Universal Variational Functionals of Electron Densities, FirstOrder Density Matrices, and Natural SpinOrbitals and Solution of the vRepresentability Problem
Abstract
Universal variational functionals of densities, firstorder density matrices, and natural spinorbitals are explicitly displayed for variational calculations of ground states of interacting electrons in atoms, molecules, and solids. In all cases, the functionals search for constrained minima. In particular, following Percus [Formula: see text] is identified as the universal functional of Hohenberg and Kohn for the sum of the kinetic and electronelectron repulsion energies of an Nrepresentable trial electron density ρ. Q[ρ] searches all antisymmetric wavefunctions Ψ_{ρ} which yield the fixed. ρ. Q[ρ] then delivers that expectation value which is a minimum. Similarly, [Formula: see text] is shown to be the universal functional for the electronelectron repulsion energy of an Nrepresentable trial firstorder density matrix γ, where the actual external potential may be nonlocal as well as local. These universal functions do not require that a trial function for a variational calculation be associated with a ground state of some external potential. Thus, the vrepresentability problem, which is especially severe for trial firstorder density matrices, has been solved. Universal variational functionals in HartreeFock and other restricted wavefunction theories are also presented. Finally, natural spinorbital functional theory is compared with traditional orbital formulations in density functional theory.
 Publication:

Proceedings of the National Academy of Science
 Pub Date:
 December 1979
 DOI:
 10.1073/pnas.76.12.6062
 Bibcode:
 1979PNAS...76.6062L