A Lorenz gauge formulation for TDDFT

TL;DR

This paper extends TDDFT to include electrodynamic fields using Lorenz gauge, enabling more accurate simulations of molecular responses to electromagnetic stimuli with preserved gauge-invariance.

Contribution

It introduces a Lorenz gauge formulation for TDDFT, incorporating retarded potentials and a computationally efficient method for evaluating them.

Findings

Successful application to small molecules like water and benzene

Demonstrates gauge-invariance in weak magnetic fields

Provides a practical approach for electrodynamic TDDFT simulations

Abstract

We describe the inclusion of electrodynamic fields in Time-Dependent Density Functional Theory (TDDFT) by incorporating both the induced scalar and vector potentials within the time-dependent Kohn-Sham equation. The Hamiltonian is described in both the Coulomb and Lorenz gauges, and the advantages of the latter are outlined. Integral expressions are defined for the retarded potentials of each gauge and a methodological approach to evaluate these nontrivial expressions with low computational cost is adopted. Various molecular structures of relatively small sizes are studied, including water, benzene, and conductive carbon chains. Absorption cross sections resulting from both pulse and boost excitations suggest a preserved gauge-invariance of the proposed formal approach to TDDFT in the weak magnetic field limit.