Kenneth E. Edgecombe

A Simple Measure of Electron Localization in Atomic and Molecular-Systems

We introduce in this work a new approach to the identification of localized electronic groups in atomic and molecular systems. Our approach is based on local behavior of the Hartree–Fock parallel‐spin pair probability and is completely independent of unitary orbital transformations. We derive a simple ‘‘electron localization function’’ (ELF) which easily reveals atomic shell structure and core, binding, and lone electron pairs in simple molecular systems as well.

Cr2 in Density-Functional Theory - Approximate Spin Projection

Abstract The ground-state potential energy curve of Cr 2 is examined using three density-functional exchange-correlation approximations: the local spin-density approximation (LSDA), the gradient-corrected BLYP approximation, and the recent B3P86 approximation incorporating a small admixture of exact exchange. An attempt is made in this work to project, at least approximately, the pure singlet energy from the usual Cr 2 antiferromagnetic broken-symmetry state. The effect of this approximate spin projection is significant. Only the B3P86 functional is found to give good agreement with experiment after spin projection. Moreover, we obtain a double-well potential energy curve which has been suggested by other theoretical (non-DFT) studies and even by experiment.

One‐particle density matrices along the molecular bonds in linear molecules

The bonding in a number of σ‐bonded diatomic and linear triatomic molecules is interpreted in terms of the one‐particle density matrix (ODM) along the bond axis. Special attention is drawn to the off‐diagonal contributions of the ODM in a two‐dimensional position space representation, which are shown to be indicative of a bonding or antibonding covalent interaction between the atomic centers.

Pseudoatoms of the electron density

The theory of molecular structure, developed by Bader and co‐workers, has met with considerable success and is now being applied to many aspects of chemistry. One finding, however, that has complicated the theory is that of non‐nuclear attractors, that is, pseudoatoms. In this study we examine basis set and to some extent electron correlation effects on the appearance and disappearance of non‐nuclear attractors in Li2, Na2, Na4, and Na5. The appearance of a pseudoatom in a lithium molecule correlates remarkably well with the size of the region, in an atomic calculation, of −∇2ρ(r) for the valence shell of the atom. This and the fact that the pseudoatom is also present in the promolecule indicates that the pseudoatoms are remnants of or, in fact, are portions of atoms that are not perturbed enough in the molecule to remove an essentially atomic characteristic.

A topological electron density analysis of tricoordinate phosphorus inversion processes

Abstract This paper describes the application of topological electron density analysis to inversion processes in tricoordinate phosphorus systems. The calculations are at the Hartree-Fock self-consistent-field level using the 6-311G ∗∗ basis sets. Of particular interest are the approximate T-shaped transition states reported by Dixon and co-workers (J. Am. Chem. Soc., 108 (1986) 2461, 6821). The role that the lone pair of electrons on phosphorus plays in determining the geometry of the transition state is analyzed through the laplacian of the electron density. It is shown that the species that will invert through the T-shaped process have distances, from P to the maximum in the non-bonded charge concentration, ranging from 1.408 a.u. to 1.417 a.u., whereas those species that invert through the classical process have distances ranging from 1.432 a.u. to 1.452 a.u.

A Hybrid Double-Layer Master-Slave Model For Multicore-Node Clusters

The Double-Layer Master-Slave Model (DMSM) is a suitable hybrid model for executing a workload that consists of multiple independent tasks of varying length on a cluster consisting of multicore nodes. In this model, groups of individual tasks are first deployed to the cluster nodes through an MPI based Master-Slave model. Then, each group is processed by multiple threads on the node through an OpenMP based All-Slave approach. The lack of thread safety of most MPI libraries has to be addressed by a judicious use of OpenMP critical regions and locks. The HPCVL DMSM Library implements this model in Fortran and C. It requires a minimum of user input to set up the framework for the model and to define the individual tasks. Optionally, it supports the dynamic distribution of task-related data and the collection of results at runtime. This library is freely available as source code. Here, we outline the working principles of the library and on a few examples demonstrate its capability to efficiently distribute a workload on a distributed-memory cluster with shared-memory nodes.

Nonnuclear Maxima in the Charge Density

Abstract Basis-set and electron-correlation effects on the appearance and disappearance of nonnuclear maxima in the electron density are examined in Li2 , Na2 , Na4 and Na5 . It is shown that nonnuclear attractors can be removed in all cases except Li2 . The appearance of a pseudoatom in a lithium molecule correlates remarkably well with the size of the region, in an atomic calculation, of V2r(r) for the valence shell of the atom. This and the fact that the pseudoatom is also present in the promolecule indicate that the pseudoatoms are remnants of, or in fact are portions of, atoms that are not perturbed enough in the molecule to remove an essentially atomic characteristic.