Improved tensor-product expansions for the two-particle density matrix

We present a new density-matrix functional within the recently introduced framework for tensor-product expansions of the two-particle density matrix. It performs well both for the homogeneous electron gas as well as atoms. For the homogeneous electron gas, it performs significantly better than all previous density-matrix functionals, becoming very accurate for high densities and outperforming Hartree-Fock at metallic valence electron densities. For isolated atoms and ions, it is on a par with previous density-matrix functionals and generalized gradient approximations to density-functional theory. We also present analytic results for the correlation energy in the low density limit of the free electron gas for a broad class of such functionals.Comment: 4 pages, 2 figure

Thermodynamics as an alternative foundation for zero-temperature density functional theory and spin density functional theory

Thermodynamics provides a transparent definition of the free energy of density functional theory (DFT), and of its derivatives - the potentials, at finite temperatures T. By taking the T to 0 limit, it is shown here that both DFT and spin-dependent DFT (for ground states) suffer from precisely the same benign ambiguities: (a) charge and spin quantization lead to "up to a constant" indeterminacies in the potential and the magnetic field respectively, and (b) the potential in empty subspaces is undetermined but irrelevant. Surprisingly, these simple facts were inaccessible within the standard formulation, leading to recent discussions of apparent difficulties within spin-DFT.Comment: RevTeX, to appear in Phys. Rev.

Interaction energy functional for lattice density functional theory: Applications to one-, two- and three-dimensional Hubbard models

The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). The single-particle density matrix $\gamma_{ij}$ with respect the lattice sites is considered as the basic variable of the many-body problem. A new approximation to the interaction-energy functional $W[\gamma]$ is proposed which is based on its scaling properties and which recovers exactly the limit of strong electron correlations at half-band filling. In this way, a more accurate description of $W$ is obtained throughout the domain of representability of $\gamma_{ij}$, including the crossover from weak to strong correlations. As examples of applications results are given for the ground-state energy, charge-excitation gap, and charge susceptibility of the Hubbard model in one-, two-, and three-dimensional lattices. The performance of the method is demonstrated by comparison with available exact solutions, with numerical calculations, and with LDFT using a simpler dimer ansatz for $W$. Goals and limitations of the different approximations are discussed.Comment: 25 pages and 8 figures, submitted to Phys. Rev.

A step back: Hydrogen abstraction from methane using a semiempirical molecular orbital method

Several studies have new been completed using semiempirical molecular orbital methods to learn about various aspects of diamond growth. Whole reaction mechanisms for diamond epitaxy have been proposed on the basis of these calculations with supporting evidence from experiment. Attempts have been made to understand the roles of hydrogen atoms, methyl groups, acetylene groups and charged species in diamond film growth from both hot filament and plasmas sources. For the semiempirical method to provide a reasonable description of a diamond film, it is essential that molecular species and configurations to be encountered in the system be included in the parameterization of the method. One way to verify appropriateness of the method is by testing it against simple systems for which detailed experimental measurements and ab initio calculations are available. Unfortunately, the semiempirical methods used in earlier studies have never been tested against simple known systems closely resembling the ones of interest to diamond films. Here we propose to make just such a test, the simplest being the abstraction of hydrogen from methane by a hydrogen atom. Not only is the system simple, but also both experimental and highly accurate theoretical results known for the transition state energy and geometry, key parameters for comparison. The results are reported after a brief review of the computational methods. 10 refs., 3 figs

Carbon atom, dimer and trimer chemistry on diamond surfaces from molecular dynamics simulations

Spectroscopic studies of various atmospheres appearing in diamond film synthesis suggest evidence for carbon atoms, dimers, or trimers. Molecular dynamics simulations with the Brenner hydrocarbon potential are being used to investigate the elementary reactions of these species on a hydrogen-terminated diamond (111) surface. In principle these types of simulations can be extended to simulations of growth morphologies, in the 1-2 monolayer regime presently

Reactive transport at Ti-C interfaces

Our understanding of the dynamical properties of the solid-state synthesis process is highly fragmented. One approach to developing a more thorough concept of these processes is to design numerical prototypes of these systems on microscopic and atomic levels. The beginnings of an atomic level description are presented using the Ti + C reaction as a guide for constructing an idealization. The potential surface energy for Ti is approximately by a pairwise sum of Lennard-Jones 4- 10 functions. The parameters for these functions are derived from experimental cohesive energies, lattice constants and isothermal compressibilities. The self-diffusion constant of molten Ti and its radial distribustion function are estimated via a molecular dynamics calculation

Barriers to the nucleation of methyl groups on the diamond (111) surface

Questions about the mechanism of diamond film growth by low-pressure, plasma-assisted chemical vapor deposition methods have persisted for some time now. As an attempt to explore one aspect of the problem, we examine the energetics of several adsorbed diamond (111) surfaces. The adsorbates are mixtures of methyl groups and hydrogen atoms. The model for these systems is the molecular orbital hamiltonian of Dewar and coworkers. From these calculations we find that H adsorbtion is preferred due both to bond energy and steric effects. Thus nucleation of a cluster of three or more methyl groups, as assumed in earlier work, is energetically very demanding. 6 refs., 3 figs

Revisiting the Al/Al?O? interface: Coherent interfaces and misfit accommodation

We study the coherent and semi-coherent Al/?-Al2O3 interfaces using molecular dynamics simulations with a mixed, metallic-ionic atomistic model. For the coherent interfaces, both Al-terminated and O-terminated nonstoichiometric interfaces have been studied and their relative stability has been established. To understand the misfit accommodation at the semi-coherent interface, a 1-dimensional (1D) misfit dislocation model and a 2-dimensional (2D) dislocation network model have been studied. For the latter case, our analysis reveals an interface dislocation structure with a network of three sets of parallel dislocations, each with pure-edge character, giving rise to a pattern of coherent and stacking-fault-like regions at the interface. Structural relaxation at elevated temperatures leads to a further change of the dislocation pattern, which can be understood in terms of a competition between the stacking fault energy and the dislocation interaction energy at the interface. Our results are expected to serve as an input for the subsequent dislocation dynamics models to understand and predict the macroscopic mechanical behavior of Al/?-Al2O3 composite heterostructures.Materials Science and EngineeringMechanical, Maritime and Materials Engineerin