B2PLYP functional

Grimme extended the double hybrid density functional formalism to be able to compute BCD. For a test suite of six molecules, performance of B2PLYP is notably better than for B3LYP. 

These coefficients are determined by the TDKS calculation for each atomic pair and trio. Since these values are fixed after one TDKS calculation, these dispersion calculations are not a bottleneck in the DFT-D3 calculations. For DFT-D3 functionals, the BLYP-D3 and B2PLYP-D3 functionals have recently been suggested (Grimme et al. 2010). In the Mx-series and other semiempiri-cal dispersion-corrected functionals, dispersion interactions are incorporated in a similar manner, although only the term is usually retained. This type of dispersion correction is clearly efficient, because dispersion interactions are easily incorporated with high accuracy by using only functionals. However, it has been reported that the calculated results depend on the parameters used and the R decay of the dispersion interaction cannot be reproduced. 

In order to verify that they are correspond to reagents, calculations with frozen C.O distances were performed. Obtained data were using to calculation of electronic activation energies and thermodynamical functions in terms of normal mode vibrations in B2PLYP. Kinetic characteristics calculations are presented in Tables 7.1 and 7.2. Results of calculation of rate constants and comparison with literature data are presented in Figs. 7.3 and 7.4. 

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. 

B2PLYP and mPW2PLYP are called double-hybrid density functionals (DHDFs), since they mix in not only some exact exchange but also some correlation calculated by the MP2 method. 

Rms errors in kcal/mol for the S22 test set for some density functionals that did well on this set are 0.31 for wB97X-D, 0.33 for B2PLYP-D3, and 0.34 for BLYP-D3 [L. Goerigk and S. Grimme, Phys. Chem. Chem. Phys., 13,6670 (2011)] as compared with 0.44 for B3LYP-D3. 

CH3)2N). In order to ensure consistency of results, the wave functions approximation for all studied molecules was performed using the DFT(B2PLYP) method [37]. Only for the (CF3)2NONO and (CH3>2NONO molecules previously published the DFT(B3LYP) results [27] were used. 

In this chapter the electronic structure of nitrous acid (MONO), alkaline nitrites (MONO), halogen nitrites (XONO), peroxynitrous acid (HOONO) and a range of organic nitrites (RONO), have been studied using the topological analysis of Electron Localisation Function for the DFT(B2PLYP)/aug-cc-pVTZ and DFT (B3LYP)/aug-cc-PVTZ approximated wave function. 

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. 

Figure 10.3 Performance of selected hybrid, (B3LYP [99], B97-1 [100], PBEO [101], M06 [103, 112], HSE06 [113]), long-range corrected (CAM-B3LYP [102], LC-a)PBE [114], a)B97 [104]), and meta-hybrid (M06-2X [103, 112]) DFT functionals, including also their dispersion-corrected DFT-D counterparts [108, 115] for the computation of enharmonic vibrational wavenumbers at the GVPT2 level. The inset shows results obtained by correction of the harmonic part at the higher lever level of theory (B2PLYP, CCSD(T)) In conjunction with enharmonic corrections computed at the B3LYP level.

B2PLYP-D3 Semiempirical + perturbation Combination with Perturbation Theories and Semiempirical Dispersion-Corrected Functionals 0.29 [50]... 

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