Full minimal coupling Maxwell-TDDFT: An ab initio framework for light-matter interaction beyond the dipole approximation

We report an , nonrelativistic QED method that couples light and matter self-consistently beyond the electric dipole approximation and without multipolar truncations. This method is based on an extension of the Maxwell-Pauli-Kohn-Sham approach to a full minimal coupling Hamiltonian, where the space- and time-dependent vector potential is coupled to the matter system, and its back reaction to the radiated fields is generated by the full current density. The implementation in the open-source code is designed for massively parallel multiscale simulations considering different grid spacings for the Maxwell and matter subsystems. Here, we show applications of this framework to simulate renormalized Cherenkov radiation of an electronic wave packet, magneto-optical effects with nonchiral light in nonchiral molecular systems, and renormalized plasmonic modes in a nanoplasmonic dimer. We show that in some cases, the beyond-dipole effects cannot be captured by a multipolar expansion Hamiltonian in the length gauge. Finally, we discuss further opportunities enabled by the framework in the field of twisted light and orbital angular momentum, inelastic light scattering, and strong-field physics. Published by the American Physical Society 2025