A comparison of computational and model approaches to the two-coupled anharmonic oscillator problem in five-membered ring compounds

Abstract

The bend/twist eigenvalues and transitions of 2,5-dihydrofuran, cyclopentanone, cyclopentene, silacyclopentane, and germacyclopentane are calculated with a two-dimensional hamiltonian in several different ways, viz. using two-dimensional isotropic harmonic oscillator basis functions, a directproduct basis set consisting of two one-dimensional anharmonic oscillator functions, a similar set of basis functions improved in the fashion of partial SCF, evaluating explicitly the perturbation corrections up to third order, and seeking the series limit for these corrections by means of Padé approximants. These eigenvalues and transitions are compared for the four methods, and compared also with previous experimental measurements and with previous calculations. The merits or disadvantages of the methods are discussed in relation to the degree of coupling of the two modes. Substantially different values for the potential constants of sila- and germacyclopentane are suggested.