Global solutions of Hartree-Fock theory and their consequences for strongly correlated quantum systems

We present a density matrix approach for computing global solutions of Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. Equality of the upper-and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities from the standard solution of the Euler-Lagrange equations. Applications are made to the potential energy curves of the H4 dimer and the N2 molecule.