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

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 Moller-Plesset perturbation (MP2 and MP3), and the complete active spa ce self-consistent field (CASSCF) methods, in order to study the effec ts of electron correlation. The 6-31G, 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 MP3/6-31G and CASSCF/6-31G* levels provide reasonable vibrational fo rce 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 ef fects of nondynamic electron correlation are large on the vibrational frequencies of the e(u) CO stretching and b(lg) CC stretching modes. T he origin of the large effects of electron correlation on these vibrat ional frequencies is studied by examining the calculated force constan ts in detail. It is found that a reasonable vibrational force field ca n also be obtained by taking an average of those at the HF/6-31G and MP2/6-31G levels. This method is also applied to the in-plane Vibrati onal force field of benzene. The relation between the definition of mo lecular symmetry coordinates and the calculated force constants is dis cussed, in terms of the atomic motions corresponding to the unit displ acements along the defined coordinates and the origin of the potential energy gained by those vibrational motions.