\(\renewcommand{\AA}{\text{Å}}\)

# pair_style lebedeva/z command

## Syntax

    pair_style [hybrid/overlay ...] lebedeva/z cutoff

## Examples

    pair_style hybrid/overlay lebedeva/z 20.0
    pair_coeff * * none
    pair_coeff 1 2 lebedeva/z  CC.Lebedeva   C C

    pair_style hybrid/overlay rebo lebedeva/z 14.0
    pair_coeff * * rebo        CH.rebo       C C
    pair_coeff 1 2 lebedeva/z  CC.Lebedeva   C C

## Description

The lebedeva/z pair style computes the Lebedeva interaction potential as described in (Lebedeva1) and (Lebedeva2). An important simplification is made, which is to take all normals along the z-axis.

The Lebedeva potential is intended for the description of the interlayer interaction between graphene layers. To perform a realistic simulation, this potential must be used in combination with an intralayer potential such as AIREBO or Tersoff facilitated by using pair style hybrid/overlay. To keep the intralayer properties unaffected, the interlayer interaction within the same layers should be avoided. This can be achieved by assigning different atom types to atoms of different layers (e.g. 1 and 2 in the examples above).

Other interactions can be set to zero using pair_style none.

\[\begin{split}E = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij}\\ V_{ij} = & B e^{-\alpha(r_{ij} - z_0)} \\ & + C(1 + D_1\rho^2_{ij} + D_2\rho^4_{ij}) e^{-\lambda_1\rho^2_{ij}} e^{-\lambda_2 (z^2_{ij} - z^2_0)} \\ & - A \left(\frac{z_0}{r_ij}\right)^6 + A \left( \frac{z_0}{r_c} \right)^6 \\ \rho^2_{ij} = & x^2_{ij} + y^2_{ij} \qquad (\mathbf{n_i} \equiv \mathbf{\hat{z}})\end{split}\]

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.

The provided parameter file (CC.Lebedeva) contains two sets of parameters.

- The first set (element name “C”) is suitable for normal conditions and is taken from (Popov1)

- The second set (element name “C1”) is suitable for high-pressure conditions and is taken from (Koziol1)

Both sets contain an additional parameter, S, that can be used to facilitate scaling of energies and is set to 1.0 by default.

## Restrictions

This pair style 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_style none, pair_style hybrid/overlay, pair_style drip, pair_style ilp/graphene/hbd, pair_style kolmogorov/crespi/z, pair_style kolmogorov/crespi/full.

## Default

none

(Lebedeva1) I. V. Lebedeva, A. A. Knizhnik, A. M. Popov, Y. E. Lozovik, B. V. Potapkin, Phys. Rev. B, 84, 245437 (2011)

(Lebedeva2) I. V. Lebedeva, A. A. Knizhnik, A. M. Popov, Y. E. Lozovik, B. V. Potapkin, Physica E: 44, 949-954 (2012)

(Popov1) A.M. Popov, I. V. Lebedeva, A. A. Knizhnik, Y. E. Lozovik and B. V. Potapkin, Chem. Phys. Lett. 536, 82-86 (2012).

(Koziol1) Z. Koziol, G. Gawlik and J. Jagielski, Chinese Phys. B 28, 096101 (2019).