Resolutions of the Coulomb operator. Part III. Reduced-rank Schrödinger equations.

We consider a modified Schrödinger equation wherein the electron-electron repulsion terms r(ij)(-1) are approximated by truncated one-particle resolutions. Numerical results for the He atom and H2 molecule at the Hartree-Fock, second-order Møller-Plesset, and configuration interaction levels show that the solutions of the resulting reduced-rank Schrödinger equations converge rapidly, and that even low-rank approximations can yield energies with chemical accuracy.