Advances in local hybrid exchange-correlation functionals: From thermochemistry to magnetic-resonance parameters and hyperpolarizabilities

摘要

A short overview of recent advances in our lab regarding the construction and validation of local hybrid functionals is given. Local hybrids are a promising new generation of exchange-correlation functionals, in which exact exchange is admixed in a position-dependent fashion. The admixture is controlled by a so-called local mixing function (LMF). We discuss different strategies to construct LMFs (semiempirical vs. ab initio), different levels of the implementation of local hybrids (self-consistent vs. nonself-consistent), and some methodological aspects associated with the calculation of second-order magnetic properties (a coupled-perturbed scheme for general hyper-GGA functionals). Some examples for the performance of local hybrids in the description of various molecular properties are provided. We focus in particular on an evaluation of longitudinal (hyper)polarizabilities of model hydrogen chains, known to be a challenge for semilocal density functionals. Here local hybrids give closer agreement with experiment than the B3LYP global hybrid. Notably, however, an LMF g(r) = 0.48 τ_W/τ without proper asymptotic behavior performs better than an LMF g(r) = erf(0.22 s) (s is the dimensionless density gradient), which has the correct long-range behavior. Similar results are also found for the (hyper)polarizabilities of the noble-gas atoms.