A TIME-DEPENDENT FUNCTIONAL THEORY FOR THE ELECTRON-ION SYSTEM

It is shown that a time-dependent single particle potential upsilon(e) (rt) and a time-dependent force on the ion F(lkt) with a given fixed initial state of the combined electron-ion system, leading respectively to a given v-representable electronic density n(rt) and ionic displacement R(lkt), are determined so that a map (upsilon(e),F) --> (n,R) is invertible. This formulation allows us to address the effective self-consistent ion dynamics of the electron-ion system in contrast to existing treatments such as those based on the Car-Parrinello approach by replacing the fictitious Lagrangian introduced there by a precise action principle. Based on this, some schemes are derived to calculate the density, the displacement, etc. using the stationary action principle and some convenient choices of a suitably parametrised state vector.