Showing papers by "Alex Zunger published in 1977"

Self-consistent numerical-basis-set linear-combination-of-atomic-orbitals investigation of the electronic structure and properties of TiS2

Abstract: A fully-self-consistent numerical-basis-set linear-combination-of-atomic-orbitals calculation of the electronic structure of Ti${\mathrm{S}}_{2}$ is reported using the method described previously. The calculated band structure differs considerably from those previously obtained by non-self-consistent muffin-tin models. Comparison with experiment shows that the calculated optical properties for energies below 16 eV and the various characteristics of the valence and conduction bands agree very well with optical-absorption and electron-energy-loss data as well as with photoemission, x-ray absorption, and appearance-potential spectra. A small indirect gap (0.2-0.3 eV) occurs at the points $M$ and $L$ in the Brillouin zone with a larger direct gap (0.8 eV) at $\ensuremath{\Gamma}$. We suggest that the characteristic semi-metallic large $g$ value observed experimentally originates from a near coincidence of the band gap with the enhanced spin-orbit splitting which is consistent with the soft-x-ray data and our band model. The bonding mechanism in Ti${\mathrm{S}}_{2}$ is discussed in detail; it is shown by a direct calculation of the self-consistent charge density and the transverse effective charge that the system is predominantly covalent with small static ionic character and large dynamic ionicity. In contrast with muffin-tin $X\ensuremath{\alpha}$ models, the bonding is found to be largely due to Ti $4s4p$ to S $3p$ bonds and a much weaker Ti $3d$ to S $3p$ bond. The effects of muffin-tin approximation and self-consistency are discussed in detail. Extrapolation of these results to the case of Ti${\mathrm{Se}}_{2}$ is made and the possible origin of its charge-density wave is discussed.

Ground- and excited-state properties of LiF in the local-density formalism

Abstract: The band structure, charge density, x-ray scattering factor (and their behavior under pressure), equilibrium lattice constant, and cohesive energy of the prototype ionic solid LiF were determined using our recently developed self-consistent numerical basis set (non-muffin-tin) linear-combination-of-atomic-orbitals method, within the local-density formalism (LDF). The details of the bonding and the effects of exchange and correlation on the electronic structure are discussed with reference to the conventional picture of ionic bonding. Remarkably good agreement is found with the observed data for the ground-state properties of the system. Contrary to the results of previous band studies, the conventional band-structure approach to excitation energies (i.e., identifying them with the band eigenvalue differences) is found to fail completely in accounting for the observed data in the entire x-ray and optical spectral region when fully self-consistent solutions of the LDF one-particle equation with no further approximation to the crystal potential are obtained. It is found that in the presence of some spatial localization of the initial or final crystal states, the spurious self-interaction terms, as well as the polarization and orbital relaxation self-energy effects are of a similar order of magnitude as the Koopmans'-like interband terms. In order to treat these effects within the LDF self-consistently, we describe the excitation processes as transitions involving point-defect-like states in the solid calculated by a supercell method in which the excitation energies are determined as total-energy differences between (separately calculated) excited- and ground-state configurations. The excited state is represented as a superlattice of locally excited sites using large (8-and 16-atom) unit cells, each containing a single excited site. We find, in the self-consistency limit, that a small but finite degree of spatial localization of the excited states exists even for valence excitations, inducing thereby self-interaction as well as self-energy relaxation and polarization effects. The LDF model is found to account very well for both interband and exciton transitions over the entire spectral region (12-695 eV) and to yield definite predictions regarding the exciton bandwidths and series limits.

Self-consistent numerical-basis-set linear-combination-of-atomic-orbitals model for the study of solids in the local density formalism

Abstract: A new approach to the fully self-consistent solution of the one-particle equations in a periodic solid within the Hohenberg-Kohn-Sham local-density-functional formalism is presented. The method is based on systematic extensions of non-self-consistent real-space techniques of Ellis, Painter, and collaborators and the self-consistent reciprocal-space methodologies of Chaney, Lin, Lafon, and co-workers. Specifically, our approach combines a discrete variational treatment of all potential terms (Coulomb, exchange, and correlation) arising from the superposition of spherical atomiclike overlapping charge densities, with a rapidly convergent three-dimensional Fourier series representation of all the multicenter potential terms that are not expressible by a superposition model. The basis set consists of the exact numerical valence orbitals obtained from a direct solution of the local-density atomic one-particle equations and (for increased variational freedom) virtual numerical atomic orbitals, charge-transfer (ion-pair) orbitals, and "free" Slater one-site functions. The initial crystal potential consists of a non-muffin-tin superposition potential, including nongradient free-electron correlation terms calculated beyond the random-phase approximation. The usual multicenter integrations encountered in the linear-combination-of-atomic-orbitals tight-binding formalism are avoided by calculating all the Hamiltonian and other matrix elements between Bloch states by three-dimensional numerical Diophantine integration. In the first stage of self-consistency, the atomic superposition potential and the corresponding numerical basis orbitals are modified simultaneously and nonlinearly by varying (iteratively) the atomic occupation numbers (on the basis of computed Brillouin-zone averaged band populations) so as to minimize the deviation, $\ensuremath{\Delta}\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$, between the band charge density and the superposition charge density. This step produces the "best" atomic configuration within the superposition model for the crystal charge density and tends to remove all the sharp "localized" features in the function $\ensuremath{\Delta}\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ by allowing for intra-atomic charge redistribution to take place. In the second stage, the three-dimensional multicenter Poisson equation associated with $\ensuremath{\Delta}\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ through a Fourier series representation of $\ensuremath{\Delta}\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ is solved and solutions of the band problem are found using a self-consistent criterion on the Fourier coefficients of $\ensuremath{\Delta}\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$. The calculated observables include the total crystal ground-state energy, equilibrium lattice constants, electronic pressure, x-ray scattering factors, and directional Compton profile. The efficiency and reliability of the method is illustrated by means of results obtained for some ground-state properties of diamond; comparisons are made with the predictions of other methods.

Ground-state electronic properties of diamond in the local-density formalism

Abstract: We use our previously reported method for solving self-consistently the local-density one-particle equations in a numerical-basis-set linear combination of atomic orbitals expansion to study the ground-state charge density, x-ray structure factors, directional Compton profile, total energy, cohesive energy, equilibrium lattice constant, and behavior of one-electron properties under pressure of diamond. Good agreement is obtained with available experiment data. The results are compared with those obtained by the restricted Hartree-Fock model: the role of electron exchange and correlation on the binding mechanism, the charge density, and the momentum density is discussed. I. INTRODU(.'TION The local density functional (LDF) formalism of Hohenberg, Kohn, and Sham, " and its recent extension as a local spin-density functional formalism, ' form the basis of a new approach to the study of electronic structure in that the effects of exchange and correlation are incorporated directly into a charge- density- dependent potential term that is determined self -consistently from the solution of an effective one-particle equation. Applications of the LDF formalism to atoms+' and molecules' have yielded encouraging results. Similar applications for solids are complicated by (i) the need to con sider both the short-range and the long- range multicenter crystal potential having nonspherical components, (ii) the difficulties in obtaining full self-consistency in a periodic system, and (iii) the need to provide a basis set with sufficient variational flexibility. Hence, theoretical. studies of ground- state electronic properties of solids in the LDF formalism have been mainly l.imited to muffin-tin models for the potential, " non-selfconsistent schemes, ' treatments of simplified jellium models'0 or spherical cellular schemes We have recently proposed"" a general selfconsistent method for solving the LDF formalism one-particle equation for realistic solids using a numerical-basis-set LCAO (linear combination of atomic orbitals) expansi. on and retaining all nonspherical parts of the crystal potential. We have demonstrated a rapid convergence of the selfconsistent (SC) cycle when the treatment of the full crystal charge density is suitably apportioned between real- space and Fourier- transformed reciprocal-space parts and have indicated the large degree of variational flexibility offered by a nonlinearly optimized (exact) numerical atomiclike basis set. We have shown that all multicenter interactions as well as the nonconstant parts of the crystal potential are efficiently treated by a three- dimensional Diophantine integration scheme.