Generalized Born–Oppenheimer treatment of Jahn–Teller systems in Hilbert spaces of arbitrary dimension: theory and application to a three-state model potential

Abstract

Generalized Born–Oppenheimer equations including the geometrical phase effect are derived for three- and four-fold electronic manifolds in Jahn–Teller systems near the degeneracy seam. The method is readily extendable to N-fold systems of arbitrary dimension. An application is reported for a model threefold system, and the results are compared with Born–Oppenheimer (geometrical phase ignored), extended Born–Oppenheimer, and coupled three-state calculations. The theory shows unprecedented simplicity while depicting all features of more elaborated ones.