Unrestricted Hartree-Fock Model Research Articles

Intuitive local picture for spin polarization of chemical bonds

AbstractThe spin polarization of chemical bonds near radical centers is investigated by an analytical spin unrestricted Hartree–Fock model with numerical examples. The centroid analysis of localized molecular orbitals is also introduced to obtain an intuitive local picture for the spin polarization. The alternation of spin alignments in molecules are discussed with orbital symmetries and Hund's rule through chemical bonds. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

A self-consistent calculation of the energy bands in ferromagnetic nickel

The results of a calculation, in which the unrestricted Hartree–Fock model was applied to the case of nickel in the ferromagnetic state, are presented here. Comparisons with the experimental data are shown which suggest that this procedure may give an acceptable model of the ground state of a ferromagnetic solid.

Theoretical Studies on the Structures, Thermodynamic Properties, Detonation Properties, and Pyrolysis Mechanisms of Spiro Nitramines

Density function theory (DFT) has been employed to study the geometric and electronic structures of a series of spiro nitramines at the B3LYP/6-31G level. The calculated results agree reasonably with available experimental data. Thermodynamic properties derived from the infrared spectra on the basis of statistical thermodynamic principles are linearly correlated with the number of nitramine groups as well as the temperature. Detonation performances were evaluated by the Kamlet-Jacobs equations based on the calculated densities and heats of formation. It is found that some compounds with the predicted densities of ca. 1.9 g/cm3, detonation velocities over 9 km/s, and detonation pressures of about 39 GPa (some even over 40 GPa) may be novel potential candidates of high energy density materials (HEDMs). Thermal stability and the pyrolysis mechanism of the title compounds were investigated by calculating the bond dissociation energies (BDE) at the B3LYP/6-31G level and the activation energies (E(a)) with the selected PM3 semiempirical molecular orbital (MO) based on the unrestricted Hartree-Fock model. The relationships between BDE, E(a), and the electronic structures of the spiro nitramines were discussed in detail. Thermal stabilities and decomposition mechanisms of the title compounds derived from the B3LYP/6-31G BDE and the UHF-PM3 E(a) are basically consistent. Considering the thermal stability, TNSHe (tetranitrotetraazaspirohexane), TNSH (tetranitrotetraazaspiroheptane), and TNSO (tetranitrotetraazaspirooctane) are recommended as the preferred candidates of HEDMs. These results may provide basic information for the molecular design of HEDMs.

Unrestricted Hartree–Fock then and now

AbstractThe unrestricted Hartree–Fock model of interacting electrons originated as an approximation that incorporates exchange‐polarization effects for open‐shell atoms and molecules. Spontaneous symmetry‐breaking is described by this model, in particular for dissociating covalent bonds, but is limited to exchange in the Hartree–Fock context. When this model is extended to an orbital functional theory, which can include quantitative effects of electronic correlation, it becomes a widely applicable formalism for many‐body theory. This conceptual extension is discussed. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

The exclusion principle for interacting electrons: Kohn–Sham versus Thomas–Fermi

AbstractMany anomalies and paradoxes in density‐functional theory arise from the assumption that an exact mean‐field theory of electrons requires only local potential functions. It is shown here that this assumption arises from a logical hiatus in deriving orbital‐based Kohn–Sham theory, which incorporates the exclusion principle for electrons, from density‐based Hohenberg–Kohn theory, which does not. The inconsistencies are removed by building the exclusion principle into density‐based theory from the outset. This logic replaces any implication regarding exact local potential functions by explicit specification of nonlocal potentials determined by exact N‐electron theory. These general results are examined here in the unrestricted Hartree–Fock variational model, using a two‐electron atom in its lowest triplet state 1s2s 3S as a test case to illustrate the implied inconsistencies and their resolution. It is shown that implications of the unrestricted Hartree–Fock model are not modified if overlap products are included in its variational functional. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Computational studies on the infrared vibrational spectra, thermodynamic properties, detonation properties, and pyrolysis mechanism of octanitrocubane

The molecular geometries, infrared vibrational spectra, and thermodynamic properties of octanitrocubane (ONC) are calculated using the density functional theory (DFT) method at the B3LYP/6-31G* level. The IR frequency scaling factor 0.9501 suitable for polynitrocubanes is obtained at the B3LYP/6-31G* level, and the calculated IR frequencies of ONC are scaled. The accurate heat of formation 726.47 kJ/mol of ONC in gas phase is obtained via designed isodesmic reaction in which the cubane cage skeleton has been kept. The sublimation enthalpy, density, and heat of formation for ONC crystal are also calculated, and they are 220.63 kJ/mol, 2.189 g/cm3, and 505.84 kJ/mol, respectively. In addition, the estimated detonation velocity and detonation pressure of ONC are 10.26 mm/ms and 520.86 kbar, respectively. Finally, the pyrolysis mechanism of ONC is studied using various theoretical methods, i.e., MP2, DFT, and selected MINDO/3 semiempirical MO, based on the unrestricted Hartree–Fock model. The calculated results show that the pyrolysis initiation reaction of ONC, i.e., rate-controlling step, is to form a diradical by the single C–C bond breaking in the cube. The second C–C bond breaking is easily followed to form a nitrocyclooctatetraene. The calculated activation energy for the pyrolysis initiation reaction of ONC, obtained from B3LYP/6-31G* method, is 155.30 kJ/mol, which this rather large activation energy indicates that ONC is a new type of energetic material with less sensitivity and better thermal stability, and has highly exploitable values.

A spectroscopic study of ground state of lithium hydride with the HPHF model

In this work, matrix equations for obtaining the half-projected Hartree-Fock (HPHF) function from pseudo-eigenvalue equations in a non-orthogonal basis are given, similarly as in the unrestricted Hartree-Fock model. The potential energy curve for the ground state of the LiH molecule is calculated by using a 6-311(2d,2p) gaussian basis set. Finally, in order to test the HPHF model, some spectroscopic parameters are calculated. Relatively good agreement with experiment is found for the anharmonicity constant.

Chemisorption and the electronic structure of transition metal oxides and transition metals bonded to oxide surfaces

Abstract Some simple transition metal oxides such as NiO have incomplete atomic subshells and yet are highly insulating. This implies a high degree of electronic localization and also indicates that the chemical bonds are saturated. In this respect these oxides are similar to alkaline earth oxides such as MgO. The analogy extends to their surface properties. MgO and NiO, for example, are both good catalysts although a pure, perfect surface of either seems inactive. It is argued that defects or impurities are required to activate the perfect surface and that catalytic properties relate weakly, at best, to the nature of the cation. These oxides are contrasted with the more studied industrial catalyst which consists of a group of transition metal ions bonded to an oxide surface. The electronic structure properties which determine the behaviour of such catalysts are explored in terms of the unrestricted Hartree-Fock model augmented with explicit inclusion of correlation. The results obtained produce a satisfactory band structure and describe surface prupcrties adequately.

Absorption spectrum of manganian andalusite: Cluster calculation by an ab initio method

AbstractThe ground state and the first few excited states of an MnO69− cluster are calculated in the unrestricted Hartree–Fock model. The state ordering is 5B1 g, 5A1 g, 5B2 g, and 5Eg as can be expected from simpler models. Consistent with the results by the same method for copper complexes, we obtain d–d transition energies about one half or less of the experimental energies. The charge transfer spectrum is subject to a large spin polarization in the sense that the lowest charge transfer state (5Eu) has five unpaired spins on Mn.

Renormalization for collective motion within a truncated space of the spherical shell model. II. Projected frame in a schematic model

In paper I, [ Ann. Phys. (N.Y.) 94 (1975)] the matrix elements of effective operators in an intrinsic frame of the spherical shell model, that were determined by an iterative, renormalization technique, were shown to be analytically equivalent to those from a deformed, unrestricted Hartree-Fock model for the case of 20Ne with a schematic quadrupole-quadrupole Hamiltonian. This paper shows the numerical comparison of the results from the renormalized spherical shell model and the projected, deformed Hartree-Fock model in the laboratory frame with states of definite angular momentum. Good agreement is found for the full iterative, renormalization results and those from the variation-after-projection Hartree-Fock model.