The energy of a molecule in an external electrostatic field can be expanded as
is the unperturbed energy,
is the component of the field in the i direction,
is the permanent dipole moment
is the polarizability
are the first and second hyperpolarizability tensors, respectively.
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.
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook