Program package for numerical solving time-independent Schrödinger equation for vibrational problems: Inclusion of coordinate dependent reduced masses

Abstract

In this article an improved program package for variational solving of the time-independent Schrödinger equation (SE) is presented. The program is coded in FORTRAN-95 and is aimed to solve the vibrational SE on a generalized potential energy hypersurface (PES), typically constructed pointwise by quantum chemical calculations. The procedure consists of fitting of the hypersurface to either cubic splines or displaced Gaussians. The central part is the discrete representation of the vibrational Hamiltonian on a uniform grid according to the Fourier Grid Hamiltonian (FGH) scheme. The FGH is tuned for expression of the vibrational problem in terms of generalized internal coordinates (bond distances, angles, torsions, etc.), which is the most convenient and hence widely used representation for chemical systems. In the formalism of generalized internal coordinates the reduced masses assume quite a sophisticated coordinate-dependent form. The FGH matrix is diagonalized and its eigenvalues and eigenfunctions are analyzed giving rise to observables that can be compared with the experimental data (vibrational spectroscopy in the first place). We tested the package for three distinct chemical problems; namely, the umbrella inversion of ammonia, OH stretching motion of sodium hydrogen bissulfate, and hydrogen dynamics in soybean lipoxygenaze-1 (SLO-1), yielding good agreement with the available experimental and previously published computational data. The program package is available from the authors on request.