We have developed a novel method for molecular mechanics calculations and normal-mode analysis. It is based on symmetry of local units that constitutes the given molecule. Compared with general valence force field calculations, the number of free parameters is reduced by 40-80% in our procedure. It was found to reproduce very well the vibrational frequencies and mode compositions of aromatic compounds and porphyrins, as shown by comparison with DFT calculations. A slightly altered force field obtained from Ni(II) porphin was then used to calculate the structure and the normal modes of several meso-substituted Ni(II) porphyrins which are known to be subject to significant ruffling and/or saddling distortions. This method satisfactorily reproduces their nonplanar structure and Raman band frequencies in the natural abundance and isotopic derivative spectra. The polarization properties of bands from out-of-plane modes are in accordance with the predicted nonplanar distortions. Moreover, we found that some of the modes below 800 cm -1 which appear intense in the Raman spectra contain considerable contributions from both in-plane and out-of-plane vibrations, so that the conventional mode assignments become questionable. We also demonstrate that the intensity and polarization of some low-frequency Raman bands can be used as a (quantitative) marker to elucidate type and magnitude of out-of-plane distortions. These were recently shown to affect heme groups of hemoglobin, myoglobin, and, in particular, of cytochrome c.

A novel method was developed for molecular mechanics calculations and normal mode analysis. In this approach, the number of free parameters is strongly reduced compared with other empirical force Ðelds. and in contrast to them is generally smaller than the number of available wavenumber values. The molecule is subdivided into local units, each of which is constituted by a distinct atom and its nearest neighbors. The vibrational force Ðeld is then expressed as the sum over the contributions from all local units, and each local unitÏs potential function is assumed to depend solely on the atomic positions within the unit. Local units often exhibit high symmetry, because each atom forms bonds which are characteristic of its valencies and hybridization state, and the bonds are therefore arranged in a symmetrical way. This local (pseudo)symmetry imposes group theoretical restrictions that reduce the number of possible interaction parameters. As suggested by ab initio results, the internal force constants of each local unit are transferable to other molecules. It is therefore possible to calculate the internal force constants of each local unit from small molecules and these are then used to calculate the potential of large molecules such as porphyrins. A series of alkanes, ethene, some homo-and heterocyclic aromatic compounds and porphyrins were analyzed. The results for the normal mode wavenumbers and their eigenvectors are comparable to those reported in the literature and to results from DFT calculations [ B3-LYP/6-31G(d) ] . The force constants were close to those obtained from ab initio calculations using local symmetry coordinates for ethene, ethane and propane. Moreover, the above procedure reproduces very well the vibrational wavenumbers and mode compositions of aromatic compounds and porphyrins, as shown by comparison with DFT calculations. In contrast to general valence force Ðeld calculations, the number of free parameters is reduced by 40-80% .

No abstract

We measured the polarized resonance Raman spectra of Cu(II)-2,2,7,8,12,13,17,18-octamethylchlorin in CS 2 at various excitation wavenumbers in a spectral region covering the Q y , Q x and B x optical absorption bands. Additionally, we measured the FTIR-Raman spectrum of the highly overcrowded spectral region between 1300 and 1450 cm −1 . The spectral decomposition was carried out by a self-consistent global fit to all spectra obtained. The thus identified Raman and IR lines were assigned by comparison with the resonance Raman spectra of Cu(II)-octaethylporphyrin, by utilizing their depolarization ratio dispersions and by a normal mode analysis. The latter was based on a modified transferable molecular mechanics force field of Ni (II)-octaethylporphyrin [E. Unger, M. Beck, R.J. Lipski, W. Dreybrodt, C.J. Medforth, K.M. Smith and R. Schweitzer-Stenner, J. Phys. Chem. B 103, 10229 (1999)]. A comparison of normal mode patterns obtained for Cu(II)-octamethylchlorin and Cu(II)-octaethylporphyrin revealed that some modes are significantly distorted by the reduction of the pyrrole ring, in accordance with results which Boldt et al. reported earlier for Ni(II)-octaethylchlorin [N.J. Boldt, F.J. Donohoe, R.R. Birge and D.F. Bocian, J. Am. Chem. Soc. 109, 2284]. In contrast to conclusions drawn from this study, however, the results of our vibrational analysis and several further lines of evidence suggest that the normal modes of corresponding chlorines and porphyrins are still comparable, because they display contributions from the same local coordinates. Thus, the classical normal mode classification developed for metalloporphyrins is also applicable to metallochlorins. Finally, we performed a preliminary analysis of the absorption spectrum and the resonance excitation profiles and depolarization ratio dispersions of some Raman lines. The results show that the electronic properties of Cu(II)-octamethylchlorin can still be described in terms of Gouterman's four orbital model [M. Gouterman, J. Chem. Phys. 30, 1139Phys. 30, (1959]. In regions of the Q bands, Raman scattering of A 1 modes is determined by interferences between Franck-Condon coupling and interstate Herzberg-Teller coupling between Q x .Q y / and B x .B y / states. The B 2 modes are resonance enhanced by Herzberg-Teller coupling between Q x and Q y and between Q x .Q y / and B y .B x /. Franck-Condon coupling of A 1 modes with large contributions from C a C m stretching vibrations is comparatively strong for Q x . This is interpreted as reflecting the expansion of the chlorin macrocycle by an electronic transition into this excited state.