Many-body dispersion energy method

The many-body dispersion energy method (MBD@rsSCS) of Tkatchenko et al. [130,137] is based on the random phase expression of correlation energy

whereby the response function is approximated by a sum of atomic contributions represented by quantum harmonic oscillators. The expression for dispersion energy used in our k-space implementation of the MBD@rsSCS method (see Ref. [136] for details) is as follows

where is the frequency-dependent polarizability matrix and 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 are obtained using an atoms-in-molecule approach as employed in the pairwise Tkatchenko-Scheffler method (see Ref. [137,136] for details); the input reference data for non-interacting atoms can be optionally defined via parameters

VDW_SR |
= 0.83 | scaling parameter |

LVDWEXPANSION |
=.FALSE..TRUE. | write the two- to six- body contributions to MBD |

dispersion energy in the output file (OUTCAR) - noyes | ||

LSCSGRAD |
=.TRUE..FALSE. | compute gradients - yesno |

Details of implementation of the MBD@rsSCS method in VASP are presented in J. Phys: Condens. Matter 28, 045201 (2016).

IMPORTANT NOTES:

- this method requires the use of POTCAR files from the PAW dataset version 52 or later
- the input reference
data for non-interacting atoms are available only for elements
of the first six rows of periodic table except of lanthanides.
If the system contains other elements, the user must provide
the free-atomic parameters for all atoms in the system
via
`VDW_alpha`,`VDW_C6`,`VDW_R0`(described in sec. 6.77.3) defined in the INCAR file. - the charge-density dependence of gradients is neglected
- this method is incompatible with the setting
`ADDGRID=.TRUE.` - it is essential that a sufficiently dense FFT grid (controlled via
`NGFX(Y,Z)`) is used in the DFT-TS - we strongly recommend to use`PREC=Accurate`for this type of calculations (in any case, avoid using`PREC=Low`). - the method has sometimes numerical problems if highly
polarizable atoms are located at short distances.
In such a case the calculation terminates
with an error message (
`Error(vdw_tsscs_range_separated_k): d_lr(pp)<=0`). Note that this problem is not caused by a bug but rather it is due to a limitation of the underlying physical model. - analytical gradients of energy are implemented (fore details see Ref. [136]) and hence the atomic and lattice relaxations can be performed
- due to the long-range nature of dispersion interactions, the convergence of energy with respect to the number of k-points should be carefully examined
- a default value for the free-parameter of this method (
`VDW_SR`=0.83) is available only for the PBE functional. If the functional other than PBE is used, the value of`VDW_SR`must be specified in INCAR.