Hartree-Fock Scheme Research Articles

Keywords

There is some controversy over the question of the correct adsorption site for formate on Cu(100). On the basis of SEXAFS and NEXAFS studies Stöhr et al. favour a bridge site with oxygen atoms near fourfold hollows, while Woodruff et al. bring photoelectron diffraction studies to bear argue for a bridge site with the oxygen atoms almost on top of Cu atoms. We calculate the total energies for the two arrangements, optimising the distance of the formate from the Cu surface, using a self-consistent Hartree-Fock scheme with a Gaussian basis. We find the Woodruff structure more stable by some 0.38 eV per formate radical. We calculate the binding energy to be 1.74 eV per formate radical.

Keywords

There is some controversy over the question of the correct adsorption site for formate on Cu(100). On the basis of SEXAFS and NEXAFS studies Stöhr et al. favour a bridge site with oxygen atoms near fourfold hollows, while Woodruff et al. bring photoelectron diffraction studies to bear argue for a bridge site with the oxygen atoms almost on top of Cu atoms. We calculate the total energies for the two arrangements, optimising the distance of the formate from the Cu surface, using a self-consistent Hartree-Fock scheme with a Gaussian basis. We find the Woodruff structure more stable by some 0.38 eV per formate radical. We calculate the binding energy to be 1.74 eV per formate radical.

Compton scattering study and electronic structure of different phases of NH4NO3

In this paper, we present energy bands, density of states and the nature of hydrogen bonding in different temperature-dependent phases of NH4NO3, namely phases II (357–398 K), III (305–357 K) and IV (257–305 K), using the full potential linearized augmented plane wave and linear combination of atomic orbitals (LCAO) methods. Both band structure calculations show the insulating character of the II–IV phases of NH4NO3. In addition, we have reported the isotropic Compton profile of NH4NO3(IV) measured using 661.65 keV γ-radiation from a 137Cs isotope. The experimental momentum density has been compared with that based on density functional theory (DFT) and Hartree–Fock schemes within the LCAO method. It is seen that the LCAO with hybridization of DFT and Hartree–Fock (so-called B3LYP) gives better agreement with the present Compton profile measurement.

Static and dynamic coupled perturbed Hartree-Fock vibrational (hyper)polarizabilities of polyacetylene calculated by the finite field nuclear relaxation method

The vibrational contribution to static and dynamic (hyper)polarizability tensors of polyacetylene are theoretically investigated. Calculations were carried out by the finite field nuclear relaxation (FF-NR) method for periodic systems, newly implemented in the CRYSTAL code, using the coupled perturbed Hartree-Fock scheme for the required electronic properties. The effect of the basis set is also explored, being particularly important for the non-periodic direction perpendicular to the polymer plane. Components requiring a finite (static) field in the longitudinal direction for evaluation by the FF-NR method were not evaluated. The extension to that case is currently being pursued. Whereas the effect on polarizabilities is relatively small, in most cases the vibrational hyperpolarizability tensor component is comparable to, or larger than the corresponding static electronic contribution.

Hyperpolarizability of two electron atoms under spherically confined Debye plasma

Pilot calculations on the hyperpolarizability of He, the first neutral member of the two electron sequence, have been performed under spherical confinement with a view to analyse the effect of pressure on such non linear optical properties. Detailed investigations have also been performed for the first time on the hyperpolarizability due to the effect of screened Coulomb potential obtained from a surrounding Debye plasma environment. Variation perturbation theory within coupled Hartree-Fock scheme has been adopted to estimate the non linear optical properties under such external confinement. For a given plasma coupling strength, the hyperpolarizability value is found to reduce systematically with decrease of radius of confinement, while the same is found to increase continuously with increasing plasma coupling strength determined by gradual enhancement of the screening parameter for a given radius of confinement. Under strong confinement the hyperpolarizability value is found to be negative. The estimated free atom hyperpolarizability is consistent with the existing coupled Hartree-Fock result.

Second-Order Contribution of the Incompressibility in Asymmetric Nuclear Matter

With the complementarity of the nucleonic three-body force, we present the saturation points of symmetric nuclear matter with different interactions adopted within the Brueckner—Hartree—Fock scheme, and a more accurate empirical parameterization function for the equation of state of symmetric nuclear matter and pure neutron matter. On the basis of this fit formula, the symmetry energy and its derivatives are investigated, and ultimately the higher-order coefficient of the isobaric incompressibility for isospin asymmetric nuclear matter is predicted.

Electronic structure, optical properties and Compton profiles of Bi 2S 3 and Bi 2Se 3

In this paper, we present the Compton profiles of Bi 2S 3 and Bi 2Se 3 using our 20 Ci 137Cs Compton spectrometer. To compare our experimental data, we have computed the Compton profiles, energy bands and density of states using linear combination of atomic orbitals with density functional theory (DFT) and Hartree-Fock (HF) scheme. It is seen that hybrid functional involving HF and DFT approximations gives a relatively better agreement with experimental momentum densities than other approximations of DFT. We have also reported the band structure, density of states, valence charge densities, dielectric functions and electron energy loss spectra using full potential linearized augmented plane wave scheme. On the basis of charge densities, Mulliken’s population data and equal-valence-electron-density profiles, Bi 2S 3 is found to be more ionic than Bi 2Se 3. The calculated dielectric functions for the parallel and perpendicular polarizations show a small anisotropic effect. The electron energy loss spectrum for Bi 2Se 3 is found to be in good agreement with the available experimental data.

Electric field effects on nuclear magnetic shielding of the 1:1 and 2:1 (homo and heterochiral) complexes of XOOX′ (X, X′ = H, CH3) with lithium cation and their chiral discrimination

The set of 1:1 and 2:1 complexes of XOOX' (X, X' = H, CH(3)) with lithium cation has been studied to determine if they are suitable candidates for chiral discrimination in an isotropic medium via nuclear magnetic resonance spectroscopy. Conventional nuclear magnetic resonance is unable to distinguish between enantiomers in the absence of a chiral solvent. The criterion for experimental detection is valuated by the isotropic part of nuclear shielding polarisability tensors, related to a pseudoscalar of opposite sign for two enantiomers. The study includes calculations at coupled Hartree-Fock and density functional theory schemes for (17)O nucleus in each compound. Additional calculations for (1)H are also included for some compounds. A huge static homogeneous electric field, perpendicular to the magnetic field of the spectromer, as big as ≈1.7 × 10(8) V m(-1) should be applied to observe a shift of ≈1 ppm for (17)O magnetic shielding in the proposed set of complexes.

Nuclear matter equation of state using density-dependent M3Y nucleon–nucleon interactions

The main motivation of this work is to study the isospin-asymmetric nuclear matter (NM) equation of state using the density-dependent M3Y-Paris and Reid effective interactions in their CDM3Y version. To do so, the CDM3Y parameters for both interactions are linked in simple formulae to the saturation density, energy per nucleon and incompressibility, K0, of symmetric NM using the same non-relativistic Hartree–Fock scheme as used by Khoa et al. New sets of the CDM3Y-Paris (Reid) density dependences are deduced to generate different equations of state starting from very soft one, K0 = 150 MeV, up to the stiff one with K0 = 300 MeV. The properties of isospin-symmetric and asymmetric NM, up to pure neutron matter (PNM), and the nuclear density range and stiffness of bound asymmetric NM are then explored for the equations of state with the incompressibility range of 200–300 MeV. With conspicuous differences for all considered NM quantities even at sub-saturation densities, the most investigated equations of state yield soft nuclear symmetry energy at the high densities with a maximum value lying in the range ρ0-3ρ0. Only the CDM3Y-Paris (Reid) interaction characterized with the incompressibility value 240 MeV (230 MeV) predicts NM pressure consistent with previous constraints on both symmetric NM and PNM pressure. Finally, the behavior of the asymmetric NM saturation density, energy per nucleon and incompressibility is investigated as a function of the isospin-asymmetry, I ≡ (ρn −ρp)/ρ.

Electron momentum density distribution in Cd 3P 2

A study of electron momentum density distribution in Cd 3P 2 is reported in this work. The measurement of Compton profile is carried out on a polycrystalline sample using 59.54 keV gamma-rays emanating from an 241Am radioisotope. The theoretical calculations are performed using linear combination of atomic orbitals method following the Hartree–Fock and a posteriori density functional theories. The spherically averaged theoretical Compton profiles are in good agreement with the measurement. The best agreement is, however, shown by the Hartree–Fock scheme. Simple ionic model calculations for a number of configurations ( Cd + x ) 3 ( P − 3 x / 2 ) 2 ( 0.0 ⩽ x ⩽ 2.0 in step of 0.2) are also performed utilizing free atom profiles. The ionic model supports transfer of 2.0 electrons per Cd atom from 5 s state to 3 p state of P.

Electronic and optical properties of iron pyrite

We have computed for the first time the energy bands, density of states and Compton profiles of FeS 2 using linear combination of atomic orbital approach. To interpret the theoretical Compton profiles, we have measured the first ever experimental Compton profiles along [1 1 0] and [1 0 0] directions using 100 mCi 241Am Compton spectrometer. The absolute profiles and the anisotropies in momentum densities are well explained by the hybridisation of Hartree–Fock scheme and density functional theory. In addition, to explore the utility of FeS 2 in photovoltaics, we have also discussed the optical properties using full potential linearised augmented plane wave method.

Calculation of the first static hyperpolarizability tensor of three-dimensional periodic compounds with a local basis set: A comparison of LDA, PBE, PBE0, B3LYP, and HF results

The computational scheme for the evaluation of the second-order electric susceptibility tensor in periodic systems, recently implemented in the CRYSTAL code within the coupled perturbed Hartree-Fock (HF) scheme, has been extended to local-density, gradient-corrected, and hybrid density functionals (coupled-perturbed Kohn-Sham) and applied to a set of cubic and hexagonal semiconductors. The method is based on the use of local basis sets and analytical calculation of derivatives. The high-frequency dielectric tensor (epsilon(infinity)) and second-harmonic generation susceptibility (d) have been calculated with hybrid functionals (PBE0 and B3LYP) and the HF approximation. Results are compared with the values of epsilon(infinity) and d obtained from previous plane-wave local density approximation or generalized gradient approximation calculations and from experiment. The agreement is in general good, although comparison with experiment is affected by a certain degree of uncertainty implicit in the experimental techniques.

Direct and indirect solutions of gap equations

Electronic correlation in extended systems is often treated by pairing orbitals or spin orbitals, which are occupied in the restricted Hartree-Fock scheme, with virtual ones. The minimization condition can be expressed as a so-called gap equation for the gap created in the band as a result of the pairing. The gap equation is usually solved directly by iteration. Its solution determines the degree of pairing and thus the new spin orbitals. Indirectly the same result can be obtained by solving the effective equations for these new spin orbitals.

Elongation cutoff technique armed with quantum fast multipole method for linear scaling

A linear-scaling implementation of the elongation cutoff technique (ELG/C) that speeds up Hartree-Fock (HF) self-consistent field calculations is presented. The cutoff method avoids the known bottleneck of the conventional HF scheme, that is, diagonalization, because it operates within the low dimension subspace of the whole atomic orbital space. The efficiency of ELG/C is illustrated for two model systems. The obtained results indicate that the ELG/C is a very efficient sparse matrix algebra scheme.

Spontaneous symmetry breaking approach to La 2CuO 4 properties: Hints for matching the Mott and Slater pictures

Special solutions of the Hartree–Fock (HF) problem for Coulomb interacting electrons described by a simple model of the Cu–O planes in La 2CuO 4 are presented. One of the mean field states obtained, is able to predict some of the most interesting properties of this material, such as its insulator character and the antiferromagnetic order. The natural appearance of pseudogaps in some states of this material is also indicated by another of the HF states obtained. These surprising results follow after eliminating spin and crystal symmetry restrictions usually imposed on the single particle HF orbitals, by employing the rotational invariant formulation of the HF scheme originally introduced by Dirac. Therefore, it is exemplified here, how up to know considered strong correlation effects, can be described by improving the HF solution of the considered system. In other words, it has been argued, that defining correlation effects as the ones shown by the system and not predicted by the HF best (lowest energy) solution, allows to explain important, up to know considered as strong correlation properties, as simple mean field ones. The discussion also helps to clarify the role of the antiferromagnetism and pseudogaps in the physical properties of the HTSC materials and indicates a promising way to start conciliating the Mott and Slater pictures in the physics of the transition metal oxides and other strongly correlated electron systems.

On the use of the exact exchange optimized effective potential method for static response properties

AbstractIn the present work, we question the notion that the modified Kohn–Sham orbital energies and smaller HOMO‐LUMO gaps, produced from the exact exchange optimized effective potential (EXX‐OEP) method, might significantly improve the paramagnetic contribution to the NMR chemical shifts compared with the regular Hartree–Fock (HF) scheme. First of all, it is shown analytically that if there is such a local potential that produces the HF energy, and the Kohn–Sham orbitals are obtained as a result of separate rotations of the occupied and virtual HF orbitals, any static magnetic property obtained from the coupled perturbed HF method will be identical to that obtained from the EXX‐OEP approach. In fact the EXX‐OEP method is equivalent to the improved virtual orbitals (IVO) scheme in which the energies of the virtual orbitals are modified by an effective potential. It is shown that the IVO procedure leaves static response properties unchanged. To test our analysis numerically we have employed several variants of the EXX‐OEP method, based on the expansion of the local exchange potential into a linear combination of fit functions. The different EXX‐OEP schemes have been used to calculate the NMR chemical shifts for a set of small molecules containing C, H, N, O, and F atoms. Comparison of the deviation between experimental and calculated chemical shifts from the HF, the EXX‐OEP, and the common energy denominator approximation (CEDA) approximation to the EXX‐OEP methods has shown that for carbon, hydrogen, and fluorine the EXX‐OEP methods do not yield any improvement over the HF method. For nitrogen and oxygen we have found that the EXX‐OEP performs better than the HF method. However, in the limit of infinite fit basis set and, as a consequence of it, a perfect fit of the HF potential the EXX‐OEP and the HF methods would afford the same chemical shifts according to our theoretical analysis. Unfortunately, without a perfect fit the chemical shifts from the EXX‐OEP method strongly depend on the fit convergence. In our opinion, the EXX‐OEP method should not be used for response properties as it is numerically unstable. Thus, any apparent improvement of the EXX‐OEP method over the HF scheme for a finite fit basis set must be considered spurious. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Optical characterization of ground states of polyacene

We investigate the ground-state properties of polyacene in terms of an extended Peierls-Hubbard Hamiltonian with particular emphasis on its structural instability of two types: double bonds in a cis pattern and those in a trans pattern. Calculating the polarized optical conductivity spectra within and beyond the Hartree-Fock scheme, we reveal a striking contrast between the cis and trans configurations. The two Peierls-distorted states are almost degenerate in their energetics but quite distinct in their optics.

Electronic Structure and Compton Profiles of Tungsten

The energy bands, density of states and Compton profiles of tungsten have been computed using band structure methods, namely the spin-polarized relativistic Korringa-Kohn-Rostoker (SPR-KKR) approach as well as the linear combination of atomic orbitals with Hartree-Fock scheme and density functional theory. The full potential linearized augmented plane wave scheme to calculate these properties and the Fermi surface topology (except the momentum densities) have also been used to analyze the theoretical data on the electron momentum densities. The directional Compton profiles have been measured using a 100 mCi 241Am Compton spectrometer. From the comparison, the measured anisotropies are found to be in good agreement with the SPR-KKR calculations. The band structure calculations are also compared with the available data.

Band-edge absorption spectroscopy of [formula omitted] multilayer nanocomposites

CdSe / a - SiO x multilayer nanocomposites containing CdSe nanocrystals between a -SiO x thin layers have been produced by sequential thermal vacuum deposition of CdSe and SiO x on quartz substrates. Strong confinement effect has been observed in absorption spectra. Average size of nanocrystals was estimated from the absorption spectra discriminating between confinement, oxidation and artificial effects. Areal density of nanocrystals in CdSe sublayers was estimated to be ∼ 10 12 cm - 2 . Oxidation of nanocrystals was observed as a decreasing of optical absorption in the region above the optical band-gap energy. The binding energies of Cd–O and Se–O bonds have been calculated as a function of the inter-atomic distances for the Cd 17 Se 17 cluster bounded to SiO 4 fragment in the framework of self-consistent Hartree–Fock scheme by means of the semi-empirical PM3 method in approximation of NDDO (neglect of diatomic differential overlapping). The greater energy has been found for Cd–O bonds ( ∼ 123.5 kcal / mol ) that evidences the preferred oxidation of Cd facets of CdSe nanocrystals.

Relativistic chiral Hartree-Fock description of nuclear matter with constraints from nucleon structure and confinement

We present a relativistic chiral effective theory for symmetric and asymmetric nuclear matter taken in the Hartree-Fock scheme. The nuclear binding is ensured by a background chiral invariant scalar field associated with the radial fluctuations of the chiral quark condensate. Nuclear matter saturation is obtained once the scalar response of the nucleon-generating three-body repulsive forces is incorporated. For those parameters related to the scalar sector and quark confinement mechanism inside the nucleon we make use of an analysis of lattice results on nucleon mass evolution with quark mass. The other parameters are constrained as much as possible by standard hadron and nuclear phenomenology. Special attention is paid to the treatment of the propagation of the scalar fluctuations. The rearrangement terms associated with in-medium modified mass and coupling constants are explicitly included to satisfy the Hugenholtz-Van Hove theorem. We point out the important role of the tensor piece of the rho exchange Fock term to reproduce the asymmetry energy of nuclear matter. We also discuss the isospin dependence of the Landau nucleon effective mass.