Advances in Local Hybrid Functionals

Local hybrids\footnote{ Jaramillo, J; Scuseria, G. E.; Ernzerhof, M. \textit{J. Chem. Phys.} \textbf{2003}, $118$, 1068} provide a promising new generation of exchange-correlation functionals for the simultaneous accurate description of various properties (atomization energies, reaction barrier heights,\footnote{ Kaupp, M.; Bahmann, H.; Arbuznikov, A. V. \textit{J. Chem. Phys.}, \textbf{2007}, $127$, 194102} NMR chemical shifts,\footnote{ Arbuznikov, A. V.; Kaupp, M. \textit{Chem. Phys. Lett.} \textbf{2007}, $442$, 496} energetics of transition-metal systems, etc.) Compared to traditional (global) hybrids (e.g., B3LYP), instead of a constant exact-exchange admixture, local hybrids employ a position-dependent one. The latter is governed by a so-called \textit{local mixing function} (LMF), and this is the crucial quantity controlling the performance of local hybrids. Here we present and compare new results obtained with LMFs derived both in a semiempirical way and using \textit{ab initio} considerations, e.g., the adiabatic connection formalism.\footnote{ Arbuznikov, A. V.; Kaupp, M. \textit{J. Chem. Phys.} \textbf{2008}, $128$, 214107} The former approach yields better results, while the latter brings valuable insights into the performance and limits of local hybrids.