Scalar relativistic explicitly correlated R12 methods.

Combinations of explicitly correlated R12 wave functions with relativistic Douglas-Kroll-Hess (DKH) Hamiltonians are discussed. We considered several ways to incorporate the relativistic terms into the second-order Moller-Plesset R12 method and applied them to the helium isoelectronic series to investigate their accuracy and numerical stability. Among the approaches are the evaluation of the relativistic terms via double resolution-of-the-identity and the explicit evaluation of all terms up to O(c(-4)) using the Pauli Hamiltonian. Numerical collapse of the latter can be avoided if the R12 amplitudes are determined by Kato's cusp condition. Closed formulas for new two-electron integrals that include the mass-velocity term have been derived and implemented into the LIBINT2 integral library. The proposed approaches are not restricted to DKH and can be combined with other one- and two-component relativistic Hamiltonians.