  A novel treatment of non-adiabatic couplings is proposed. The derivation
starts from the long-known, but not well-known, fact that the wave function of
the complete system of elctrons and nuclei can be written, without
approximation, as a Born-Oppenheimer-type product of a nuclear wavefunction,
X(R), and an electronic one, Phi_R(r), which depends parametrically on the
nuclear configuration R. From the variational principle we deduce formally
exact equations for Phi_R(r) and X(R). The algebraic structure of the exact
nuclear equation coincides with the corresponding one in the adiabatic
approximation. The electronic equation, however, contains terms not appearing
in the adiabatic case, which couple the electronic and the nuclear
wavefunctions and account for the electron-nuclear correlation beyond the
Born-Oppenheimer level. It is proposed that these terms can be incorporated
using an optimized local effective potential.
