Adiabatic electronic flux density: a Born-Oppenheimer Broken Symmetry ansatz

TL;DR

This paper introduces a novel Born-Oppenheimer broken symmetry ansatz that generates a non-zero electronic flux density consistent with nuclear quantum dynamics, addressing a long-standing issue in electronic flux calculations.

Contribution

The authors propose a computationally inexpensive ansatz using pairwise anti-symmetrically translated vibronic densities to approximate electronic flux density within the Born-Oppenheimer framework.

Findings

Correct nodal structure of flux density in ${ m H}_2^+$

Symmetry properties preserved at all times

Flux density derived from standard quantum chemistry outputs

Abstract

The Born-Oppenheimer approximation leads to the counterintuitive result of a vanishing electronic flux density upon vibrational dynamics in the electronic ground state. To circumvent this long known issue, we propose using pairwise anti-symmetrically translated vibronic densities to generate a symmetric electronic density that can be forced to satisfy the continuity equation approximately. The so-called Born-Oppenheimer broken symmetry ansatz yields all components of the flux density simultaneously while requiring only knowledge about the nuclear quantum dynamics on the electronic adiabatic ground state potential energy surface. The underlying minimization procedure is transparent and computationally inexpensive, and the solution can be computed from the standard output of any quantum chemistry program. Taylor series expansion reveals that the implicit electron dynamics originates from non-adiabatic coupling to the explicit Born-Oppenheimer nuclear dynamics. The new approach is applied to the ${\rm H}_2^+$ molecular ion vibrating in its ${}^2\Sigma^+_g$ ground state. The electronic flux density is found to have the correct nodal structure and symmetry properties at all times.