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

Abstract

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.

The many faces of halogen bonding: a review of theoretical models and methods

“…In a gross generalization, XB accuracy improves according to ‘Jacob's ladder’ (see Table and Figure ). This ladder is a DFT metaphor where on each rung an extra component is added to the exchange‐correlation terms, producing the well‐known order of: local density approximation (LDA), generalized gradient approximation (GGA), meta‐GGA, hybrid (or meta‐hybrid), and double‐hybrid (DH) family of functionals. The higher the rung, the more expensive the method, especially on the DH, where an MP2 type of correlation is added.…”

“…In addition to being in the pinnacle of DFT accuracy for XB, the DHs have the advantage of being extremely robust for most other chemical properties . It is indeed more expensive than lower rungs on Jacob's ladder, plus it requires bigger basis sets to take advantage of its superiority.…”

“…In this sense, DHs are a safe choice and a superb Pauling point. Any well‐parametrized DH will work well on XB dissociation energies, but perhaps the DSD options have a slight edge . For geometry optimizations the DH functionals are a good option, but their higher computational cost probably does not justify their use …”

The INV24 test set: how well do quantum-chemical methods describe inversion and racemization barriers?

“…104 In double hybrids, parts of the semilocal DFT correlation are replaced by nonlocal second-order perturbation theory. Herein, we limit our assessment to six double hybrids that have shown to be very promising in rigorous benchmark studies: B2PLYP, 105 B2GPPLYP, 54 DSD-BLYP, 106 DSD-PBEP86, 107 DSD-PBEB95, 108 and PWPB95. 49 Additionally, we also include a B2PLYP variant that has been specifically parametrized for barrier heights and kinetics (B2KPLYP).…”

The behavior of active diffusiophoretic suspensions: An accelerated Laplacian dynamics study

“…One can think of functionals with correlation energy computed by formulas suggested by WFT (e.g., second-order perturbation theory) as multicoefficient correlation methods combining WFT and DFT or one can think of them as having nonlocal correlation functionals, in which case they are called doubly hybrid functionals or double hybrid functionals. [128][129][130][131][132][133][134][135][136][137][138][139][140][141][142][143][144][145][146][147] One can also use many-body wave function theory to build on a KS starting point, as in GW theory [148][149][150][151] (a many-body theory where G denotes a Green's function and W denotes a screened Coulomb interaction).…”