\(\renewcommand{\AA}{\text{Å}}\)

# pair_style kolmogorov/crespi/z command

## Syntax

    pair_style [hybrid/overlay ...] kolmogorov/crespi/z cutoff

## Examples

    pair_style hybrid/overlay kolmogorov/crespi/z 20.0
    pair_coeff * * none
    pair_coeff 1 2 kolmogorov/crespi/z  CC.KC   C C

    pair_style hybrid/overlay rebo kolmogorov/crespi/z 14.0
    pair_coeff * * rebo                 CH.rebo    C C
    pair_coeff 1 2 kolmogorov/crespi/z  CC.KC      C C

## Description

The kolmogorov/crespi/z style computes the Kolmogorov-Crespi interaction potential as described in (Kolmogorov). An important simplification is made, which is to take all normals along the z-axis.

\[\begin{split}E = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\ V_{ij} = & e^{-\lambda(r_{ij} -z_0)} \left[ C + f(\rho_{ij}) + f(\rho_{ji}) \right] - A \left( \frac{r_{ij}}{z_0}\right)^{-6} + A \left( \frac{\textrm{cutoff}}{z_0}\right)^{-6} \\ \rho_{ij}^2 = & \rho_{ji}^2 = x_{ij}^2 + y_{ij}^2 \qquad \qquad (\mathbf{n}_i \equiv \mathbf{\hat{z}}) \\ f(\rho) = & e^{-(\rho/\delta)^2} \sum_{n=0}^2 C_{2n} \left( \rho/\delta \right)^{2n}\end{split}\]

It is important to have a sufficiently large cutoff to ensure smooth forces. Energies are shifted so that they go continuously to zero at the cutoff assuming that the exponential part of \(V_{ij}\) (first term) decays sufficiently fast. This shift is achieved by the last term in the equation for \(V_{ij}\) above.

This potential is intended for interactions between two layers of graphene. Therefore, to avoid interaction between layers in multi-layered materials, each layer should have a separate atom type and interactions should only be computed between atom types of neighboring layers.

The parameter file (e.g. CC.KC), is intended for use with metal units, with energies in meV. An additional parameter, S, is available to facilitate scaling of energies in accordance with (vanWijk).

This potential must be used in combination with hybrid/overlay. Other interactions can be set to zero using pair_style none.

## Restrictions

This fix is part of the INTERLAYER package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

## Related commands

pair_coeff, pair_none, pair_style hybrid/overlay, pair_style drip, pair_style ilp/graphene/hbn. pair_style kolmogorov/crespi/full, pair_style lebedeva/z

## Default

none

(Kolmogorov) A. N. Kolmogorov, V. H. Crespi, Phys. Rev. B 71, 235415 (2005)

(vanWijk) M. M. van Wijk, A. Schuring, M. I. Katsnelson, and A. Fasolino, Physical Review Letters, 113, 135504 (2014)