On the third-order nonlinear optical responses of cis and trans stilbenes - a quantum chemistry investigation.

The second hyperpolarizabilities (γ) of the stilbene molecular switch in its trans and cis forms have been calculated using quantum chemistry methods to address their third-order nonlinear optical contrasts, to assess the reliability of lower-cost DFT methods, and to make comparisons with experiments. First, the reference CCSD(T) method shows that trans-stilbene presents a γ‖ value twice larger than its cis isomer (its γTHS value is 2.7 times larger). Among more cost-effective methods, reliable results are obtained at MP2 as well as with DFT, provided the CAM-B3LYP or ωB97X-D XCFs are employed. Supplementary DFT calculations have investigated the relationships between the accuracy of the exchange-correlation functionals, the fulfillment of Koopmans' theorem, and the delocalization error, and they demonstrated that satisfying Koopmans' theorem is not the condition for the best accuracy but that functionals with small delocalization errors are generally efficient. Using the selected CAM-B3LYP, large γ enhancements by about 70% (trans-stilbene) and 50% (cis-stilbene) have been evidenced when accounting for solvent effects using an implicit solvation model (IEFPCM), even for apolar solvents. Then, the frequency dispersion of the γ responses has been described using Bishop polynomial expansions, allowing comparisons with a broad set of experimental data. To a certain extent, no systematic agreement between the calculations and the measured values was found. On the one hand, the agreement is satisfactory for the γ(-ω;ω,-ω,ω) quantities, provided that the dominant vibrational contribution is taken into account. On the other hand, the agreement is poor for the γ(-2ω;ω,ω,0) and γ(-3ω;ω,ω,ω) quantities, while some inconsistencies between experimental values are also highlighted.

A quantum chemical investigation of the second hyperpolarizability of p-nitroaniline.

Recent measurements of the third harmonic scattering responses of molecules have given a new impetus for computing molecular second hyperpolarizabilities (γ) and for deducing structure-property relationships. This paper has employed a variety of wavefunction and density functional theory methods to evaluate the second hyperpolarizability of the p-nitroaniline prototypical push-pull π-conjugated molecule, addressing also numerical aspects, such as the selection of an integration grid and the impact of the order of differentiation vs the achievable accuracy by using the Romberg quadrature. The reliability of the different methods has been assessed by comparison to reference Coupled-Cluster Singles and Doubles with perturbative treatment of the Triples results. On the one hand, among wavefunction methods, the MP2 scheme offers the best accuracy/cost ratio for computing the static γ. On the other hand, using density functional theory, γ remains a challenging property to compute because all conventional, global hybrid or range-separated hybrid, exchange-correlation functionals underestimate static γ values by at least 15%. Even tuning the range-separating parameter to minimize the delocalization errors does not enable to improve the γ values. Nevertheless, the original double-hybrid B2-PLYP functional, which benefits from 27% of PT2 correlation and 53% Hartree-Fock exchange, provides accurate estimates of static γ values. Unfortunately, the best performing exchange-correlation functionals for γ are not necessarily reliable for the first hyperpolarizability, ß, and vice versa. In fact, the ß of p-nitroaniline (pNA) could be predicted, with a good accuracy, with several hybrid exchange-correlation functionals (including by tuning the range-separating parameter), but these systematically underestimate γ. As for γ, the MP2 wavefunction method remains the best compromise to evaluate the first hyperpolarizability of pNA at low computational cost.