A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Interleukin-15 Treatment Induces Weight Loss Independent of Lymphocytes

Obesity is a chronic inflammatory condition characterized by activation and infiltration of proinflammatory immune cells and a dysregulated production of proinflammatory cytokines. While known as a key regulator of immune natural killer (NK) cell function and development, we have recently demonstrated that reduced expression of the cytokine Interleukin-15 (IL-15) is closely linked with increased body weight and adiposity in mice and humans. Previously, we and others have shown that obese individuals have lower circulating levels of IL-15 and NK cells. Lean IL-15 overexpressing (IL-15 tg) mice had an accumulation in adipose NK cells compared to wildtype and NK cell deficient obese IL-15−/− mice. Since IL-15 induces weight loss in IL-15−/− and diet induced obese mice and has effects on various lymphocytes, the aim of this paper was to determine if lymphocytes, particularly NK cells, play a role in IL-15 mediated weight loss. Acute IL-15 treatment resulted in an increased accumulation of NK, NKT, and CD3+ T cells in adipose tissue of B6 mice. Mice depleted of NK and NKT cells had similar weight loss comparable to controls treated with IL-15. Finally, IL-15 treatment induces significant weight loss in lymphocyte deficient RAG2−/−γc−/− mice independent of food intake. Fat pad cross-sections show decreased pad size with cytokine treatment is due to adipocyte shrinkage. These results clearly suggest that IL-15 mediates weight loss independent of lymphocytes

Facile synthesis and electrochemical properties of octahedral gold nanocrystals

High-yield octahedral gold nanocrystals of *45 nm in size have been facilely synthesized by one-pot reduction of HAuCl4 using formic acid in cetyltrimethylammonium bromide (CTAB) aqueous solution. The results showed that CTAB can promote the formation of single-crystalline nucleation and preferentially adsorb on the (111) planes of gold nanocrystals, resulting in the formation of octahedral gold nanocrystals. Formic acid acted as not only a mild reducing agent, but also could promote the formation of (111) facet. The octahedral gold nanocrystals exhibited similar cyclic voltammetry (CV) curves to single-crystal Au (111) electrode and excellent electrocatalytic activity for methanol oxidation. This synthetic strategy may open new route for facile synthesis of shape-controlled metal nanoparticles