3.20 $C_6$/$R^6$ corrections for long-range van der Waals interactions

Note that the vdw part of the forces may be separately converged to (if set) sc_accuracy_forces.

This method is commonly referred to as the Tkatchenko-Scheffler method. The procedure is as follows. First, the normal self-consistency cycle is completed for a semilocal or hybrid density functional, most commonly PBE or PBE0. Second, the resulting self-consistent electron density is used to create interatomic (pairwise) $C_6$ coefficients. A simple pairwise van der Waals term is then added once to the self-consistent total energy from the preceding semilocal or hybrid functional. In other words, the Tkatchenko-Scheffler method is normally employed as a post-processing term in a non-self-consistent way, not during the self-consistency cycle. Since it needs to be combined with a different density functional, you would normally use it like this (example for “PBE+vdW”):

  xc pbe
  vdw_correction_hirshfeld

Three more caveats: (1) Do not use this method together with the local-density approximation (LDA) unless you know exactly what you are doing. The LDA already contains a spurious interaction term that will lead to very strange results if added to a pairwise van der Waals term. (2) Do not simply apply this method to a metallic system unless you know what you are doing. (3) This is also not the (very different) functional commonly known as the Langreth-Lundqvist or vdw-DF functional. [76] FHI-aims contains at least two implementations of vdw-DF for those who are interested, but either implementation is much slower than the Tkatchenko-Scheffler pairwise interatomic sum.

This flag adds the Tkatchenko-Scheffler vdW functional as a part of the given exchange-correlation (XC) functional. In a self-consistent scheme, the contribution of the vdW potential, $v_{\mathrm{vdW}}[n(𝐫)]=\delta E_{\mathrm{vdW}}[n(𝐫)]/\delta n(𝐫)$, is added to the XC potential to form the total effective potential in the Kohn-Sham equations. As a result, the van der Waals interatomic contributions affect the total electron density and are computed at each self-consistent cycle, until convergence is reached. In this way, it is possible to evaluate the effects of vdW interactions on the electron density and electronic properties, going beyond the vdW a posteriori correction of the total DFT energy.

Note: Do not use this self-consistent flag during a relaxation. The self-consistent forces are not implemented (yet) for the Tkatchenko-Scheffler vdW functional and this will lead to inconsistency errors.

Alternative implementation of the TS method via the Libmbd library [138] that provides some extra features compared to the vdw_correction_hirshfeld and vdw_correction_hirshfeld_sc implementations. The main difference is the use of the Ewald summation to sum the $1/R^6$ sum in the periodic case, which makes the use of the vdw_convergence_threshold keyword obsolete. Furthermore, forces and stress are available also in the self-consistent case. This implementation does not honor the vdw_pair_ignore and hirshfeld_param keywords.

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  self_consistent=<logical> [default: .false.] turns on self-consistency as explained under vdw_correction_hirshfeld_sc.

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  vdw_params_kind=<string> [default: "ts"] specifies the set of free-atom vdW parameters (${\alpha }_0$, $C_6$, $R_{\text{vdW}}$) used. "ts" uses the original set of parameters, "tssurf" uses values from the so-called vdW${}^{\text{surf}}$ approach [267] for some of the elements. The used parameters are listed here.

The user needs to specify the interaction parameters for all atomic pairs in the system (i.e. for CNOH, there are 10 atomic pairs). This is done by putting “vdw_pairs $N$”, where $N$ is the number of pairs. This should be followed by $N$ lines of “vdw_coeff atom_i atom_j $C_{6ij}$ $R_{ij}^0$ $d$”, where $C_{6ij}$ is the $C_6$ coefficient for the interaction between atom_i and atom_j, $R_{ij}^0$ is the corresponding vdW radius and $d$ is the damping function parameter. A choice $d$=20 is suggested for all atomic pairs. An example for C-C interaction is: “vdw_coeff C C 30.00 5.59 20.0”.