Hyperpolarizability
Definition and meaning of Hyperpolarizability in chemistry.
Hyperpolarizability is a measure of how nonlinearly a molecule's induced dipole moment responds to an applied electric field, capturing the higher-order terms that go beyond ordinary (linear) polarizability.
In more detail
When an electric field E is applied to a molecule, the induced dipole moment can be expanded as a power series, mu = alpha*E + beta*E^2 + gamma*E^3 + ..., where alpha is the linear polarizability, beta is the first hyperpolarizability, and gamma is the second hyperpolarizability. A nonzero beta requires the molecule to lack a center of symmetry, since in a centrosymmetric molecule reversing the field must reverse the dipole exactly, forcing the even-order beta term to vanish. Large hyperpolarizabilities typically arise in conjugated molecules with strong electron donor and acceptor groups (push-pull systems), which is why such compounds are studied for nonlinear optical (NLO) applications.
Key facts
| Symbols | beta (first hyperpolarizability), gamma (second hyperpolarizability) |
|---|---|
| SI units | C·m3·V-2 (beta); C·m4·V-3 (gamma) |
| Symmetry requirement | Nonzero beta requires a noncentrosymmetric molecular structure |
| Field | Physical Chemistry |
Urea, (NH2)2CO, is a classic reference compound with a sizable first hyperpolarizability, arising from charge transfer between its amine donor groups and carbonyl acceptor group, and is used as a calibration standard in NLO measurements such as second harmonic generation.
Frequently asked questions
Why does hyperpolarizability matter in materials science?
A large first hyperpolarizability underlies nonlinear optical effects such as second harmonic generation and electro-optic switching, which are exploited in photonic and laser devices.
Why is the first hyperpolarizability zero for a molecule like CO2?
CO2 has a center of symmetry, so reversing the applied field direction must exactly reverse the induced dipole. Since the beta*E^2 term does not change sign under this reversal, symmetry forces beta to equal zero.