A Basis-Free Phase Space Electronic Hamiltonian That Recovers Beyond Born-Oppenheimer Electronic Momentum and Current Density

TL;DR

This paper introduces a basis-free phase-space electronic Hamiltonian that accurately captures electronic momentum and current density beyond the Born-Oppenheimer approximation, enabling efficient simulations of chiral and spin-related phenomena.

Contribution

It proposes a novel phase-space Hamiltonian that does not rely on atomic orbitals, maintaining momentum conservation and recovering electronic properties beyond traditional methods.

Findings

Maintains momentum conservation in quantum-classical dynamics.

Recovers electronic momentum and current density effectively.

Offers a computationally inexpensive approach for complex simulations.

Abstract

We present a phase-space electronic Hamiltonian $\hat{H}_{PS}$ (parameterized by both nuclear position $\mathbf{X}$ and momentum $\mathbf{P}$) that boosts each electron into the moving frame of the nuclei that are closest in real space -- without presuming the existence of an atomic orbital basis. We show that $(i)$ quantum-classical dynamics along such a Hamiltonian maintains momentum conservation and $(ii)$ diagonalizing such a Hamiltonian can recover the electronic momentum and electronic current density reasonably well. In conjunction with other reports in the literature that such a phase-space approach can also recover vibrational circular dichroism (VCD) spectra, we submit that the present phase-space approach offers a testable and powerful approach to post-Born-Oppenheimer electronic structure theory. Moreover, the approach is inexpensive and can be immediately applied to simulations of chiral induced spin selectivity experiments (where the transfer of angular momentum between nuclei and electrons is considered critical).