In order to take care for the singularity (also removing the double counting of exchange-correlation) obtained with this expression, $$E_\mathrm{vdW} = \frac{C^6}{R^6}$$

many type of damping functions are utilized. Such as,

$$E_\mathrm{vdW} = \frac{C^6}{R^6} \cdot f_\mathrm{famp}(r)$$

One such damping function is, (Grimme type, Fermi function)

$$f_\mathrm{damp}(r) = \frac{s_6}{1+\exp\left[ -B\left(\frac{r^{AB}}{s_r R^{AB}_\mathrm{vdW}}\right)\right]}$$

when, $r$ = interatomic distance, $R^{AB}_\mathrm{vdW}$ or (R) is summation of vdW radius of two atoms $s_6$ and $s_r$ are two parameters. $s_6$ depend upon the XC functional and $s_r$ is another scaling factor. $B$ is the exponent.

Literature$^{[1]}$ suggests that value for $B$ is found by setting $f_\mathrm{damp} = 0.99$ when $r = 1.2 \cdot R$.

Also, the value of these parameters can also be found from here.

To my knowledge, these values are optimized for each functional. Is there any physical meaning to these values of the parameters? Actually, I am more interested in the $s_r$ value and if this has any physical significance...

[1] J Chem Phys, 116, 515(2002)



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