Quantum chemical treatment of local electronic states in crystals. Titanium Carbide and Nitride

The electronic structure of the 63-and 219-atomic clusters in TiC and TiN is calculated by the DV cluster method. The new possibilities for modeling the boundary conditions of the cluster in crystal are discussed. To calculate the effective charges on atoms, a new procedure is applied whereby the electron density is integrated over the intemuclear space.     

Asymptotic boundary conditions in cluster simulation of electronic structures for infinite and semi-infinite crystals. 1. infinite crystals

A new method is proposed for determining the local electronic structure of an infinite or a semi-infinite crystal using asymptotically accurate boundary conditions imposed on the matrix elements of Green's functions in the lattice point representation for the boundary atoms of the cluster. The boundary conditions are determined in a self-consistent manner from cluster calculations. Introduction of these conditions is equivalent to the calculation of the out-of-cluster region of the crystal; this gives a continuous spectrum of electronic states, which is in good agreement with the crystal spectrum. Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences. Translated fromZhurmal Struktumoi Khimii, Vol. 37, No. 1, pp. 3–13, January–February, 1996. Translated by I. Izvekova     

Density of non-Bloch electron states in perfect cubic crystals

This paper gives an abbreviated method for the calculation of the density of states of a crystal on the basis of that band theory in which the crystal electron states are represented by the standinglike wave functions classified according to the point-group symmetry species. The crystal is a large but finite sphere filled regularly with atoms, and the wave functions are quantized at the boundary of the sphere. The Bloch theorem is not satisfied in this theory since the wave functions are not basis functions of the irreducible representations of the translation subgroup. On the other hand, a theorem is established that the density of states can be made up of contributions given by all irreducible representations of the crystal point group, any contribution being proportional to the square of the dimension of the irreducible representation. In distinction to a former approach, the band structure is calculated solely from the energy eigenvalues obtained with the aid of the diagonalization process of the Wannier–Slater differential operator. A simple cubic lattice with an s atomic orbital on each lattice site is taken as an example, and the results are compared with Bloch's theory.     

SPC cluster modeling of metal oxides: ways of determining the values of point charges in the embedded cluster model

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Self-consistent embedding theory for locally correlated configuration interaction wave functions in condensed matter

We present new developments on a density-based embedding strategy for the electronic structure of localized feature in periodic, metallic systems [see T. Kluner et al., J. Chem. Phys. 116, 42 (2002), and references therein]. The total system is decomposed into an embedded cluster and a background, where the background density is regarded as fixed. Its effect on the embedded cluster is modeled as a one-electron potential derived from density functional theory. We first discuss details on the evaluation of the various contributions to the embedding potential and provide a strategy to incorporate the use of ultrasoft pseudopotentials in a consistent fashion. The embedding potential is obtained self-consistently with respect to both the total and embedded cluster densities in the embedding region, within the framework of a frozen background density. A strategy for accomplishing this self-consistency in a numerically stable manner is presented. Finally, we demonstrate how dynamical correlation effects can be treated within this embedding framework via the multireference singles and doubles configuration interaction method. Two applications of the embedding theory are presented. The first example considers a Cu dimer embedded in the (111) surface of Cu, where we explore the effects of different models for the kinetic energy potential. We find that the embedded Cu density is reasonably well-described using simple models for the kinetic energy. The second, more challenging example involves the adsorption of Co on the (111) surface of Cu, which has been probed experimentally with scanning tunneling microscopy [H. C. Manoharan et al., Nature (London) 403, 512 (2000)]. In contrast to Kohn-Sham density functional theory, our embedding approach predicts the correct spin-compensated ground state.     

Relativistic effects in low-energy spin-dependent electron collisions with rare-gas atoms

The relativistic effects in low-energy spin-dependent electron scattering from rare-gas atoms Ar, Kr and Xe are analyzed by comparing the results obtained respectively with Dirac-Fock, Cowan's quasirelativistic Hartree-Fock and non-relativistic Hartree-Fock wave functions for target atoms. It is shown that the intra-target relativistic effects, in particular the explicit spin dependences of the one-electron orbitals of Dirac-Fock atomic wave function, create apparet quantitative changes in the spin polarization parameters at some collision energies and scattering angles.     

Hole polarons in pure BaTiO3 studied by computer modeling

Self‐trapped hole polarons in technologically important perovskite‐type ceramic of BaTiO₃ have been modeled by means of the quantum chemical method modified for crystal calculations. The computations are carried out in the self‐consistent field (SCF) manner using the embedded molecular cluster model. The spatial configuration of a hole polaron, displacement of defect‐surrounding atoms, and wave functions of the polaron ground and excited states are obtained and analyzed. The probability of spontaneous hole self‐trapping is estimated in the perfect lattice of the BaTiO₃ crystal by calculating the value of the hole self‐trapping energy as a difference of the atomic relaxation energy and the hole localization energy. This value is found to be negative, −1.49 eV, which demonstrates the preference of the self‐trapped polaron state. The calculated polaron absorption energy, 0.5 eV, is discussed in light of the available experimental data. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 358–366, 2000     

DFT calculations of solids with LAPW and WIEN2k

In solids one often starts with an ideal crystal that is studied on the atomic scale at zero temperature. The unit cell may contain several atoms (at certain positions) and is repeated with periodic boundary conditions. Quantum mechanics governs the electronic structure that is responsible for properties such as relative stability, chemical bonding, relaxation of the atoms, phase transitions, electrical, mechanical, optical or magnetic behavior, etc. Corresponding first principles calculations are mainly done within density functional theory (DFT), according to which the many-body problem of interacting electrons and nuclei is mapped to a series of one-electron equations, the so-called Kohn-Sham (KS) equations. One among the most precise schemes to solve the KS equations is the linearized-augmented-plane-wave (LAPW) method that is employed for example in the computer code WIEN2k to study crystal properties on the atomic scale (see www.wien2k.at). Nowadays such calculations can be done—on sufficiently powerful computers—for systems containing about 100 atoms per unit cell. A selection of representative examples and the references to the original literature is given.     

Quasi-relativistic approximation in the SCF-MO-LCAO method

A quasi-relativistic approach to the MO-LCAO method is formulated taking into account the relativistic effects with an accuracy up to (v/c)² terms, the relativistic part of the electronic interaction in the Hamiltonian being neglected. In the framework of this approximation a set of SCF equations of the Roothaan form is derived; here only the relativistic analogue to the closed shell systems with one-determinant wave functions is considered. In so doing three types of relativistic corrections arise which are quite similar to those of the Pauli equation for one-electron atoms. The new matrix elements appearing due to these corrections can be reduced to some common integrals, which have to be calculated with relativistic radial atomic functions. The method allows a semi-empirical approach to the problem and does not require the Dirac four-component atomic functions (unknown in the most cases), thus making possible approximate quasi-relativistic electronic structure calculations of heavy-atom compounds.     

Electric field-derived point charges to mimic the electrostatics in molecular crystals

Because of the way the electrostatic potential is defined in a crystal, it is not possible to determine potential-derived charges for atoms in a crystal. To overcome this limitation, we present a novel method for determining atomic charges for a molecule in a crystal based on a fit to the electric field at points on a surface around the molecule. Examples of fits to the electric field at points on a Hirshfeld surface, using crystal Hartree-Fock electron densities computed with a DZP basis set are presented for several organic molecular crystals. The field-derived charges for common functional groups are transferable, and reflect chemical functionality as well as the subtle effects of intermolecular interactions. The charges also yield an excellent approximation to the electric field surrounding a molecule in a crystal for use in cluster calculations on molecules in solids.     

Electronic structure of a uranium impurity center in zircon

The electronic structure of a large fragment of the crystal lattice of zircon ZrSiO₄ with a uranium impurity atom replacing the zirconium atom was investigated using the completely relativistic discrete variation (DV) cluster method. The results are compared with the data of a similar calculation of the ideal ZrSiO₄ crystal. An analysis of the overlap populations and effective charges on the atoms of the matrix and impurity showed that chemical binding of uranium with the environment is covalent, and the electron density redistribution caused by this substitution changes not only the impurity and the nearest environment, but also the atoms of the next coordination spheres.     

The distribution of electronic charge in the ground state of cubic boron nitride

The distribution of electronic charge in cubic boron nitride is investigated using the bond orbital wave functions recently calculated by Coulson and Doggett. Plots of the one-electron density function, in the (110) plane, are found to be insensitive to the choice of atomic basis functions, in contradistinction to the previously calculated effective atomic charges. A number of structure amplitudes are also calculated for each of the bond orbital wave functions.     

Electronic structure of crystals: Embedded quantum cluster with overlap

We consider a crystal as partitioned into a localized molecular cluster (containing a defect or not) and an embedding region. Within the Hartree–Fock formalism, an expression is derived for an effective potential due to the embedding region of crystal. This potential is part of the cluster Fock operator and requires input from a perfect crystal calculation. Special features of the derivative are rigorous inclusion of cluster-embedding overlap and orthogonality between single-electron states of the embedding region and the function-space manifold of the cluster; physically correct normalization of the Fock eigenstates; and a nontrivial total-energy algorithm. Computational requirements are qualitatively compared with those for an isolated cluster. The method allows for intracluster (and intraembedding) correlation and can be adapted straightforwardly to local density functional approaches. Fundamental aspects of the embedding problem are addressed in a general formulation that is, nevertheless, oriented toward explicit calculations. © 1995 John Wiley & Sons, Inc.     

Geometry optimization using tuned and balanced redistributed charge schemes for combined quantum mechanical and molecular mechanical calculations

We performed geometry optimizations using the tuned and balanced redistributed charge algorithms to treat the QM-MM boundary in combined quantum mechanical and molecular mechanical (QM/MM) methods. In the tuned and balanced redistributed charge (TBRC) scheme, the QM boundary atom is terminated by a tuned F link atom, and the charge of the MM boundary atom is properly adjusted to conserve the total charge of the entire QM/MM system; then the adjusted MM boundary charge is moved evenly to the midpoints of the bonds between the MM boundary atom and its neighboring MM atoms. In the tuned and balanced redistributed charge-2 (TBRC2) scheme, the adjusted MM boundary charge is moved evenly to all MM atoms that are attached to the MM boundary atom. A new option, namely charge smearing, has been added to the TBRC scheme, yielding the tuned and balanced smeared redistributed charge (TBSRC) scheme. In the new scheme, the redistributed charges near the QM-MM boundary are smeared to make the electrostatic interactions between the QM region and the redistributed charges more realistic. The TBRC2 scheme and new TBSRC scheme have been tested for various kinds of bonds at a QM-MM boundary, including C-C, C-N, C-O, O-C, N-C, C-S, S-S, S-C, C-Si, and O-N bonds. Charge smearing is necessary if the redistributed charges are close to the QM region, as in the TBSRC scheme, but not if the redistributed charge is farther from the QM region, as in the TBRC2 scheme. We found that QM/MM results using either the TBRC2 scheme or the TBSRC scheme agree well with full QM results; the mean unsigned error (MUE) of the QM/MM deprotonation energy is 1.6 kcal/mol in both cases, and the MUE of QM/MM optimized bond lengths over the three bonds closest to the QM-MM boundary, with errors averaged over the protonated forms and unprotonated forms, is 0.015 ? for TBRC2 and 0.021 ? for TBSRC. The improvements in the new scheme are essential for QM-MM boundaries that pass through a polar bond, but even for boundaries that pass through C-C bonds, the improvement can be quite significant.     

Molecular tight-binding method. I. Many-electron method for hole bands of molecular crystals

A method for calculating ab initio electronic excitation energies of molecular crystals, based on a many-electron tight-binding approximation, is described. The method follows Frenkel's model for excitons and allows a many-electron treatment of the band-structure problem of molecular crystals. The case of hole bands is studied in detail and various versions of the method are considered. A computational scheme is proposed, in which approximate correlation corrections to the HFR matrix equations of the one-electron LCMO method are calculated. The main effects contributing to these corrections are the effect of relaxation of a molecular ion, the effect of intramolecular electronic-correlation change, and the effect of polarization of the remaining molecules in a crystal. The method developed in the present paper is applied to calculation of the hole bands of the HCP helium crystal.     

Incompletely symmetric non-bloch electron states in perfect cubic crystals. II. Density of states in the FCC lattice

The electron density of both the perturbed and unperturbed crystal can be made up of individual terms described by the basis functions of irreducible representations of the crystal point group. For the perfect FCC lattice, a detailed comparison was made between the density of states, calculated in terms of the LCAO wave functions classified according to representations of the crystal point group, and the density of states, provided by the Bloch theory.     

Anion substitution in zinc chalcogenides

Anion substitution effects on the structure and energy of zinc chalcogenides were studied with the semiempirical molecular orbital method MSINDO. Cyclic clusters of different sizes were chosen as model systems. The convergence of the bulk properties of the perfect clusters with increasing cluster size was tested. Single and multiple substitution of oxygen atoms in zinc oxide by sulfur and of sulfur atoms in zinc sulfide by oxygen served to determine the energetics of substitution for these two cases. It was found that the substitution of oxygen by sulfur in ZnO is easier than the substitution of sulfur by oxygen in ZnS in agreement with experimental results. The interaction between two oxygen atoms vs. two selenium atoms in zinc sulfide was investigated. Oscillations of the cluster energy in dependence of the distance between the two doping atoms were observed. These are explained by the relative sites of the doping atoms in the crystal lattice. The magnitude of the oscillations is smaller in ZnS:Se than in ZnS:O, because the difference between the anion radii of S2- and Se2- is smaller than between S2- and O2-. This is also reflected in the band gap.