DFT-D2 method of Grimme

LVDW= .TRUE. | .FALSE. (Available as of VASP.5.2.11)

Default: LVDW=.FALSE.

Popular density functionals are unable to describe correctly van der Waals interactions resulting from dynamical correlations between fluctuating charge distributions. A pragmatic method to work around this problem has been given by the DFT-D approach [120], which consists in adding a semi-empirical dispersion potential to the conventional Kohn-Sham DFT energy:

$$E_{DFT-D} = E_{KS-DFT} + E_{\rm disp}.$$ (6.88)

In the DFT-D2 method of Grimme [121], the van der Waals interactions are described via a simple pair-wise force field, which is optimized for several popular DFT functionals. The dispersion energy for periodic systems is defined as

$$E_{\rm disp} = -\frac{s_6}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{... ...,0}-{\bf r}^{j,{\bf L}}\vert^6} f(\vert{\bf r}^{i,0}-{\bf r}^{j,{\bf L}}\vert),$$ (6.89)

where the summations are over all atoms $N_{at}$ and all translations of the unit cell ${L}=(l_1,l_2,l_3)$, the prime indicates that $i\not=j$ for ${L}=0$, $s_6$ is a global scaling factor, $C_6^{ij}$ denotes the dispersion coefficient for the atom pair $ij$, ${r}^{i,{L}}$ is a position vector of atom $i$ after performing ${L}$ translations of the unit cell along lattice vectors. In practice, terms corresponding to interactions over distances longer than a certain suitably chosen cutoff radius contribute only negligibly to $E_{\rm disp}$ and can be ignored. The term $f(r^{ij})$ is a damping function

$$f(r^{ij}) = \frac{1}{1+e^{-d(r^{ij}/R_0^{ij}-1)}},$$ (6.90)

whose role is to scale the force field such as to minimize contributions from interactions within typical bonding distances. Combination rules for dispersion coefficients $C_6^{ij}$ and vdW radii $R^{ij}$ are

$$C_6^{ij} = \sqrt{C_6^i C_6^j},$$ (6.91)

and

$$R_0^{ij} = R_0^i+ R_0^j,$$ (6.92)

respectively. The global scaling parameter $s_6$ has been optimized for several different DFT functionals such as PBE ($s_6=0.75$), BLYP ($s_6=1.2$), and B3LYP ($s_6=1.05$).

The DFT-D2 method can be activated by setting LVDW=.TRUE. Optionally, the forcefield parameters can be controlled using the following flags (the default values are listed):

VDW_RADIUS	= 30.0	cutoff radius (Å) for pair interactions
VDW_SCALING	= 0.75	global scaling factor $s_6$
VDW_D	= 20.0	damping parameter $d$
VDW_C6	= $C_6$,...	$C_6$ parameters ( $Jnm^6mol^{-1}$) for each species defined in POSCAR
VDW_R0	= $R_0$,...	$R_0$ parameters (Å) for each species defined in POSCAR

The default values for VDW_C6 and VDW_R0 are compiled in Tab. 2. As the potential energy, interatomic forces as well as stress tensor are corrected by adding contribution from the forcefield, simulations such as the atomic and lattice relaxations, molecular dynamics, and vibrational analysis can be performed. The number of atomic pairs contributing to $E_{\rm disp}$ and the estimated vdW energy are written in OUTCAR (check lines following the expression 'Grimme's potential'). The forces and stresses written in OUTCAR contain the vdW correction but the corrected energy should be read from OSZICAR (energies in OUTCAR do not contain the vdW term).

IMPORTANT NOTE: The defaults for VDW_C6 and VDW_R0 are defined only for the first five rows of periodic table of elements (see Tab. 2) - if the system contains other elements the user must provide the corresponding parameters.

Table 2: Parameters used in the empirical force-field of Grimme [121].

Element	C$_6$	R$_0$	Element	C$_6$	R$_0$
	Jnm$^6$mol$-1$	Å		Jnm$^6$mol$-1$	Å
H	0.14	1.001	K	10.80	1.485
He	0.08	1.012	Ca	10.80	1.474
Li	1.61	0.825	Sc-Zn	10.80	1.562
Be	1.61	1.408	Ga	16.99	1.650
B	3.13	1.485	Ge	17.10	1.727
C	1.75	1.452	As	16.37	1.760
N	1.23	1.397	Se	12.64	1.771
O	0.70	1.342	Br	12.47	1.749
F	0.75	1.287	Kr	12.01	1.727
Ne	0.63	1.243	Rb	24.67	1.628
Na	5.71	1.144	Sr	24.67	1.606
Mg	5.71	1.364	Y-Cd	24.67	1.639
Al	10.79	1.716	In	37.32	1.672
Si	9.23	1.716	Sn	38.71	1.804
P	7.84	1.705	Sb	38.44	1.881
S	5.57	1.683	Te	31.74	1.892
Cl	5.07	1.639	I	31.50	1.892
Ar	4.61	1.595	Xe	29.99	1.881