Beyond Wavelets: Exactness theorems and algorithms for physical calculations

This paper develops the use of wavelets as a basis set for the solution of physical problems exhibiting behavior over wide-ranges in length scale. In a simple diagrammatic language, this article reviews both the mathematical underpinnings of wavelet theory and the algorithms behind the fast wavelet transform. This article underscores the fact that traditional wavelet bases are fundamentally ill-suited for physical calculations and shows how to go beyond these limitations by the introduction of the new concept of semicardinality, which leads to the profound, new result that basic physical couplings may be computed {\em without approximatation} from very sparse information, thereby overcoming the limitations of traditional wavelet bases in the treatment of physical problems. The paper then explores the convergence rate of conjugate gradient solution of the Poisson equation in both semicardinal and lifted wavelet bases and shows the first solution of the Kohn-Sham equations using a novel variational principle.Comment: 16 pages, 8 figures. Will appear in Computer Simulation Studies in Condensed Matter Physics XII, Eds. D.P. Landau, S.P. Lewis, and H.B. Schuttler (Springer Verlag, Heidelberg, Berlin 1999

Impact of octahedral rotations on Ruddlesden-Popper phases of antiferrodistortive perovskites

This work presents the most detailed and extensive theoretical study to date of the structural configurations of Ruddlesden-Popper (RP) phases in antiferrodistortive (AFD) perovskites and formulates a program of study which can be pursued for RP phases of any AFD perovskite system. We systematically investigate the effects of oxygen octahedral rotations on the energies of RP phases in AFD perovskites (A_n+1 B_n O_3n+1) for n = 1...30, providing asymptotic results for n --> infinity that give both the form of the interaction between stacking faults and the behavior of such stacking faults in isolation. We find an inverse-distance interaction between faults with a strength which varies by as much as a factor of two depending on the configuration of the octahedra. We find that the strength of this effect can be sufficient to (a) stabilize or destabilize the RP phase with respect to dissociation into the bulk perovskite and the bulk A-oxide and (b) affect the energy scales of the RP phase sufficiently to constrain the rotational states of the octahedra neighboring the stacking faults, even at temperatures where the octahedra in the bulk regions librate freely. Finally, we present evidence that the importance of the octahedral rotations can be understood in terms of changes in the distances between oxygen ions on opposing sides of the RP stacking faults.Comment: 18 pages, 12 figures, 6 table

Material limitations of carbon-nanotube inertial balances: on the possibility of intrinsic yoctogram mass resolution at room temperature

We present a theoretical study of the intrinsic quality factor of the fundamental flexural vibration in a carbon nanotube and its dependence on temperature, radius, length and tension. In particular, we examine three- and four-phonon decays of the fundamental flexural mode within quantized elasticity theory. This analysis reveals design principles for the construction of ultrasensitive nanotube mass sensors: under tensions close to the elastic limit, intrinsic losses allow for \emph{single yoctogram} mass resolution at room temperature, while cooling opens the possibility of \emph{sub-yoctogram} mass resolution.Comment: 4 pages, 3 figure

Efficient classical density-functional theories of rigid-molecular fluids and a simplified free energy functional for liquid water

Classical density-functional theory provides an efficient alternative to molecular dynamics simulations for understanding the equilibrium properties of inhomogeneous fluids. However, application of density-functional theory to multi-site molecular fluids has so far been limited by complications due to the implicit molecular geometry constraints on the site densities, whose resolution typically requires expensive Monte Carlo methods. Here, we present a general scheme of circumventing this so-called inversion problem: compressed representations of the orientation density. This approach allows us to combine the superior iterative convergence properties of multipole representations of the fluid configuration with the improved accuracy of site-density functionals. Next, from a computational perspective, we show how to extend the DFT++ algebraic formulation of electronic density-functional theory to the classical fluid case and present a basis-independent discretization of our formulation for molecular classical density-functional theory. Finally, armed with the above general framework, we construct a simplified free-energy functional for water which captures the radial distributions, cavitation energies, and the linear and non-linear dielectric response of liquid water. The resulting approach will enable efficient and reliable first-principles studies of atomic-scale processes in contact with solution or other liquid environments.Comment: 34 pages, 11 figure

Cluster assimilation and collisional filtering on metal-oxide surfaces

We present the first ab initio molecular dynamics study of collisions between metal-oxide clusters and surfaces. The resulting trajectories reveal that the internal degrees of freedom of the cluster play a defining role in collision outcome. The phase space of incoming internal temperature and translational energy exhibits regions where the collision process itself ensures that each cluster which does not rebound from the surface assimilates seamlessly onto it upon impact. This filtering may explain recent observations of a "fast smoothing mechanism" during pulsed laser deposition.Comment: 4 pages, 3 figures, submitted to PRL (updated in response to referees' comments

"Kohn-Shamification" of the classical density-functional theory of inhomogeneous polar molecular liquids with application to liquid hydrogen chloride

The Gordian knot of density-functional theories for classical molecular liquids remains finding an accurate free-energy functional in terms of the densities of the atomic sites of the molecules. Following Kohn and Sham, we show how to solve this problem by considering noninteracting molecules in a set of effective potentials. This shift in perspective leads to an accurate and computationally tractable description in terms of simple three-dimensional functions. We also treat both the linear- and saturation- dielectric responses of polar systems, presenting liquid hydrogen chloride as a case study.Comment: 4 pages, 2 eps-figures, submitted to Physical Review Letter

New physics of grain boundaries in bcc metals from the atomic level: molybdenum as a case study

We present a systematic trend study of the symmetric tilt grain boundaries about the axis in molybdenum. Our results show that multiple structural phases, some incorporating vacancies, compete for the boundary ground state. We find that at low external stress vacancies prefer to bind to the boundaries in high concentrations, and moreover, that external stress drives structural phase transitions which correspond to switching the boundaries on and off as pipe-diffusion pathways for vacancies. Finally, we present physical arguments which indicate these phenomena are likely to occur in the other bcc transition metals as well.Comment: 6 pages, 3 figures, 7 tables Replacement made minor changes to (a) the title and (b) the margin spacin

The Hopgrid algorithm: multilevel synthesis of multigrid and wavelet theory

The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an efficient representation of functions which exhibit localized bursts of short length-scale behavior. Applications such as computing the electrostatic field in and around a molecule should benefit from both approaches. In this work, we demonstrate how a novel interpolating wavelet transform, which in itself is the synthesis of finite element analysis and wavelet theory, may be used as the mathematical bridge to connect the two approaches. The result is a specialized multigrid algorithm which may be applied to problems expressed in wavelet bases. With this approach, interpolation and restriction operators and grids for the multigrid algorithm are predetermined by an interpolating multiresolution analysis. We will present the new method and contrast its efficiency with standard wavelet and multigrid approaches.Comment: 14 pages, 11 figure

Universal iso-density polarizable continuum model for molecular solvents

Implicit electron-density solvation models based on joint density-functional theory offer a computationally efficient solution to the problem of calculating thermodynamic quantities of solvated systems from firstprinciples quantum mechanics. However, despite much recent interest in such models, to date the applicability of such models in the plane-wave context to non-aqueous solvents has been limited because the determination of the model parameters requires fitting to a large database of experimental solvation energies for each new solvent considered. This work presents an alternate approach which allows development of new iso-density models for a large class of protic and aprotic solvents from only simple, single-molecule ab initio calculations and readily available bulk thermodynamic data

Tensor product expansions for correlation in quantum many-body systems

We explore a new class of computationally feasible approximations of the two-body density matrix as a finite sum of tensor products of single-particle operators. Physical symmetries then uniquely determine the two-body matrix in terms of the one-body matrix. Representing dynamical correlation alone as a single tensor product results in a theory which predicts near zero dynamical correlation in the homogeneous electron gas at moderate to high densities. But, representing both dynamical and statistical correlation effects together as a tensor product leads to the recently proposed ``natural orbital functional.'' We find that this latter theory has some asymptotic properties consistent with established many-body theory but is no more accurate than Hartee-Fock in describing the homogeneous electron gas for the range of densities typically found in the valence regions of solids. PACS 71.10.-w 71.15.Mb, Accepted for publication in Physical Review BComment: New figures, better converged result