Abstract
We present sets of real 3-Γ symbols which correspond to explicitly given irreducible matrix representations for the two double group hierarchies T* ⊃ C *3 and T* ⊃ C *2 . They fit into the formalism exposed in a previous paper [1] on the general theory of 3-Γ symbols and coupling coefficients and illustrate much of the discussion in a subsequent one [2] treating the particular properties of the double groups.
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Damhus, T., Harnung, S. E., Schäffer, C. E.: paper I in this series
Same, paper II in the series
Same, paper III in the series
Devine, S. D.: J. Chem. Phys. 47, 1844 (1967)
E.g., Schäffer, C. E.: Struct. Bond. 5, 68 (1968); Cotton, F. A., Wilkinson, G.: Advanced inorganic chemistry, p. 45, 4th Ed., New York: Wiley & Sons, 1980
Nakazaki, M., Naemura, K.: J. Chem. Soc. Chem. Commun. 911 (1980)
Dance, I. G.: J. Chem. Soc. Chem. Commun. 818 (1980)
Damhus, T.: Linear Algebra Appl. 32, 125 (1980)
Biedenharn, L. C., Brouwer, W., Sharp, W. T.: The algebra of representations of some finite groups. Rice University Studies 54, No. 2 (1968).
Coexeter, H. S. M., Moser, W. O. J.: Generators and relations for discrete groups, 4th Ed., Berlin: Springer 1980
Frobenius, F. G.: Sitzungsber. Königl. Preuss. Akad. 330 (1899)
Damhus, T.: Double groups as symmetry groups for spin-orbit coupling Hamiltonians, submitted to Match
Damhus, T., Harnung, S. E., Schäffer, C. E.: paper V in this series
Same, paper VI in the series
Butler, P. H.: Symmetries in science, pp. 99–100, Gruber, B., Millman, R. S. (eds.). New York: Plenum Press 1980
Butler, P. H.: Point group symmetry applications. New York: Plenum Press 1981
Bickerstaff, R. P., Damhus, T.: Intern. J. Quantum Chem. (in press)
Damhus, T.: J. Math. Phys. 22, 7 (1981)
Golding, R. M., Newmarch, J. D.: Molec. Phys. 33, 1301 (1977)
Lulek, B.: Acta Phys. Polonica A55, 165 (1979)
Butler, P. H., Wybourne, B. G.: Internat. J. Quantum Chem. 10, 615–628 (1976)
Griffith, J. S.: The theory of transition metal ions. Cambridge: University Press 1971; first impression 1961
Damhus, T.: licentiate (Ph.D.) thesis, University of Copenhagen, 1984
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Damhus, T., Harnung, S.E. & Schäffer, C.E. Phase-fixed double-group 3-Γ symbols. IV. Real 3-Γ symbols and coupling coefficients for the group hierarchies T* ⊃ C *3 and T* ⊃ C *2 . Theoret. Chim. Acta 65, 405–417 (1984). https://doi.org/10.1007/BF00550837
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DOI: https://doi.org/10.1007/BF00550837