Editing Gaussian orbital (section)

== Rationale ==

The use of Gaussian orbitals in electronic structure theory (instead of the more physical [[Slater-type orbital]]s) was first proposed by [[S. Francis Boys|Boys]]<ref>{{cite journal|first1=S. F.|last1=Boys|title=Electronic Wave Functions. I. A General Method of Calculation for the Stationary States of Any Molecular System|jstor=98423 | journal= Proc. R. Soc. Lond. A |volume=200 |issue=1063|pages=542–554|year=1950|bibcode=1950RSPSA.200..542B|doi=10.1098/rspa.1950.0036|s2cid=122709395|url=http://elib.bsu.by/handle/123456789/154387}}</ref> in 1950. The principal reason for the use of Gaussian [[Basis set (chemistry)|basis functions]] in molecular quantum chemical calculations is the 'Gaussian Product Theorem', which guarantees that the product of two GTOs centered on two different atoms is a finite sum of Gaussians centered on a point along the axis connecting them. In this manner, four-center integrals can be reduced to finite sums of two-center integrals, and in a next step to finite sums of one-center integrals. The speedup by 4-5 orders of magnitude compared to [[Slater orbitals]] outweighs the extra cost entailed by the larger number of basis functions generally required in a Gaussian calculation.

For reasons of convenience, many quantum chemistry programs work in a basis of Cartesian Gaussians even when spherical Gaussians are requested, as integral evaluation is much easier in the Cartesian basis, and the spherical functions can be simply expressed using the Cartesian functions.<ref>{{cite journal|last=Schlegel|first=H.|author2=Frisch, M.|title=Transformation between Cartesian and pure spherical harmonic Gaussians|journal=International Journal of Quantum Chemistry|year=1990|volume=54|issue=2|pages=83–87|doi=10.1002/qua.560540202 |s2cid=94417974 }}</ref>
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{{cite journal|last=Mathar|first=Richard J.|title=Mutual Conversion of Three Flavors of Gaussian Type Orbitals|journal=International Journal of Quantum Chemistry|year=2002|volume=90|issue=1|pages=227–243|doi=10.1002/qua.10085|arxiv=physics/9907051 |bibcode=2002IJQC...90..227M|s2cid=119100125 }}
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