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MODEL C0
010C111“
VIBRATIONAL SPECTROSCOPY AND STRUCTURAL PROPERTIES OF
MODEL COMPOUNDS OF PHOTOSYNTHETIC REACTION CENTER AND
CY TOCHROME OXIDASE
Hong Zhang
A DISSERTATION
Submitted to
Michigan State University
In partial firlfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Chemistry
1995
HBMTIO'N"
COMPOUND
OTOCHRO
The I
sclar energy
order to ass
scparation p
photoinducu
base 90th
Moh‘ed‘ m-
sxate is dete
500 picosec
Observed by
Charge SCpa
Showed tha1
ABSTRACT
VIBRATIONAL SPECTROSCOPY AND STRUCTURAL PROPERTIES OF MODEL
COMPOUNDS OF THE PHOTOSYNTHETIC REACTION CENTER AND THE
CY TOCHROME C OXIDASE
By
Hong Zhang
The photosynthetic reaction center is a protein complex that converts captured
solar energy into electrical and chemical energy in the first steps of photosynthesis. In
order to assess the effects of structural and electronic properties on its initial charge
separation process, different model compounds were synthesized. In this work, the
photoinducted charge separated state of a covalently linked magnesium porphyrin and free
base porphyrin heterodimer complex (Mg-H2) is investigated by picosecond time-
resolved, two-color, pumpcprobe resonance Raman spectroscopy. The charge separated
state is detected within 30 picoseconds of laser excitation; recombination occurs within
500 picoseconds. The time scales of the charge transfer and recombination processes
observed by Raman are consistent with those measured earlier by optical methods. In the
charge separated state of the Mg-Hz diporphyrin complex, vibrational mode correlations
showed that the magnesium porphyrin cation half of the dimer is in its 2A1u electronic
state. The free base porphyrin anion half of the charge transfer state has vibrational
characteristic that are interpreted in terms of data available on the free base
octaethylporphyrin anion.
In previous work of this lab, time-resolved vibrational spectroscopy has been used
to investigate the reduction of dioxygen by mitochondrial enzyme, cytochrome oxidase. A
series of intermediates were detected and assigned to oxy (F eZ+-02), PCTOXY [Fey-0'4?
(H)] and fenyl (Fe4+ =0) species. In this work, 1). semi-empirical calculation has been
Performed on the peroxy species to evaluate the effect of electron transfer on the bond
Hong Zhang
cleavage and bond formation. The Fé+-O'-O‘(H) bonding interaction and excited state
transition energies are calculated. Their impacts on electronic structure and conformation
are compared to experimental results. 2). the u-oxo compounds have been widely
suggested existing in difi'erent enzyme catalytic cycles which included the cytochrome c
oxidase. A series of synthesized porphyrin based u-oxo complexes (i.e., Fe-O-F e and F e-
O-Cu) have been characterized by resonance Raman and other analytical techniques.
Their structural implications on enzyme catalytic cycle are discussed.
A particle in a one-dimensional box is a classic quantum theory problem.
However, it has been discussed mostly in the position space and its momentum
distributions is misdescribed or incompleted in many textbooks. In this worlg we present
a simplified and explicit expression of a flee particle in momentum space.
I would
financial suppor
Prof C ukier, Pr
people gave me
State, amongt
the first laser
anthesized m
communicate.
Gardner and‘
“Melting, a;
many dexice
My 5
their Patient
“1‘ “Dec:
Tang and
ChOice Ofs
ACKNOWLEDGMENTS
I would like to thank Prof. G. T. Babcock for his guidance, especially his
financial supports during last two years of this thesis work. I would also like to thank
Prof. Cukier, Prof. Chang and Prof. Nocera to serve in my guidance committee. Many
people gave me support, encouragement and friendships during my stayed at Michigan
State, among them, Mary Tecklenburg and Tony Oertling taught me how to operate
the first laser I used, a K+laser, many years ago; W. Wu, Ying Liang and Nil Bag
synthesized many fine model compounds used in this thesis work; Einhard Schmidt
communicated spectroscopic data of p-oxo compounds; Craig Essenmacher, Matt
Gardner and Wenjun Shi discussed with me the computer programming and molecular
modeling, and the machine shop and electronic shop of Chemistry Department made
many devices which were essential to our experiments.
My special thanks go to my wife, Jingyang Lin and my daughter, Lillian for
their patient and support during this long period of time. It has not been easy for me, it
was especially hard for them. Finally, I would like to thank my mother, Xiuchun
Tang, and my father, Min Zhang. Their expectation since I was a little boy made me
choice of science as career and, I finally fulfilled my education.
iv
llST OF TABLES
LIST OF FIGLRE
Cilil’TEll ONE
Summar
The Pho
Resonar
Time-re
Cytochr
General
I.\DO l
Momer
CHAPTER N"
introd
Gener
Resul
Discu
Aclm
CWTER T
Sum
Inlrr
TABLE OF CONTENTS
LIST OF TABLES .................................................................................
LIST OF FIGURES .................................................................................
CHAPTER ONE GENERAL INTRODUCTION ...................................
Summary ........................................................................................
The Photosynthetic Reaction Center ...............................................
Resonance Raman .........................................................................
Time-resolved Resonance Raman ..................................................
Cytochrome c Oxidase ..................................................................
General Computational Methods ...................................................
INDO Methods .............................................................................
Momentum Distribution of a Particle in a One-dimensional Box
CHAPTER TWO PICOSECOND TIME-RESOLVED RESONANCE
RAMAN SPECTROSCOPY AND SEMI-EMPIRICAL
CALCULATIONS OF THE CHARGE SEPARATED
STATE OF MG-FREE BASE DIPORPHYRINS ..........
Introduction ..................................................................................
General Experimental Section ........................................................
Instrumentation of Time-resolved Resonance Raman Set -up ..........
Results ..........................................................................................
Discussion ......................................................................................
Acknowledgment ..........................................................................
CHAPTER THREE THE VIBRATIONAL CHARACTERIZATION OF
SYNTHESIZED u-oxo BRIDGED DIPORPHYRIN
COMPLEXES IRON PORPHYRIN/COPPER
CLUSTERS .............................................................
Summary ........................................................................................
Introduction ...................................................................................
Methods .........................................................................................
Results and Discussion ...................................................................
Acknowledgment ..........................................................................
CHAPTER FOUR STRUCTURAL IMPLICATIONS ON ELECTRONIC
AND VIBRATIONAL PROPERTIES OF THE
PEROXYHEME INTERMEDIATE OF OXYGEN
REDUCTION OF CYTOCHROME OXIDASE,
A SEMI-EMPIRICAL QUANTUM CHEMISTRY
V
PAGE
vii
ix
43
44
48
48
66
84
102
108
108
109
110 .
110
135
Summao'
lntroducti
Methods
Results ..
Discussio
Conclusic
Acknowlr
CHGAPTER Fm
lntroduct
Obtaining
Determinr
Remarks
Most Prc
ACknowl
STUDY ....................................................................
Summary .......................................................................................
Introduction ..................................................................................
Methods .........................................................................................
Results ...........................................................................................
Discussion .....................................................................................
Conclusion ....................................................................................
Acknowledgment ..........................................................................
CHGAPTER FIVE MOMENTUM DISTRIBUTIONS FOR A PARTICLE IN A
BOX ........................................................................
Introduction ..................................................................................
Obtaining a Momentum Wave Function ...............................................
Determining the Probability Distribution ..............................................
Remarks .........................................................................................
Most Probable Momentum .............................................................
Acknowledgment ..........................................................................
138
138
139
146
147
188
192
193
200
201
202
204
206
2 12
212
4.1
4.2
4,3
4.4
4.5
1.1
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
4.1
4.2
4.3
4.4
4.5
LIST OF TABLES
Observed Frequencies (cm'l) and Assignments from Time-resolved
Resonance Raman Experiments of Oxygen Reduction Intermediates
by Cytochrome Oxidase. ..............................................................
Focusing Spot Size of the Six Inch Doublet Lens. ............................
Monochromator Paramaters Used for Throughput Factor Calculation.
Quantum Efficiency and Preamplifier Gain. ..................................
Resonance Raman Frequencies (cm'l) of Mg, Free Base Porphyrins,
Mg-Mg Diporphyrin and Mg-H2 Diporphyrin. ..............................
Resonance Raman Frequencies (cm'l) for Mg+-2H" Diporphyrin
Compounds and Their Corresponding Parent Cation and
Anion Radicals. ..............................................................................
Ground State Orbital Coefficients of HOMO and LUMO of the
Neutral Diporphyrin Complexes. ...................................................
a Orbital Coefficients of HOMO of the Cation Diporphyrin
Complexes; ....................................................................................
b. Net Charge Densities of the Cation Diporphyrin Complexes.
a Orbital Coefficients of HOMO of the Anion Diporphyrin
Complexes; ....................................................................................
b. Net Charge Densities of the Anion Diporphyrin Complexes.
Charge distribution on a standard peroxy-heme structure: Fe-O-O
angle equals to 110.8°, O-O bond length equals to 1.45 A°. .......
Ground State Orbital Description of the Standard Peroxy Complex.
Ground State Orbital Description of the Standard Oxy Complex.
Excited State Transition for a Standard Peroxy Structure:
Fe-Ol = 1.90 A°; o-o = 2.45 A° (Assigments Are Given to
These Transitions Whose Transition Energies Are Lower
Than the Soret Band). ....................................................................
Excited State Transition for a Standard Peroxy structure:
Fe-Ol = 2.1 A; 0-0 = 2.45 A (Assigments Are Given to
These Transitions Whose Transition Energies Are Lower
Than the Soret Band). ....................................................................
vii
27
63
65
77
78
86
87
88
89
90
160
161
162
163
165
46
4,1
4.8
49
410
4.11
Ground S
Complex
lmidazole
Ground 5
Complex
Iermina
Charge 1
hydrope
from th
bond le
Charge
angle e
Charg
00mp“
Iefinn
equal
Char
has t
Fe-C
IO 1 .
4.6
4.7
4.8
4.9
4.10
4.11
4.12
5.1
Ground State Orbital Description of an Isomer of the Peroxy
Complex, Hydroperoxy-l. A Proton Has Been Shifted from
Imidazole Ring to the Terminal Oxygen. .......................................
Ground State Orbital Description of a Protonated Peroxy
Complex, Hydroperoxy-Z. A Proton Has Been added to the
Terminal Oxygen. ..........................................................................
Charge distribution on an isomer of the peroxy-heme complex,
hydroperoxy-l. A proton has been shifted to the terminal oxygen
from the imidozale ring: Fe-O-O angle equals to 110.8°, o-o
bond length equals to 1.45 A°. .......................................................
Charge distribution on a standard peroxy-heme structure: Fe-O-O
angle equals to 110.8°, Fe—O bond length equals to 1.90 A°. ........
Charge distribution on an isomer of the standard peroxy-heme
complex, hydroperoxy-l. A proton has been shifted to the
terminal oxygen from the imidozale ring: Fe-O-O angle
equals to 110.8°, Fe-O bond length equals to 1.90 A°. ..................
Charge distribution on hydroperoxy-heme complex, a proton
has been added to the terminal oxygen from the imidozale ring:
Fe-O-O angle equals to 110.8°, Fe-O bond length equals
to 1.90 A°. ......................................................................................
Charge distribution on the standard peroxy-heme complex,
dioxygen are rotated above the porphyrin plane: O-O bond
eclipses the x-axis at 0 = 0°, FeoO-O angle equals to 110.8°,
Fe-O bond length equals to 1.90 A°. .............................................
The Most Probable Momentum Pm in different States .................
viii
167
168
I69
170
171
172
173
209
2.1
2.2
2.3
2.4
2.5
2.6
The posrher:
Electron trar
the bacterial
The schema:I
time-resolveI
pulse genera
certain time
State at a dit‘
Porphyrm a
The mocha
respiratory c
reduced to l
Simulations
intermediate
(reprinted in '
G T. Babcol
MS'HQ dipo
The piCOSCCl
a)- aVerage F
580 nm and,
Waiso n
LIST OF FIGURES
1.1 The posthetic groups in the bacterial reaction center. ....................
1.2. Electron transfer sequence and lifetime of intermediates in
the bacterial photosynthetic reaction center. ..................................
1.3. The schematic outline of two color, two pulse picosecond
time-resolved resonance Raman experiments. The first laser
pulse generates a population of an excited state. After a
certain time delay, the second laser pulse probes the excited
state at a different wavelength. ......................................................
1.4 Porphyrin and its derivatives. ........................................................
1.5 The cytochrome oxidase: a enzyme in the mitochondrial
respiratory chain. It catalyzes the reaction in which 02 is
reduced to H20. ............................................................................
1.6 Simulations of concentration-time profiles for possible
intermediates in the dioxygen reduction by cytochrome oxidase
(reprinted from C. Varotsis, Y. Zhang, E. H. Appleman and
G. T. Babcock Proc. Natl. Acad. Sci. USA, 1993, 90, 237). .........
2.1 Mg-H2 diporphyrin complex. ........................................................
2.2 The picosecond time-resolved resonance Raman set-up. ...............
2.3 a). average power dependence of pulse repetition rates at
580 nm and; b) peak power dependence of pulse repetition
rate at 580 nm. ...............................................................................
2. 4 Measurements of the spot size at focus point for a 6’ doublet
lens at a). 580 nm; b) 430 nm. ........................................................
2- 5 The collection optics for resonance Raman experiments. ..............
2- 5 Absorption spectra of MgOEP, MgEtioP, Mg-Mg diporphyrin
and Mg-I-Iz. ....................................................................................
ix
2.8
2.9
I»)
'»_.
o
3.lb
3.11:
3.1d
3.2
Resonance R
diporphyrin 1
laser line is 2
Two color p .
spectra of MI
(a). Probe be
(b). 30 psec '
(c). 500 psecl
lhe pump brl
430nm. Sc
Difference s
(a). Spectrur
lb). Spectrurl
Subtraction I
Two color p
of .\lg~H2 d;
powers are 1"
SPCCUUm a
taken at 5 n.
SPeCtIum t2;-
for 55 minlrl
TOp and $10:
for the “pacrl
165.70 and ’.
The X’Iay Cl
diporphmn
TOP and sidl
fOr the iron
The Strucure
CIUSteis.
The l’eSOnaEL
e CXCllat 1.
11m . I
acetic
2.7 Resonance Raman spectra of HZOEP, MgOEP, Mg-Mg
diporphyrin and Mg-Hz diporphyrin complex. Excitation
laser line is at 413.1 nm. ................................................................ 70
2.8 Two color pump-probe, time-resolved resonance Raman
spectra of Mg-Hz diporphyrin complex.
(a). Probe beam only;
(b). 30 psec delay;
(c). 500 psec delay.
The pump beam is at 580 nm. The probe beam is at
430 nm. Solvent peaks are marked with an asterisk (*). .............. 72
2.9 Difference spectra of Mg-Hz diporphyrin complex.
(a). Spectrum (b) minus spectrum (a) of Fig. 2.8;
(b). Spectrum (c) minus spectrum (a) of Fig. 2.8.
Subtraction method is described in the text. .................................. 74
2.10 Two color pump-probe, time-resolved resonance Raman spectra
of Mg-Hz diporphyrin complex taken at 2.0 ns delay, laser
powers are 120 mW at 580 nm and 45 mW at 430 nm.
spectrum a the probe only spectrum; from b. to g. were
taken at 5 minute accumulation time for each spectrum; h. is the
spectrum taken after sample has been under laser irradiance
for 55 mininutes. ............................................................................ 75
3.1a Top and side views of the X-ray ctrystallographic strucure
for the “pacman” iron diporphyrin. The Fe-O-Fe angle is
165.7° and the Fe-O bond length is 1.759 A°. ............................... 113
3. lb The X-ray ctrystallographic strucure for the DPX iron
diporphyrin. ...................................................................................... 115
3.10 Top and side views of the X-ray ctrystallographic strucure
for the iron diporphycene. The Fe-O-F e angle is 145°
and the Fe-O bond length is 1.77 A°. ............................................. l 17
3 - 1d The strucure for the iron porphryin-copper/iron ligands
clusters. ............................................................................................ 119
3 - 2 The resonance Raman spectra of iron diporphyrin ("Pacman").
The excitation is 413.1 nm and the laser power is 15 mW.
The top spectrum is taken from the same sarnple but with
1 pm acetic acid was added. ............................................................ 121
X
3.4
3.7
3.8
4.1
4.2
The resonar.
The excitatl.
The top spe.’
with l um a
The mom:
excitation is’
topspectrun
l um acetic
The correla:
ll-oxo bridgl
angle are fit
vibrational 1
here [3.8-3.
3.3
3.4
3.5
3.6
3.7
3.8
4.1
4.2
The resonance Raman spectra of iron diporphyrin (DPX).
The excitation is 413.1 nm and the power is 15 mW.
The top spectrum is taken from the same sample but
with 1 um acetic acid was added. ....................................................
The resonance Raman spectra of iron diporphycine. The
excitation is 413.1 nm and the power is 15 mW. The
top spectrum is taken from the same sample but with
1 pm acetic acid was added. ............................................................
The correlation of the Fe-O-Fe angle to the symmetric
u-oxo bridge vibration. The x-ray data of the Fe-O-F e
angle are from reference 10. The IR and Raman
vibrational frequencies are from the literatures sited
here [3.8-3.11, 3.14-3.16]. .............................................................
The correlation of the Fe-O-Fe angle to the asymmetric
u-oxo bridge vibration. The x-ray data and the IR and
Raman vibrational frequencies are cited from the same
source as Figure 5. ...........................................................................
The resonance Raman spectra of iron/copper cluster.
The excitation is 413.1 nm and the power is 15 mW.
The top spectrum is taken from the same sample but
with 1 pm acetic acid was added. ....................................................
The resonance Raman spectra of iron/iron cluster. The
excitation is 413.1 nm and the power is 15 mW. The
top spectrum is taken from the same sample but with
1 pm acetic acid was added. ............................................................
a). the proposed dioxygen reduction scheme by cytochrome
oxidase, b). kinetic simulation of the concentration-time profiles .
for proposed intermediates, reprinted from C. Varotsis et al.
Proc. Natl. Acad Sci. 1993, 90, 237. .............................................
The peroxy structures used in our calculations:
a). standard peroxy;
123
125
127
129
131
133
143
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
5.1
b). hydrr
terminal
c). hydr
The con
oxygen 1
angle eq
The 3-[3
peroxy s
Compui
Fe-O =‘.
Compu‘
Fe-O=
Compu
Fe~0 =
The co
ox‘l'ge!’
aIlgle c
The 3-
hydro;
The 3.
hydro]
The 3
hydro
The V
”‘38
Mo“.
Va] U6
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
5.1
b). hydroperoxy-l, a proton is shifted from imidazole ring to
terminal oxygen;
c). hydroperoxy-Z, a proton is added to the standard peroxy. ......
The correlations of net charge distribution at iron, end-on
oxygen and terminal oxygen vs. the F e-O- distance. F e-O-O
angle equals to 110.80, O-O bond length equals to 1.45 A°. ........
The 3-D view of the computed electronic spectra of the standard
peroxy species at different Fe-O- distances. ..................................
Computed electronic spectrum of the standard peroxy species:
Fe-O =1.9 A0, 0-0 = 1.45 A°. .......................................................
Computed electronic spectrum of the hydroperoxy—l species:
Fe-O =1.9 n°, 0-0 = 1.45 A°. .......................................................
Computed electronic spectum of the hydroperoxy-2 species:
Fe-O =1.9 n°, 0-0 = 1.45 n°. .......................................................
The correlations of net charge distribution at iron, end-on
oxygen and terminal oxygen vs. the O-O distance. Fe-O-O
angle equals to 110.8°, Fe-O bond length equals to 1.90 A°. .......
The 3-D view of the computed electronic spectra of the
hydroperoxy-l species at different O-O distances. .......................
The 3-D view of the computed electronic spectra of the
hydroperoxy-2 species at different O-O distances. ........................
The 3-D view of the computed electronic spectra of the
hydroperoxyZ-l species at different F e-O distances. .......................
The variation of the empirical paraterized INDO-SCF
energies as a function of the F e-O torsion angle. ..........................
Momentum distribution of a particle in a box at various
values of n. .....................................................................................
xii
145
150
152
154
175
177
179
181
183
185
187
208
The aim of
Properties 0
OXFgen red
Chapter We
”met r
ConSlder th
rmflance .
The secon:
of the 0X}!
req'ew the
feasibility.
\
Chapter One
GENERAL INTRODUCTION
Summary
The aim of this thesis work is to characterize the vibrational, electronic and structural
properties of model compounds of the photosynthetic reaction center protein and the
oxygen reduction intermediates of cytochrome c oxidase. In the first part of this
chapter we briefly review the structure and functions of the biological electron transfer
complex, the photosynthetic reaction center, and its model compounds. We also
consider the theory and technical background of resonance Raman and time-resolved
resonance Raman spectroscopy and their application to biologically relevant systems.
The second part of this chapter gives a brief introduction to current progress in studies
of the oxygen reduction mechanism by the cytochrome oxidase enzyme. We also
review the theoretical background of semi-empirical computational methods and the
feasibility of applying these methods to large biological molecules.
1.1 The Photo:
The con
is one of the fu
H20 +
In this eqila
Photosynthet,
the absorptil
dioxide ll‘
Splitting of
Itactions
PhOIOSh'SIe:
a PIOduct
of Photos}
chromoph
Al
phOtogym
bacterial
Up from
Pfilgpep.
m0lecul
Howe“
is in fag
acids.
1.1 The Photosynthetic Reaction Center
The conversion of the energy of light into chemical energy and electrical energy
is one of the fundamental processes of life. The basic equation is:
H20 + (:02 fish—t > (CHZO) + 02
In this equation, (CHZO) represents carbohydrate, primarily sucrose and starch.
Photosynthetic organisms are able to oxidize organic and inorganic compounds upon
the absorption of light. They use the extracted electron for the fixation of carbon
dioxide [1, 2]. The most important product is oxygen that is produced from the
splitting of water. In green plants photosynthesis is mediated by two kinds of light
reactions. Photosystem I generates reducing power in the form of NADPH.
Photosystem 11 transfers electrons from water to photosystem I and evolves oxygen as
a product. The primary charge separation occurs in the photosynthetic reaction center
of photosystem II [3, 4]. This reaction center is a complex consisting of peripheral
chromophores and integral membrane proteins.
Although the detailed structure and location of the reaction center in
photosystem II is unclear today, the structure of the reaction center from purple
bacteria has been resolved by x-ray crystallography [5, 6]. The reaction center is built
up from four polypeptides. One of them is a c-type cytochrome. The remaining three
polypeptides are called L, M and H because they have light, medium and heavy
molecular weights as deduced from their electrophoretic mobility on SDS-PAGE.
However, later experiments [7, 8] on amino acid sequences showed that the H subunit
is in fact the smallest with 258 amino acids, followed by the L subunit with 273 amino
acids. The M subunit is the largest polypeptide with 323 amino acids. The L and M
Figure 1.1 The posthetic groups in the bacterial reaction center.
Bacterial Reaction Center
subunits show
evolutionarily
are further rel
the helices of
In aid
molecules, IV
photosyntheti
in the L and
the hydropho
Other side of
'accessory‘
c(minds wit]
PROM, on t
two When:
The
also Called
eleqmn Ire
HOWEVEI’ , l
5
subunits show sequence identity of about 25% and are therefore homologous and
evolutionarily related proteins. In the crystal, the structurally similar L and M subunits
are fitrther related by a pseudo-twofold symmetry axis through the core, and between
the helices of a four-helix bundle motif.
In addition to the polypeptide backbone, there are four bacteriochlorophyll
molecules, two bacteriopheophytin molecules and two quinone molecules in the
photosynthetic reaction center (Fig. 1.1). These prosthetic groups are evenly arranged
in the L and M subunits. Two of the bacteriochlorophyll molecules form a dimer in
the hydrophobic pocket close to the symmetry axis between L and M subunits. At the
other side of the membrane a ferrous non-heme iron is located on this C2 axis. Two
”accessory” bacteriochlorophyll molecules, BchlL and Bcth, make hydrophobic
contacts with the dimer on one side and the bacteriopheophytin molecules, PheoL and
PheoM, on the other side. Subsequent to the bacteriopheophytins in the structure are
two quinone molecules, Q A and QB-
The initial electron separation occurs at the bacteriochlorOphyll dimer, which is
also called the special pair [4]. In principle, two pathways could be used for the
electron transfer process, one is along the L side and another is along the M side.
However, only the L side is used in nature [9, 10]. The parallel orientation of the
special pair and the close association of the dimer bacteriochlorophyll, accessory
bacteriochlorophyll and pheophytin ring systems facilitates the transfer of the electrons
[l 1]. Experiments [10, 12-24] have shown that upon electron separation at the special
pair (Fig. 1.2), within 3 picosecond, an electron is transferred to the PheoL. From the
PheoL the electron further migrates to QA in 200 picoseconds. The electron then
passes through the L subunit, to the second quinone, QB. This is a comparatively slow
process, taking about 100 microseconds. The forward electron transfer rate from
special pair to QA is more than eight orders of the magnitude faster than that of the
Figure 1.2 Electron transfer sequence and lifetime of intermediates in the bacterial
photosynthetic reaction center.
.oom 285:0
4a./
-0
+
m
a 8m
1.3m
ed
(A9) Kfiraua
1 cm.—
.. cw;
bark reaction. T1
of the photon ene
This phel
snails of co
chlorophyll-port
and carptenopo
the photophysi
Many spectros
50].transient2
77] have beer
successful ex
electron trans
are the Struc
Chang‘s gI’OL
transient abs
8
back reaction. The large difference allows the reaction center to capture almost 100%
of the photon energy it absorbs.
This phenomenon has stimulated efforts to model photosynthesis in artificial
systems of covalently and noncovalently linked chlorophyll-chlorophyll [25],
chlorophyll-porphyrin [26], porphyrin-porphyrin [27-33] porphyrin-quinone [34-40],
and carptenoporphyrin [41,42] complexes. Extensive reviews of the general topics of
the photophysics of the photosynthetic model compounds have been given [43].
Many spectroscopic techniques, such as EPR [44-48 ], X-ray crystallography [28, 49,
50], transient absorption [32, 33, 36, 51-58], emission [59] and, resonance Raman [68-
77] have been employed to investigate these model systems. Among the especially
successful experiments is the use of transient absorption spectra to monitor the
electron transfer process in these model complexes. Of specific interest to this study
are the structurally well defined Mg-Hz diporphyrin complexes synthesized by Dr.
Chang's group [27]. In particular, these compounds have been studied by picosecond
transient absorption and emission spectroscopy [51-54]. An intramolecular charge
separated excited singlet state of the MgI-Hz' is formed within about 6 picosecond
following rt-rt" excitation. The charge separated state then decayed to the ground
state radiationlessly or through the triplet manifolds. The correlation of charge
recombination rates with polarizable solvents was also investigated. To understand the
relationship of structure and conformation of porphyrin macrocycle to the charge
transfer reactions, a resonance Raman and picosecond time-resolved resonance Raman
study of the above diporphyrin complexes is presented in Chapter 2 of this thesis.
Both theoretical studies [60-62] and experimental evidence [23, 24] on
bacterial photosynthetic reaction centers and mutants [63] have suggested that
coherent nuclear motion or coherence in electronic coupling, or both, play a role in
the kinetic evolution of the dimer excited state and in the following primary electron
transfer process. Vibrational relaxation is a good measure of the transient structure
change and thus.
empirical analw
cation, anion and
Chapter 2. The
to the charge se;
1.2 Resonance
Raman
demoted. a 9
initial state (g
emission tak
Rents. The
‘31“ Wine 1
iSPOntanec
meaningfl
apparent .
band. '1
resonant
Concerm
whee;
“bran:
USqu\
amet.
$01» a
9
change and thus, should give new insight into this process. Consequently, semi-
empirical analysis of orbital occupancy and electronically structure of the neutral,
cation, anion and the electronic excited neutral diporphyrin complexes is also given in
Chapter 2. The implication of these results to the relationship of vibrational structure
to the charge separated state is discussed.
1.2 Resonance Raman
Raman scattering is a concerted process during which an incident photon is
destroyed, a scattering photon is created, and the system undergoes a transition from an
initial state to a final state. This is not a process in which sequential absorption and
emission take place because there are is no measurable time delay between the two
events. The energy-time uncertainty principle At°AE~ rt/4h thus allows the process to
take place even if there is no energy level to match the energy of the incident photon
(spontaneous Raman scattering), since the absorption does not populate a physically
meaningful intermediate state. However, there are many special features that become
apparent when an irradiation frequency is chosen close to a broad optical absorption
band. The resonant signals are drastically enhanced in scattering from optically
resonant chromophores, and thus good data can be obtained with sample
concentrations as low as 10'6 M. Scattering from the non-resonant pigments of the
polypeptides and other parts of proteins or organic compounds will not complicate the
vibrational spectrum. These attributes make resonance Raman a very attractive and
useful technique in biological applications.
The basic concepts of resonance Raman have been given by many review
articles and textbooks [64-67]. The intensity of a Raman transition from state m to n
for a system of randomly oriented molecules is given by
Where To is the 11
up, is the trans
scattered polarlza
from second 0rde
“357611,, and p
T, 15 3 damping
3“ intermediate
energies Vm
exciting One qu
e‘Cllléltion (1.2.2
Scattering With
(V. . V0!) for $0
10
(L094): i(apa ),,.,,,|2 (1.2.1)
pa
Where 10 is the incident light intensity, V5 is the frequency of the scattered light, and
am is the transition polarizability tensor, and p and 0 specify the incident and
scattered polarizations, respectively. The elements of the polarizability tensor derived
from second order perturbation theory are given by
< mlpp|e>< e|p0|n>
I
he (Vg-Vm)-Vo+ir¢
(apa )W. =
(1.2.2)
< mlpale >< elpp|n >
(Ve_ Vn)+ Vo+ir¢
where up and pro are the dipole moment operators, Va is the incident laser frequency,
1‘, is a damping factor for the eth intermediate state, and | e> is the wave function for
an intermediate state with energy vc. The initial state (m) and the final state (n) have
energies v," and v", respectively. In the simplest case, n is produced from m by
exciting one quantum of a particular vibration. When v0 << ve - vm both terms in
equation (1.2.2) are frequency independent and one observes non-resonant Raman
scattering with the scattering intensity proportional to v34. When v0 approaches
(ve - v,,,) for some optical transition that has a nonzero transition moment, the 6th term
in the sum becomes dominant and resonance enhancement of the Raman scattering is
observed. Since the energy denominator minimizes under these conditions only for
the first term in equation (1.2.2), the (nonresonant) second term can be neglected in
most case of resonance Raman scattering.
Figure 1.3
II
The schematic outline of two color, two pulse picosecond time-resolved
resonance Raman experiments. The first laser pulse generates a
population of an excited state. After a certain time delay, the second
laser pulse probes the excited state at a different wavelength.
Flared Dolly
/__-- -
12
0<>uuz
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In addition
Raman spectrosco
[67]. First reson
Raman signals fr
detecting the Spec
broad absorbanc:
solutions Secon
carotenoid, have 1
effect Their strc
are easily access
re5011330: Rama
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multichannel, cl
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“anosecond and
In the next sectir
U TimN‘esoh
13
In addition to the above resonance efi‘ect, there are several other advantages of
Raman spectroscopy relative to other vibrational techniques in biological applications
[67]. First, resonance Raman spectra can be obtained from aqueous solutions since
Raman signals from water are very weak so that they interfere only minimally in
detecting the spectral features of the sample. In contrast, water has very strong and
broad absorbances that hinder application of infrared spectroscopy to aqueous
solutions. Secondly, many prosthetic groups in enzymes, such as heme, chlorin and
carotenoid, have conjugated aromatic structures that are ideal for the resonance Raman
effect. Their strong absorption in the visible-ultraviolet region (from 350 to 550 nm)
are easily accessed by available laser lines. Another important advantage is that
resonance Raman can be relatively easily applied to obtain time-resolved spectra
because the detection technique of the Raman experiment can accommodate
multichannel, charge-coupled device detection. This is a very useful feature in
monitoring intermediates and reaction mechanisms. New approaches include
nanosecond and picosecond time-resolved Raman techniques. This will be discussed
in the next section.
1.3 Time-resolved resonance Raman
Time-resolved resonance Raman spectroscopy refers to the recording of Raman
spectra in a short time after a laser pulse initiates a chemical process in the sample.
As a scattering phenomenon, the Raman process has very short intrinsic lifetimes. The
Raman spectrum of fast events can be recorded with time resolution as short as
allowed by the laser excitation line broadening resulting from the uncertainty principle.
The one picosecond time-scale can be reached, with a bandwidth of the order of 10
cm’l. Thus the time-resolved resonance Raman has obvious applications for
characterizing transient species, photobiological processes, and excited state
properties. Several techniques have been implemented to investigate the biological
poms. T'hef
light pulse init
early stage 0
experiments t
systems, inclur
major disadva
pump and the
therefore, can
To 0v
developed. "l
1354!! flashes
lwmflizatior
avoid the pr
probe PUlse
probe Spectr
basiconnin.
men'menu
popuhilo“
l4
process. The first is a one pulse pump-probe experiment in that the leading edge of the
light pulse initiates the photoprocess and tailing edge of the pulse monitors it. In the
early stage of the development of time-resolved Raman spectroscopy, a few
experiments that employed this method were applied to several photochemical
systems, including the visual pigment rhodopsin [68-70] and hemoglobin [71-74]. The
major disadvantage of this approach is that there is no real time delay between the
pump and the probe. The various photoprocesses that occurred in the excited state,
therefore, can not be easily differentiated.
To overcome this limitation, two-color, pump-probe experiments have been
developed. Two pulse, time-resolved resonance Raman with the wavelength of two
laser flashes separated by less than 20 nm has been carried out to study photo-
isomerization in carotenoid system [75-78]. Although this technique can effectively
avoid the problem of one pulse pump-probe experiment by physically delaying the
probe pulse relative to the pump pulse, the pump frequency will interfere with the
probe spectrum as the monochromator can not, in general, totally separate them. The
basic outline for a two color, two pulse time-resolved Raman technique adapted in our
experiments is illustrated in Figure 1.3. First, a pump laser pulse generates a
population of an excited state or a photoinitiated intermediate state. Then, after a
certain time delay, a second laser pulse at a different wavelength is used to probe this
transient species. The probe pulse is usually at least 30 nm apart from the pump pulse
in order for the monochromator to distinguish them. Recently, this scheme has been
used to investigate the photo-isomerization of stilbene derivatives [79, 80].
Another major concern in picosecond time-resolved Raman experiments is the
balance of the laser pulse energy and average laser power. Large pulse energies are
preferred in order to pump enough molecules to initiate a photoprocess for further
detection. On the other hand, average laser power is crucial to the probe pulse for the
detection of these photoinitiated intermediates. At present two types of experimental
set-ups are used
pump and detec
rate is in the MI
of mW range).
advantages of t
repetition rate I
the dye laser pi
Hz and averagr
for other exper
ideal method
quantum yield
accumulation .
the Sample ar
lll'l‘th’amed CV81
(ASE) PTOduc
Signa]s difficl
31’0": two er
constructed a:
In a t
retlonancc Ra
mirage“ an
energy of th
ecluilibn'Um ‘
Piece,“ then
melon Ra;
Provide the .
“1th 10w‘no
15
set-ups are used. The first is the direct use of the optimized dye laser outputs as the
pump and detection sources for the experiments [7 5-78]. The typical pulse repetition
rate is in the MHz range. High sampling rate, high average power (usually in the 105
of mW range), and stability for the detection of Raman scattering are the major
advantages of this technique. The second approach uses the high peak power, low
repetition rate laser pulses by using Nd:YAG laser or regenerator amplifier to pump
the dye laser pulse. The typical pulse repetition rate after the amplification is 10 - 50
Hz and average power is about 10 mW [70-74, 80]. Although this set-up is suitable
for other experiments such as transient emission and absorption, it is, however, not an
ideal method for the Raman experiments. As Raman is a low-probability, low-
quantum yield process and usually needs many sampling cycles, the long-time
accumulation with the laser flashes of large peak power may cause photodamage of
the sample and other nonlinear Raman processes [80]. In addition to that, other
unwanted events, such as the usually large amount of amplified spontaneous emission
(ASE) produced during the pulse arnplifred process, can make detection of the Raman
signals difficult [73, 80]. Afier considering both advantages and disadvantages of
above two types of set-up, the low peak power, high repetition rate apparatus has been
constructed and used in our picosecond time-resolved experiments.
In a brief summary, the major requirements for the set-up of time-resolved
resonance Raman spectroscopy are: a) a wide tunable range of radiation to enable the
excitation and probing of the samples at their absorption peaks; b) sufficient peak
energy of the laser pulse ( > 50 n] and < 50 p11) to produce considerable non-
equilibrium concentrations of transient species at a Raman detectable level and yet to
prevent thermal damage to the samples; c) sufficient average power (~10mW) for
efficient Raman signal detection; d) short duration of laser pulse (10'9-10'12
sec.) to
provide the temporal resolution required; e) high sensitivity of the detecting system
with low-noise levels, which requires efficient collection optics for scattering photons,
agood quality m
other my high
detection, such a
1.4 Porphyrin r
Porphyri:
systems. These
They are all st
Sll’llClUICS.
(bacterialkhlor
been particular
PIOVide excelle
the Pomhyrin r
Pigments pros.
resllottsible f0
“ample, fesc
mcceSSflll 1y I.
hemoglClbln an
16
a good quality monochromator to disperse the Raman signal and reject fluorescence or
other stray light background, and a highly sensitive detector for Raman signal
detection, such as the recently developed CCD camera.
1.4 Porphyrin and its derivatives
Porphyrin and its derivatives (Fig. 1.4) are common among many biological
systems. These prosthetic groups usually play key roles in enzyme cooperativity [81].
They are all strong scattering centers as the result of their conjugated resonance
structures. In recent years, resonance Raman studies on porphyrins,
(bacterial)chlorins, and hemeproteins enzyme systems and their model complexes have
been particularly interesting and productive [67, 81]. The above chromophores
provide excellent Raman spectra that are rich in information about the conformation of
the porphyrin conjugate macrocycle. Also, resonance Raman scattering from these
pigments provides insight that is mechanistically important as they are usually
responsible for the photochemistry and catalytical cycles of proteins [67]. For
example, resonance Raman and time-resolved resonance Raman have been
successfully used to monitor the oxygen binding mechanism [69-71, 74] of
hemoglobin and the oxygen reduction process of cytochrome c oxidase [82-88].
As proposed, a long term project in the lab is to use time-resolved resonance
Raman scattering to investigate the electron transfer reactions in the photosynthetic
reaction center proteins. The time period for the initial charge separation, electron
transfer, and charge recombination within the photosynthetic reaction center is from a
few picoseconds to microseconds, well in the time range for Raman spectra to be
Figure 1.4
17
Porphyrin and its derivatives.
18
:toEoeamaomm
5320
5:3an
recorded. An
relatively large
transfer steps, ‘
reaction is, nor
90], it is assur
electron transfi
suggested tha
vibrationally r
separation [91
0f Rhodobacte
about two pi
cohermces’ “
adiame proc
mains. as J
Mace, will 1
1.5 Cytoth r0
1“ “10
ATP (Adeno:
(Nimfinarnid
This pro
19
recorded. An intriguing feature of the photosynthetic reaction center complex is the
relatively large distance between the pigments involved in the fast initial electron
transfer steps, which are about 11 A° apart. The initial photosynthetic electron transfer
reaction is, nonetheless, highly efficiency. In conventional electron transfer theory [89,
90], it is assumed that vibrational relaxation takes place on a time scale faster than
electron transfer and that electron transfer reaction is essentially nonadiabatic. It was
suggested that electron transfer from an excited state that is not completely
vibrationally relaxed could be the origin of the high quantum yield of the charge
separation [91]. Recently, femtosecond stimulated emission spectroscopy of a mutant
of Rhodobacter capsulatus [23, 24] was able to detect oscillating components lasting
about two picoseconds. These oscillations may be attributed to the vibrational
coherences, which suggests that the primary charge separation may be a coherent and
adiabatic process coupled to low-frequency vibrational modes. Excited state Raman
scattering, as a technique for directly probing the anharmonicity of the potential energy
surface, will be an ideal tool for the task to resolve this issue.
1.5 Cytochrome c Oxidase
In most aerobic organisms oxidative phosphorylation is the process in which
ATP (Adenosine Triphosphate) is formed as electrons are transferred from NADH
(N icotinamide Adenine Dinucleotide) to dioxygen by a series of electron carriers [92].
This process is carried out by respiratory assemblies that are located in the inner
membrane of mitochondria The step-by—step electron transfer from NADH to
dioxygen occurs through a chain of three large enzyme complexes, NADH-Q
reductase, cytochrome 0 reductase, and cytochrome oxidase. Electrons flow within
these complexes, which pierce the inner mitochondrial membrane, and lead to the
pumping of protons across the membrane. Electrons are carried from NADH-Q
20
Figure 1.5 The cytochrome oxidase: a enzyme in the mitochondrial respiratory
chain. It catalyzes the reaction in which 02 is reduced to H20.
21
reductaseto cu;
lorm of ubiquin;
croductaseto cy
C)l0ClllO‘.
chain, catalyzes
this thermodjnz
proton gradieni
aimllographic
of high quali'
dimensional or
shape and its ;
Slbunit; of wl
genome [96].
l Cu» QTOC
llllordinate 1h.
binuclear clu;
“1° remarmi
lllocllromec
Molei
aleCtrons prc
Moreover, 11
Spm regimen
51°le and i
reducuOn of
organiSmS
mmPOund, i:
has allowed 2
22
reductase to cytochrome c reductase, the second complex of the chain, by the reduced
form of ubiquinone. Cytochrome c, a small protein, shuttles electrons from cytochrome
c reductase to cytochrome oxidase, the final component in the chain.
Cytochrome oxidase, the last of the mitochondrial enzymes in the respiratory
chain, catalyzes the four-electron reduction of molecular oxygen to water and couples
this thermodynamically favorable reaction to the formation of an electrochemical
proton gradient across the membrane, i.e., proton pumping. The detailed x-ray
crystallographic structure of this protein is unknown at present time, owing to the lack
of high quality crystalline material. However, electron micrographs of two-
dimensional crystalline arrays of cytochrome oxidase have been able to give its overall
shape and its position in the membrane [93-95]. This complex contains at least eight
subunits, of which three, subunits I, II and III, are encoded by the mitochondrion's own
genome [96]. Among the subunits I and II, four metal centers (Fig. 1.5), cytochrome
a, CuA, cytochrome a3, and Gus, are bonded and mediate the redox chemistry and
coordinate the translocation of protons. Cytochrome a3 and CuB combine to form a
binuclear cluster that is the site of dioxygen binding and reduction to H20 [97, 98].
The remaining metal redox active sites function as electron mediators between
cytochrome c and the binuclear center.
Molecular oxygen is an ideal terminal electron acceptor. Its high affinity for
electrons provides a large thermodynamic driving force for oxidative phosphorylation.
Moreover, molecular oxygen is in its triplet ground electronic state, which imposes
spin restrictions on its reaction with singlet state reductants. Molecular oxygen reacts
slowly and is kinetically stable unless activated by a catalyst. However, the partial
reduction of molecular oxygen may generate highly hazardous intermediates in aerobic
organisms. In particular, superoxide anion radical 02', a highly destructive
compound, is formed by transfer of a single electron to dioxygen. Evolution in Nature
has allowed aerobic organisms to treat the reduction of dioxygen into water safely and
-
6111'
inte
we
used
“hi:
the 1
Diox
with
4;-
“filer:
23
efficiently: the basic principle is that the enzyme must not release partially-reduced
intermediates. Cytochrome oxidase meets this crucial criterion by binding dioxygen in
its a3-Cu3 center. The donation of two electrons, one from a3 and another possibly
from CuB, converts it into a dianion, or the peroxy form 022'. Whether protons are
involved at this stage is currently unknown. The input of another electron then leads to
the formation of a ferryl intermediate in which iron is formally in the +4 oxidation
state. Water is formed and released following acceptance of a second electron, and
leaves OH" bound to a3. Two additional electrons serve to reduce the binuclear center
back to its original oxidation state.
The mechanisms of dioxygen reduction by cytochrome oxidase has been
extensively studied by a variety of spectroscopic methods [97]. The most commonly
used technique is optical spectroscopy. The Gibson-Greenwood flow-flash technique,
which is widely adopted in different kinetic studies, is based on this method [99, 100]:
the laser flash photodissociates the CO from the fully reduced cytochrome oxidase.
Dioxygen introduced in a mixing step before the photodissociation of CO will react
with this enzyme and different reaction products can be monitored. One major
application of this technique is to establish the kinetic scheme, i.e., reaction rates for
possible intermediates. Recent experiments with a double flash techniques have
suggested that 02 first binds to the Cu}; site before it migrates to the a3 site for further
reactions [101]. Several other optical experiments also support this observation [102-
104]. FI'IR has also been used for this propose. Since this technique is usually
sensitive to the high wavenumber vibrational modes, it has been used to monitor the
initial CO binding to the Cu}; cluster, and it suggested that dioxygen may follow the
same pathway [105-107]. This technique has also been used to study the structures of
different ligand adducts in the a3 - CuB binuclear center [108]. As resonance Raman is
a vibrational spectroscopy that directly gives binding site information, especially due to
its sensitivity in the low frequency region (200 cm'1 ~1000 cm'l), it has recently been
appli
the a
with
suco
oxid;
Feb
isoto
oxid;
How
the s
the t
Shout
protc
imen
Cl'l'Stz
Men”
l"(lull
meth<
metal
Dacka
24
applied to study the 0; reaction mechanism [82-88, 109]. Resonance Raman
experiments of different mutants of plant oxidase have been useful in clarification of
the a3 - CuB binding site information and possible interaction of this binuclear center
with peptide backbones [109]. Time-solved resonance Raman has also been
successfully applied to monitor the dioxygen reactions with fully reduced cytochrome
oxidase. As showed in Table 1.1, vibrational modes belonging to the Fe2+-02,
Fe3+=0 and Fe3+—OI-I' species have been detected and confirmed by oxygen-18
isotope experiments. Based on these experimental results, a reaction scheme for the
oxidation of fully reduced cytochrome oxidase by dioxygen has been proposed [97].
However, several major issues in this scheme remained to be answered, among them
the structure of a proposed peroxy species, Fey-022‘, has not yet been continued in
the transient Raman experiments despite the fact that simulations of concentration-
time profiles (Figure 1.6) for these intermediates indicate that this species, if it exists,
should build-up to a detectable level [85]. The assignment of this intermediate and its
protonated form, Fey-Oz-(H) is also unclear [85, 87, 97]. Since these are transient
intermediates, it is impossible to use other static techniques, such as x-ray
crystallography to characterize their structural details. The proper model of the
reaction mechanism needs both experimental evidence and theoretical support. It
would be useful to clarify some of these issues by theoretical computational chemistry
methods.
Several ab-initio and semiempirical methods have been used to study
electronic structure of porphyrin and its derivatives [110], and 02 binding to
metalloporphines [111]. Among those methods, a semiempirical computational
package, ZINDO, is our choice for the study of possible cytochrome oxidase
25
Simulations of concentration-time profiles for possible intermediates in
the dioxygen reduction by cytochrome oxidase (reprinted from C.
Varotsis, Y. Zhang, E. H. Appleman and G. T. Babcock Proc. Natl.
Acad Sci. USA. 1993, 90. 237).
Figure 1.6
Relative pepulatlon
26
0.84
Fez°.Cu° '(Oz)
0.4 0.6 0.8 1.0
Time (ms)
Table 1.1
Resonance
Oudasc
Possible in
l
i Babcocka
i Kimgawab
c
M
a from [85
27
Table 1.1 Observed Frequencies (cm'l) and Assignments from Time-resolved
Resonance Raman Experiments of Oxygen Reduction Intermediates by Cytochrome
Oxidase.
Possible intermediates F e2+ -Oz Fe3+ -O-O' Fe4+ =O Fe2+ -OH'
Babcocka 572 358 790 458
Kitagawab 571 785 804 450
Rousseauc 568 786 450
a. from [85]; b. from [87]; c. from [88].
momethaie
and the ca;
discuss son
implication
l. 6 Gen er
The
by using t
and relatii
energies t
Wmmatior
Ho
SCthdingr
fmile linea
l" which lh
p mph? to n
28
intermediates because of its ability to treat transition metal ions (heme iron) [112-116]
and the capabilities of our computer facilities. In chapter four of this thesis we will
discuss some of our computational results on peroxy and hydroperoxy species and their
implication to the catalytic cycle of cytochrome oxidase.
1. 6 General Computational Methods
The Hamiltonian for an electron system in a molecular system can be written as
I; = H 0070+ Z r..-1 (1.6.1)
by using the Ham-Oppenheimer approximation and neglecting spin-orbital, spin-spin,
and relativistic effects [117]. I} care stands for the sum of the kinetic and potential
energies of all the electrons excluding those in the valence shell, and the double
summation is the total energy of the Coulomb repulsion of all pairs of electrons i and j.
However, in most cases, it is impossible to solve the eigenvalues for the
Schrodinger equation analytically. The usual approximation is to represent ‘1’ as a
finite linear combination of antisymmetrical functions (D k of M03 (0 ,0-
\v = z A.o.<
(1.62)
k
in which the coefficients A]: are determined by the application of the variation
principle to minimize the total energy expression
E =< \ylle >< who > (1.6.3)
Tneiuncti
of MOS c
descnbec
B;
electrons
named thi
this appm
averaged
constructic
Combinaric
In this LCAC
density 0, p0;
the u“paired e
the AO’ Iv . ll
configllrations
29
The functions (I) k are represented by the determinants
(I) t: dull” “,.,,,¢ “I (1.6.4)
of MOs of electrons in different spatial and/or spin configurations. For this reason, the
described method is termed configuration interaction (CI).
By introducing an effective one-electron "Fock" operator, F, valid for all
electrons, only a single representative eigenvalue problem
Frpi= 5,40,. (1.6.5)
named the Hartree-Fock equation, has to be solved to obtain solutions for the MOs. In
this approximation, each electron moves independently from the other electrons in an
averaged Coulomb field arising from the other electrons and the nuclei. The
A
construction of F for molecules is normally performed in the framework of a linear
combination of N atomic orbitals (AOs), z, , built to approximate the MOs:
N
$.- = Z civlv (1.6.6)
V
In this LCAO-MO formalism, the square of the coefficients Civ represents the electron
density or population in the AO, xv, in the MO (p, . In particular, if (p, is occupied by
the unpaired electron of a doublet radical, I Ch, I2 represents the unpaired spin density in
the A0, 1,, . In a multidetennental CI treatment, the spin densities of all contributing
configurations have to be summed up according to the weighting factor Ak of
Equation [1.6.2] to give the total spin density.
for
lhr
30
The Fock operator of Equation [1.6.5] can be represented in the LCAO-MO
formalism by a Fock matrix in the AO basis set 1,, having the elements
N
va= hpy+§p..[(#VIla)-(Mlv0)/21 (1.6.7)
where
h ”V = Icoro~rnngrall p(l) f} core Z yd Tl (1'68)
(“'1"): ll Z.(1)Z.(1)riil.l,dr.drz “'69)
two- electron Coulom b integral
and electron density matrix
n
O
P716 = 2 cm ' Cia' (1.6.10)
I
By applying the variation principle to the total Fock energy, we get a set of
“Roothaan” equations
2 (va — giSpv)civ = O (1611)
for the orbital energies and MO coefficients c“, The elements of the matrix S #V are
the AO overlap integrals
I z I, x ,d 2' (1.6.12)
tie
01 0
0f i'li
31
Equation (1.6.11) is an eigenvalue problem that has to be solved iteratively, as
F IIV requires the MO coefficients on, of the final solution. This follows from the
appearance of the electron density matrix Pm, in the effective electron repulsion field.
The normal procedure is to start from some approximate solution for the cw and, by
inserting the improved solution into F W, to carry the iterations to a point that self-
consistency is reached, i.e., when the changes in the cm, decrease beyond a given
accuracy limit. These final “ self-consistent field (SCF) solutions yield the desired
“LCAO-MOs” (p; and their orbital energies 8;. A ground state electron configuration
4), ,..., (0,0, is then produced by consecutively filling these MOs with all electrons
according to the Autbau principle, in order of increasing values of 3;.
1.7 INDO Method
The INDO semiempirical method is based on the “ intermediate neglect of
differential overlap” (INDO) approximation developed by Pople and Beveridge [117].
The INDO procedure is basically an extension of the zero-differential overlap (ZDO)
approximation, which assumes a vanishing “differential overlap”
1.1.617 = 0 (1.7.1)
between different AO basis functions in all of the space (dr is an infinitesimal volume
element). This has the consequence that only two-electron integrals of the form
(mow) = 7 ,.. (1.7.2)
or one pair AOs, have to be retained. This approximation greatly reduces the number
of nonvanishing integrals to a stage where SCF calculations, even on large biological
molecules, become feasible on computer.
form
Tnc
cxc'n
de‘i"
32
By the INDO extension to include all valence orbitals, the fiill SCF-MO
formalism becomes applicable to molecular systems without any symmetry restriction.
The term “ intermediate neglect” points to the retention of one center-two electron
exchange integrals
x... = (HVIuV) (1.7.3)
These integrals make partial allowance for the different interactions taking place
between two electrons with parallel or antiparallel spins. For open-shell systems, such
as radical ions, the INDO methods conventionally employ “different orbitals for
different spins” method [117]. This approach leads to two coupled Fock equations
for a-spin (spin up) and B-spin (spin down). This method is known as the
“Unrestricted Hartree-Fock” (UHF) MO treatment.
For large systems with more than 100 electrons, the UHF treatment has the
serious disadvantage of admitting an increasing number of higher multiplet states (e.g.
S =3/2, 5/2, ...) to the total wavefunction, ending up in unacceptably large expectation
values of the total spin-angular momentum operator. A solution to this problem is
offered by the “half-electron” method of Dewar et al [118] which produces ground
state energies of open-shell systems in the frame-work of a restricted Hartree-Fock
(RI-IF) treatment. It has the additional advantage that only one Fock matrix has to be
worked with during the SCF procedure. The well-known failure of this method is that
it completely ignores all spin polarization effects which, in a UHF treatment, follow
automatically from the UHF approach. The spin polarization effects have to be
recovered in a subsequent perturbation treatment. Different computational algorithms
and parameterization procedures have been developed [114, 119, 120].
The ZINDO program used in our calculations is an INDO level approximation
developed by Zemer and co-workers [112-116] which includes parameterization of
par
the:
par.
inte
later
oper
131)
from
and
Where
no i
33
transition-metal complexes. This computational package contains two semi-empirical
parameterization procedures: INDO/l and INDO/s.
INDO/l method is an INDO method for calculating geometry (so-called
theoretical gamma) of the molecules. Its parameterization procedure is similar to other
INDO methods but transition metals can be included.
lNDO/s method refers to the INDO method with a spectroscopic
parameterization (experimental gamma). and includes extensive configuration
interaction (CI) for the calculation of excited state energies, i.e., the Optical spectra
[112-114]. The original program for CI procedures required a close-shell system. The
later development of Rumer CI method has overcome this shortcoming, hence the
open shell transition metal complexes, such as Cu complexes and the cation or anion
transition metal compounds can be calculated [116]. Because of the requirement of
INDO/s parameterization, the coulomb integrals are computed in algorithms different
from INDO/ 1
7 AB = f, (1.7.4)
and
‘3 _ f, 1.7.5
y [unvv - 2f, ( )
A B + RAB
7;”; + y vv
where f, is a constant that is semi-empirically parameterized by ZINDO mehtod and
7 2,, and 7’ C, are two-electron one center Coulomb integrals.
1.8 r
prol:
pres
of tl
and
34
1.8 momentum distribution of a particle in a one-dimensional box
A particle in a one-dimensional box has been a classic quantum theory
problem. It, however, has been discussed mostly in position space and, is incorrectly
presented in the momentum space in many textbooks. In Chapter five, as a final part
of this thesis, we discuss a free particle in momentum space and obtained a simplified
and explicit expression for its momentum distribution.
Ref
'I-J
35
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PlC'
N) SE)‘
OF SIG-Fl
CHAPTER TWO
PICOSECOND TIME-RESOLVED RESONANCE RAMAN SPECTROSCOPY
AND SEMI-EMPIRICAL CALCULATIONS OF THE CHARGE SEPARATED STATE
OF MG-FREE BASE DIPORPHYRINS‘
Summary
The photoinducted charge separated state of a covalently linked magnesium porphyrin
and free base porphyrin heterodimer complex (Mg-H2) was investigated by picosecond
time-resolved, two-color, pump-probe resonance Raman spectroscopy. The charge
separated state is detected within 30 psec of laser excitation; recombination occurs
within 500 psec. The time scales of the charge transfer and recombination processes
observed by Raman are consistent with those measured earlier by optical methods (I.
Fujita et al, J. Phys. Chem. 86 (1982) 3754). The vibrational data were analyzed by
comparing with resonance Raman spectra of ground state diporphyrin complexes and
monomer porphyrin cation and anion radicals. In the charge separated state of the Mg-
H2 diporphyrin complex, vibrational mode correlation showed that the magnesium
porphyrin cation half of the dimer is in its 2A1u electronic state. The free base
porphyrin anion half of the charge transfer state has vibrational characteristics that are
interpreted in terms of data available on the free base octaethylporphyrin anion.
INDO/l and INDO/s calculations on such diporphyrin model compounds also support
the model of vibrational-electronic coupling we employed here.
"' Part of results published on Phys. Chem. Lett. 1995, 234, 133 (Co-authors with E.
Schmidt, W. Wu, C. K. Chang and GT Babcock.
43
11 lntrod
lhe
solar ener
The initia
the transit
mion [I]
therefore,
P106885. '
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recombin
studied b'
[14] and i
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macrocyc
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proceSSe:
PhOIoind
Step8 111a]
’Mmbin
44
2.1 Introduction
The photosynthetic reaction center is a protein complex that converts captured
solar energy into electrical and chemical energy in the first steps of photosynthesis.
The initial charge separation in the bacterial photosynthetic reaction center results in
the transient formation of a bacteriochlorophyll dimer cation and a bacteriopheophytin
anion [1]. The structure and electronic properties of this cation-anion radical pair are,
therefore, likely to be key to understanding the mechanism of the charge separation
process. In order to gain insight into factors that control the charge separation process,
such as structural conformation, energy transfer, bond distance, solvation and charge
recombination, different diporphyrin model compounds have been developed [2] and
studied by transient absorption spectroscopy [3-12], emission spectroscopy [13], EPR
[14] and X—ray crystallography [15-17].
In general, research work on photoinduced electron transfer involving
macrocyclic complex of porphyrin and chlorophylls can be divided into three
categories. First, a number of experiments investigate electron transfer between
macrocycles [34, 9-13]. Since the primary electron separation in photosynthesis
occurs between chlorophylls, it is important to understand these macrocycle structures
which can localize and stabilize the charges. Second, much work has been done on
relationships of distance, free energy, solvent effect, structural dependence of both
photoinduced charge separation reactions and subsequent charge recombination
processes [5, 6]. Third, since, in photosynthetic charge separations, an initial
photoinduced charge separation is followed by a sequence of dark electron transfer
steps that proceed at rates sufficiently fast to compete with the series of back-electron
recombination processes, several studies have focused on developing supramolecular
systems that mimic the stepwise nature of this process. Such work includes porphyrin-
who
porphni
Se
propertir
fluoreso
generally
tochniqc
0n the c
resolved
incident
process.
Pomhyn
monomr
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not yet I
Spectros
The rest
P001137]
monitm
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In
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“Elem;
(“My
Phone),c
45
porphyrin-quinone complexes [18-22], porphyrin-carotenoids complexes [23],
porphyrin-polyene-quinone complexes [24].
Several spectroscopic methods can produce information on internal vibrational
properties of macromolecules. They include neutron scattering, resonance
fluorescence, optical absorption, IR and Raman. However, as these methods produce
generally broad electronic linewidths when applied to macromolecules, most of these
techniques give much less information in the condensed phase than in the gas state.
On the other hand, resonance Raman produces sharp line spectra that contained well-
resolved vibrational information as phase relationships are retained between the
incident monochromatic laser light and the scattered photons in Raman scattering
process. With its unique advantage of being able to detect structural changes in the
porphyrin macrocycle, resonance Raman spectroscopy has been used to examine
monomeric cation [25-29] and anion porphyrin radicals [30-33], chlorophyll-porphyrin
heterodimer [34] and sandwich type diporphyrins [35 and references therein]. The
ground state orbital assignments and vibrational properties of these oxidized and
reduced porphyrin systems are reasonably well understood. Although its potential has
not yet been fully exploited in excited state studies, time resolved resonance Raman
spectroscopy has been used to monitor the excited porphyrin triplet state [32, 36-40].
The results indicated that dynamic Jahn-Teller distortion plays an important role in the
porphyrin triplet excited state and showed that Raman scattering was a useful tool to
monitor excited state dynamics. The excited state Raman approach has recently been
extended to the picosecond time scale and metalloporphyrin excited singlet states [41].
In the work here, we report the use of picosecond time-resolved, two color
pump-probe resonance Raman to detect directly the charge separated state of the
covalently linked magnesium porphyrin and free base porphyrin heterodimer complex
(Mg-H2), a classic model compound which acquires charge transfer character upon
photoexcitation [36], shown in Figure 1. Our experimental results indicate that, in the
Figure 2.1. Mg-H2 diporphyrin complex.
47
O . .5 co = I 7:
azuamu-253-52-?50- u «a _ .
i
1111. /
\\ z m z
12 :z - _,
fi
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and n
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resolve
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the prc
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48
high frequency region, the Raman bands of the charge separated state can be
interpreted within the context of the Raman shifis of monomer porphyrin cation and
anion radicals. These results are explained within Gouterrnan's model for porphyrin
and metalloporphyrin orbital occupancy [42]. Our work shows that the charge
separated state of an optically excited porphyrin complex can be assessed by time-
resolved resonance Raman spectroscopy.
2.2 General Experimental Section
Mg-Hz diporphyrin compounds and most of other metal and free base porphyrins
were kindly provided by Dr. Chang's lab. They were synthesized and purified by using
the procedures described by Chang and co-workers [43]. Spectroscopic grade
methylene chloride (J. T. Baker) was used as the solvent in the spectroscopic studies
we report. Absorption spectra were recorded on a Perkin-Elmer 1-5
spectrophotometer. The cw resonance Raman spectra were obtained by using the
413.1 nm laser line of a Coherent K+ laser or the 441.6 nm line of a He-Cd laser.
Laser power was about 15 mW at the sample. Raman scattering was dispersed into a
Spex 1877 triplemate monochromator and recorded by a CCD detector (Spex
Spectrum One).
2.3 Instrumentation of time-resolved resonance Raman set-up
The picosecond Raman set-up has been crucial to the success of those
experiments we designed and much effort of this thesis work has been on the
instrumentation. During a period of about five years, the instruments have been
modified several times and have improved significantly. In an early version of our
time-resolved Raman set-up, a Coherent 76s Antare laser produced a pulse train of 32
MHz, 70 picoseconds at 532 nm. This seeding picosecond laser with 1.2 W was used
to pump a Coherent 702 dye laser. The output pulse from the dye laser at
49
Figure 2.2 The picosecond time-resolved resonance Raman set-up.
50
O<>ut2
or» IL
or»
, . «2 e3. EMT!
NE 2.3 , no TI»?
4
3.53 t
22.35
V
A tfir _ _
fl
23:5
3.30 cozoo:oo.
58 can:
.\
53-5029on!
090-12
Shh not sit
miner has
all 680 nr
resonance
repetition
large amo
ot'pealr p
green reg:
The
given in 1
With secc
roll), an
scanty]
used 861'
°P€Tated
MHz re]
laser an:
am0 co
High 8,
minimiz
51
580 nm with about 50 mW was then amplified by a dye amplifier pumped by an
excimer laser. After the Raman shift cell, two wavelengths, 580 nm (fundamental)
and 680 nm (first Stokes shift) were available with enough power for time-resolved
resonance Raman experiments. The long duration pulse (17 ~ 22 ns) and low
repetition rates (10 to 50 Hz) of the excimer laser led to inefficient dye pumping, to a
large amount of amplified spontaneous emission (ASE), and to non-linear fluctuation
of peak power. The anti-Stokes laser line at 500 nm which covered the important
green region, did not have sufficient power and stability for Raman scattering.
The picosecond Raman set-up we used in the experiments described here is
given in Figure 2.2. It consisted of the Coherent mode-locked Antares Nd:YAG laser
with second and third harmonic generators. The output beams at 355 nm (about 800
mW), and at 532 nm (2.2 W), were used to pump two dye lasers, each equipped with
a cavity damper (Coherent models 702 and models 7200, respectively). One dye laser
used Stilbene 420 with a tunable range of 425 nm to 460 nm, while the other dye laser
operated with Rhodarnine 6G and had a tunable range of 575 nm to 620 nm. At a 1
MHz repetition rate, the typical output energy/pulse was 110 nJ for the yellow dye
laser and 35 n] for the blue dye laser. Both pulses had a FWHM = 4 - 5 psec in their
auto correlation traces without any further assumption of pulse shape correction.
High grade 051/10) refractive optics were used in the beam pathway in order to
minimize pulse broadening. The pump beam was tuned to 580 nm, which
corresponds to one of the Q band peaks of Mg-Hz (see Fig. 2.7 below). For the
charge separated state, there is a broad absorption band in the charge separated state
in the Soret region from about 400 nm to 460 nm [6, 12]. The probe beam was
chosen to be 430 nm because this wavelength is close to the maximum output of Our
blue dye laser. The 430 nm blue beam traversed a fixed distance and the 580 nm
yellow beam was directed through a variable optical delay line. The two beams
were combined at a dichroic mirror. The collimated beams were then focused onto the
sands bl ‘
were meas
section for
yield pror
condition:
order to a
abackscz
light was
of the res
Spectrogr.
Model Ll
using the
trace amc
sample ui
311d after
during or.
also Perle
The
the eXper
monochro
(I) FOCUS]
52
sample by a doublet lens (Newport, model PAC058). The sizes of the focused spots
were measured as 30 pm for 580 nm and 28 pm at 430 nm (please see the following
section for details). Resonance Raman scattering is a low-probability, low-quantum
yield process, and therefore requires high irradiance at the sample. Resonance
conditions involve high electronic absorption and hence heating of the sample. In
order to avoid the heating problems, samples were spun in a cylindrical quartz cell and
a backseattering geometry with an angle of ~1350 was used. The Raman scattered
light was passed through a narrow beam filter centered at ~ 440 nm in order to get rid
of the residual scattered yellow pumping beam, before it was collected with a single
spectrograph (ISA, THR 640) and detected by a CCD detector (Princeton Instruments
Model LN1152/UV with EEV 1154x298 chip). Samples were degassed three times by
using the freeze-pump-thaw method on a vacuum line. This procedure is important as
trace amount of oxygen dissolved in the solution may cause the photooxidation of the
samfle under repetitive laser pulses [44]. Absorption spectra were checked before
and afier each Raman measurement and indicated that sample damage did not occur
during the Raman measurements. Further control resonance Raman experiments were
also performed to insure the sample integrity.
There are several major factors in the instrument that are key to the success of
the experiment. They are focusing spot size, optical aberration, and Optimization of
monochromator and detector. We discuss them separately as following.
(a) Focusing spot size
In order to take the advantage of the high laser pulse repetition rate, low peak
power of our experimental set-up, a tight focusing at the sample is desired. A smaller
spot size will lead to a larger amount of molecules being pumped into the
photoexcited state for further photophysical process and, therefore, for Raman
detection. The theoretical focus spot size is given by
53
Figure 2.3 a). average power dependence of pulse repetition rates at 580 nm and;
b). peak power dependence of pulse repetition rate at 580 nm.
power ("1M
54
250 -
O
. a
200 ~
l
g 150 ..
E,
33
3 100 u .
O
m
50 -
. O\.\ .
0 _ o———o .
m r I T I V I V _ I ' I
0 50 100 150 200 250
N (dividing # of cavity dumper)
120
4
1 MHz
100 u b
l
80 -
cu
m
‘5 -I
a
\
E 60 ..
3.8 MHz
0.38 MHz
0.152 MHz
40 .4 T ‘2\
.L .1.
20 I f T ' l ' l J I ' I
0 50 100 150 200 250
N (dividing it of cavity dumper)
55
Figure 2.4 Measurements of the spot size at focus point for a 6’ doublet at a).580 nm;
b). 430 nm. .
56
120
are-‘4 /~.
40*
Laser power (mW)
20—l
\
Y
I
3.20
Micrometer reading (mm)
‘ J ' I ' I
3.12 3.14 3.16 3.18
60d
50 d
.. \
‘
o
1
.
Laser Power (mW)
10-1
f
I ‘ T I
51.150 51.175 51.200
Micrometer reading (mm)
57
Figure 2.5 The collection optics for resonance Raman experiments.
58
55.2
83
60:00.00
3.0505988 on. .o
.3 .893
nher
diam
lengt
lense
ware
suital
from
mode
both
focus
Whrcl
result
acros
the q
Ofthr
focus
lb) T;
Operai
rm}, ,
Sperm
59
S=2.442.*(f/D) (2.1)
where l. is the wavelength used, f is the focal length of the lens and, D is the
diameter of the focusing lens. According to this equation, a lens with short focus
length and large diameter will give a small focused spot. Although specially designed
lenses, such as best-form lenses which are designed to minimize the spherical
aberration over a narrow range of wavelengths, will give the perfect images at specific
wavelength regions for the propagation of a single incoming Gaussian beam, it is not
suitable for our task as our experiments have to cover a wide range of wavelengths,
from about 600 nm to 400 nm. The lens we chose was a six inch doublet (Newport,
model PAC058) that has taken consideration of the chromatic aberration, as we used
both blue and yellow laser lines simultaneously in our experiments. The sizes of the
focused spots were measured by both pinholes and a standard night-forge experiment,
which correlated the optical power and focusing spot size. Figure 2.3 and 2.4 gave the
results of the night-forge experiments. In brief, a sharp edge razor was moved slowly
across the focus point as the transmitted laser power was recorded. The diameter of
the central spot, the so-called the Airy disc, is defined as containing 86.5% (1 - 1/e2)
of the total optical energy. The experimental results and theoretical calculation of the
focusing spot size were given in Table 1.
(b) The chromatic aberration
When a lens or a optical system uses many wavelengths at the same time or
operates a continuum of wavelengths, as the refractive index of optical material varies
with wavelength, the focal properties of a simple lens will vary as well. This is so-
called chromatic aberration. Glasses exhibit normal dispersion in the visible
spectrum, so the refractive index is higher for blue light than for red light. The ability
60
of the lens to bend rays is thus stronger in the blue, and the focal length of a convex
glass lens is shorter for blue light than for red light. In order to avoid this type of
optical aberration, one must use achromatic doublet lenses. A typical doublet consists
of two lenses of different optical glasses placed in close contact. The two lenses have
a common radius of curvature so that they fit intimately over their entire surface. An
index-matched cement is used to eliminate the individual reflections from the two
interior surfaces. By a proper choice of glasses, the doublet can have the same focal
lengths for the designed wavelengths. In light of above consideration, a six inch
diffraction limited achromatic doublet (Newport PAC058) was used in our two color,
time-resolved experiments.
(c) Optimization of the monochromator and detector system
The rigorous characterization of the dispersion of a monochromator is given by
its F number. How the F number of a monochromator is calculated is a complicated
procedure. However the F number can be interpreted approximately as the ratio of the
axial distance from entrance slit to the holographic grating and the diameter of the
grating. In order to avoid underfilling or overfrlling of the monochromator grating, the
collection optics were designed so that they matched the F number of the
monochromator (Figure 2.5). The monochromator and detector were aligned with the
standard procedure suggested in the ISA instrumental manual. First, with the mirror
masks, a He-Ne laser line at 632.8 nm was aligned through the collection optics and
the centers of the mirrors and grating of the monochromator. Further optimization was
then done by using the image mode of the CCD detector, i.e., at a small aperture of the
entrance slit, a sharp mercury line was imaged at the CCD detector; by adjusting the
detector position a sharp, even image was centered. This image was moved
horizontally on the CCD chip when the monochromator grating was moved. However
the above image was always at the vertical center of the CCD chip for a good
61
alignmenL. Finally, different mercury lines were tested for correct wavelength and
maximum intensity. The monochromator resolution was optimized by using CCl4
triplet solvent lines. These three lines were distinguishable at a 10 um entrance width.
In practical time-resolved experiments, a 5 mm height and a 120 um width of the
entrance slit was used, which results in a spatial resolution of 4~5 cm’l.
Throughput optimization is one of the most challenging topics in spectrometer
performance. After careful alignment and optimization of the J-Y R640 single
monochromator and collection optics, we setup for the picosecond time-resolved
Raman experiments by carrying out an estimate of throughput factors for both the
R650 and a standard OMAIII triplemonochromator routinely used in the laser lab.
This ratio was then compared with the experimental data in order to characterize the
efficiency of the J-Y R640 monochromator. The monochromator throughput factor is
the product of the source area viewed, the solid angle collected by the
monochromator, the transmission factor of the monochromator optics, and the slit
function. The final equation for throughput factor is given by [46]
¢o= B, WZHQTode (2.2)
where B; is the source spectral reliance. At the same laser power level, it is close to
the same for both the R640 single monochromator and the OMAIII. W is the entrance
slit width and H is the entrance slit height of the monochromator, respectively. The Q
is the solid angle of the monochromator, which is defined as
7r/4
= W (23’
f/n is the f number of the monochromator. For R640 single monochromator and
OMAIII, fin is 5.7 and 10, respectively. Top is a factor that accounts for the effect of
f is th.
11101101
Table
011A
.ele
Hower
Single
Ohm
ratio 0:
Photor
62
absorption, refection and scattering loss of the optical components. For each mirror
and grating, the optical intensity will decrease by about 4%. Rd is the reciprocal linear
dispersion of the monochromator, which is given by
_ Acosfl
- f(sina + sinfl)
R d (2.4)
f is the f number of the focusing lens, a and ,6 are entrance and dispersion angle of the
monochromator, respectively. The numerical values for the above factors are listed in
Table 2.1. The throughput ratio for the J-Y R-640 single monochromator and the
OMA III is
¢°(R640) = 1.755 (2.5)
(po(0MAIII)
However, in order to compare with the signals detected by the CCD detector from the
single monochromator and the intensified photodiode array detector (IPDA) from the
OMAIII triple monochromator, we must convert the above throughput ratio into the
ratio of detector counts.
CCD or IPDA . .
Photons -> detector X Preacrinplrfier --> Récordtrsng
quantum efficiency am oun
63
Table 2.1. Focusing Spot Size of the Six Inch Doublet Lens
Wavelength h D = 1 inch Defi= 0.35 inch Exp.
580 nm 8.54 pm 24. 4 pm 30 pm
430 nm 6.23 um 17.8 um 28 um
64
Table 2.2. Monochromator Paramaters Used for Throughput Factor Calculation
132, w H a To, Rd
J-Y R-650 1 100 um 10 um 0.8847 0.963 0.6 nm/mm
OMAIII 1 100 um 10 um 0.6648 0.9610 1.4 nm/mm
65
Table 2.3. Quantum Efficiency and Preamplifier Gain
at 440 nm CCD IPDA
(Princeton Blue coated 11525)
Quantum Efficiency 20 % 10 %
Preamplifier Gain 5 e'/counts l e'lcounts
Photon/Count Convertion 25 photons/count 10 photons/count
66
At 440 nm, the quantum efficiency and preamplifier gain for both CCD and IPDA are
listed in Table 2.2. Considering both throughput factors and detector efficiency, the
ratio of the theoretical counts is estimated as
Counts(R650) _ ¢.(R650»(CCD Ph0’°%ow,,)
Counts 0mm ' photon
( ) ¢,(0M.4111 )*(IPDA /coum)
= 0.702 (2.6)
Considering three more slits in the filter stages in OMAIII, if 5% loss occurs on each
slit, the above throughput ratio becomes
Counts(R650)
=0.702/ 0.95 3=032 .7
Counts(0MA111) ( ) (2 )
Under normal daily experimental conditions, J-Y monochromator with the
LN1152/UV CCD can easily produce about 6000 counts/sec. while OMAIII with an
IPDA detector generates about 4000 counts. This result (Table 2.3) demonstrates that
the J-Y R-650 monochromator we setup works efficiently.
2.4 Results
The UV-visible absorption spectra of magnesium octaethylporphyrin
(MgOEP), covalently linked magnesium-magnesium diporphyrin (Mg-Mg), and Mg-
H2 are shown in Figure 2.6. The Soret maxima for the two dimers are blue shifted
relative to that of the monomer porphyrin. These spectral shifts are characteristic of
porphyrin ring-ring interaction in the excited states and are attributed to exciton
coupling in the diporphyrin complex [47-50]. This effect, which depends on the
relative orientation of the monomer transition dipoles in the dimer, is such that the
transition to the higher energy excited state is allowed and the transition to the lower
67
Figure 2.6 Absorption spectra of MgOEP, Mg-Mg and Mg-Hz diporphyrins.
A henrnfinn
68
coznromnxx
700
7. (nm)
69
Figure 2.7 Resonance Raman spectra of HZOEP, MgOEP, Mg-Mg diporphyrin and
Mg-Hz diporphyrin complex. Excitation laser line is at 413.1 nm.
7O
mom?
vwmw
own?
man?
ommv
Nmmw
Mg—ZH
03:
1600
1520
3”:
no:
3:300
1600
1400
1200
1000
- Raman Shift (cm‘1)
71
Figure 2.8 Two color pump-probe, time-resolved resonance Raman spectra of
Mg-H2 diporphyrin complex. (a). Probe beam only; (b). 30 psec delay;
(c). 500 psec delay. The pump beam is at 580 nm. The probe beam is at
430 nm. Solvent peaks are marked with an asterisk ("').
72
a. probe only
b. 30 psec delay
c. 500 psec delay
1384
1556
1600
r
1200
I
1400
. Raman Shift (cm'l)
1600
73
Figure 2.9 Difference spectra of Mg-H2 diporphyrin complex. (a). Spectrum (b)
minus spectrum (a) of Fig. 2.8; (b). Spectrum (c) minus spectrum (a) of
Fig. 2.8. Subtraction method is described in the text.
74
com _.
.
p-53 5cm 85?.
co: com v
. .
L691
9991
.88 com .o
CV91
8781
down on .m
9881
Figure 2.10
75
Two color pump-probe, time-resolved resonance Raman spectra of
Mg-Hz diporphyrin complex taken at 2.0 ns delay, laser powers are
120 mW at 580 nm and 45 mW at 430 nm. spectrum a the probe
only spectrum; from b. to g. were taken at 5 minute accumulation
for each spectrum; h. is the spectrum taken afier sample has been
under aser irradiance for 55 mininutes.
76
1600 1400 1250
Raman Shift (cm'l)
77
Table 2.4. Resonance Raman Frequencies (cm'l) of Mg, Free Base Porphyrins,
Mg-Mg Diporphyrin and Mg-Hz Diporphyrin
MgOEP MgEtioPa H20EPb Mg-Mg rug-112°
010 1608 1614 1609 1614 (HZP)d
1610 (MgP)
82 1579 1584 1580 1585 1585 (MgP)
1580 (H2?)
011 1552 1552 1545 1552 (MgP)
1546 (HZP)
03 1475 1477 1482 1477 1478
029 1397 1397
04 1371 1369 1369 1369 1369
CHZwag 1321 1312 1316
CH2 twist 1261 1257 1259
013 1211 1214 1211 1226
05 1136 1135 1131 1133 1135
‘
a Also from ref. [53]; b Also from ref. [33]; c This work; d HZP and MgP
are free base porphyrin half and Mg porphyrin half of the Mg-Hz
diporphyrin complex, respectively.
78
$3 .eo. see o “a: do. see o 5.: we 52.2 o
mom. “on. mom.
”on. oo«. .11: .5m. awn. obm_ 4:
4mm. ohm_
on:
now. own. ~4m_ 44m.
how. an“. awn. Nam. new. on“. ..o
on“. own. new. own.
no“. man. ”on. men. ooo_ _mm_ m:
22 3o. :2
...... o_o_ o_o_ moo. h_o_ a_o_ ¢_o
are: fa: nTame”: awe": o +60»: 30»: o 52.65. .505
«.863. :2: was 6.80 32am wimp—camotou
:2; 98 3:33:50 5.2935 IIN1+mE .3 3.53 6.32.262"— 55 352.80.»— .mN 039—.
79
energy excited state is forbidden in the cofacial type diporphyrins. For the Mg-Hz
heterodimer, a Q band peak centered at 581 nm allows us to take advantage of the
maximum output of our picosecond yellow dye laser, which peaks around this
wavelength.
Figure 2.7 shows ground state resonance Raman spectra of MgOEP, free base
octaethylporphyrin (HZOEP), Mg-Mg and Mg-H2 with 413.1 nm excitation.
From the vibrational frequencies and the depolarization ratios observed, we are able
to assign vibrational modes of Mg—H2 diporphyrin compounds (Table 2.4). The Soret
excited resonance Raman spectrum of HZOEP closely resembles those of the
metalloporphyrins, despite the fact that HZOEP has D2,, symmetry rather than the D41,
symmetry of the metalloporphyrins [33, 38, 51]. As the core sizes of Mg porphyrin
and free base porphyrin are very similar, it is not surprising that MgOEP and H20EP
have similar Raman band assignments . The vibrational modes of OEP monomers
correlate well with those of the Mg-H2 heterodimer, indicating that the two porphyrin
macrocycles of the dimer have minimal interaction in the ground state. Similar
behavior has been observed in other neutral dimeric metalloporphyrins [34]. One
notable difference between the Raman spectra of the dimers and those of the
monomers, however, is that the peak intensity of CH2 twisting motions of the
monomer species, which occur in the 1260 cm'1 region [33, 52, 53], decrease in the
diporphyrin Raman spectra Apparently, those torsional motions are constrained by the
covalent linkages that attach the porphyrin rings of the dimer [Fig 2.1] so that
l‘esonance Raman active conformations are minimized.
The positive detection of the charge separated state relies on directly monitoring
the charge separated species. Most of the picosecond transient absorption
measurements were carried out at wavelengths of 600 nm to 700 nm where are the
region of characteristic charge separated state absorption. Previous studies have
indicated that spectral characterization of porphyrin excited states is difficult at
80
wavelengths from 400 nm to 500 nm region due to overlapping absorption bands of
the singlet, triplet and radical species. However, it is possible to identify these species
in the ultraviolet region according to their life time [12].
The generation and decay of the charge separated state of Mg-Hz have been
previously studied by optical methods [3-6]. In brief, within 6 psec of photoexcitation
one electron transfer from the Mg porphyrin (MgP) to the free base porphyrin (HZP)
occurs with high quantum yield [3]. The major fraction of the dimers in this charge
separated state lives ~ 200 psec before charge recombination occurs; a small fraction
of those species in the charge separated state (< 4% quantum yield) decays via a long-
lived state with a life time of ~ 5 ns [3, 4]. The low quantum yield of fluorescence
quenching of these compounds in CHZClz solvent, in which the charge-transfer state
and the lowest singlet state is about 150 to 200 meV apart, implies that charge transfer
is the dominant deactivation pathway. This provides us with an ideal temporal
situation within which to probe the charge transfer state without interference from
other excited states (porphyrin singlet and triplet states) species, which have life times
in the nsec to msec time scale in Mg and free base porphyrins [54]. The psec time-
resolved resonance Raman spectra of Mg-Hz obtained with 580 nm pump and 430 nm
probe with pump subtracted are shown in Figure 2.8. New features appear near 1384
curl, 1556 cm"1 and 1600 cm'1 with the 30 psec delay and are assigned to the Mg”-
II; charge transfer state. At 500 psec, those features decay as charge recombination
Occurs. This latter observation confirms that the charge separated state is detected at
early times. In order to assess these spectral changes in detail, the difference spectra
are obtained and are shown in Figure 2.9. The spectrum in the probe only experiment
is subtracted from those obtained with both pump and probe by using the 1423 cm’1
Solvent peak as reference. At 30 psec time delay, peaks occur at 1348 cm'l, 1384
Cm“‘, 1543 cm'l, 1556 cm'1 and 1597 cm'1 in the difference spectrum. The inverse
peak at 1370 cm'1 is due to both lost ground state population and increasing stray light
81
background in the two beam experiment. At 500 psec time delay, although some lost
population remains, the positive-going Raman peaks that were apparent at shorter time
delays have diminished significantly. This result is consistent with the charge
recombination rate obtained in the transient absorption experiments [3, 4]. The inverse
peaks at 1370 cm'1 and in the 1580 cm'1 region in the 500 psec spectrum indicate that
a fraction of molecules has not returned to the ground state at this time; moreover, the
absence of positive-going features in the 500 psec Spectrum suggests that the longer-
lived metastable states (possibly the 5 nsec state detected by Netzel (see above)) do not
have significant resonance Raman cross sections at “ex = 430 nm. We can eliminate
irreversible photodamage as a source of the 500 psec lost ground state population as
control optical experiments before and afler the Raman measurements yielded identical
optical spectra Further supporting evidence comes from the resonance Raman spectra
taken at 2.0 ns delay. These experiments were designed with long time accumulations
at much extensive laser irradiance in order to test the possible photodamage of the
sample. All of these spectra [Fig. 2.10] lack the charge separated state peaks and
basically give the same features as the ground state spectrum.
Transient optical absorption spectra have shown that there is a broad feature in
the charge separated state that extends from 610 nm to 700 nm. As monomers, the
IVIgP+ cation and the HZP’ anion maximize at ~665 nm and ~635 nm, respectively [3-
6]. The absorption band of the charge transfer state of the heterodimer thus shows a
l’easonable correspondence with the composite difference spectrum calculated from
the oxidation of MgOEP and reduction of HZOEP [3]. The optical results suggest
that, in the heterodimer charge separated state, MgP+ and H2P' retain monomer
Characteristics. Accordingly, the assignment (Table 2.5) of the vibrational modes of
the Mg-porphyrin (MgP) cation of the Mg+-H2- diporphyrin is made by analyzing
patterns that have been established previously for the vibrational modes of MOEP
cations (CuOEP, ZnOEP, MgOEP) [ZS-29]. The assignment of the 1597 cm'1 band
82
to the on and 02 modes is made because, in the high frequency region, modes
involving primarily Cbe stretching (on and 02) increase in frequency as the result
of removing one electron from the porphyrin all, orbital. In general, this assignment
is close to what is predicted by metalloporphyrin 2A1u cation core size correlation
[17,18]. Similar results have been reported for the singly-oxidized, sandwich-type,
diporphyrin cation complex [35]. In 2A1u metalloporphyrin cation radicals, modes
involving primarily CaCm stretching character decrease in frequency. However, the
010 mode, which has CaCm character, is usually weak in the neutral species and in
our experiments the 010 mode in the MgP+ cation of the heterodimer can not be
identified. The U4 mode, the oxidation state marker in heme proteins, is the most
strongly enhanced mode observed for neutral ground state metalloporphyrins when
Soret excitation is used. This mode shifts down and loses intensity in the resonance
Raman spectra of the 2A1“ type 7: cation radical and is assigned to 1348 cm'1 in the
MgP+ cation.
The assignments of the vibrational modes of the free base anion (HzP') in
Mg1-H2’ are made by analogy to those of the OEP anions [33]. In the monomer, both
02 and on modes down shift upon oxidation (Table 2.5). Accordingly, modes in the
heterodimer charge transfer state that occur at 1556 cm'1 and 1543 cm'1 are assigned
to those two vibrations, respectively. This relatively large shift pattern is consistent
with earlier results for monomeric HZOEP' anions [33], which have been interpreted
to indicate that excess electron density in the anion radical is localized at the porphyrin
peripheral atoms rather than at those at the center. The U4 mode of the monomeric
HZOEP‘ anion shifts only two wavenumbers relative to its parent neutral HZOEP
Species. If this is the case for the Mg+-H2’, the 134 mode of the HzP’ anion overlaps
the strong ground state 04 band and its exact frequency will be obscured by the large
negative ground state contribution in the 1370 cm'1 region.
83
We now turn to the assignment of the Raman band at 1384 cm'1 in the charge
‘ separated state. In the D4,, symmetry of closed shell neutral porphyrins, ajg, big and
b2; vibrations are Jahn-Teller active, whereas modes of the azg symmetry are not.
However, in the lower symmetry case, 323 modes can be Jahn-Teller active as a result
of removing an electron from the am or an orbitals to form the metalloporphyrin
cation [42]. The 1384 cm'1 peak is, however, unlikely to arise from the Mg!” cation
of Mg+-H2' as there are no strong resonance Raman active vibrations of the
metalloporphyrin cation in this region. On the other hand, this vibration can be
assigned to the 020 mode of the HZP' because there is a significant enhancement of a
depolarized mode in this region in the resonance Raman spectrum of the H20EP-
anion [33]. The Jahn-Teller effect is expected to be small in the free base porphyrin
anions, as it is already in D21I symmetry. A rationale for strong B-state resonance
enhancement of non-totally symmetric modes has been provided in the earlier work on
the HZOEP anion [33]. The 020 vibration belongs to the bra mode of the free base
porphyrin. In D21, symmetry, Herzberg-Teller coupling, which mixes nondegenerate
porphyrin excited states, occurs through the blg modes. Thus the 1320 vibration can
gain intensity via Herzberg-Teller coupling between anion low-lying excited states.
The data and analysis presented here allow us for the first time to get a
preliminary picture of the vibrational properties of the charge separated state of the
diporphyrin complex. We have observed the ground state and the charge separated
state of the Mg-Hz diporphyrin complex by using resonance Raman and time-resolVed
resonance Raman spectroscopy. The interpretation of the time-resolved spectra
described in this paper is based on a comparison with the known spectra of
metalloporphyrins, free base porphyrin, and their cation and anion derivatives and
indicate that we can decompose the charge transfer state spectrum into contributions
from the anion and cation halves of the diporphyrin complex.
84
2.5 Discussion
In the previous section we discussed the use of two color picosecond Raman
pump and probe techniques to dynamically measure the relative population of electron
density on Mg-Hz diporphyrin complex. The similarity of the vibrational patterns
between the diporphyrin complex and the porphyrin cation and anion radicals leads us
to think that the principal force in altering the force constants in the Mg+-H2- charge
separated state is the electron density distribution between two porphyrin rings, and
that the possible orbital occupancies in Mg+-H2_ are similar to these of Mg porphyrin
cation and free base porphyrin anion. It would be interested to explore this idea
further by investigating in detail the orbital distributions and electronic states of
porphyrin cation, anion and diporphyrin excited states.
Gouterman treated the vibronic coupling and optical spectra of porphyrin rt
macrocycle by using a cyclic polyene model of linear combinations of one electron
promotions between the two accidentally degenerate highest occupied orbitals, am and
a2“, and two lowest unoccupied orbitals, eg under D4,, symmetry [42]. The Q bands in
the visible region can be constructed from a subtractive combination of two
promotions, and the Soret bands originate from an additive combination of two
promotions. This interpretation is known as the four-orbital model. Since
Gouterman’s work, the general features of the a1“, a2“, and e8 orbitals, as well as the
general predictions of the four-orbital model, have been reproduced by many different
MO calculations on a variety of porphyrin derivatives.
The semi-empirical INDO/s computational methods employed here have been
described previously [55-57] and have been applied in studies of the electronic spectra
of several heme porphyrin and chlorin systems [58]. Several modifications have been
done, however, to the original computational package in order to apply it to large
molecular systems such as the diporphyrin complexes discussed here. A more detailed
description of modification of the subroutines to increase the maximum number of
85
atoms allowed and to modify the CI matrix in this package, along with an input
example, are available upon request. Briefly, the molecular coordinates for
diporphyrin complex were adapted from X-ray crystallographic data [17]. SCF
calculations were performed to obtain the ground state MO descriptions.
Subsequently, electronic wave function for 15 ground states orbitals (orbital # 100 to
114) and 15 lowest excited states orbitals (orbital # 115 to 130) of the complex were
calculated by performing the singlet excited CI procedure [56, 57]. A total of the
lowest 35 excited singlet sates were calculated.
2.5.1 Ground State
The ground states of neutral diporphyrin complexes at different ring-ring
distances, were calculated by SCF method. The frontier orbitals (HOMO and
LUMO) are given in the Figure 11 and their orbital coefficients are listed in Table 2.6.
Similar to their monomer porphyrin counterparts, the highest four HOMOs have an,
properties (HzP is treated in D411 symmetry) characterized by large unpaired spin
densities at a carbons adjacent to the nitrogen atoms or a2u properties with large spin
densities at meso-carbons and on the nitrogen atoms. The lowest'four LUMOs are of
eg symmetry with re electron densities at ,6 and meso positions. The calculations show
that for ring-ring distance less than 3.5 A, i.e., in Van der Waals contact, there are
strong orbital mixing between the two porphyrin rings. The coefficients of the orbitals
are evenly distributed among two rings. This could be the case of exciton states as the
result of strong ring-ring interaction. At ring-ring distances from 3.5 A to 4.5 A, there
is a transition period, orbital mixing decreases as the ring-ring distance increases. The
HOMOs have more mixing between MgP and HZP than the LUMOs. For ring-ring
distances larger than 4.5 A, however, the two porphyrins basically retain their
monomer properties. The orbital coefficients are very similar to those of the monomer
porphyrins. More than 95% of orbital density is localized in MgP or H2P rings. The
86
Table 2.6. Ground State Orbital Coefl'icients of HOMO and LUMO of the Neutral
Diporphyrin Complexes
C C Cmeso
Orbital °‘ '3
iii/symmetry MgP H2? MgP H29 MgP H29 MgP H2?
1 1 “321.1 0.06 0.100 0.265 0.148
0.050 0.094 0.262 0.180
112m,“ 0.20 0.110 0.005 0.004
0.234 0.126 0.004 0.004
113/a,“ 0.05 0.09 0.270 0.155
0.05 0.079 0.255 0.174
114m,“ 0.235 0.125 0.005 0.005
0.198 0.103 .030 0.003
115/e3 0.109 0.100 0.155 0.078
0.191 0.143 0.170 0.088
115/e, 0.123 0.110 0.160 0.07
0.125 0.120 0.225 0.100
117/6: 0.169 0.139 0.210 0.09
0.138 0.118 0.155 0.650
113/e. 0.155 0.130 0.200 0.09
0.106 0.091 0.185 0.073
87
Table 2.7a Orbital Coefficients of HOMO of the Cation Diporphyrin Complexes
Ca CB CMBSO N
Orbital
#lsymmetry M8? H2? ME? “21’ MgP HZP MgP H211
III/a... 0.242 0.114 0.098 0.130
llZ/azu
0.182 0.156 0.225 0.239
113/32..
0.277 0.123 0.114 0.165
1141/31“
0.119 0.116 0.318 0.235
Table 2.7b. Net Charge Densities of the Cation Diporphyrin Complexes
88
Rin -Ring Distance 3.3 3.5 3.8 4.0 4.5
(A
MgP:
Mg + H 1.970 1.973 1.930 1.829 1.834
Ca 1.310 1.315 1.188 1.093 1.085
CB 0488 -0.484 -0.498 -0.504 -0.503
Cmeso -0.282 -0.275 -0.201 -0. 101 -0. 100
N -1.625 -1.603 -1.456 -1.326 -1.318
Total 0.885 0.926 0.963 0.991 -0.998
H21); 1.580 1.570 1.620 1.722 1.720
H
C0L 0.940 0.939 0.940 0.948 0.936
C13 0698 -0.704 -0.705 -0.705 -0.714
Cm” -0.282 -0.289 -0.336 -0.320 -0.312
N -l.465 -1.473 -1.485 -1.638 -1.628
Total 0.075 0.043 0.034 0.007 0.002
89
Table 2.8a Orbital Coefficients of HOMO of the Anion Diporphyrin Complexes
. Cot Cp Cmeso N
#metry MgP H2? M8? HzP MgP H2? M8? H2?
115/e: 0231 0.189 0.190 0.102
1 16/e, 0.203 0. 191 0235 0.143
1 17/03 0.195 0.179 0.260 0.180
118/8: 0.141 0.157 0.280 0.240
Table 2.8b. Net Charge Densities of the Anion Diporphyrin Complexes
Rin -Ring Distance 3.3 3.5 3.8 4.0 4.5
(A
MgP:
Mg + H 1.405 1.424 1.498 1.552 1.574
Cu 1.00 1.012 1.006 1.009 1.003
CB -0.666 -0.653 -0.688 -0.750 -0.743
Cmeso -O.340 -0.321 -0.312 -0.303 -0.302
N -1.535 -1.529 -1.533 -1.532 -1.539
Total -0. 136 -0.067 -0.029 -0.024 -0.007
H21); 1.222 1.217 1.210 1.197 1.197
H
Ca 0.776 0.759 0.765 0.746 0.778
CB -0.965 -0.980 -0.976 -0.952 -O.936
Cmeso -0.382 -0.395 -0.405 -0.413 -0.443
N -l.476 -1.489 -1.532 -1.552 -1.588
gTotal -0.825 -0.888 -0.938 -0.974 -0.992
91
order of HOMOs in increasing energy is a2u(H2P) < al,,(HzP) < a2u(MgP) < al,,(MgP)
with a small gap between them (< 0.01 au.). However, at larger ring-ring distance,
the a2u(MgP) orbital drops bellow H2P's an, and an, orbitals. The lower D2,1
symmetry of the HzP, which causes the splitting of the near degenerate al,, and a2u
orbitals, and the exciton interaction at short porphyrin ring-ring distance may account
for the above change in orbital orders. On the other hand, the change in ring-ring
distance has little effect on LUMOs. The order of LUMOs in increasing energy is 2
egtnzP1< 2 c.0430.
2.5.2 The Cation and Anion Radicals
Mg porphine cation radical has been studied experimentally with EPR and
ENDOR [14, 59] and theoretically with the ZINDO semi-empirical method [57]. Our
results on this monomer radical were very similar to those reported, i.e., an 2A“,
configuration. The orbital distribution and electron occupancy of the diporphyrin
cation and anion radical were calculated by UHF procedures. The results from ROHF
methods were similar to those from UHF. The geometries of the diporphyrins used in
calculations were the same as those for their parent diporphyrin compound, but an
electron was added or subtracted from the complex. The results are given in Table 2.7
and Table 2.8. It is expected that at large ring-ring distance (> 4.0) the electronic
Structure of diporphyrin radicals is similar to their parental monomer porphyrin
radicals and the charge is localized. However, it is clear that, even if at very close
rifig-ring distance, 3.5 A, the cation radical has an 1A to configuration with more than
93% orbital coefficients concentrated on the MgP side. The electron density analysis
also indicates that 0.93 (at 3.5 A) and 0.99 (at 4.0 A) of the charge is localized at MgP
macrocycle. ENDOR studies of the special pair in bacterial reaction centers showed
tl'Iat the oxidized dimers behave like supennolecules, however, the unpaired spin
density is unevenly distributed over both rings [60]. Considering that the
92
electrochemical potential difference between and MgP and H2P is much larger than
that of the two BChl molecules in the special pair, it is not surprising that charge is
localized at the electrostatically favorable MgP ring. The calculations of the orbital
distribution and the electron occupancy also indicates that the diporphyrin anion
radical has an 2E3 configuration with 90% of orbital coefficients is on H2P ring. The
electron density analysis shows that 0.89 of the unpaired electron is localized at the
H2P macrocycle at a ring-ring distance equal to 3.5 A.
In contrast to these radicals, at the Van der Waals distance, their parent neutral
diporphyrin complexes show strong ring-ring orbital mixing. Nevertheless, cation and
anion diporphyrin radicals are in a stable configuration which is similar to the
monomer porphyrin cation or anion. No mixing occurs in these diporphyrin cation and
anion radicals. This is a very interesting result as it implies that: 1) at least for the
ground state, the diporphyrin cation and anion radicals have retained their monomer
porphyrin properties; 2) without significantly alter the porphyrin macrocycle structure,
diporphyrin complex can have strong exciton coupling before the charge transfer
occurs. The same diporphyrin structure can also localize cation or anion radical at one
Of porphyrin rings that is electrochemical favorable for stabilizing the charge after the
initial charge separation. The implications of these results will be discussed in next
section.
2.5.3 The CI Results
The CI wavefunctions from the combination of exciting an electron from fifteen
highest occupied orbitals into sixteen lowest unoccupied orbitals were obtained by
using ZINDO/s. The low-lying excited states up to the Soret bands, their transition
energies and oscillator strengths at ring-ring distance equal to 3.5 A, 4.0 A and 4.5 A
are listed in Table 2.9, 2.10 and 2.11. For ring-ring distances larger than 4.5 A, the
excited states can be characterized simply as either monomeric 7t—> 7:9 states or as
93
linear combinations of the monomeric states. The first group of excited states with
MgP to H2P charge transfer characters are calculated around the 18000 to 20000 cm'1
region, higher than the Q bands of porphyrin macrocycles which is consistent with
previous ab-inito calculation results on similar model compounds [61]. For ring-ring
distances less than 3.5 A, severe mixing of intennacrocyclic wavefirnctions occurs.
All the transitions are dimeric in character and no clear charge transfer bands can be
detected. Furthermore, at such distances, the geometries of the two porphyrins are
probably strongly distorted [15]. The most interesting region is the ring-ring distance
between these two extremes, from 3.5 A to 4.5 A. Calculation results indicate this is a
mixing region such that the localized, monomer-like 1t-> 7st excited states, the
delocalized dimeric exciton states and the charge transfer states are observed. Two
low-lying excited states whose major components are MgP to H2P charge transfer are
detected below the diporphyrin Q bands. These results are consistent with the
experimental picosecond transient absorption data on the same diporphyrin complexes,
which show that two electron transfer bands lay below the porphyrin Q bands [3-6].
The four locally excited 7t—> 71* states, which are essentially identical to the two lowest
rc-> 11* transitions of monomer porphyrin, are assigned to the Q bands for this
diporphyrin complexes. Some high-lying states and Soret bands are also assigned
according to their transition symmetry and oscillator strengths. More interestingly, a
group of mixing excited 7t—> 11* states, i.e. simultaneous MgP to HZP transition and
HZP to MgP transition which is similar to exciton coupling, are detected between Q
bands and Soret bands. Those bands disappear at ring-ring distances large than 4.5 A.
The fact that the calculation results from this intermediate region are mostly consistent
with the experimental data implies that exciton states may play an active role in the
electron transfer process of those diporphyrins. From the diporphyrin cation and anion
results in the previous section, we find that without significantly altering the porphyrin
macrocycle structure, the same diporphyrin structure can have strong exciton coupling
94
Table 2.9. Electronic Transitions and Assignments of the Diporphyrin Complexes at
3.5A° Ringflng Distance
Transition
Energy (cm'l) Transition Assigments (Major components) Oscillator Strength
12105 CT (Mg -> HZP) 0.0004
12256 or (Mg -> 1121’) 0.0001
15440 Q (MgP: x-n“) 0.0346
16259 Q (MgP: rt-rt‘); Q (HZP: x-n‘) 0.0895
18162 Q (11sz fi-tt‘) 0.0144
18340 CT (MgP-> HZP); Q (MgP: n-rt‘) 0.0013
20041 CT (HZP-> MgP); Q (11sz n-n') 0.0006
20422 Q: (11sz rt-rt‘) 0.0034
23429 x-x‘(MgP) 0.0334
24159 CT (HzP-> MgP); x-rt‘(MgP) 0.0494
24579 n—x‘ (1129» MgP + Mg -> H2?) 0.0277
24795 rt-n‘ (1121b MgP + Mg -> 1121’) 0.0046
26079 n-u‘ (1-12P-> MgP + Mg .> 112?) 0.0008
27121 xex‘ (I-IzP-> MgP + Mg -> HZP) 0.0010
27605 rt-x“; CT (MgP-> H2P) 0.2540
29653 CT (1-12P-> MgP); rt—n‘(MgP) 0.0121
29745 rt—n‘ 0.0174
29931 rt-tt‘ (MgP) 0.0820
3101 l n-x‘ 0.0004
31805 x-rt‘ 0.1442
Table 2.9. Continue
95
32362
32525
x—u‘
Soret rt-x‘
0.5555
1.2502
96
Table 2.10. Electronic Transitions and Assignments of the Diporphyrin Complexes at
4.0 A° mating Distance
Transition
Energy (cm'l) Transition Assigments (Major components) Oscillator Strength
14288 CT (MgP -> H2P); Q (MgP: n—rt“) 0.0054
15471 CT (MgP -> H2P) 0.0028
16046 Q (x-n‘); CT (MgP .> H2?) 0.0362
16604 Q (11sz n—n‘) 0.1032
19726 Q (Hsz n-tt‘) 0.0002
20961 CT (MgP -> 1129);: n-fi’ (MgP) 0.0060
21496 CT (1121» MgP) 0.0001
21660 CT (1128 .> Mg); n—tt' (112?) 0.0007
23772 x-x‘ (HZP) 0.0125
24208 x—x‘ (HZP) 0.0007
24654 CT (1121’ -> Mg) 0.0053
25370 t-fi" (1121:» MgP + Mg -> H2?) 0.0286
26386 x—tt‘ (HzP-> MgP + Mg -> HZP) 0.0858
27384 n-‘K‘ (11211» MgP + Mg .> H29) 0.0029
28184 stats 0.0013
28993 x—x‘ 0.0387
29713 Soret n—n“ 0.7078
30195 x—x‘ 0.1 195
32542 Soret u—n‘ 3.3810
33108 ’ t-l‘ 0.6688
Table 2.11. Electronic Transitions and Assignments of the Diporphyrin Complexes at
97
4.5Ao Ring-Rio Distance
Transition
Energy (cm'l) Transition Assigments (Major components) Oscillator Strength
14350 Q (11sz n-n‘) 00094
15932 Q (MgP: n—rt‘) 0.0162
16220 Q (MgP: u—n‘) 0.0371
16590 Q (11sz n-n“) 0.0944
20664 CT (Mg -> HZP) 0.0000
20961 CT (MgP-> HZP); n—tt‘(MgP) 0.0009
22195 CT (HzP-> MgP) 0.0000
22513 CT (HZP -> Mg); u-n*(1-12P) 0.0001
25043 x-tt'mzP) 0.0469
25606 rt-x‘ (HZP); CT (HzP-> MgP) 0.0002
25727 x-n‘ (112P-> MgP + Mg -> H2P) 0.0003
26070 x-tt“ (I-IzP-> MgP 4» Mg -> HZP) 0.0612
26354 n—rt“ (HZP-> MgP + Mg -> H2P) 0.0168
27177 x-tt" (MgP); CT (MgP-> H2P) 0.0004
28271 7041‘ 0.0026
29337 u—x" 0.2760
29674 Soret rt—rt‘ 0.7231
30057 n—n“ 0.1686
32133 Soret n—rt' 4.1876
33230 n—tt‘ 0.1821
98
before the charge transfer occurs and delocalize the cation or anion radical at one of
the porphyrin rings. Therefore, exciton states may couple into the forward electron
separation. Furthermore, the experimental results reveal that Mg-Hz diporphyrins
with long length, flexible side-chain linkages seen to prefer a closer conformation than
its side chain length [3-4] and Mg-Hz diporphyrins given a short ring-ring distance
will tend to separated from each other by taking a “slipped” structure [17]. The
consistency of our calculation results with the experiments suggest that this is an
important intermediate region key to the electron transfer reactions that occur in these
diporphyrin complexes. Electron transfer reactions are less efficient as the results of
less interaction at large ring-ring distance (>4.5 A° ) or orbital contamination at short
ring-ring distance (< 3.5 A°).
These structures in the intermediate ring-ring distance region may also have
another important function in the CT reactions, by minimizing the reorganization
energy. It has been established both in experiments and in theories that porphyrin
excited S, state is somewhat closer to the ground state in conformation than is the
excited T, state, which experiences various distortions that arise from Jahn-Teller
effects [42]. During the course of inter-system crossing from excited S, to the T,
states, the change of the porphyrin conformation must go through a period that is
favorable to the occur of the electron transfer reaction. Those structures may be more
similar to the S, state structures or to the triplet state structures. Time-resolved Raman
spectroscopy is the best method to detect the above structure changes. According to
the Fermi Golden Rule of electron transfer reaction, the reaction rate is a products of
an electronic matrix element squared, IVIZ, and a 'vibrational term which involves a
thermally weighted sum of Franck-Condon factors, FC: kg=(4rtz/h)|V|2'FC. The
matrix element V contains the dependence of the rate on the orientation of the electron
donor and acceptor and their separation distance. The Franck-Condon factors contain
the dependence on the density of states and total nuclear reorganization energy. For
99
electron transfer reactions in liquid medium, the Franck-Condon factors include
contributions from both solvent motion, which are sufficiently low in frequency that
they can be treated classically at most temperatures, and internal vibrations of the
electron donor and acceptor, which usually must be handled quantum mechanically
[62-64]. Therefore, in order to account properly for the quantum mechanical nature of
the high frequency molecular vibrations, the frequencies and reorganization energies
of these individual internal modes must be known [65]. Since such information is not
usually available, the rate of electron transfer reaction are usually described by using
models that employ a single ”average” quantized vibrational mode with a frequency
considered appropriate for the systems of interest [66-68]. Often a value close to
1500 cm‘1 is chosen for this averaged frequency, as this is close to the frequencies of
skeletal stretching vibrations of aromatic systems. Clearly the assumption of a single
high frequency mode is at best a rough approximation. However, from our
experimental data in the high frequency region, the modes which are most active, i.e.
with large Raman intensity or shifts in the electron-transfer process, are those modes
which relate to the porphyrin skeletal motions in the 1300 cm'1 to 1500 cm'1 range,
such as v; and V2,, of the anion and v2 and v” of the cation.
Under the sum of state expression of resonance Raman effect, the Raman tensor
is the sum of a F ranck-Condon term and a Herzeberg-Teller term.
1
—IM(R.)I’2 ' '. +
h wag-071-11.}
all." =
(2.8)
< mlRle >< e|n > + < m|e >< e|R|n >1
1
-|M(Ro)l"lM!(Ro)IX .
h (17...; — (UL-Ire
In the Franck-Condon situation, excited state potential has a quite different shape and
internuclear position from the ground state. In terms of the electron transfer, this will
100
require a large reorganization energy. This is not consist with the experimental data on
this diporphyrin complexes since the charge separation is efficient. In order to achieve
the maximum electron transfer efficiency, the reorganization energy should be small.
Our calculation results indicate that the porphyrin dimer may serve this propose well
under certain structures. Its structures are favorable for exciton coupling, which
allows the charge delocalizes between the two porphyrin rings, which may serve as a
precursor to the subsequent electron transfer reaction. After the electron transfer
reaction the same structure with minimal alteration can also stabilize the changes in the
charge separated state. In these systems, the excited state potential surface is nearly
the same as that of the ground state, thus the vibrational wavefunctions are orthogonal.
The Franck-Condon term in the Raman tensor expression only gives Rayleigh
scattering. Under this circumstance the matrix element of does not require
total symmetric. The Hezeberg-Teller term dominates the Raman scattering. This is a
possible cause of activation of the nonsymmetric modes in the charge separated state,
such as v20 mode, although it is an open question as to whether they come from a
conformation during the charge transfer process or they are belong the metastable
structure of final electron-separated states. In other words, the conformation of those
nonsymmetric modes may have two functions, first to activate the electron-transfer
process; second to stabilize the charge-separated species.
This initial interpretation has interesting implications for the molecular dynamics
that accompany charge transfer. Several factors may be envisioned that could produce
substantial structure changes in the charge separated state. In the diporphyrin case,
the two porphyrin rings are nearly in van der Waals contact [17]. Although this type of
porphyrin ring-ring interaction has only small effects on the ground state vibrations
[Fig 3 and Table 1], its efl‘ect may be enhanced in the excited state and in the charge
transfer state. For example, geometry changes have been observed for porphyrin
dimers upon formation of the corresponding singly oxidized cation radicals [15, 16].
101
For the dimers we studied here, if the charge separated state involves an electron
transfer from the a,,, orbital of the Mg porphyrin to the eg orbital of the free base
porphyrin, as our data indicate, then rotation in the x-y plane of the cationic ring
relative to the anionic ring by ~ 450 will produce maximum in-phase overlap of the
orbitals. Although the covalent links will restrict this process, some rotation might be
expected and this would produce shifts in 7: electron density and ring distortion, which
would, in turn, cause vibrational mode shifts. Resonance Raman spectroscopy [35] on
lanthanide porphyrin sandwich complexes and their cation radicals also shows that
there are vibrational manifestations of porphyrin-porphyrin 1t—7t interaction [see also 7,
13]. Moreover, resonance Raman spectroscopy of the ground state special pair of
bacterial reaction center [70-73] has detected several low-frequency peaks that are
proposed to arise from modes that are unique to the dimer by using several excitation
wavelengths in the 800 - 910 nm range. Thus, nonsymmetric modes may also gain
intensity from this kind of ring-ring interaction. However, from the analysis of our
transient Raman data, we conclude that the effect of ring-ring interactions on the
charge transfer state of the diporphyrin complexes of Fig 1, are minor in the high
frequency region (A > 1200 cm'l), in comparison with the effects of oxidation and
reduction of the two porphyrin rings. The changes in force constant in the charge
separated state are basically dominated by the formation of cation/anion porphyrin
radicals. Other factors are not large enough to change appreciably the overall
character of the high frequency normal modes.
Our results indicate that, in the charge separated state of the Mg-H2 diporphyrin
complex, the MgP+ cation half of the dimer is in its 2A1u electronic state. The HZP'
anion half in the charge transfer state has vibrational characteristics that are typical of
the free base octaethylporphyrin anion. Further resonance Raman studies on porphyrin
excited states at short times are ongoing in our lab, and will give us a more detailed
102
model of the vibrational dynamics that occur upon photoexcitation and charge transfer
transitions in porphyrin-based systems.
2.6 Acknowledgment
We thank Dr. T. Carter for technical help on the psec laser instrumentation.
Support is acknowledged from grant GM 25480 (to G.T.B.) of the US. National
Institute of Health.
103
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CHAPTER THREE
THE VIBRATIONAL CHARACTERIZATION OF THE SYNTHESIZED 1.1-OX0
BRIDGED DIPORPHYRIN COMPLEXES AND IRON PORPHYRINICOPPER
CLUSTERS
Summary
Resonance Raman spectroscopy has been used to characterize u-oxo vibrations in
synthetic iron diporphyrin, diporphycene, iron porphyrin/Cu and iron porphyrin/Fe
complexes- The u-oxo symmetric vibrations were detected at 406 cm‘1 and 452 cm“1
for the iron diporphyrin and diporphycene, respectively. The aymmetric vibrations
were Observed at 818 cm'1 and 824 cm'1 for iron porphyrin/Cu cluster and iron
porphyrin/ iron clusetr. Further evidence supporting these bridge vibrations comes
from mode shifts in the protonated samples. The linear correlation of u-oxo bridge
vibrations and the M-O-M angle suggests that the M-O-M angle is a good indication
Of the bridge strength in these compounds.
—\
108
109
3.1 Introduction
The u-oxo dimer is a structure that has been proposed to exist in the active-site
of several metalloenzymes. It has thus been the subject of much spectroscopic study
[1-7]. Resonance Raman and IR spectroscopies have proven to be important methods
for vibrational structural determinations. These techniques are particularly suitable for
the characterization of bridge vibrations and have been used to probe the u—oxo type
bridged structure in the reaction mechanisms of several important enzymes and model
systems, such as the possible detoxification pathway of the malaria pigment [8, 9], the
respiratory hemerythrin of many invertebrates [10, 11], and the reduction of dioxygen
into water in the catalytic cycle of cytochrome c oxidase [12, 13]. These techniques
were also applied to the potentially physiologically important u—oxo diporphyrins [14-
16]. Recently, several porphyrin-based Fe-O-Fe and Cu-O-Fe complexes have been
synthesized with [17] and without [5-7] the supporting covalent linkages between the
di-metal centers. They have also been characterized by X-ray crystallography. These
molecules, aimed to model the structure of the copper-heme a3 complexes of the
cytochrome c oxidase enzyme, are of importance to characterize with Raman
spectroscopy in order to make contact with the in vivo studies underway in several labs
[18-24]. The comparison of the vibrational modes of the model compounds with the
in vivo system may clarify several important issues of the reaction mechanism in the
enzyme system. These include mode assignments of the intermediates, the local
environments and coordination numbers of the Cu}; site, and the reaction mechanism
and kinetic scheme. Of particular interest to this work, we report resonance Raman
studies of a series of Fe—O-Fe diporphyrin compounds and Fe-O-Cu complexes [17].
These compounds have been characterized by X-ray crystallography recently, and have
shown well-defined distances between the two metal centers, as they are constrained
by an aromatic linkage, in addition to the u—oxo bridge (Figure 3.1a, b and c).
110
3.2 Methods
The synthesis of diiron and iron-copper complexes and the incorporation of the
1.1-oxo bridge were performed by Chang and co-workers and will be published
elsewhere [17]. methylene chloride (for spectrophotometry, J. T. Baker) was distilled
from CaClz and used as the solvent in the spectroscopic studies. Absorption spectra
were recorded on a Perkin-Elmer k-S spectrophotometer. The cw resonance Raman
spectra were obtained by using the 413.1 nm laser line of a Coherent K+ laser. Laser
power was about 15 mW at the sample. The backseattering geometry was used in
Raman measurements. Raman scattering was dispersed into a Spex 1877 triplemate
monochromator and recorded by a CCD detector (Spex Spectrum One).
3.3 Results and Discussion
Compound 1, shown in Figure 3.1a, is a u-oxo iron porphyrin dimers whose
structure has been determined by X-ray crystallography [17]. Two M-O-M vibrational
stretching motions have been detected in several u-oxo compounds [10,11, 13-16].
The symmetric stretching mode appears at about 350 ~ 550 cm"1 and an asymmetric
stretching mode is at 700 ~ 900 cm'l. Figure 3.2 shows the Rarnan spectra of this
diporphyrin compound. Only the symmetric mode is predicted to be Raman active due
to the exclusion rule of total symmetric groups [18]. However, since the aromatic side
chain and the two closely packed porphyrins destroy the perfect linear Fe-O-Fe
symmetry, the asymmetric mode may also be Raman active. Recently, X-ray
crystallographic experiments on u-oxo iron diporphyrin compounds have indicated this
oxo bridge can be protonated and will, furthermore, break into hydroxide species [4,
19]. The 406 cm'1 and 822 cm‘1 peaks in the u-oxo species in Figure 3.1a can be
tentatively assigned to the symmetric and asymmetric u-oxo vibrations, respectively, as
the 406 cm"1 mode down-shifted to the 387 cm"1 and the 822 cm'1 mode decreased
111
greatly in intensity when 1 pm of acetic acid was added. Positive identification of the
origin of these modes will require with 180 labeled samples. However, the fact that
these modes are missing in spectra of the monomeric porphyrin starting material lends
support to our assignment.
Figure 3.3 and Figure 3.4 give the resonance Raman spectra of another iron
diporphyrin (DPX) and an iron diporphycene u-oxo complexes [Figure 3.1b and 3.1
c]. pH sensitive modes have been found at 387 cm'1 for the DPX and 452 cm'1 for
diporpycene and are assigned as the Fe-O-Fe symmetric stretching vibration.
Further evidence supporting the assignments in Figures 3.2 to 3.4 is that the
frequency of the u-oxo symmetric vibrations can be correlated empirically to the Fe-O-
Fe angle, determined by X-ray crystallographic data [9]. A plot of the Fe-O-Fe angles
vs. the symmetric and asymmetric u-oxo stretching vibrations is given in Figures 3.5
and 3.6, respectively. In order to overlap with the sp hybrid orbitals of the oxygen, the
ideal angle for Fe-O-Fe is 180°. Actually, this is the case for most iron porphyrin p.-
oxo dimers [20-24]. However, if the two porphyrin rings are constrained by other
covalent linkages [25] or the u-oxo bridge is protonated [19], this angle will become
substantially smaller. In the iron diporphyrin compound studied here, the Fe-O-Fe
angle is 164.7° and the distance between the two iron centers is 3.51A°. The two
Porphyrin rings are overlapped nearly perfectly (Figure 1a) and D4,| symmetry, without
considering side chain linkage, is retained in the dimer. This conformation differs
from the "slipped" equilibrium position of similar diporphyrin complexes [26]. These
Considerations suggest that there is a strong interaction in the diporphyrin system.
Sul‘prisingly, however, the 406 cm'1 p-oxo vibration fits well in the angle-vibration
112
Figure 3.1a Top and side views of the X-ray ctrystallographic strucure
for the “pacman” iron diporphyrin. The Fe-O-Fe angle is 165.70
and the Fe-O bond length is 1.759 A°.
114
Figure 3.1b The X-ray ctrystallographic strucure for the DPX iron diporphyrin.
115
116
Figure 3.1c Top and side views of the X-ray ctrystallographic strucure for the
iron diporphycene. The Fe-O-Fe angle is 145° and the Fe-O bond
length is 1.77 A°.
118
Figure 3.1d The strucure for the iron porphryin-copper/iron ligands clusters.
120
Figure 3.2 The resonance Raman spectra of iron diporphyrin ("Pacman"). The
excitation is 413.1 nm and the power is 15 mW. The top spectrum is
taken from the same sample but with 1 pm acetic acid was added.
121
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122
Figure 3.3 The resonance Raman spectra of iron diporphyrin (DPX). The
excitation is 413.1 nm and the power is 15 mW. The top spectrum is
taken from the same sample but with 1 pm acetic acid was added.
123
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124
Figure 3.4 The resonance Raman spectra of iron diporphycene. The excitation is
413.1 nm and the power is 15 mW. The top spectrum is taken from the
same sample but with 1 pm acetic acid was added.
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125
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126
Figure 3.5 The correlation of the Fe-O-Fe angle to the symmetric u-oxo bridge
vibration. The x-ray data of the Fe-O-F e angle are from reference 10.
The IR and Raman vibrational frequencies are from the literatures sited
here [3.8-3.11, 3.14-3.16].
127
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128
Figure 3.6 The correlation of the Fe-O-Fe angle to the asymmetric u-oxo bridge
vibration. The x-ray data and the IR and Raman vibrational frequencies
are cited from the same source as Figure 3.5.
129
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130
Figure 3.7 The resonance Raman spectra of iron/copper cluster. The excitation is
413.1 nm and the power is 15 mW. The top spectrum is taken from the
same sample but with 1 pm acetic acid was added.
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132
Figure 3.8 The resonance Raman spectra of iron/iron cluster. The excitation is
413.1 nm and the power is 15 mW. The top spectrum is taken from the
same sample but with 1 pm acetic acid was added.
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correlation shown in Figure 3.5, in spite of the fact that both diporphyrin complexes
have been strongly distorted from their slipped conformations [26] and the u-oxo
bridging angle is smaller than most u-oxo iron porphyrins.
For the iron diporphycene u-oxo compound, X-ray data give an Fe-OoFe angle
of 145° and the Fe-O bond length of 1.77 A°. This structure also shows the same
correlation between frequency and bridging angle for the Fe-O-fe symmetric stretch
[Figure 3.5]. With structures of this type, the non-bonding iron dyz orbital may
become involved in the Fe-O bonding interaction. The bridging oxygen, therefore,
may favor an sp2 hybridization in order to maximize the overlap of its hybrid orbitals
to the iron d orbitals. The possible cooperative interactions of the dz2 and dyz orbitals
in this type of bond increases the iron to oxygen charge transfer and thus polarizes the
Fe-O bond. A slightly longer Fe-O bond (1.77 A° in iron diporphycene and 1.759 A°
in iron diporphyrin) and a larger angle between the two porphycene planes support this
hypothesis. Thus, u-oxo vibrational modes act as markers of the iron-oxygen bridge
bond type.
Figure 3.1d shows another type of Fe-O-FeP and Cu-O-FeP complexes. In
these compounds, one iron or copper center is ligated to four nitrogen atoms rather
than bonded into a porphyrin ring. As predicted, this lack of symmetry enhances the
asymmetric stretching vibration. Raman spectroscopy has detected asymmetric modes
at 818 cm'1 and 824 cm'1 for Cu-O-FeP and Fe-O-FeP complex, respectively [Figures
3.6 and 7.7]. Similar to the diporphyrin cases, this bridge vibration is altered after
protonation. If the asymmetric vibration-angle correlation in Figure 3.5 holds for this
type of compound, we predict their u-oxo angles to be approximately 155° +/- 5°.
Again, positive assignment of these modes awaits isotopic labeling studies.
The main goal of the present study was to perform spectroscopic investigations
of the u-oxo bridged model compounds of cytochrome oxidase. In time-resolved
resonance Raman studies of oxygen reduction in cytochrome oxidase, the vibrational
13$
modes near the 800 cm'1 region were assigned to the (hydro)peroxy type intermediates
[27]. However, no Fe-O stretching modes in the model peroxy compounds have been
reported at such high frequencies to date. Since the u-oxo asymmetric stretching mode
was detected around the 800 cm‘1 region, and the fact that this mode was observed in
the iron porphyrin/copper cluster studied above, one should consider the possibility of
u—oxo type intermediates. These complexes are potential structural models for reaction
intermediates that directly link the a3 heme iron with the CuB site in cytochrome
oxidase enzyme. However, if this is the case, the time course of the reaction
arethsatism [28] needs to be modified since this type of compounds is suggested to
occur late in the cycle of dioxygen reduction [2].
Further efforts will be focused on the vibrational characterization of other u-
oxo derivatives of the diporphyrin and/or iron porphyrin-copper clusters. With the
help of the X-ray crystallographic structures and isotopically labeled samples some
interesting questions raised by the kinetic studies of the dioxygen/cytochrome oxidase
reaction by time-resolved resonance Raman spectroscopy can be clarified.
3.4 Acknowledgment
We thank Ms. Y. Liang and Dr. N. Bag for preparing the compounds used in
this study and Dr. C. K. Chang for helpful discussion. Support is acknowledged from
grants GM 25480 (to G.T.B.) and GM xxxxx (to C.K.C.) of the US. National Institute
of Health.
136
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CHAPTER FOUR
STRUCTURAL IMPLICATIONS ON ELECTRONIC AND VIBRATIONAL
PROPERTIES OF THE PEROXYHEME INTERMEDIATE OF OXYGEN REDUCTION
BY CY TOCHROME OXIDASE, A SEMI-EMPIRICAL QUANTUM CHEMISTRY
STUDY
Summary
In previous studies by this lab time resolved resonance Raman spectroscopy has
been used to investigate the reduction of dioxygen by the mitochondrial enzyme,
cytochrome oxidase (C. Varotsis et al. Proc. Natl. Acad. Sci. 1993, 90, 237). A
series of intermediates in the 02 reduction cycle were detected and assigned to oxy
(Fe2"’-Oz), peroxy [Fe3+-O"-O'(H)] and ferryl (Fe‘+=0). Simulation of the kinetic
scheme of the postulated reaction sequence indicates that following rapid 02 binding,
a series of progressively slower steps occurs. This process allows the various transient
species to build up to the concentration sufficient for their detection by time resolved
techniques. In the work reported in this chapter, intermediate neglect of differential
overlap (INDO) semi-empirical calculations were performed on oxy and peroxy
species to evaluate the effect of electron transfer on bond cleavage and bond formation
during the reduction of 02 to water. The re3*-o--o-(H) bonding interaction and
excited state transition energies were calculated. A group of low lying charge transfer
states were determined for the peroxy species. The impact on electronic
configurations and dioxygen bonding structures are compared to experimental results.
The charge transfer from iron to dioxygen is sensitive to the dioxygen orientation and
its 1" orbital interactions with iron d orbitals. Our results indicate that the peroxy
species is photoreactively different from the oxy species.
138
139
4.1 Introduction
Cytochrome oxidase is the terminal enzyme in the respiratory chain of most
aerobic organisms. This mitochondrial enzyme catalyzes the four-electron reduction
of molecular oxygen to water and couples this thermodynamically favorable reaction to
the generation of an electrochemical proton gradient across the membrane. Two
hemes, cytochrome a and cytochrome a3, and two redox active copper centers, Cu A
and CuB, mediate the redox chemistry and coordinate the translocation of protons.
Cytochrome a3 and Cu]; combine to form a binuclear cluster that is the site of
dioxygen binding and reduction to H20. The remaining redox metal active sites
function as electron transfer mediators between cytochrome c and the binuclear center
[14].
The characteristics of dioxygen binding to proteins has been a fundamental
question that has concerned researchers studying this and other oxygen-metabolizing
enzymes. Besides cytochrome oxidase, dioxygen reactions with cytochrome P450 [5],
hemoglobin [6] and myoglobin [7] have been extensively studied by both experimental
and theoretical methods. Since the determination of the X-ray structure of hemoglobin
and myoglobin in the sixties, many synthetic heme-dioxygen complexes have been
prepared [8]. The necessary and sufficient conditions for dioxygen binding to a heme
group are now understood qualitatively well, and model compounds have played a
particularly important role in developing this understanding. However, the local
environments in the protein, which are different from the model compounds, may
substantially modify the dioxygen binding geometry and, thus its reactivity. For
instance, hydrogen bonding between the terminal oxygen and the distal residue in oxy
hemoglobin and oxy myoglobin has been demonstrated [6, 7].
Some reaction intermediates, peroxy species, for example, proposed in the
dioxygen reactions with cytochrome oxidase and cytochrome P-450, are unstable and
140
thus, are unable to be prepared experimentally in model systems easily. The use of
theoretical quantum chemistry to study the dioxygen binding properties in these
biological systems, therefore, is a natural alternative and has been widely applied in the
last decade [9]. Different dioxygen binding transient structures and conformations
developed from experimental evidence can be constructed and examined by theoretical
methods. Since the use of the entire protein structure in a quantum chemical study is
too complicated to be practical, many theoretical studies have employed model iron-
porphyrin complexes [IO-21]. Many of these works have examined the possible
electronic configurations of the Fe-OZ complex and its electronic ground state for
which both a superoxo type electronic structure, Fe(III)-02', and a neutral spin-paired
electronic structure, Fe(II)-02, are supported by experimental data [22, 23]. These
computational results, in general, are quite sensitive to the quantum chemical methods
used and the surrounding ligand environment assumed. The interaction with the
environment may thus be an important factor that influences the dioxygen geometry in
real systems and could be responsible for part of the differences observed between
molecular model computations and experimental data Nevertheless, these works have
reflected the diverse range of chemistry encountered in these systems and have given
useful information in understanding the catalytic processes involved with dioxygen
complexation and reaction.
Dioyxgen reduction by cytochrome oxidase has been extensively studied by a
variety of spectroscopic techniques [24-59]. In biological systems the activation and
bond cleavage of dioxygen require the injection of electrons into the reactive site and
subsequent electron and proton transfer steps to reduce dioxygen into water. Due to
the unique ligand-binding kinetics of the binuclear center, the rate limiting step in the
overall process occurs late in the proton transfer reaction. Reaction intermediates
during this catalytic cycle, therefore, can build up to a detectable level for experimental
measurements [34]. Because of its advantage in directly probing the protein binding-
141
site structures, time-resolved resonance Raman spectroscopy adapting a Gibson-
Greenwood flow-flash scheme [24-25] has been applied successfully to this purpose
[27]. This approach has stimulated extensive studies of the dioxygen reduction
reaction by fully reduced cytochrome c oxidase [27-43]. As shown in Figure 4.1a,
several intermediate species have been detected and a basic reaction scheme for the
oxidation of fully reduced cytochrome oxidase by dioxygen has been proposed [34].
The kinetic simulation of concentration-time profiles for these proposed intermediates
is given in Figure 4.1b.
In spite of significant progress in understanding the dioxygen reduction
reaction catalyzed by the cytochrome oxidase enzyme, many questions remain. One of
the more controversial issues is the assignment of the signals associated with the
possible peroxy species, a key intermediate in the scheme shown on Figure la, in the
time-resolved resonance Raman experiments. First, the short life-time of this possible
intermediate makes its detection difficult. Secondly, the complicated electronic
configurations of the possible end-on and side-on dioxygen binding conformations to
the heme and, the coupling of the Fe-O bond to the peroxy O-O bond may give this
species unique structural and, therefore, vibrational properties. Thirdly, the possible
hydrogen bonding and/or CuB center ligation to the terminal oxygen in the end-on
conformation can also contribute to the structure and function of this species. As the
function of the protein cannot be separated from the firndamental chemistry of the
particular metal active-site structure and its local environments, synthetic models of
small molecular complexes that resemble these intermediates have been given great
consideration [8, 61-63] and have helped us to understand several reaction
intermediates of oxygen reduction by cytochrome oxidase [60]. However, the only
porphyrin-based peroxy species has been prepared synthetically and characterized by
X-ray crystallography is a Mn porphyrin peroxy complex [63]. The semi-empirical
quantum mechanical methods, therefore, have been employed here to study possible
142
Figure 4.1 a). the proposed dioxygen reduction scheme by cytochrome oxidase,
b). kinetic simulation of the concentration-time profiles for proposed
intermediates, reprinted from C. Varotsis et al. Proc. Natl. Acad. Sci.
1993, 90, 237
143
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144
Figure 4.2 The peroxy structures used in our calculations: a). standard peroxy; b).
hydroperoxy-1, a proton is shifted from imidazole ring to terminal
oxygen; c). hydroperoxy-2, a proton is added to the standard peroxy.
I45
146
heme-peroxy intermediates. The structures of the standard peroxy form and its
protonated forms (hydroperoxy) [see Figure 4.2] were chosen as targets to investigate
their electronic and structural properties and their possible biological relevance to the
cytochrome oxidase reaction sequence.
Several ab-initio and semi-empirical calculations have been done to study the
electronic structures of porphyrin derivatives [65], and the 02 binding to the porphine
peripheries [9-21]. For model compounds involving a porphyrin macrocycle and its
ligands, the use of ab-initio methods is prohibitive [66] due to the large number of
basis functions required to represent the system accurately. Among the semi-empirical
quantum chemistry methods, a computational package, ZINDO [67-70], is our choice
for studies of possible dioxygen intermediates catalyzed by the cytochrome oxidase
because of its proven ability to treat transition metal ions (heme) [IO-12, l7] and the
capability of our computer facilities.
4.2 Methods
All calculations of the model peroxy complexes were carried out in a SGI-xz-
4000 machine by using a spin-restricted open-shell INDO method, which has been
described in detail elsewhere [67-70]. Empirical parameterization with the Weiss-
Mataga-Nishimoto formula was employed [71]. The electronic spectra were
calculated by using single excitation within the INDO semi-empirical approximations
(INDO/s). In general, the configuration interaction (CI) calculations are performed by
exciting electrons from the occupied orbitals of a reference configuration, often the
ground state configuration, into virtual orbitals. As many as possible ground state
orbital and excited virtual orbitals should be used in carrying out CI calculations to
improve the overall accuracy of the molecular wave function. In our work here, CIs
were considered by exciting the electron from the highest 16 occupied orbitals to the
lowest 8 unoccupied orbitals, as the number of CIs are limited to 210 by the software.
l47
These configurations were generated by using Rumer diagram techniques [70].
Oscillator strengths were also calculated for each excited state relative to the ground
state.
The geometrical parameters for the peroxy model compound were modified
from X-ray data [23]. The porphyrin crystal structure was modified to a porphine-like
conformation [Figure 4.2a-c]. D41, symmetry labels were used for the calculated M03
and states as they are traditionally in porphyrin chemistry, although the actual complex
has lower symmetry. The Fe-Nporphyrin distance was set to 2.01 A°. The iron-
Nimidazole distance was set to 2.02 A0 without any further modification during the
calculations. The orientation of the complexes was such that the pyrrole nitrogens of
the porphyrin macrocycle bisect the x and y axes and the Fe binding atom of the axial
ligands lie on the z axis [Figure 2]. The imidazole ligand was basically in the y-z
plane. The bent end-on dioxygen binding geometry to the porphyrin plane was used
throughout the ground state and excited state transition calculations except where
otherwise indicated.
4.3 Results
a). Changes in end-on oxygen position vs. electronic configurations and
charge transfer.
The computed net atomic charges for a doublet peroxy species (Figure 4.2a) at
various Fe-Ol distances but at a fixed 01-02 distance are given in Table 4.1. In the
remainder of this chapter, 01 will be designated the bound oxygen and 02 will be
designated the terminal oxygen. The correlations of net charge distribution at the iron,
bound oxygen and terminal oxygen vs. the Fe—Ol distance are plotted on Figure 4.3.
An interesting result is that the net charge distribution at the oxygen moiety is similar
to that in superoxo species. There is substantial amount (> 0.7) of excess negative
charge at the terminal oxygen. However, the net excess negative charge is much less
148
on the bound oxygen. The rest of the negative charge is delocalized into the porphyrin
macrocycle, particularly on the nitrogen atoms. Previous semi-empirical calculations
of dioxygen binding to ferrous heme model compounds also gave a similar charge
distribution pattern [20]. The iron is at an intermediate electron distribution state
between the electronic configurations of the ferrous and ferric states. The Mulliken
population analysis confirms these results: the d-orbital population is (dx2.y2) = 1.98,
(dx) = 1.95, (dw) = 1.13, (1,,2 = 0.66 at r(Fe-Ol) = 1.90 A° and (d 3.)?) = 1.97, (dx,) =
1.96 , (dw) = 1.03 and dz2 = 0.67 at r(Fe-Ol) = 2.1 A°. While the net charge density
at the terminal oxygen remains approximately constant, an increase in Fe-Ol distance,
which minics a photodissociation process, enhances the charge transfer from iron to
the bound oxygen (Figure 4.3). However, this increase is not large enough to make an
Fe(III)~O"-O' electron configuration, a conventional structure for the peroxy species
that is often proposed in the literature [34]. On the other hand, an almost linear
correlation of the increase of net charge density on the oxygen atoms to the increase of
the Fe-Ol bond length [Figure 3] suggests that there are not other bond breaking/bond
making processes accompanying the photodissociation of peroxy intermediates. This
is consistent with photolability results in the time-resolved resonance Raman on the
early time scale of the dioxygen reaction with fully reduced cytochrome oxidase [31].
Table 4.2 shows the ground state atomic orbital compositions of the principal
molecular orbitals used in the configuration interaction calculations of a heme-peroxy
complex at Fe-Ol distances of 1.9 A0 and 2.1 A°. For comparison, the ground state
orbital compositions of standard dioxygen-heme binding structures at identical Fe-O
distance are also listed (Table 4.3). For the orbital occupancies of the oxy-heme
complex, the results from our calculations are similar to those reported in the literature
[10]. The major components of the HOMOs and LUMOs are basically a1", a2“ and
eg configurations, which is consistent with the four orbital model of porphines [72].
Relative to the oxy-heme complex, the major changes in the orbitals of the peroxy-
149
Figure 4.3 The correlations of net charge distribution at iron, end-on oxygen and
terminal oxygen vs. the Fe-O- distance. Fe-O-O angle equals to
110.8°, O-O bond length equals to 1.45 A°.
Net Charge on Fe
NetCharge on Dioxygen
150
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1.7 1.8 1.9 2.0 2.1 2.2
r A° (Fe-O)
151
Figure 4.4 The 3-D view of the computed electronic spectra of the standard peroxy
species at different Fe-O- distances.
152
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Figure 4.5 Computed electronic spectrum of the standard peroxy species: Fe-O
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heme complex occur in the HOMOs. The two highest occupied MOs, lying slightly
higher than the porphyrin an, and a2u orbitals, are dyz and oxygen It in character,
which demonstrates the importance of these orbitals in the peroxy-heme species.
Table 4 and 5 give the excited state transitions and major components for the above
peroxy structure at Fe-O distances of 1.9 A0 and 2.1 A°. Figure 4.4 gives three
dimensional views of the electronic transitions of this peroxy species at different Fe-
01 distances. Consistent with the analysis of the charge distribution data discussed
above, the Optical spectrum clearly shows that a set of oxygen to porphyrin charge
transfer transitions lie below the Q band absorption range. Furthermore, these CT
bands are photoreactive and can lead to dissociation, as an increase of Fe-Ol bond
distance moves these CT states to lower energies. This behavior is similar to the oxy-
heme species: decreasing energy of the charge transfer transitions with increasing iron-
dioxygen distance and no barrier to dissociation [10]. This observation is also
supported by time-resolved resonance Raman experimental results of the dioxygen
reaction with fully reduced cytochrome oxidase [31]. More specifically, the above
experiments have demonstrated that both the oxy adduct and the three-electron-
reduced species (peroxy equivalent) are photolabile at high photon flux. The
requirement for high photon flex presumably arises from the low transition oscillator
strengths suggested by the results of our calculations presented here ( oscillator
strength ~ 0.03 for the charge transfer transitions of the peroxy species). There are
also several sets of charge-transfer transitions between the Q bands and Soret bands.
Both 0 11: to porphyrin 1: CT and porphyrin 1t - 1! transitions are photodissociative.
However, a group of porphyrin It to imidazole 1! CT transitions which carry
intermediate oscillator strength and occur between the Soret and Q bands (Figure 4.4)
are stable during the photodissociation of the iron-peroxy complex, because these
transitions are not directly involved in the peroxide-heme bonding.
156
As discussed previously, the local protein environment, particularly the
hydrophobic nature of the heme pocket formed by the amino-acid residues in its
vicinity may have a significant influence on oxygen binding properties and structures.
The existence of hydrogen bonding between the terminal oxygen and the distal
residues has been suggested in the proposed peroxy intermediates in the oxidase
reaction [1, 34]. The presence and the nature of the axial ligand, which is on the
opposite side of the porphyrin plane with respect to the dioxygen ligand, is also
expected to play a role in influencing iron-oxygen bonding, in particular because this
ligand governs in part the electronic charge-transfer from the iron to the oxygen atoms.
Thus, an isomeric form of the peroxy species, formed by shifting a proton from the
imidazole to the terminal oxygen, hydroperoxy-1 (Figure 4.2b), and a protonated
peroxy, formed by adding an additional proton to the terminal oxygen of the standard
peroxy structure, hydroperoxy-2 (Figure 4.2c), are also considered here. The ground
state orbital occupancies of the hydroperoxy-1 and hydroperoxy-2, are listed in Table
4.6 and 4.7. The computed charge distribution on isomer hydroperoxy-1 at different
Fe-Ol distances is listed on Table 4.8. The optical transitions of the peroxy, its
isomer, hydroperoxy-1 and the protonated peroxy, hydroperoxy-2, at standard nuclear
configurations, Fe-Ol = 1.90 A° and 01-02 = 1.45 A0 are plotted in Figures 4.5 to
4.7. The changes in the optical spectra are due to perturbations to both ground and
excited states (compare Table 4.2 to Table 4.6 and 4.7). The protonation of the
terminal oxygen lowers the oxygen 1: orbitals in energy more than that of the porphyrin
1t orbitals. The low-lying oxygen rt to porphyrin CT bands, which are significant in the
peroxy species, are eliminated in the terminal oxygen protonated forms, hydrOperoxy-l
and -2. On the other hand, bands due to the charge transfer from imidazole to the
porphyrin and to the d orbitals of the iron become predominate in the hydroperoxy-l
isomer, presumably because a proton is transferred from the imidazole ring to the
terminal oxygen on the opposite side to form an imedazolate ligand. Similarly, the
157
spectra of the protonated peroxy species, hydroperoxy-2, lacks not only the low-lying
oxygen 1: to porphyrin CT bands but also the imidazolate to porphyrin ring-ring
transitions. The addition of the proton causes a relatively large perturbation in the
peroxy electronic configuration. This effect results in the production of excited state
transitions with greater intensity in the Soret band region [see Figure 4.7]. The most
interesting transitions in the hydroperoxy-2 species formed during the protonation step
discussed above are the iron d orbitals to porphyrin charge transfers. These bands mix
into the Soret transitions and neutralize the negative charge distribution of the
porphyrin ring, particularly on the prrrole atoms (see Table 4.11).
b). Changes in oxygen-oxygen bond length vs. the electronic configurations
and charge transfer.
The computed net atomic charges for a doublet state peroxy species with an
end-on geometry at various 01-02 distances but a fixed Fe-Ol distance (1.90 A0) are
given in Table 4.9. The correlations of net charge distribution at iron, bound oxygen
(01) and terminal oxygen (02) vs. the 01-02 distance are plotted in Figure 4.8. For
comparison, the charge distribution in hydroperoxy-l and hydroperoxy-2 are also listed
in Tables 4.10 and 4.11. In contrast to the dissociation of the peroxy species from the
heme moiety (Figure 4.3), extension and eventual cleavage of the CO bond leads to
significant electron rearrangements. This is best shown in the change of the net charge
distribution vs. the increase of the 0-0 bond distance (Figure 4.8). Similar to the
change in Fe-Ol bond distance (Figure 4.3), the analysis of the charge distribution at
various 01-02 distances indicates that this peroxy complex also prefers a Fe-O-O'
configuration mixed with Fe(II) and Fe(III) rather than a pure the Fe(III)-O'-O' form.
It has been well established by resonance Raman experiments that the v, vibration
mode can serve as an oxidation state marker of the heme group [73]. The v4 band
occurs at 1355 em'1 for the ferrous species (Fey) and at 1371 cm'1 for the ferric
158
species (Fey). The time-resolved resonance Raman spectra of dioxygen reactions
with the fully reduced cytochrome oxidase [31] show that the v4 band shifts from
1355 cm'1 to 1371 cm'1 when a photon photolyzes CO and initiates dioxygen
reduction to form initial 02-a3 complex. However, in the time scale from 100 us to
500 us, the diminishing 1355 cm'1 band begins to recover to a level comparable with
the 1371 cm'1 peak. This observation, whose origin is unclear in terms of the
previous discussion, therefore, can be explained by the possible formation of
F e(II)/Fe(III)-O-O- intermediate rather than the Fe(III)-O--O- species.
While the charge density distribution undergoes little change at the porphyrin
ring and at the imidazole as the terminal oxygen moves from the bound oxygen (Table
4.10), increasing distance favors the charge transfer from the iron and porphyrin ring
to the dioxygen, particularly to the terminal oxygen. The most interesting observation
is that while the net charge on the end-on oxygen atom increases steadily, the changes
in net charge on iron and the terminal oxygen atom are much larger. The rapid
increase in negative charge at terminal oxygen at r(O-O) from 1.2 to 1.45 A° indicates
strong potential reactivity of the terminal oxygen. The shallow well structure at about
r(O-O) =1.45 A° for the terminal oxygen gives an indication of a metastable form of
this species. This bent end-on structure, as its terminal oxygen extends away from the
porphyrin moiety and accumulates significant net negative charge, is rendered more
reactive with a positive charge or a proton to form a hydrogen-bonded structure as
compared to the side-on oxygen conformation [9]. Since the charge distribution is
different between the two oxygens, the terminal oxygen is easier to break away than
the bound oxygen when a proton or the CuB cluster attacks the peroxy species. The
plot of the charge distribution vs. the 0-0 bond distance Figure 4.8 reveals that the
transition region from the oxy to peroxy and, to the possible cleavage of the terminal
oxygen, occurs in the range of r(O-O) distance from 1.40 A° to the 1.48 A°. A
detailed comparison of the electronic transitions of the peroxy (Figure 4.5) and
159
hydroperoxy forms (Figures 4.6 and 4.7) shows that the 0 It to porphyrin 1: charge-
transfer transitions in the spectral region between the Q bands and Soret bands gain
considerable intensity in the hydroperoxy forms (see also Figures 4.9-4.11, three
dimensional plots of the hydroperoxy-l and hydroperoxy-2 at different Fe-O and O-O
bond distances), which suggests that the cleavage of the oxygen-oxygen bond rather
than the iron-bound oxygen bond is more favorable than dissociation of the dioxygen
species under these conditions. The heterogeneous dissociation mechanism of the
terminal oxygen gives the proposed ferryl species (scheme 1). Recently, light-induced
cleavage of the oxygen-oxygen bond was observed in the low temperature Raman
studies of peroxy-heme complex [74].
c). Changes in Cporpby-Fe-O-O torsion angles and dioxygen rotation
barrier above the porphyrin plane.
Table 12 lists the computed net atomic charges for the standard, doublet state
peroxy species at various Fe-O torsion angles. The rotation of the peroxy species
above the porphyrin plane does not produce any noticeable modifications of the
electron density. This result indicates that there is little mixing and coupling between
the oxygen 1“ orbital and porphyrin am and a2u orbitals. Although the peroxy species
discussed here is taken as occuring in a bent, end-on binding conformation, certain
interactions between iron dxy and dioxygen rt“ orbitals are expected. However, this
type of dxy to W“ back bonding has to be weak in the bent, end-on peroxy structure;
otherwise, rotating the 0-0 above the porphyrin plane will significantly alter the
charge distribution on the oxygen atoms.
160
Table 4.1. Charge distribution on a standard peroxy-heme stnlcture: Fe-O-O angle equals
to 110.8°, o-o bond length equals to 1.45 A°.
rec-0)A° Q(Fe) (2(01) «02) Q Q
(Porphyrin) (Imidazole)
1.7 1.236 -0.258 -0.720 -1.332 0.074
1.8 1.210 -0.289 -0.720 -1.287 0.086
1.9 1.184 -0.314 -0.724 -1.241 0.095
2.0 1.163 -0.335 -0.729 -1.203 0.104
2.1 1.138 -0.349 -0.733 -1.164 0.108
2.2 1.112 -0.357 -0.734 -1.133 0.112
2.3 1.087 -0.362 -0.732 -1 . l 11 0.118
161
Table 4.2. Ground State Orbital Description of the Stande Peroxy Complex
Orbital # Orbital Occupanocies o
Fe-01=1.90 A Fe-Ol = 2.1 A
90 62% d 24% porphy o; 4% dz2 99% eg"
89 99% e’g‘x 1% d 2 2 66% dxy; 27% pzorphy o; 4% dz2
88 96% eg"; 2%(122 90%b1u; 5% dz2 ;3°/odxy
87 100%b1u 52%lmldrr17%01r;11%imido;
22% porphy rt
86 82%imid7r;17%imido 81%imidrt;17%imido
85 99% bzu 100% b2u
84 69% imid o; 25% imid rt 88% imid o; 5% imid rt; 2% dz 2
83 82% imid 7t; 13% imid o 81% imid 7t; 15% imid o
82 99% eg: 98% eg“ ;
81 98% eg“ 96% eg“; 2% O 7:
80 85%dyz;13%07r 93%dyz;5%07t
79 82%0y1t; 9% dz2 69%0y;1t 12% dz2; 13%00
78 5;6%Ort 39%81u;4%dyz92%Orr,3%dyz
77 47% 0 7t; 45% am; 4% dyz 98% am
76 98% 82“ 99% 32a
75 52% dxzi 41% porphy rt 54% eg; 44% dxz
74 88% eg; 8% O 7: 90% eg; 4% 0 7t
73 76% dx2-y2;15% a22u; 1% o rt 38% dx2-y2, 60% am
72 83% eg; 14% d,‘2 _y2 ; 1% 0 It; 98% eg
1% imid 7t
71 100 blu 53% dx2 -y 2;40% porphy
70 68% imid 7t; 23% porphy 7r; 8% 98% blu
dxz
69 53% eg; 19% dxz; 1% 0 rt
68 85% eg; 7% dxzi 6% imid rt
67 98% eg; 1% dyz
162
Table 4.3. Ground State Orbital Description of the
Standard Oxy Complex
Orbital # Orbital Occupangies
Fe-Ol = 1.90 A
90 98% eg’; 2% dz2
89 95% eg"
88 61% dxy; 27% porphy o; 1% dz2
87 100% blu
86 99% imid n’
85 93% imid 1"; 2% dz2
84 100% b2u
83 98% imid rt’
82 64% eg“; 22% O 7!; 22% dyz
81 95% eg“; 2% 0 it; 2% dyz;
1% dxz
80 48 % eg"; 37% 0 7t; 12% dyz
79 99% 3111
78 98% a2“;
77 32% 0 7t; 36% dyz; 31% eg
76 52% eg; 40% dxz; 5% 0 rt
75 70% imid 7t; 28% eg
74 64%au;11%07r;15%00;
3% dx -y2
73 72% bl“; 26% imid rt; 1% dx2-y2
72 44% a u; 25% O 1:; 24% O o;
2% dz ; 1% dxz
71 87% d,‘2.y2 ; 8% porphy; 7% 0
7t; 4% O o
70 84% eg; 8% dyz; 5% 0 7t
69 96% eg; 4% dyz
68 90% eg; 4% dyz; 6% clxz
67 37% dxz; 36% eg; 11% O o; 15%
imid 1t
163
Table 4.4. Excited State Transition for a Standard Peroxy Structure: Fe-Ol = 1.90 A;
0.0 = 2.45 A (Assigments Are Given to These Transitions Whose Transition Energies
Are Lower Than the Soret Band).
Transition Transition Major Components
Energy (cm-1) Oscillator strength
6311.8 0.0000 dxz -> dyz; 07: (0.80)
7040.8 0.0000 0,2,2 -> dyz; ott (0.87)
7983.7 0.0296 On -> eg‘ (0.71)
8244.9 0.0021 Orr (0.44); 022 (0.36) -> eg"
10390.8 0.0202 Orr; alu -> eg‘
10904.8 0.0051 Orr; alu -> eg“
11455.7 0.0013 Orr -> eg“
11580.4 0.0085 dyz -> eg“; 07: -> eg“
11993.5 0.0037 01: -> eg“
12605.2 0.0017 07: -> eg“
16378.1 0.0656 a1u -> eg‘ ( 0.46); 82“ -> eg‘I (0.41) Q
16583.3 0.0501 alu -> eg“ ( 0.42); alu -> eg“ (0.44) Q
19704.2 0.0045 “In -> imid K“
20909.1 0.0021 01: -> imid m (0.57); dyz -> imid m- (0.36)
21521.0 0.0030 07: (0.51); alu (0.40) -> qu
22728.6 0.0029 On -> imid m
23648.4 0.0158 dxz -> eg“
24171.5 0.0024 Orr (0.32); 81“ (0.29) -> b2“; dxz -> eg" (0.20)
24323.8 0.0139 82“ -> b2u (0.18); 01: (0.17), a1u (0.08)-> dyz; dxz
' (0.10) -> eg";
24486.6 0.0110 dxz -> eg‘
24580.1 0.0092 32u -> b2u
24818.7 0.0731 32u -> imid 7r
25199.7 0.0059 a2u -> imid 7t
25570.7 0.0017 07: -> b2"
25948.3 0.0562 01: -> b2u (14); dxz -> eg‘ (0.38);
26481.9 0.0037 01: -> b2u
26596.0 0.0829 01: -> imid it, o
26978.2 0.1168 82“ (0.28) -> eg“; a1u (0.28) -> eg“;
27100.8 1.3006 320 (0.27) -> eg“; alu (0.19) -> eg"; Soret
27797.2 0.9048
27873.2
28074.2
28175.2
28320.1
28872.4
28930.7
29246.9
29307.8
29490.5
29944.5
29963.1
30139.7
30296.7
30488.8
30654.7
30772.7
31324.8
31503.0
0.2194
0.0042
0.2237
0.0661
0.0019
0.0611
0.1591
0.0099
0.0433
0.0439
0.0106
0.0571
0.0103
0.0206
0.0126
0.0159
0.0134
0.0044
164
165
Table 4.5. Excited State Transition for a Standard Peroxy structure: Fe-Ol = 2.1 A; 0-0
= 2.45 A (Assigments Are Given to These Transitions Whose Transition Energies Are
Lower Than the Soret Band).
Transition Transition Major Components
Energy (cm‘l) Oscillator strength
3598.8 0.0001 Orr -> eg‘I (0.48); dyz (0.47)
5231.5 0.0001 t1,z (0.60); 0,2,} (0.29) -> dyz
5802.4 0.0221 01: -> eg"
5937.1 0.0043 dx2-y2 (0.51); dxz (0.22); ); ->dyz
7037.6 0.0006
7673.8 0.0002
8538.5 0.0013 07: -> eg’ (0.87)
8661.3 0.0003 On -> eg“ (0.84)
9209.1 0.0106 07: -> eg“ (0.72)
9692.5 0.0058 07: -> eg“ (0.68)
10012.9 0.0024 al,, (0.62); 01: (0.23).> eg“
11584.5 0.0004
13011.8 0.0001
14605.7 0.0001
15885.5 0.0009
16133.2 0.0720 am (0.40); 32u (0.55)-> eg‘ Q
16353.0 0.0596 a“, (0.42); an (0.55)-> eg" Q
17059.2 0.0003
17328.2 0.0000
18104.3 0.0012 071 -> imid 1V (0.90)
19293.4 0.0010 Orr -> imid 11?" (0.73)
19781.1 0.0001
21371.8 0.0053 an, -> b2; (0.72)
21502.9 0.0035 alu -> b2u* (0.95)
21957.0 0.0009
22248.7 0.0000
22462.2 0.0030 Orr -> 02u*(0.87)
22490.0 0.0065 011 -> b2u*(0.81)
22872.6 0.0000
23361.8 0.0090 ott (0.67); 022 (0.23) -> imid 0*
23559.6 0.0179 01: -> b2; (0.61)
23949.0
24144.3
24355.2
24605.4
24650.4
24718.6
24902.7
25313.5
25734.4
25775.7
26139.5
26821.2
26993.0
27134.7
27414.2
27601.7
27665.4
28059.6
28679.5
29079.6
29232.2
29315.1
30055.9
30222.8
30259.3
31028.3
31 167.8
31445.4
0.0009
0.0018
0.0720
0.0091
0.0046
0.0117
0.0112
0.0175
0.0038
0.0002
0.0251
0.0138
1.1623
0.2952
0.1544
0.0682
0.5357
0.9829
0.0062
0.0100
0.0637
0.0015
0.0008
0.0315
0.0422
0.0287
0.0115
0.0026
166
dxz -> eg‘I (0.34); 07: -> imid 0'" (0.39)
82“ -> imid it!" (0.75)
d,‘z -> eg"I (0.61)
Orr -> imid 71* (0.81)
am -> imid 11* (0.77)
820 -> b2tt"(0.41); dxz ; eg -> 68" (0.27)
3211 -> bzu‘(0.27); d,‘z ; eg -> eg“ (0.35)
dxz -> eg‘ (0.56)
071: -> imid 7" (0.86)
3111 (0.22); 32a (0.28)-> eg" Soret
167
Table 4.6. Ground State Orbital Description of an Isomer of the
Peroxy Complex, Hydroperoxy-l. A Proton Has Been
Shified from Imidazole Ring to the Terminal Oxygen
Orbital # Orbital Occupangies
Fe-Ol = 1.90 A
90 98% imid n‘
89 99% alu‘
88 98% eg"l
87 99% eg‘
86 60% dzz, 17% porphy o; 10% porphy
7t; 10% imid o"
85 55% dxy; 25% porphy 6*;17% porphy
1t.
84 85% bzu;l4% dxy
83 100% blu'I
82 97% eg"; 1% dxz
81 99% eg“
80 94% dyz; 3% O 7:
79 99% am
78 94% imid rt
77 97% “Zn
76 32% imid rt; 26% imid o; 17% dxz;
16% porphy rt
75 55% eg; 20% dxz; 14% imid 1t; 9%
imid o
74 58% imid It; 23% imid o; 10% porphy
71; 5% d,‘z
73 75% eg; 17% O 7:; 2% imid 7t
72 98% blu
71 92% 82“; 6% imid 0’
70 80% dx1-y1; 12% porphy 71:; 5% imid o
69 95% eg; 2% O 7:
68 98% eg;
67 62% O 7:; 26% porphy 1r; 5% dxz; 3%
dyz
168
Table 4.7. Ground State Orbital Description of a Protonated
Peroxy Complex, Hydroperoxy-Z. A Proton Has Been
added to the Terminal Oxygen
Orbital # Orbital Occupangies
Fe-Ol = 1.90 A
90 98% eg‘
89 99% alu‘
88 50% dz’; 28% porphy rt; 16% imid
0"; 2% dxy
87 62% d ; 32% porphy o
86 98% imld rt'
85 89% imid 0*; 9% imid rt“; 2% dz2
84 99% b2“
83 98% imid rt"
82 96% eg“
81 98% eg“
80 94% dyz; 4% O rt
79 99% “In
78 98% aZu
77 72% eg; 27% d,‘z
76 58% imid rt; 40% eg
75 96% eg
74 98% 32u
73 60% b1“; 39% imid rt
72 98% eg;
71 96% eg; 1% XLYZ;
70 80% dx’-y" 16% porphy rt
69 95% eg; 2% O rt
68 98% eg;
67 58% O rt; 30% porphy rt; 4% dxz;
2% dyz
169
Table 4.8. Charge distribution on an isomer of the peroxy-heme complex, hydroperoxy-1.
A proton has been shifted to the terminal oxygen from the imidozale ring: Fe-O-O angle
equals to 110.8°, O-O bond length equals to 1.45 A°.
r(1"'e-0)A‘\o Q(Fe) 0(01) 0(02) Q Q
(Pomhyrin) (Imidazole)
1.5 1.322 -0.271 -0.235 -1.296 -0.751
1.6 1.299 -0.318 -0.237 -1.245 -0.734
1.7 1.272 -0.356 -0.241 -1.196 -0.716
1.8 1.245 -0.387 -0.247 -1.151 -0.698
1.9 1.219 -0.412 -0.254 -1.109 -0.682
2.0 1.195 -0.432 -0.260 -1.066 -0.669
2.1 1.175 -0.448 -0.266 -1.040 -0.658
2.2 1.158 -0.463 -0.271 -1.009 -0.651
2.3 1.145 -0.477 -0.275 -0.985 -0.643
2.4 1.136 -0.491 -0.279 -0.962 -0.638
170
Table 4.9. Charge distribution on a stande peroxy-heme structure: Fe-O-O angle equals
to 110.8°, Fe—O bond length equals to 1.90 A°.
r(0-0)A° one) 0(01) 0(02) Q Q
(Porphyrin) (Imidazole)
1.1 1.009 -0.150 -0.078 -1.942 0.111
1.2 0.991 -0. 146 -0.345 -1.563 0.063
1.3 1.003 -0. 191 -0.362 -1.517 0.067
1.4 1.060 -0.225 -0.513 -1.402 0.080
1.45 1.184 -0.314 -0.724 -1.234 0.088
1.5 1.197 -0.338 -0.744 -1.214 0.099
1.6 1.211 -0.375 -0.764 -1. 176 0.104
1.7 1.219 -0.407 -0.766 -l.153 0.107
1.8 1.222 -0.437 -0.755 -1.141 0.111
2.0 1.220 -0.495 -0.707 -1.131 0.113
171
Table 4.10. Charge distribution on an isomer of the standard peroxy-heme complex,
hydroperoxy-1. A proton has been shifted to the terminal oxygen from the imidozale
ring: Fe-O-O angle equals to 110.8°, Fe-O bond length equals to 1.90 A°.
r(0-0)A° Q(Fe) 0(01) 0(02) Q Q
(Porphyrin) (Imidazole)
1.1 1.169 -0.333 -0.150 -1.196 -0.697
1.3 1.210 -0.400 -0.223 -1.133 -O.683
1.45 1.219 -0.412 -0.254 -1.112 -0.679
1.6 1.222 -0.410 -0.279 -1.097 -0.677
1.8 1.223 -0.394 -0.319 -1.077 -0.672
2.0 1.226 -0.371 -0.374 -1.048 -0.664
172
Table 4.11. Charge distribution on hydr0peroxy-heme complex, a proton has been added
to the terminal oxygen from the imidozale ring: Fe-O-O angle equals to 110.8°, Fe-O
bond length equals to 1.90 A°.
r(0-0)A° Q(Fe) 0(01) 0(02) Q Q
(Porphyrin) (Imidazole)
1.1 1.160 -0.259 -0.107 -1.366 -0.653
1.3 1.237 -0.364 -0.217 -1.256 -0.641
1.45 1.250 -0.383 -0.250 -1.225 -0.640
1.6 1.255 -0.385 -0.274 -1.210 -0.636
1.8 1.257 -0.374 -0.308 -1.188 -0.636
2.0 1.258 -0.355 -0.352 -1.161 -0.632
173
Table 4.12. Charge distribution on the standard peroxy-heme complex, dioxygen are
rotated above the porphyrin plane: O-O bond eclipses the x-axis at 0 = 0°, Fe-O-O angle
equals to 110.8°, Fe-O bond length equals to 1.90 A°.
9 (degree) Q ( Fe) Q (01) QIOZ)
0 1.184 -0.314 -0.724
15 1.186 -0.315 -0.724
30 1.186 -0317 -0.714
45 1.190 -0319 -0701
60 1.188 -0319 -0710
75 1.186 -0.318 -0.726
90 1.185 -0317 -0730
174
Figure 4.6 Computed electronic spectrum of the hydroperoxy-1 species: Fe-O
=1.9 A0, 0-0 = 1.45 A°.
175
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Figure 4.7 Computed electronic spectrum of the hydroperoxy-2 species: Fe-O
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177
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178
Figure 4.8 The correlations of net charge distribution at iron, end-on oxygen and
terminal oxygen vs. the CO distance. Fe-O-O angle equals to 110.8°,
Fe-O bond length equals to 1.90 A°.
Net charge on Fe
Net Charge on Dioxygen
179
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1.0 - O—~o——O
-O.2 -1
bond 0
«0.4 -4
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1.0 12 1.4 1.6 l 8 2 0
r A° (O-O)
180
Figure 4.9 The 3-D view of the computed electronic spectra of the hydroperoxy-1
species at different O-O distances.
181
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Figure 4.10 The 3-D view of the computed electronic spectra of the hydroperoxy-2
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Figure 4.11 The 3-D view of the computed electronic spectra of the hydroperoxy-1
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Figure 4.12 The variation of the empirical paraterized INDO-SCF energies as a
function of the Fe-O torsion angle.
187
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The variation of the empirically parameterized INDO-SCF energies as a
function of the Fe-O torsion angle is shown in Figure 4.12. Similar to the dioxygen
binding to the heme complex [11], energy minima of the peroxy species occur at 0 °,
90 ° and 180 °, corresponding to the peroxy species eclipsing and staggering the x-axis.
The local minimum at 90 ° is, however, higher in energy than those at 0 ° and 180 °,
probably due to rectangular type Jahn-Teller distortion on the porphyrin macrocycle
[72]. Similar behavior was also observed for the side-on peroxy adduct of a
manganoporphyrin [63]. On the other hand, the peroxy species is rotationally less
hindered about the porphyrin plane than the oxy-heme complex, as the rotational
barrier (~ 2 kcal/mol) of the peroxy is smaller than that of the dioxygen adduct (~ 7
kcal/mol) [l 1]. This, in turn, can be explained by the longer Fe-O and 0-0 bonds in
the peroxy fonns.
4.4 Discussion
The analysis of the electronic transitions of these possible peroxy intermediates
shows that both Soret and Q bands are very stable in energy. They are not affected to a
great extent by the peroxy-heme geometry, nor by the difference in binding species,
i.e., the standard peroxy, its isomeric hydroperoxy-1, and proton-added hydroperoxy-2.
However, the oxygen to porphyrin ring charge-transfer transitions caused by the added
electron density located on oxygens in the peroxy conformation in the standard peroxy
species are eliminated from the hydroperoxy-l and the hydroperoxy-2. The
hydroperoxy-1, which has the same negative charge as the peroxy form, lacks oxygen
to porphyrin charge transfer transitions because the negative charge is neutralized by
the proton shifted from the imidazole ring. This species has imidazole to porphyrin
and imidazole to iron charge transfer states, as expected for a negative imidazole
ligand. However, most of these transitions that carry oscillator strength lie higher than
the Soret bands, see Figure [6]. The high-lying CT channels are less peroxy-
189
photodissociable because of their higher energy levels and because of the lack of
mixing of the imidazolate orbitals with those involved in the heme-peroxy binding
mechanism. These excited states, however, may influence electron delocalization to
the porphyrin periphery and the iron center because they strongly mix into the Soret
transitions. They may also take part in oxygen reduction by fully reduced cytochrome
oxidase by facilitating the formation of non-photolabile products at later stages in the
reaction.
In the standard peroxy species, the lower photodissociating channel, which
consists of a manifold of charge-transfer states, is accessible either by direct excitation
or decay from the higher energy 1t-1t"I singlet states that give rise to the Q and Soret
bands. As pointed out early, dissociation of the peroxy from the heme plane would not
contribute to the non-photolabile products in oxygen reaction with the cytochrome
oxidase. Since the formation of end-on peroxy-heme is a natural extension of end-on
dioxygen-heme species, the transition from the oxy to the standard peroxy can be
considered as a relaxation process afier the injection of an electron to the heme a;
reactive site. This conformation further discriminates the two oxygen atoms by their
charge distribution, and hence, their redox ability. This is probably the key to the
enzyme catalyzed oxygen reduction [1, 34]. Considering the overlap of iron d}.z orbital
with the oxygen. py orbital in the bent end-on peroxy structure, this uneven
configuration makes the bound oxygen orbitals overlap more strongly the iron d
orbitals than those on the terminal oxygen. As the terminal oxygen accumulates more
net negative charge than the bound oxygen, it is more susceptible to attack by a proton
to form the hydroperoxy intermediate. The presence and the nature of the distal CuB,
which is on the same side of the porphyrin plane as the bound dioxygen, is also
expected to play a role in the geometry of the dioxygen-heme binding. On the other
hand, the transient species with the standard peroxy conformation is very reactive and,
therefore, short-lived. A proton transfer or the ligation of CuB cluster to the terminal
190
oxygen is necessary in order to trap this end-on binding structure. Otherwise, we
speculated that this intermediate will transform to a side-on conformation to equalize
the electronic configuration on two oxygen atoms. As iron porphyrin itself could not
distinguish two oxygen atoms, the protein local environment may be at the origin of
modifications of the electronic configurations of the oxygen atoms and therefore, the
dioxygen-heme binding geometry. For example, a model of mutant and wild-type
carbon monoxy cytochrome oxidase has suggested that three histidine residues,
Hi3284, -333, and -334 are ligated to the Cu]; center [29]. One of these residues may
serve as the proton donor or form a hydrogen bonding to the peroxy type dioxygen-
heme complex under certain conditions, especially low pH.
As it can be seen from Table 4.4 and 4.5, both the Soret and Q transitions are
mainly x-y polarized. Although Fe-O stretch is z-polarized in character, resonance
Raman was, however, able to detect this vibrational mode by exciting at Soret region.
The bent dioxygen-heme binding geometry may explain this experimental result. The
coupling of the oxygen p1: orbitals to the iron dxz and dyz orbitals mixes the porphyrin
x-y polarized n—m' transitions into the z-polarized transition of the Fe-O- bond, the
interaction of the On: (py) orbitals with the 1: orbitals on the porphyrin periphery may
also contribute to this phenomenon. The existence of Or: to porphyrin 1: transitions in
the oxy-heme dioxygen adduct supports this hypothesis [10-1 1]. In the peroxy case,
the weak coupling of the O-O n: to the Fe-O 1: is expected because the dioxygen anti-
bonding orbitals are occupied by an additional electron. Its Fe-O-O angle (1 108°) is
larger than that of the oxy adduct, which renders the 0 It to porphyrin 1: transitions
weaker [see Figure 10]. On the other hand, even weaker coupling of the O-O 1: to the
Fe-O it is expected in the protonated terminal oxygen forms, the hydroperoxy-l and
the hydroperoxy-2, because of the lack of the strong Or: to porphyrin 1: transitions in
these species. This may explain the observation that the detection of the Fe-O
l9l
stretching mode by vibrational methods is more difficult in the peroxy species than that
in oxy species.
Traditionally, the peroxy species is constructed as two negative charges
localized on the oxygen atoms. This is probably true in many inorganic peroxy
complexes because the ligands coordinated to the metal centers are incapable of
delocalizing excessive electrons. However, our calculations indicate that the
porphyrin resonance ring structure, especially its pyrrole nitrogen atoms, is a strong
contender with the bound oxygen atom for delocalizing the electron density in the
peroxy species. Our results show that there is no need to have a true peroxy species,
Fe(III)-O--O-, as an intermediate in the dioxygen reduction cycles. Since the
dissociation of the peroxy species is fatal to the physiological function of the enzyme,
this reaction would not be, therefore, a favorable process in Nature. The extra
electrons introduced during the dioxygen-enzyme reactions can be delocalized on the
porphyrin macrocycle to form a superoxo-like species. This superoxo-like
conformation has a stronger Fe-O bond and is, therefore, less dissociable than is the
standard peroxy form. A proton transfer reaction will convert this species into an even
more stable protonated form, hydroperoxy-1. As the iron is in a mixed valence
configuration, the Fe-O stretching mode is somewhat different from the standard
peroxy species. The Fe-O- bond in the superoxo-like peroxy is more polarized and
slightly longer than the Fe(II)-O- bond in the oxy species, but less polarized than the
conventional Fe(III)«O'- bond. Both the oxy-heme species and the superoxo-like
peroxy species are expected to have iron d to oxygen TI" backbounding. Since the
superoxo-like peroxy species have smaller perturbation from the oxy species than that
expected for the standard peroxy conformation, the vibrational mode of this species is
expected to be close to the oxy species, around 570 cm'l. Although there is no
resonance Raman experiment to confrnn this prediction, a likely explanation is that,
according to the kinetic scheme (Figure 1b), the possible overlap of the oxy and the
192
peroxy species at the same time domain and their similarity in vibrational properties
are expected to complicate the observation of the peroxy species in this region.
Another possibility is that the existence and the fast converting of oxy, peroxy,
hydroperoxy-l and -2 intermediates couple their charge-transfer bands so that the
transient absorption spectra near the Soret region are also mixtures of the above
species. Resonance Raman spectroscopy, therefore, can not effectively distinguish
them in this excitation region.
4.5 Conclusion
In this work, INDO calculations have been performed to study the peroxy-heme
complex and its protonated terminal oxygen forms, i.e., hydroperoxy-l and
hydroperoxy-2 [Figure 3]. The electron density distribution and the excited electronic
state properties as functions of several geometrical conformations and parameters,
have been analyzed in terms of the iron d, porphyrin 1r and oxygen 1t“ orbital
interactions. The analysis of the electron density distribution reveals that in the end-on
dioxygen geometry negative charge is mainly distributed on the terminal oxygen and
porphyrin macrocycle and iron is basically in an intermediate valence configuration.
The effect of the molecular surrounding was considered. In particular, the charge-
transfer transitions that account for the extra features to the red of the Q bands were
found for the bent end-on peroxy species. These CT transitions have calculated
oscillator strengths higher than those of the standard oxy-heme complexes [10]. Since
these CT bands lie about or lower than that of Q bands, excitation in the red region
should give appreciable photodissocation signal of the peroxy species. Time-resolved
resonance Raman results on oxygen reduction catalyzed by cytochrome oxidase also
indicated that this species is photodissociable [l 1]. In order to stabilize this
intermediate, a proton is required for addition to the terminal oxygen. As expected,
these low-lying CT bands are extinguished in the protonated peroxy forms. The end-
193
on dioxygen structure favors the accumulation of negative charge at the terminal
oxygen. Thus, a mechanism that involves heterogeneous cleavage of the oxygen-
oxygen bond is preferred, rather than the simple dissociation of the peroxy from the
heme moiety. The CT transitions with calculated oscillator strengths intermediate
between those calculated for the Q and Soret bands are found for all three model
intermediates. The character of the charge transfer is however, some what different in
each complex. In the peroxy forrn, oxygen 1: is mixed into the porphyrin a1u orbital
and CT transitions are predominately from the oxygen wt to the porphyrin 1:. In the
hydroperoxy-1 isomer, both iron d orbitals and imidazole ring orbitals are involved in
the CT to the porphyrin 1t orbitals. However, the majority of the CTs that carry
oscillator strength are the imidazole to porphyrin transitions, which are equal or higher
than the porphyrin Soret bands. There are few transitions between Q and Soret bands
that are signifith in intensity. In the hydroperoxy-2 intermediate, in addition to the
porphyrin rt-rr transitions, CTs are from iron d orbitals to the porphyrin macrocycle but
with an extensive coupling of the CT from oxygen to the porphyrin rt. Thus, the
excitation between the Q bands and Soret bands is most likely to be useful in
monitoring the protonated peroxy forms.
In conclusion, in spite of using INDO level calculations, the present results
give new information about the electronic and geometrical conformation of possible
peroxy intermediates in heme enzymes. Further experiments have been suggested in
order to test these computational predictions. If they could be experimentally
confirmed in the oxygen reaction with cytochrome oxidase, these calculations would
be powerful ways to probe the nature of oxygen binding site in the protein
environments.
4.6 Acknowledgment
194
We thank Prof. M. Zemer for kindly providing us his ZINDO programs and
Dr. Bendale for helpful discussion on implements of above computational package.
Support is acknowledged from grant GM 25480 (to G.T.B.) of the US. National
Institute of Health.
195
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CHAPTER 5
QUANTUM CHEMISTRY OF THE MOMENTUM DISTRIBUTIONS FOR A
PARTICLE IN A BOX‘
Summary
A particle in a one-dimensional box is a widely used classical model system for
the introductory of the quantum mechanism [1-8] and quantum chemistry [9-13]. In
most cases, however, only the position distributions of the particle is discussed. In this
work, we focus on the momentum distributions for systems in energy eigenstates of the
particle-in-a-box Hamiltonian. We obtain simple, explicit expressions for the
probability distributions of observing an arbitrary momentum p for a system in state
Th, and demonstrate the nonclassical features of the momentum distribution. For the
lowest energy eigenstate, with n=1, the momentum distribution peak at p=0, rather
than at the values ih/Za predicted from En. With an increase in quantum number
from n=1 to n=2, the distribution bifurcates, and the maxima for the nth level approach
i p" as it increases, thus illustrating the transition from quantal to classical behavior.
"' Results published on Journal of Chemical Education, 1995, 72, 149 (Co-authors
withY. Liang and Y. X. Dardenne).
200
201
5.1 Introduction
We consider a particle of mass in a one-dimensional box of length a described
by time-independent Schrodinger equation [1-9]:
d2 9100/de + 8p2mE/h2 \P(x) = o (0..(1))|2 (3)
where ¢,(p) is the momentum wave function for the state W..(P)- The momentum
wave function (1),,(p) is found by Fourier transformation of wn(x) [1,2, 10]
(PAP) = 579g) 8in(§;3-)CXP(-27ripx / h)dx (9)
Therefore, for the particle in a box, in the state V6.00.
a
then Vn(x) is not an eigenfunction of the momentum operator. Only if
wn(x) = exp(iimrx/ a) holds without spatial restriction is a momentum eigenfunction
obtained.
The corresponding probability densities to observe the momentum in the
infinitesimal range dp about p are
205
' 2h .
(EXP; )sz(£;—q)
1021(1)) = (p, __ 1),), (n even, n=2k)
21'
or
2h
(EXPL. ”052(2)?”
p2k—1(p) = (p2 _ p; )2 ('1 Odds n: 2k’l) (12)
Zk-l
where k=1, 2, 3,
the figure shows the momentum probability densities for the particle in the first
several energy eigenstates. The figure and eq 12 show clearly that there is a nonzero
probability density to obtain many values other than inh/ 2a from a given momentum
measurement.
A discussion of the momentum probability distribution can be found in the text
Quantum Mechanics by Cohen-Tannoudji, Diu and Laloe [1]; they provide a physical
interpretation in terms of "diffraction functions". However, they do not simplify to the
explicit forms of our eq 10 and 12, and we have not found these in any other texts.
The momentum distribution of a particle for different n values are plotted on
Figure 1. From eq 12, one can find the maxima and minima of the momentum
distribution. From dflpfldp: 0, the conditions for the maxima are
h
COKE - -2(—:;) (r1 even patip )
h 123. p’ ’ 2"
01’
2(BE
ramp“): , E” , (n odd, p¢ip2k_,) (13)
206
These equations can be solved numerically. The minima of the momentum
distributions occur when p( p) = 0, that is, when
sin(p:__7_r —)= 0 (n even,p¢:tpu)
01"
cos(— h): 0 (n odd, ptzthH) (14)
The separation between typical minima in the momentum distribution is obviously n-
independent and equal to h/a.
5.4 Remarks
1. The momentum distribution of a particle in a box gives a definite probability
for observing values of p other than those corresponding to the eigen energies of the
particle. Interestingly, in analogy with the nodes in the position distribution of the
particle (points in space where the particle has zero probability density), the
momentum distributions also have zeroes at special values of the momentum. In even
n states (n=2k), the particle cannot have the momentum values of p=lh/a, where lack,
whereas in odd n states (n=2k-l), momentum values of p=(21-l)h/2a (with (#1:)
cannot be observed. We can regard the momentum wave function as a standing wave
set up in the momentum space, but it is amplitude-modulated.
2. The momentum of the particle in an eigenstate averages to zero due to the
symmetry of momentum distribution; p( p) is an even function of p. Thus,
(p) = [pp.(p)dp= jut. (xx—dxw. (x)dx= o (15)
207
Figure 5.1 Momentum distribution of a particle in a box at various values of n.
A. ._
208
rant!)
A
A
m
M1
«3.213....
sofn
13(l86220
209
Table 1. The most probable momentum pm in different states.
n Pm(:th/2a)
1 0.000
2 1.675
3 2.790
4 3.845
5 4.950
10 9.985
210
the probability densities at zero momentum are
1921(0) = O
01'
8a
p”"(0) - (2k-1)’hzr2 (16)
In even n states, one cannot observe the particle with zero momentum (the probability
is zero), whereas in odd It states, one does observe zero momentum of the particle with
a certain probability. Surprisingly, in the state w,(x), with n=1, the most probable
momentum is zero, rather than ip, = h/ 2a. When It becomes larger (for odd n), the
probability of finding the particle with zero momentum decreases.
3. The uncertainty product 5p6x is bounded below, according to the
Heisenberg uncertainty principle. Its value is n-dependent for particle-in-a-box energy
eigenstates, as shown next. the average value of the position for the particle is
(x). = [w.(x)xw.(x)dx = (3)[xsin2(fi)dx=a/2 (17)
-co 0 0 a
as expected. The average value of x2 is
4n27r2
3
(it). = [won’t/Aw: =(§)§xsin’(—’1;3‘-)abc = (gum — 2) (18)
thus the root-mean-square deviation of the position for the particle is
211
a. = J. -: = <—,%,,>./<","’ -2>
The mean value of p2 is given by
< p: >= [p’p.