Gaussian basis set approach to one-loop self-energy

We report a method for the evaluation of the one-loop self-energy, to all orders in the external binding field, using a Gaussian basis set expansion. This choice of basis is motivated by its widespread use in molecular calculations. For a one-electron atom, our results show excellent agreement with those obtained using the exact Dirac--Coulomb wave functions. The developed method can be of interest for high-precision studies of heavy few-electron molecular systems, where the rigorous computation of QED corrections is currently a formidable task.