# Graphical unitary group approach

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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.[1] Later, Shavitt[2][3] introduced the graphical aspect (GUGA) drawing on the earlier work of Paldus.[4]

Computer programs based on the GUGA method have been shown to be highly efficient.[5] [6] offering certain performance advantages over the older, sometimes called traditional, techniques for CSF construction. However traditional methods can offer other advantages[7] such as the ability to handle degenerate symmetry point groups, such as ${\displaystyle C_{\infty v}}$.

## References

1. ^ M. Moshinsky (1968). Group Theory and the Many Body Problem. New York: Gordon and Breach. ISBN 0-677-01740-5.
2. ^ Shavitt, Isaiah (1977). "Graph theoretical concepts for the unitary group approach to the many-electron correlation problem". International Journal of Quantum Chemistry. 12: 131–148. doi:10.1002/qua.560120819.
3. ^ Shavitt, Isaiah (1978). "Matrix element evaluation in the unitary group approach to the electron correlation problem". International Journal of Quantum Chemistry. 14: 5–32. doi:10.1002/qua.560140803.
4. ^ Paldus, Josef (1976). "Unitary-group approach to the many-electron correlation problem: Relation of Gelfand and Weyl tableau formulations". Physical Review A. 14 (5): 1620–1625. Bibcode:1976PhRvA..14.1620P. doi:10.1103/PhysRevA.14.1620.
5. ^ Brooks, Bernard R; Laidig, William D; Saxe, Paul; Handy, Nicholas C; Schaefer, Henry F (1980). "The Loop-Driven Graphical Unitary Group Approach: A Powerful Method for the Variational Description of Electron Correlation". Physica Scripta. 21 (3–4): 312–322. Bibcode:1980PhyS...21..312B. doi:10.1088/0031-8949/21/3-4/013.
6. ^ D.C. Sherrill; H.F. Schaeffer III (1999). The Configuration Interaction Method: Advances in Highly Correlated Approaches. Advances in Quantum Chemistry. 34. Academic Press. pp. 143–270. ISBN 0-12-034834-9.
7. ^ A.D. McLean; M. Yoshimine; B.H. Lengsfield; P.S. Bagus; B. Liu (1991). "ALCHEMY II, A Research Tool for Molecular Electronic Structure and Interactions". In E. Clementi. Modern Techniques in Computational Chemistry (MOTECC-91). Leiden: ESCOM Science Publishers. ISBN 90-72199-10-3.