Calculation of vibrational spectra of linear tetrapyrroles. 1. Global setsof scaling factors for force fields derived by ab initio and density functional theory

An approach has been developed for calculating the vibrational spectra of l inear methine-bridged tetrapyrroles constituting the chromophoric sites of various photoreceptor proteins. Using Pulay's scaling procedure (Pulay, P.; Fogarasi, G.; Pongor, G.; Boggs, J. E.; Vargha, A. J. Am. Chem. Sec. 1983, 105, 7037), scaling factors were determined for a set of 10 training molec ules which mimic structural elements of the tetrapyrrole target molecules. Geometries and force fields were calculated at three theoretical levels, i. e., by the Hartree-Fock (HF), second-order Moller-Plesset perturbation (MP2 ), and B3LYP density functional theory methods using 6-31G* basis sets. A g lobal optimization yielded sets of 14, 11, and 10 scaling factors for HF, M P2, and B3LYP, respectively. B3LYP provided the best results both with rega rd to the geometries and the vibrational frequencies. The root-mean-square deviation for the calculated frequencies was 11 cm(-1) for B3LYP as compare d to 13 and 17 cm(-1) for HF and MP2, respectively. On the basis of the Mor se model for an anharmonic oscillator, an expression was derived for correc ting scaling factors for the anharmonicity changes in (deuterio) isotopomer s. The effects of hydrogen bonding interactions via N-H ... O=C bonds on th e structures and vibrational spectra were studied in the case of maleimide. For the N-H stretching, deformation, and out-of-plane wagging vibrations, modifications of the scaling factors are required in order to reproduce the vibrational spectra of the hydrogen bonded dimer. The IR and Raman intensi ties calculated by the B3LYP method were found to agree well with experimen tal spectra. For the Raman intensities, a fourth-order differentiation form ula was derived for the numerically accurate calculation of polarizability derivatives with respect to Cartesian displacements, by using the finite fi eld method.