Hyperpolarizabilities anisotropy

Fowler, P. W., Buckingham, A. D. (1989). The magnetic hyperpolarizability anisotropy of some two-electron systems. Molecular Physics, 57,681. 

Figures 1-3 display the basis set dependence of the average polarizability, (a), the polarizability anisotropy, Aa, and the vector component of the first hyperpolarizability,...

The birefringence in external electric and magnetic fields (the Kerr and Cotton-Mouton effects) can be explained by the anisotropy of the properties of the medium that is due to either the orientation of anisotropic molecules in the external field (the Langevin-Bom mechanism) or the deformation of the electric or magnetic susceptibilities by this field, i.e., to hyperpolarizabilities (Voight mechanism). The former mechanism is effective for molecules that are anisotropic in the absence of the field and... 

The Kerr effect is also often used to determine the polarizabilities of molecules [1,9, 10]. In the general case, the Kerr constant has a complicated relation with the polarizability anisotropy, dipole moment and hyperpolarizability of a molecule. As a result, the problem of a separation of the contributions to the Kerr constant from these values is appeared. The separation diflhculties lead to the increase of errors of the method (10-20 %). Only for the gas media composed of non-polar molecules... 

Here, the anisotropy polarizability As and the mean second hyperpolarizability are written in the form... 

---