Journal of Mathematical Chemistry

, Volume 50, Issue 6, pp 1570–1581 | Cite as

Excess hyperpolarizabilities: the irreducible tensor approach

Open Access
Original Paper

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.

Keywords

Irreducible tensors First hyperpolarizability Second hyperpolarizability Collision-induced phenomena 

Notes

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.

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Nonlinear Optics Division, Faculty of PhysicsAdam Mickiewicz UniversityPoznańPoland

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