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

Strongly coupled binuclear uranium-oxo complexes from uranyl oxo rearrangement and reductive silylation

The most common motif in uranium chemistry is the d0f0 uranyl ion [UO2]21 in which the oxo groups are rigorously linear and inert. Alternative geometries, such as the cis-uranyl, have been identified theoretically and implicated in oxo-atom transfer reactions that are relevant to environmental speciation and nuclear waste remediation. Single electron reduction is now known to impart greater oxo-group reactivity, but with retention of the linear OUO motif, and reactions of the oxo groups to form new covalent bonds remain rare. Here, we describe the synthesis, structure, reactivity and magnetic properties of a binuclear uranium–oxo complex. Formed through a combination of reduction and oxo-silylation and migration from a trans to a cis position, the new butterfly-shaped Si–OUO2UO–Si molecule shows remarkably strong UV–UV coupling and chemical inertness, suggesting that this rearranged uranium oxo motif might exist for other actinide species in the environment, and have relevance to the aggregation of actinide oxide clusters.JRC.E.6-Actinides researc