# improper_style amoeba command

## Syntax

``` LAMMPS
improper_style amoeba
```

## Examples

``` LAMMPS
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](improper_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](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](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-place. 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](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)

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

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

## Restrictions

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

## Related commands

[improper_coeff](improper_coeff), [improper_harmonic](improper_harmonic)

## Default

none