# pair_style wf/cut command

## Syntax

``` LAMMPS
pair_style wf/cut cutoff
```

-   cutoff = cutoff for wf interactions (distance units)

## Examples

``` LAMMPS
pair_style        wf/cut 2.0
pair_coeff        1 1 1.0 1.0 1 1  2.0
```

## Description

The *wf/cut* (Wang-Frenkel) style computes LJ-like potentials as
described in [Wang2020](Wang2020). This potential is by construction
finite ranged and it vanishes quadratically at the cutoff distance,
avoiding truncation, shifting, interpolation and other typical
procedures with the LJ potential. The *wf/cut* can be used when a
typical short-ranged potential with attraction is required. The
potential is given by which is given by:

$$\phi(r)= \epsilon \alpha \left(\left[{\sigma\over r}\right]^{2\mu} -1 \right)\left(\left[{r_c\over r}\right]^{2\mu}-1\right)^{2\nu}$$

with

$$\alpha=2\nu\left(\frac{r_c}{\sigma}\right)^{2\mu}\left[\frac{1+2\nu}{2\nu\left[(r_c/\sigma)^{2\mu}-1\right]}\right]^{2\nu+1}$$

and

$$r_{min}=r_c\left[\frac{1+2\nu}{1+2\nu(r_c/\sigma)^{2\nu}}\right]^{1/{2\nu}}$$

$r_c$ is the cutoff.

Comparison of the non-truncated Lennard-Jones 12-6 potential (red
curve), and the WF potentials with $\mu=1$ and $\nu=1$ are shown in the
figure below. The blue curve has $r_c =2.0$ and the green curve has
$r_c =1.2$ and can be used to describe colloidal interactions.

![image](JPG/WF_LJ.jpg){.align-center}

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

-   $\epsilon$ (energy units)
-   $\sigma$ (distance units)
-   $\nu$
-   $\mu$
-   $r_c$ (distance units)

The last coefficient is optional. If not specified, the global cutoff
given in the pair_style command is used. The exponents $\nu$ and $\mu$
are positive integers, usually set to 1. There is usually little to be
gained by choosing other values of $\nu$ and $\mu$ (See discussion in
[Wang2020](Wang2020))

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

**Mixing, shift, table, tail correction, restart, rRESPA info**:

This pair style does not support the [pair_modify](pair_modify) mixing
and table options.

The [pair_modify](pair_modify) tail and shift options are not relevant
for this pair style as it goes to zero at the cut-off radius.

This pair style writes its 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.

This pair style does not support the use of the *inner*, *middle*, and
*outer* keywords of the [run_style respa](run_style) command.

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

## Restrictions

This pair style can only be used if LAMMPS was built with the EXTRA-PAIR
package. See the [Build package](Build_package) doc page for more info.

## Related commands

[pair_coeff](pair_coeff)

**Default:** none

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

::: {#Wang2020}
**(Wang2020)** X. Wang, S. Ramirez-Hinestrosa, J. Dobnikar, and D.
Frenkel, Phys. Chem. Chem. Phys. 22, 10624 (2020).
:::