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 C2H4s

摘要

In this paper we propose and test a method for computing numerically exact vibrational energynlevels of a molecule with six atoms. We use a pruned product basis, a non-product quadrature, thenLanczos algorithm, and the exact normal-coordinate kinetic energy operator (KEO) with the πtnμπnterm. The Lanczos algorithm is applied to a Hamiltonian with a KEO for which μ is evaluated atnequilibrium. Eigenvalues and eigenvectors obtained from this calculation are used as a basis to obtainnthe final energy levels. The quadrature scheme is designed, so that integrals for the most importantnterms in the potential will be exact. The procedure is tested on C2H4. All 12 coordinates are treatednexplicitly.We need only ∼1.52 × 108nquadrature points. A product Gauss grid with which one couldncalculate the same energy levels has at least 5.67 ×1013npoints. © 2011 American Institute of Physics.