# A COMPARISON OF APPROACHES FOR SOLUTIONS TO THE COUPLED TWO-DIMENSIONAL ANHARMONIC OSCILLATOR

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 Title: A COMPARISON OF APPROACHES FOR SOLUTIONS TO THE COUPLED TWO-DIMENSIONAL ANHARMONIC OSCILLATOR Creators: Smithson, T. L.; Wieser, H.; Paul, R.; Briss, F. W. Issue Date: 1983 Publisher: Ohio State University Abstract: Experience indicates that the bend/twist skeletal deformations of a number of 5- and 6- membered ring compounds should be described in terms of a coupled two-dimensional anharmonic oscillator (1). In the past, two slightly different variational approaches have been used to obtain the required solution, one using as basis the two-dimensional isotropic harmonic oscillator functions (2,4), the other the direct product formed from the one-dimensional anharmonic oscillator functions (3,4). We have explored alternative methods for obtaining the solutions, namely one using the Rayleigh-Schr$\ddot odinger$ perturbation theory with Pad\’{e} approximants, and one SCF- like modification of the variational product basis set approach. The abilities of all the methods for solving the Hamiltonian are compared for a number of molecular systems. Some of the problems associated with the methods are discussed in the context of highly coupled vibrations. (1) L. A. Carreira, R. C. Lord, and T. B. Malloy, JR., in Topics in Current Chemistry"", vol. 82, Springer-Verlag (1979). (2) L. A. Carreira, I. M. Mills, and W. B. Person. J. Chem. Phys. 56, 1444 (1972). (3) T. Ikeda and R. C. Lord, J. Chem. Phys. 56, 4450 (1972). (4) L. E. Bauman, P. M. Killough, J. M. Cooke, J. R. Villarreal, and J. Laane, J. Phys. Chem. 86, 2000 (1982). Description: Author Institution: Department of Chemistry, University of Calgary; Department of Chemistry, University of Alberta Edmonton URI: http://hdl.handle.net/1811/11864 Other Identifiers: 1983-MH-13