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Integral invariants for high-symmetry open-shell molecules.

1. Invariant representations of electron repulsion integrals

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Abstract

A numerical procedure for expanding electron repulsion integrals 〈mm|nn〉 on degenerate molecular orbitals of γ symmetry (γ=e, t, g, h) into integral invariants (reduced matrix elements) Hk(γ, γ) is suggested. The latter are analogous in their sense to Slater-Condon parameters Fk(l, l) for atoms with an electronic configuration lN. The method is applicable to nonlinear molecules of arbitrary symmetries, including “not readily reducible” groups.

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References

  1. C. C. J. Roothaan,Rev. Mod. Phys.,32, No. 2, 179–185 (1960).

    Article  Google Scholar 

  2. K. Hirao and H. Nakatsuji,J. Chem. Phys.,59, No. 3, 1457–1462 (1973).

    Article  CAS  Google Scholar 

  3. K. Hirao, ibid.,60, No. 8, 3215–3222 (1974).

    Article  CAS  Google Scholar 

  4. R. Carbo and J. M. Riera,A General SCF Theory, Lecture Notes in Chemistry, Vol. 5, Springer, Berlin (1978).

    Google Scholar 

  5. B. N. Plakhutin, Physical and Mathematical Sciences’ Doctoral Dissertation, Moscow State University, Moscow (1995).

    Google Scholar 

  6. B. N. Plakhutin, to appear in:J. Math. Chem.

  7. J. C. Slater,Quantum Theory of Atomic Structure, Vols. 1 and 2, McGraw-Hill, New York (1960).

    Google Scholar 

  8. B. N. Plakhutin,Chem. Phys. Lett.,227, 396–400 (1994).

    Article  CAS  Google Scholar 

  9. C. C. J. Roothaan and J. H. Detrich,Phys. Rev. A,27, 29–56 (1983).

    Article  CAS  Google Scholar 

  10. G. Fieck and J. Wirsich,Int. J. Quant. Chem.,18, 753–773 (1980).

    Article  CAS  Google Scholar 

  11. I. G. Kaplan,Symmetry of Many-Electron Systems [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  12. H. A. Jahn,Acta Crystallogr.,2, 30–33 (1949); S. Bhagavantam and D. Suryanarayana,ibid.,2, 21–26 (1949).

    Article  CAS  Google Scholar 

  13. E. P. Wigner, in:Quantum Theory of Angular Momentum, L. C. Biedenharn and H. Van Dam (eds.), Academic Press, New York (1965), pp. 87–133.

    Google Scholar 

  14. D. T. Sviridov and Yu. F. Smirnov,Theory of the Optical Spectra of Transition Metal Ions [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  15. B. I. Zhilinskii,Theory of Complex Molecular Spectra [in Russian], Moscow University, Moscow (1989).

    Google Scholar 

  16. D. C. Harris and M. D. Bertolucci,Symmetry and Spectroscopy. An Introduction to Vibrational and Electronic Spectroscopy, Vol. 12, Oxford University, New York (1978).

    Google Scholar 

  17. B. N. Plakhutin,Zh. Strukt. Khim.,38, No. 1, 3–13 (1997).

    Google Scholar 

  18. G. Racah,Phys. Rev.,61, Nos. 3, 4, 186–197 (1942).

    Article  CAS  Google Scholar 

  19. G. E. Forsythe and C. B. Moler,Computer Solution of Linear Algebraic Systems, Prentice-Hall, New York (1967).

    Google Scholar 

  20. B. N. Plakhutin, to appear in:Zh. Strukt. Khim.

  21. M. Haser,J. Chem. Phys.,95, No. 11, 8259–8265 (1991).

    Article  CAS  Google Scholar 

  22. G. T. Klimko, M. M. Mestechkin, B. N. Plakhutin, G. M. Zhidomirov, and R. A. Evarestov,Int. J. Quant. Chem.,37, No. 1, 35–50 (1990).

    Article  CAS  Google Scholar 

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G. K. Boreskov Institute of Catalysis, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 1, pp. 3–17, January–February, 1998.

This work was supported by RFFR grants No. 96-03-01167 and 96-03-34035.

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Plakhutin, B.N. Integral invariants for high-symmetry open-shell molecules.. J Struct Chem 39, 1–13 (1998). https://doi.org/10.1007/BF02873818

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  • DOI: https://doi.org/10.1007/BF02873818

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