  We prove existence and uniqueness of solutions to the initial-value problem
associated with a class of time-dependent Kohn-Sham equations coupled with
Newtonian nuclear dynamics. We consider a pure power exchange term within a
generalisation of the Local Density Approximation (LDA), identifying a range of
exponents for the existence and uniqueness of $H^2$ solutions to the Kohn-Sham
equations.
