A Hybrid Scheme for Calculating Correlated and Frequency-Dependent First and Second Hyperpolarizabilities of Molecules in Solution: A Case Study on Para-Disubstituted Benzene Derivatives

A computational protocol is developed to evaluate the second- and third-order nonlinear optical (NLO) properties of donor–acceptor benzene derivatives, incorporating ab initio electron correlation, frequency dispersion, and solvent effects, with the aim of achieving high predictive accuracy. The computational scheme encompasses (i) high-level CCSD(T) calculations of the static first (β) and second (γ) hyperpolarizabilities, (ii) the assessment of the performance of the CAM-B3LYP and M06-2X exchange–correlation DFT functionals to evaluate β and γ values, (iii) the use, after assessment of its effectiveness, of the multiplicative scheme to evaluate second harmonic generation responses, (iv) the evaluation of the frequency dispersion factors on β and γ by using Bishop's frequency-dispersion polynomials, and their use, in combination with the multiplicative correction scheme, to evaluate third harmonic generation second hyperpolarizabilities. This hybrid approach is shown to closely reproduce the experimental trends, although systematic quantitative deviations still remain with respect to experimental values. The relationships linking the NLO responses, the molecular structures, and other electronic and optical properties are also unrevealed. In particular, it is found that the amplitude of the β and γ responses are correlated to Hammett's parameters, which quantify the electron-donating or electron-withdrawing effects of the chemical substituents, and to the bond order alternation within the phenyl ring, related to its quinoid character.