Full minimal coupling in the self-consistent Maxwell-TDDFT first principles framework

In the realm of quantum chemistry and materials science, the dipole approximation (DA) is by far the most widely used treatment of light-matter coupling, owing to the typically longer wavelength of light compared to the size of the matter system. However, in many relevant situations, in particular dealing with nanoplasmonics and non-equilibrium quantum matter, local fields arise upon interaction with external fields, with spatial features that can be no longer be considered in the long wavelength limit. Moreover, core level spectroscopies which demand UV or x-ray pulses cannot be treated within this approximation either. Going beyond the DA to properly account for the self-induced fields is then relevant, but their theoretical treatment is challenging.



In this work, we propose an efficient fully ab initio approach to couple electrons, nuclei and photons based on a density-functional reformulation of the non-relativistic Pauli-Fierz Hamiltonian of quantum electrodynamics, taking the mean field approximation for the nuclei and photons, and accounting for the full spatial and time dependence of the electromagnetic fields in the so-called full minimal coupling Hamiltonian. This implies solving numerically the coupled Ehrenfest–Maxwell–Pauli–Kohn–Sham equations derived in Ref. [1]. This method has been recently implemented in the Octopus package [2], where the time dependent Kohn-Sham equations are solved self-consistently alongside Maxwell’s equations re-written in the Riemann-Silberstein formulation. By doing so, their equation of motion becomes a Schrödinger-type of equation with inhomogenous terms, given by the total current density from the matter system. By simulation of light-driven molecular systems, we illustrate the emergent features of such a full minimal coupling and assess the accuracy of approximate light-matter coupling terms arising from different orders of the multipole expansion, namely electric-dipole and electric-quadrupole/magnetic-dipole terms.



[1] R. Jestädt, M. Ruggenthaler, M.J.T. Oliveira, A. Rubio, and H. Appel. Adv. Phys. 68:4, 225 (2019)

[2] N. Tancogne-Dejean, M. J. T. Oliveira, et al. J. Chem. Phys. 152, 124119 (2020)