Global solutions of restricted open-shell Hartree-Fock theory from semidefinite programming with applications to strongly correlated quantum systems

摘要

We present a density matrix approach for computing global solutions ofrestricted open-shell Hartree-Fock theory, based on semidefinite programming(SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantumsystems. While wave function approaches to Hartree-Fock theory yield an upperbound to the Hartree-Fock energy, we derive a semidefinite relaxation ofHartree-Fock theory that yields a rigorous lower bound on the Hartree-Fockenergy. We also develop an upper-bound algorithm in which Hartree-Fock theoryis cast as a SDP with a nonconvex constraint on the rank of the matrixvariable. Equality of the upper- and lower-bound energies guarantees that thecomputed solution is the globally optimal solution of Hartree-Fock theory. Thework extends a previously presented method for closed-shell systems [S.Veeraraghavan and D. A. Mazziotti, Phys. Rev. A89, 010502R (2014)]. Forstrongly correlated systems the SDP approach provides an alternative to thelocally optimized Hartree-Fock energies and densities with a certificate ofglobal optimality. Applications are made to the potential energy curves of C2,CN, Cr2, and NO2.