Graphical unitary group approach

Graphical unitary group approach (GUGA) is a technique used to construct Configuration state functions (CSFs) in computational quantum chemistry. As reflected in its name, the method uses the mathematical properties of the unitary group.

The foundation of the unitary group approach (UGA) can be traced to the work of Moshinsky.{{Cite book|author=M. Moshinsky|title=Group Theory and the Many Body Problem|publisher=Gordon and Breach|location= New York |year=1968|isbn= 0-677-01740-5}} Later, Shavitt{{cite journal| doi=10.1002/qua.560120819| title=Graph theoretical concepts for the unitary group approach to the many-electron correlation problem| year=1977| last1=Shavitt| first1=Isaiah| journal=International Journal of Quantum Chemistry| volume=12| pages=131–148}}{{cite journal| doi=10.1002/qua.560140803| title=Matrix element evaluation in the unitary group approach to the electron correlation problem| year=1978| last1=Shavitt| first1=Isaiah| journal=International Journal of Quantum Chemistry| volume=14| pages=5–32}} introduced the graphical aspect (GUGA) drawing on the earlier work of Paldus.{{cite journal| doi=10.1103/PhysRevA.14.1620| title=Unitary-group approach to the many-electron correlation problem: Relation of Gelfand and Weyl tableau formulations| year=1976| last1=Paldus| first1=Josef| journal=Physical Review A| volume=14| issue=5| pages=1620–1625|bibcode = 1976PhRvA..14.1620P }}

Computer programs based on the GUGA method have been shown to be highly efficient.{{Cite journal|doi =10.1088/0031-8949/21/3-4/013|title =The Loop-Driven Graphical Unitary Group Approach: A Powerful Method for the Variational Description of Electron Correlation|year =1980|last1 =Brooks|first1 =Bernard R|last2 =Laidig|first2 =William D|last3 =Saxe|first3 =Paul|last4 =Handy|first4 =Nicholas C|last5 =Schaefer|first5 =Henry F|journal =Physica Scripta|volume =21|issue =3–4|pages =312–322|bibcode = 1980PhyS...21..312B }}{{cite book|author1=D.C. Sherrill |author2=H.F. Schaeffer III |title=The Configuration Interaction Method: Advances in Highly Correlated Approaches|series=Advances in Quantum Chemistry |volume= 34 |year=1999|publisher= Academic Press|pages=143–270|isbn=0-12-034834-9}} offering certain performance advantages over the older, sometimes called traditional, techniques for CSF construction. However traditional methods can offer other advantages{{Cite book|author1=A.D. McLean |author2=M. Yoshimine |author3=B.H. Lengsfield |author4=P.S. Bagus |author5=B. Liu |

chapter=ALCHEMY II, A Research Tool for Molecular Electronic Structure and Interactions|

title= Modern Techniques in Computational Chemistry (MOTECC-91)| editor=E. Clementi|publisher=ESCOM Science Publishers|location= Leiden|year=1991|isbn =90-72199-10-3}} such as the ability to handle degenerate symmetry point groups, such as $C\_\{\backslash infty\; v\}$.