Hartree-Fock Model Research Articles

Some spin and spin‐free aspects of coulomb correlation in molecules

AbstractA spin component analysis of the cumulant (irreducible) density matrices is provided. In particular, the spin‐up spin‐down cumulant density matrix, π, is considered as the most general definition of the Coulomb‐hole density matrix. The local atomic cumulants produced from π, turn out to be the most important components of the atomic charge and spin correlators. These spin‐up spin‐down components, vanishing in the restricted Hartree–Fock model, reflect directly an effect of the Coulomb correlation on the generalized Wiberg bond order indices and Penney–Dirac bond orders. A spin‐free algorithm for computing spin correlators and related local spins is proposed. The algorithm is implemented numerically at full configuration interaction (FCI) and simple coupled‐cluster (CC) levels. The presented analysis is exemplified by some FCI and CC doubles computations on small hydrides and typical carbenes and cumulenes. © 2012 Wiley Periodicals, Inc.

EOS of neutron-rich matter and pure neutron matter

We report the equation of state (EOS) of pure neutron matter (PNM) and neutron-rich matter (NRM) for the realistic Urbana V14 two nucleon interaction, obtained by using a Variational Monte Carlo (VMC) method. Also, many body interactions are included as a phenomenological density dependent term in the potential. The binding energy per nucleon is calculated for different densities and various isospin asymmetry parameters. Our results on NRM and PNM are compared with relativistic Brueckner-Hartree-Fock theory and relativistic Hartree-Fock model with the unitary correlation operator method. The results obtained in this study show reasonable agreement with both of these relativistic Hartree-Fock approaches. We also compare the binding energies obtained in this study with those obtained by various authors employing different methods and techniques.

Oscillator strengths for lines of astrophysical interest in Rh II

Aims. This work reports oscillator strengths for transitions of astrophysical interest in singly ionized rhodium. Methods. Seventeen radiative lifetimes in Rh + have been measured with the time-resolved laser-induced fluorescence technique and combined with theoretical branching fractions calculated using a relativistic Hartree-Fock model including core-polarization effects to obtain oscillator strengths. Results. On the basis of the good agreement between theory and experiment for the lifetimes, new reliable oscillator strengths have been deduced for a set of 113 Rh II transitions in the spectral range 153–418 nm.

Two Hartree-Fock models for the vacuum polarization

Two Hartree-Fock models for the vacuum polarization

Properties of Symmetric Uclear Matter with Skyrme Iteractios

Symmetric nuclear matter properties such as binding energy, pressure, saturation density and incompressibility are investigated in the Skyrme Hartree-Fock model. A new set of Skyrme parameters for symmetric nuclear matter is obtained by the fitting of Variational Monte Carlo method results to density-dependent Skyrme type energy. The results obtained are in good agreement with those obtained with selected Skyrme parameter sets in the literature.

Semiempirical, Hartree-Fock, density functional, and second order Moller-Plesset perturbation theory methods do not accurately predict ionization energies and electron affinities of short- through long-chain [n]acenes

AbstractVertical, well-to-well, and adiabatic ionization energies (IEs) and electron affinities (EAs) were calculated for the n=1-10 [n]acenes using a wide range of semiempirical, Hartree-Fock, density functional, and second order Moller-Plesset perturbation theory model chemistries. None of the model chemistries examined were able to accurately predict the IEs or EAs for both short- through mid-length [n]acenes, as well as for extrapolations to the polymeric limit, when compared to available experimental and benchmark theoretical data. Provided a minimal basis set size is employed, basis set effects on predicted IEs and EAs are not significant relative to the choice of model chemistry. The poor IE/EA prediction performance for the parent [n]acenes likely extends to their substituted derivatives and heteroatom substituted analogs. Consequently, caution should be exercised in the application of non-high level calculations for estimating the IE/EA of these important classes of materials.

Statistical Study For The prediction of pKa Values of Substituted Benzaldoxime Based on Quantum Chemicals Methods

Multiple regression analysis was used for the calculation of pKa values of 15 substituted benzaldoximes by using various types of descriptors as parameters. These descriptors are based on quantum mechanical treatments. They were derived by employing semi-empirical calculation represented by the PM3 model and an Abinitio method expressed by Hartree-Fock(HF) model performed at the 6-311 G(d, p) level of theory. The parameters tested for their ability to represent the variations observed in the experimental pKa(s) are atomic and structural properties including Muliken charges on the atoms of hydroxyl group and C=N bond, the angle <TEX>$C_6-C_1-C_7$</TEX>, and length of O-H bond. Molecular properties are also used like energies of HOMO and LUMO, hardness(<TEX>${\eta}$</TEX>), chemical potential(<TEX>${\mu}$</TEX>), total energy(TE), dipole of molecule(DM), and electrophilicity index(W). The relation between pKa values and each of these parameters of the studied compounds is investigated. Depending on these relations, two sets of parameters were constructed for comparison between the PM3 and HF methods. The results obtained favor the Abinitio method for such applications although both models proved to have high predictive power and have sufficient reliability to describe the effect of substituents on pKa values of benzaldoxime compounds under consideration which is clear from the values of correlation coefficient <TEX>$R^2$</TEX> obtained and the consistency between the experimental and the calculated values.

Relativistic description of finite nuclei based on realisticNNinteractions

A set of relativistic mean-field models is constructed, which includes the Hartree and Hartree-Fock (HF) approximations accounting for the exchange of isoscalar and isovector mesons as well as the pion. Density-dependent coupling functions are determined to reproduce the components of the nucleon self-energy at the Fermi surface, obtained within the Dirac-Brueckner-HF (DBHF) approach by using a realistic nucleon-nucleon interaction. It is investigated to which extent the various mean-field models can reproduce the DBHF results for the momentum dependence of the self-energies and the total energy of infinite matter. Also, the mean-field models are used to evaluate the bulk properties of spherical closed-shell nuclei. We find that the HF model, which allows for the exchange of $\ensuremath{\sigma},\phantom{\rule{0.28em}{0ex}}\ensuremath{\omega},\phantom{\rule{0.28em}{0ex}}\ensuremath{\rho}$, and $\ensuremath{\delta}$ mesons and pions, yields the best reproduction of the DBHF results in infinite matter and also provides a good description of the properties of finite nuclei without any adjustment of parameters.

A study of Λ hypernuclei within the Skyrme–Hartree–Fock model

We investigate the properties of the single Lambda hypernuclei within a Skyrme-Hartree-Fock (SHF) model. The parameters of the Skyrme type effective lambda-nucleon (Lambda N) interaction are obtained by fitting to the experimental Lambda binding energies of hypernuclei with masses spanning a wide range of the periodic table. Alternative parameter sets are also obtained by omitting nuclei below mass number 16 from the fitting procedure. The SHF calculations are performed for the binding energies of the Lambda single-particle states over a full mass range using the best fit parameter sets obtained in these fitting procedures and the results are compared with the available experimental data. The data show some sensitivity to the parameter sets obtained with or without including the nuclei below mass 16. The radii of the Lambda orbits in the hypernuclear ground states and the Lambda effective mass in nuclear matter show some dependence on different parameter sets. We present results for the total binding energy per baryon of the hypernuclei over a large mass region to elucidate their stability as a function of the baryon number. We have also employed the our best fit Lambda N parameter sets to investigate the role of hyperons in some key properties of neutron stars.

Local Defects are Always Neutral in the Thomas–Fermi–von Weiszäcker Theory of Crystals

The aim of this article is to propose a mathematical model describing the electronic structure of crystals with local defects in the framework of the Thomas-Fermi-von Weizsacker (TFW) theory. The approach follows the same lines as that used in {\it E. Cances, A. Deleurence and M. Lewin, Commun. Math. Phys., 281 (2008), pp. 129--177} for the reduced Hartree-Fock model, and is based on thermodynamic limit arguments. We prove in particular that it is not possible to model charged defects within the TFW theory of crystals. We finally derive some additional properties of the TFW ground state electronic density of a crystal with a local defect, in the special case when the host crystal is modelled by a homogeneous medium.

The Jastrow correlation function method in the relativistic Hartree–Fock model for nuclear matter

We study the properties of nuclear matter with the Jastrow correlation function method in the relativistic Hartree–Fock framework. We correlate the strong repulsive effect between two nucleons in a short-range region by taking the Jastrow correlation function on the nucleon trial wavefunction. This correlation function is determined by the variational principle for the total binding energy of the nuclear many-body system. We find that the equation of state of pure neutron matter with a realistic nucleon–nucleon potential, Bonn potential, is overestimated as compared with the one in the relativistic Brueckner–Hartree–Fock model. It is caused by the energy contribution from the short-range correlation on the kinetic energy, which is calculated explicitly in our method. Furthermore, we also demonstrate that the Jastrow correlation function method plays the same role as another short-range correlation method, unitary correlation operator method, for the nucleon–nucleon potential in relativistic Hartree–Fock theory. For the symmetric nuclear matter, the binding energy at the saturation density is weaker than the empirical data for the lack of tensor effect in the Hartree–Fock model.

Antiferromagnetic Order in Multiband Hubbard Models for Iron Pnictides

We investigate multiband Hubbard models for the three iron 3d t(2g) bands and the two iron 3d e(g) bands in LaOFeAs by means of the Gutzwiller variational theory. Our analysis of the paramagnetic ground state shows that neither Hartree-Fock mean-field theories nor effective spin models describe these systems adequately. In contrast to Hartree-Fock-type approaches, the Gutzwiller theory predicts that antiferromagnetic order requires substantial values of the local Hund's-rule exchange interaction. For the three-band model, the antiferromagnetic moment fits experimental data for a broad range of interaction parameters. However, for the more appropriate five-band model, the iron e(g) electrons polarize the t(2g) electrons and they substantially contribute to the ordered moment.

Lattice theory of pseudospin ferromagnetism in bilayer graphene: Competing interaction-induced quantum Hall states

In mean-field theory, bilayer graphene's massive Dirac fermion model has a family of broken-inversion-symmetry ground states with charge gaps and flavor-dependent spontaneous interlayer charge transfers. We use a lattice Hartree-Fock model to explore the lattice scale physics of graphene bilayers, which has a strong influence on ordering energy scales and on the competition between distinct ordered states. We find that inversion symmetry is still broken in the lattice model and estimate that the transferred areal densities are $~$${10}^{\ensuremath{-}5}$ electrons per carbon atom, that the associated energy gaps are $~$${10}^{\ensuremath{-}2} \mathrm{eV}$, that the ordering condensation energies are $~$${10}^{\ensuremath{-}7}$ eV per carbon atom, and that the differences in energy between competing ordered states is $~$${10}^{\ensuremath{-}9}$ eV per carbon atom. We find that states with a quantized valley Hall effect are lowest in energy, but that the coupling of an external magnetic field to spontaneous orbital moments favors the broken-time-reversal-symmetry states that have quantized anomalous Hall effects. Our theory predicts nonmonotonic behavior of the band gap at neutrality on the potential difference between layers, in qualitative agreement with recent experiments.

Static and Dynamic Chain Structures in the Mean-Field Theory

We give a brief overview of recent work examining the presence of $\alpha$-clusters in light nuclei within the Skyrme-force Hartree-Fock model. Of special significance are investigations into $\alpha$-chain structures in carbon isotopes and $^{16}$O. Their stability and possible role in fusion reactions are examined in static and time-dependent Hartree-Fock calculations. We find a new type of shape transition in collisions and a centrifugal stabilization of the $4\alpha$ chain state in a limited range of angular momenta. No stabilization is found for the $3\alpha$ chain.

Synthesis, Antibacterial Activity and Quantum-Chemical Studies of Novel 2-Arylidenehydrazinyl-4-arylthiazole Analogues

A new series of 2-arylidenehydrazinyl-4-arylthiazole derivatives (2a-k) was designed and synthesized through a rapid, simple, and efficient methodology in excellent isolated yield. These compounds were screened for in vitro antimicrobial activities against eight bacteria, e.g. Bacillus cereus, Staphylococcus aureus, Bacillus subtilis, Bacillus megaterium, Pseudomonas aeruginosa, Shigella dysenteriae, Salmonella typhi, Escherichia coli, and three fungi e.g. Aspergillus oryzae, Candida albicans, and Saccharomyces cerevis. The results indicate that some of the compounds exhibit strong antibacterial activity, depending on the bacterial strain, but show virtually no antifungal activity. The structure-antibacterial activity relationships were studied using some physicochemical and quantum-chemical parameters with the ab initio Hartree-Fock model at the RHF/6-31G level of theory. A good qualitative correlation between predicted lipophilic parameters and antibacterial activity has been found.

Atomic data for VUV lines of astrophysical interest in singly ionized rhodium

The first theoretical transition probabilities and oscillator strengths are reported for Rh II lines of astrophysical interest in the VUV region (100–200 nm). They have been obtained through the use of a pseudo-relativistic Hartree–Fock model including core-polarization effects and the accuracy has been estimated to be about 10–15% through a comparison with new experimental lifetimes measured using the time-resolved laser-induced fluorescence technique.

ChemInform Abstract: Gaussian Density Functional Calculations on the Allyl and Polyene Radicals: C3H5 to C11H13

The electronic structure of the allyl radical C3H5 and the polyene radicals C5H7, C7H9, C9H11, and C11H13 have been calculated using the linear combination of Gaussian‐type orbitals‐local spin density method. In contrast to the results obtained using the Hartree–Fock model, which show large errors, the geometries are in excellent agreement with multiconfiguration self‐consistent‐field calculations and with experiment. LSD yields a C2v symmetry for the allyl radical, while the polyenes C5H7 to C11H13 have C–C bonds alternating between single and double bonds. The harmonic vibrational frequencies were calculated for the allyl radical and C5H7 (the 1,4‐pentadienyl radical). The unscaled vibrational frequencies calculated for the allyl radical are in excellent agreement with experiment.

Tensor effects in shell evolution atZ,N=8, 20, and 28 using nonrelativistic and relativistic mean-field theory

Tensor effects in shell evolution are studied within the mean-field approach. Particular attention is paid to the analysis of the magic gaps in different regions of the nuclear chart, namely, $Z,N=8$, 20, and 28. Hartree-Fock calculations with Skyrme and Gogny interactions are performed where the tensor term has a zero and finite range, respectively. Results obtained with and without the tensor component are compared between them and with the experimental data, when available. To complete this analysis, the tensor effect is also investigated within the relativistic Hartree-Fock model, where the exchange of $\ensuremath{\rho}$ mesons and pions is taken into account. It turns out that the tensor effect in the evolution of the magic gaps can be more easily identified in the cases $Z,N=8$ and 20, whereas the interpretation of the effect is more complicated for $Z$ or $N=$ 28. Consequently, we indicate the regions defined by the magic numbers 8 and 20 as suitable for fitting the tensor parameters in a mean-field approach: We suggest to include explicitly the data associated to these gap evolutions in the fitting procedures. In general, with the parametrizations used in this work (which have not been fitted on these data), the mean-field results obtained with the tensor contribution do not reproduce the experimental trend, that is, the reduction of the gaps at 8 and 20 that is observed when going toward the drip lines. Since some of the considered nuclei have $N=Z$, a discussion will be devoted to the interpretation of the experimental data concerning these nuclei and to the Wigner-energy correction.

Temperature dependence of single-particle properties in isospin-symmetric and -asymmetric matter within the Dirac–Brueckner–Hartree–Fock model

The understanding of the interaction of nucleons in nuclear and neutron-rich matter at non-zero temperature is important for a variety of applications ranging from heavy-ion collisions to nuclear astrophysics. In this paper we apply the Dirac–Brueckner–Hartree–Fock method along with the Bonn B potential to predict single-particle properties in symmetric nuclear matter and neutron-rich matter at finite temperature. It is found that temperature effects are generally small but can be significant at low density and momentum.

Theoretical and experimental analysis of titanium Compton profile using 137Cs

The objective of this study is to measure the Compton profile of a titanium coating on a glass substrate, comparing it with a profile computed by the Hillman and Skilman program based on the Hartree-Fock model. The experimental Compton profile was obtained using 661.7keV gamma-rays from a (1)Ci (137)Cs source and a 3''x3'' NaI(Tl) detector. The experimental, theoretical and unfolded Compton profiles of titanium have been compared. The results illustrate the breadth of experimental Compton profile in comparison with the two others. This difference can be mainly attributed to the Doppler broadening effect, the final quantum state of the electron and partly by the approximations implemented in the theoretical model.