DFT-D3 method

The DFT-D3 method of Grimme et al. [92,93] is supported to include a vdW interaction with default parameters for the GGA-PBE functional. The following keywords are relevant for the DFT-D3 method.

  scf.dftD                     on            # on|off, default=off
  version.dftD                  3            # 2|3, default=2
  DFTD3.damp                   bj            # zero|bj, default=bj
  DFTD.Unit                    AU            # Ang|AU
  DFTD.rcut_dftD            100.0            # default=100 (DFTD.Unit)
  DFTD.cncut_dftD              40            # default=40 (DFTD.Unit)
  DFTD.IntDirection         1 1 1            # default=1 1 1 (1:on 0:off)

When you include the DFT-D2 or DFT-D3 calculation, turn on 'scf.dftD'. For DFT-D2 use version.dftD=2 and for DFT-D3 version.dftD=3. The DFT-D3 implemented here supports both zero and Becke-Johnson (BJ) damping functions [93]. The cutoff radius for the interaction is given by 'DFTD.rcut_dftD' and for the coordination number calculation 'DFTD.cncut_dftD'. The units are given by 'DFTD.Unit' and the suggested defaults for both cutoff values are in AU. Also, the interaction for image atoms can be cut along the a-, b-, and c-axes by 'DFTD.IntDirection', where 1 means that the interaction is included, and 0 not. Also, the periodicity for each atom can be controlled as in the case of the DFT-D2 method by

  <DFTD.periodicity 
  1   1
  2   1
  3   1
  4   1
  ....
  DFTD.periodicity>

where the first column is a serial number which is the same as in the 'Atoms.SpeciesAndCoordinates', and the second column is a flag which means that 1 is periodic, and 0 is non-periodic for the corresponding atom. By considering the periodicity or non-periodicity of each atom, the interaction is automatically cut when they are non-periodic.

The main modifications are placed at only two routines: DFTD3vdW_init.c and Calc_EdftD() of Total_Energy.c. In DFTD3vdW_init.c, you can easily change the parameters for the vdW correction, and in Calc_EdftD3() of Total_Energy.c you can confirm how they are calculated.

Parameters for other functionals may be set through the following keywords

  DFTD.scale6            1     # default=0.75|1.0 (for DFT-D2|DFT-D3)
  DFTD.scale8       0.7875     # default=0.722|0.7875 (for PBE with zero|bj damping)
  DFTD.sr6           1.217     # default=1.217 (for PBE)
  DFTD.a1           0.4289     # default=0.4289 (for PBE)
  DFTD.a2           4.4407     # default=4.4407 (for PBE)

The '$s_{6}$' and '$s_{8}$' global scaling value of Eq. (3) in Grimme's paper [92] is given by 'DFTD.scale6' and 'DFTD.scale8'. The global scaling parameters are functional and damping-function dependent. The parameter 'sr6' of Eq. (6) in [92] needs to be set when using the zero damping function while the parameters 'a1' and 'a2' of Eq. (6) in [93] need to be set when choosing BJ damping.

As an example for the DFT-D3 calculation, the interaction energy between two benzene molecules in a parallel structure with $D_{6h}$ symmetry is shown as a function of the inter-distance in Fig. 49. All the input files for the calculations can be found in a directory 'work/DFT-D3/', and they are

  Dimer-Ben-10.0.dat  Dimer-Ben-3.88.dat  Dimer-Ben-4.5.dat  Mono-Ben-1.dat
  Dimer-Ben-3.3.dat   Dimer-Ben-3.89.dat  Dimer-Ben-5.0.dat  Mono-Ben-2.dat
  Dimer-Ben-3.4.dat   Dimer-Ben-3.8.dat   Dimer-Ben-6.0.dat  Mono-Ben.dat
  Dimer-Ben-3.6.dat   Dimer-Ben-3.9.dat   Dimer-Ben-7.0.dat
  Dimer-Ben-3.86.dat  Dimer-Ben-4.0.dat   Dimer-Ben-8.0.dat
  Dimer-Ben-3.87.dat  Dimer-Ben-4.2.dat   Dimer-Ben-9.0.dat

After optimizing the monomer using 'Mono-Ben.dat', the total energy of dimer in a variety of inter-distance was calculated using 'Dimer-Ben-#.dat' (#=3.3-9.0), where the structure of the benzene molecule is the same as the structure of monomer obtained by the first calculation. The monomer calculations with a counterpoise correction were performed by 'Mono-Ben-1.dat' and 'Mono-Ben-2.dat'. The optimum inter-distance is found to be 3.87 Å, which is well compared with a reported value (3.89 Å) computed with density fitted local second-order Møller–Plesset perturbation theory (DF-LMP2) [94]. The counterpoise corrected interaction energy is 1.73 kcal/mol being in good agreement with a reported value (1.7 kcal/mol) [94], while the basis set superposition error is found to be large.

Figure 49: The interaction energy of between two benzene molecules in a parallel structure with $D_{6h}$ symmetry. The counterpoise corrected interaction energy is shown by the triangle. All the input files for the calculations can be found in a directory 'work/DFT-D3/.