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WIREs Comput Mol Sci
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Double‐hybrid density functionals

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Double‐hybrid density functionals (DHDFs) are reviewed in this study. In DHDFs parts of conventional density functional theory (DFT) exchange and correlation are replaced by contributions from nonlocal Fock‐exchange and second‐order perturbative correlation. The latter portion is based on the well‐known MP2 wave‐function approach in which, however, Kohn–Sham orbitals are used to calculate its contribution. First, related methods preceding this idea are reviewed, followed by a thorough discussion of the first modern double‐hybrid B2‐PLYP. Parallels and differences between B2‐PLYP and its various successors are then outlined. This discussion is rounded off with representative thermochemical examples demonstrating that DHDFs belong to the most robust and accurate DFT approaches currently available. This analysis also presents hitherto unpublished results for recently developed DHDFs. Finally, how double‐hybrids can be combined with linear‐response time‐dependent DFT is also outlined and the value of this approach for electronically excited states is shown. WIREs Comput Mol Sci 2014, 4:576–600. doi: 10.1002/wcms.1193 This article is categorized under: Electronic Structure Theory > Density Functional Theory
Functional principle of double‐hybrids in the DFT and WFT ‘worlds’.
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Structures of the dye test set (left). Mean (MDs) and mean absolute deviations (MADs) in eV for the entire test set for various TD‐DFT methods and for the CC2 approach (right). Values are taken from Refs and and calculated herein for TD‐PBE and TD‐PBE0 (with TURBMOLE). All values have been obtained with the def2‐TZVPP AO basis set.
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Reaction formulas and optimized structures of the three reaction energy examples.
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Jacob's Ladder for GMTKN30. The values shown are weighted total mean absolute deviations in kcal/mol averaged for each rung of the ladder and obtained at the quadruple‐ζ basis‐set level (see Ref ).
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Dissociation curve of the argon dimer with B2‐PLYP and B2‐PLYP‐D3. Results are based on the aug‐cc‐pVQZ AO basis set which provides results quite close to the basis set limit for this property. As a comparison CCSD(T)/CBS results are shown (based on aug‐cc‐pVTZ/aug‐cc‐pVQZ extrapolations). ΔE is the interaction energy between the two argon atoms. All calculations were carried out with TURBOMOLE.
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