Maschio Lorenzo, Rérat Michel, Kirtman Bernard, Dovesi Roberto
Dipartimento di Chimica and NIS (Nanostructured Interfaces and Surfaces) Centre, Università di Torino, via Giuria 5, I-10125 Torino, Italy.
Equipe de Chimie Physique, IPREM UMR5254, Université de Pau et des Pays de l'Adour, 64000 Pau, France.
J Chem Phys. 2015 Dec 28;143(24):244102. doi: 10.1063/1.4937770.
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.
我们描述了一种基于2n + 1规则的完全解析方案的实现，用于在CRYSTAL代码[R. Dovesi等人，《国际量子化学杂志》114, 1287 (2014)]中计算周期性一维（聚合物）、二维（平板）和三维（晶体）系统的耦合微扰哈特里 - 福克和科恩 - 沙姆动态第一超极化率张量β(-ωσ; ω1, ω2)，该代码使用局部高斯型基组。直流泡克尔斯（dc - P）张量和二次谐波产生（SHG）张量作为特殊情况包含在内。验证了：（i）满足对称性要求；（ii）以LiF为例，无限周期聚合物的结果与外推的有限低聚物计算结果一致，同样，对于二维平板和三维晶体的构建也是如此；（iii）对于低频，值收敛到静态情况；（iv）通过四次项再现了将直流泡克尔斯效应、二次谐波产生和一般过程联系起来的毕晓普 - 德凯色散公式。对多层MoS2的初步二次谐波产生计算令人满意地再现了实验数据。
