Merge pull request #394 from jaapkroe/kolmogorov-crespi

\documentclass[12pt]{article}

\thispagestyle{empty}

\begin{document}

\begin{eqnarray*}

  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 ~\hspace{2cm} (\mathbf{n_i}\equiv\hat \mathbf{z})\\

  f(\rho) & = &  e^{-(\rho/\delta)^2} \sum_{n=0}^2 C_{2n} \left( \rho/\delta \right) ^{2n}

\end{eqnarray*}

\end{document}

"eff/cut"_pair_eff.html,

"exp6/rx"_pair_exp6_rx.html,

"gauss/cut"_pair_gauss.html,

"kolmogorov/crespi/z"_pair_kolmogorov_crespi_z.html,

"lennard/mdf"_pair_mdf.html,

"list"_pair_list.html,

"lj/charmm/coul/long/soft (o)"_pair_charmm.html,

pair_hbond_dreiding.html

pair_hybrid.html

pair_kim.html

pair_kolmogorov_crespi_z.html

pair_lcbop.html

pair_line_lj.html

pair_list.html

"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c

:link(lws,http://lammps.sandia.gov)

:link(ld,Manual.html)

:link(lc,Section_commands.html#comm)

:line

pair_style kolmogorov/crespi/z command :h3

[Syntax:]

pair_style hybrid/overlay kolmogorov/crespi/z cutoff :pre

[Examples:]

pair_style hybrid/overlay kolmogorov/crespi/z 20.0

pair_coeff * * none

pair_coeff 1 2 kolmogorov/crespi/z  CC.KC   C C :pre

pair_style hybrid/overlay rebo kolmogorov/crespi/z 14.0

pair_coeff * * rebo                 CH.airebo  C C

pair_coeff 1 2 kolmogorov/crespi/z  CC.KC      C C :pre

[Description:]

The {kolmogorov/crespi/z} style computes the Kolmogorov-Crespi interaction 

potential as described in "(KC05)"_#KC05. An important simplification is made, 

which is to take all normals along the z-axis. 

:c,image(Eqs/pair_kolmogorov_crespi_z.jpg)

It is important to have a suffiently large cutoff to ensure smooth forces. 

Energies are shifted so that they go continously to zero at the cutoff assuming 

that the exponential part of {Vij} (first term) decays sufficiently fast.

This shift is achieved by the last term in the equation for {Vij} 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 neighbouring layers.

The parameter file (e.g. CC.KC), is intended for use with metal 

"units"_units.html, with energies in meV. An additional parameter, {S}, 

is available to facilitate scaling of energies in accordance with 

"(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 "Making

LAMMPS"_Section_start.html#start_3 section for more info.

[Related commands:]

"pair_coeff"_pair_coeff.html

"pair_none"_pair_none.html

"pair_style hybrid/overlay"_pair_hybrid.html

[Default:] none

:line

:link(KC05) 

[(KC05)] A. N. Kolmogorov, V. H. Crespi, Phys. Rev. B 71, 235415 (2005)

:link(vanWijk) 

[(vanWijk)] M. M. van Wijk, A. Schuring, M. I. Katsnelson, and A. Fasolino, 

Physical Review Letters, 113, 135504 (2014)