Avoided Crossings in Bound Potential-Energy Curves of Diatomic Molecules: Derivation and Analysis of the Vibrational Hamiltonian

Abstract

As a first step in analyzing the effect of an avoided crossing on the spectrum of a diatomic molecule, a formalism is presented for dealing with the vibrational problem. A mathematically well‐defined procedure is given for going from potential curves exhibiting an avoided crossing (such as would be obtained by solving exactly the eigenvalue problem associated with the complete electronic Hamiltonian for fixed nuclei) to two crossing potential curves and an interaction function. These latter curves, though less meaningful physically than the former, lead to a pair of relatively simple coupled differential equations (similar to those arising in other vibronic problems) which must be solved to determine the vibrational wavefunctions and energy levels. The order of magnitude and mass dependence of the interaction terms in the coupled differential equations are examined.