# pair_style mm3/switch3/coulgauss/long command¶

## Syntax¶

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¶

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)

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

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

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

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 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 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 command as in the examples above, or in the data file or restart files read by the read_data or 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 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 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, 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 command. They do not support the inner, middle, outer keywords.

## Restrictions¶

These styles are part of the USER-YAFF package. They are only enabled if LAMMPS was built with that package. See the Build package doc page for more info.

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