A real-space perturbation theory for electronic correlation

We introduce a method for treating electronic correlation in which a correlation factor is optimized using Hylleraas variational perturbation theory. The factor is defined by a number of parameters which grows only linearly with system size. We test the theory on two-electron atoms using the shielded-nucleus Hamiltonian at zeroth order, obtaining −2.9035 a.u. for helium. The convergence of the method is investigated, and energies and intracule densities are compared with accurate variational results. The application of the theory to an N-electron problem with a Hartree–Fock Hamiltonian at zeroth order is discussed.