MINIMAL ADIABATIC APPROXIMATION OF MOLECULAR-ENERGIES

The minimal necessary and sufficient condition for Hamiltonians to yie ld so-called adiabatic energies of molecules is determined and used to formulate the non-perturbative non-variational Minimal Adiabatic Appr oximation for obtaining them. No finite electronic energy eigenvalues which result from this theory can become accidentally degenerate at an y localized configuration of their nuclei, thus establishing a general 'non-crossing' rule of overall molecular potentials, which obviates t he Jahn-Teller effect entirely on an adiabatic basis. The resulting el ectronic energy eigenfunctions are single-valued continuous bounded ap propriately differentiable functions of their parametric nuclear coord inates and cannot have any geometric phase factor ascribed to them. Th e ground-state electronic energy eigenfunctions cannot have any phase factors which depend on nuclear configuration affixed to them and stil l retain their ground-state status. The ground-state electronic energy eigenvalues are bounded from below by those of the Born-Oppenheimer a pproximation and from above by those of the Born-Huang approximation, as are their corresponding ground-state total energies.