C6 parameters

We consider the London’s formula: <math>E=3/2alphaa</math>

then arrived at an approximate expression for the C6 coefficient describing the vdW interaction between two atoms or molecules A and B.

<math>Insert formula here</math>

In case of A = B, we obtain <math>Insert formula here</math>

In solid metals fcc and hpc (surfaces), we calculated dipole moments and polarizabilities by integration of calculated charge densities vs applied external electric field (E).

All surface simulations will be represented by different slab thickness and an external electric field perpendicular to the slab will be imposed using the method implement in VASP and then:

1. The electronic charge densities for different values of electric field is computed; the different between this values and charge density without electric field is plotted against the distance from the bottom of the cell.

2. The integration of the curve give us the differential charge, q, we can use this value to compute the surface dipole moment (). We define the position vector like:

<math>Insert formula here</math>

3. We have the dipole, then, We can plot it versus the external electric field. The slope corresponds to the polarizability, in eAng/V.

4. Finally, these polarizabilities can be used to calculated the coefficients, as described below.

Table 1: Parameters for metals

Metals C6 (Jnm^6/mol) R0(Å)

Ni 2.6263 1.357

Pd 5.0242 1.374

Pt 5.3667 1.387

Cu 2.7404 1.261

Ag 5.4809 1.438

Au 7.3079 1.450

Ru 4.1678 1.639

Pb 18.155 1.749