Non-adiabatic crossing of energy levels

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 ψ1 (x/R), ψ2 (x/R) be two electronic eigenfunctions of a molecule with stationary nuclei. Let these eigenfunctions have the property that for R≫R0, ψ1 has polar characteristics, ψ2 homopolar; while at R≪R0, ψ2 has polar characteristics, ψ1 homopolar. In the region R=R0 these two eigenfunctions may be said to exchange their characteristics.