Hi, I have been working calculating the non linear optical properties of several molecules with Gaussian ('09, revision C), and in the outputs I have some values that represent the non linear parameter (in this case, γ) in several directions (e.g. γxxxx or γxxyy). I have read some papers that present "average values", like , that are defined with the sum of some of these, but I'm interested in obtaining the magnitude of the tensor, not an average. As the hyperpolarizabilities are tensors the procedure is a little bit more complicated than with vectors, and I have not found an easy way to calculate it with the values printed by Gaussian. Someone can recommend me a paper that explains this, or even tell me the correct procedure to get it?
Thanks.
I'm not quite sure about the magnitude being just the sum of the values in the direction, but the symmetry property may be the reason there are less than 81 terms.
The equation for calculating magnitude of second hyperpolarizability (γ) can be found in Section 3.200.7 of latest version of Multiwfn manual. The latest version of Multiwfn is able to directly calculate this quantity based on output file of polar=gamma task of Gaussian, an example is given in Section 4.200.7 of the manual. Multiwfn code and its manual are freely available at http://sobereva.com/multiwfn.
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