# improper_style ring command

Accelerator Variants: *ring/omp*

## Syntax

``` LAMMPS
improper_style ring
```

## Examples

``` LAMMPS
improper_style ring
improper_coeff 1 8000 70.5
```

## Description

The *ring* improper style uses the potential

$$\begin{aligned}
E = &\frac{1}{6} K \left(\Delta_{ijl} + \Delta_{ijk} + \Delta_{kjl} \right)^6 \\
\Delta_{ijl} = & \cos{\theta_{ijl} - \cos{\theta_0}} \\
\Delta_{ijk} = & \cos{\theta_{ijk} - \cos{\theta_0}} \\
\Delta_{kjl} = & \cos{\theta_{kjl} - \cos{\theta_0}}
\end{aligned}$$

where $K$ is a prefactor, $\theta$ is the angle formed by the atoms
specified by (i,j,k,l) indices and $\theta_0$ its equilibrium value.

If the 4 atoms in an improper quadruplet (listed in the data file read
by the [read_data](read_data) command) are ordered i,j,k,l then
$\theta_{ijl}$ is the angle between atoms i,j and l, $\theta_{ijk}$ is
the angle between atoms i,j and k, $\theta_{kjl}$ is the angle between
atoms j,k, and l.

The \"ring\" improper style implements the improper potential introduced
by Destree et al., in Equation (9) of [(Destree)](Destree). This
potential does not affect small amplitude vibrations but is used in an
ad-hoc way to prevent the onset of accidentally large amplitude
fluctuations leading to the occurrence of a planar conformation of the
three bonds i-j, j-k and j-l, an intermediate conformation toward the
chiral inversion of a methine carbon. In the \"Impropers\" section of
data file four atoms: i, j, k and l are specified with i,j and l lying
on the backbone of the chain and k specifying the chirality of j.

The following coefficients must be defined for each improper type via
the [improper_coeff](improper_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:

-   $K$ (energy)
-   $\theta_0$ (degrees)

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

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.

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

## Restrictions

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

## Related commands

[improper_coeff](improper_coeff)

::: {#Destree}
**(Destree)** M. Destree, F. Laupretre, A. Lyulin, and J.-P. Ryckaert, J
Chem Phys, 112, 9632 (2000).
:::