Conformational dependence of the second hyperpolarizability of quadrupolar molecules

Hatree-Fock calculations at ab initio and semiempirical levels were carried out for the averaged polarizability 〈α〉 and second hyperpolarizability 〈γ〉 of two pairs of quadrupolar isomers with different donor and acceptor groups. These properties were correlated with the antibonding/bonding π occupation number (π∗/π ratio). It was found that isomers with extended π systems had low π∗/π ratios and high 〈α〉 and 〈γ〉 values, while low 〈α〉 and 〈γ〉 values were obtained for isomers with large π∗/π ratios and no extended π system. The PM3 and PM6 〈α〉 values were found to be in excellent agreement with the HF/6-31+G(d,p) ones. The PM3 values for 〈γ〉 were significantly larger than those calculated by HF/6-31+G(d,p), with an average PM3/HF ratio of 1.43. The PM6 results were noticeably better with a ratio of 0.85. The calculation of 〈α〉 and 〈γ〉 at MP2/6-31+G(d,p) level for representative isomers showed that the contribution of the electron correlation to their values was small and that the HF/6-31+G(d,p) method provides reliable values at much lower computational cost.