# A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry - Physics > Chemical Physics

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Abstract: We present here a review of the fundamental topics of Hartree-Fock theory inQuantum Chemistry. From the molecular Hamiltonian, using and discussing theBorn-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fockequations for the electronic problem. Special emphasis is placed in the mostrelevant mathematical aspects of the theoretical derivation of the finalequations, as well as in the results regarding the existence and uniqueness oftheir solutions. All Hartree-Fock versions with different spin restrictions aresystematically extracted from the general case, thus providing a unifyingframework. Then, the discretization of the one-electron orbitals space isreviewed and the Roothaan-Hall formalism introduced. This leads to a expositionof the basic underlying concepts related to the construction and selection ofGaussian basis sets, focusing in algorithmic efficiency issues. Finally, weclose the review with a section in which the most relevant modern developments(specially those related to the design of linear-scaling methods) are commentedand linked to the issues discussed. The whole work is intentionallyintroductory and rather self-contained, so that it may be useful for nonexperts that aim to use quantum chemical methods in interdisciplinaryapplications. Moreover, much material that is found scattered in the literaturehas been put together here to facilitate comprehension and to serve as a handyreference.

Author: ** Pablo Echenique, J. L. Alonso**

Source: https://arxiv.org/