Calculation of Vibrational Spectra of Linear Tetrapyrroles. 1. Global Sets of Scaling Factors for Force Fields Derived by ab Initio and Density Functional Theory Methods

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Abstract

An approach has been developed for calculating the vibrational spectra of linear 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. Soc. 1983, 105, 7037), scaling factors were determined for a set of 10 training molecules 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 Møller−Plesset perturbation (MP2), and B3LYP density functional theory methods using 6-31G* basis sets. A global optimization yielded sets of 14, 11, and 10 scaling factors for HF, MP2, and B3LYP, respectively. B3LYP provided the best results both with regard to the geometries and the vibrational frequencies. The root-mean-square deviation for the calculated frequencies was 11 cm-1 for B3LYP as compared to 13 and 17 cm-1 for HF and MP2, respectively. On the basis of the Morse model for an anharmonic oscillator, an expression was derived for correcting scaling factors for the anharmonicity changes in (deuterio) isotopomers. The effects of hydrogen bonding interactions via N−H···OC bonds on the 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 intensities calculated by the B3LYP method were found to agree well with experimental spectra. For the Raman intensities, a fourth-order differentiation formula was derived for the numerically accurate calculation of polarizability derivatives with respect to Cartesian displacements, by using the finite field method.

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