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We introduce a method to carry out zero-temperature calculations withindensity functional theory (DFT) but without relying on the Born-Oppenheimer(BO) approximation for the ionic motion. Our approach is based on thefinite-temperature many-body path-integral formulation of quantum mechanics bytaking the zero-temperature limit and treating the imaginary-time propagationof the electronic variables in the context of DFT. This goes beyond thefamiliar BO approximation and is limited from being an exact treatment of bothelectrons and ions only by the approximations involved in the DFT component. Wetest our method in two simple molecules, H$_2$ and benzene. We demonstrate thatthe method produces a difference from the results of the BO approximation whichis significant for many physical systems, especially those containing lightatoms such as hydrogen; in these cases, we find that the fluctuations of thedistance from its equilibrium position, due to the zero-point-motion, iscomparable to the interatomic distances. The method is suitable for use withconventional condensed matter approaches and currently is implemented on top ofthe periodic pseudopotential code SIESTA.

Density functional theory beyond the Born-Oppenheimer approximation: accurate treatment of the ionic zero-point motion