First-principles evaluation of the second harmonic generation response of reference organic and inorganic crystals

Using the CRYSTAL17 package at the coupled-perturbed Kohn–Sham (CPKS) level, periodic boundary conditions first-principles calculations are enacted to predict the second harmonic generation second-order nonlinear optical (NLO) susceptibility, χ(2), values of six historical NLO crystals. This selection allowed the comparison between state-of-the-art calculations and experiment. Several computational aspects are tackled to define conditions where the results are converged with respect to the range of lattice summations, to the number of k-points in the first Brillouin zone, to the order of the multipole expansions for evaluating the long-range part of the electrostatic interactions, as well as to the atomic basis set size. A valence triple zeta basis set supplemented with polarization functions has been selected. Then, χ(2) calculations have been performed using a range of exchange-correlation functionals (XCFs). Results show the large impact of the amount of Hartree–Fock (HF) exchange on the amplitude but also on the sign on the χ(2) tensor components. To a given extent, these amplitude effects are consistent with results on molecules, but the sign reversal effects and the non-monotonic behavior of the χ(2) tensor components as a function of the amount of HF exchange are scarcely found for molecules. Then, using the recommended range-separated hybrid XCFs, the CPKS scheme leads to good agreement with experimental data for potassium dihydrogenophosphate, urea, and χZXX(2) of LiNbO3. The agreement is more questionable for χZZZ(2) of LiNbO3 whereas it remains poor for ammonium dihydrogenophosphate and 2-methyl-4-nitroaniline, with large underestimations by about a factor of 3, opening a path to further fine-tuning of the ranges of inclusion of HF exchange.