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 (this parameter is obsolete as of VASP.5.3.3).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 given values are the default ones):

• VDW_RADIUS=50.0 : cutoff radius (in $\mathrm {\AA}$) 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 ($\mathrm {\AA}$) for each species defined in the POSCAR file
• LVDW_EWALD=.FALSE. : the lattice summation in $E_{\mathrm {disp} }$ expression is computed by means of Ewald's summation (.TRUE. ) or via a real space summation over all atomic pairs within cutoff radius VDW_RADIUS (.FALSE.). (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. The defaults for parameters controlling the damping function (VDW_S6, VDW_SR, VDW_D) are available for the PBE (GGA=PE), BP, revPBE, PBE0, TPSS, and B3LYP functionals. If any other functional 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. As of VASP.5.3.4, the default value for VDW_RADIUS has been increased from 30 to 50 $\mathrm {\AA}$. 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

VDW_RADIUS, VDW_S6, VDW_SR, VDW_SCALING, VDW_D, VDW_C6, VDW_R0, LVDW_EWALD, IVDW, DFT-ulg, DFT-D3

---