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

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Abstract
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 total wave-function is single valued. The compensation occurs in a manner that keeps the energy of the state continuous even across a `topological transition', 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 conical intersection of potential surfaces. The consistency of the method is illustrated by Gedankenexperiments in a non-symmetric Jahn-Teller situation and a spin-orbit coupled doublet.