Open-shell Hartree-Fock Theory Research Articles

The Emergence of the Hexagonal Lattice in Two-Dimensional Wigner Fragments.

At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density profiles of fragments of Wigner crystals from first principles. To simulate Wigner fragments, we use Clifford periodic boundary conditions and a renormalized distance in the Coulomb potential. Moreover, we show that high-spin restricted open-shell Hartree-Fock theory becomes exact in the low-density limit. We are thus able to accurately capture the localization in two-dimensional Wigner fragments with many electrons. No assumptions about the positions where the electrons will localize are made. The density profiles we obtain emerge naturally when we minimize the total energy of the system. We clearly observe the emergence of the hexagonal crystal structure, which has been predicted to be the ground-state structure of the two-dimensional Wigner crystal.

Combined open shell Hartree-Fock theory of atomic and molecular systems constructed from noncharged scalar nuclear Fermi particles. II. Fermi particles with rest mass <I>m</I> ≠ 1

Combined open shell Hartree-Fock theory of atomic and molecular systems constructed from noncharged scalar nuclear Fermi particles. II. Fermi particles with rest mass <I>m</I> ≠ 1

Combined open shell Hartree-Fock theory of atomic and molecular systems constructed from noncharged scalar particles

By the use of condition of relativistic covariance, Dirac group theory, Clifford algebra and complete orthonormal sets of w ða � Þ -self-frictional exponential type orbitals (w ða � Þ -SFETOs) introduced by the author in standard convention, the Hartree-Fock (HF) theory is suggested for multideterminantal single configuration states with any number of open shells of atoms and molecules constructed from the Standard Model-Fermi (SM-F) particles with m 6 0;s ¼ 0; and e ¼ 0 defined in the Standard Model of particle physics. It is shown that the origin of stability of these systems is the quantum damping or self-frictional forces produced by the SM-F particle itself. As an application, we have presented the periodic table for the SM-F atomic elements using Pauli principle of spinless noncharged identical SM-F particles. V C 2014 Physics Essays Publication .( http://dx.doi.org/10.4006/0836-1398-27.3.351) Resume´: Par l'utilisation de la condition de covariance relativiste, theorie des groupes de Dirac, algebre de Clifford et des ensembles complets de orthonormeesw ða � Þ -auto-friction orbitales de type exponentielle (w ða � Þ

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

We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. While wave function approaches to Hartree-Fock theory yield an upper bound to the Hartree-Fock energy, we derive a semidefinite relaxation of Hartree-Fock theory that yields a rigorous lower bound on the Hartree-Fock energy. We also develop an upper-bound algorithm in which Hartree-Fock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. The work extends a previously presented method for closed-shell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A 89, 010502-R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of C2, CN, Cr2, and NO2.

Comment on “Combined open shell Hartree–Fock theory of atomic-molecular and nuclear systems” [J. Math. Chem. 42 (2007) 177

Comment on “Combined open shell Hartree–Fock theory of atomic-molecular and nuclear systems” [J. Math. Chem. 42 (2007) 177

Application of combined Hartree-Fock-Roothaan theory to atoms with an arbitrary number of closed and open shells of any symmetry

The applicability of a combined open-shell Hartree-Fock theory of atomic-molecular and nuclear systems to the states of a single configuration which has the arbitrary symmetry of open shells is explicitly demonstrated by calculations based on the combined Hartree-Fock-Roothaan equations for atoms. As examples of an application of the combined theory using single-zeta Slater-type basis sets, the calculations have been performed for the lowest states of the lowest and excited electronic configurations of carbon and nitrogen atoms containing one-, two- and three-open shells. For the case of single-open shells for carbon and nitrogen atoms, the double-zeta basis-set calculations are also presented. The results of computer calculations for the orbitals, kinetic and total energies, linear combination coefficients and virial ratios are given.

Unified theoretical treatment of analytic first and second energy derivatives in open-shell Hartree—Fock theory

Second derivatives of polyatomic potential energy hypersurfaces are of widespread importance to problems in theoretical chemistry. A formalism is presented which allows the analytic evaluation of energy second derivatives from restricted Hartree—Fock wavefunctions for arbitrary closed- or open-shell molecular systems. The present method makes use of previously reported integral second-derivative techniques and earlier advances in the solution of the open-shell coupled perturbed Hartree—Fock equations. The applicability of the new method is demonstrated in studies of the first excited singlet state of formaldehyde, for which the equilibrium geometry and vibrational frequencies have been determined with two different basis sets.

Orbital energies and Koopmans' theorem in open-shell Hartree-Fock theory

In (restricted) open-shell Hartree-Fock theory, the eigenvalues of the effective hamiltonian do not have the usual significance as negative ionization potentials (Koopmans' theorem). By defining orbital energies in terms of certain energy expectation values, it is possible to obtain analogues of Koopmans' theorem, and to discuss the energetics of other types of electron transfer.