# pair_style mm3/switch3/coulgauss/long command

## Syntax

pair_style style args

• style = mm3/switch3/coulgauss/long

• args = list of arguments for a particular style

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 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 mm3/switch3/coulgauss/long style evaluates the MM3 vdW potential (Allinger)

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

, which goes 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)

• $$r_v$$ (distance)

• $$\gamma$$ (distance)

## Mixing, shift, table, tail correction, restart, rRESPA info

Mixing rules are fixed for this style as defined above.

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

## 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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