Real-World Predictions from Ab Initio Molecular Dynamics Simulations - Multiscale Molecular Methods in Applied Chemistry - page 128

With N at being the number of atoms in the system, C i 6 denotes the dispersion
coefficient for an atom pair ij , s 6 is a global scaling factor that only depends on the
DFT functional used, and R ij is an interatomic distance. To avoid near-singularities
the damping function f dmp was added:

1

f dmp ð R Þ¼

Þ :

(39)

1 þ e a ð R = R 0 1

is a scaling factor [ 54 ]. The
C 6 coefficients were partly taken from the literature [ 54 ], but also newly averaged
over possible hybridization states of the individual atoms. Mixing rules of the
following kind:

Here R 0 is the sum of van der Waals radii and a

C j 6

C i 6

2

C i 6 ¼ (40)

C j 6

C i 6 þ

were applied. This approach was termed DFT-D2 by Grimme [ 56 ].
As the fragment densities of hydrogen bonded systems significantly overlap,
these kinds of interactions are well described by standard DFT. However, if errors
of 10-30% need to be corrected, Grimme recommended his dispersion correction
scheme. As a consequence, Grimme mentioned the fact that steep damping
functions need to be applied in order to retain the original DFT description as
closely as possible in hydrogen bonded systems [ 54 ]. An improvement of the
original approach followed in 2006 [ 55 ], where Grimme stated that the following
shortcomings were addressed:

1. Consistent atomic parameters ( C 6 coefficients) were only available for elements
H, C-Ne, but studies of supramolecular structures or problems in material
science require parameters for elements from the whole periodic table.
2. Test calculations for molecules with third-row elements showed systematic
errors.
3. Adding the dispersion energy to the KS-DFT energy led to inconsistencies for
“normal” thermochemistry, e.g., atomization energies: the dispersion correction
is zero for the free atom and always nonzero (and large) for the molecule.

In order to account for these problems Grimme reduced the scaling factor from
1.22 to 1.10, which improved computed intermolecular distances for systems with
heavier atoms [ 55 ]. Smaller values of from the damping functions were chosen

which provided larger corrections at intermediate distances and at negligible
dispersion energies for typical covalent bonding situations. Furthermore, Grimme
applied a new combination rule:

a

q

C i 6 C i 6 ¼ C 6

(41)