## Wikipedia - Hyperpolarisierbarkeit 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 $E=E^{\text{o}}- \unicode[Times]{x3BC}_{i}\ F_{i}- \frac{1}{2}\ \unicode[Times]{x3B1} _{ij}\ F_{i}\ F_{j}- \frac{1}{6}\ \unicode[Times]{x3B2} _{ijk}\ F_{i}\ F_{j}\ F_{k}- \frac{1}{24}\ \unicode[Times]{x3B3} _{ijkl}\ F_{i}\ F_{j}\ F_{k}\ F_{l}- \text{...}$ where $$E^{\text{o}}$$ is the unperturbed energy, $$F_{i}$$ is the component of the field in the i direction, $$\unicode[Times]{x3BC}_{i}$$ is the permanent @D01761@, $$\unicode[Times]{x3B1}_{ij}$$ is the @P04711@ tensor, and $$\unicode[Times]{x3B2}_{ijk}$$ and $$\unicode[Times]{x3B3}_{ijkl}$$ are the first and second hyperpolarizability tensors, respectively. $$\unicode[Times]{x3B2}$$ is a third order symmetric tensor that measures the second order response of the molecular @E01929@ 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]