Stochastic perturbation theory: a low-scaling approach to correlated electronic energies

We discuss a stochastic implementation of M?ller-Plesset (MP) theory based upon the concept of a "graph," a set of connected Slater determinants. We show how contributions from an arbitrary level, MPn, of perturbation theory can be expressed diagrammatically in terms of graphs, and that these may be stochastically sampled to give a good estimate of the energy. We show this to be the case for Ne, Ar, N2, and H2O molecules. N-molecule chains of He atoms and H2 molecules at equilibrium and stretched geometries show an effective scaling of O[N(2.6)] and O[N(5.6)] for MP2 and MP3 theories.     

Surface segregation energies in low-index open surfaces of bimetallic transition metal alloys

We present a database of 24 × 24 segregation energies of single transition metal impurities in low-index surfaces of transition metal hosts, calculated using the localized self-consistent Green’s function (LSGF) method, in combination with the atomic sphere approximation including a multipole correction to the electrostatic potential and energy. The surface energies of facets for fcc and bcc transition metals, and the more stable of the two facets of hcp transition metals are also calculated and compared with available theoretical results. Insights derived should be useful for determining the nature of active sites in a variety of catalytic reactions employing bimetallic catalysts.     

On the cluster approach for calculating electronic energies of solid surfaces

A scheme for calculating electronic energy states of infinite solid surface systems by a cluster approach under the framework of the method of linear combinations of atomic orbitals is presented. The basis functions consist of atomic-like orbitals confined within a cluster whereas the Hamiltonian is that of the infinite solid. The latter circumvents the difficulty arising from the auxiliary boundary of the cluster which is not the true surface of the solid. All the multicenter integrals appearing in the Hamiltonian matrix can be evaluated exactly by means of the technique of Gaussian orbitals. This cluster-basis method is applied to the chlorine-adsorbed silicon (111) surface using several different clusters. The results are compared with those of the same Hamiltonian with basis functions extending over the entire solid in the Bloch-sum form. Criteria for optimal selection of clusters are suggested.     

Secondary ion emission from clean and K-covered Ni surfaces near threshold impact energies

Clean and K-covered Ni surfaces are bombarded with low energy (10–500 eV) beams of He⁺, Ne⁺, Ar²⁺, and Kr⁺ ions, and the emitted ion yield is measured as a function of beam energy. The apparent threshold energies for K⁺ and Ni⁺ emission are proportional to the ionic binding energies of K⁺ and Ni⁺ to the Ni surface. From comparison of the ion and neutral yield curves, it is suggested that these ions are emitted via momentum transfer collisions similar to neutral sputtering.     

A perturbation approach to the density functional theory of adsorption

A modified treatment of an exact density functional theory for non-uniform fluids due to Saam and Ebner is presented and a perturbation method of solution is proposed which avoids the need for a local density approximation. For hard-core fluids near a hard wall the equation for the equilibrium density reduces tothe wall-particle version of the RHNC approximation.     

A local approach to the computation of correlation energies of molecules

A new variational approach is introduced for the calculation of correlation energies of molecules. It is based on the local character of the correlated electron motion. Based on the approach we calculate correlation energies for simple systems. These include various Hubbard models as well as a model of the H₆-ring for which exact results are available. Our finding is that the proposed approach appears to be simpler and more economical for numerical work than conventional CI-methods. More than 90% of the correlation energy is obtained in all cases considered.     

A chemical approach to understanding oxide surfaces

Chemical bonding has often been ignored in favor of physics based energetic considerations in attempts to understand the structure, stability, and reactivity of oxide surfaces. Herein, we analyze the chemical bonding in published structures of the SrTiO_3, MgO, and NiO surfaces using bond valence sum (BVS) analysis. These simple chemical bonding theories compare favorably with far more complex quantum mechanical calculations in assessing surface structure stability. Further, the coordination and bonding of surface structures explains the observed stability in a readily comprehensible manner. Finally, we demonstrate how simple chemical bonding models accurately predict the adsorption of foreign species onto surfaces, and how such models can be used to predict changes in surface structures.     

An approach to prediction of microstructure formation near friction surfaces at large plastic strains

The paper develops an approach to formulation of constitutive equations for predicting the microstructure formation in a thin material layer near surfaces with high friction stresses in material forming processes. The approach is based on the use of the strain rate intensity factor. An equation relating the layer thickness to the strain rate intensity factor is proposed. A similarity condition that provides the same layer thickness at appropriate friction surface points in full-scale and model experiments is derived. The condition implies that the degree of strain inhomogeneity and hence the degree of inhomogeneity of material properties depends on the scale factor. As an example, compression of a thin layer between parallel plates is considered. Assuming validity of the proposed equation, a relationship is established between the parameters of compression and the layer thickness with essentially changed microstructure.     

Polarization effects and work function differences for transition metal surfaces: A perturbation LCAO MO approach

An analytical LCAO MO perturbation model has been developed for treating the polarization p-d contributions to the internal surface dipole moments of transition metal surfaces. The results are applied for treating changes in work functions (Ø) under chemisorption. The main conclusions are as follows. (1) Chemisorption of electropositive A (such as alkali metals) will always decrease Ø on all surfaces. (2) Chemisorption of electronegative A (such as H or halogens) can result in either increase or decrease in Ø depending on the nature of A and M. The smallest differences in A vs. M electronegativity are most likely to produce the paradoxical change ΔØ<0. The results obtained agree with experiment.     

Competitive segregation of impurities on the surface of polycrystalline copper

The competitive segregation of sulfur, carbon, and phosphorus on the surface of polycrystalline copper and the segregation kinetics of sulfur in the temperature range 675–875 K have been investigated by Auger electron spectroscopy. The equilibrium segregation energies of impurities and the sulfur diffusion parameters in the near-surface region of copper with a thickness d ≤ 5 μm have been calculated on the basis of the experimental data.     

Electric field perturbation due to impurities in GaAs through single electron transistor

The present work shows the presence of inevitable impurities in the semi-insulating GaAs domains when one is developing a single electron transistor (SET) and alters the quantization mechanism of single electron tunneling through the island. It is also indicated that these impurities decrease the amount of energy required to change the number of electrons on the island, which leads to a drastic reduction of SET quality. A theoretical model has been presented for elucidating the I–V characteristics of GaAs nano-crystals. It is found that this proposed model fits well the experimental data.     

Defects within the landau theory: A perturbation approach

We discuss the continuum medium theory that enables us to find the defect contribution to phase transition anomalies with the use of only a few phenomenological parameters. The theory is invalid in the immediate vicinity of the phase transition temperature and for high concentration of defects. The possibilities of interpretation of experimental data on the basis of the theory are also discussed.     

A novel approach to the acoustic characterisation of porous road surfaces

Porous road surfaces offer an effective means of reducing the generation and propagation of noise from road traffic. However, the porosity of these surfaces can deteriorate over time, leading to a reduction in their noise reducing properties. Efficient methods are therefore required for monitoring this performance. Existing techniques for performing in-situ measurements of acoustic absorption are unsuitable for use within the traffic stream. Static measurements using time domain Maximum Length Sequence (MLS) based techniques have been demonstrated to offer advantages over traditional techniques, presenting the opportunity for measurements under dynamic conditions. This paper describes the design of a system for carrying out dynamic MLS-based measurements. Results are presented which demonstrate that stable dynamic measurements can be carried out at speeds of up to 30 km/h.     

A Markovian approach to atomic scattering from rough surfaces

Atomic scattering intensities from surfaces in a rough state are calculated, in the hard wall model, separating a form (or geometrical) factor from a statistical factor and neglecting all the edge effects. Attention has been paid more to the statistics than to the scattering problem. In principle only incoherent scattering occurs from a rough surface. This incoherent line shape is calculated for square and hexagonal lattices under the basic assumption that the surface level is a Markov process in two dimensions.     

Singular effects of impurities near the ferromagnetic quantum-critical point

Systematic theoretical results for the effects of a dilute concentration of magnetic impurities on the thermodynamic and transport properties in the region around the quantum critical point of a ferromagnetic transition are obtained. In the quasiclassical regime, the dynamical spin fluctuations enhance the Kondo temperature. This energy scale decreases rapidly in the quantum fluctuation regime, where the properties are those of a line of critical points of the multichannel Kondo problem with the number of channels increasing as the critical point is approached, except at unattainably low temperatures where a single channel wins out.     

Variational approach to hard sphere segregation under gravity

It is demonstrated that the minimization of the free energy functional for hard spheres and hard disks yields the result that excited granular materials under gravity segregate not only in the widely known "Brazil nut" fashion, i.e., with the larger particles rising to the top, but also in reverse "Brazil nut" fashion. Specifically, the local density approximation is used to investigate the crossover between the two types of segregation occurring in the liquid state, and the results are found to agree qualitatively with previously published results of simulation and of a simple model based on condensation.     

A singular perturbation approach to first passage times for Markov jump processes

We introduce singular perturbation methods for constructing asymptotic approximations to the mean first passage time for Markov jump processes. Our methods are applied directly to the integrai equation for the mean first passage time and do not involve the use of diffusion approximations. An absorbing interval condition is used to properly account for the possible jumps of the process over the boundary which leads to a Wiener-Hopf problem in the neighborhood of the boundary. A model of unimolecular dissociation is considered to illustrate our methods.