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We show how to significantly reduce the number of energy bands required tomodel the interaction of light with crystalline solids in the velocity gauge.We achieve this by deriving analytical corrections to the electric currentdensity. These corrections depend only on band energies, the matrix elements ofthe momentum operator, and the macroscopic vector potential. Thus, thecorrections can be evaluated independently from modeling the interaction withlight. In addition to improving the convergence of velocity-gauge calculations,our analytical approach overcomes the long-standing problem of divergences inexpressions for linear and nonlinear susceptibilities.

Adiabatic corrections for velocity-gauge simulations of electron dynamics in periodic potentials