance. Thus, the
charge-dependent terms cause the potential to extend to much greater distances than
does the neutral potential. Equation 5.5 also predicts that the depth of the potential
well will increase signiﬁcantly over that predicted from the neutral potential (Equa-
tion 5.3), so the assumption of orientational averaging made for the uncharged case
is no longer valid, and the result would be an even more stable structure for the van

der Waals complex. Overall, the largest contributions to the van der Waals potential

125

 

 

 

Figure 5.6. Detail of the X—ray crystal structure of ferricytochrome c (1hrc.pdb) ex-
amining possible interactions of the protein with the n-electron density of the por-
phyrin. Polar and charged residues are rendered as light and dark gray stick ﬁgures,
respectively. Nonpolar residues are omitted from the ﬁgure so that the resulting
non-polar cavity is made clear. Nearest-neighbor distances are shown between the
porphyrin and several residues: the hydroxyl group on Y67 (3.27 A), the nitrogen
atom on W59 (5.29 A), and the nitrogen on K79 (6.71 A). The Y67, W59 and K79
residues are shown in black. The interior water molecule (Wat-112, black sphere) is
3.77 A from the porphyrin.

126

are those arising from the London-dispersion interactions and those involving nearby

polar or charged residues.

An assessment of the protein-derived structures that are near enough to the por-
phyrin in ZnCytc to form a coupled van der Waals mode can be made on the basis
of the X-ray crystal structure of FeCytc because the two proteins assume the same
or similar structures in solution. As noted above, the conformation of the porphyrin
and the conﬁguration of the axial ligands to the metal ion are likely to differ in FeCytc
and ZnCytc because of the speciﬁcs of the coordination chemistry of the two metals.
The structures of horse-heart ZnCytc and ferrocytochrome c in solution have been
compared using 2D-NMR spectroscopy.149'150 The conﬁgurations of the polypep-
tide backbone and amino-acid side chains of the Fe11 and ZnII proteins are apparently
quite comparable judging from the proton chemical shifts. Anni et a1.149 conclude
that the side chains of H18 and M80 are suitably arranged so that they can interact
with the ZnII ion as axial ligands just as indicated by the FeCytc X-ray crystal struc-
ture. The X-ray crystal structure of ZnCytc from horse heart is not available; however,
the structures of Fe:ZnCytc cocrystals from tuna have been solved by Winkler, Gray,
and coworkers.151 The Fem-containing sites in the asymmetric unit exhibit struc-
tures that are qualitatively comparable to those of the ZnH-containing sites. Thus,
although some differences from the crystal structure should be expected in solution,
it is reasonable to use the crystal structure of FeCytc from horse heart as a guide for
that of ZnCytc in the following analysis.

Figure 5.6 depicts the polar and charged residues in FeCytc that contribute to
the environment of the porphyrin. None of these groups are close enough to the
n-electron density of the porphyrin to make a coupled van der Waals mode. The
distances shown in Figure 5.6 are those for the shortest nearest-neighbor vectors
between the porphyrin and a labeled polar or charged residue. The Tr-electrons are

delocalized over the entire porphyrin ring, however, so the magnitude of the van der

127

 

Waals interactions would be smaller than indicated by the distance measurements.
The nearest charged residue is a lysine residue (K79), but it lies greater than 6 A
at closest approach from the nearest atom in the porphyrin macrocycle. The lysine
residue (K13) that crosses in front of the heme in Figure 5.6 is approximately 10 A
from the porphyrin. The nearest polar groups in the surrounding protein medium
that are not directly coordinated to the metal ion are the tyrosine and tryptophan
residues, Y67 and W59. As shown in Figure 5.6, these residues are at least 3 and
5 A from the porphyrin macrocycle, respectively, so their interactions with the N'-
electron density are weak. Polar interactions with nearby bulk water molecules can
be neglected because the porphyrin is exposed along the equatorial plane (see Fig-
ure 5.1). The conserved interior water molecule Wat-112 (Wat-166 in yeast iso-I-
cytochrome c152) is hydrogen bonded to the nearby N52, Y67 and T78 residues.153
It is ~3.8 A from the porphyrin (see Figure 5.6), so its contribution to the signal will
also be negligible.

The main contributions to the coupled van der Waals interactions between
the protein and the porphyrin’s n-electron density in ZnCytc arise from London-
dispersion interactions with non-polar residues. These residues ﬁll the majority of
the cavity adjacent to the porphyrin in the native state (see Figure 5.6). The line-
shape resulting from these interactions wﬂl be very broad because of the wide range
of distances and orientations with respect to the porphyrin. The modulation compo-
nents from polar residues, if they were present, would exhibit higher frequencies and
narrower lineshapes. The trend of the mode frequency as a function of the solvent
dipole moment obtained in the previous work on ZnTMPyP suggests a frequency in
the nonpolar limit near 70 cm‘l.88 The mean frequency (79 cm‘l) and broad line-
shape (or rapid damping) of the van der Waals interaction observed in the native state

of ZnCytc is consistent with these expectations.

128

 

These observaﬁons allow a suggestion about the nature of the vibrational coher-
ence in the purple-bacterial photosynthetic reaction center43‘45’48'51v 76 that arises
from van der Waals modes. The overall spectrum should contain an underlying broad
lineshape arising from the interactions of non-polar residues in the surroundings of
the primary electron donor P. Narrower lineshapes, from interactions of dipolar or
charged residues, will be superimposed on the broad background. This description
is consistent with the observations made by Vos, Martin and co-workers in their stud-
ies of the effects of point mutations on the vibrational coherence in the Rhodobacter
sphaeroides reaction centers.50 The mutations swapped nonpolar for polar, polar for
nonpolar, or polar for charged residues. The spectrum from each mutant was unique
in having one or more relatively narrow lines at different frequencies but these vary-
ing features were superimposed on a broad background lineshape that was indepen-
dent of the mutation. Thus, we suggest that the sharper components arise from
dipole-dipole interactions involving an amino acid near the porphyrin, and the in-
variant broad background lineshape arises from the London-dispersion interactions

with adjacent groups.

5.5.1 Conclusions

The principal result of this chapter is that rapidly damped contributions to the vi-
brational coherence in ZnCytc arise from van der Waals interactions between the
porphyrin and the surrounding protein medium. The expansion of the core and ran-
domization of the surrounding structure effectively quenches these interactions in
the molten-globule state. The van der Waals potential that accounts for the modu-
lation components in the vibrational coherence is dominated by London-dispersion
interactions; charged and polar residues are too distant in the native structure from
the porphyrin to contribute signiﬁcantly to the signal. The speciﬁc interactions that

gain resonance Raman intensity via coupling to the Tr—>Tr* transition of the por-

129

phyrin are those that are capable of directly attacking the Tr-electron density. In the
photosynthetic reaction center, the low-frequency vibrational modes that are coupled
to the primary and secondary charge-separation reactions probably arise from van
der Waals interactions between the redox-active chromophores and the surrounding
protein medium. The local structure around a chromophore can tune the mean fre-
quency of the interaction through the addition of polar or charged groups. These
ﬁndings provide a possible mechanism that accounts for the ability of the surround-
ing protein structure to optimize the efficiency of the energy-storing electron-transfer

reactions in photosynthesis.

130

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