Describing materials properties and behavior over increasing scales of dimension and complexity requires an optimal balance of completeness and accuracy in solving the local density equations. In this study, the convergence properties of a set of schemes that aim to achieve increasing accuracy are systematically examined according to the hierarchical approximations upon which they are based. Specifically, the Harris density functional (HDF) and related schemes that express the total energy in terms of atomic densities and limited self-consistency are compared within a single consistent framework. Convergence of the HDF energy relative to input density is first tested by carrying out calculations within the non-self-consistent atom fragment and self-consistent atom fragment (SCAF) approximations and then by supplementing the SCAF density by increasing numbers of partial waves about each atomic site using the self-consistent partial wave (SCPW) method. The construct of the SCPW method, that solves the local density equations with controlled precision according to the number of partial waves in the site density expansions, enables this study. The rapid convergence of structural properties with an increasing number of partial waves on each site, sometimes even with only L=0 partial waves, provides additional justification for HDF-based tight-binding and molecular dynamics methods where the interatomic potentials are obtained from the superposition of atomiclike densities. The convergence of ground state structural properties is demonstrated by application to the set of molecules: carbon monoxide, water, orthosilicic acid (H4SiO4), formamide (HCONH2), iron pentacarbonyl [Fe(CO)(5)], and dimanganese decacarbonyl [Mn-2(CO)(10)].

First-principles atomic cluster calculations have been carried out in the local density approximation to understand the segregation behavior and strengthening effects of boron in Ni3Al. The binding energy of boron is calculated in lattice fragment clusters representing the perfect crystal, as well as various defect sites. The agreement between trends in energetics determined for small clusters and periodic supercells indicates the dominant role of boron’s interaction with nearest-neighbors of the host. The stereochemical factor underlying boron’s preferential bonding to nickel atoms in four-fold planar coordination (i.e., sp3 hybridization) suggests a mechanism for the boron-effect in Ni3Al: increased cohesion provides a driving force for B segregation to open sites, such as at Ni-enriched grain boundary sites, and the strengthening is a result of strong localized Ni–B covalent bond formation.

The importance of local structure to the physical properties of alloys is receiving increasing attention. Recent measurements of the short-range nanoscale structure in metallic solid solution alloys reveal both the local chemical order and the chemically sensitive nearneighbor distances. These measurements are made possible by intense and tunable synchrotron X radiation; X-ray energy is adjusted to vary the x-ray scattering contrast between atoms in the solid solution. We discuss the local structures in NiFe binary alloys and compare the observed structures to trends calculated from first principles cluster models that identify the role of the local bonding. The small cluster models are found to exhibit trends in agreement with measured Ni-Fe. Ni-Ni and Fe-Fe near neighbor distances. From the cluster models we infer the mechanisms responsible for the observed average lattice and pair correlation lengths in NiFe alloys.

The computational advantage and accuracy of the Harris method is linked to the simplicity and adequacy of the reference-density model. In an earlier paper, we investigated one way the Harris functional could be extended to systems outside the limits of weakly interacting atoms by making the charge density of the interacting atoms self-consistent within the constraints of overlapping spherical atomic densities. In the present study, a method is presented for augmenting the interacting atom charge densities with symmetrized partial-wave expansions on each atomic site. The added variational freedom of the partial waves leads to a scheme capable of giving exact results within a given exchange-correlation approximation while maintaining many of the desirable convergence and stability properties of the original Harris method. Incorporation of the symmetry of the cluster in the partial-wave construction further reduces the level of computational effort. This partial-wave cluster method is illustrated by its application to the dimer ${\mathrm{C}}_{2}$, the hypothetical atomic cluster ${\mathrm{Fe}}_{6}$${\mathrm{Al}}_{8}$, and the benzene molecule.

A method based on steepest-descent algorithms is described for calculating one-electron occupation numbers in finite-atomic-cluster calculations. Unlike zero-temperature Fermi-Dirac statistics, the technique can be used to determine fractional occupation numbers in those cases where they give the lowest self-consistent-field energy. Applications to the iron atom and an iron-aluminum cluster illustrate the principles of the method.

Contemporary electronic-structure methods avoid shape approximations but in doing so encounter the difficult problem of integral evaluation over complicated interstitial volumes. In this paper, we present a simple and efficient technique for applying rapidly convergent Gaussian product formulas to general interstitial regions. Like the recent methods of Boerrigter, te Velde, and Baerends, it is based upon partitioning space into Voronoi cells and atomic spheres. In the present work, introduction of a general pseudospherical local-coordinate system unifies the integration procedures and effects a simplified approach. A systematic procedure is derived for determining the number of Gaussian points required for a specified level of numerical precision.

We present results from a theoretical study of the localized bonding in atomic clusters consisting of octahedral nickel hosts and interstitial atoms from the lithium row of the Periodic Table. Trends in impurity binding energies and the effects of impurities on the elastic properties of the host are established by comparison of total energies and interatomic forces of the doped clusters with results for the bare host. Properties of the host cluster are strongly dependent upon impurity atom type. An orbital analysis identifies the microchemical mechanisms through which the elastic properties of the host respond to changes in impurity-host bond character, as we progress from strongly electropositive lithium to strongly electronegative fluorine. The tendency of Li and F to form ionic bonds destabilizes and weakens the Ni host cluster. A bonding mode which is predominantly covalent characterizes the remainder of the first-row series. A nonuniform variation of impurity-induced strain and elastic properties of the host is found, with midrow atoms B, C, and N effecting an appreciable strengthening of the host. Trends in the stability and strengthening character of the midrow series of atoms is a result of competing atom size and covalency effects. There is good qualitative correspondence between the trends and relative effects of different impurities in this study and the observed effects of first-row impurities on the cohesive properties of metallic host interfaces. This relationship suggests the microchemical properties of the cluster model may serve to identify atomic-level factors important to understanding macroscopic impurity effects in grain-boundary segregation.

The eigenvalues of the single-particle equations of density-functional theory are shown to define dynamic orbital forces which can serve, in the Mulliken sense, as a semiquantitative basis for understanding chemical binding. Local-spin-density calculations for first-row diatomic molecules demonstrate that the type of bond-length change accompanying a change in occupation number of a given one-electron orbital is predicted with consistent accuracy by the associated dynamic orbital force.

Impurity-dopant effects on grain-boundary cohesion have been studied in a first-principles local spin-density atomic-cluster model of octahedral hole sites in nickel. Rigorous calculations of the total energy and gradient forces on the host atoms show that boron (an enhancer of cohesion) increases the maximum sustainable restoring force in the cluster, and sulfur (an embrittler) decreases the value of this force, consistent with observed segregation behaviors of these atoms.

The force field in an atomic cluster, given as the direct gradient of the total energy in the density-functional formalism, is expressed in terms of components corresponding to the solutions of the one-particle Schr\"odinger equation. The resulting relationship between eigenfunctions and orbital forces provides a useful framework for analysis of the bonding in the system. The expression for the orbital force is given as the sum of a traditional Hellmann-Feynman term and an orbital derivative term which cancels the first-order error due to basis-set incompleteness. The sum of orbital forces gives the total gradient force on the nuclei in the system to essentially the same accuracy as the total-energy surface itself. Results are reported for an all-electron calculation of the orbital forces in the copper dimer. This first local-spin-density calculation of the gradient force for a transition-metal dimer represents a challenging test because of the heavy core. By the introduction of a simple screening force, an orbital cohesive force is defined which provides an interesting and useful framework for quantifying the relative contribution of the molecular orbitals to the chemical bond. The effects of core polarization and valence hybridization and their compensating influence are demonstrated in the results.

The principle of augmentation, used to introduce inner-atom core structure into slowly varying basis functions, is applied to Gaussian orbitals to define a new basis set for highly accurate total-energy calculations for atomic clusters within the density-functional formalism. Diffuse Gaussian-orbital tails are matched continuously and differentiably to inner-atom numeric radial functions at the atomic-sphere radius. Major advantages of Gaussian-orbital basis sets are acquired without the need for numerous Gaussians of large exponent for the core region. The numeric functions used inside the atom permit essentially exact solutions for that region. Procedures are described which recover use of the efficient integral algorithms for the Gaussian-orbital-tail matrix elements. The interactions over the structured inner-atom region are treated by efficient integrand smoothing and integration procedures for the sphere. The new augmented Gaussian basis removes the primary limitations on the use of Gaussian orbitals for heavy atoms. As an illustration the method is applied to the copper dimer in an all-electron framework within the local-spin-density approximation (LSDA). The calculated binding energy, equilibrium separation, and first ionization potential of ${\mathrm{Cu}}_{2}$ are within 2% of experiment within the $X\ensuremath{\alpha}$ model. Excitation energies are better described within more recent refined exchange-correlation functionals. These all-electron results show the LSDA model predicts a slightly contracted bond length for ${\mathrm{Cu}}_{2}$, consistent with bulk LSDA calculations for the $3d$ transition-metal series.

The Hohenberg-Kohn-Sham density-functional equations in the local spin-density approximation (LSDA) have been solved with essentially no loss of accuracy for dimers of the first row of the Periodic Table with the use of a fully-self-consistent spin-polarized Gaussian-orbital approach. Spectroscopic constants (binding energies, equilibrium separations, and ground-state vibrational frequencies) have been derived from the calculated potential-energy curves. Intercomparison of results obtained using the exchange-correlation functionals of Slater (scaled exchange or $X\ensuremath{\alpha}$, Gunnarsson and Lundqvist (GL), and Vosko, Wilk, and Nusair (VWN) permits assessment of the relative merits of each and serves to identify general shortcomings in the LSDA. Basic trends are similar for each functional, but the treatment of the spin dependence of the exchange-correlation energy in the GL and VWN functionals yields a variation of the binding energy across the series which is more systematic than that in the $X\ensuremath{\alpha}$ approximation. Agreement between the present results and those of Dunlap, Connolly, and Sabin in the $X\ensuremath{\alpha}$ approximation confirms the accuracy of the variational charge-density-fit procedure used in the latter work. The refinements in correlation treatment within the VWN functional are reflected in improvements in binding energies which are only slight for most dimers in the series. This behavior is attributed to the error remaining in the exchange channel within the LSDA and demonstrates the necessity for self-interaction corrections for more accurate binding-energy determinations. Within the current LSDA, absolute accuracies of the VWN functional for the first-row dimers are within 2.3 eV for binding energies, 0.07 a.u. for bond lengths, and \ensuremath{\sim}200 ${\mathrm{cm}}^{\ensuremath{-}1}$ for vibrational frequencies.

The virial expression valid in density-functional theory contains an integral over the gradient of the effective exchange-correlation potential. The significance of this term in correcting the noninteracting kinetic and electrostatic energies is discussed in this work. From the gradient integral in the local density approximation an expression is derived for the kinetic-energy part of the exchange-correlation energy density, and its connection with the derivation of von Barth and Williams is discussed. To illustrate the application of these developments to the molecular case, results are presented from Gaussian-orbital cluster calculations for ${\mathrm{H}}_{2}$. In this study the forces in the dimer are calculated using the Hellmann-Feynman and virial theorems, and results are compared with the force obtained by direct interpolation from the binding-energy curve. The usefulness of the various methods for calculating the force is discussed.

Self-consistent Hartree-Fock-Slater molecular cluster models for the chemisorption of first row atoms on Ni(100) surfaces are presented. Energy levels and ground state charge distributions for XNiS clusters with the adatom X = H, C, N, O located in C4 V symmetry at a fixed height of h = 2.0 au above the surface are given. The variation of properties with h was studied in detail for the case of oxygen. Theoretical results compare rather well with experimental photoelectron and energy loss data. Local-densities-of-states diagrams are used to clarify the interaction between adsorbate levels and metal conduction bands.