Hartree-Fock Formalism Research Articles

Defects in titanates

Electronic, structural and optical properties of titanates (BaTiO3, SrTiO3, CaTiO3 and PbTiO3) containing different point defects are reviewed and discussed in the present work. The results are obtained using a quantum-chemical method based on the Hartree-Fock formalism and utilising the Large Unit Cell (LUC) and the Embedded Molecular Cluster (EMC) models. The outcomes of the computations are compared and discussed in the light of the available experimental data. The formation of Jahn-Teller (JT) polarons and bipolarons due to the presence of some point defects in the titanate crystals are found to be very important in order to understand better the behaviour of these materials. In particular, such phenomena as the non-linear photoconductivity in BaTiO3, the drastic increase in the electrical conductivity in CaTiO3 and BaTiO3 crystals, and the superconductivity in SrTiO3 could be completely or partially explained by the presence of JT polarons and different interacting mechanisms between these defects.

The strong dimer of Ge 60, Ge 116

The strong dimer of Ge 60, Ge 116, is considered for MNDOd and AM1 type semiempirical quantum chemical calculations within the limitations of restricted Hartree–Fock formalism. Both methods predict this, yet non-existent, structure to be stable but highly endothermic. Some geometrical and quantum chemical data are presented.

Pseudo-spin–orbit potential in the relativistic Hartree–Fock formalism

The pseudo-spin symmetry (PSS) is investigated in the framework of the relativistic Hartree–Fock approximation (RHFA). The Dirac equation is reduced to a Schrödinger like equation for the small component of the nucleon spinor. Though this equation reveals that the symmetry appears to be broken even in the Σ S D + Σ 0 D =0 limit, where Σ S D and Σ 0 D are the direct (Hartree) scalar and time component of the vector nucleon self-energies, respectively, pseudo-spin symmetry is approximately conserved. The behavior of the single-particle potentials and of the wave functions of both neutron and proton pseudo-spin doublets in the 40Ca and 48Ca nuclei are analyzed. There is no dominance of the term dependent on the pseudo-orbital angular momentum (containing the pseudo-centrifugal barrier) compared to the pseudo-spin–orbit potential (PSOP). The contributions to the energy of each pseudo-spin doublet (PSD) level coming from all terms entering the equation for the small component of the Dirac spinor are calculated. The quasi-degeneracy of the PSD levels in the RHFA can be explained by a compensation of the differences between these contributions. The effect of the self-consistency is comparable to that of the PSOP itself.

Nuclear rainbow and the EOS of cold nuclear matter

Elastic scattering of strongly-bound light nuclei at energies of 10–70 MeV/nucleon shows the phenomenon of “Rainbow scattering” which is associated with strongly attractive potentials and deflections into “negative” angles. This process involves a strong overlap of nuclear densities (up to twice the saturation density of nuclear matter), but rather weak absorption due to the high Q-values for excitations and high separation energies of nucleons. In particular, elastic 16O + 16O scattering has been studied with high precision, over a wide range of angles and energies. At high energies, a systematics of primary Airy minima has been established, while at lower energies higher-order Airy structures were identified. Elastic data at all energies are consistently described by the potentials obtained from a self-consistent folding model using a weakly density dependent nucleon-nucleon interaction. This same density dependent interaction gives, within the Hartree-Fock formalism, a soft equation of state (EOS) for cold nuclear matter (with the nuclear incompressibility K ≈ 230 MeV). We also show that the Pauli-blocking, expected at large density overlap, is strongly reduced if the mean field contribution to the relative momenta of nucleons in the dinuclear system is treated self-consistently. Similar study of other refractive systems also confirms the soft EOS for cold nuclear matter.

The H atom in CaTiO 3 : Structure and electronic properties

In the present work we explore the effects that an H impurity produces upon the geometry and electronic structure of the CaTiO 3 crystal considering the cubic and orthorhombic crystallographic lattices of the material. A quantum-chemical method based on the Hartree-Fock formalism and the periodic large-unit-cell model is used throughout the work. The analysis of the results shows that the interstitial H impurity binds to one of the O atoms forming the so-called O-H group. At equilibrium, the O-H distances are found to be equal to 0.89 and 1.04 Å for cubic and orthorhombic lattices respectively. Atomic displacements and relaxation energies are analysed comparing the obtained results in the cubic lattice with those in the orthorhombic lattice. In the cubic phase the computed relaxation energy of vicinity of the O-H group is found to be equal to 1.1 eV and the atomic displacements generally obey the Coulomb law. So, the negatively charged O atoms move outwards from the defective region by about 0.09 Å while the positively charged Ti and Ca atoms move towards the defective region by about 0.05 and 0.01 Å respectively. A similar effect is observed in the orthorhombic lattice of CaTiO 3 doped with an H atom. It is necessary to mention that different O positions in the orthorhombic structure are considered for the O-H bond creation. The computed relaxation energies of the atomic displacements in this structure are found to be equal to 2.3 and 2.1 eV depending on the crystallographic type of the bonding O atom.

Effect of interstitial hydrogen on structural and electronic properties of BaTiO3

Abstract We investigate the geometry and electronic structure of an interstitial H atom in the BaTiO3 crystal considering both cubic and tetragonal crystallographic lattices. A quantum-chemical method based on the Hartree-Fock formalism is used throughout the study. Interstitial H is found to bind to one of the O atoms, forming the so-called OH group. At equilibrium, the O-H distances are found to be 0.89 and 0.91 Å for cubic and tetragonal lattices respectively. The performed automated geometry optimization procedure of the defective region shows considerable outward movements of atoms closest to the impurity. The role of the H impurity in ferroelectric polarization in the BaTiO3 crystal is analysed using the results obtained in connection with the available experimental data on ferroelectric perovskites.

Electrical resistivity and thermoelectric power of molten gallium: Theory versus experiment

Abstract We present our new accurate measurements on the electrical resistivity and thermopower of liquid gallium as a function of temperature. To interpret our experimental data we used, for the first time to our knowledge (earlier calculations used the pseudopotential formalism), ab initio calculations of the electrical resistivity ρ(E) and of the thermoelectric power Q(E) of liquid gallium as functions of energy. This formalism has the great advantage of including a full-energy dependent calculation of the thermopower. To construct the phase shifts we used the experimental pair correlation function. To calculate the resistivity and thermopower we used both the structure factor obtained experimentally and that calculated with hard spheres. The results are compared and discussed. Various potentials based on the Hartree-Fock formalism and using different exchange contributions have been used. Overall agreement between calculation and experiment is obtained. It seems, however, that the Kohn-Sham value of t...

Large-scale modelling of the phase transitions in KTa 1− xNb xO 3 perovskite solid solutions

We use quantum chemical method of the intermediate neglect of the differential overlap (INDO) based on the Hartree–Fock formalism for a large-scale modelling of the atomic and electronic structure of KNb x Ta 1− x O 3 (KTN) perovskite solid solutions. Results for periodic defect models (large unit cell) of 40 and 320 atoms are compared with 135-atom INDO cluster calculations. Periodic Nb impurities in KTaO 3 reveal clear off-center displacement beginning with the smallest calculated concentrations, so does an isolated Nb impurity in a cluster INDO calculation. The magnitude of Nb off-center displacement is close to the X-ray-absorption fine-structure observation (0.27 a.u.). In contrast, Ta impurities in KNbO 3 always remain on-center, due to higher ionicity of Ta as compared to Nb atom. Using the calculated energy gain due to the off-center displacements of Nb atoms for several concentrations of Nb in KTN, we construct the non-empirical Ginzburg–Landau-type functional for the excess energy. The coefficients of this functional are concentration dependent. This dependence allows to define the type of the concentration-induced phase transition in KTaO 3 alloyed by Nb.

Calculations of radiation-induced point defects, polarons and excitons in ferroelectric perovskites

We review results of our recent large-scale computer simulations of radiation-induced point defects, excitons and polarons in ABO 3 perovskite crystals, focusing mostly on KNbO 3 and KTaO 3 as representative examples. We have calculated the atomic and electronic structure of defects, their optical absorption, defect-induced electron density redistribution, and activation energies for defect migration. The majority of our results were obtained using the quantum-chemical method of the intermediate neglect of differential overlap (INDO) based on the Hartree–Fock formalism, as well as the shell model (SM). The main findings are compared with those obtained by means of ab initio density functional theory (FP-LMTO) first-principles calculations.

Computer Modeling of Point Defects in Perovskite Crystals

The results of calculations for mixed perovskite KNb x Ta 1 m x O 3 (KTN) solid solutions are presented and discussed. The semiempirical method of the intermediate neglect of differential overlap (INDO) based on the Hartree-Fock formalism predicts magnitudes of the Nb off-center displacements which are in agreement with EXAFS data. Results are compared with ab initio FP-LMTO first-principles calculations. The latter formalism and the semiempirical INDO methods are combined for the study of hole and electron polarons in perovskites. We calculated the defect migration energies using INDO method and classical shell model (SM) for the cubic phase of the KNbO 3 . The migration energies for the O vacancy obtained by these methods are reasonably close and agree with the only experimental estimate available of 1 eV.

Modeling of defects and surfaces in perovskite ferroelectrics

The ab initio linear muffin-tin orbital method combined with density functional theory (local approximation) and the semiempirical method of the intermediate neglect of differential overlap (INDO) based on the Hartree-Fock formalism are used for the study of the F centers and the hole polarons in KNbO 3 perovskite crystals. We present and discuss results of the calculations for SrTiO 3 (1 0 0) surface relaxation with different terminations (SrO and TiO 2) using an ab initio methods based on Hartree-Fock (HF) and density functional theory (DFT) formalisms. We compare our results with previous ab initio and shell model (SM) calculations and LEED experiments.

High pressure Raman studies on the structural conformation of oligophenyls

The goal of this combined experimental and computational study is to investigate the structural conformation of oligo( para-phenylenes) in the crystalline phase, in particular the planarity of this type of molecules. To this end we have performed Raman experiments on para-terphenyl and para-quaterphenyl in a pressure range from 0 to 70 kbar and at temperatures from 10 to 300 K. The positions and the relative intensities of the C–C interring stretch mode at 1280 cm −1 and the C–H in-plane bend mode at 1220 cm −1 have been tracked. We find that upon increasing temperature at ambient pressure the intensity ratio I 1280/ I 1220 drops rapidly at temperatures that coincide with the crystallographic phase transition for the investigated materials. At ambient temperature also, this intensity ratio drops rapidly upon increasing pressure up to about 15 kbar. In the computational part, the Raman frequencies and activities of isolated 3P and 4P molecules were calculated within restricted Hartree–Fock formalism with the interring tilt angles varying from 0 to 90°. These calculations confirm that the I 1280/ I 1220 intensity ratio can be related to the planarity of the molecules. Three-dimensional bandstructure calculations within density functional theory were applied to determine phonon frequencies and estimate Raman activities for the polymer poly( para-phenylene). These simulations show that the same conclusions hold for crystalline environment.

First hyperpolarizabilities of dipolar photoconductive chromophores: an approach toward monolithic molecular materials for photorefractivity

Second-order optical nonlinearities of a series of dipolar photoconductive chromophores have been investigated by semiempirical quantum chemical calculations using time-dependent Hartree–Fock formalism in conjunction with PM3 parameter and experimental evaluation of the first molecular hyperpolarizability ( β). A linear correlation between the measured and calculated β values was observed, and the structure–property relationship discussed in terms of the structural variation. It was noted that the optical nonlinearities of the dipolar photoconductive molecules with carbazole, indole, or indoline as donor units are large enough for the electrooptic and photorefractive applications.

A new spd tight-binding model of magnetism in transition metals

We present the extension of an efficient spd tight-binding model to the case of spin polarized materials by including electron–electron interactions, in an extended Hubbard–Hartree–Fock formalism. It is applied with success to rhodium and palladium clusters and slabs.

First-principles and semiempirical calculations for bound-hole polarons inKNbO3

The ab initio linear muffin-tin-orbital formalism and the semiempirical method of the intermediate neglect of the differential overlap based on the Hartree-Fock formalism are combined for the study of the hole polarons (a hole trapped nearby the cation vacancy) in a cubic phase of ${\mathrm{KNbO}}_{3}$ perovskite crystals. The 40-atom and 320-atom supercells were used, respectively. We predict the existence of both one-site and two-site (molecular) polarons with close optical absorption energies (0.9 eV and 0.95 eV). The relevant experimental data are discussed.

Experimental electrical resistivity and thermopower of molten germanium interpreted with muffin-tin potential calculations

We present our new accurate measurements on the electrical resistivity and thermopower of liquid germanium as a function of temperature. To interpret our data we used ab initio calculations of the electrical resistivity and of the thermoelectric power Q(E) of liquid germanium as a function of energy. The calculations have been performed within a self-consistent method in which the conduction band bottom has been matched with the muffin tin zero. Various potentials have been used especially the potential based on the Hartree-Fock formalism and the potential derived from the density functional theory which take into account the exchange and correlation effects. As result the new prescriptions improve significantly the resistivity and the thermopower with respect to the methods commonly used.

A new partitioning scheme for molecular interacting systems within a multiconfigurational or monoconfigurational Hartree–Fock formalism

A new partitioning scheme for molecular interacting systems within a multiconfigurational or monoconfigurational Hartree–Fock formalism

A new partitioning scheme for molecular interacting systems within a multiconfigurational or monoconfigurational Hartree–Fock formalism

A new partitioning scheme for molecular interacting systems within a multiconfigurational or monoconfigurational Hartree–Fock formalism

Deformed HF calculation for 76Ge 76Se double-betadecay

The two-neutrino double-beta decay (2-decay) for 76Ge 76Se is studied within the framework of the deformed Hartree-Fock formalism. An interaction given by Kuo and modified by Ahalpara et al is used. The results of our model calculation are compared with those obtained using the shell model and the quasiparticle random phase approximation. The role of the deformation, pairing and Coulomb interaction in double-beta decay is investigated. We have found that the inclusion of both deformation and pairing influences the 2-decay matrix element significantly.

A new partitioning scheme for molecular interacting systems within a multiconfigurational or monoconfigurational Hartree-Fock formalism

A new partitioning scheme for molecular interacting systems within a multiconfigurational or monoconfigurational Hartree-Fock formalism