General anharmonic local mode approach to molecular vibrations

Abstract

An algebraic approach to describe the vibrational excitations of molecules is presented. The model is established in a local mode scheme and involves an anharmonization procedure in which the local harmonic oscillators associated to each internal degree of freedom are substituted by Morse oscillators through the introduction of U(2) algebras. This anharmonization corresponds exactly to the dominant Morse matrix elements involved in the harmonically coupled anharmonic oscillator (HCAO) model introduced by Child and Lawton. An application to methane is presented. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 465–481, 1999

Theoretical Study of Vibrationally Averaged Dipole Moments for the Ground and Excited C═O Stretching States of trans-Formic Acid

“…9,29,30 Since our treatment is based on the normal mode, we use the term "single mode method" to distinguish this approach from the conceptually different local mode theory of molecular vibrations. [31][32][33] The second approach is a multidimensional limited vibrational configuration interaction (VCI) methodology, 25,34 which includes all vibrational coordinates. A third approach, the multidimensional degeneration-corrected second-order perturbation theory, 25 was also tested with very similar results to those obtained by VCI, as observed previously for other vibrationally averaged properties.…”

“…The normal mode coordinate is treated as independent from all other vibrational degrees of freedom. This approach is analogous to the simple local mode model, which has proven very useful in the investigations of overtone vibrations involving predominantly X−H stretching, , including the O−H stretch of FA. ,, Since our treatment is based on the normal mode, we use the term “single mode method” to distinguish this approach from the conceptually different local mode theory of molecular vibrations. − The second approach is a multidimensional limited vibrational configuration interaction (VCI) methodology, , which includes all vibrational coordinates. A third approach, the multidimensional degeneration-corrected second-order perturbation theory, was also tested with very similar results to those obtained by VCI, as observed previously for other vibrationally averaged properties…”