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# improper_style ring command

Accelerator Variants: ring/omp

## Syntax

    improper_style ring

## Examples

    improper_style ring
    improper_coeff 1 8000 70.5

## Description

The ring improper style uses the potential

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

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 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). 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 command as in the example above, or in the data file or restart files read by the read_data or 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 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 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 when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

## Symmetry convention

For the ring improper style, the second atom in the quadruplet is the atom of symmetry; all other atoms are considered interchangeable. This convention is relevant for operations that require knowledge of how atoms are ordered, such as automatic assignment of new improper types by fix bond/react.

## Restrictions

This improper style can only be used if LAMMPS was built with the EXTRA-MOLECULE package. See the Build package doc page for more info.

## Related commands

improper_coeff

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