R. A. Evarestov

Local characteristics of crystal electronic structure in the Hartree-Fock method

The formalism developed in molecular theory for calculation of local electronic-structure characteristics in a nonorthogonal atomic basis is generalized to systems with translational symmetry. Expressions have been derived to describe the bond orders, covalency, and valence in a crystal for restricted and unrestricted Hartree-Fock methods. Nonempirical electronicstructure calculations and an analysis of chemical bonding in the TiO2, Ti2O3, and TiO titanium oxide crystals have been performed.

Symmetrical transformation of basic translation vectors in the supercell model of imperfect crystals and in the theory of special points of the Brillouin zone

The matrices of the symmetrical transformations for all the three-dimensional Bravais lattices are found. These matrices may be applied for the investigation of physical properties of single defects in crystals in the supercell model. The corresponding transformations of reciprocal lattices with a not more than 32-fold decrease of the Brillouin zone volume are used for the generation of special point sets for the approximative numerical integration over the Brillouin zone in cubic crystals with simple, face-centred and body-centred lattices.

Quantum mechanics–molecular dynamics approach to the interpretation of x-ray absorption spectra

The quantum mechanics-molecular dynamics approach to the simulation of configuration-averaged EXAFS spectra is proposed, and its application is discussed for the example of the Ti K-edge EXAFS spectrum in cubic perovskite SrTiO(3). Proper use of ab initio quantum mechanics allows a number of empirical parameters, used in the molecular dynamics simulation, to be reduced, whereas the molecular dynamics allows us to account for temperature effects. All together, the approach provides a way of accounting for static and dynamic disorder in EXAFS signals from the coordination shells above the first one, where many-atom (multiple-scattering) effects are often important.

Supercell Model of V-Doped TiO2: Unrestricted Hartree-Fock Calculations

The host crystal space group and the point defect site symmetry group being given the procedure of generation of the imperfect space group in the supercell or periodic defect model is considered. The approach developed is applied to the symmetry analysis of the possible space groups of metal-doped rutile and anatase structures in the supercell model. The results of unrestricted Hartree-Fock calculations of the V-doped rutile electronic structure (an impurity atom charge, valence states, an impurity level position in the energy gap) are given. Supercells of 36, 60, 84 atoms chosen on the base of the symmetry analysis are calculated. The convergence of the results with the supercell increasing is demonstrated.

Calculations of electronic structure of the UF6 molecule and the UO2 crystal with a relativistic pseudopotential

The influence of relativistic effects on the properties of uranium hexafluoride was considered. Detailed comparison of the spectrum of one-electron energies obtained in the nonrelativistic (by the Hartree-Fock method), relativistic (by the Dirac-Fock method), and scalar-relativistic (using a relativistic potential of the uranium atom core) calculations was carried out. The methods of optimization of atomic basis in the LCAO calculations of molecules and crystals are discussed which make it possible to consider distortion of atomic orbitals upon the formation chemical bonds. The influence of the atomic basis optimization on the results of scalar-relativistic calculations of the molecule UF6 properties is analyzed. Calculations of the electronic structure and properties of UO2 crystals with relativistic and nonrelativistic pseudopotentials are fulfilled.

Electronic structure of crystalline uranium nitrides UN, U2N3 and UN2: LCAO calculations with the basis set optimization

The results of LCAO DFT calculations of lattice parameters, cohesive energy and bulk modulus of the crystalline uranium nitrides UN, U2N3 and UN2 are presented and discussed. The LCAO computer codes Gaussian03 and Crystal06 are applied. The calculations are made with the uranium atom relativistic effective small core potential by Stuttgart-Cologne group (60 electrons in the core). The calculations include the U atom basis set optimization. Powell, Hooke-Jeeves, conjugated gradient and Box methods are implemented in the authors optimization package, being external to the codes for molecular and periodic calculations. The basis set optimization in LCAO calculations improves the agreement of the lattice parameter and bulk modulus of UN crystal with the experimental data, the change of the cohesive energy due to the optimization is small. The mixed metallic-covalent chemical bonding is found both in LCAO calculations of UN and U2N3 crystals; UN2 crystal has the semiconducting nature.

The hartree-fock method and density-functional theory as applied to an infinite crystal and to a cyclic cluster

The basic properties of the one-electron density matrix of a crystal are considered. It is shown that when the Brillouin zone special-point technique, developed earlier for calculating the electron density and local exchange potentials, is directly applied to the case of a nonlocal exchange potential, the calculated density matrix is not idempotent and physically meaningless divergences appear. To surmount these difficulties, a scheme is developed for interpolating the density matrix over the Brillouin zone in reciprocal space. A modification of the Hartree-Fock method for an infinite crystal is proposed in which the equations of the cyclic-cluster model are satisfied automatically. The electronic structures of perfect crystals of BNhex, silicon, and rutile are calculated using the Hartree-Fock method and the density-functional theory.

Symmetry and stability of nanotubes based on titanium dioxide

The process of rolling a monolayer of bulk crystal with biperiodical planar lattice to the nanotube was analyzed. It was shown by an example of the carbon nanotubes how the tube symmetry can be revealed through the analysis of symmetry of graphene layers (the layer group with a hexagonal planar lattice) and its changes at the rolling to form the tube. The developed approach can be used to analyze the symmetry of any nanotube. A computer program we developed is discussed that allows to determine the nanotube symmetry using the data on the symmetry and coordinates of the atoms in the nanolayer and get the coordinates of the atoms in the unit cell of the nanotube which can be used for the further quantum-chemical calculations. The method and results of ab initio calculations of the titanium dioxide monolayer stability in the LCAO basis optimized for the bulk crystal, using the hybrid exchange-correlation potential PBE0 are presented. Symmetry properties of nanotubes obtained by rolling the three- and six-plane monolayers (101) and (001) of anatase are discussed. Atomic and electronic structure of TiO2 nanotubes found by geometry optimization is analyzed. It is shown that titanium dioxide nanotubes based on the three-plane monolayers with hexagonal and square lattice are approximately of the same stability. The data on the stability of nanotubes are essential for the synthesis of new nanomaterials based on titanium dioxide.

Calculations of the electronic structure of crystalline SrZrO3 in the framework of the density-functional theory in the LCAO approximation

The electronic structures of four well-known modifications of crystalline SrZrO3 with different symmetries, namely, the cubic (Pm3m), tetragonal (I4/mcm), and two orthorhombic (Cmcm, Pbnm) modifications, are calculated in the framework of the density-functional theory in the basis set of the linear combination of atomic orbitals (LCAO). A comparative analysis of the electronic properties of the crystals under consideration is performed on the basis of the calculated band structures and densities of states (the total densities of states and the densities of states projected onto the atomic states). The calculated relative stabilities of the different modifications are in good agreement with the experimental data on the phase transitions in the SrZrO3 crystal: the low-temperature modifications with lower symmetry are more stable. The ionicities of chemical bonding in different modifications of crystalline SrZrO3 are compared by analyzing the Mulliken populations and constructing the localized Wannier functions for the occupied energy bands.

Hartree-Fock Study of the Chemical Bonding in Crystalline Titanium Oxides: TiO2, Ti2O3, TiO

Titanium oxides from a wide row of compounds with stoichiometric and nonstoichiometric chemical composition with different valence states of the cation atom. The aim of this work is study of local electronic properties of titanium oxides in the oxidation states of Ti (IV, III, II).