Add documentation

\documentclass[12pt]{article}

\usepackage{amsmath}

\usepackage{bm}

\begin{document}

\begin{eqnarray*}

E &=& \frac{1}{2} \sum_{i} \sum_{j\notin\text{layer}\,i} (\phi_{ij} + \phi_{ji}) \\

\phi_{ij} &=& f_\text{c}(x_r) \left[ e^{-\lambda(r_{ij} - z_0 )} \left[C+f(\rho_{ij})+  g(\rho_{ij}, \{\alpha_{ij}^{(m)}\}) \right]- A\left (\frac{z_0}{r_{ij}} \right)^6 \right] \\

\end{eqnarray*}  

\end{document}

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

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

:link(ld,Manual.html)

:link(lc,Commands_all.html)

:line

pair_style drip command :h3

[Syntax:]

pair_style hybrid/overlay drip \[styles ...\] :pre

styles = other styles to be overlayed with drip (optional) :ul

[Examples:]

pair_style hybrid/overlay drip

pair_coeff * * none

pair_coeff * * drip  C.drip  C :pre

pair_style hybrid/overlay drip rebo

pair_coeff * * drip  C.drip     C

pair_coeff * * rebo  CH.airebo  C :pre

pair_style hybrid/overlay drip rebo

pair_coeff * * drip  C.drip     C NULL

pair_coeff * * rebo  CH.airebo  C H :pre

[Description:]

Style {drip} computes the interlayer interactions of layered materials using

the dihedral-angle-corrected registry-dependent (DRIP) potential as described

in "(Wen)"_#Wen1, which is based on the "(Kolmogorov)"_#Kolmogorov1 potential

and provides an improvded prediction for forces.

The total potential energy of a system is

:c,image(Eqs/pair_drip.jpg)

where the {r^-6} term models the attractive London dispersion,

the exponential term is designed to capture the registry effect due to

overlapping {pi} bonds, and {fc} is a cutoff function.

This potential (DRIP) only provides the interlayer interactions between

graphene layers. So, to perform a realistic simulation, it should be used in

combination with an intralayer potential such as "REBO"_pair_airebo.html and

"Tersoff"_pair_tersoff.html.

To keep the intralayer interactions unaffected, we should avoid applying DRIP

to contribute energy to intralayer interactions. This can be achieved by

assigning different molecular IDs to atoms in different layers, and DRIP is

implemented such that only atoms with different molecular ID can interact with

each other. For this purpose, "atom style"_atom_style.html "molecular" or

"full" has to be used.

On the other way around, "REBO"_pair_airebo.html ("Tersoff"_pair_tersoff.html

or any other potential used to provide the intralayer interactions) should not

interfere with the interlayer interactions described by DRIP. This is typically

automatically achieved using the commands provided in the {Examples} section

above, since the cutoff distance for carbon-carbon interaction in the intralayer

potentials (e.g. 2 Angstrom for "REBO"_pair_airebo.html) is much smaller than

the equilibrium layer distance of graphene layers (about 3.4 Angstrom).

If you want, you can enforce this by assigning different atom types to atoms in

different layers, and apply an intralayer potential to one atom type.

See "pair_hybrid"_pair_hybrid.html for details.

:line

The "pair_coeff"_pair_coeff.html command for DRIP takes {4+N} arguments, where

{N} is the number of LAMMPS atom types. The fist three arguments must be fixed

to be {* * drip}, the fourth argument is the path to the DRIP parameter file,

and the remaining N arguments specifying the mapping between element in the

parameter file and atom types. For example, if your LAMMPS simulation has 3 atom

types and you want all of them to be C, you would use the following pair_coeff

command:

pair_coeff * * drip  C.drip  C C C :pre

If a mapping value is specified as NULL, the mapping is not performed. This

could be useful when DRIP is used to model part of the system where other

element exists. Suppose you have a hydrocarbon system, with C of atom type 1

and H of atom type 2, you can use the following command to inform DRIP not to

model H atoms:

pair_style hybrid/overlay drip rebo

pair_coeff * * drip  C.drip     C NULL

pair_coeff * * rebo  CH.airebo  C H :pre

NOTE: The parameter file developed in "(Wen)"_#Wen1 is provided with LAMMPS (see

the "potentials" directory).

:line

[Mixing, shift, table, tail correction, and restart info]:

This pair style does not support the pair_modify mix, shift, table,

and tail options.

This pair style does not write their information to binary restart files, since

it is stored in potential files. Thus, you need to re-specify the pair_style and

pair_coeff commands in an input script that reads a restart file.

[Restrictions:]

This pair style is part of the USER-MISC package. It is only enabled if LAMMPS

was built with that package.  See the "Build package"_Build_package.html doc

page for more info.

This pair potential requires the "newton"_newton.html setting to be "on" for

pair interactions.

The {C.drip} parameter file provided with LAMMPS (see the "potentials"

directory) is parameterized for metal "units"_units.html. You can use the DRIP

potential with any LAMMPS units, but you would need to create your own cutstom

parameter file with coefficients listed in the appropriate units, if your

simulation doesn't use "metal" units.

[Related commands:]

"pair_style lebedeva_z"_pair_lebedeva_z.html,

"pair_style kolmogorov/crespi/z"_pair_kolmogorov_crespi_z.html,

"pair_style kolmogorov/crespi/full"_pair_kolmogorov_crespi_full.html,

"pair_style ilp/graphene/hbn"_pair_ilp_graphene_hbn.html.

:line

:link(Wen1)

[(Wen)] M. Wen, S. Carr, S. Fang, E. Kaxiras, and E. B. Tadmor, Phys. Rev. B, 98, 235404 (2018)

:link(Kolmogorov1)

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

   pair_dipole

   pair_dpd

   pair_dpd_fdt

   pair_drip

   pair_dsmc

   pair_eam

   pair_edip

pair_style coul/diel, Axel Kohlmeyer, akohlmey at gmail.com, 1 Dec 11

pair_style coul/shield, Wengen Ouyang (Tel Aviv University), w.g.ouyang at gmail dot com, 30 Mar 18

pair_style dipole/sf, Mario Orsi, orsimario at gmail.com, 8 Aug 11

pair_style drip, Mingjian Wen, University of Minnesota, wenxx151 at umn.edu, 17 Apr 19

pair_style edip, Luca Ferraro, luca.ferraro at caspur.it, 15 Sep 11

pair_style extep, Jaap Kroes (Radboud U), jaapkroes at gmail dot com, 28 Nov 17

pair_style gauss/cut, Axel Kohlmeyer, akohlmey at gmail.com, 1 Dec 11