Excess hyperpolarizabilities: the irreducible tensor approach

摘要

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 ${{sf T}_{alpha,beta},{sf T}_{gammadelta}}$ , 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.