Accurate mapped trigonometric discrete variable representations for Coulomb singularities in molecules: Applications with H-2(+) and H-2 in cylindrical coordinates

Mapped discrete variable representations using the sine and cosine polynomials are purposed to accurately solve the stationary electronic Shrodinger equation of molecules. In this method, the grid points densely cluster around the positions of the nuclei but sparse enough in other regions. The electronic states of H-2(+) and H-2 molecules are calculated by a preconditioned inexact spectral transform method in cylindrical coordinates for illustrating. A spectral convergence behaviour of eigenvalues of the electronic state of the H-2(+) molecule but slower convergence behaviour for the H-2 molecule are observed, due to the repulsive singularity between electrons in the H-2 molecule. (C) 2014 Elsevier B.V. All rights reserved