Efficient electromagnetic potential calculations within ground state and time dependent density functional theory.*

Electromagnetic potentials play a fundamental role in ground and excited state calculations of Density Functional Theory (DFT). One method for the calculation of such potentials is to directly solve their corresponding differential equations. In this work, the equivalent integral expressions of those potentials are evaluated within their spectral representation. Such integral expressions play a critical role in handling problems ranging from hybrid functionals to the calculation of retarded potentials within the time-dependent Kohn-Sham equation. The simplest of these are FFT procedures used to evaluate the static Poisson integral within ground-state calculations. We extend the use of these integral expressions to time-dependent retarded electromagnetic potentials in both the Lorenz and Coulomb gauges and demonstrate the efficiency of the approach. We use this method for the calculation of several electronic structures using a real-time real-space TDDFT approach. Finally, the various gauge-fixing conditions are compared to assure alignment in the limit of small magnetic fields and the advantages of the Lorenz gauge are outlined.