Comparison between a generalized electronic diabatic approach and the Born-Oppenheimer separation scheme in inertial frames

We discuss a generalized electronic diabatic (GED) approach to diagonalize the exact Hamiltonian of an n-electron system which embeds an "external" background of positive charges. This Hamiltonian, denoted by H-e(q, xi), is defined in an inertial frame, and it contains a quantum part ( the electrons with coordinates q) and a classical part ( the external charges in a three-dimensional configuration xi). We derive a GED basis set {psi(k)(q)} using an operator H-e(q, xi(0)) for a single configuration xi(0), and then show that these are also eigenfunctions for any other H-e( q, xi); only the ordering of eigenvalues may depend on xi (i.e., k = k(xi)). The GED functions can also be used to represent the eigenstates of a fully quantum-mechanical system of electrons and nuclei. We discuss briefly the differences between the present procedure and the standard Born - Oppenheimer (BO) technique in the "clamped-nuclei" approximation. As illustration, we show how chemical changes emerge as transitions among diabatic states mediated by an electromagnetic field.