Electronic non-adiabatic states

TL;DR

This paper introduces a new theoretical framework for non-adiabatic states in electron-nuclear systems, deriving exact coupled equations that extend the Born-Oppenheimer approximation by including electron-nuclear correlation effects.

Contribution

It presents a formal derivation of exact equations for electronic and nuclear wavefunctions that incorporate non-adiabatic couplings beyond the traditional Born-Oppenheimer approximation.

Findings

Derived formally exact coupled equations for electron-nuclear wavefunctions.

Identified additional terms coupling electronic and nuclear states beyond adiabatic approximation.

Proposed incorporating these terms via an optimized local effective potential.

Abstract

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.