Nonrelativistic non-Born–Oppenheimer approach for calculating atomic and molecular spectra using all-particle explicitly correlated Gaussian functions

Very accurate calculations of atomic and molecular spectra require accounting for the coupling of the motions of the nuclei and electrons. To fully account for the nucleus–electron coupling, the nuclei and electrons forming the system have to be treated on an equal footing without assuming the Born–Oppenheimer approximation (non-BO). This can be done by first separating out the Hamiltonian representing the motion of the center of mass from the total nonrelativistic Hamiltonian of the system and then using in the calculation the remaining part of the Hamiltonian that represents the system's internal state. In this work, we review some recent developments of methods by our group for non-BO calculations of atoms and molecules and the results obtained in these calculations. In particular, the review focuses on the challenges of the non-BO calculations and ways to overcome these challenges.