DFT-D2

In the DFT-D2 method of Grimme, the correction term takes the form:

$E_{\mathrm{disp}} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}} {}^{\prime} \frac{C_{6ij}}{r_{ij,L}^{6}} f_{d,6}({r}_{ij,\mathbf{L}})$

where the first two summations are over all $N_{at}$ atoms in the unit cell and the third summation is over all translations of the unit cell ${\mathbf{L}}=(l_1,l_2,l_3)$ where the prime indicates that $i\not=j$ for ${\mathbf{L}}=0$. $C_{6ij}$ denotes the dispersion coefficient for the atom pair $ij$, ${r}_{ij,\mathbf{L}}$ is the distance between atom $i$ located in the reference cell $\mathbf{L}=0$ and atom $j$ in the cell $L$ and the term $f(r_{ij})$ is a damping function whose role is to scale the force field such as to minimize the contributions from interactions within typical bonding distances. In practice, the terms in the equation for $E_{\mathrm{disp}}$ corresponding to interactions over distances longer than a certain suitably chosen cutoff radius (VDW_RADIUS, see below) contribute only negligibly to $E_{\mathrm{disp}}$ and can be ignored. Parameters $C_{6ij}$ and $R_{0ij}$ are computed using the following combination rules:

$C_{6ij} = \sqrt{C_{6ii} C_{6jj}}$

and

$R_{0ij} = R_{0i}+ R_{0j}.$

The values for $C_{6ii}$ and $R_{0i}$ are tabulated for each element and are insensitive to the particular chemical situation (for instance, $C_6$ for carbon in methane takes exactly the same value as that for C in benzene within this approximation). In the DFT-D2 method, a Fermi-type damping function is used:

$f_{d,6}(r_{ij}) = \frac{s_6}{1+e^{-d(r_{ij}/(s_R\,R_{0ij})-1)}}$

whereby the global scaling parameter $s_6$ has been optimized for several different DFT functionals such as PBE ($s_6=0.75$), BLYP ($s_6=1.2$) or B3LYP ($s_6=1.05$). The parameter $s_R$ is usually fixed at 1.00. The DFT-D2 method can be activated by setting IVDW=1|10 or by specifying LVDW=.TRUE. (this parameter is obsolete as of VASP.5.3.3). Optionally, the damping function and the vdW parameters can be controlled using the following flags (the default values are listed):

• VDW_RADIUS=50.0 : cutoff radius (in $\AA$) for pair interactions
• VDW_S6=0.75 : global scaling factor $s_6$ (available in VASP.5.3.4 and later)
• VDW_SR=1.00 : scaling factor $s_R$ (available in VASP.5.3.4 and later)
• VDW_SCALING=0.75 : the same as VDW_S6 (obsolete as of VASP.5.3.4)
• VDW_D=20.0 : damping parameter $d$
• VDW_C6=[real array] : $C_6$ parameters ($\mathrm{Jnm}^{6}\mathrm{mol}^{-1}$) for each species defined in the POSCAR file
• VDW_R0=[real array] : $R_0$ parameters ($\AA$) for each species defined in the POSCAR file
• LVDW_EWALD=.FALSE. : decides whether the lattice summation in $E_{\mathrm{disp}}$ expression by means of Ewald's summation is computed (available in VASP.5.3.4 and later)

The performance of PBE-D2 method in optimization of various crystalline systems has been tested systematically in reference .

Important: It is recommended to use the more advanced and more accurate method DFT-D3.

Mind: The defaults for VDW_C6 and VDW_R0 are defined only for elements in the first five rows of the periodic table (i.e. H-Xe). If the system contains other elements the user has to define these parameters in INCAR.

Mind: The defaults for parameters controlling the damping function (VDW_S6, VDW_SR, VDW_D) are available only for the PBE functional. If a functional other than PBE is used in a DFT-D2 calculation, the value of VDW_S6 (or VDW_SCALING in versions before VASP.5.3.4) has to be defined in INCAR.

Mind: As of VASP.5.3.4, the default value for VDW_RADIUS has been increased from 30 to 50 $\AA$.

Mind: Ewald's summation in the calculation of $E_{\mathrm{disp}}$ calculation (controlled via LVDW_EWALD) is implemented according to reference and is available as of VASP.5.3.4.

Related tags and articles

IVDW, DFT-D3, Tkatchenko-Scheffler method, Tkatchenko-Scheffler method with iterative Hirshfeld partitioning, Self-consistent screening in Tkatchenko-Scheffler method, Many-body dispersion energy, dDsC dispersion correction

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