# pair_style lj/cubic command

Accelerator Variants: *lj/cubic/gpu*, *lj/cubic/omp*

## Syntax

``` LAMMPS
pair_style lj/cubic
```

## Examples

``` LAMMPS
pair_style lj/cubic
pair_coeff * * 1.0 0.8908987
```

## Description

The *lj/cubic* style computes a truncated LJ interaction potential whose
energy and force are continuous everywhere. Inside the inflection point
the interaction is identical to the standard 12/6
[Lennard-Jones](pair_lj) potential. The LJ function outside the
inflection point is replaced with a cubic function of distance. The
energy, force, and second derivative are continuous at the inflection
point. The cubic coefficient A3 is chosen so that both energy and force
go to zero at the cutoff distance. Outside the cutoff distance the
energy and force are zero.

$$\begin{aligned}
E & = u_{LJ}(r) \qquad r \leq r_s \\
  & = u_{LJ}(r_s) + (r-r_s) u'_{LJ}(r_s) - \frac{1}{6} A_3 (r-r_s)^3 \qquad r_s < r \leq r_c \\
  & = 0 \qquad r > r_c
\end{aligned}$$

The location of the inflection point $r_s$ is defined by the LJ
diameter, $r_s/\sigma = (26/7)^{1/6}$. The cutoff distance is defined by
$r_c/r_s = 67/48$ or $r_c/\sigma = 1.737...$ The analytic expression for
the the cubic coefficient $A_3 r_{min}^3/\epsilon = 27.93...$ is given
in the paper by Holian and Ravelo [(Holian)](Holian).

This potential is commonly used to study the shock mechanics of FCC
solids, as in Ravelo et al. [(Ravelo)](Ravelo2).

The following coefficients must be defined for each pair of atom 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, or by mixing as described below:

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

Note that $\sigma$ is defined in the LJ formula as the zero-crossing
distance for the potential, not as the energy minimum, which is located
at $r_{min} = 2^{\frac{1}{6}} \sigma$. In the above example,
$\sigma = 0.8908987$, so $r_{min} = 1.0$.

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

Styles with a *gpu*, *intel*, *kk*, *omp*, or *opt* suffix are
functionally the same as the corresponding style without the suffix.
They have been optimized to run faster, depending on your available
hardware, as discussed on the [Accelerator packages](Speed_packages)
page. The accelerated styles take the same arguments and should produce
the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP, and
OPT packages, respectively. They are only enabled if LAMMPS was built
with those packages. See the [Build package](Build_package) page for
more info.

You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the [-suffix command-line
switch](Run_options) when you invoke LAMMPS, or you can use the
[suffix](suffix) command in your input script.

See the [Accelerator packages](Speed_packages) page for more
instructions on how to use the accelerated styles effectively.

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

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

The lj/cubic pair style does not support the [pair_modify](pair_modify)
shift option, since pair interaction is already smoothed to 0.0 at the
cutoff.

The [pair_modify](pair_modify) table option is not relevant for this
pair style.

The lj/cubic pair style does not support the [pair_modify](pair_modify)
tail option for adding long-range tail corrections to energy and
pressure, since there are no corrections for a potential that goes to
0.0 at the cutoff.

The lj/cubic 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.

The lj/cubic pair style can only be used via the *pair* keyword of the
[run_style respa](run_style) command. It does not support the *inner*,
*middle*, *outer* keywords.

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

## Restrictions

This pair style is part of the EXTRA-PAIR package. It is 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

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

:::: {#Holian}
::: {#Ravelo2}
**(Holian)** Holian and Ravelo, Phys Rev B, 51, 11275 (1995).
:::
::::

**(Ravelo)** Ravelo, Holian, Germann and Lomdahl, Phys Rev B, 70, 014103
(2004).