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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

[math]\displaystyle{ E_{\mathrm{disp}} = -\int_{\mathrm{FBZ}}\frac{d{\mathbf{k}}}{v_{\mathrm{FBZ}}} \int_0^{\infty} {\frac{d\omega}{2\pi}} \, {\mathrm{Tr}}\left \{ \mathrm{ln} \left ({\mathbf{1}}-{\mathbf{A}}^{(0)}_{LR}(\omega) {\mathbf{T}}_{LR}({\mathbf{k}}) \right ) \right \} }[/math].

However, the two methods differ in the model used to approximate the atomic polarizabilities ([math]\displaystyle{ \alpha_p^{\text{AIM}} }[/math]) needed to define tensor[math]\displaystyle{ \mathbf{A}^{(0)}(\omega)({\mathbf{k}}) }[/math]. The MBD@rsSCS makes use of the pre-computed static polarizabilities of neutral atoms ([math]\displaystyle{ \alpha_p^{\text{atom}} }[/math])

[math]\displaystyle{ \alpha_p^{\text{AIM}} = \alpha_p^{\text{atom}} \frac{V^{\text{eff}}_p}{V^{\text{atom}}_p} }[/math],

whereby the volume ratios between interacting and non-interacting atoms ([math]\displaystyle{ \frac{V^{\text{eff}}_p}{V^{\text{atom}}_p} }[/math]) is obtained using conventional Hirshfeld partitioning[3]. Although the MBD@rsSCS/FI employs a similar scaling relation:

[math]\displaystyle{ \alpha_p^{\text{AIM}}(\omega) = \alpha_p^{\text{FI}}(\omega) \frac{V^{\text{eff}}_p}{V^{\text{FI}}_p} }[/math],

it relies on Gould's model[1] of frequency-dependent polarizabilities ([math]\displaystyle{ \alpha_p^{\text{FI}}(\omega) }[/math]) 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].

Usage

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 [math]\displaystyle{ \beta }[/math]
  • 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 [math]\displaystyle{ \left(1-\mathbf{A}^{(0)}_{LR}(\omega) {\mathbf{T}}_{LR}({\mathbf{k}})\right) }[/math] 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

  1. ↑ a b T. Gould and T. Bučko, C6 Coefficients and Dipole Polarizabilities for All Atoms and Many Ions in Rows 1–6 of the Periodic Table, J. Chem. Theory Comput. 12, 3603 (2016).
  2. ↑ a b c T. Gould, S. Lebègue, J. G. Ángyán, and T. Bučko, A Fractionally Ionic Approach to Polarizability and van der Waals Many-Body Dispersion Calculations, J. Chem. Theory Comput. 12, 5920 (2016).
  3. ↑ F. Hirshfeld, Bonded-atom fragments for describing molecular charge densities, Theor. Chim. Acta 44, 129 (1977).
  4. ↑ P. Bultinck, C. Van Alsenoy, P. W. Ayers, and R. Carbó Dorca, J. Chem. Phys. 126, 144111 (2007).
  5. ↑ T. Bučko, S. Lebègue, T. Gould, and J. G. Ángyán, J. Phys.: Condens. Matter 28, 045201 (2016).
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