  We introduce a method to carry out zero-temperature calculations within
density functional theory (DFT) but without relying on the Born-Oppenheimer
(BO) approximation for the ionic motion. Our approach is based on the
finite-temperature many-body path-integral formulation of quantum mechanics by
taking the zero-temperature limit and treating the imaginary-time propagation
of the electronic variables in the context of DFT. This goes beyond the
familiar BO approximation and is limited from being an exact treatment of both
electrons and ions only by the approximations involved in the DFT component. We
test our method in two simple molecules, H$_2$ and benzene. We demonstrate that
the method produces a difference from the results of the BO approximation which
is significant for many physical systems, especially those containing light
atoms such as hydrogen; in these cases, we find that the fluctuations of the
distance from its equilibrium position, due to the zero-point-motion, is
comparable to the interatomic distances. The method is suitable for use with
conventional condensed matter approaches and currently is implemented on top of
the periodic pseudopotential code SIESTA.
