Integrals for non-Born-Oppenheimer calculations of molecules with three nuclei

Variational molecular calculations without assuming the Born-Oppenheimer approximation of states corresponding to zero total angular momentum require the use of spherically symmetric basis functions explicitly depending on the electron-electron, electron-nucleus, and nucleus-nucleus distances. In our calculations, such functions have been the explicitly correlated Gaussians. For molecules with three nuclei, the Gaussians have to be multiplied by powers of all three internuclear distances to describe the highly correlated motion of the nuclei. In this work we have derived formulae for the overlap and the Hamiltonian matrix elements for such basis functions. Implementation of the formulae presents some unconventional numerical difficulties related to maintaining the required precision of the calculation. The implementation problems are discussed.