First hyperpolarizabilities of 1,3,5-tricyano-2,4,6-tris(styryl)benzene derivatives: Ab initio studies and Hammett correlation

First hyperpolarizabilities (β) of the 1,3,5-tricyano-2,4,6- tris(styryl)benzene derivatives were studied by an ab initio method (HF/6-31G). The β values of these molecules increase with increase in donor strength, reaching a maximum value of 262 × 10^-30 esu with an oxyanion as the donor. Also, the electronic charge is more delocalized, and the HOMO-LUMO energy gap (ΔE) and the bond length alternation (BLA) decrease with the same variation of the donor. Noteworthy is the excellent linear relationship between β and 1/ΔE² and σ_gas⁺. These results may serve as a useful guideline for the design of two-dimensional octupoles with large first hyperpolarizabilities.