Electronic and nuclear motion and their couplings in the presence of a magnetic field

We investigate the performance of an adiabatic separation of electronic and nuclear motion in the presence of a magnetic field and find that the diagonal term of the nonadiabatic coupling elements must be added to the nuclear equation of motion in the Born-Oppenheimer approximation. As an alternative to the Born-Oppenheimer approximation we introduce the so-called screened Born-Oppenheimer approximation which is particularly suited to describe the adiabatic separation of electronic and nuclear degrees of freedom in a magnetic field. A new interpretation of the well-known gauge-centering phases is given. Furthermore, we provide a qualitative discussion of some of the effects of the off-diagonal nonadiabatic coupling elements.