Vibrational analysis of the squarate ion based on ab initio molecular orbital calculations. A practical method to calculate vibrational force fields of non-bond-alternating conjugated molecules

摘要

Vibrational analysis of the squarate ion is performed on the basis of ab initio molecular orbital calculations; Theribrational force field is calculated with the Hartree-Fock (HF), the second- and third-order Moller^Plesset pertur- bation (MP2 and MP3), and the complete active space self-consistent field (CASSCF) methods, in order to study the Sffects of electron correlation. The 6-31G*, 6-31+G*, and 6-31+G(df) basis sets are used for the purpose of examining he basis-set dependence of the results of calculations. It is found that the calculations at the MP3/6-31G* and CASSCF/ 5-31G* levels provide reasonable vibrational force fields for the squarate ion. The 6-31+G* and 6-31+G(df) basis sets ire not suitable for calculating the out-of-plane force field. The effects of nondynamic electron correlation are large on he vibrational frequencies of the eu CO stretching and 6tg CC stretching modes, the origin of the large effects of electron lorrelation oh these vibrational frequencies is studied by examining the calculated force constants in detail. It is found hat a reasonable vibrational force field can also be obtained by taking an average of those at the HF/6-31G* arid MP2/6- I1G* levels. This method is also applied to'the in-plane vibrational force field of benzene. The relation between the lefinition of molecular symmetry coordinates and the calculated force constants is discussed, in terras of the atornic notions corresponding to the unit displacements along the defined coordinates and the origin of the potential energy jained by those vibrational motions.