Abstract
The irreducible spherical and Cartesian tensors built of the products of two interaction tensors: the second order tensor resulting from the product of two second order tensors \({{\sf T}_{\alpha\,\lambda}\,{\sf T}_{\lambda\,\beta}}\) contracted once with the index λ, third order tensor \({{\sf T}_{\alpha\,\beta\,\lambda} {\sf T}_{\lambda\,\gamma}}\) appearing as a product of the third order interaction tensor \({{\sf T}_{\alpha\,\beta\,\lambda}}\) and the second order one \({{\sf T}_{\lambda\,\gamma}}\) contracted once with the index λ and the fourth order product of two second order tensors \({{\sf T}_{\alpha\,\beta}\,{\sf T}_{\gamma\delta}}\), have been considered. This type of products is encountered, e.g., within the London’s dispersive energy formula, inside the second-order virial coefficients of many physical parameters such as the dielectric constant, the Kerr constant, the induced polarizability and hyperpolarizability of a pair of molecules and in other induced quantities. Our results are applied explicitly to the excess induced first and second pair hyperpolarizability.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Kielich S.: Prog. Opt. XX, 155 (1983)
G. Maroulis, T. Bancewicz, B. Champagne, A.D.Buckingham (eds.), Atomic and Molecular Nonlinear Optics: Theory, Experiment and Computation. A Homage to the Pioneering Work of Stanisaw Kielich (1925–1993)(IOS Press, Amsterdam, 2011)
Frommhold L.: Collision-induced Absorption in Gases. Cambridge University Press, Cambridge (1993)
T. Bancewicz, Y. Le Duff, J.-L. Godet, Modern Nonlinear Optics, Part 1, Advances in Chemical Physics, Vol. 119, 2nd edn, ed. by M. Evans (Wiley, New York, 2000), pp. 89–126
Kaatz P., Shelton D.P.: Mol. Phys. 88, 683 (1996)
Głaz W., Bancewicz T., Godet J.-L.: J. Chem. Phys. 122, 224323 (2005)
Bancewicz T., Głaz W., Godet J.-L., Maroulis G.: J. Chem. Phys. 129, 124306 (2008)
Kielich S.: Nonlinear Molecular Optics. Nauka, Moscow (1981)
Maroulis G.: J. Phys. Chem. A 104, 4772 (2000)
Bancewicz T., Maroulis G.: Phys. Rev. A 79, 042704 (2009)
Bancewicz T., Maroulis G.: Chem. Phys. Lett. 498, 349 (2010)
Li X., Hunt K.L.C.: J. Chem. Phys. 100, 7875 (1994)
Li X., Hunt K.L.C., Pipin J., Bishop D.M.: J. Chem. Phys. 105, 10954 (1996)
Buckingham A.D., Concannon E.P., Hands I.D.: J. Phys. Chem. 98, 10455 (1994)
Bancewicz T.: J. Chem. Phys. 111, 7440 (1999)
Bancewicz T.: Mol. Phys. 50, 173 (1983)
Gray C.G., Gubbins K.E.: Theory of Molecular Fluids. Vol. 1: Fundamentals. Clarendon Press, Oxford (1984)
Varshalovich D.A., Moskaliev A.N., Khersonskii V.K.: Quantum Theory of Angular Momentum. World Scientific, Singapore (1988)
Maker P.D.: Phys. Rev. A 1, 923 (1970)
Jerphagnon J., Chemla D., Bonneville R.: Adv. Phys. 27, 609 (1978)
Stone A.J.: Mol. Phys. 29, 1461 (1975)
Andrews D.L., Ghoul W.A.: J. Chem. Phys. 75, 530 (1981)
Hunt K.L.C.: Chem. Phys. Lett. 70, 336 (1980)
Acknowledgments
This paper has been supported by the research project Nb. N N202 069939 sponsored by The Government of Poland. I would like to thank very much George Maroulis for many illuminating discussions.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Bancewicz, T. Excess hyperpolarizabilities: the irreducible tensor approach. J Math Chem 50, 1570–1581 (2012). https://doi.org/10.1007/s10910-012-9990-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-012-9990-0