Hybrid functionals double

1 Double Hybrid Functionals Incorporation of the unoccupied Kohn-Sham orbitals to create fifth-rung methods has been difficult. The one approach that has seen some application to organic chemistry is the semiempirical double hybrid approach of Grimme. The approach begins with a hybrid (jGA functional of the form 

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In order to make improvements over the LSDA, one has to assume that the density is not uniform. The approach that has been taken is to develop functionals that are dependent on not only the electron density but also derivatives of the density. This constitutes the generalized gradient approximation (GGA) and is the second rung on Jacob s Ladder. The third rung, meta-GGA functional, includes a dependence on the Laplacian of the density (V p) or on the orbital kinetic energy density (t). The fourth row, the hyper-GGA or hybrid functionals, includes a dependence on exact (HF) exchange. Finally, the fifth row incorporates the unoccupied Kohn-Sham orbitals. This is most widely accomplished within the so-called double hybrid functionals. 

In [170] the authors obtain a test set of ten molecules of specific atmospheric interest in order to evaluate the performance of various Density Functional Theory (DFT) methods in (hyper)polarizability calculations as well as established ab initio methods. The authors make their choice for these molecules based on the profound change in the physics between isomeric systems, the relation between isomeric forms and the effect of the substitution. In the evaluation analysis the authors use arguments chosen from the information theory, the graph theory and the pattern recognition fields of Mathematics. The authors mentioned the remarkable good performance of the double hybrid functionals (namely B2PLYP and mPW2PLYP) which are for the first time used in calculations of electric response properties. 

S. Kofimann, B. BCirchner, F. Neese. Performance of modern density functional theory for the prediction of hyperfine structure meta-GGA and double hybrid functionals. Mol Phys., 105 (2007) 2049-2071. 

Because of its computational efficiency and good results for molecular properties, the MP2 method is one of the two most commonly used methods for including correlation effects on molecular ground-state equilibrium properties. (The other widely used method is the density-functional method—Section 16.5.) Also, in perhaps the most accurate form of density-functional theory, the MP2 correlation energy (16.13) is multiplied by an empirical constant and added to the density functional energy to give improved results see the discussion of double-hybrid functionals in Section 16.5. 

Double hybrid functionals add a dependence on the unoccupied KS orbitals. 

The biggest problem in DPT is the choice of the functional approximation. In many cases, computationally cheap (meta-)GGAs (e.g.,BLYP, PBE,orTPSS) can be recommended. Such functionals should not be used when the self-interaction error (e.g., in charged open shell systems) plays a role. Then, hybrid functionals are required which also have less tendency for over-polarization. The currently highest level of approximation in DPT is represented by double-hybrid functionals (e.g., B2PLYP) that also perform very well for non-covalent interactions. 

Modified functionals, which are generated to account for dispersion effects, have been also utilised for gold systems. Double hybrid functionals, which include MP2 equations to calculate a part of the correlation energy, have been shown to give accurate results for gold phosphine complexes and dimers, if additionally a D3 correction is applied. Regarding the use of hybrid functionals in combination with the D2/D3... 

Recently introduced double-hybrid functionals (see [30] and the references therein) recover dispersion energy, but only to a hmited extent, as nonlocal correlation terms are too small to recover the full non-covalent interaction energy [28]. They are also considerably more computationally expensive than GGA, mGGA, and even hybrid functionals. 

Wilson and coworkers assessed the performance of 13 hybrid-GGA, hybrid-meta-GGA, and double-hybrid DFT functionals on the cc-CA-TM/11 dataset [83]. The hybrid B97-1 [42, 84] functional and the double-hybrid functional mPW2-PLYP [85] were found to give the best performance over experimental results with mean absolute deviations of 7.2 and 7.3 kcal mol . The dataset (cc-CA-TM/11) is rather diverse and consists of AyH of 193 3d transition metal molecules (Sc(C5H5)3 and (Cr03)3, halides, oxides, and heavy chalcogenides, hydrides, nitrides, small clusters, metal carbonyls, and other coordination complexes) [86]. 

Double numerical basis set Double-numerical + polarization basis mPW2-PLYP double-hybrid functional Double-vacancy defect of graphene sheet Effective core potential EE + vdW method... 

J.M.L. (2008) Highly accurate first-principles benchmark data sets for the parametrization and validation of density functional and other approximate methods. Derivation of a robust, generally applicable, double-hybrid functional for thermochemistry and thermochemical kinetics.. Phys. Chem. A, 112, 12868-12886. 

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