Ultrafast irradiation can drive the electrons in a material out of thermal equilibrium with the nuclei, producing hot, transient electronic states that modify the interatomic potential energy surface. We present, for the first time, a rigorous formulation of two-temperature molecular dynamics that can accommodate these electronic effects in the form of electronic-temperature-dependent force fields. Such a force field is presented for silicon which is shown to faithfully reproduce the ab initio-derived thermodynamics of the diamond phase for electronic temperatures up to 2.5 eV, as well as the structural dynamics observed experimentally under nonequilibrium conditions in the femtosecond regime. This includes nonthermal melting on a sub-picosecond timescale to a liquid-like state for electronic temperatures above ~ 1 eV. The methods presented in this paper lay a rigorous foundation for the large-scale atomistic modelling of electronically-driven structural dynamics with potential applications spanning the entire field of radiation damage.