Recurrence Formulas for Fully Exponentially Correlated Four-Body Wavefunctions

Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (>= -1) of all the interparticle distances r_ij, multiplied by an exponential containing an arbitrary linear combination of all the r_ij. These integrals are generalizations of those encountered using Hylleraas basis functions, and include all that are needed to make energy computations on the Li atom and other four-body systems with a fully exponentially correlated Slater-type basis of arbitrary quantum numbers. The only quantities needed to start the recursion are the basic four-body integral first evaluated by Fromm and Hill, plus some easily evaluated three-body "boundary" integrals. The computational labor in constructing integral sets for practical computations is less than when the integrals are generated using explicit formulas obtained by differentiating the basic integral with respect to its parameters. Computations are facilitated by using a symbolic algebra program (MAPLE) to compute array index pointers and present syntactically correct FORTRAN source code as output; in this way it is possible to obtain error-free high-speed evaluations with minimal effort. The work can be checked by verifying sum rules the integrals must satisfy.Comment: 10 pages, no figures, accepted by Phys. Rev. A (January 2009

Ultrathin graphitic structures and carbon nanotubes in a purified synthetic graphite

A new class of carbon structure is reported, which consists of microscale graphitic shells bounded by curved and faceted planes containing two to five layers. These structures were originally found in a commercial graphite produced by the Acheson process, followed by a purification treatment. The particles, which could be several hundreds of nanometres in size, were frequently decorated with nanoscale carbon particles, or short nanotubes. In some cases, nanotubes were found to be seamlessly connected to the thin shells, indicating that the formation of the shells and that of the nanotubes are intimately connected. The structures are believed to form during a purification process which involves passing an electric current through the graphite in the presence of a reactive gas. In support of this, it is shown that similar particles can be produced in a standard carbon arc apparatus. With their extremely thin graphene walls and high surface areas, the new structures may have a range of useful properties

Structural transformation of graphite by arc-discharge

The formation of novel structures by the passage of an electric current through graphite is described. These structures apparently consist of hollow three-dimensional graphitic shells bounded by curved and faceted planes, typically made up of two graphene layers. The curved structures were frequently decorated with nano-scale carbon particles, or short nanotubes. In some cases, nanotubes were found to be seamlessly connected to the thin shells, indicating that the formation of the shells and the nanotubes is intimately connected. Small nanotubes or nanoparticles were also sometimes found encapsulated inside the hollow structures, while fullerene-like particles were often seen attached to the outside surfaces. With their high surface areas and structural perfection, the new carbon structures may have applications as anodes of lithium ion batteries or as components of composite materials

Bond Length - Bond Valence Relationships for Carbon - Carbon and Carbon - Oxygen Bonds

In the present study, relationships are developed for determining bond orders (also referred to as bond valences or bond numbers) from published bond lengths for carbon-carbon (C-C) and carbon-oxygen (C-O) bonds. The relationships are based on Pauling’s empirical formula s = exp((Ro-R)/b)), where s is the bond order, R is the corresponding bond length, Ro is the unit valence bond length, and b is a fitting parameter. We use a recently derived relationship for the b parameter in terms of the bonding atoms’ published atomic orbital exponents. The resulting equations were checked against published x-ray diffraction (XRD) data for 176 carbon systems with 540 published C-C bond lengths, and 50 oxygen systems having 72 published C-O bond lengths. The C-C and C-O bond length-valence relationships are shown to have sufficient applicability and accuracy for use in any bonding environment, regardless of physical state or oxidation number

Atmospheric aerosols: A literature summary of their physical characteristics and chemical composition

This report contains a summary of 199 recent references on the characterization of atmospheric aerosols with respect to their composition, sources, size distribution, and time changes, and with particular reference to the chemical elements measured by modern techniques, especially activation analysis