Properties and applications of the average interparticle distance
The first and second moment operators are used to define the origin invariant shape and size of a molecule or functional group, as well as expressions for the distance between two electrons and the distance between an electron and a nucleus. The measure of molecular size correlates quite well with an existing theoretical measure of molecular volume calculated from isodensity contours. Also, the measure of size is effective in predicting steric effects of substituents which have been measured experimentally. The electron-electron and electron-nuclear distances are related to components of the Hartree-Fock energy. The average distance between two-electrons can model the Coulomb energy quite well, especially in the case of localized molecular orbitals. The average distance between an electron and a nucleus is closely related to the electron-nuclear attraction energy of a molecule.
Connected moments expansion: A new tool for quantum many-body theory.
The connected-moments expansion (CMX) for the ground-state energy is derived from the Horn-Weinstein theorem. This new technique possesses several striking advantages over traditional approaches to calculation of the ground-state energy. Like perturbational theories, the CMX series is conceptually simple but is easier to derive and program and is usually convergent even for very ``crude'' trial kets. Numerical examples reveal potential applicability of CMX for calculation of the correlation energy when the trial ket has the form of multideterminant wave function.
New records of Grania (Clitellata, Enchytraeidae) in the Northeast Atlantic (from Tromsø to the Canary Islands), with descriptions of seven new species
Previous northeast Atlantic records of Grania have been mainly from Germany, southern Scandinavia, and the Atlantic shores of France, Spain and Ireland. They were referred to eight species, with one, G. atlantica, reported from the continental slope. We have examined various unpublished collections from sources spanning from the Canary Islands to the Norwegian Arctic. Apart from new information on morphology, taxonomy, and distribution of known species, we describe seven new taxa (G. canaria, G. fortunata, G. mauretanica, G. aquitana, G. vikinga, G. torosa, and G. papillinasus). The collection of G. papillinasus from 2630-2885 m represents a new depth record for Enchytraeidae. Twenty-five of the now 57 Grania species occur in the North Atlantic. The North Atlantic drift moderates sea temperatures along the northeast Atlantic coasts, probably facilitating the wide latitudinal range of some taxa, as well as actual dispersal within the region. A "chaetal index" (chaetal length : chaetal foot length) is proposed to differentiate L-shaped chaetae at the species level. Complex relationships within the "type 6 group" of Grania suggest that groupings established using certain combinations of penial, chaetal and spermathecal patterns may not be monophyletic. For a better phylogenetic resolution, additional morphological details of these and other characters are needed.