Many-body dispersion energy
The many-body dispersion energy method (MBD@rsSCS) of Tkatchenko et al.,[1][2] invoked by setting IVDW=202, is based on the random-phase expression for the correlation energy
- [math]\displaystyle{ E_c = \int_{0}^{\infty} \frac{d\omega}{2\pi} \mathrm{Tr}\left\{\mathrm{ln} (1-v\chi_0(i\omega))+v\chi_0(i\omega) \right\} }[/math]
whereby the response function [math]\displaystyle{ \chi_0 }[/math] is approximated by a sum of atomic contributions represented by quantum harmonic oscillators. The expression for the dispersion energy used in the VASP k-space implementation of the MBD@rsSCS method (see reference [3] for details) is as follows:
- [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]
where [math]\displaystyle{ {\mathbf{A}}_{LR} }[/math] is the frequency-dependent polarizability matrix and [math]\displaystyle{ \mathbf{T}_{LR} }[/math] is the long-range interaction tensor, which describes the interaction of the screened polarizabilities embedded in the system in a given geometrical arrangement. The components of [math]\displaystyle{ \mathbf{A}_{LR} }[/math] are obtained using an atoms-in-molecule approach as employed in the pairwise Tkatchenko-Scheffler method (see references [2][3] for details).
Details of the implementation of the MBD@rsSCS method in VASP are presented in reference [3].
Usage
The input reference data for non-interacting atoms can be optionally defined via the parameters VDW_ALPHA, VDW_C6, and VDW_R0 (described by the Tkatchenko-Scheffler method). This method has one free parameter ([math]\displaystyle{ \beta }[/math]) that must be adjusted for each exchange-correlation functional. The default value of [math]\displaystyle{ \beta }[/math]=0.83 corresponds to the PBE functional (GGA=PE). If another functional is used, the value of [math]\displaystyle{ \beta }[/math] must be specified via VDW_SR in the INCAR file.
The following optional 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_ALPHA, VDW_C6, VDW_R0 : 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[4] for details
Mind:
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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 with fractionally ionic model for polarizability
References
- ↑ A. Tkatchenko, R. A. DiStasio, Jr., R. Car, and M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012).
- ↑ a b A. Ambrosetti, A. M. Reilly, and R. A. DiStasio Jr., J. Chem. Phys. 140, 018A508 (2014).
- ↑ a b c d T. Bučko, S. Lebègue, T. Gould, and J. G. Ángyán, J. Phys.: Condens. Matter 28, 045201 (2016).
- ↑ T. Gould, S. Lebègue, J. G. Ángyán, and T. Bučko, J. Chem. Theory Comput. 12, 5920 (2016).