On the Combination of TDDFT with Molecular Dynamics: New Developments

In principle, we should not need the time-dependent extension of density-functional theory (TDDFT) for excitations, and in particular not for Molecular Dynamics (MD) studies: the theorem by Hohenberg and Kohn teaches us that for any observable that we wish to look at (including dynamical properties or observables dependent on excited states) there is a corresponding functional of the ground-state density. Yet the unavailability of such magic functionals in many cases (the theorem is a non-constructive existence result) demands the development and use of the alternative exact reformulation of quantum mechanics provided by TDDFT. This theory defines a convenient route to electronic excitations and to the dynamics of a many-electron system subject to an arbitrary time-dependent perturbation. This is, in fact, the main purpose of inscribing TDDFT in a MD framework -the inclusion of the effect of electronic excited states in the dynamics. However, as we will show in this review, it may not be the only use of TDDFT in this context. In this manuscript, we review two recent proposals: In Section 1.2, we show how TDDFT can be used to design efficient gsBOMD algorithms -even if the electronic excited states are in this case not relevant. The work described in Section 1.3 addresses the problem of mixed quantum-classical systems at thermal equilibrium.