The Importance of the DFT method on the computation of the second hyperpolarizability of semiconductor clusters of increasing size: A critical analysis on prolate aluminum phosphide clusters

Abstract

The importance of the density functional theory (DFT) methods on the computation of cluster hyperpolarizabilities is discussed. The performance of the conventional BLYP, BP86, BPW91, B3LYP, B3PW91, and B3P86 functionals in the computation of the second hyperpolarizability of aluminum phosphide prolate clusters up to 60 atoms is compared with the ''half and half functionals'' BHandH and BHandHLYP and to the long-range corrected functionals LC-(BLYP, BP86, BPW91), CAM-B3LYP, and wB97XD. The presented results demonstrate that when long-range corrections are incorporated on pure and hybrid functionals their performance is vastly affected. What is more, the obtained DFT results are compared with second-order Møller-Plesset perturbation theory (MP2) all electron calculations. It is shown that all the long-range outcomes are bracketed by the MP2 and Hatree-Fock (HF) values. The relative ordering of the obtained longitudinal hyperpolarizabilities follows strictly the trend MP2 > CAM-B3LYP > wB97XD > LC-(BLYP, BP86, BPW91) > HF.

Third-order nonlinear optical susceptibility of crystalline oxide yttria-stabilized zirconia

“…For the sake of briefness a more detailed discussion of these outcomes are given in Appendix. Here we will only mention that the observed method behavior, characterized by notable oscillations in the computed bulk-nonlinearities is in line with previous studies [28][29][30] performed on finite atomic semiconductor nanoclusters. Interestingly, the current computations reveal that the known pathology of pure DFT functionals effect, concerns as well the computed dielectric constants for which experimental are available (see values listed in Table 1).…”

“…Bearing in mind that the computation of third order susceptibilities of molecules, polymers and solids greatly depend on the quantum chemical method applied, [28][29][30] we computed the third order optical nonlinearities of pure and doped bulk systems using three DFT functionals within the generalized gradient approximation (GGA). These are the pure Perdew, Burke, and Ernzerhof (PBE) [31] exchange-correlation functional, its hybrid counterpart PBE0 [32] and the Becke, three-parameter, Lee-Yang-Parr exchange-correlation functional (B3LYP).…”

From Pyridine Adduct of Borabenzene to (In)finite Graphene Architectures Functionalized with N → B Dative Bonds. Prototype Systems of Strong One- and Two-Photon Quantum Transitions Triggering Large Nonlinear Optical Responses

“…34 The static dipole (hyper)polarizabilities reported in this work have been computed either analytically within the coupled perturbed Hartree-Fock/Kohn-Sham approaches 35,36 (CPHF, CPKS) or via the finite field (FF) approximation (see ref. [37] and references therein). Details about the accuracy thresholds used during the FF computations is provided in supporting material.…”

Nonlinear optical response of endohedral all-metal electride cages 2e−Mg2+(M@E12)2−Ca2+(M = Ni, Pd, and Pt; E = Ge, Sn, and Pb)

“…For NLO calculations, it has been reported that the values of first hyperpolarizability (β 0 ) are quite sensitive to the basis set used. [33][34][35][36][37][38] Zalesny and his coworkers have found CAM-B3LYP is a successful DFT method for calculating hyperpolarizabilities of large system. 39 Then the calculations of equilibrium geometries and corresponding properties of all-metal electride cage molecules Mg(M@E 12 )Ca (E = Ge, Sn, and Pb; M = Ni, Pd, and Pt) with all real frequencies have been performed using the CAM-B3LYP functional.…”