Compensation of the electronic geometric phase by the nuclear part of the wave-function

The nuclear equation in the Born-Oppenheimer scheme for electron-ion bound states is solved by a method that ensures that the nuclear part compensates for the geometrical (Berry) phase in the electronic part and that the tota l wave-function is single valued. The compensation occurs in a manner mat k eeps the energy of the state continuous even across a 'topological transiti on', i.e. for a change of parameters that removes the electronic degeneracy . The method ties the phase to the behaviour of the nuclear part near the c onical intersection of potential surfaces. The consistency of the method is illustrated by Gedankenexperiments in a non-symmetric Jahn-Teller situatio n and a spin-orbit coupled doublet.