Spin-component-scaled double hybrids: An extensive search for the best fifth-rung functionals blending DFT and perturbation theory

Following up on an earlier preliminary communication (Kozuch and Martin, Phys. Chem. Chem. Phys. 2011, 13, 20104), we report here in detail on an extensive search for the most accurate spin-component-scaled double hybrid functionals [of which conventional double hybrids (DHs) are a special case]. Such fifth-rung functionals approach the performance of composite ab initio methods such as G3 theory at a fraction of their computational cost, and with analytical derivatives available. In this article, we provide a critical analysis of the variables and components that maximize the accuracy of DHs. These include the selection of the exchange and correlation functionals, the coefficients of each component [density functional theory (DFT), exact exchange, and perturbative correlation in both the same spin and opposite spin terms], and the addition of an ad-hoc dispersion correction; we have termed these parametrizations "DSD-DFT" (Dispersion corrected, Spin-component scaled, Double-hybrid DFT). Somewhat surprisingly, the quality of DSD-DFT is only mildly dependent on the underlying DFT exchange and correlation components, with even DSD-LDA yielding respectable performance. Simple, nonempirical GGAs appear to work best, whereas meta-GGAs offer no advantage (with the notable exception of B95c). The best correlation components appear to be, in that order, B95c, P86, and PBEc, while essentially any good GGA exchange yields nearly identical results. On further validation with a wider variety of thermochemical, weak interaction, kinetic, and spectroscopic benchmarks, we find that the best functionals are, roughly in that order, DSD-PBEhB95, DSD-PBEP86, DSD-PBEPW91, and DSD-PBEPBE. In addition, DSD-PBEP86 and DSD-PBEPBE can be used without source code modifications in a wider variety of electronic structure codes. Sample job decks for several commonly used such codes are supplied as electronic Supporting Information.