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Based on the work done by an electromagnetic field on an atomic or molecularelectronic system, a general gauge invariant formulation of transientabsorption spectroscopy is presented within the semi-classical approximation.Avoiding multipole expansions, a computationally viable expression for thespectral response function is derived from the minimal-coupling Hamiltonian ofan electronic system interacting with one or more laser pulses described by asource-free, enveloped electromagnetic vector potential. With a fixed-basisexpansion of the electronic wave function, the computational cost ofsimulations of laser-driven electron dynamics beyond the dipole approximationis the same as simulations adopting the dipole approximation. We illustrate thetheory by time-dependent configuration interaction and coupled-clustersimulations of core-level absorption and circular dichroism spectra.

Transient spectroscopy from time-dependent electronic-structure theory without multipole expansions