Abstract
It is shown that a time-dependent single particle potential ν 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 ν-representable electronic density n( rt) and ionic displacement R(lKt) , are determined so that a map (ν e , F)→(n, R) is invertible. This formulation allows us to ad dress 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 fictitous 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.
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