I'm working on a calculation of the second hyperpolarizability "\beta" of a compound with D(3) symmetry, and I am trying to figure out how the tensor \beta transforms under a coordinate rotation about the z axis (the three-fold symmetry axis). I know that if we have two bases x and x' with a linear transformation tensor T such that x' = xT, that the "ordinary" polarizability tensors "\alpha" and "\alpha^{\prime}" in the two coordinate systems are related by \alpha^{\prime} = T^{-1} \alpha T, but I'm not sure what the transformation rule is for a rank-3 tensor when the coordinate system is rotated. Thanks for your help.(adsbygoogle = window.adsbygoogle || []).push({});

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# NLO question (second hyperpolarizability tensor)

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