Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated (r12-)MR-CI. II. Ground-state energies of first-row atoms and positive atomic ions

The recently proposed (explicitly correlated) r12-MR-CI and r12-MR-ACPF (averaged coupled-pair functional) methods are applied to the computation of the clamped-nuclei nonrelativistic ground-state energies of the first-row atoms and their positive ions. For the neutral atoms we obtain accuracies of −0.05 (He and Li), −0.013 (Be), +0.12 (B), −0.1 (C and N), +0.3 (O) and +0.6 (F and Ne) mEh. Our energies of B–F are by far the best available. In all cases, the energy eigenvalues of the Schrödinger equation are calculated to better than chemical accuracy (1 kcal/mol). Since our method is completely general, this, for the first time, implies the possibility of performing quantum chemical calculations of general many-electron systems where the error of the computed energy is not any more very large compared to the desired accuracy.