hyperpolarizability (of nth order) 

https://doi.org/10.1351/goldbook.HT07053
The energy of a molecule in an external electrostatic field can be expanded as E=Eo−μi Fi−12 αij Fi Fj−16 βijk Fi Fj Fk−124 γijkl Fi Fj Fk Fl−... where Eo is the unperturbed energy, Fi is the component of the field in the i direction, μi is the permanent dipole moment, αij is the polarizability tensor, and βijk and γijkl are the first and second hyperpolarizability tensors, respectively. β is a third order symmetric tensor that measures the second order response of the molecular electric dipole moment to the action of an external electric field and is thus often referred to as dipole hyperpolarizability.
Source:
PAC, 1999, 71, 1919. (Glossary of terms used in theoretical organic chemistry) on page 1946 [Terms] [Paper]
Citation: 'hyperpolarizability (of nth order)' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.HT07053 RIS BibTex EndNote
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Last revised: February 24, 2014