# improper_style harmonic command¶

Accelerator Variants: harmonic/intel, harmonic/kk, harmonic/omp

## Syntax¶

improper_style harmonic


## Examples¶

improper_style harmonic
improper_coeff 1 100.0 0


## Description¶

The harmonic improper style uses the potential

$E = K (\chi - \chi_0)^2$

where $$\chi$$ is the improper angle, $$\chi_0$$ is its equilibrium value, and $$K$$ is a prefactor. Note that the usual 1/2 factor is included in $$K$$.

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 $$\chi$$ is the angle between the plane of I,J,K and the plane of J,K,L. Alternatively, you can think of atoms J,K,L as being in a plane, and atom I above the plane, and $$\chi$$ as a measure of how far out-of-plane I is with respect to the other 3 atoms.

Note that defining 4 atoms to interact in this way, does not mean that bonds necessarily exist between I-J, J-K, or K-L, as they would in a linear dihedral. Normally, the bonds I-J, I-K, I-L would exist for an improper to be defined between the 4 atoms.

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)

• $$\chi_0$$ (degrees)

$$\chi_0$$ is specified in degrees, but LAMMPS converts it to radians internally; hence $$K$$ is effectively energy per radian^2.

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.

## Restrictions¶

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

none