User:Szggr/sandbox/Tkatchenko-Scheffler method

The Tkatchenko-Scheffler (TS) method is a computational chemistry method to model van der Waals parameters based on free atomic data. The model gives a good approximation for the $C_{6}$ pairwise interaction term.

Formulation

A good approximation for van der Waals interactions is a pairwise approximation in the form:

$E_{vdW}=-{\frac {1}{2}}\sum _{A,B}f_{damp}(R_{AB},R_{A}^{0},R_{B}^{0})C_{6AB}R_{AB}^{-6}$ (1)

The sum is over all atoms in the system $A,B$, the function $f_{damp}(R_{AB},R_{A}^{0},R_{B}^{0})$ is a damping function that, in general, can depend on the free atom van der Waals radii and the distance between atoms $A$ and $B$. The damping function used in the original method is:

$f_{damp}(R_{AB},R_{A}^{0},R_{B}^{0})={\frac {1}{1+\exp {[-d(-1+R_{AB}/s_{R}R_{AB}^{0})]}}}$ (2)

with using the sum of atomic radii $R_{AB}^{0}=R_{A}^{0}+R_{B}^{0}$ and having $s_{R}$ and $d$ as free parameters to fit.

According to the formula of Equation (1), a full description of the van der Waals forces in this approximation consists of determining the $C_{6AB}$ coefficients for the set of atomic radii used. The Tkatchenko-Scheffler method expressed the heteronuclear parameter $C_{6AB}$ as a function of homonuclear $C_{6AA}$ parameters with the following combination rule:

$C_{6AB}={\frac {2C_{6AA}C_{6BB}}{{\frac {\alpha _{B}}{\alpha _{A}}}C_{6AA}+{\frac {\alpha _{A}}{\alpha _{B}}}C_{6BB}}}$ (3)

The original work is based on free atom reference data of Chu and Dalgarno.

External links

• www.example.com