Bernard M. Pettitt

Fast Multipole Methods for Particle Dynamics.

The growth of simulations of particle systems has been aided by advances in computer speed and algorithms. The adoption of algorithms to solve N-body simulation problems has been less rapid due to the fact that such scaling was only competitive for relatively large N. Our work seeks to find algorithmic modifications and practical implementations for intermediate values of N in typical use for molecular simulations. This article reviews fast multipole techniques for calculation of electrostatic interactions in molecular systems. The basic mathematics behind fast summations applied to long ranged forces is presented along with advanced techniques for accelerating the solution, including our most recent developments. The computational efficiency of the new methods facilitates both simulations of large systems as well as longer and therefore more realistic simulations of smaller systems.

Collinear reaction surface for He and ArH

An LCAO‐SCF ccalculation is presented for the potential energy surface for He and ArH. The calculation was done using contracted gaussian basis sets on a Honeywell 6660 computer using the MOLE quantum chemistry program. (AIP)

Theoretical Compton profile anisotropies in molecules and solids. VI. Compton profile anisotropies and chemical binding

An interesting empirical relationship between zero point Compton profile anisotropies ΔJ (0) and nuclear charges is noted. It is shown that, for alkali halide molecules AB, to a good approximation ΔJ (0) =N ln(Zb/Za).

Theoretical Compton profile anisotropies in molecules and solids. IV. Parallel–perpendicular anisotropies in alkali fluoride molecules

Calculations of Compton profiles and parallel–perpendicular anisotropies in alkali fluorides are presented and analyzed in terms of molecular charge distributions and wave function character. It is found that the parallel profile associated with the valence pi orbital is the principal factor determining the relative shapes of the total profile anisotropies in the low momentum region.

Theoretical Compton profile anisotropies in molecules and solids. III. Relationship of parallel–perpendicular anisotropies to charge distributions in alkali chloride molecules

Total Compton profiles and anisotropies associated with momentum distribution along vectors parallel and perpendicular to bond axes in alkali chloride molecules are calculated and related to changes in charge distributions accompanying bond formation.

Theoretical Compton profile anisotropies in molecules and solids. V. Lithium and sodium bromide diatomics

Anisotropies associated with momentum distributions along vectors parallel and perpendicular to bond axes in alkali bromide molecules are computed and analyzed. An attempt is made to relate these to charge cloud deformations accompanying molecular formation. Our analysis indicates that the parallel profile associated with the valence pi orbital is the dominating factor determining the relative shapes of the total profile anisotropies in the low momenta regions pz ?0.5.

Simple bond length dependence : A correspondence between reactive fluid theories

Two elementary models of reactive fluids are examined, the first being a standard construction assuming molecular dissociation at infinite separation; the second is an open mixture of nondissociative molecules and free atoms in which the densities of free atoms and molecules are coupled. An approximation to the density of molecules, to low order in site density, is derived in terms of the classical associating fluid theory variously described by Wertheim [J. Chem. Phys. 87, 7323 (1987)] and Stell [Physica A 231, 1 (1996)]. The results are derived for a fluid of dimerizing hard spheres, and predict dependence of the molecular density on the total site density, the hard sphere diameter, and the bond length of the dimer. The results for the two reactive models are shown to be qualitatively similar, and lead to equivalent predictions of the molecular density for the infinitely short and infinitely long bond lengths.

Numerical simulation of the sedimentation of a tripole-like body in an incompressible viscous fluid☆

In this note, we discuss the application of a methodology combining distributed Lagrange multiplier based fictitious domain techniques, finite-element approximations and operator splitting, to the numerical simulation of the motion of a tripole-like rigid body falling in a Newtonian incompressible viscous fluid. The motion of the body is driven by the hydrodynamical forces and gravity. The numerical simulation shows that the distribution of mass of this rigid body and added moment of inertia compared to a simple cylinder (circular or elliptic) plays a significant role on the particle-fluid interaction. Apparently, for the parameters examined, the action of the moving rigid body on the fluid is stronger than the hydrodynamic forces acting on the rigid body.

Theory of the chemical bond. V. Bond polarities of post‐transition hydrides

A classical derivation of a dipole moment model derived earlier by a quantum mechanical implicit perturbation technique is given. This model is used to determine the bond polarities of the post transition (Groups IIIA–VIIA) hydrides. The polarity measures the extent of charge transfer in a bond. Polarities of alkali halides and posttransition hydrides are used to illustrate the gradual change in bond polarities with nuclear charge across the periodic table.

Theoretical Compton profile anisotropies in molecules and solids. VII. Zero point Compton profile anisotropies and bond polarities in alkali halide diatomic molecules

A correlation between bond polarities and zero point Compton profile anisotropies is shown for alkali halide molecules. The correlation derives from the fact that both quantities are determined by molecular binding and antibinding forces and are thus functionally related to nuclear charge ratios.