Free-electron model for hyperpolarizability of the π-electron system in benzene

The hyperpolarizabilities of benzene have been calculated using a free-electron model for the π-electron system. The first hyperpolarizability is identically zero. For the second hyperpolarizability only the components γ_zzzz; γ_xxxx; γ_yyyy; γ_zzxx; γ_zzyy; γ_xxyy are non-zero. Some of these γ quantities show dispersion near the characteristic absorption band of the benzene molecule. The polarizability α of the π-electron system also shows similer dispersion.