Non-adiabatic crossing of energy levels

TLDR

Energy level crossings have long been a subject of debate. The study illustrates key features by examining a polar–homopolar state crossing in a molecule. The authors analyze two electronic eigenfunctions whose polar and homopolar character exchange as the internuclear distance R passes through a critical value R₀. At R = R₀ the eigenfunctions exchange their polar and homopolar characteristics.

Abstract

The crossing of energy levels has been a matter of considerable discussion. The essential features may be illustrated in the crossing of a polar and homopolar state of a molecule. Let ψ 1 ( x /R), ψ 2 ( x /R) be two electronic eigenfunctions of a molecule with stationary nuclei. Let these eigenfunctions have the property that for R≫R 0 , ψ 1 has polar characteristics, ψ 2 homopolar; while at R≪R 0 , ψ 2 has polar characteristics, ψ 1 homopolar. In the region R=R 0 these two eigenfunctions may be said to exchange their characteristics.