Total dispersion energy and eighth-order contribution for two (threefold coordinated) carbon atoms with BLYP and TPSS. For comparison the corresponding curve with DFT-D2 is also given.
First-order energies (PBE0/def2-QZVP) for C–C, C–N, and C–O interactions. The cutoff distance is determined as the distance for which the energy equals the cutoff energy (4.5 kcal/mol).
Comparison of and values from Ref. 75.
Structure of a hypothetical molecule (PBE/TZVP optimized) to illustrate the concept of fractional coordination numbers.
2D interpolation scheme for the dispersion coefficients (top) and cut through the surface for CC, NN, and OO atom pairs with . Note the mentioned increase in the value for decreasing CN.
Comparison of molecular coefficients from DFT-D3 results and from Ref. 49 with experimental DOSD values. The solid line has a slope of unity and an intercept of zero.
Left: Comparison of MAD values for different functionals without dispersion correction (DFT), with the old (DFT-D2), and new (DFT-D3) versions. Right: MAD values averaged over nine DFs (excluding BP86 and PBE) for the different subsets.
Comparison of MAD values for different functionals without dispersion correction (DFT), with the old (DFT-D2), and new (DFT-D3) versions. Left: WATER27 benchmark set. Right: HEAVY28 benchmark set.
Comparison of relative energies for tripeptide conformations (PCONF benchmark set) with different functionals. Left: old (DFT-D2) and right, new versions of DFT-D. The lines are just drawn to guide the eye.
Dissociation energies [TZV(2d,p) AO basis] for the porphine dimer (left) and a bucky-ball catcher complex with for two DFs and DFT-D3. Values for DFT-D2 in parentheses.
Comparison of MAD values for two thermochemical benchmarks without dispersion correction (DFT), with the old (DFT-D2) and new DFT-D3 versions. Left: Diels–Alder reaction energies (DARC set); right: dimerization energies of molecules.
Relative energies (in kcal/mol, def2-QZVP-ECP60 for DFT) in comparison to CCSD(T) reference values for 2D (left) and 3D (middle and right) forms of the cluster with and without dispersion correction and the PBE functional.
Asymptotic region of the potential energy curves for dissociation of . We compare the dispersion energy of the DFT-D methods with the correlation energy contribution in the CCSD(T) treatment which is to a very good approximation at these distances.
Potential energy curves (def2-TZVP-ECP28) for dissociation of benzene from an Ag(111) surface with and without dispersion corrections. The inset shows the cluster model composed of 56 Ag atoms. Unrelaxed monomer structures using the experimental lattice constant for bulk Ag are taken.
Overview of current DFT methods to account for London dispersion interactions.
Computed coefficients (in a.u.).
Comparison of computed (PBE38/daug-def2-QZVP) and experimental coefficients (in a.u., is given) for rare gas trimers.
Optimized DFT-D3 parameter values and MAD for the fit set and for the S22 benchmark set (values for DFT-D2 in parentheses). The entries are ordered according to increasing MAD.
Comparison of “best” MADs for the S22 benchmark set with DFT (and for comparison) some wave function (WF) based methods.
Results for a benchmark set of 28 complexes containing heavy nuclei (termed HEAVY28). Reference dissociation energies (CCSD(T)/CBS with counterpoise correction) and deviations for three different DFs with DFT-D3 are given in kcal/mol.
Computed interlayer dissociation energy of two graphene sheets in meV/atom with different DFs. Structures with fixed interlayer distance. Extrapolated to infinite sheet size from graphene models with 24, 54, 96, and 150 carbon atoms in one sheet using the TZV(2d,p) AO basis. The estimated numerical (extrapolation) accuracy is ±2%. For details, see Ref. 102.
Reference [est. CCSD(T)/CBS] dissociation energies for alkaline metal complexes and clusters and deviations (including mean values) for B2PLYP and TPSS functionals (all data in kcal/mol). Negative values indicate underbinding.
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