Geometric phase in two Kramers doublets molecular systems

The geometric phase in two Kramers doublets molecular systems is considered. We obtain the general formula for the gauge potential arising from the vibronic interaction and spin–orbit interaction between two Kramers doublet electronic levels. Simple models for the Jahn–Teller and Renner–Teller problems with spin–orbit coupling are considered. It is demonstrated that the energy spectra obtained by the Born–Oppenheimer approximation with the gauge potential agree quite well with the exact energy spectra in strong vibronic cases. It is also shown that the inclusion of the scalar gauge potential is important in order to obtain accurate zero point energy. As an application, vibronic levels of the X̃ 2E′ state of Cu3 are reexamined including spin–orbit interaction.