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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
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.  for details) is as follows
is the frequency-dependent polarizability
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_alpha, VDW_C6, VDW_R0
(described in sec. 6.77.3).This method has one free parameter () that must be adjusted
for each exchange-correlation functional. The default value of
(0.83) corresponds to PBE functional;
if other functional is used,
the value of must be specified via VDW_SR
The MBD@rsSCS method is invoked by
defining IVDW=202. Optionally, the following
parameters can be user-defined:
||write the two- to six- body contributions to MBD
||dispersion energy in the output file (OUTCAR) - noyes
||compute gradients - yesno
Details of implementation of the MBD@rsSCS method in VASP
are presented in
J. Phys: Condens. Matter 28, 045201 (2016).
- 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. ) 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.
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