Efficient pointwise representations for vibrational wave functions: Eigenfunctions of H+3

Abstract

The successive truncation–diagonalization method described in previous work [Z. Bac̆ić, R. M. Whitnell, D. Brown and J. C. Light, Comp. Phys. Comm. (to be published)] is generalized to a three‐dimensional discrete variable representation (DVR). The use of the 3D DVR leads to a sparse Hamiltonian matrix that makes the transformations used in the successive truncation‐diagonalization technique very efficient. The method is applied to J=0 H+ 3 using a hyperspherical coordinate system. Full symmetry adaptation of the DVR is used allowing a complete resolution of the vibrational eigenfunctions into the D 3h irreducible representations. Converged eigenvalues up to ∼20 000 cm− 1 are reported for all representations. This method is thereby shown to be both efficient and accurate for calculating triatomic vibrational states with large amplitude motion.