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

Soft-X-Ray Photoabsorption of the No Dimer

X-ray absorption spectra are reported for the first time for the (NO)(2) dimer at both the nitrogen and oxygen K edges, the data being obtained from (NO)(2) multilayers formed on Ag{111}. The spectra display distinctive features which suggest an electronic structure for excited states of this species. Density functional theory studies of the core-hole excited states provide the basis for spectral assignments at the nitrogen K edge, allowing the identification of the N 1s electron promotion into the 2b(1), 2a(2), 7b(2), 8a(1) and 8b(2) orbitals. Correlations are found between the experimental integrated oscillator strengths of the two pi* states, at the nitrogen K edge, and the N-localized 2p coefficients of the unoccupied orbitals of the ((1)A(1)) state