Global Solutions of Hartree-Fock Theory and their Consequences for Strongly Correlated Quantum Systems

摘要

We present a density matrix approach for computing global solutions ofHartree-Fock theory, based on semidefinite programming (SDP), that gives upperand lower bounds on the Hartree-Fock energy of quantum systems. Equality of theupper- and lower-bound energies guarantees that the computed solution is theglobally optimal solution of Hartree-Fock theory. For strongly correlatedsystems the SDP approach requires us to reassess the accuracy of theHartree-Fock energies and densities from standard software packages forelectronic structure theory. Calculations of the H$_{4}$ dimer and N$_{2}$molecule show that the energies from SDP Hartree-Fock are lower than those fromstandard Hartree-Fock methods by 100-200 kcal/mol in the dissociation region.The present findings have important consequences for the computation andinterpretation of electron correlation, which is typically defined relative tothe Hartree-Fock energy and density.