Single‐mode versus multimode calculations of Raman intensities of cytochrome c
1.J. Tang and A. C. Albrecht, in Raman Spectroscopy, edited by H. Szymanski (Plenum, New York, 1970);
1.A. C. Albrecht and M. C. Hutley, J. Chem. Phys. 55, 4438 (1971).
2.P. M. Champion and A. C. Albrecht, J. Chem. Phys. 71, 1110 (1979).
3.P. M. Champion and A. C. Albrecht, J. Chem. Phys. 72, 6498 (1980).
4.G. J. Small and E. S. Yeung, Chem. Phys. 9, 379 (1975).
5.M. Zgierski, J. A. Shelnutt, and M. Pawlikowski, Chem. Phys. Lett. 68, 262 (1979).
6.J. A. Shelnutt, J. Chem. Phys. 72, 3948 (1980);
6.see also J. A. Shelnutt, J. Chem. Phys. 74, 6644 (1981), where a multi mode point of view is included. However, the perturbation approach used there invokes ground state vibrational wave functions as a basis set and must diverge exponentially in coupling strength/number of CF active vibrations. It therefore is limited to cases in which there are only a small number of weakly coupled vibrations, and cannot incorporate the more extensive multimode model we regard as valid for the cytochrome c problem.
7.The actual value for the FWHM of is probably somewhat less than see P. M. Champion and R. Lange, J. Chem. Phys. 73, 5947 (1980);
7.P. M. Champion and G. J. Perreault, J. Chem. Phys. 75, 490 (1981).
8.B. Stallard (unpublished results).
9.The assumption that the damping factor, is independent of the vibrational state is made in order to facilitate the comparison between the single‐mode (Ref. 6) and multimode (Ref. 2) models, both of which employ this approximation. B is interesting to note, however, that if we assign different damping factors to the 0‐0 and 0‐1 transitions of (i.e., and and consider only single‐mode A‐term scattering), we have [from Eqs. (2) and (3)] (experimental). This, however, would imply that the lifetime of the zero‐point state of is two times shorter than the vibrationally excited state of This is quite an unusual result and so, for the present, we prefer the simplifying approximation
10.We have used the experimentally observed value for taken from Ref. 6 in which the single‐mode model for explaining the REP of is put forth. In fact the Raman line shows anomalous polarization when excited in the region between the 0‐0 and 0‐1 transitions of [see D. W. Collins, D. B. Fitchen, and A. Lewis, J. Chem. Phys. 59, 5714 (1973)]. This polarization behavior is not accounted for within the single‐mode model as treated either here or in Ref. 6. In fact, the anomalous polarization behavior in may be due either to accidental degeneracy of Raman modes of different symmetry or to the lowering of the point group of the heme system. In the latter case the polarizability tensor for totally symmetric modes could contain an antisymmetric component. In the case of accidental degeneracy, the value of relevant to the single‐mode model under discussion must have a lower bound of 48. If, on the other hand, the anomalous polarization has its origins in breakdown of symmetry, the REP in the region must be modeled to include antisymmetric scattering. In any case the extent of anomalous scattering at the 0‐0 and 0‐1 transitions of (the points of reference taken here) is greatly reduced from that seen midway between these bands (see Collins et al.). Furthermore, for excitation, no anomalous polarization is encountered. The dominant role of simple, symmetric, A‐term scattering in the REP seems to successfully mask antisymmetric contributions to the polarizability tensor, whatever their origins. The argument presented here will show how the single‐mode model is unable to rationalize, consistently, the bandwidth and the REP of Logic dictates that we employ parameters in our argument which favor the single‐mode model. It is only for this reason that what may really be a lower limit of is accepted as its correct value, just as we have taken the phasing of the A and B amplitudes (Fig. 1) to be optimal for the single‐mode model.
11.We note that Soret band preresonance profiles of analogous modes in other heme systems are fit quite well using only the A‐term contribution; see T. C. Strekas, J. A. Packer, and T. G. Spiro, J. Raman Spectrosc. 1, 197 (1973).
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