DFT-D3 method

Figure 16.5 Computed (TDDFT/PBE38) Cg dispersion coefficients (in Bohr°) for the whole periodic table (up to Pu), which are used in the DFT-D3 method- For each element the free atom value (lower value, light colored circle) and the coefficient (upper value, darker color) for the atom in a saturated chemical environment (with the highest coordination number according to the DFT-D3 scheme, e.g., four for carbon and three...

Our dispersion-corrected computations at ZORA-BLYP-D3/TZ2P (the computational details are described in [62], except that we have now also included dispersion corrections using Grimme s third-generation DFT-D3 method, as described in [86]) revealed that all halogen-substituted bisphosphine palladium complexes... 

This simple approach has recently been improved regarding accuracy, less empiricism (the most important parameters Ro and Ce are computed ab initio), and general applicability to most elements of the periodic table (Grimme et al. 2010). An important change in this so-caUed DFT-D3 method is that the Ce dispersion coefficients are dependent on the molecular structure which accounts for subtle effects, e.g., the hybridization state of an atom changes. 

Dispersion corrections to DFT and HF (including semiempirical methods) have recently been reviewed [59, 60] and hence only a brief description is given. Asymptotically correct approaches are either atom-pair-based (e.g., DFT-D3 [42], XDM [61], or Tkatchenko-Scheffler (TS)-vdW [62]) or compute the dispersion energy from the electron density (called vdW-DF [25, 63]). For recent work on the... 

The Q coefficients (and derived Cg) in the D3 method have been computed using a modified form of this relation, where the a(ia>) are computed nonempirically by TDDFT and A and B are reference molecules from which atomic values are derived [42]. Because the reference system can also be a molecular cluster modeling a solid environment, special coefficients for atoms in the bulk can be derived [68]. The final form for the DFT-D3 two-body part of the dispersion energy employs the so-called Becke-Johnson (BJ) damping [61, 69] and truncates the expansion at Cg... 

For system-specific FePc/Au(lll) with vdW-DF method reported reasonable results, where the molecule-substrate distance is 3.10 A and the adsorption energy is 105.1 kcal/mol. In the same systems, the DFT-D3, DFT-TS, and OptB86b-vdW methods given out adsorption energies of 110, 102, and 105 kcal/mol and the molecule-substrate distance of 3.13, 3.19 and 3.10 A, respectively [83]. The difference between those results is small, so the van der Waals interactions should... 

The most recent method considered is DFT-D3 [35]. Previous DFT-D methods did not distinguish between different valence states of an atom in a molecule, that is the dispersion coefficients in Eq. (11.1) for sp and sp carbon atoms should differ, as dispersion coefficients decrease upon oxidation of an atom and increase upon reduction. To obtain accurate dispersion coefficients, the concept of atomic fractional coordination number was introduced in DFT-D3. The dispersion coefficients in Eq. (11.1) depend on the atomic fractional coordination number and the latter depends on an atom s geometrically closest neighbors. The D3-correction has continuous dispersion coefficients C even if chemical reaction occurs in a model system (i.e., dispersion coefficients change smoothly when an atom s valence or oxidation state changes), which is very efficient. Indeed, this allows smooth forces and therefore may be used in quantum molecular dynamics. For example, in the simple transition state of the Sj.j2 reaction [F CHj F ], the fractional coordination number of the carbon atom is 4.1 and that of fluorine atom is 0.57. DFT-D3 contains eighth-order terms with w = 8 and the eighth-order dispersion coefficients Cg in Eq. (11.1) are computed from for the same atom pairs. 

Finally, it is also interesting to evaluate the Hartree-Fock (HF) method. While this method was developed independently of DFT and is subject to systematic improvement towards exact ab initio numerical solution of the electronic structure problem, it can be regarded as resulting from a standard DFT application using exact exchange and no correlation and hence to also provide an application of DFT. As the Hartree-Fock method does not include electron correlation effects such as London dispersion at all, it provides a very poor description of non-covalent interactions. However, recent studies surprisingly showed that HF can reach the accuracy of GGA functionals when dispersion corrected [17, 79]. Hence we also test the HF-D3(BJ) approach. 

Table 5.2 shows a performance of ab initio, DFT, and force field methods, as well as EFP, on the S22 dataset [28]. The second-order perturbation theory, MP2, tends to overestimate the dispersion forces, which becomes obvious from significant errors in describing dispersion-dominated complexes. On the other hand, HF and many popular DFT methods do not describe dispersion at all, again resulting in dramatic errors in dispersion-dominated S5 ems. Augmenting the DFT functionals with dispersion corrections like in BLYP-D3 [29] or >B97X-D [30] dramatically improves their performance. Classical force fields are significantly in error... 

To support the reaction mechanism and to better understand the role of each species, the authors performed B3LYP-D3 density functional theory (DFT) calculations. Interestingly, the method was applied to a broad spectrum of substrates, and a lead compound with impressive inhibitory activity against a number of cancer cell lines was also identified. 

Hobza and coworkers performed a comparative study of Ag, Au, and Pd atoms binding to graphene [114] with electron correlation (CCSD(T) and MP2 with Douglas-Kroll Hamiltonians), conventional (i.e., LDA and GGA) and dispersionaccounting DFT methods (PBE-D3, M06-2X, vdW-DF, and EE -I- vdW). Binding of these metals to graphene is of varied nature, but it is due to electron correlation, as ROHF/ANO-RCC-VTZP benzene-metal potential energy curves have no minima. 

---