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.

We dedicate this paper to our mutual dear friend and colleague, Frank C. Adam, who recently died so suddenly at the prime of his life. For the many years of happy association, Frank was to us a continuous source of inspiration and seemingly bottomless wisdom. In his quiet and unassuming way he contributed immeasurably to our efforts and motivation, for which we shall be forever grateful.

Based on the Ph.D. Thesis of T. L. Smithson, 1982, The University of Calgary. Present address: DREV 2459 Blvd. Pie XI Nord, C. P. 8800, Courcelette, Qufibec, Canada, G0A 1R0.

We dedicate this paper to our mutual dear friend and colleague, Frank C. Adam, who recently died so suddenly at the prime of his life. For the many years of happy association, Frank was to us a continuous source of inspiration and seemingly bottomless wisdom. In his quiet and unassuming way he contributed immeasurably to our efforts and motivation, for which we shall be forever grateful.

Based on the Ph.D. Thesis of T. L. Smithson, 1982, The University of Calgary. Present address: DREV 2459 Blvd. Pie XI Nord, C. P. 8800, Courcelette, Qufibec, Canada, G0A 1R0.

Notes

We dedicate this paper to our mutual dear friend and colleague, Frank C. Adam, who recently died so suddenly at the prime of his life. For the many years of happy association, Frank was to us a continuous source of inspiration and seemingly bottomless wisdom. In his quiet and unassuming way he contributed immeasurably to our efforts and motivation, for which we shall be forever grateful.

Based on the Ph.D. Thesis of T. L. Smithson, 1982, The University of Calgary. Present address: DREV 2459 Blvd. Pie XI Nord, C. P. 8800, Courcelette, Qufibec, Canada, G0A 1R0.