# pair_style lebedeva/z command

## Syntax

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

## Examples

``` LAMMPS
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)](Leb01) and [(Lebedeva2)](Leb02). 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](pair_airebo) or [Tersoff](pair_tersoff) facilitated by
using pair style [hybrid/overlay](pair_hybrid). 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*.

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

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)](Popov)
-   The second set (element name \"C1\") is suitable for high-pressure
    conditions and is taken from [(Koziol1)](Koziol)

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](Build_package) page for more info.

## Related commands

[pair_coeff](pair_coeff), [pair_style none](pair_none), [pair_style
hybrid/overlay](pair_hybrid), [pair_style drip](pair_drip), [pair_style
ilp/graphene/hbd](pair_ilp_graphene_hbn), [pair_style
kolmogorov/crespi/z](pair_kolmogorov_crespi_z), [pair_style
kolmogorov/crespi/full](pair_kolmogorov_crespi_full).

## Default

none

------------------------------------------------------------------------

::: {#Leb01}
**(Lebedeva1)** I. V. Lebedeva, A. A. Knizhnik, A. M. Popov, Y. E.
Lozovik, B. V. Potapkin, Phys. Rev. B, 84, 245437 (2011)
:::

::: {#Leb02}
**(Lebedeva2)** I. V. Lebedeva, A. A. Knizhnik, A. M. Popov, Y. E.
Lozovik, B. V. Potapkin, Physica E: 44, 949-954 (2012)
:::

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

::: {#Koziol}
**(Koziol1)** Z. Koziol, G. Gawlik and J. Jagielski, Chinese Phys. B 28,
096101 (2019).
:::