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

Estimating genomic instability mediated by Alu retroelements in breast cancer

Alu-PCR is a relatively simple technique that can be used to investigate genomic instability in cancer. This technique allows identification of the loss, gain or amplification of gene sequences based on the analysis of segments between two Alu elements coupled with quantitative and qualitative analyses of the profiles obtained from tumor samples, surgical margins and blood. In this work, we used Alu-PCR to identify gene alterations in ten patients with invasive ductal breast cancer. Several deletions and insertions were identified, indicating genomic instability in the tumor and adjacent normal tissue. Although not associated with specific genes, the alterations, which involved chromosomal bands 1p36.23, 1q41, 11q14.3, 13q14.2, occurred in areas of well-known genomic instability in breast and other types of cancer. These results indicate the potential usefulness of Alu-PCR in identifying altered gene sequences in breast cancer. However, caution is required in its application since the Alu primer can produce non-specific amplification

Theoretical studies of inorganic and organometallic reaction mechanisms. 14. beta-hydrogen transfer and alkene/alkyne insertion at a cationic iridium center

Recent experimental work shows that alkanes can be activated by Cp*Ir(PMe3)(CH3)(+) at room temperature to generate olefin complexes. The reaction begins with alkane activation by oxidative addition (OA) followed by reductive elimination (RE) of methane and then olefin formation by the beta-H transfer from the bound alkyl. Ab initio calculations and density functional theory (DFT) studies of ethane activation by CpIr(PH3)(CH3)(+) (1) to generate CpIr(PH3)(eta(2)-C2H4)(H)(+) (7) show that the beta-H transfer from CpIr(PH3)(C2H5)(+) (5) to 7 is exothermic by 12 and 16 kcal/mol with a very low barrier of 0.7 and 0.4 kcal/mol at the DFT and CCSD levels, respectively. Thus, the rate-determining step in alkane dehydrogenation to olefin complexes by Cp*Ir(PMe3)(CH3)(+) is the alkane OA step. These results are in very good agreement with the experimental work of Bergman and co-workers. A strong stabilizing interaction between either ethylene or acetylene and CpIr(PH3)(CH3)(+) leads to high activation barriers (25-36 kcal/mol) for the insertion processes of ethylene or acetylene. In comparison to ethylene, the insertion reaction of acetylene with the CpIr(PH3)(CH3)(+) complex is more favorable. Thus, the dimerization of terminal alkynes catalyzed by cationic iridium complexes is plausible