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

摘要

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 M?ller-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.