Dispersion-corrected functionals

Finally, the semiempirical dispersion-corrected functionals are a modification of conventional semiempirical functionals (see Seet. 5.6) for dispersion effects. DFT-D functionals such as the BLYP-D, B3LYP-D, and B97-D functionals (Antony and Grimme 2006) and several Mx-series funetionals sueh as the M05-2x and M06-2x functionals (Zhao and Truhlar 2008) are ineluded in these semiempirical dispersion-corrected functionals. In the DFT-D functionals, there are three versions, DFT-Dl, DFT-D2, and DFT-D3, based on the level of dispersion corrections. For a deep understanding of the dispersion corrections, it is interesting to examine the highest level DFT-D3 functional (Grimme et al. 2010),... 

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. 

Fig. 6.4 Calculated potential energy curves of At2 in terms of the inter-atomic distance Kohn-Sham potential energy curves of pure GGA and LC-GGA functionals (left) and of dispersion-corrected functionals (right). For comparison, the curve of the CCSD(T) method (see Sect. 3.5) is also illustrated. The 6-311- -- -G(3df, 3pd) basis functions are used. See Tsuneda and Sato (2009)...

As a benchmark set for the quantitative validation of dispersion corrections, Hobza and coworkers suggested the S22 set (Jurecka et al. 2006), which contains 22 weakly bonded dimers. This S22 benchmark set provides interaction energies of hydrogen-bonded, dispersion-bonded and mixed complexes, which are the calculated results of the CCSD(T) method at the complete basis set (CBS) limit (Riley et al. 2010). Due to its convenience, this benchmark set has been used not only in testing the accuracies of dispersion corrections but also in determining the adjustable parameters of semiempirical dispersion-corrected functionals. Table 6.1 displays the mean absolute deviations (MAD) of various dispersion-corrected DPT calculations for the S22 benchmark set in ascending order. This table shows clearly that, independent of the dispersion corrections combined, the LC-tvdW methods... 

The complex is emissive in the solid state and weakly emissive in acetonitrile solution. Density-functional theory calculations employed a long-range dispersion-corrected functional. An energy... 

Zahn, S. Kirchner, B. (2008). Validation of dispersion corrected functional theory for ionic Iquid systems, /. Phys. Chem. A 112 8430. 

Dispersion-corrected functionals. The functional names as shown above, but with -D, -D2, and -D3 added to the name, for example, B97-D, B3LYP-D3. They are also present in some Minnesota-group functionals, for example, M06. Dispersion corrections can improve structures and energies, especially where hybrid functionals are found to underbind, but some notable failures have also been reported, so far, mainly anecdotally. 

CUB97X-D LC + semiempirical Semiempirical Dispersion-Corrected Functionals and Long-Range Exchange Interactions 0.22 [66]... 

BLYP-D3 Semiempirical Semiempirical Dispersion-Corrected Functionals 0.23 [50]... 

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