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Self-consistent screening in Tkatchenko-Scheffler method

A computationally efficient way to account for electrodynamic response effects, in particular the interaction of atoms with the dynamic electric field due to the surrounding polarizable atoms was proposed by Tkatchenko et al. [130]. In this method, termed TS+SCS, the frequency-dependent screened polarizabilities $ \alpha^{SCS}(\omega)$ are obtained by solving the self-consistent screening equation:

$\displaystyle \alpha_{i}^{SCS}(\omega) = \alpha_{i}(\omega) - \alpha_{i}(\omega) \sum_{i \neq j} \tau_{ij} \alpha_{j}^{SCS}(\omega),$ (6.104)

where $ \tau_{ij}$ is the dipole-dipole interaction tensor and $ \alpha_{i}(\omega)$ is the effective frequency-dependent polarizability, approximated by

$\displaystyle \alpha_{i}(\omega) = \frac{\alpha_{i}}{1+\left ( \omega / \omega_i \right )^2},$ (6.105)

with the characteristic mean excitation frequency $ \omega_i = \frac{4}{3} \frac{C_{6ii}}{(\alpha_{i})^2}$. The dispersion coefficients are computed from the Casimir-Polder integral:

$\displaystyle C_{6ii} = \frac{3}{\pi} \int_0^{\infty} \alpha_{i}^{SCS}(\omega) \alpha_{i}^{SCS}(\omega)  d\omega.$ (6.106)

The van der Waals radii of atoms are obtained by rescaling the radii computed using DFT-TS:

$\displaystyle R_{0i}^{SCS} = \left ( \frac{\alpha_{i}^{SCS}}{\alpha_{i}} \right )^{1/3} R_{0i}.$ (6.107)

The dispersion energy is computed using the same equation as in the original TS method (eq. 6.87) but with corrected parameters $ C_{6ii}^{SCS}$, $ \alpha_{i}^{SCS}$, and $ R_{0i}^{SCS}$. The TS+SCS method is invoked by defining IVDW=2$ \vert$20 and LVDWSCS=.TRUE. In addition to parameters controlling the DFT-TS method (see sec. 6.77.3), the following optional parameters can be user-defined:

VDW_SR = 0.97 scaling factor $ s_R$
SCSRAD = 120. cutoff radius (Å) used in $ \tau_{ij}$ calculation
LSCSGRAD = .TRUE.$ \vert$.FALSE. compute SCS contribution to gradients - yes$ \vert$no
LSCALER0 = .TRUE.$ \vert$.FALSE. use eq. 6.107 to re-scale parameter $ R_0$ - yes $ \vert$ no

Details of implementation of the TS+SCS method in VASP and the performance tests made on various crystalline systems are presented in Phys. Rev. B. 87, 064110 (2013).


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