An efficient new method for calculating eigenvalues and spectra of van der Waals complexes

Abstract

We present a new method of solving the Schrödinger equation for vibration–rotation levels of van der Waals complexes, which exploits a novel way of avoiding problems associated with poor convergence of radial basis sets. This ‘‘iterative secular equation’’ or ISE method is based on the secular equation/perturbation theory approach of Hutson and Le Roy [J. Chem. Phys. 83, 1197 (1985)]. It begins with a secular equation built from a small radial basis set which provides an initial approximation to the state of interest, and then uses a perturbation theory approach to determine optimal improvements to this initial basis set, iterating until the solution is converged. While it effectively solves the close coupled equations for the system of interest, the growth of computational effort with the number of coupled channels N is distinctly slower than the N3 behavior associated with conventional close coupling calculations. The present implementation also obtains solutions for a few states at a time, a feature that makes it particularly efficient when only a small number of states are of interest. The new method is illustrated by application to truly bound levels of the Ar–HCl complex and to predissociating levels of the He–HF and He–C2H2 complexes.