\(\renewcommand{\AA}{\text{Å}}\)

# improper_style inversion/harmonic command

## Syntax

    improper_style inversion/harmonic

## Examples

    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:

Note that the inversion/harmonic angle term evaluation differs to the 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 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)

- \(\omega_0\) (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.

## Symmetry convention

For the inversion/harmonic improper style, the first 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 MOFFF package. See the Build package doc page for more info.

## Related commands

improper_coeff

## Default

none