title: Treating singularities present in the Sutcliffe-Tennyson vibrational Hamiltonian in orthogonal internal coordinates.
abstract: Two methods are developed, when solving the related time-independent Schrodinger equation (TISE), to cope with the singular terms of the vibrational kinetic energy operator of a triatomic molecule given in orthogonal internal coordinates. The first method provides a mathematically correct treatment of all singular terms. The vibrational eigenfunctions are approximated by linear combinations of functions of a three-dimensional nondirect-product basis, where basis functions are formed by coupling Bessel-DVR functions, where DVR stands for discrete variable representation, depending on distance-type coordinates and Legendre polynomials depending on angle bending. In the second method one of the singular terms related to a distance-type coordinate, deemed to be unimportant for spectroscopic applications, is given no special treatment. Here the basis set is obtained by taking the direct product of a one-dimensional DVR basis with a two-dimensional nondirect-product basis, the latter formed by coupling Bessel-DVR functions and Legendre polynomials. With the basis functions defined, matrix representations of the TISE are set up and solved numerically to obtain the vibrational energy levels of H3+. The numerical calculations show that the first method treating all singularities is computationally inefficient, while the second method treating properly only the singularities having physical importance is quite efficient.
authors.affiliation: Department of Theoretical Chemistry, Eötvös University, H-1518 Budapest 112, PO Box 32, Hungary.
authors.forename: Gábor
authors.initials: G
authors.lastname: Czakó
authors.forename: Viktor
authors.initials: V
authors.lastname: Szalay
authors.forename: Attila G
authors.initials: AG
authors.lastname: Császár
authors.forename: Tibor
authors.initials: T
authors.lastname: Furtenbacher