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Unified Treatment for Arbitrary-rank Cartesian Electric and Magnetic Multipole Moment Operators

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Abstract

In this study, the theory of cartesian electric and magnetic multipole moments is extended in a unified way. The general analytical expressions for distinct components of arbitrary rank cartesian electric and magnetic multipole moment operators are derived as linear combination of corresponding spherical operators, which can be used as interconversion between cartesian and spherical electric and magnetic multipole moment tensors. The transformation properties, such as translation and rotation of cartesian electric and magnetic multipole moments are given in a very simple general form. The relationship between distinct and linearly independent components of cartesian multipole moment tensors in system of linear symmetry is also presented. The formulae obtained in this paper can be utilized to calculate the interaction energies between charge distributions.

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References

  1. Buckingham A.D. (1967). Advan. Chem. Phys. 12:107

    Article  CAS  Google Scholar 

  2. Levine B.F., and Bethea C.G. (1978). J. Chem. Phys. 69:5240

    Article  CAS  Google Scholar 

  3. Ward J.F., and Miller C.K. (1979). Phys. Rev. A19:826

    Google Scholar 

  4. Rajan S., Lalita K., and Babu S.V. (1974). J. Magn. Reson. 16:115

    CAS  Google Scholar 

  5. Gray C.G. (1969). J. Chem. Phys 50:549

    Article  CAS  Google Scholar 

  6. Barron L.D., and Buckingham A.D. (1975). Ann. Rev. Phys. Chem. 26:381

    Article  CAS  Google Scholar 

  7. Schwartz C. (1955). Phys. Rev 97:380

    Article  CAS  Google Scholar 

  8. Magnasco V., Costa C., and Figari G. (1990). J. Mol. Struct. 204:229

    Google Scholar 

  9. Magnasco V., Costa C., and Figari G. (1990). J. Mol. Struct 206:235

    Google Scholar 

  10. Buckingham A.D., and Fowler P.W. (1985). Can. J. Chem. 63:2018

    Article  CAS  Google Scholar 

  11. Gray C.G., and Lo B.W.N. (1976). Chem. Phys 14:73

    Article  CAS  Google Scholar 

  12. Gray C.G. (1968). Can. J. Phys. 46:135

    Google Scholar 

  13. Buckingham A.D., and Stiles P.J. (1972). Mol. Phys. 24:99

    Article  CAS  Google Scholar 

  14. McLean A.D., and Yoshimine M. (1967). J. Chem. Phys. 47:1927

    Article  CAS  Google Scholar 

  15. Kielich S. (1965). Physica 31:444

    Article  CAS  Google Scholar 

  16. Raab R.E. (1975). Mol. Phys 29:1323

    Article  CAS  Google Scholar 

  17. Stone A.J. (1975). Mol. Phys 29:1461

    Article  CAS  Google Scholar 

  18. Hoffmann P. (1991). J. Phys. A 24:35

    Google Scholar 

  19. Gradshteyn I.S., and Ryzhik I.M. (1995). Tables of Integrals, Series and Products. Academic Press, New York

    Google Scholar 

  20. (a) T. Özdoğan, Ph.Thesis D., “The Unified Theory of Electric Multipole Moment Tensors and Application to Polyatomic Molecules”, Ondokuz Mayis University, 2000, Samsun, Turkey. (b) T. Özdoğan and Orbay M., Czech. J. Phys. 52 (2002) 1297.

  21. Blatt J.M., and Weisskopf V.F. (1952). Theoretical Nuclear Physics. Wiley, New York

    Google Scholar 

  22. Guseinov I.I. (1998). Int. J. Quantum Chem. 68:145

    Article  CAS  Google Scholar 

  23. Guseinov I.I. (1998). J. Mol. Struct. Theochem 427:263

    Article  CAS  Google Scholar 

  24. Wigner E.P. (1940). Group Theory. Academic Press, New York

    Google Scholar 

  25. Guseinov I.I. (1996). J. Mol. Struct. Theochem. 366:119

    Article  CAS  Google Scholar 

  26. Isnard P., Robert D., and Galatry L. (1976). Mol. Phys. 31:1789

    Article  CAS  Google Scholar 

  27. Cipriani J., and Silvi B. (1982). Mol. Phys. 45:259

    Article  CAS  Google Scholar 

  28. Price S.L., Stone A.J., and Alderton M. (1985). Mol. Phys. 52:987

    Article  Google Scholar 

  29. Stogryn P.E., and Stogryn A.P. (1966). Mol. Phys. 11:371

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Rize Faculty of Arts and Sciences, Karadeniz Technical University, Rize, Turkey

    Telhat Özdoğan

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  1. Telhat Özdoğan
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Correspondence to Telhat Özdoğan.

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Özdoğan, T. Unified Treatment for Arbitrary-rank Cartesian Electric and Magnetic Multipole Moment Operators. J Math Chem 42, 201–214 (2007). https://doi.org/10.1007/s10910-006-9093-x

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  • DOI: https://doi.org/10.1007/s10910-006-9093-x

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