Editing Gaussian orbital (section)

==Molecular integrals==
Taketa et al. (1966) presented the necessary mathematical equations for obtaining matrix elements in the Gaussian basis.<ref>{{cite journal|last=Taketa|first=Hiroshi|author2=Huzinaga, Sigeru |author3=O-ohata, Kiyosi |title=Gaussian-Expansion Methods for Molecular Integrals|journal=Journal of the Physical Society of Japan|year=1966|volume=21|issue=11|pages=2313–2324|doi=10.1143/JPSJ.21.2313|bibcode = 1966JPSJ...21.2313T }}</ref> Since then much work has been done to speed up the evaluation of these integrals which are the slowest part of many quantum chemical calculations. Živković and Maksić (1968) suggested using [[Hermite]] Gaussian functions,<ref>{{cite journal|last=Živković|first=T.|author2=Maksić, Z. B.|title=Explicit Formulas for Molecular Integrals over Hermite-Gaussian Functions|journal=Journal of Chemical Physics|year=1968|volume=49|issue=7|pages=3083–3087|doi=10.1063/1.1670551 |bibcode = 1968JChPh..49.3083Z }}</ref> as this simplifies the equations. McMurchie and Davidson (1978) introduced recursion relations,<ref>{{cite journal|last=McMurchie|first=Larry E.|author2=Davidson, Ernest R.|title=One- and two-electron integrals over Cartesian Gaussian functions|journal=Journal of Computational Physics|year=1978|volume=26|issue=2|pages=218–31|doi=10.1016/0021-9991(78)90092-X|bibcode = 1978JCoPh..26..218M |url=https://digital.library.unt.edu/ark:/67531/metadc1057442/}}</ref> which greatly reduces the amount of calculations.  [[John Pople|Pople]] and Hehre (1978) developed a local coordinate method.<ref>{{cite journal|last=Pople|first=J. A.|author2=Hehre, W. J.|title=Computation of electron repulsion integrals involving contracted Gaussian basis functions.|journal=J. Comput. Phys.|year=1978|volume=27|issue=2|pages=161–168|doi=10.1016/0021-9991(78)90001-3|bibcode = 1978JCoPh..27..161P }}</ref>  Obara and Saika introduced efficient recursion relations in 1985,<ref>{{cite journal|last=Obara|first=S.|author2=Saika, A.|title=Efficient recursive computation of molecular integrals over Cartesian Gaussian functions|journal=J. Chem. Phys.|year=1986|volume=84|issue=7|pages=3963–74|doi=10.1063/1.450106|bibcode = 1986JChPh..84.3963O }}</ref>  which was followed by the development of other important recurrence relations. Gill and Pople (1990) introduced a 'PRISM' algorithm which allowed efficient use of 20 different calculation paths.<ref>{{cite journal|last=Gill|first=Peter M. W.|author2=Pople, John A.|title=The Prism Algorithm for Two-Electron Integrals|journal=International Journal of Quantum Chemistry|date=December 1991|volume=40|issue=6|pages=753–772|doi=10.1002/qua.560400605|url=http://rscweb.anu.edu.au/~pgill/papers/026PRISM.pdf|accessdate=17 June 2011}}</ref>