Quantum-Electrodynamical Time-Dependent Density Functional Theory. I. A Gaussian Atomic Basis Implementation

TL;DR

This paper introduces a Gaussian basis implementation of QED-TDDFT that models electron-photon interactions in optical cavities, highlighting the importance of higher-energy states in strong coupling regimes.

Contribution

It presents a novel implementation of QED-TDDFT using dimensionless amplitudes and a symmetric coupling matrix, enabling detailed analysis of electron-photon states.

Findings

Higher-energy off-resonance states significantly influence polariton energies.

The implementation facilitates future development of analytic derivatives.

Effects of dipole self-energy and approximations on eigenstates are analyzed.

Abstract

Inspired by the formulation of quantum-electrodynamical time-dependent density functional theory (QED-TDDFT) by Rubio and coworkers, we propose an implementation that uses dimensionless amplitudes for describing the photonic contributions to QED-TDDFT electron-photon eigenstates. The leads to a symmetric QED-TDDFT coupling matrix, which is expected to facilitate the future development of analytic derivatives. Through a Gaussian atomic basis implementation of the QED-TDDFT method, we examined the effect of dipole self-energy, rotating wave approximation, and the Tamm-Dancoff approximation on the QED-TDDFT eigenstates of model compounds (ethene, formaldehyde, and benzaldehyde) in an optical cavity. We highlight, in the strong coupling regime, the role of higher-energy and off-resonance excited states with large transition dipole moments in the direction of the photonic field, which are automatically accounted for in our QED-TDDFT calculations and might substantially affect the energy and composition of polaritons associated with lower-energy electronic states.