Many-body dispersion energy with fractionally ionic model for polarizability

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A variant of Many-body dispersion energy method based on fractionally ionic model for polarizability of Gould[1], hereafter dubbed MBD@rsSCS/FI, has been introduced in Ref.[2] Just like in the original MBD@rsSCS, dispersion energy in MBD@rsSCS/FI is computed using

.

However, the two methods differ in the model used to approximate the atomic polarizabilities () needed to define tensor. The MBD@rsSCS makes use of the pre-computed static polarizabilities of neutral atoms ()

,

whereby the volume ratios between interacting and non-interacting atoms () is obtained using conventional Hirshfeld partitioning[3]. Although the MBD@rsSCS/FI employs a similar scaling relation:

,

it relies on Gould's model[1] of frequency-dependent polarizabilities () and charge densities of non-interacting fractional ions combined with iterative Hirshfeld partitioning[4]. Obviously, the MBD@rsSCS and the MBD@rsSCS/FI are equivalent for non-polar systems, such as graphite, but typically yield distinctly different results for polar and ionic materials[2].

The MBD@rsSCS/FI method is invoked by setting IVDW=263. Optionally, the following parameters can be user-defined (the given values are the default ones):

  • VDW_SR=0.83 : scaling parameter
  • LVDWEXPANSION=.FALSE. : writes the two- to six- body contributions to the MBD dispersion energy in the OUTCAR (LVDWEXPANSION=.TRUE.)
  • LSCSGRAD=.TRUE. : compute gradients (or not)
  • VDW_R0 : radii for atomic reference (see also Tkatchenko-Scheffler method)
  • ITIM=1: if set to +1, apply eigenvalue remapping to avoid unphysical cases where the eigenvalues of the matrix are non-positive, see reference[2] for details


Mind:
  • This method requires the use of POTCAR files from the PAW dataset version 52 or later.
  • The parametrization of reference data is available only for elements of the first six rows of the periodic table except of the lanthanides.
  • The charge-density dependence of gradients is neglected.
  • This method is incompatible with the setting ADDGRID=.TRUE..
  • It is essential that a sufficiently dense FFT grid (controlled via NGXF, NGYF and NGZF ) is used. We strongly recommend to use PREC=Accurate for this type of calculations (in any case, avoid using PREC=Low}).
  • The method has sometimes numerical problems if highly polarizable atoms are located at short distances. In such a case the calculation terminates with an error message Error(vdw\_tsscs\_range\_separated\_k): d\_lr(pp)<=0. Note that this problem is not caused by a bug, but rather it is due to a limitation of the underlying physical model.
  • Analytical gradients of the energy are implemented (fore details see reference [5]) and hence the atomic and lattice relaxations can be performed.
  • Due to the long-range nature of dispersion interactions, the convergence of energy with respect to the number of k-points should be carefully examined.
  • A default value for the free-parameter of this method is available only for the PBE (VDW_SR=0.83) and SCAN (VDW_SR=1.12) functionals. If any other functional is used, the value of VDW_SR must be specified in the INCAR file.

Related tags and articles

VDW_ALPHA, VDW_C6, VDW_R0, VDW_SR, LVDWEXPANSION, LSCSGRAD, IVDW, Tkatchenko-Scheffler method, Self-consistent screening in Tkatchenko-Scheffler method, Tkatchenko-Scheffler method with iterative Hirshfeld partitioning, Many-body dispersion energy

References