Electromagnetic fields and dielectric response in empirical tight-binding theory

Relativistic and nonrelativistic empirical tight-binding theory is generalized to incorporate time-dependent electromagnetic fields in a gauge-invariant manner that does not introduce any extra adjustable parameters. Based on this approach, it is shown that explicit expressions can be derived for the effective mass tensor, the effective Land\'e g factor, the current, the frequency-dependent transverse dielectric function, and the wave-vector- and frequency-dependent longitudinal dielectric function. A finite basis analogue of the optical f-sum rule is derived and shown to impose a condition on tight-binding parameters.