Density-driven self-consistent-field method: Density-constrained correlation energies in the helium series

The electron-correlation energies, calculated with the wave functions constrained to the Hartree-Fock density, are computed for the helium series and are compared with the exact (unconstrained) correlation energies. Imposition of the density constraints increases the energies by a surprisingly small amount. Both the l=0 (s) and l=1 (p) limit differences between the constrained and exact energies are demonstrated to scale like the reciprocal of the square of the atomic numbers. The computational results are rationalized by introducing rigorous definitions of the dynamical and nondynamical correlation energies