Bounds on the overlap of the Hartree-Fock, optimized effective potential, and density functional approximations with the exact energy eigenstates

Abstract

In this paper, we examine the limits of accuracy of the single determinant approximations (Hartree-Fock, optimized effective potential, and density functional theory) to the exact energy eigenstates of many electron systems. We show that an approximate Slater determinant of S(z)=M gives maximum accuracy for states with S=M, provided that perturbation theory for the spin up minus spin down potential is applicable. The overlap with the exact energy eigenstates with S not equal M is much smaller. Therefore, for the case that the emphasis is on wave functions, one must use symmetry preserving theories, although this is at the expense of accuracy in energy.