A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

Details A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

2007-05-02

arxiv.org/abs/0705.0337v3

Molecular Physics 105 (2007) 3057-3098

Physics

Chemical Physics

64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn packages

Scientific paper

10.1080/00268970701757875

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.

Affiliated with

Also associated with

No associations

Rating

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-675293