High order finite difference algorithms for solving the Schrodinger equation in molecular dynamics

The view of considering global Pseudospectral methods (Sinc and Fourier) as the infinite order limit of local finite difference methods, and vice vers a, finite difference as a certain sum acceleration of the pseudospectral me thods is exploited to investigate high order finite difference algorithms f or solving the Schrodinger equation in molecular dynamics. A Morse type pot ential for iodine molecule is used to compare the eigenenergies obtained by a Sinc Pseudospectral method and a high order finite difference approximat ion of the action of the kinetic energy operator on the wave function. Two- dimensional and three-dimensional model potentials are employed to compare spectra obtained by fast Fourier transform techniques and variable order fi nite difference. It is shown that it is not needed to employ very high orde r approximations of finite differences to reach the numerical accuracy of p seudospectral techniques. This, in addition to the fact that for complex co nfiguration geometries and high dimensionality, local methods require less memory and are faster than pseudospectral methods, put finite difference am ong the effective algorithms for solving the Schrodinger equation in realis tic molecular systems. (C) 1999 American Institute of Physics. [S0021-9606( 99)30147-1].