title: Calculation of the dynamic first electronic hyperpolarizability β(-ω(σ); ω(1), ω(2)) of periodic systems. Theory, validation, and application to multi-layer MoS2.
abstract: We describe our implementation of a fully analytical scheme, based on the 2n + 1 rule, for computing the coupled perturbed Hartree Fock and Kohn-Sham dynamic first hyperpolarizability tensor β(-ωσ; ω1, ω2) of periodic 1D (polymer), 2D (slab), and 3D (crystal) systems in the CRYSTAL code [R. Dovesi et al., Int. J. Quantum Chem. 114, 1287 (2014)], which utilizes local Gaussian type basis sets. The dc-Pockels (dc-P) and second harmonic generation (SHG) tensors are included as special cases. It is verified that (i) symmetry requirements are satisfied; (ii) using LiF as an example, the infinite periodic polymer result agrees with extrapolated finite oligomer calculations and, likewise, for the build-up to a 2D slab and a 3D crystal; (iii) the values converge to the static case for low frequencies; and (iv) the Bishop-deKee dispersion formulas relating dc-P, SHG, and general processes are reproduced through quartic terms. Preliminary SHG calculations on multi-layer MoS2 satisfactorily reproduce experimental data.
authors.affiliation: Dipartimento di Chimica and NIS (Nanostructured Interfaces and Surfaces) Centre, Università di Torino, via Giuria 5, I-10125 Torino, Italy.
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Maschio
authors.affiliation: Equipe de Chimie Physique, IPREM UMR5254, Université de Pau et des Pays de l'Adour, 64000 Pau, France.
authors.forename: Michel
authors.initials: M
authors.lastname: Rérat
authors.affiliation: Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA.
authors.forename: Bernard
authors.initials: B
authors.lastname: Kirtman
authors.affiliation: Dipartimento di Chimica and NIS (Nanostructured Interfaces and Surfaces) Centre, Università di Torino, via Giuria 5, I-10125 Torino, Italy.
authors.forename: Roberto
authors.initials: R
authors.lastname: Dovesi