Fundamental vibrational frequencies of small polyatomic molecules from density-functional calculations and vibrational perturbation theory

Abstract

An extensive study of fundamental frequencies and anharmonic vibrational constants for polyatomic molecules obtained from Becke three parameter Lee–Yang–Parr (B3LYP) and Becke–Perdew (BP86) density functional calculations is presented. These calculations are based on standard perturbation theory, and are compared to correlation-corrected vibrational self-consistent field (CC-VSCF) calculations for the water dimer. The anharmonic corrections obtained from density-functional calculations compare well with experimental values and with results from correlated ab initio methods. While fundamental frequencies from B3LYP calculations are reliable, they are considerably too small for BP86 calculations. Consequently, the good agreement of unscaled harmonic frequencies from BP86 calculations with experimental frequencies is due to an error cancellation effect. This is of importance for the prediction of vibrational spectra for large molecules, because the perturbation theory approach naturally becomes unreliable for very large molecules due to the increasing number of anharmonic resonance effects. These resonances seriously limit the applicability of perturbation theoretical approaches to anharmonic vibrational constants, whereas the computational effort for the calculation of cubic and quartic force constants, is feasible because calculations can be performed very efficiently by a parallelized calculation of harmonic force constants for several structures, which are distorted along the normal coordinates, followed by numerical differentiation.