We present two new exchange-correlation functionals for hybrid Kohn-Sham electronic structure calculations based on the nonseparable functional form introduced recently in the N12 and MN12-L functionals but now with the addition of screened Hartree-Fock exchange. The first functional depends on the density and the density gradient and is called N12-SX; the second functional depends on the densi...

Abstract The Hartree-Fock equations are widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle methods. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equations in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potenti...

We show how the Hartree approximation (HA) can be used to study the quantum discrete self-trapping (QDST) equation, which in turn provides a model for the quantum description of several interesting nonlinear effects such as energy localization, soliton interactions, and chaos. The accuracy of the Hartree approximation is evaluated by comparing results with exact quantum mechanical calculations ...

We study the properties of neutron stars adopting relativistic equations of state of neutron star matter, calculated in the framework of the relativistic Brueckner–Hartree–Fock approximation for electrically charge neutral neutron star matter in beta–equilibrium. For higher densities more baryons (hyperons etc.) are included by means of the relativistic Hartree– or Hartree–Fock approximation. T...

We have performed an assessment of the Hartree-Fock perturbative correction (HFPC) on a large and diverse set of molecules and reactions. Errors in both absolute and reaction energies with respect to converged secondary basis Hartree-Fock results are reported for a wide spectrum of primary/secondary basis set combinations. These results show that using an adequate primary basis, HFPC can accura...

It is a well known fact that mean-field approximation to the nuclear many-body problem introduces center-of-mass (CM) spurious components in the solutions. In particular, Hartree-Fock self-consistent mean-fields obtained using realistic forces in a non-relativistic approach have been considered, and the corresponding CM corrections have been calculated for the energy [1, 2] as well as for other...

The optimized δ-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the varia-tional principle. This technique is discussed in the λφ 4 model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the δ expansion are compared with those obtained with the traditional ...

In this paper we study the semiclassical limit for the pseudo-relativistic Hartree equation √ −ε2∆ +m2u+ V u = (Iα ∗ |u|) |u|p−2u, in R , where m > 0, 2 ≤ p < 2N N−1 , V : R N → R is an external scalar potential, Iα(x) = cN,α |x|N−α is a convolution kernel, cN,α is a positive constant and (N − 1)p−N < α < N . For N = 3, α = p = 2, our equation becomes the pseudo-relativistic Hartree equation wi...

We investigate the asymptotic behavior of solutions to semi-classical Schrödinger equations with nonlinearities of Hartree type. For a weakly nonlinear scaling, we show the validity of an asymptotic superposition principle for slowly modulated highly oscillatory pulses. The result is based on a highfrequency averaging effect due to the nonlocal nature of the Hartree potential, which inhibits th...

The isospin dependence of the spin-orbit potential is investigated for an effective Skyrme-like energy functional suitable for density dependent Hartree-Fock calculations. The magnitude of the isopin dependence is obtained from a fit to experimental data on finite spherical nuclei. It is found to be close to that of relativistic Hartree models. Consequently, the anomalous kink in the isotope sh...