Minimal adiabatic approximation of molecular energies

Abstract

The minimal necessary and sufficient condition for Hamiltonians to yield so-called adiabatic energies of molecules is determined and used to formulate the non-perturbative non-variational Minimal Adiabatic Approximation for obtaining them. No finite electronic energy eigenvalues which result from this theory can become accidentally degenerate at any localized configuration of their nuclei, thus establishing a general ‘non-crossing’ rule of overall molecular potentials, which obviates the Jahn-Teller effect entirely on an adiabatic basis. The resulting electronic energy eigenfunctions are single-valued continuous bounded appropriately differentiable functions of their parametric nuclear coordinates and cannot have any geometric phase factor ascribed to them. The ground-state electronic energy eigenfunctions cannot have any phase factors which depend on nuclear configuration affixed to them and still retain their ground-state status. The ground-state electronic energy eigenvalues are bounded from below by those of the Born-Oppenheimer approximation and from above by those of the BornHuang approximation, as are their corresponding ground-state total energies.