Magnetoconfined levels in a parabolic quantum dot: An analytical solution of a three-dimensional Fock-Darwin problem in a tilted magnetic field

The energy spectrum of an electron confined in a quantum dot (QD) with a three-dimensional anisotropic parabolic potential in a tilted magnetic field was found analytically. The theory describes exactly the mixing of in-plane and out-of-plane motions of an electron caused by a tilted magnetic field, which could be seen, for example, in the level anticrossing. For charged QDs in a tilted magnetic field we predict three strong resonant lines in the far-infrared-absorption spectra.

Basis set convergence in Hartree-Fock calculations of some diatomic molecules containing first and second-row atoms

Investiga-se a convergência de conjuntos de bases em direção ao limite numérico da energia Hartree-Fock (HF) total para as seqüências hierárquicas dos conjuntos de bases XZP e ccpVXZ. Para as duas hierarquias, melhoramentos significativos são obtidos com cada incremento em X. Para estimar o limite do conjunto de base completo, uma forma exponencial foi usada. Entre as várias aproximações consideradas aqui, uma extrapolação exponencial de três parâmetros aplicada aos resultados TZP, QZP e 5ZP deu os limites do conjunto de bases mais precisos. Em adição, energias HF dos orbitais moleculares ocupados mais altos de algumas moléculas diatômicas foram calculadas com o conjunto 5ZP e comparadas com as correspondentes obtidas com o conjunto cc-pV5Z e com um método numérico HF.

Adapted Gaussian basis sets for atoms from Li through Xe generated with the generator coordinate Hartree-Fock method

Utiliza-se o método coordenada geradora Hartree-Fock para gerar bases Gaussianas adaptadas para os átomos de Li (Z=3) até Xe (Z=54). Neste método, integram-se as equações de Griffin-Hill-Wheeler-Hartree-Fock através da técnica de discretização integral. Comparam-se as funções de ondas geradas neste trabalho com as funções de ondas Roothaan-Hartree-Fock de Clementi e Roetti (1974) e com outros conjuntos de bases relatados na literatura. Para os átomos estudados aqui, os erros em nossas energias totais relativos aos limites numéricos Hartree-Fock são sempre menores que 7,426 milihartree.

On boundary value problems for Willmore surfaces and Hartree-Fock theory of pseudo-relativistic atoms

Magdeburg, Univ., Fak. für Mathematik, kumulative Habil.-Schr., 2011

Spin polarized neutron matter and magnetic susceptibility within the Brueckner-Hartree-Fock approximation

The Brueckner-Hartree-Fock formalism is applied to study spin polarized neutron matter properties. Results of the total energy per particle as a function of the spin polarization and density are presented for two modern realistic nucleon-nucleon interactions, Nijmegen II and Reid93. We find that the dependence of the energy on the spin polarization is practically parabolic in the full range of polarizations. The magnetic susceptibility of the system is computed. Our results show no indication of a ferromagnetic transition which becomes even more difficult as the density increases.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

Ab initio study of MF2 (M=Mn, Fe, Co, Ni) rutile-type compounds using the periodic unrestricted Hartree-Fock approach

The ab initio periodic unrestricted Hartree-Fock method has been applied in the investigation of the ground-state structural, electronic, and magnetic properties of the rutile-type compounds MF2 (M=Mn, Fe, Co, and Ni). All electron Gaussian basis sets have been used. The systems turn out to be large band-gap antiferromagnetic insulators; the optimized geometrical parameters are in good agreement with experiment. The calculated most stable electronic state shows an antiferromagnetic order in agreement with that resulting from neutron scattering experiments. The magnetic coupling constants between nearest-neighbor magnetic ions along the [001], [111], and [100] (or [010]) directions have been calculated using several supercells. The resulting ab initio magnetic coupling constants are reasonably satisfactory when compared with available experimental data. The importance of the Jahn-Teller effect in FeF2 and CoF2 is also discussed.

Traces of functions in Fock spaces on lattices of critical density

Following a scheme of Levin we describe the values that functions in Fock spaces take on lattices of critical density in terms of both the size of the values and a cancelation condition that involves discrete versions of the Cauchy and Beurling-Ahlfors transforms.

Pointwise estimates for the Bergman kernel of the weighted Fock space

We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in $L^{2}(e^{-2\phi}) $ where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. We derive estimates for the canonical solution operator to the inhomogeneous Cauchy-Riemann equation and we characterize the compactness of this operator in terms of $\Delta\phi$.

Analytical Dirac-Hartree-Fock-Slater screening function for atoms (Z=1-92)

An analytical approximation, depending on five parameters, for the atomic screening function is proposed. The corresponding electrostatic potential takes a simple analytical form (superposition of three Yukawa potentials) well suited to most practical applications. Parameters in the screening function, determined by an analytical fitting procedure to Dirac-Hartree-Fock-Slater (DHFS) self-consistent data, are given for Z=1¿92. The reliability of this analytical approach is demonstrated by showing that (a) Born cross sections for elastic scattering of fast charged particles by the present analytical field and by the DHFS field practically coincide and (b) one-electron binding energies computed from the independent-particle model with our analytical field (corrected for exchange and electrostatic self-interaction) agree closely with the DHFS energy eigenvalues.

UMA FORMA SIMPLIFICADA DE DEDUZIR AS EQUAÇÕES DE HARTREE E HARTREE-FOCK

AbstractAlternative considerably simpler ways of obtaining the Hartree and Hartree-Fock equations are presented. These alternatives do not replace the formal demonstrations, which should be introduced in undergraduate or graduate courses according to the required level of student training. However, the use of the present approaches allows a student-friendlier introduction of the basic principles of electronic structure calculations as a prior teaching resource to the formal demonstrations. General implications and comparisons between the Hartree and Hartree-Fock energies are discussed.