# improper_style inversion/harmonic command

## Syntax

``` LAMMPS
improper_style inversion/harmonic
```

## Examples

``` LAMMPS
improper_style inversion/harmonic
improper_coeff 1 18.776340 0.000000
```

## Description

The *inversion/harmonic* improper style follows the Wilson-Decius
out-of-plane angle definition and uses an harmonic potential:

$$E = K \left(\omega - \omega_0\right)^2$$

where $K$ is the force constant and $\omega$ is the angle evaluated for
all three axis-plane combinations centered around the atom I. For the IL
axis and the IJK plane $\omega$ looks as follows:

![image](JPG/umbrella.jpg){.align-center}

Note that the *inversion/harmonic* angle term evaluation differs to the
[improper_umbrella](improper_umbrella) due to the cyclic evaluation of
all possible angles $\omega$.

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)
-   $\omega_0$ (degrees)

If $\omega_0 = 0$ the potential term has a single minimum for the planar
structure. Otherwise it has two minima at +/- $\omega_0$, with a barrier
in between.

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

## Restrictions

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

## Related commands

[improper_coeff](improper_coeff)

## Default

none