.. index:: pair_style kolmogorov/crespi/z

pair_style kolmogorov/crespi/z command
======================================

Syntax
""""""

.. code-block:: LAMMPS

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

Examples
""""""""

.. code-block:: LAMMPS

   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 :ref:`(Kolmogorov) <KC05>`. An important simplification is made,
which is to take all normals along the z-axis.

.. math::

   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}

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 :math:`V_{ij}` (first term) decays sufficiently fast.
This shift is achieved by the last term in the equation for :math:`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
:doc:`units <units>`, with energies in meV. An additional parameter, *S*\ ,
is available to facilitate scaling of energies in accordance with
:ref:`(vanWijk) <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 USER-MISC package.  It is only enabled if
LAMMPS was built with that package.  See the :doc:`Build package <Build_package>` doc page for more info.

Related commands
""""""""""""""""

:doc:`pair_coeff <pair_coeff>`,
:doc:`pair_none <pair_none>`,
:doc:`pair_style hybrid/overlay <pair_hybrid>`,
:doc:`pair_style drip <pair_drip>`,
:doc:`pair_style ilp/graphene/hbn <pair_ilp_graphene_hbn>`.
:doc:`pair_style kolmogorov/crespi/full <pair_kolmogorov_crespi_full>`,
:doc:`pair_style lebedeva/z <pair_lebedeva_z>`

**Default:** none

----------

.. _KC05:

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

.. _vanWijk:

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