Lower Bounds for Energy Levels of Molecular Systems

Abstract

It is shown that the Hamiltonian H for a molecule in which the nuclei are regarded as fixed has the form H = Σ Hα + H′, where H′ is positive and each Hα has known eigenvalues and eigenvectors. A procedure is developed for the calculation of lower bounds to the eigenvalues of H. The optimization of the procedure and the existence of the eigenvalues are discussed.