Pseudospectral time-dependent density functional theory

Time-dependent density functional theory (TDDFT) is implemented within the Tamm-Dancoff approximation (TDA) using a pseudospectral approach to evaluate two-electron repulsion integrals. The pseudospectral approximation uses a split representation with both spectral basis functions and a physical space grid to achieve a reduction in the scaling behavior of electronic structure methods. We demonstrate here that exceptionally sparse grids may be used in the excitation energy calculation, following earlier work employing the pseudospectral approximation for determining correlation energies in wavefunction-based methods with similar conclusions. The pseudospectral TDA-TDDFT method is shown to be up to ten times faster than a conventional algorithm for hybrid functionals without sacrificing chemical accuracy.     

Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function

ABSTRACT

Explicit analytical expressions are presented for the density derivative, ?g_HS(R; ρ)/?ρ, of the Percus–Yevick approximation to the hard-sphere radial distribution function for R ≤ 6σ, where σ is the hard-sphere diameter and ρ = (N/V)σ³ is the reduced density, where N is the number of particles and V is the volume. A FORTRAN program is provided for the implementation of these for R ≤ 6σ, which includes code for the calculation of g_HS(R; ρ) itself over this range. We also present and incorporate within the program code convenient analytical expressions for the numerical extrapolation of both quantities past R = 6σ. Our expressions are numerically tested against exact results.     

From moment graphs to intersection cohomology

We describe a method of computing equivariant and ordinary intersection cohomology of certain varieties with actions of algebraic tori, in terms of structure of the zero- and one-dimensional orbits. The class of varieties to which our formula applies includes Schubert varieties in flag varieties and affine flag varieties. We also prove a monotonicity result on local intersection cohomology stalks. Received: 9 November 2000 / Published online: 24 September 2001     

Molecular simulation of chemical reaction equilibria by Kinetic Monte Carlo

ABSTRACT

We describe a new algorithm for the molecular simulation of chemical reaction equilibria, which we call the Reactive Kinetic Monte Carlo (ReKMC) algorithm. It is based on the use of the equilibrium Kinetic Monte Carlo (eKMC) method (Ustinov et al., J. Colloid Interface Sci., 2012, 366, 216–223) to generate configurations in the underlying nonreacting system and to calculate the species chemical potentials at essentially zero marginal computational cost. We consider in detail the typical case of specified temperature, T and pressure, P, but extensions to other thermodynamic constraints are straightforward in principle. In the course of this work, we also demonstrate an alternative method for calculating simulation box volume changes in NPT ensemble simulations to achieve the specified P. We consider two sets of example reacting systems previously considered in the literature, and compare the ReKMC results and computational efficiencies with those of different implementations of the REMC algorithm (Turner et al., Molec. Simulation, 2008, 34, 119–146).     

Spectroscopic and ab initio characterization of the [ReH9]2- ion

The dynamics and bonding of the hydrido complex Ba[ReH9], containing the D3h face-capped trigonal prismatic [ReH9]2- ion, have been investigated by vibrational spectroscopy and density functional theory (DFT). The combination of infrared, Raman, and inelastic neutron-scattering (INS) spectroscopies has enabled observation of all the modes of the [ReH9]2- ion for the first time. We demonstrate that calculations of the isolated [ReH9]2- ion are unable to reproduce the INS spectrum and that the complete unit cell must be considered with periodic DFT to have reliable results. This is shown to be a consequence of the long-range Coulomb potential present. Analysis of the electronic structure shows that the bonding between the rhenium and the hydrogen is largely covalent. There is a small degree of covalency between the prism hydrides and the barium. The counterion is crucial to the stability of the materials; hence, variation of it potentially offers a method to fine-tune the properties of the material.     

Prediction of polymerization shrinkage using molecular modeling

Group interaction modeling (GIM) is used to predict the changes in the volume and, therefore, shrinkage of a wide variety of commonly encountered acrylate and methacrylate monomers during polymerization. The predictions of the model are in excellent agreement with experimental data available in the literature. It is demonstrated that, given appropriate estimations of the ultimate matrix morphology, GIM can be used to give estimates of polymerization shrinkage in three‐dimensional crosslinked polymer networks that relate well to experimental data available for dental composite matrices. GIM provides a very useful framework within which the phenomenon of polymerization shrinkage can be considered. The approach challenges certain common misconceptions relating conversion to shrinkage. The limitations of this approach are discussed, and targets for future research are clearly outlined that could extend the scope of this methodology to encompass novel systems for which morphological information is not available. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 528–548, 2003     

An Efficient Algorithm for Non-Point Source Pollution Management Problems

A dynamic programming (DP) algorithm is proposed for a class of non-point source pollution control problems. The formulation deals with the selection of a spatial distribution of management practices in such a way as to meet a control agency's sediment pollution target. The inherently combinatorial nature of these problems — stemming from the discrete nature of the decision variables, which are production, conservation and mechanical control practices — gives them a special integer programming structure. This paper focuses on the DP formulation and the computer implementation of this algorithm. The approach is shown to be informative, robust and relatively efficient. Furthermore, the paper demonstrates that dynamic programming can be used to generate sensitivity analysis information for multiple-choice knapsack problems.     

On a Functional Differential Equation of Determinantal Type

We solve the functional equations for suitable functions f, g and h subject to x + y + z = 0.These equations essentially characterise the Weierstrass p-functionand its degenerations. 1991 Mathematics Subject Classification39B22, 30D05, 33E05.