Efficient evaluation of one-center three-electron Gaussian integrals

An algorithm is presented for the efficient evaluation of two types of one-center three-electron Gaussian integrals. These integrals are required to avoid the resolution-of-identity (RI) approximation in explicitly correlated linear R12 methods. Without the RI approximation, it is possible to enforce rigorously the strong orthogonality of the second-order Moller-Plesset R12 ansatz. A test calculation is performed using atomic Gaussian-type orbitals of the neon atom.