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

 Pablo Echenique∗†‡and J. L. Alonso†‡ 

†Departamento de F ́ısica Te ́orica, Universidad de Zaragoza,Pedro Cerbuna 12, 50009, Zaragoza, Spain. 

‡Instituto de Biocomputaci ́on y F ́ısica de los Sistemas Complejos (BIFI),Edificio Cervantes, Corona de Arag ́on 42, 50009, Zaragoza, Spain

.(May 2007)

 

We present here a review of the fundamental topics of Hartree-Fock theory in QuantumChemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer ap-proximation, 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 deriva-tion of the final equations, as well as in the results regarding the existence and uniquenessof their solutions. All Hartree-Fock versions with different spin restrictions are systematicallyextracted from the general case, thus providing a unifying framework. Then, the discretizationof 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 andselection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close thereview with a section in which the most relevant modern developments (specially those relatedto the design of linear-scaling methods) are commented and linked to the issues discussed. Thewhole work is intentionally introductory and rather self-contained, so that it may be usefulfor 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 hereto facilitate comprehension and to serve as a handy reference.

 

 https://core.ac.uk/download/pdf/36046448.pdf