\(\renewcommand{\AA}{\text{Å}}\)

# improper_style amoeba command

## Syntax

    improper_style amoeba

## Examples

    improper_style amoeba
    improper_coeff 1 49.6

## Description

The amoeba improper style uses the potential

\[E = K (\chi)^2\]

where \(\chi\) is the improper angle and \(K\) is a prefactor. Note that the usual 1/2 factor is included in \(K\).

This formula seems like a simplified version of the formula for the improper_style harmonic command with \(\chi_0\) = 0.0. However the computation of the angle \(\chi\) is done differently to match how the Tinker MD code computes its out-of-plane improper for the AMOEBA and HIPPO force fields. See the Howto amoeba doc page for more information about the implementation of AMOEBA and HIPPO in LAMMPS.

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 atoms I,K,L are considered to lie in a plane and atom J is out-of-plane. The angle \(\chi_0\) is computed as the Allinger angle which is defined as the angle between the plane of I,K,L, and the vector from atom I to atom J.

The following coefficient 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)

Note that the angle \(\chi\) is computed in radians; hence \(K\) is effectively energy per radian^2.

## Symmetry convention

For the amoeba 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 AMOEBA package. See the Build package doc page for more info.

## Related commands

improper_coeff, improper_harmonic

## Default

none