  We show that the time dependent single electron, nuclear density matrix of an
interacting electronic system coupled to nuclear degrees of freedom can be
exactly reproduced by that of an electronic system with arbitrarily specified
electron-electron interactions coupled to the same nuclear degrees of freedom,
given the initial density matrix of the interacting system. This formalism
enables the construction of rigorous time dependent density functional theories
to study nonadiabatic electronic dynamics. We obtain the Runge-Gross and Van
Leeuwen theorems as special cases in the adiabatic limit.
