Electronic and Vibronic Contributions to the Band Splitting in Optical

7064

J. Phys. Chem. B 2001, 105, 7064-7073

Electronic and Vibronic Contributions to the Band Splitting in Optical Spectra of Heme Proteins Reinhard Schweitzer-Stenner* and Dan Bigman Department of Chemistry, UniVersity of Puerto Rico, Rı´o Piedras Campus, San Juan, Puerto Rico PR00931 ReceiVed: February 22, 2001; In Final Form: May 3, 2001

We have employed Rayleigh-Schro¨dinger perturbation theory to obtain a simple quantum mechanical model to simulate the influence of asymmetric distortions on the optical spectra of metalporphyrins. The model is based on Gouterman’s classical four orbital model and considers group theoretical restriction for the interactions between different electronic states. In heme proteins, asymmetric distortions of the porphyrin macrocycle are induced by axial ligands, asymmetric peripheral substituents, and the anisotropic protein environment. They give rise to electronic and vibronic perturbations, which cause additional mixing between vibronic states and, for B1g-type perturbations, also, a split of the Q and B states, which are 2-fold degenerated in symmetric porphyrins exhibiting a D4h symmetry. To compare our calculations with experimentally observed splits of the Q band in the spectra of various ferrocytochrome c (Manas et al. J. Phys. Chem. B. 1999, 103, 6344) we estimated vibronic matrix elements from resonance Raman data of horse heart cytochrome c and some metalloporphyrins in solution. We investigated different combinations of electronic and vibronic perturbations to show evidence that both contribute equally to the observed Q-band split. Moreover, we found that vibronic perturbations give rise to different Q- and B-band splitting, in agreement with what was experimentally observed for asymmetrically distorted hemes and porphyrins. Our theoretical insights do not support the notion that a uniform electric field causes a splitting of bands in the optical spectrum of porphyrins.

Introduction The function of heme proteins is to a significant extent governed by interactions between the prosthetic heme groups and various amino acid residues of the heme cavity.1 The latter constitutes an asymmetric environment by some covalent and multiple noncovalent interactions with the chromophore.2 Numerous studies have been performed to explore the influence of the proximal and distal histidine on the electronic structure and the spin state of the central iron atom,3 the orientation of ligands, and the association and dissociation rate constants of ligand binding.4-6 The proximal histidine was thereby found to have a particularly strong impact on the latter, because it provides a strong axial crystal field for the central metal atom7,8 and gives rise to asymmetric distortions of heme group via noncovalent interactions between its Cδ and C atoms with the pyrrole nitrogens.5,9,10 With respect to the influence of other amino acid residues in the heme cavity, our present knowledge is still limited. Gellin et al. showed that in human hemoglobin Val FG5 interacts with one of the heme’s vinyl groups and that this interaction transduces conformational changes from the protein to the heme group.9 More recently, Jentzen et al.11,12 have analyzed the X-ray structure of the heme groups of numerous proteins to identify and classify their out-of-plane distortions. They found that the heme c groups of various cytochrome c molecules exhibit significant ruffling and also some saddling and waving distortions. These distortions are mostly conserved in cytochromes for which the amino acids between the cysteine linkages to the heme group are homologous, whereas differences were obtained for segments with * To whom correspondence [email protected].

should

be

addressed.

E-mail:

different numbers or types of residues.12 This observation provides very strong evidence that the small segment between the cysteine linkages causes most of the nonplanar distortions. Information about symmetry lowering perturbations of the heme group in ferrocytochrome c were also derived from optical and resonance Raman spectroscopy. Already forty years ago, a magnetic dichroism study by Sutherland and Klein13 had revealed a Q-band splitting of 120 cm-1 for horse heart (hh) ferrocytochrome c. Shortly afterward, Collins et al. observed significant dispersions of the depolarization ratio of various resonance Raman lines of this ferrocytochrome c species,14 which they interpreted as indicative to a split between the Qx and Qy transitions of the heme group due to asymmetric electronic perturbations.15 A similar rational, though more theoretically substantiated, was invoked by Zgierski and Pawlikowski.16 Friedman et al. observed a Q-band splitting in the absorption bands and in the resonance excitation profiles of some Raman lines of cytochrome c and b5.17 Schweitzer-Stenner and Dreybrodt,18 Zgierski,19 Bobinger et al.,20 and Schweitzer-Stenner et al.21 analyzed the depolarization ratio dispersion and the resonance excitation profiles of various hh cytochrome c resonance Raman lines to obtain electronic as well as vibronic perturbations which they interpreted as resulting from B1g-, B2g-, and A2g-type in-plane distortions of the heme group. Kubitscheck et al.22 measured the depolarization ratio dispersion of the oxidation marker band ν4 of hh ferrocytochrome at various pH and found that the heme structure does not change between pH 4.5 and 10.5.6 A comparison of Raman data from various heme proteins revealed that the heme group of ferrocytochrome c is much more affected by symmetry lowering perturbations than the active sites of hemoglobin and myoglobin, in accordance with findings by Jentzen et al.12

10.1021/jp010703i CCC: $20.00 © 2001 American Chemical Society Published on Web 06/27/2001

Optical Spectra of Heme Proteins More recently, Vanderkooi and co-workers undertook another attempt to explore the symmetry lowering of heme groups in ferrocytochrome c.23-27 They measured the Q-band spectrum of horse heart (hh), beef, porcine, tuna (th), chicken, and yeast (y) cytochrome at cryogenic temperature, which allows a better separation of overlapping bands because of the absence of thermal broadening. Thus, they obtained Q-band splitting between 80 (y) and 119 cm-1 (hh)24 with an always more intense band at lower energies. The authors performed various theoretical calculations to distinguish between different contributions to the observed band splitting. The results led them to distinguish between the influence of structural distortions of the heme (such as ruffling and saddling) and electrostatic contributions. With respect to the latter they first invoked a Stark effect, i.e., the influence of the rather strong internal electric field in the cavity. This electric field is capable of interacting with the macrocycles transition dipole moments to yield a mixing between ground state and excited states. Results from the performed calculations suggest that the thus induced splitting is small for the Q band but significant for the B band.24 In the second step, the authors considered the quadrupole moment of a charge distribution constituted by the (dipolar) axial ligands (Met 80 and His 18) and the deprotonated propionate substituents. They showed that it causes a perturbation which contains the symmetry representations A1g and B1g of the D4h point group, so that it can mix the excited states Qx, Qy, Bx, and By to yield significant splitting of the Q state.24 It should be emphasized that cytochrome c is not the only heme protein that exhibits a splitting of the optical bands. A series of optical absorption and fluorescence studies by Fidy and co-workers have revealed significant Q-band splitting for Mg-meso-porphyrins incorporated into the matrix of the isoenzyme C of horseradish peroxidase,28 which were found to increase upon binding of naphthohydroxamic acid.29 Ko¨hler et al.30 obtained similar results by combining Stark spectroscopy and spectral hole burning. They also showed that the splitting is absent in the spectra of Mg-meso-porphyrins in an ethanol/ glycerol glass. This indicates that it is caused by the protein environment and not by the peripheral substituents. The authors explained their findings in terms of an electric field, which eliminates the inversion symmetry of the heme group. Out-ofplane distortions were also invoked as a possible cause for band splitting,29,30 but it was not made clear how this could be related to the electric field of the heme pocket. More recently, Shibata and Kushida used the spectral hole burning technique to obtain a particularly large Q-band splitting for Zn-protoporphyrin and Zn-meso-porphyrin substituted in myoglobin and cytochrome c, respectively.31 They also attributed the splitting to an external electric field. Huge Q-band splits were recently obtained in the optical spectra of a myoglobin intermediate state exhibiting a water ligand bound to a ferrous iron32 and of ferrous nicotinate horse myoglobin.33 Finally, indirect evidence was provided that the B band of cyanometmyoglobin exhibits a splitting of approximately 130 cm-1.34 Doubtless all of these studies are important for developing a detailed understanding of how symmetry lowering perturbations affect the electronic properties of the heme group. We feel, however, that a comprehensive theoretical approach, which would provide the framework for taking into account all possible contributions to the observed band splitting from fundamental principles, is still outstanding. The present study is aimed at providing a starting point for a more thorough theoretical treatment of heme perturbations. The paper is organized as

J. Phys. Chem. B, Vol. 105, No. 29, 2001 7065 follows. First, we will utilize Gouterman’s four orbital model35 to demonstrate the influence of pure electronic perturbations on the optical spectrum. The possible influence of electronic fields is discussed in this context. In the second part, we calculate the influence of vibronic perturbations on the optical spectrum. We show that their contributions are significant and that they cannot be neglected in the analysis of band splitting phenomena. Electronic Perturbations General Theory. The basic theory for the influence of porphyrin distortions on the electronic structure of porphyrins was outlined in other papers.35-37 In the following, we present it from a somewhat more general point of view and discuss the influence of different types of distortions on the optical spectrum in more detail than it was done in these studies. We assume that a metalporphyrin (heme) in a D4h symmetry is subjected to an external potential field. The electronic Hamiltonian of the system is then written as

H ˆ el ) H ˆ el,0 + V

(1)

The eigenfunctions corresponding to the Hamiltonian H ˆ el,0 can be attributed to the 50:50 states, i.e., the singlet ground state |g〉 and the excited states |Q0x,y 〉 and |B0x,y 〉. The latter are 2-fold degenerate and exhibit Eu symmetry.35 Thus, electronic interactions between the two excited states require that the symmetry representation of the potential V contains contributions from A1g, B1g, B2g, or A2g symmetry. For a coupling between the ground state and the excited state, the perturbing potential must have Eu symmetry. That leads us to the matrix representation of H ˆ el:

[

H ˆ el ) Eg

Eu V gQ x

Eu V gQ y

Eu 1g 2g V gQ EQ0 + V BQQ V BQQ x Eu 2g V gQ V BQQ y

Eu V gB x

Eu V gB y

1g 1g 2g 2g V AQB + V BQB V BQB + V AQB

1g 2g 2g 1g 1g EQ0 - V BQQ V BQB - V AQB V AQB - V BQB

Eu B1g B2g 1g 1g 2g 2g E V gB V AQB + V BQB V BQB - V AQB B0 + V BB V BB x Eu 2g 2g 1g 1g V 2g V gB V BQB + V AQB V AQB - V BQB BB y

EB0 - V BBB1g

]

(2)

This equation represents the electronic Hamiltonian taking into account contributions from electronic perturbations of the porphyrin macrocycle. Eg, EQ0, and EB0 are the energies of the unperturbed Q and B states. The electronic interaction matrix elements V Γlm are written as V Γlm ) 〈l|VΓ|m〉 where l and m label the excited states Q and B. Γ is the symmetry representation of the potential in the D4h point group. The Hamiltonian is expressed in the basis formed by |g〉, |Q0x 〉, |Q0y 〉, |B0x 〉, and |B0y 〉. One can generally assume that the matrix elements V ΓQB of the asymmetric perturbations B1g, B2g, and A2g are small compared with the respective energy difference. This is not 1g . We therefore followed Gouternecessarily the case for V AQB 1g man35 by diagonalizing the matrix above with respect to V AQB to obtain the so-called unmixed electronic states. Subsequently, we applied Rayleigh-Schro¨dinger time-independent perturbation theory to account for the remaining nondiagonal elements of H ˆ el. Thus, we obtained the following expressions for the

7066 J. Phys. Chem. B, Vol. 105, No. 29, 2001

Schweitzer-Stenner and Bigman

ground-state energy and the energy differences between Qx′ and Qy′ (Bx′ and By′) of the perturbed molecule:

Eg′ ) Eg +

Eu 2 (V gQ ) x

E g - EQ

+

Eu 2 (V gQ ) y

Eg - EQ

+

Eu 2 (V gB ) x

Eg - E B

+

Eu 2 (V gB ) y

Eg - E B

1g 1g ∆EQ ) EQx′ - EQy′ ) 2V BQQ - 2 sin (2ν)V BQB 1g ∆EB ) EBx′ - EBy′ ) 2V BBB1g + 2 sin (2ν)V BQB

(3)

for the eigenenergies. Eg, EQ, and EB are the eigenenergies of the unmixed states of the unperturbed macrocycle. The degree of unmixing is given by the parameter ν which is determined 1g 37 by the matrix element V AQB . We have neglected the matrix B2g B2g B2g elements V QQ, V BB, and V QB in eq 3 for the following reason. As we will show below, these perturbation energies are proportional to distortions along the same nuclear coordinates that also determine vibronic coupling and thus resonance Raman cross sections. Various Raman data suggest, however, that vibronic coupling of B2g-type modes is generally weak. The consideration would unnecessarily complicated our analysis at this point without providing any additional insights. For the transition dipole moments of the perturbed molecule we obtained:

Rx′Q ) RQx +

1g 2g V AQB V BQB RBx + RB E Q - EB EQ - E B y

Ry′Q ) RQy -

1g 2g V BQB V AQB RBy RB EQ - EB E Q - EB x 0

(4)

y

that the entire dipole strength of the Q band in the unperturbed state results from unmixing of the 50:50 states.35,38 Resonance Raman studies, however, have provided evidence that there is a small Q-band dipole moment even for the 50:50 states,39 which we neglect in this study. Structural Interpretation of Heme Perturbations. Thus far, we have not discussed the possible origin of asymmetric perturbations. In principle, the heme cavity and the peripheral substituents provide a highly anisotropic environment, which can induce planar and nonplanar distortions either directly by covalent and noncovalent bonding or indirectly by its electric field. It is physically incorrect to distinguish between heme distortions and electric fields as different possible reasons for the obtained splitting of optical bands, as it has been done in the papers of Manas et al.24,25 and Rasnik et al.27 On the contrary, every perturbational potential is capable of inducing distortions in the ground as well as in the excited states.40 To illustrate the relationship between distortion and perturbation we first remind the reader on the concept of static normal coordinate deformation (SNCD) introduced by Shelnutt and co-workers.11 A given distortion ∆ of a molecule can therefore be described by:

∑Γ ∆Γ ) ∑Γ ∑j δqjΓj

∆Γg )

j

∂VΓ ∂qΓj

g

(6)

(Ωgj )2

where ∂VΓ/∂qΓj is a vibronic coupling operator, which describes potential changes caused by the vibration of the jth normal mode qΓj exhibiting the D4h symmetry Γ. Apparently, this effect is allowed for all symmetry representations of the point group, because the vibronic coupling operator always transforms like A1g or contains this representation, irrespective of the choice of Γ. This implies that every perturbing potential induces corresponding structural changes into the ground state, which can be classified in terms of SNCDs as described by eq 5.

V )

For the sake of simplicity, we assume RQx ) - sin VRBx , i.e.,

∆)

〈∑ | | 〉 g

Γ

1g 2g V BQB V AQB RQy + RQ EB - EQ E B - EQ x

y

A perturbation potential VΓ gives rise to a distortion ∆Γ of the ground state, which is induced via vibronic intrastate vibronic coupling:36

To interpret the perturbation potentials in structural terms we write them as a Taylor expansion of the Hamiltonian of the unperturbed system with respect to SNCDs. This yields

1g 2g V BQB V AQB Rx′B ) RBx + RQx RQ EB - EQ E B - EQ y

Ry′B ) RBy -

where δqjΓj denotes the amplitude of the SNCD along the jth normal coordinate exhibiting the symmetry Γ in the D4h point group. As shown in recent analyses of isolated porphyrins and heme groups, ∆ is generally dominated by distortions along the normal coordinates of the lowest wavenumber modes of the respective symmetry distortion.11

(5)

∑i

∂H ˆ el,0 ∂qΓi i

δqjΓi i

+

∑i ∑j

∂2H ˆ el,0 ∂qΓi i∂qΓj j

δqjΓi iδqjΓj j

(7)

Mixing of the two Eu type states requires that Γi of the first term is A1g, B1g, B2g, and B2g. Hence, it accounts for in-plane distortions of the heme macrocycle. In this case, the symmetry of the operator ∂H ˆ el,0/∂qΓi i is that of the distortion, i.e., Γi.36 The situation is different for the second-order term in eq 7, which accounts for out-of-plane distortions A1u (propellering), A2u (doming), B1u (ruffling), and B2u (saddling). The symmetry of the coupling operator ∂2Hel,0/∂qΓi i∂qΓj j is given by the product Γi X Γj. As shown by Jentzen et al.,11 the most prominent nonplanar distortions in ferrocytochrome c are ruffling (∆B1u ) 1 Å) and to a minor extent saddling (∆B2u ) -0.23 Å) and waving (∆Ex ) 0.122 Å, ∆Ey ) 0.161 Å). The latter is related to Eg symmetry and does therefore not contribute to electronic mixing of Q and B. The combination of saddling and ruffling yields a product symmetry of B1u X B2u ) A2g. Thus, their contribution to electronic perturbation is reflected by matrix elements V QA2gxBy which, as outlined above, cannot cause any splitting of optical bands by itself. With respect to out-of-plane distortions this would require an additional contribution from propellering (A1u) and doming (A2u), which combined with saddling (B2u) and ruffling (B1u) would respectively yield perturbations of B2g symmetry. These, however, are certainly very small because propellering and doming are negligible in ferrocytochrome c. The same argument holds for a B1g-type potential, which would arise, from the combination of propellering and ruffling or doming and saddling. We can therefore conclude that the out-of-plane distortions give rise only to

Optical Spectra of Heme Proteins potentials of A2g and of course also of A1g symmetry (B1u X B1u), so that they alone do not cause any substantial splitting.41 Although various Raman studies provide strong evidence for the occurrence of in-plane distortions in heme proteins,14-16,18-20 they are mostly neglected. This is particularly unjustified for ferrocytochrome c. As shown by Jentzen et al., most of the heme groups in ferrocytochromes exhibit significant in-plane distortions. For hh ferrocytochrome c, they obtained ∆B1g ) 0.115 Å, ∆B2g ) 0.144 Å, and ∆A2g ) 0.063 Å.11 On a first view, this looks small compared with the above values for ruffling and saddling. One has to take into account, however, that in-plane distortions contribute to the perturbation potential in first order. The corresponding matrix elements are an order of magnitude larger than the second-order terms reflecting the out-of-plane distortions.36,42 Therefore, all of the above in-plane distortions can be expected to contribute significantly to VΓ. Thus, we have B1g distortions as the sole electronic contribution to the observed splitting. As shown by Manas et al.,24 one possible source for a B1gtype perturbation is the quadrupole field constituted by the dipole moments of the proximal and distal histidine and the negative charges of the heme’s propionic acid substituents. The strength of this perturbation is linear related to the gradient of the electric field in the heme cavity. The theoretical calculations of the authors suggest that this perturbation may be responsible for a significant part of the observed splitting. We agree with this notion. Ko¨hler et al. employed30 spectral hole-burning experiments to compare the Q bands of Mg-meso-porphyrin in an ethanolglycerol glass and in the horseradish peroxidase matrix and found that the splitting requires the protein environment. This is not surprising. The most effective symmetry lowering of this porphyrin can be expected to result from the propionic acids. Group theoretical considerations suggest that they would be mostly of B2g symmetry.10 As we have argued above the corresponding electronic perturbation energies are weak. Interactions between Excited States. Equation 3 shows that B1g-type perturbations can split the Q and B states. A2g perturbations do not contribute to band splitting in the absence of B2g-type perturbations. The amount of splitting is always identical for both excited states, because the four orbital model 1g ) -V BBB1g. predicts that V BQQ The dipole moments (eq 4) are also affected by asymmetric perturbations. If B1g-type perturbations are present, intrastate 1g ,V BBB1g) causes splitting into two bands of the coupling (V BQQ 1g same intensity, whereas interstate coupling (V BQB ) causes a splitting and an intensity distribution between the split Q bands, i.e., one gets more intensity at the expense of the other one.19-21 2g V AQB can further increase or decrease this asymmetry. This intensity redistribution has been obtained for various cytochromes.23,24 Interaction between the Heme and a Uniform Electric Field. Manas et al.24 also investigated the direct influence of the electric field in the cavity. They showed that a (quadratic) Stark effect may occur in that a uniform electric field B E interacts with induced transition dipole moments. The strength of this interaction depends on the corresponding transition dipole moment. As a consequence, the Stark effect were predicted to cause a much larger splitting for the B than for the Q band, despite the larger energy difference between B and ground

J. Phys. Chem. B, Vol. 105, No. 29, 2001 7067 state.25 Moreover, the authors calculated a large blueshift of the optical spectrum. In view of the fact that a significant electric field is indeed present in the heme cavity of heme proteins29,30,43 this type of interaction deserves to be evaluated more thoroughly. As argued above a coupling between ground and excited state requires a perturbing potential of Eu symmetry. Equation 4 suggests that it may change the overall dipole strength of the transition into the Q and B states, depending on the values of the parameters. The potential created by the interaction of a transition dipole with an electric field is written as

V ) -µ bFB E

(8)

The entire potential must transform like A1g, but the mixing would be because of the transition dipole moment b µF.

bF|l〉E B V Eglu ) 〈g|µ

(9)

E transforms indeed like Eu (l labels where b µF (F ) x and y) and B again the excited heme states). As a consequence of this symmetry restriction, the uniform electric field cannot cause any band splitting, because by|QByy 〉 and Ex ) Ey. However, if the angle 〈g|µ bx|QBxx 〉 ) 〈g|µ between B E and the molecular coordinate system of the heme macrocycle (x and y along the NFeN lines) is different from 45 and 315°, Ex differs from Ey. In this case, one can decompose the electric field into two contributions, i.e.

B E)

() ( ) () (

E′ E(cos θ - sin θ) E E + x ) + E E 0 0

)

(10)

The first part of eq 10 transforms like the representation Eu in the coordinate system of the unperturbed molecule and appears Eu in the matrix elements V gQ ,V EgBu x,y. The second part transform x,y like a rotation around the z axes perpendicular to the heme plane and thus such as the representation A2g. This part of the electric 2g , but as shown above, this field can therefore contribute to V AQB type of perturbation does not cause any band splitting by itself. If, however, the latter is present because of other perturbations, it follows from eq 4 that the A2g component of the electric field can indeed change the dipole moment ratio RQx /RBy and, thus, the intensity ratio of Qx0 and Qy0. We agree with the notion of Manas et al.24 saying that the Stark effect may cause a blue shift of the optical spectrum. If one assumes an electric field of 13 MV/cm, one obtains Eu Eu Eu ) V gQ ) 237 cm-1 and V EgBu x ) V gB ) 1184 cm-1. From V gQ x y y this it follows that the Q and B bands are upshifted by approximately 125 and 180 cm-1, respectively. This implies that the Stark effect also increases the difference between Q and B band. Vibronic Perturbations In a first step, we use time-independent perturbation theory to expand the total vibronic wave function in the basis of crude Born-Oppenheimer states:37

|l,V〉 ) |l〉|V〉 +

cΓlmi (qi)

∑ ∑ Γi i E + Ω - E l

where

l

|m〉|V + 1〉 m

(11)


∂Hel,0 cΓlmi ) 〈l| Γ |m〉〈1|qΓi i|0〉 ∂qi i


(12)

contains two matrix elements. 〈l|∂H ˆ el,0/∂qΓi i|m〉 describes the vibronic coupling between two electronic states |l〉 and |m〉 because of the ith normal mode qΓi i exhibiting the symmetry Γi in the point group of the unperturbed molecule and 〈1|qΓi i|0〉 is the vibrational transition matrix element. |V〉 and |V + 1〉 denote the pure vibrational states of the molecule. If one identifies |l〉 and |m〉 with |Q0x 〉, |Q0y 〉, |B0x 〉, and |B0y 〉, group theory dictates that Γi ) A1g, B1g, B2g, and A2g. In the presence of asymmetric perturbations Γ, the vibronic coupling matrix elements have to be rewritten as follows:40

cΓlm

∂Hel,0 ) 〈l| + ∂qΓi i

∑ Γ j

∂VΓj ∂qΓi i

|m〉〈1|qΓi i|0〉

(13)

The first term in eq 13 transforms like Γi, and the second one transforms like the product representation Γi X Γj. In what follows, we confine ourselves on perturbations of the symmetry type B1g, because they are likely to provide the strongest contribution to band splitting. Second, we consider only the intrastate coupling (cΓQQ and cΓBB) contributions of modes in the low frequency region and additionally the interstate HerzbergTeller coupling (cΓQB) of the ν19 mode, which is of A2g symmetry and has been frequently shown to dominate the QV band of the optical spectrum.36,37 Three types of modes were considered the Raman bands of which appear in the low-frequency part of the Raman spectra of heme proteins,46 i.e., A1g-type modes, substituent modes, and Eu modes. For A1g modes, the influence of B1g perturbations is reflected by vibronic matrix elements 1g cQA1gx,yXB Qx,y

)

1g cAQQ

(

2g 2g (V19) + cBQB (V19))2 (cAQB

EQx′ - EBy′ - ΩV19

-

∆EB,0 ≡ EBx′,0 - EBy′,0 ) EBx′ - EBy′ 2g 2g (V19) + cBQB (V19))2 (-cAQB

EBx′ - EQy′ - ΩV19

-

(14)

The substituent modes gain their intensity from mixing with macrocycle modes. Depolarization ratios of their resonance Raman bands suggest that they can be approximately considered as A1g modes even in the presence of asymmetric perturbations.44 Eu modes do not interact between the excited states in D4h. In the presence of an Eu perturbation VEu, however, the operator in second-order term of eq 13 transforms like the product Eu X Eu ) A1g x B1g x B2g x A2g. Moreover, the Eu mode splits into two components, one which is assignable to the combination A1g x B1g and the other one to B2g x A2g.47 As shown below, polarized bands assignable to A1g x B1g appear in the lowfrequency Raman spectra of ferrocytochrome c with significant intensity. They can be treated like A1g modes in the presence of B1g perturbations so that their vibronic coupling is described by eq 14. In accordance with results from resonance Raman data,37 we assume that vibronic coupling is in the weak coupling limit so that only the two lowest vibronic states of each oscillator (El,Vi)0,1, νi: vibrational quantum number of the ith normal mode) have to be taken into consideration for all excited states. Thus, we obtain the following splitting between the vibronic energies of the respective lowest energy states El,0 by secondorder perturbation theory:

+

Ωi

2g 2g (V19) + cBQB (V19))2 (-cAQB

EQy′ - EBx′ - ΩV19

∑i

4cABB1g(Vi)cBBB1g(Vi)

+

Ωi

2g 2g (V19) + cBQB (V19))2 (cAQB

(15)

EBy′ - EQx′ - ΩV19

Equation 15 accounts for the vibronic mixing between the vibrational ground state and the first excited vibrational states of the excited electronic states. The first terms denote the energies of the perturbed electronic state as given by eq 3. They also appear in the denominators. The second terms are sums over the intrastate vibronic coupling contributions of the considered low-frequency modes. For modes of A1g symmetry in D4h, a B1g type perturbations gives rise to additional vibronic perturbation matrix elements the corresponding coupling operator of which transforms like B1g (eq 13). They also appear in the second terms in eq 15 and affect the split between the Qx(Bx) and Qy(By) energies. As outlined above, the symmetric component of Eu modes is also associated with A1g- and B1g-type coupling so that they can also contribute to band splitting. The third accounts for interstate Herzberg Teller coupling between Q and B states by the A2g-type mode ν19. The matrix elements 2g in these terms also result from B1g perturbation (eq 13). cBQB The corresponding splits of the first vibrational levels of the excited states are written as

∆EQ,1i ≡ EQx′,1i - EQy′,1i ) EQx′ - EQy′ -

1g cBQQ

A1g B1g 1g cBA1gx,yXB Bx,y ) cBB ( cBB

∑i

∆EQ,0 ≡ EQx′,0 - EQy′,0 ) EQx′ - EQy′ -

1g 1g 4cAQQ (Vi)cBQQ (Vi)

1g 1g 4cAQQ (Vi)cBQQ (Vi) Ωi

∆EQ,1ν19 ≡ EQx′,1ν19 - EQy′,1ν19 ) 2g 2g (V19) + cAQB (V19))2 × EQx′ - EQy′ + (cBQB

[

]

1 1 + EQx′ - EBy′ + ΩV19 EQx′ - EBy′ - ΩV19 2g 2g (cBQB (V19) - cAQB (V19))2 × 1 1 + EQy′ - EBx′ + ΩV19 EQy′ - EBx′ - ΩV19

[

]

∆EB,1i ≡ EBx′,1i - EBy′,1i ) EBx′ - EBy′ -

4cABB1g(Vi)cBBB1g(Vi) Ωi

∆EB,1ν19 ≡ EBx′,1ν19 - EBy′,1ν19 )

[

2g 2g EBx′ - EBy′ + (cBQB (V19) - cAQB (V19))2 ×

]

1 1 + EBx′ + ΩV19 - EQy′ EBx′ - EQy′ - ΩV19

[

2g (V19) (cBQB

+

2g cAQB (V19))2

×

]

1 1 + (16) EBy′ + ΩV19 - EQx′ EBy′ - EQx′ - ΩV19

These equations account for vibronic coupling of the vibrational states |Vi ) 1〉 with |Vi ) 0〉 and |Vi ) 2〉. Mixing between

Optical Spectra of Heme Proteins

J. Phys. Chem. B, Vol. 105, No. 29, 2001 7069

vibrational levels of different modes can be described by higher order perturbation theory, but this can be neglected for the weak coupling limit.36 Finally, we have to calculate the dipole moments for the transitions into the excited states. In the case of weak vibronic coupling, the transitions into the vibrational ground states remain unaffected. For the transitions into the first excited vibrational states, one obtains Q Rx′,1 ) i

Q Rx′,1 ν19

1g 1g cAQQ (Vi) + cBQQ (Vi) Q Rx′ Ωi

Q Ry′,1 ) i

1g 1g cAQQ (Vi) - cBQQ (Vi) Q Ry′ Ωi

B2g 2g cQB (ν19) + cAQB (ν19) B ) R EQx′ + Ωi - EBy y′ Q Ry,1 ) ν19

B Rx′,1 ) i

cABB1g(Vi) + cBBB1g(Vi) B Rx′ Ωi

B Rx′,1ν ) 19

2g 2g cBQB (ν19) - cAQB (ν19) R EQy′ + Ωi - EBx′ y′

B Ry,1 ) i

cABB1g(Vi) - cBBB1g(Vi) B Ry′ Ωi

2g 2g cBQB (ν19) - cAQB (ν19) Q R EBx′ + Ωi - EQy′ y′

B Ry′,1ν 19

[ (

∑ ∑

F)x,y l)Q,B

A. Vibronic Matrix Elements heme vibration ν53 ν9 ν51 ν8 ν50 substituent mode proprionic acids substituent mode proprionic acids substituent mode thioether linkage substituent mode thioether linkage substituent mode thioether linkage substituent mode thioether linkage ν7

frequency [cm-1]

1g cABB1g ) cAQQ [cm-1]

200 264 304 345 356 371

34 30 19 58 45 57

375

57

391

63

400

63

412

65

421

65

690

180

B1g 1g cBB ) -cBQQ [cm-1]

23 8 13 15 30

36

B. Electronic Parameters designation

2g 2g cBQB (ν19) + cAQB (ν19) Q ) R (17) EBy′ + Ωi - EQx′ x′

Now we are in the position to calculate the absorption spectrum by using the equation

(ν˜ ) ) ν˜

TABLE 1: Fixed Vibronic and Electronic Parameters Used for the Simulation of Heme Spectraa

RlFΓl

+

(ElF - Eg - ν˜ )2 + Γ2l l RF,V Γ i l

(ElF - Eg + Ωi - ν˜ )2 + Γ2l Q Γ RF,1ν 19 Q

)

+ B RF,1ν Γ 19 B

EQ EB ΓQ ΓB 1g HAQB

17900 24200 80 225 -1200

a The vibronic parameters were estimated by utilizing the coupling parameters reported in ref 44. 1g 1g , cBQQ , cABB1g, and cBBB1g of lowbronic coupling parameters cAQQ frequency modes between 200 and 700 cm-1, we proceeded as follows. With respect to cABB1g and cBBB1g, we utilized results obtained by Schomaker and Champion.44 They determined the Franck-Condon coupling constants S of multiple Raman bands of ferrocytochrome c measured with B-band excitation by using the transform approach developed by Hizhnyakov and Tehver45 S is related to cABB1g by

+

(EQF - Eg + Ων19 - ν˜ )2 + ΓQ2

parameter value [cm-1]

]

(EBF - Eg + Ων19 - ν˜ )2 + ΓB2

cABB1g(i) ) xSΩ(i) (18)

This is the final equation we used in the simulation to be described below. Simulations of Absorption Spectra Table 1 lists the coupling parameters of the low-frequency modes and of ν19 (1a) and the electronic parameters used for our simulation. With respect to ν19, the Herzberg-Teller 2g ) 800 cm-1 was estimated from the correparameter cAQB sponding values obtained for the resonance Raman excitation profiles of various Ni-porphyrins in organic solvents.37 It is in agreement with an earlier estimation made by Zgierski for 2g ferrocytochrome c.19 The corresponding cBQB value of (200 cm-1 reflecting the vibronic B1g perturbation were assumed to be by a factor of 4 smaller. That is in agreement with relative values of vibronic perturbation matrix elements of ν19 derived from the depolarization ratio dispersion observed for porphyrins with symmetry lowering perturbations.21 To estimate the vi-

(19)

The authors did not consider the influence of asymmetric perturbations. We estimated their contribution as follows. For the modes exhibiting A1g symmetry in D4h (ν9, ν8, and ν7; cf. Table 1), we assume that cBBB1g accounts for 20% of their total coupling strength. Some of the bands in the low-frequency region arise from modes having Eu symmetry in D4h.46 As shown above, they become Raman active solely by symmetry lowering distortions of Eu symmetry. In the point group of the lower symmetry, they generally split into a symmetric and an asymmetric mode. Because all of the bands in the low-frequency Raman spectrum of ferrocytochrome c are more or less polarized46 (Unger, unpublished results), it follows that they are assignable to the symmetric component. With respect to vibronic coupling, however, they should exhibit a much stronger contribution from B1g-type vibronic coupling than the A1g-type modes.47 Hence, we assume that cBBB1g for 40% of the total coupling strength. The third group of bands in the low-frequency region was assigned either to out-of-plane modes (their intensities are two weak for consideration in our approach) or to vibrations of the proprionic acids and of the thioether linkages.46

7070 J. Phys. Chem. B, Vol. 105, No. 29, 2001 Their Raman intensity is likely to result from vibrational mixing with macrocycle modes. Because the above substituents do not induce B1g-type perturbations we conservatively assume that cBBB1g contributions to the overall coupling strength are negligibly small. Unfortunately, there are essentially no experimental data for 1g 1g the determination of the cAQQ and cBQQ of low-frequency modes. 1g is only slightly larger The four orbital model predicts that cAQQ A1g or smaller than cBB, whereas the corresponding B1g paramters solely show a different sign. However, corresponding parameters obtained for high-frequency A1g modes of various porphyrins37 1g and heme proteins21,48 suggest that cAQQ is generally smaller by A1g 1g a factor of 2 to 3 than cBB whereas cBQQ and cBBB1g either follow 1g | is even larger the predictions of the four orbital model or |cBQQ B1g 21,48 As a consequence, the Raman bands of these than cBB. modes are relatively weak with Q0 and QV band scattering. This, however, seems not to apply to low-frequency modes. Measurements of ferrocytochrome c Raman spectra with QV-band excitation by Hu et al.46 rather reveal relatively strong intensities for the bands of the modes listed in Table 1. This indicates that the prediction of the four orbital model provides a good guess for the vibronic coupling strength. Thus, we assumes that 1g 1g cAQQ ) cABB1g and cBQQ ) -cBBB1g, for our simulations. The electronic A1g parameter V QB was estimated from the experimentally observed intensity ratio of the Q0 and B0 bands of ferrocytochrome 1g 1g 1g and V BQQ were assumed to be much smaller than V AQB . c. V BQB Different values were used for these parameters in the simulations described below. The Lorentzian halfwidth of the Q bands (80 cm-1) was taken from the low temperature study of Manas et al.24 Correspondingly, we assumed a reduced halfwidth of 225 cm-1 for the B band. For the sake of simplicity, we have neglected interstate Herzberg-Teller coupling for the low frequency modes. To affect optical absorption, they have to be significantly larger than the intrastate coupling parameters because of the energy gap between Q and B band. This is not likely to be the case for modes having A1g symmetry in D4h.37 Figure 1 shows seven different calculations of the Q-band region. In a first step, we omitted all electronic and vibronic contributions from asymmetric perturbations and calculated the Q0 band combined with the vibronic sidebands assignable to the heme vibrations in Table 1. This yields the black spectrum in Figure 1a, which is also inserted in Figure 1 parts b and c for comparison. Next we allowed electronic perturbations 1g 1g ) -V BBB1g ) 30 cm-1 and V BQB ) 100 cm-1. This yielded a V BQQ Q0 splitting of approximately 130 cm-1 and an asymmetric band profile as shown in Figure 1b (red spectrum). This band shape is pretty similar to that experimentally obtained for beef, tuna, and chicken cytochrome c.24 The splitting and the asymmetry is also imposed on the vibronic sidebands of the low-frequency modes. The corresponding contribution from ν19 at higher frequency shows a split without any intensity redistribution. This results from the fact that this sideband gets its intensity from interstate vibronic coupling with the B state. The two remaining spectra (blue and green) in Figure 1b were calculated by considering only vibronic perturbations with the parameter values listed in Table 1. The blue spectrum was obtained with 2g cBQB (ν19) ) 200 cm-1. It shows a clear splitting of nearly 150 cm-1 and two Q0 bands of practically identical intensity. The splitting is also imposed on the QV sidebands though less than obtained for the pure electronic perturbations. For the green 2g spectrum, we only changed the sign of cBQB (ν19) and obtained a much reduced Q0 band splitting which is smaller than the


Figure 1. Simulation of the Q-band spectrum for different electronic and vibronic parameters. (A) Spectrum of the undistorted heme group; 1g (B) spectra depicting the influence of electronic (red: V BQB ) 100 B1g 2g -1 -1 cm and V QQ ) 10 cm ) and vibronic perturbations (blue: cAQB ) B2g A2g B2g -1 -1 -1 800 cm and cQB ) 200 cm ; green: cQB ) 800 cm and cQB ) -200 cm-1); (C) spectra depicting the combined influence of electronic 1g 1g and vibronic perturbations (red: V BQB ) -100 cm-1, V BQQ ) -20 A2g 2g 1g cm-1, cQB ) 800 cm-1, and cBQB ) 200 cm-1; blue: V BQB ) 100 cm-1, 1g 2g 2g 1g V BQQ ) 20 cm-1, cAQB ) 800 cm-1, and cBQB ) 200 cm-1; green: V BQB ) B1g A2g B2g -1 -1 -1 100 cm , V QQ ) 20 cm , cQB ) 800 cm , and cQB ) -200 cm-1). The (black) spectra in Figure 1A is also displayed in parts B and C for comparison.

spectral bandwidth. This shows that the vibronic contributions of the low-frequency modes and of ν19 add up for positive 2g cBQB (ν19), whereas they are subtractive for negative values. Thus, the total influence of vibronic coupling on band splitting depends to a major extent on the sign of the matrix elements. The spectra in Figure 1c were calculated assuming that electronic as well as vibronic perturbations are operative. The red spectrum 1g 1g ) -100 cm-1and V BQQ ) -20 cm-1. was calculated for V BQB For the vibronic parameters, we again used the values in Table 2g 1 and a positive value for cBQB (ν19). Thus, we obtained a large splitting of approximately 250 cm-1. A similar effect was obtained for the vibronic sideband assignable to ν19. To calculate the blue spectrum in Figure 1c, we only changed the sign of the electronic perturbation matrix elements. Apparently, the splitting of Q0 nearly disappears and that of QV(ν19) is significantly reduced. This shows that under the assumed conditions vibronic and electronic contributions cancel out, so that the net splitting is small. The green spectrum was again

Optical Spectra of Heme Proteins

J. Phys. Chem. B, Vol. 105, No. 29, 2001 7071 Figure 2b illustrates another important impact of the vibronic perturbations. While they do not change the intensities of B0x and B0y in the weak coupling limit, they redistribute intensities between corresponding vibronic sidebands. We have simulated this for the blue spectrum in Figure 2a. Apparently, Bx0 shows a dip on its low energy side, which does not appear in the profile of By0. This results from the fact, that the B1g perturbation (cBBB1g) reduces Franck-Condon coupling for the former and increases it for the latter.34

Figure 2. Simulation of the B-band spectrum for different electronic and vibronic parameters. (A) Total absorption (black: spectrum of the 1g 1g undistorted heme group; red: V BQB ) -100 cm-1, V BQQ ) -20 cm-1, A2g B2g 1g 1g -1 -1 cQB ) 800 cm , and cQB ) 200 cm ; blue: V BQB ) 100 cm-1, V BQQ ) A2g B2g -1 -1 -1 20 cm , cQB ) 800 cm , and cQB ) 200 cm ). (B) Comparison of the total absorption spectrum with the band profiles Bx and By. The electronic and vibronic parameters are those used for the blue spectrum in Figure 2A. 1g 1g calculated with the negative values for V BQB and V BQQ but with B2g -1 a negative value for cQB(ν19) (-200 cm ). This reduces splitting to approximately 130 cm-1 and produces an asymmetry between the intensities of Q0x and Qy0. This spectra is again very similar to some of the experimental spectra reported by Manas et al.24 The simulations for the B band are visualized in Figure 2a. The color code was chosen to allow a comparison with the spectra in Figure 1, i.e., spectra with the same color were calculated with same electronic and vibronic perturbation parameters. The black spectrum therefore just depicts the B0 band combined with the vibronic sideband contributions from the low frequency modes without any splitting. The blue spectrum exhibits only a slight broadening and a reduction of the peak intensity which is indicative of some splitting which cannot be resolved because it is smaller than the spectral bandwidth. We performed a calculation with a largely reduced bandwidth to obtain a split of only 40 cm-1. This is by a factor of 4 smaller than the splitting obtained for the blue Q band in Figure 1c. On the contrary, the blue spectrum in Figure 2a appears significantly broadened because of a band splitting of approximately 155 cm-1. Thus, our result predicts that in the framework of the four orbital model the B band may appear much less or significantly more split than the Q band, depending on the sign of the electronic and vibronic matrix elements. Generally a strong (vibronic) splitting in the Q band corresponds to a weak split of the B band and vice versa.

Discussion Our study has unambiguously shown that a reliable analysis of band splitting in the optical spectra in heme proteins and porphyrins must be based on a thorough quantum mechanical approach, which takes into consideration electronic and vibronic perturbations as well as restrictions imposed by group theoretical selections rules and Gouterman’s four orbital model. We like to emphasize that our study is not aimed at analyzing the various Q-band splits reported in the literature.23-25,28-31 The results of our study rather suggest that the Q-band spectrum alone does not provide a sufficient basis for such an analysis, because the observed splits and intensity redistributions can be accounted for by various combinations of electronic and vibronic perturbations. In principle, the latter can only be determined from the resonance excitation profiles and depolarization ratio dispersion of at least all those modes, which display significant Raman intensity. As demonstrated for cytochrome c46 and other heme proteins,34 the situation might get very complicated because of the presence of many overlapping bands of intermediate intensity in the low-frequency region the combined coupling strength of which suffices for affecting the optical band shape. Whereas some efforts has been undertaken to determine the vibronic coupling parameters of porphyrin and heme modes in the high-frequency region,37 only very limited information has yet been obtained for low-frequency modes. For the Soret band region, the coupling parameters of some modes were determined from Raman and absorption measurements.34,44,49-51 However, only one of these studies deals with the impact of asymmetric vibronic perturbations.34 To our best knowledge, no reliable data about low-frequency modes are available for the Q-band region. Our laboratory is planning a project to fill this gap by Raman dispersion studies on some selected heme proteins. A somewhat less elaborate approach, which, however, may provide at least some more insights about the balance between electronic and vibronic distortions, involves the measurement of polarized optical spectra of heme protein crystals. Eaton and Hochstrasser pioneered this type of research more than thirty years ago.52 They measured the dispersion of the absorption coefficients for light polarized parallel to the crystal axes. Their data unambiguously show that the B as well as the Q bands of nearly all prominent heme proteins are split because of asymmetric perturbations of the respective heme group. If combined with the optical spectra of the corresponding molecules in solution and with Raman spectra taken with B-band excitation, a theoretical analysis can reveal the splitting of the B band and disentangle contributions from electronic and vibronic perturbations.34 For the Q band, however, this strategy is more difficult to employ, because the interpretation of Raman cross sections is not straightforward owing to the break down of the Born Oppenheimer approximation.37 Three conclusions drawn from our results deserve to be emphasized. The band splitting does not correlate with the magnitude of distortions. If contributions from electronic and vibronic



perturbations are of the same order of magnitude but exhibit different signs, they cancel out in the expressions for the eigenenergies. Thus, band splitting might be negligible even in the presence of strong distortions. On the other side, two bands with comparable band splitting do not necessarily indicate that the asymmetric distortions are similar. This can be illustrated by comparing hh and tuna cytochrome c, for which Manas et al.24 determined splits of 119 and 104 cm-1, respectively. The SNCD analysis of Jentzen et al.,11 however, reveals quite different B1g-type distortions, namely, 0.115 Å for hh and 0.06 Å for tuna cytochrome c. On the other hand, yeast cytochrome c exhibits a B1g distortion of 0.09 Å, which is just between hh and tuna, but it’s band splitting was found to be very small (80 cm-1).24 A somewhat more reliable parameter with respect to electronic perturbations is the extinction coefficient ratio for Qx0 and Qy0, because it depends in first order only on the 1g and intermanifold electronic interaction matrix element V BQB A2g V QB. In fact, it follows from eq 11 that 2

2

RQy - RQx ) -2

+ R R EB - E Q

1g V BQB

2g V AQB Q B

(20)

where R2 ) xR2x +R2y for Q and B. In the absence of A2g 1g perturbations, V BQB can thus directly be determined from the intensity ratio for Qx0 and Qy0. The splits of Q and B bands are different in the presence of Vibronic perturbations. Our simulations reveal that in the presence of electronic and vibronic perturbations the B- and Q-band splitting are significantly different. If only electronic perturbations were operative, both splits would be identical. The different influence of vibronic coupling on Q and B bands becomes apparent by comparing the equations for the corresponding splits described by eq 16. For the calculation of ∆EB, 1g 1g ) -V BBB1g and cBQQ ) -cBBB1g we have used the relations V BQQ dictated by the four orbital model in order to facilitate the comparison of ∆EB and ∆EQ.21 An inspection of eq 15 reveals that the first three terms of ∆EB and ∆EQ have opposite signs, whereas the fourth term, which accounts for interstate HerzbergTeller coupling, has the same sign in both equations. If the latter is comparable with the third term (intrastate coupling), their contributions add up for one state and cancel out for the other one. The above finding provides an important criterion for identifying the influence of vibronic perturbations on the optical spectra of heme and porphyrins. In fact, the spectra of many porphyrins and heme groups in asymmetric environment exhibit a much larger Q-band splitting.32,33,53 This holds in particular for hydroporphyrins which all exhibit a large Q-band splitting because of the reduction of one or more of their pyrrole groups but always a very moderate B-band splitting.54 The results obtained in the present study suggest that the vibronic contributions are at least partially responsible for this discrepancy. Manas et al.25 reported an opposite effect for Zn-substituted cytochrome c in that they observed a much larger splitting for the B band, i.e., 296 cm-1 compared with 122 cm-1 observed for the Q band.20,55 Although our theory could in principle account for such a difference, we find this result surprising because it indicates a significant difference between Znsubstituted and iron ferrocytochrome c. For the latter, such a large splitting can be ruled out by the depolarization ratios of several Raman bands measured with B-band excitation.20,21 An electric field may cause band splitting Via Vibronic perturbations. We have argued above that electronic distortions

due to a uniform electric field cannot cause band splitting for reasons of symmetry. This situation, however, is different for vibronic coupling. Electric fields exhibiting Eu symmetry induce vibronic activity of Eu modes, which are inactive in D4h. Because the vibronic matrix elements contain A1g and B1g contributions, band splitting can be induced or modified depending on the coupling strength, which is proportional to the gradient of the electric field with respect to the respective Eu-normal coordinate. If one can show that Eu perturbations are predominantly caused by electric fields, one could use the intensities and polarization properties of bands from Eu modes as a measure for the electric field gradient. We hope that this study stimulates further experimental work, which will eventually lead to a more thorough understanding on how the structural and electronic properties of porphyrins and hemes are influenced by an asymmetric environment, as it generally exists in proteins Acknowledgment. R.S.S. acknowledges support for this research from an EPSCOR-NSF Grant entitled “The influence of asymmetric and nonplanar distortions on functional properties of metalloporphyrins in solution and in proteins”. References and Notes (1) Ten Eck, L. F. Hemoglobin and myoglobin. In The Porphyrins; Dolphin, D., Ed.; Academic Press: New York, 1978; Vol. III. (2) Warshel, A. Proc. Natl. Acad. Sci. U.S.A. 1977, 74, 1789. (3) Walker, A. Proton NMR and EPR Spectroscopy of Paramagnetic Metalloporphyrins. In The Porphyrin Handbook; Kadish, K. M., Smith, K. M., Guilard, R., Eds.; Academic Press: San Diego, 2000; Vol. 5, p 36. (4) Friedman, J. M.; Stepnoski, R. A.; Stavola, M.; Ondrias, M. R.; Cone, R. L. Biochemistry 1982, 21, 2022. (5) Friedman, J. M. Science 1985, 228, 1274. (6) Schweitzer-Stenner, R.; Wedekind, D.; Dreybrodt, W. Biophys. J. 1986, 49, 1077. (7) Kozlowski, P. M.; Spiro, T. G.; Be´rces, A.; Zgierski, M. Z. J. Phys. Chem. B 1998, 102, 2603. (8) Kozlowski, P. M.; Spiro, T. G.; Zgierski, M. Z. J. Phys. Chem. B 2000, 104, 10659. (9) Gellin, B. R.; Karplus, M. Proc. Natl. Acad. Sci. 1977, 74, 801. (10) Schweitzer-Stenner, R. Q. ReV. Biophys. 1989, 22, 381. (11) Jentzen, W.; Song, X.-Z.; Shelnutt, J. A. J. Phys. Chem. B 1997, 101, 1684. (12) Jentzen, W.; Ma, J.-G.; Shelnutt, J. A. Biophys. J. 1998, 74, 753. (13) Sutherland, J. C.; Klein, M. P. J. Chem. Phys. 1972, 51, 76. (14) Collins, D. W.; Fitchen, D. B.; Lewis, A. J. Chem. Phys. 1973, 59, 5741. (15) Collins, D. W.; Champion, P. M.; Fitchen, D. B. Chem. Phys. Lett. 1976, 40, 416. (16) Zgierski, M. Z.; Pawlikowski, M. Chem. Phys. 1982, 65, 335. (17) Friedman, J. M.; Rousseau, D. L.; Adar, F. Proc. Natl. Acad. Sci. 1977, 74, 2607. (18) Schweitzer-Stenner, R.; Dreybrodt, W. J. Raman Spectrosc. 1985, 16, 111. (19) Zgierski, M. Z. J. Raman Spectrosc. 1988, 19, 23. (20) Bobinger, U.; Schweitzer-Stenner, R.; Dreybrodt, W. J. Raman Spectrosc. 1988, 20, 191. (21) Schweitzer-Stenner, R.; Bobinger, U.; Dreybrodt, W. J. Raman Spectrosc. 1991, 92, 65. (22) Kubitscheck, U.; Dreybrodt, W.; Schweitzer-Stenner, R. Spectrosc. Lett. 1986, 19, 681. (23) Reddy, K. S.; Angiolillo, P. J.; Wright, W. W.; Laberge, M.; Vanderkooi, J. M. Biochemistry 1996, 35, 12820. (24) Manas, E. S.; Vanderkooi, J. M.; Sharp, K. A. J. Phys. Chem. B 1999, 103, 6344. (25) Manas, E. S.; Wright, W. W.; Sharp, K. A.; Friedrich, J.; Vanderkooi, J. M. J. Phys. Chem. B 2000, 104, 6932. (26) Laberge, M.; Ko˜hler, M.; Vanderkooi, J. M.; Friedrich, J. Biophys. J. 1999, 77, 3293. (27) Rasnik, I.; Sharp, K. A.; Fee, J. A.; Vanderkooi, J. M. J. Phys. Chem. B 2001, 105, 282. (28) Suisalu, A.; Mauring, K.; Kikas, J.; Levente, H.; Fidy, J. Biophys. J. 2001, 80, 498. (29) Balog, E.; Kis-Petik, K.; Fidy, J.; Ko˜hler, M.; Friedrich, J. Biophys. J. 1997, 73, 397.

Optical Spectra of Heme Proteins (30) Ko¨hler, M.; Friedrich, J.; Balog, E.; Fidy, J. Chem. Phys. Lett. 1997, 277, 417. (31) Shibata, Y.; Kushida, T. Chem. Phys. Lett. 1998, 284, 115. (32) Engler, N.; Ostermann, A.; Grassmann, A.; Lamb, D. C.; Prusakov, V. E.; Schott, J.; Schweitzer-Stenner, R.; Parak, F. G. Biophys. J. 2000, 78, 2081. (33) Sanfratello, V.; Boffi, A.; Cupane, A.; Leone, M. Biopolymers 2000 57, 291. (34) Schweitzer-Stenner, R.; Cupane, A.; Leone, M.; Lemke, C.; Schott, J.; Dreybrodt, W. J. Phys. Chem. B. 2000, 104, 4754. (35) Gouterman, M. J. Chem. Phys. 1959, 30, 1959. (36) Schweitzer-Stenner, R.; Stichternath, A.; Dreybrodt, W.; Jentzen, W.; Song, X. Z.; Shelnutt, J. A.; Faurskov-Nielsen, O.; Medforth, C. J.; Smith, K. M. J. Chem. Phys. 1997, 107, 1794. (37) Schweitzer-Stenner, R. J. Porphyrins Phthalocyanines 2001, 5, 187. (38) Shelnutt, J. A.; Cheung, L. D.; Chang, R. C. C.; Yu, N.-T.; Felton, R. H. J. Chem. Phys. 1977, 66, 3387. (39) Unger, E.; Bobinger, U.; Dreybrodt, W.; Schweitzer-Stenner, R. J. Phys. Chem. 1993, 97, 9956. (40) Shelnutt, J. A. J. Chem. Phys. 1980, 72, 3948. (41) In some of the papers reporting Q-band splits for cytochrome c and horseradish peroxidase, ruffling and saddling was invoked as a possible cause (refs 24, 29, and 30). This can be ruled out by means of group theory. Saddling and ruffling together lower the porphyrin symmetry from D4h to S4 in which the excited states are still 2-fold degenerated (cf. the correlation tables in Wilson, E. B.; Decius, J. C.; Cross, P. C. Molecular Vibrations; Dover: New York, 1980).

J. Phys. Chem. B, Vol. 105, No. 29, 2001 7073 (42) Unger, E.; Dreybrodt, W.; Schweitzer-Stenner, R. J. Phys. Chem. A 1997, 101, 5997. (43) Laberge, M.; Galantai, R.; Schay, G.; Fidy, J. Biophys. J. 2001, 80, B175. (44) Schomaker, K. T.; Champion, P. M. J. Chem. Phys. 1986, 84, 5314. (45) Hiznyakov, V.; Tehver, I. Phys. Stat. Sol. 1967, 21, 755. (46) Hu, S.; Morris, I. K.; Singh, J. P.; Smith, K. M.; Spiro, T. G. J. Am. Chem. Soc. 1993, 115, 12446. (47) Lipski, R.; Unger, E.; Dreybrodt, W.; Militello, V.; Leone, M.; Schweitzer-Stenner, R. J. Raman Spectrosc. 2001, in press. (48) Schweitzer-Stenner, R.; Dannemann, U.; Dreybrodt, W. Biochemistry 1992, 31, 694. (49) Schomaker, K. T.; Bangcharoenpaurpong, O.; Champion, P. M. J. Chem. Phys. 1984, 80, 4701. (50) Cupane, A.; Leone, M.; Vitrano, E.; Cordone, L. Eur. Biophys. J. 1995, 23, 385. (51) Cupane, A.; Leone, M.; Unger, E.; Lemke, C.; Beck, M.; Dreybrodt, W.; Schweitzer-Stenner, R. J. Phys. Chem. B 1998, 102, 612. (52) Eaton, W. A.; Hochstrasser, R. M. J. Chem. Phys. 1968, 49, 985. (53) Bersuker, I. B.; Stavrov, S. S. Coord. Chem. ReV. 1988, 88, 168. (54) Schick, G. A.; Bocian, D. F. Biochim. Biophys. Acta 1987, 102, 127. (55) Stallard, B. R.; Callis, P. R.; Champion, P. M.; Albrecht, A. C. J. Chem. Phys. 1984, 80, 70.

Electronic and Vibronic Contributions to the Band Splitting in Optical

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