Abstract
It is shown that the application of a projection operator from a given group to a function is equivalent to the successive application of projection operators from factor groups of the starting group to that function. When used with the factor groups representing the site symmetry of a position and the simplest group of interchanges of positions, this concept provides a very simple method for obtaining symmetry adapted linear combinations of basis functions.
Similar content being viewed by others
References
Cotton,F.A.: Chemical applications of group theory, 2nd ed., Chapter 6. New York: Wiley-Interscience 1971
Hall,L.H.: Group theory and symmetry in chemistry, Chapters 8 and 9. New York: McGraw-Hill Book Co., 1969
Leech,J.W., Newman,D.J.: How to use groups, Chapter 7. London: Meuthen and Co., Ltd., 1969
Altmann,S.L.: Phil. Trans. Roy. Soc. 225 A, 216 (1963)
Altmann,S.L.: Rev. Mod. Phys. 35, 641 (1963)
Longuet-Higgins,H.C.: Mol. Phys. 6, 445 (1963)
Altmann,S.L.: Proc. Roy. Soc. A298, 184 (1967)
Melvin,M.A.: Rev. Mod. Phys. 28, 18 (1956)
Flurry,Jr.,R.L.: Int. J. Quantum Chem. 65, 455 (1972)
Wilson,E.B., Decius,J.C., Cross,P.C.: Molecular vibrations, p. 113. New York: McGraw-Hill Book Co., 1955
Weyl,H.: The theory of groups and quantum mechanics, p. 306. Dover Publications, Inc., 1950
Ref. [10], p. 320
Ref. [10], p. 121
Gray,H.B., Beach,N.A.: J. Am. Chem. Soc. 85, 2922 (1963)
Herzberg,G.: Infrared and raman spectra, p. 100. Princeton: D. Van Nostrand Co., Inc., 1945
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Flurry, R.L. The use of site symmetry in constructing symmetry adapted functions. Theoret. Chim. Acta 31, 221–230 (1973). https://doi.org/10.1007/BF00526512
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00526512