Many-body dispersion energy with fractionally ionic model for polarizability

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

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

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

$\alpha_p^{\text{AIM}} = \alpha_p^{\text{atom}} \frac{V^{\text{eff}}_p}{V^{\text{atom}}_p}$,

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

$\alpha_p^{\text{AIM}}(\omega) = \alpha_p^{\text{FI}}(\omega) \frac{V^{\text{eff}}_p}{V^{\text{FI}}_p}$,

it relies on Gould's model of frequency-dependent polarizabilities ($\alpha_p^{\text{FI}}(\omega)$) and charge densities of non-interacting fractional ions combined with iterative Hirshfeld partitioning. 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.

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 $\beta$
• 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 $\left(1-\mathbf{A}^{(0)}_{LR}(\omega) {\mathbf{T}}_{LR}({\mathbf{k}})\right)$ are non-positive, see reference 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 ) 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

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