An ab initio Hartree-Fock approach aimed at directly obtaining the localized orthogonal orbitals (Wannier functions) of a crystalline insulator is described in detail. The method is used to perform all-electron calculations on the ground states of crystalline lithium fluoride and lithium chloride, without the use of any pseudo or model potentials. Quantities such as total energy, x-ray structur...

We investigate nuclear matter properties in the relativistic Brueckner approach. The in-medium on-shell T-matrix is represented covariantly by five Lorentz invariant amplitudes from which we deduce directly the nucleon self-energy. We discuss the ambiguities of this approach and the failure of previously used covariant representations in reproducing the nucleon self-energies on the Hartree-Fock...

We propose a mean field framework in which the charge and the parity symmetries of a single-particle state are broken. We break these symmetries to incorporate the correlation induced by the tensor force into a nuclear mean field model. We perform the chargeand the parity projections before variation and obtain a Hartree-Fock-like equation (chargeand parity-projected Hartree-Fock equation), whi...

This work presents a procedure to optimize the molecular geometry at the Hartree-Fock level, based on a global optimization method—the Generalized Simulated Annealing. The main characteristic of this methodology is that, at least in principle, it enables the mapping of the energy hypersurface as to guarantee the achievement of the absolute minimum. This method does not use expansions of the ene...

The Hartree-Fock equations describe atomic and molecular eletronic wave functions, based on the minimization of a functional of the energy. This can be formulated as a constrained global optimization problem involving nonconvex polynomials exhibiting many local minima. The traditional method of solving the Hartree-Fock problem does not provide a guarantee of global optimality and is very sensit...

In the limit of infinite spatial dimensions a thermodynamically consistent theory, which is valid for arbitrary value of the Coulombic interaction (U < ∞), is built for the Hubbard model when the total auxiliary single-site problem exactly splits into four subspaces with different “vacuum states”. Some analytical results are given for the Hartree-Fock approximation when the 4-pole structure for...

We study the dynamics of a Fermi gas with a Coulomb interaction potential, and show that, in a mean-field limiting regime, the dynamics is described by the Hartree-Fock equation. This extends previous work of Bardos et al. [3] to the case of unbounded interaction potentials. We also express the mean-field limit as a “superhamiltonian” system, and state our main result in terms of a Heisenberg-p...

A multi-configuration mixing approach built on essentially complex, symmetryprojected Hartree-Fock-Bogoliubov (HFB) mean fields is introduced. The mean fields are obtained by variation after projection. The configuration space consists out of the symmetry-projected HFB vacuum and the symmetry-projected twoquasiparticle excitations for even, and the symmetry-projected one-quasiparticle excitatio...