First Principles Evaluation of the Second Harmonic Generation Response of Reference Organic and Inorganic Crystals

F. Mairesse1, L. Maschio2, B. Champagne1

1 Theoretical Chemistry Laboratory, Unit of Theoretical and Structural Physical Chemistry, University of Namur (UNamur), B-5000 Namur, Belgium
2 Dipartimento di Chimica, Università degli Studi di Torino (UNITO), Torino, Italy.

By using the CRYSTAL17 package at the coupled-perturbed Kohn-Sham (CPKS) level, periodic boundary conditions (PBC) first-principles calculations have been enacted to predict the second harmonic generation (SHG) second-order nonlinear optical (NLO) susceptibility, χ(2), values of six historical NLO crystals of reference, four inorganic crystals and two molecular organic ones. This selection allowed the comparison between the state-of-the-art level of theory predictions and the most trustful experimental values. Several computational aspects have been tackled to define conditions where the results are converged with respect to the range of lattice summations, to the first Brillouin zone sampling, to the evaluation of 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 as a good compromise between accuracy and computational resources. Then, χ(2) calculations have been performed using a range of exchange-correlation functionals (XCFs), which differ mainly by the amount of HF exchange (including at short- and long-range). Results have shown the large impact of the amount of HF exchange on the amplitude but also on the sign on χ(2) tensor components. The amplitude effects are consistent with results on small and large molecules, but sign reversal effects as well as non-monotonic behavior of the χ(2) tensor components as a function of the amount of HF exchange, which are have also been observed, which is certainly unusual and seemingly more proper to the crystalline state. Then, using the recommended range-separated hybrids GGA XCFs, the CPKS scheme leads to good agreement with experimental data for a molecular organic as well as two inorganic systems. The agreement is more questionable for the remaining systems, although the order of magnitude is fairly reproduced in every case. As a matter of fact, this investigation opens also the path to later fine-tuning of the ranges of inclusion of HF exchange.