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

Abstract

Vibrational analysis of the squarate ion is performed on the basis of ab initio molecular orbital calculations. The vibrational force field is calculated with the Hartree-Fock (HF), the second- and third-order Møller-Plesset perturbation (MP2 and MP3), and the complete active space self-consistent field (CASSCF) methods, in order to study the effects of electron correlation. The 6G–31G ∗, 6–31 + G ∗, and 6–31 + G (df) basis sets are used for the purpose of examining the basis-set dependence of the results of calculations. It is found that the calculations at the MP3/6G–31G ∗ and CASSCF/ 6G–31G ∗ levels provide reasonable vibrational force fields for the squarate ion. The 6–31 + G ∗ and 6–31 + G(df) basis sets are not suitable for calculating the out-of-plane force field. The effects of nondynamic electron correlation are large on the vibrational frequencies of the e u CO stretching and b 1 g CC stretching modes. The origin of the large effects of electron correlation on these vibrational frequencies is studied by examining the calculated force constants in detail. It is found that a reasonable vibrational force field can also be obtained by taking an average of those at the HF/6G–31G ∗ and MP2/6G–31G ∗ levels. This method is also applied to the in-plane vibrational force field of benzene. The relation between the definition of molecular symmetry coordinates and the calculated force constants is discussed, in terms of the atomic motions corresponding to the unit displacements along the defined coordinates and the origin of the potential energy gained by those vibrational motions.