Adding configuration interaction to the time-dependent Hartree grid approximation

Abstract

The time-dependent Hartree grid (TDHG) method is extended into an ab initio algorithm for obtaining exact quantum wave packet dynamics. The new algorithm employs a superposition of orthogonal zeroth order time-dependent basis functions generated from a single TDHG wave packet trajectory. The superposition coefficients are themselves time-dependent, and are responsible for mixing the basis functions in such a way as to represent exact solutions of the time-dependent Schrodinger equation. Evolution of the superposition coefficients is governed by a set of first-order linearly coupled ordinary differential equations. The couplings between coefficients are given by matrix elements of a naturally identified interaction potential taken between members of the zeroth order basis. In numerical tests involving computation of S-matrix elements for collinear inelastic atom–Morse oscillator scattering the method proves accurate, flexible and efficient, and appears to be easily extendable to more complicated systems.