# pair_style lennard/mdf command¶

## Syntax¶

pair_style style args

• style = lj/mdf or buck/mdf or lennard/mdf

• args = list of arguments for a particular style

lj/mdf args = cutoff1 cutoff2
cutoff1 = inner cutoff for the start of the tapering function
cutoff1 = out cutoff for the end of the tapering function
buck/mdf args = cutoff1 cutoff2
cutoff1 = inner cutoff for the start of the tapering function
cutoff1 = out cutoff for the end of the tapering function
lennard/mdf args = cutoff1 cutoff2
cutoff1 = inner cutoff for the start of the tapering function
cutoff1 = out cutoff for the end of the tapering function

## Examples¶

pair_style lj/mdf 2.5 3.0
pair_coeff * * 1.0 1.0
pair_coeff 1 1 1.1 2.8 3.0 3.2

pair_style buck/mdf 2.5 3.0
pair_coeff * * 100.0 1.5 200.0
pair_coeff * * 100.0 1.5 200.0 3.0 3.5

pair_style lennard/mdf 2.5 3.0
pair_coeff * * 1.0 1.0
pair_coeff 1 1 1021760.3664 2120.317338 3.0 3.2


## Description¶

The lj/mdf, buck/mdf and lennard/mdf compute the standard 12-6 Lennard-Jones and Buckingham potential with the addition of a taper function that ramps the energy and force smoothly to zero between an inner and outer cutoff.

$E_{smooth}(r) = E(r)*f(r)$

The tapering, f(r), is done by using the Mei, Davenport, Fernando function (Mei).

$\begin{split}f(r) & = 1.0 \qquad \qquad \mathrm{for} \qquad r < r_m \\ f(r) & = (1 - x)^3*(1+3x+6x^2) \quad \mathrm{for} \qquad r_m < r < r_{cut} \\ f(r) & = 0.0 \qquad \qquad \mathrm{for} \qquad r >= r_{cut} \\\end{split}$

where

$x = \frac{(r-r_m)}{(r_{cut}-r_m)}$

Here $$r_m$$ is the inner cutoff radius and $$r_{cut}$$ is the outer cutoff radius.

For the lj/mdf pair_style, the potential energy, E(r), is the standard 12-6 Lennard-Jones written in the epsilon/sigma form:

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

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. 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)

• $$r_m$$ (distance units)

• $$r_{cut}$$ (distance units)

For the buck/mdf pair_style, the potential energy, E(r), is the standard Buckingham potential with three required coefficients. The two cutoffs can be omitted and default to the corresponding global values:

$E(r) = A e^{(-r/\rho)} -\frac{C}{r^6}$
• A (energy units)

• $$\rho$$ (distance units)

• C (energy-distance^6 units)

• $$r_m$$ (distance units)

• $$r_{cut}$$ (distance units)

For the lennard/mdf pair_style, the potential energy, E(r), is the standard 12-6 Lennard-Jones written in the A/B form:

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

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 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)

• $$r_m$$ (distance units)

• $$r_{cut}$$ (distance 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 distances for the lj/mdf pair style can be mixed. The default mix value is geometric. See the “pair_modify” command 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 shift option or long-range tail corrections to pressure and energy.

These 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 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 pair styles can only be used if LAMMPS was built with the EXTRA-PAIR package. See the Build package doc page for more info.

## Default¶

none

(Mei) Mei, Davenport, Fernando, Phys Rev B, 43 4653 (1991)