, ...\ . . w 3.. .x. k Lr~. fix l H . ‘ .31.... ring}: .vchg-v' THESIS (5 ’ will 3 1293 01417 llllllll\llllll‘llllllllll This is to certify that the dissertation entitled “6"“:th dmé 5% Made! CWW Yead'lmm Stu/d 4fmd'W4/C/VD/48/m’5 [35955; where}: ‘0; old-60. presented by flax/6r QH/WQ‘ has been accepted towards fulfillment PM. Equal Opportun Affirmative Action/ MSUisan try Institution of the requirements for degree in 6W" 51’? WW Majorproesrfso \IBRATIm 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 01m luv 0:... «on 301 ._OO ll W «2. 02m DO .92.! 0.9.503 e If 4 2.... >300 A Ally \ \ J o22.0 €232.00 0.1:...» >200 use“. 000 58.523005! every-2 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 W the de multichannel, cl monitoring inte “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 Referenca l. 10. 11. 12. 13. 14. 15. 16. R. K. Clayton, Photosynthesis: Physical Mechanisms and Chemical Patterns, Cambridge University Press, 1980. J. K. 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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. ' such as s recombin studied b' [14] and i In macrocyc mlegion}: macrocyc Occurs b, Which ca relations] Photoind 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 hflerodi Slound reduced not yet I Spectros The rest P001137] monitm extender In pumlhpr “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 ~M— NM— NM— :— / I IZ/ high 1 interpr anion and n separzo resolve 1.2 Ge h were kl the prc methyl: we re} W0] 413.1 n Lamp 596x 1 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. 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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 Assoc can seem can _ oou— coo— coo _ Z28 ammédom 81111103 “MO“ 038“ —1— 5:3 122 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 com. 80. A_-Eov aim 52:3— oow coo 8v _ L _ van Eon 0508 .1 _ 53> 8117 985 1701’ 81.8 srunog) 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. p.53 £6 5:3 002 cos 8» 125 0593836 06.: Boos 28 8.86 3 as. ---—————--—--P ZS? srunog 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 6233 0.92 omdém of o: of an. 03 ofl on. _ . _ . . . _ . _ p _ . b I own I So I one I con can. 55.92.... :2. 4 I Own 0593309.. .8: 6 8.52 05058.8 5.55899 55392.6 :2. e (I_ we) serouanborg [euorrerqr A 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 $233 33.5 endow o3 o: of on _ o3 ofl cm— . _ _ _ _ _ _ 332 0508:5me €2.83 aiseae on E 53.20 :me $ 80 I 2:. I can I com I cmw Iccm I oma fin coo— (1_ mo) sorouonbord [enoumqi A 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. l3l p-53 Ea 55% CON _. 002. com com oov — — — — W 30-0-9. : 28 2.82: s? stunoo 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. 9.58 gm 525 com— coo— cow ace oov 133 """""'"'” 728 momAuom Eon ocooa .1 _ 5.3 stunog 134 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 References 1. For review see G. T. Babcock and M. Wikstrom, Nature 1992, 35 6, 301. 2. W. E. Blumberg and J. Peisach, in Cytochrome Oxidase T. King eds, 1979, Elservier/North-Holland Biomedical Press, Amsterdam. p. 153. 3. C. A. Reed and J. T. Landrum, FEBS Lett. 1979, 106, 265. 4. A. Nanthakumar, et al, J. Am. Chem. Soc. 1993, 115, 8513. 5. K. D. Karlin, Science 1993, 261, 701. 6. K. D. Karlin, et al, J. Am. Chem. Soc. 1994, 116, 4753. 7. S. C. Lee and R. H. Holm, J. Am. Chem. Soc. 1993, 115, 5833. 8. C. Bremard, J. J. Girerd, P. Kowalewski, J. C. Merlin and S. Moreau, Applied Spectroscopy, 1993, 47, 1837. 9. P. Kowalewski, J. C. Merlin, C. Bremard and S. Moreau, J. Mol. Struct. 1988, I 75, 55. 10. E. P. Plowman, T. M. Loehr, C. K. Schauer and O. P. Anderson, Inorg. Chem, 1984, 23, 3553. 11. A. K. Shiemke, T. M. Loehr and J. Sanders-Loehr, J. Am. Chem. Soc. 1984, 106, 4951. 12. W. Li and G. Palmer, Biochem. 1993, 32, 1833. 13. E. Scheidt, S. C. Lee, R. H. Holm and G. T. Babcock, unpublished results. 14. J. M. Burke J. R. Kincaid and T. G. Spiro, J. Am. Chem. Soc. 1978, 100, 6077. 15. J. A. Hoffmann, Jr. and D. Bocian, J. Phys. Chem. 1985, 88, 1472. 16. C. Bremard, J. J. Girerd, P. Kowalewski, J. C. Merlin and S. Moreau, J. Raman Spectra. 1992, 23, 325. 17. C. K. Chang et 01., unpublished results. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 137 F. A. Cotton, Chemical Applications of Grou Theory 1990, J ohnWIley & Son. W. R. Scheidt, B. Cheng, M. K. Safo, F. Cukiemik, J. C. Marchon and P. G. Debrunner, J. Am. Chem. Soc. 1992, 114, 4420. A. B. Hoffman, D. M. Collins, V. W. Day, E. B. Fleischer T. S. Srivastava and J. L. Hoard, J. Am. Chem. Soc. 1972, 94, 3620. S. H. Straus, M. J. Pawlik, J. Skowyra, J. R. Kennedy, 0. P. Anderson, K. Spartanlian and J. L. Dye, Inorg. Chem. 1987, 26. 724. K. L. Lay, J. W. Buchler, J. E. Kenny, W. R. Scheidt, Inorg. Chim. Acta 1986, I23, 91. P. N. Swepston, J. A. Ibers,Acta Ctystallogr., Sect. C 1985, C41, 671. T. J. Bartczak, L. Latos-Grazynski, A. Wyslouch, Inorg. Chim. Acta 1990, 30. 711. ' J. T. Landrum, D. Grimmett, K. J. Haller W. R. Scheidt and C. A. Reed, J. Am. Chem. Soc. 1981103, 2640. J. P. Fillers, K. G. Ravichandran, I. Abdalmuhdi, A. Tulinsky and C. K. Chang, J. Am. Chem. Soc. 1986, 108, 417. T. Ogura S. Takahashi, S. Hirota, K. Shinzawa—Itoh, S. Yoshikawa, E. H. Appleman and T. Kitagawa J. Am.Chem. Soc. 1993, 115, 8527. C. Varotsis, Y. Zhang, B. H. Appleman and G. T. Babcock, Proc. Natl. Acad. Sci. USA, 1993, 90. 237. 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 unloaded Mum Em ..o .2 u o a; 7!... i658 5.9....— u. ..o .2 .8. a... 1!. 13.56 9...; .N _ ... .2 _. u e... qr... ..o .2 a. a... 33:; a... . 3.... .2 .3 u... =/.o t .3 ...u . ”ignite-EL 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 1.2 - \O O\O V V -0.4 —I -0.6 «- terminal 0 ' ' I l I I -0.8 d —l.0 -I \. dioxygen \. (bond 0 + terminal 0) ' e “1'2 T r I I I I 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 Nor Airsualul ”or o._1 N._1 \‘\ O).LC) ( n<— A. .Eov 5:262". ooom oooo _ ooow _ oooom 80mm OOOOM \“ \\\\ \ >XOMm—m \\ ‘\\\ \\h Ng&\ \ \ \‘\ \ \\\ \\ 9‘.\ \ R \&“\V\\‘. \ . . . up“... 153 Figure 4.5 Computed electronic spectrum of the standard peroxy species: Fe-O =1.9 A0, o-o = 1.45 A°. 154 nguqurodmno+mos mos A 788 >925 eoenu eoocm econ. ease. pl _ I. _ od 3 O M m o m I 3 a e A. r ...e I e... r 2 r 3 a £92. 2 .5 "Lb use. 2538 12 .2 a; u o-o ...< 8.. u can. .832: aas... e323 e 2 £3qu 155 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 A .-ES Amen—em cocom scan _ 33.x: _ — p A 53¢. o u so: 8 a 2.5 "'8 REES—Sugfiuho .2 a: u 0.6 ..< in 9o". 5908:. BEE». 05 e. 2682:: 05 Sec 3.0.2.5 52. we: :28.— a 53.2. Eaves..." 2: ..o 386$ 5 ..-Axoeoqea»: s O J a 1 :3 1 N6 1 ed I cd 1 ad I N.— F A... Wall 176 Figure 4.7 Computed electronic spectrum of the hydroperoxy-2 species: Fe-O =1.9 A0, 0-0 = 1.45 A°. 177 2.8m mos ooomN A 788 amen—em cocoa 8am _ A58— coon _ i _ _ od 0 1 2. I ...o I ed I ad I c.— v o. v "Lb r. N.— nSu+uEEoQSenB . o< an... .1. Ono .o< a; .1. Ohm 866% 38.3 2353 65 we Saba I v.— EEEB. 65 2 v0.6.3 :63 «5. :36:— a .~->xo§_e§£ 5115191111 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 /0 1.0 - O—~o——O -O.2 -1 bond 0 «0.4 -4 -0.6 —1 terminal 0 -0.8 - -1.0 - . dioxygen \I\ (bond 0 + terminal 0) O\. .12 .1 \O . '1'4 t I t T I l T I I I 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 Arlsualul N. A788 385 $26QO 58.3 be .253 199323... 182 Figure 4.10 The 3-D view of the computed electronic spectra of the hydroperoxy-2 species at different O-O distances. -A_.._.._- kw. 183 Kilsuaiul N._ .. m: .. A753 .335 $28306»: Ivy'.."vv"r_..... . ... . . .. ‘ W-mu . 19105 184 Figure 4.11 The 3-D view of the computed electronic spectra of the hydroperoxy-1 species at different Fe-O distances. 185 Kirsuoiul Nd 1 so L ed 1 ad 1 A: 1 N._ 1 A753 3.2—m 88. 88a \ \ \ \ 0“ \ \ \ \S\ \ \t‘.‘ \ \ m \\\ ‘\t\ \\ \ \ m \‘\\ \\.l§ \ \\ m_\\‘\ \ \.\ \\\ ‘ ‘ ‘\\\ \‘\ comas 358.8 65 2 26.32:: 2: 86¢ 3.35: coon me: :2er m .AAxoeoQ .Em 2: go .668. any 7.0.9383: 19103 186 Figure 4.12 The variation of the empirical paraterized INDO-SCF energies as a function of the Fe-O torsion angle. 187 38-x 2: 83:8 ca "0.0 5; .32on one—q >8" 5 5.553. ca— co— oe— c~— oc_ ¢w co ov o~ — — L — b — — _ p . AV: 0 r 3 f: . \ /\ //\ r.n4 [Afia (9015“?) £81903 188 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. 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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.