Zero-point motion of molecules: beyond Born-Oppenheimer

We have recently developed a new time-dependent density-functional theory (TDDFT)-based non-Born-Oppenheimer method for computing electron-ion structure of atomistic systems in the path integral formalism. We discuss our implementation of this exact (within the accuracy of DFT) method with a localized basis set approach. The method and the implementation can be used for both molecules and solids. First we apply this method to compute electron-ion states and zero-point energies of small molecules. Next we compare the results of these computations to results obtained from the standard (Born-Oppeheimer-based) path-integral methods used in the field. We demonstrate that at low temperatures the error of the standard path-integral approaches is large even for the systems with wide bandgaps. We discuss potential areas of applicability of our method.