Born-oppenheimer and non-born-oppenheimer, atomic and molecular calculations with explicitly correlated gaussians

The current state of efforts to use explicitly correlated Gaussian functions (ECGs) in calculations of small atomic and molecular systems with very high accuracy is studied. Such high accuracy can be achieved either by performing very precise Born-Oppenheimer (BO) calculations and correcting the results for adiabatic and nonadiabatic effects or by treating the nuclei and electrons on equal footing and explicitly including their motions in the Hamiltonian and in the wave function. It is shown that by using large basis sets of ECGs and by variationally optimizing their nonlinear parameters with a method based on the analytical energy gradient it is possible to determine the energies of ground and excited states of these systems with an accuracy approaching the accuracy of the most precise experimental measurements. In moving forward with the development of ECG techniques for very accurate BO and non-BO atomic and molecular calculations, several directions need to be considered.