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.

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.

Force constants and dipole moment derivatives of molecules from perturbed Hartree-Fock calculations II. Applications to limited basis set SCF-MO wavefunctions

The perturbed Hartree–Fock theory developed in the preceding paper is applied to LiH, BH, and HF, using limited basis‐set SCF–MO wavefunctions derived by previous workers. The calculated values for the force constant ke and the dipole‐moment derivative μ(1) are (experimental values in parentheses): LiH, ke  =  1.618(1.026)mdyn/Å,μ(1)  =  −18.77(−2.0±0.3)D/ÅBH,ke  =  5.199(3.032)mdyn/Å,μ(1)  =  −1.03(−)D/Å;HF,ke  =  12.90(9.651)mdyn/Å,μ(1)  =  −2.15(+1.50)D/Å. The values of the force on the proton were calculated exactly and according to the Hellmann–Feynman theorem in each case, and the discrepancies show that none of the wavefunctions used are close to the Hartree–Fock limit, so that the large errors in ke and μ(1) are not surprising. However no difficulties arose in the perturbed Hartree–Fock calculation, so that the application of the theory to more accurate wavefunctions appears quite feasible.

Prolapse-free relativistic Gaussian basis sets for the superheavy elements up to Uuo (Z=118) and Lr (Z=103)

Prolapse-free basis sets suitable for four-component relativistic quantum chemical calculations are presented for the superheavy elements UP to (118)Uuo ((104)Rf, (105)Db, (106)Sg, (107)Bh, (108)Hs, (109)Mt, (110)Ds, (111)Rg, (112)Uub, (113)Uut, (114)Uuq, (115)Uup, (116)Uuh, (117)Uus, (118)Uuo) and Lr-103. These basis sets were optimized by minimizing the absolute values of the energy difference between the Dirac-Fock-Roothaan total energy and the corresponding numerical value at a milli-Hartree order of magnitude, resulting in a good balance between cost and accuracy. Parameters for generating exponents and new numerical data for some superheavy elements are also presented. (c) 2007 Elsevier B.V. All rights reserved.

The generator coordinate method for a reaction coordinate coupled to a harmonic oscillator bath

This paper investigates the usefulness of the generator coordinate method (GCM) for treating the dynamics of a reaction coordinate coupled to a bath of harmonic degrees of freedom. Models for the unimolecular dissociation and isomerization process (proton transfer) are analyzed. The GCM results, presented in analytical form, provide a very good description and are compared to other methods Like the basis set method and multiconfiguration time dependent self-consistent field. (C) 1998 American Institute of Physics. [S0021-9606(98)50934-8].

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.

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.

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.

Unrestricted hartree-fock calculation of the ionization potential of small Hg_n clusters

The ionization potential of small Hg_n clusters has been calculated. For the first time good agreement with experimental results has been obtained. It is shown that interatomic Coulomb interactions are important. The energy of Hg_n^+ is calculated using the unrestricted inhomogeneous Hartree-Fock approximation. As a consequence of a change in the charge distribution in Hg_n^+ , we obtain an abrupt change in the slope of the ionization potential at the critical cluster size n_cr ~ 14. The presented results are expected to be valid for covalent clusters in between ionized van der Waals clusters and metallic clusters.

Solution of the Hartree-Fock equations for atoms and diatomic molecules with the finite element method

The finite element method (FEM) is now developed to solve two-dimensional Hartree-Fock (HF) equations for atoms and diatomic molecules. The method and its implementation is described and results are presented for the atoms Be, Ne and Ar as well as the diatomic molecules LiH, BH, N_2 and CO as examples. Total energies and eigenvalues calculated with the FEM on the HF-level are compared with results obtained with the numerical standard methods used for the solution of the one dimensional HF equations for atoms and for diatomic molecules with the traditional LCAO quantum chemical methods and the newly developed finite difference method on the HF-level. In general the accuracy increases from the LCAO - to the finite difference - to the finite element method.

Accurate Hartree-Fock-Slater calculations on small diatomic molecules with the finite-element method

We report on the self-consistent field solution of the Hartree-Fock-Slater equations using the finite-element method for the three small diatomic molecules N_2, BH and CO as examples. The quality of the results is not only better by two orders of magnitude than the fully numerical finite difference method of Laaksonen et al. but the method also requires a smaller number of grid points.