Abstract

We prove short-time 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, combining Yajima’s theory for time-dependent Hamiltonians with Duhamel’s principle, based on suitable Lipschitz estimates. We consider a pure power exchange term within a generalisation of the so-called Local Density Approximation (LDA), identifying a range of exponents for the existence and uniqueness of solutions to the Kohn–Sham equations.