# pair_style lj/switch3/coulgauss/long command

# pair_style mm3/switch3/coulgauss/long command

## Syntax

``` LAMMPS
pair_style style args
```

-   style = *lj/switch3/coulgauss/long* or *mm3/switch3/coulgauss/long*
-   args = list of arguments for a particular style

<!-- -->

    *lj/switch3/coulgauss/long* args = cutoff (cutoff2) width
      cutoff  = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
      cutoff2 = global cutoff for Coulombic (optional) (distance units)
      width  = width parameter of the smoothing function (distance units)

    *mm3/switch3/coulgauss/long* args = cutoff (cutoff2) width
      cutoff  = global cutoff for MM3 (and Coulombic if only 1 arg) (distance units)
      cutoff2 = global cutoff for Coulombic (optional) (distance units)
      width  = width parameter of the smoothing function (distance units)

## Examples

``` LAMMPS
pair_style lj/switch3/coulgauss/long    12.0 3.0
pair_coeff 1  0.2 2.5 1.2

pair_style lj/switch3/coulgauss/long   12.0 10.0 3.0
pair_coeff 1  0.2 2.5 1.2

pair_style mm3/switch3/coulgauss/long    12.0 3.0
pair_coeff 1  0.2 2.5 1.2

pair_style mm3/switch3/coulgauss/long   12.0 10.0 3.0
pair_coeff 1  0.2 2.5 1.2
```

## Description

The *lj/switch3/coulgauss* style evaluates the LJ vdW potential

$$E = 4\epsilon \left[ \left(\frac{\sigma}{r}\right)^{12}-\left(\frac{\sigma}{r}\right)^{6} \right]$$

The *mm3/switch3/coulgauss/long* style evaluates the MM3 vdW potential
[(Allinger)](mm3-allinger1989)

$$\begin{aligned}
E & = \epsilon_{ij} \left[ -2.25 \left(\frac{r_{v,ij}}{r_{ij}}\right)^6 + 1.84(10)^5 \exp\left[-12.0 r_{ij}/r_{v,ij}\right] \right] S_3(r_{ij}) \\
r_{v,ij} & =  r_{v,i} + r_{v,j} \\
\epsilon_{ij} & = \sqrt{\epsilon_i \epsilon_j}
\end{aligned}$$

Both potentials go smoothly to zero at the cutoff r_c as defined by the
switching function

$$\begin{aligned}
S_3(r) = \left\lbrace \begin{array}{ll}
                    1 & \quad\mathrm{if}\quad r < r_\mathrm{c} - w \\
                    3x^2 - 2x^3 & \quad\mathrm{if}\quad r < r_\mathrm{c} \quad\mathrm{with\quad} x=\frac{r_\mathrm{c} - r}{w} \\
                    0 & \quad\mathrm{if}\quad r >= r_\mathrm{c}
                \end{array} \right.
\end{aligned}$$

where w is the width defined in the arguments. This potential is
combined with Coulomb interaction between Gaussian charge densities:

$$E = \frac{q_i q_j \mathrm{erf}\left( r/\sqrt{\gamma_1^2+\gamma_2^2} \right) }{\epsilon r_{ij}}$$

where $q_i$ and $q_j$ are the charges on the 2 atoms, $\epsilon$ is the
dielectric constant which can be set by the [dielectric](dielectric)
command, $\gamma_i$ and $\gamma_j$ are the widths of the Gaussian charge
distribution and erf() is the error-function. This style has to be used
in conjunction with the [kspace_style](kspace_style) command

If one cutoff is specified it is used for both the vdW and Coulomb
terms. If two cutoffs are specified, the first is used as the cutoff for
the vdW terms, and the second is the cutoff for the Coulombic term.

The following coefficients must be defined for each pair of atoms types
via the [pair_coeff](pair_coeff) command as in the examples above, or in
the data file or restart files read by the [read_data](read_data) or
[read_restart](read_restart) commands:

-   $\epsilon$ (energy)
-   $\sigma$ (distance)
-   $\gamma$ (distance)

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

## 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/long pair styles can be mixed. The
default mix value is *geometric*. See the \"pair_modify\" command for
details.

Shifting the potential energy is not necessary because the switching
function ensures that the potential is zero at the cut-off.

These pair styles support the [pair_modify](pair_modify) table and
options since they can tabulate the short-range portion of the
long-range Coulombic interactions.

Thes pair styles do not support the [pair_modify](pair_modify) tail
option for adding a long-range tail correction to the Lennard-Jones
portion of the energy and pressure.

These pair styles write their information to [binary restart
files](restart), so pair_style and pair_coeff commands do not need to be
specified in an input script that reads a restart file.

These pair styles can only be used via the *pair* keyword of the
[run_style respa](run_style) command. They do not support the *inner*,
*middle*, *outer* keywords.

## Restrictions

These styles are part of the YAFF package. They are 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)

## Default

none