Keyword DISPERSION

This keyword adds an empirical dispersion term to the electronic energy and its derivatives. The correction is limited to the dipolar C$_6$ term.
Options:
ON / OFF

	ON		An empirical dispersion term is added.
	OFF		No empirical dispersion term is added.
	READ		The C$_6$ coefficients are read from the input file.
	S6=$<$Real$>$		Global scaling factor. The default value is 1.0.

Description:
The empirical dispersion energy available in deMon2k is given by [26]:

$$E_{disp} = - S_6 \, \sum_A \sum_{B > A} f(R_{AB}) \, {C_6^{AB} \over {R_{AB}^6}}%$$ (2)

Here $R_{AB}$ denotes the distance between atoms $A$ and $B$, while $S_6$ is a global scaling factor that adapts the empirical dispersion formula to the specified exchange functional [121]. The default value of $S_6 = 1$ should be used in combination with the revised PBE exchange functionals PBE98 and PBE99 (see Table 5). Their use in combination with the LYP correlation functional is recommended. The function $f(R_{AB})$ is a damping term that switches off the dispersion correction at short range. It is chosen as a Fermi type function

$$f(R_{AB}) = {1 \over {1 + e^{- \alpha \left ( {{R_{AB}} \over {R_o}} - 1 \right )} }} \> ,%$$ (3)

with the empirical parameter $\alpha$ set to 23. The symbol $R_o$ denotes the sum of the van der Waals radii [122] of the two atoms $A$ and $B$. The diatomic $C_6$ coefficients in (4.2) are calculated from the atomic $C_6$ coefficients by the formula

$$C_6^{AB} = {{2 \, C_6^A \, C_6^B} \over {C_6^A + C_6^B}} \> .%$$ (4)

For the elements H, C, N and O, atomic $C_6$ coefficients from Wu and Yang [123] are available within deMon2k. Distinct from the original suggestion, however, they are averaged over all possible hybridization states of the atom. For all other elements the $C_6$ coefficients from the universal force field [124] are used in deMon2k. The user can provide $C_6$ coefficients in the input file with the READ option of the DISPERSION keyword. User defined $C_6$ coefficients will override the default values. Different $C_6$ coefficients can be assigned to individual atoms by the atomic symbol (e.g. F1) or to atom groups by the element symbol (e.g. F) in the keyword body of DISPERSION:

 DISPERSION READ
 F1  10.74

Here the $C_6$ dispersion coefficient must be given in atomic units. Atoms for which $C_6$ coefficients are set to zero do not contribute to the deMon2k dispersion energy.