Using a pruned basis, a non-product quadrature grid, and the exact Watson normal-coordinate kinetic energy operator to solve the vibrational Schrödinger equation for C2H4

Abstract

In this paper we propose and test a method for computing numerically exact vibrational energy levels of a molecule with six atoms. We use a pruned product basis, a non-product quadrature, the Lanczos algorithm, and the exact normal-coordinate kinetic energy operator (KEO) with the π(t)μπ term. The Lanczos algorithm is applied to a Hamiltonian with a KEO for which μ is evaluated at equilibrium. Eigenvalues and eigenvectors obtained from this calculation are used as a basis to obtain the final energy levels. The quadrature scheme is designed, so that integrals for the most important terms in the potential will be exact. The procedure is tested on C(2)H(4). All 12 coordinates are treated explicitly. We need only ~1.52 × 10(8) quadrature points. A product Gauss grid with which one could calculate the same energy levels has at least 5.67 × 10(13) points.