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Experimental data for depolarization ratio dispersion (DPD) and resonance excitation profiles (REPs) with high spectral resolution (20 cm-I) are provided for seven Raman fundamentals in the region between 1150 and 1650 cm-' of the haeme spectrum from ferrocytochrome c. They cover the resonant region of the Q-band and the preresonant region of the &band. A self-consistent analysis of the depolarization ratio dispersion (DPD) and resonance excitation profiles (REPs) of these Raman lines is carried out by explicit consideration of multimode mixing. This is achieved by first formulating the Raman tensor in Loudon's formulation to fifth order for each mode, thus restricting the contribution of the fifth-order term to the vibration itself and omitting multimode contributions. By fitting this expression to the DPDs and REPs of each Raman mode, one obtains coupling parameters which in the next step are inserted into the fifth-order term of each mode. Thus one takes account of their contributions to multimode mixing. To account for contributions of lower frequency modes, an effective 'helping rest mode' was added to the multimode contributions. This procedure yields satisfactory fits to all data sets. The respective fits to the D P D and REP of the oxidation marker line at 1363 cm-' reproduce also the corresponding R E P and DPD in the resonant region of the B-band reported by Champion and Albrecht with a high degree of accuracy. The vibronic coupling parameters obtained are consistent with the weak coupling limit. Further, they confirm the validity of Gouterman's four-orbital model for ferrocytochrome c.

New experimental data for depolarization dispersion (DPD) and excitation profiles (EP) with high spectral resolution (20 cm- ') are provided for Raman fundamentals of protoporphyrin IX in ferrocytochrome c between 17000 and 22500 cm-', covering the resonant region of the Q-bands and the pre-resonant region of the B-bands. Both DPD and EPs of the lines at 1312 and 1585 cm-' (Azs), at 1363 cm-' (Als) and at 1621 cm-' (B,#) exhibit sharp structures. These result from multi-mode contributions of vibrations which give intensity to the vibronic sideband of the Q-absorption. On the basis of these highly resolved new data we have shown that the Raman tensor can be formulated in terms of Loudon's strictly timedependent perturbation formulation to third order augmented by a fifth-order term representing the multi-mode effects. From the EPs, which were measured in absolute units, we obtained values of vibronic coupling parameters for the Raman fundamentals which are consistent with the optical absorption spectra and show that vibronic coupling is weak for this type of molecule. INTRODUCGONResonance Raman scattering has been used extensively to study vibronic coupling in the excited states of porphyrin molecules. In this class of molecule, the lowest singlet excited states are located in the visible region and are therefore easily accessible to the measurement of excitation profiles (EP) and depolarization ratio dispersion (DPD) by tunable dye lasers. Under D,, symmetry, as is approximately the case for octaethylporphyrin for instance, the depolarization ratio (DPR) of the A', , B,, , A,, and B,, Raman fundamentals is independent of the exciting laser frequency.' A,, modes exhibit a value of 1/8, B1, and B2, modes a value of 3 14 and A', modes a value of infinity.Experimental results on porphyrins, which are subject to symmetry-lowering perturbations, show, however, strong dispersion of their depolarization ratio with exciting wavelength. Symmetry-lowering perturbations are either asymmetric side-chains on the porphyrin ring skeleton' or interactions of the porphyrin molecule with the protein matrix in which it is Consequently, intense theoretical work has been carried out to elucidate Raman EPs and depolarization ratios in pure D,, symmetry' and in environments of low symmetry.1,6-8 This work has led to a good understanding of vibronic couplings that determine the features exhibited by the Raman data, in both the weak and the strong coupling limits.Zgierski and Pawlikowski' have given a systematic treatment of the influence of asymmetric perturbations of electronic and vibronic origin on the EPs and DPD of metalloporphyrins and metallophthalocyanines by exact diagonalization of the corresponding energy matrix, which contains both the electronic and the vib-* Author to whom correspondence should be addressed. ronic Hamiltonian in D, , symmetry and also the symmetry-lowering environmental perturbations. The matrix is diagonalized in a basis set of products of harmonic oscillator functions and the I Qxo), I Q y o ) , I B x o ...

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