Pseudo Jahn–Teller origin of instability of molecular high-symmetry configurations: Novel numerical method and results

Abstract

The pseudo Jahn–Teller (PJT) effect as the only source of instability of molecular high-symmetry configurations in nondegenerate states is given a deeper insight by means of a novel method of ab initio evaluation of the vibronic Kv and nonvibronic K0 contributions to the curvature K=K0+Kv of the adiabatic potential energy surface in the direction of distortion. The method overcomes two essential difficulties: (1) the low accuracy in calculation of K0 because of the singularities at the nuclei where existing basis sets yield inadequate results, and (2) the lack of sufficiently accurate data on excited states (including the continuum spectrum) for calculation of Kv. This is achieved by summing up the contributions of the excited states to result in expressions with only the ground state wave function and its derivatives, and excluding the singularities by canceling mutually compensating diagonal matrix elements in K0 and Kv. After these essential changes K=K0+Kv is no longer a small difference between two large numbers, and it can be calculated with reasonable accuracy, while the separation of Kv allows one to reveal the PJT origin of the instability: the direction of distortion for which the negative Kv value overcomes the positive K0 one. A further insight into the origin of the instability is reached by estimating the relative contribution of the most active excited states for different distortions (and for the same distortions in similar compounds), since the contribution of the continuum states (the largest part of Kv) does not affect the bonding and hence the differences in Kv. Illustrative numerical calculations were carried out on several series of molecular systems: planar AH4, A=B−, C, N+, O2+, Si, planar BH3, CH3−, NH3, octahedral MH6, M=Sc3−, Ti2−, V−, Cr, Mn+, and octahedral TeF62−, IF6−, and XeF6.