A Phase-Space Electronic Hamiltonian for Molecules in a Static Magnetic Field II: Quantum Chemistry Calculations with Gauge Invariant Atomic Orbitals

TL;DR

This paper develops a gauge-invariant phase-space electronic Hamiltonian for molecules in magnetic fields, enabling practical quantum chemistry calculations that reveal novel magnetic phenomena such as non-zero electronic motion in ground states.

Contribution

It introduces a method to implement a phase-space Hamiltonian with gauge invariant atomic orbitals in quantum chemistry software, advancing the study of molecules in magnetic fields.

Findings

Observation of minimum energy structures with non-zero electronic momentum

Implementation of gauge invariant atomic orbitals in Q-Chem

Detection of non-zero electronic motion in ground states

Abstract

In a companion paper, we have developed a phase-space electronic structure theory of molecules in magnetic fields, whereby the electronic energy levels arise from diagonalizing a phase-space Hamiltonian $\hat H_{PS}(\bf{X},\bf{\Pi})$ that depends parametrically on nuclear position and momentum. The resulting eigenvalues are translationally invariant; moreover, if the magnetic field is in the $z-$direction, then the eigenvalues are also invariant to rotations around the $z-$direction. However, like all Hamiltonians in a magnetic field, the theory has a gauge degree of freedom (corresponding to the position of the magnetic origin in the vector potential), and requires either $(i)$ formally, a complete set of electronic states or $(ii)$ in practice, gauge invariant atomic orbitals (GIAOs) in order to realize such translational and rotational invariance. Here we describe how to implement a phase-space electronic Hamiltonian using GIAOs within a practical electronic structure package (in our case, Q-Chem). We further show that novel phenomena can be observed with finite $\bf{B}-$fields, including minimum energy structures with $\bf{\Pi}_{min} \ne 0$, indicating non-zero electronic motion in the ground-state.