Merge pull request #1448 from akohlmey/collected-small-changes

\documentclass[12pt]{article}

\pagestyle{empty}

\begin{document}

$$

   E(r) = \frac{A}{r^{12}} - \frac{A}{r^{6}}

   E(r) = \frac{A}{r^{12}} - \frac{B}{r^{6}}

$$

\end{document}

[Examples:]

pair_style lj/mdf 2.5 3.0

pair_coeff * * 1 1

pair_coeff 1 1 1 1.1 2.8 3.0 3.2 :pre

pair_coeff * * 1.0 1.0

pair_coeff 1 1 1.1 2.8 3.0 3.2 :pre

pair_style buck 2.5 3.0

pair_coeff * * 100.0 1.5 200.0

pair_coeff * * 100.0 1.5 200.0 3.0 3.5 :pre

pair_style lennard/mdf 2.5 3.0

pair_coeff * * 1 1

pair_coeff 1 1 1 1.1 2.8 3.0 3.2 :pre

pair_coeff * * 1.0 1.0

pair_coeff 1 1 1021760.3664 2120.317338 3.0 3.2 :pre

[Description:]

:c,image(Eqs/pair_mdf-4.jpg)

The following coefficients must be defined for each pair of atoms

types via the pair_coeff command as in the examples above, or in the

data file or restart files read by the "read_data"_read_data.html or

"read_restart commands"_read_restart.html, or by mixing as described

below:

Either the first two or all of the following coefficients must be

defined for each pair of atoms types via the pair_coeff command as

in the examples above, or in the data file read by the

"read_data"_read_data.html. The two cutoffs default to the global

values and epsilon and sigma can also be determined by mixing as

described below:

epsilon (energy units)

sigma (distance units)

:line

For the {buck/mdf} pair_style, the potential energy, {E(r)}, is the

standard Buckingham potential:

standard Buckingham potential with three required coefficients.

The two cutoffs can be omitted and default to the corresponding

global values:

:c,image(Eqs/pair_mdf-5.jpg)

\rho (distance units)

C (energy-distance^6 units)

r_m (distance units)

r_{cut}$ (distance units) :ul

r_{cut} (distance units) :ul

:line

For the {lennard/mdf} pair_style, the potential energy, {E(r)}, is the

standard 12-6 Lennard-Jones written in the $A/B$ form:

standard 12-6 Lennard-Jones written in the A/B form:

:c,image(Eqs/pair_mdf-6.jpg)

The following coefficients must be defined for each pair of atoms

types via the pair_coeff command as in the examples above, or in the

data file or restart files read by the read_data or read_restart

commands, or by mixing as described below:

data file read by the read_data commands, or by mixing as described below.

The two cutoffs default to their global values and must be either both

given or both left out:

A (energy-distance^12 units)

B (energy-distance^6 units)

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

For atom type pairs I,J and I != J, the epsilon and sigma coefficients

and cutoff distance for all of the lj/cut pair styles can be mixed.

and cutoff distances for the lj/mdf pair style can be mixed.

The default mix value is {geometric}.  See the "pair_modify" command

for details.

All of the {lj/cut} pair styles support the

"pair_modify"_pair_modify.html shift option for the energy of the

Lennard-Jones portion of the pair interaction.

The {lj/cut/coul/long} and {lj/cut/tip4p/long} pair styles support the

"pair_modify"_pair_modify.html table option since they can tabulate

the short-range portion of the long-range Coulombic interaction.

All of the {lj/cut} pair styles support the

"pair_modify"_pair_modify.html tail option for adding a long-range

tail correction to the energy and pressure for the Lennard-Jones

portion of the pair interaction.

All of the {lj/cut} pair styles write their information to "binary

restart files"_restart.html, so pair_style and pair_coeff commands do

not need to be specified in an input script that reads a restart file.

The {lj/cut} and {lj/cut/coul/long} pair styles support the use of the

{inner}, {middle}, and {outer} keywords of the "run_style

respa"_run_style.html command, meaning the pairwise forces can be

partitioned by distance at different levels of the rRESPA hierarchy.

The other styles only support the {pair} keyword of run_style respa.

See the "run_style"_run_style.html command for details.

for details. The other two pair styles buck/mdf and lennard/mdf do not

support mixing, so all I,J pairs of coefficients must be specified

explicitly.

None of the lj/mdf, buck/mdf, or lennard/mdf pair styles supports

the "pair_modify"_pair_modify.html shift option or long-range

tail corrections to pressure and energy.

These styles write their information to "binary restart

files"_restart.html, so pair_style and pair_coeff commands do not need

to be specified in an input script that reads a restart file.

These styles can only be used via the {pair} keyword of the "run_style

respa"_run_style.html command.  They do not support the {inner},

{middle}, {outer} keywords.

:line

option of "write_data"_write_data.html this can be used to move

the Coeffs sections from a data file into a separate file.

NOTE: The write_coeff command is not yet fully implemented in two

respects.  First, some pair styles do not yet write their coefficient

information into the coeff file.  This means you will need to specify

that information in your input script that reads the data file, via

the "pair_coeff"_pair_coeff.html command.

NOTE: The write_coeff command is not yet fully implemented as

some pair styles do not output their coefficient information.

This means you will need to add/copy this information manually.

:line

  int *sametag = atom->sametag;

  double **sp = atom->sp;

  double **fm = atom->fm;

  double msq,scale,fm2,energy,dts2;

  double fm2,energy,dts2;

  double cp[3],g[3];

  cp[0] = cp[1] = cp[2] = 0.0;