Kinetic energy functional in hyperspherical coordinates

Hyperspherical coordinates and a generator coordinate representation are employed to find a simple form of the kinetic energy for a general three-particle problem. An expression is developed for the determination of adiabatic hyperangular states in a local potential using the finite element method.     

The Synthesis of 3-(R)- and 3-(S)-Hydroxyeicosapentaenoic Acid

Monohydroxylated polyunsaturated fatty acids belonging to the oxylipin class of natural products are present in marine and terrestrial sources as well as in the human body. Due to their biological activities and role in diverse biosynthetic pathways, oxylipins biosynthesized from eicosapentaenoic acid and arachidonic acid have attracted great interest from the scientific community. One example is 3-hydroxyeicosapentaenoic acid where the absolute configuration at C-3 has only been tentatively assigned. In this paper, studies on acetate type aldol reactions that enabled the preparation of 3-(R)-hydroxyeicosapentaenoic acid (3R-HETE, 2) and its enantiomer are presented.     

Integral algorithm and density matrix integration scheme for ab initio band structure calculations on polymeric systems

A new program for band structure calculations of periodic one-dimensional systems has been constructed. It is distinguishable from other codes by the efficient two-electron integral evaluation and the integration schemes of the density matrix in the first Brillouin zone. The computation of polymeric two-electron integrals is based on the McMurchie Davidson algorithm and builds batches of the different cell indices included in the polymeric system. Consequently it presents efficient scaling with respect to the number of unit cells taken into account. Our algorithm takes into account fully the polymeric symmetry rather than the molecular symmetry. A semidirect procedure where only exchange integrals are computed at each SCF cycle is proposed in order to maintain balance between computation time and disk space. In addition, the integration of the density matrix over a large number of cell indices can be performed by different methods, such as Gauss-Legendre, Clenshaw-Curtis, Filon, and Alaylioglu-Evans-Hyslop. This last scheme is able to obtain an accuracy of 10(-13) a.u. on each individual density matrix element for all cell indices with only 48 k-points.     

On the complex hybridization of orbitals of s and p type

The direction of valence is defined as the direction from the atomic nucleus to the center of gravity of the hybrid density. Complex mixing coefficients of the orbitals of pure angular momentum are introduced in the hybrid. This allows a considerable extension of the hybridization concept with regard to valence angles and equivalence restrictions. General expressions for the direction consines of valence and for bond angles are given, and applications are made to several molecules with bond angles of 90 degrees or less.

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Zusammenfassung Die Valenzrichtung eines Hybrids wird als die Richtung vom Atomkern zum Schwerpunkt der Elektronendichte difiniert. Dabei werden auch komplexe Koeffizienten für die atomaren Zustandsfunktionen zugelassen, wodurch eine erhebliche Erweiterung des Hybridisierungs-konzeptes im Hinblick auf Valenzwinkel und Nebenbedingungen infolge von Äquivalenz möglich ist. Allgemeine Ausdrücke für die Richtungskosinus und Bindungswinkel werden angegeben, ebenso einige Beispiele für Moleküle mit Winkeln unter 90.

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Résumé La direction de valence est définie comme la direction joignant le noyau atomique au centre de gravité de la densité de l'hybride. Des coefficients de mélange complexes sont introduits dans l'hybride pour les orbitales de moment angulaire pur. Ceci permet une extension considérable du concept d'hybridation en ce qui concerne les angles de valence et les restrictions d'équivalence. Des expressions générales pour les cosinus directeurs des directions de valence et pour les angles de liaison sont obtenues et appliquées á plusieurs molécules dont les angles de liaison sont au plus de 90.

     

Introduction

The formalism for a configuration interaction approach is presented, in which explicit introduction of interelectronic coordinates into individual configurations is accomplished through the use of spherical Gaussian correlation factors. Formulas for all required matrix elements over these configurations are derived, and a computationally convenient algorithm to evaluate the matrix elements is presented. In addition, analysis of the form of the correlation factor shows that both angular and radial correlation can be obtained using spherical Gaussian correlation factors.