Treating the motion of nuclei and electrons in atomic and molecular quantum mechanical calculations on an equal footing: Non-Born–Oppenheimer quantum chemistry

The Born–Oppenheimer (BO) approximation is the bedrock of quantum mechanical calculations of atomic and molecular systems. However, there are effects in these systems that require departure from the BO approximations. We start this review with describing these effects and some of the previous works where calculations were performed to account for their magnitude in various atomic and molecular properties. In particular, the problem of selecting appropriate basis functions for non-BO calculations is analyzed and some examples of such calculations are presented. The last part of this review is devoted to perspectives in carrying out quantum mechanical studies of structures, spectra, and other properties of atoms and molecules in isolation and in confinement and treating both nuclei and electrons in these studies on on equal footing.