Calculation of the dynamic first electronic hyperpolarizability β(−ω σ; ω1, ω2) of periodic systems. Theory, validation, and application to multi-layer MoS2

Abstract

Articles you may be interested inCalculation of the dynamic first electronic hyperpolarizability β(−ω σ ; ω 1 , ω 2 ) of periodic systems. Theory, validation, and application to multi-layer MoS 2 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(−ω σ ; ω 1 ,ω 2 ) of periodic 1D (polymer), 2D (slab), and 3D (crystal) systems in the CRYSTAL code [R. Dovesi et al., Int. J. Quantum Chem. 114, 1287], 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 MoS 2 satisfactorily reproduce experimental data. C 2015 AIP Publishing LLC.[http://dx

Quantum‐mechanical condensed matter simulations with CRYSTAL

“…The full derivation of Equation ( 29) alongside with a robust validation of the implementation is reported in Maschio, Rérat, Kirtman, and Dovesi (2015). Such third-order rank tensor depends on the three Cartesian directions of the field t, u, v, and on three frequencies, ω σ , ω 1 , and ω 2 with ω σ = ω 1 + ω 2 .…”

“…The extension to KS-DFT has also been carried out in the previous work (Orlando, Lacivita, Bast, & Ruud, 2010) for the static case, and in Maschio et al, 2015, for the dynamic and implemented in the CRYS-TAL code. We do not repeat the DFT expression here since it is quite long (e.g., see Equation 8of Maschio et al, 2015), even though straightforward to evaluate. Among all possible choices of ω 1 an ω 2 , there are two cases of particular relevance: (a) SHG, in which ω 1 = ω 2 = ω and ω σ = 2ω and (b) dc-Pockels effect, in which ω 1 = ω, ω 2 = 0 and ω σ = ω.…”

Giant Pockels effect of polar organic solvents and water in the electric double layer on a transparent electrode

“…10 Recent advances in computational methodology for simulating nonlinear optical properties realize rigorous calculation of the dynamic electronic hyper-polarizability of crystalline systems and surfaces to reproduce experimental data. 11 Thus there is an expectation that the Pockels effect of water is a potentially solvable problem computationally. From the experimental side, there is insufficient information about which properties of water play crucial roles.…”

The CRYSTAL code, 1976–2020 and beyond, a long story

“…149 This leads to a general expression for the first hyperpolarizability of closed-shell periodic systems in the presence of frequencydependent fields, which has been implemented in CRYSTAL and validated. 150,151 Equation (8) above holds for the HF model. The extension to KS-DFT has been carried out in reference for the static case and in reference 150 for dynamic fields.…”