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

Structure and mechanism of the mammalian fructose transporter GLUT5.

糖分を細胞内に輸送する膜たんぱく質の立体構造と動きを解明 -肥満やがんの抑制策に役立つ新たな知見-. 京都大学プレスリリース. 2015-10-01.The altered activity of the fructose transporter GLUT5, an isoform of the facilitated-diffusion glucose transporter family, has been linked to disorders such as type 2 diabetes and obesity. GLUT5 is also overexpressed in certain tumour cells, and inhibitors are potential drugs for these conditions. Here we describe the crystal structures of GLUT5 from Rattus norvegicus and Bos taurus in open outward- and open inward-facing conformations, respectively. GLUT5 has a major facilitator superfamily fold like other homologous monosaccharide transporters. On the basis of a comparison of the inward-facing structures of GLUT5 and human GLUT1, a ubiquitous glucose transporter, we show that a single point mutation is enough to switch the substrate-binding preference of GLUT5 from fructose to glucose. A comparison of the substrate-free structures of GLUT5 with occluded substrate-bound structures of Escherichia coli XylE suggests that, in addition to global rocker-switch-like re-orientation of the bundles, local asymmetric rearrangements of carboxy-terminal transmembrane bundle helices TM7 and TM10 underlie a 'gated-pore' transport mechanism in such monosaccharide transporters