Partial diagonalization in solving electron-nuclear problems in molecules

Abstract

The problem of determining the total wave functions and energies of molecular stationary states reduces to solving a Schrödinger equation with a vibrational-rotational Hamiltonian. This is achieved by a unitary transformation of the molecular Hamiltonian H with its successive diagonalization on a nondegenerate electronic state ¦e〉. It is shown that the molecular wave functions related to the electronic states ¦e〉 are of the form G¦e〉¦g〉_(e), and their corresponding energy value is the sum ɛ_e + ɛ_g ^(e), where ɛ ^(e)_g and ¦g〉^(e) are the eigenvalues and eigenfunctions of the vibrational-rotational Hamiltonian, determined by means of the unitary operator G. It is shown that the total energy and molecular wave functions are uniquely determined, despite the arbitrariness in choosing G. As an example the vibrational-rotational operator and molecular wave functions are given for the simplest choice of the operator G.