# improper_style class2 command

Accelerator Variants: *class2/omp*, *class2/kk*

## Syntax

``` LAMMPS
improper_style class2
```

## Examples

``` LAMMPS
improper_style class2
improper_coeff 1 100.0 0
improper_coeff * aa 0.0 0.0 0.0 115.06 130.01 115.06
```

## Description

The *class2* improper style uses the potential

$$\begin{aligned}
E      = & E_i + E_{aa} \\
E_i    = & K [ \frac{\chi_{ijkl} + \chi_{kjli} + \chi_{ljik}}{3} - \chi_0 ]^2 \\
E_{aa} = & M_1 (\theta_{ijk} - \theta_1) (\theta_{kjl} - \theta_3) + \\
         & M_2 (\theta_{ijk} - \theta_1) (\theta_{ijl} - \theta_2) + \\
         & M_3 (\theta_{ijl} - \theta_2) (\theta_{kjl} - \theta_3)
\end{aligned}$$

where $E_i$ is the improper term and $E_{aa}$ is an angle-angle term.
The 3 $\chi$ terms in $E_i$ are an average over 3 out-of-plane angles.

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. $\chi_{ijkl}$
refers to the angle between the plane of I,J,K and the plane of J,K,L,
and the bond JK lies in both planes. Similarly for $\chi_{kjli}$ and
$\chi_{ljik}$. Note that atom J appears in the common bonds (JI, JK, JL)
of all 3 X terms. Thus J (the second atom in the quadruplet) is the atom
of symmetry in the 3 $\chi$ angles.

The subscripts on the various $\theta$s refer to different combinations
of 3 atoms (I,J,K,L) used to form a particular angle. E.g.
$\theta_{ijl}$ is the angle formed by atoms I,J,L with J in the middle.
$\theta_1$, $\theta_2$, $\theta_3$ are the equilibrium positions of
those angles. Again, atom J (the second atom in the quadruplet) is the
atom of symmetry in the theta angles, since it is always the center
atom.

Since atom J is the atom of symmetry, normally the bonds J-I, J-K, J-L
would exist for an improper to be defined between the 4 atoms, but this
is not required.

See [(Sun)](improper-Sun) for a description of the COMPASS class2 force
field.

Coefficients for the $E_i$ and $E_{aa}$ formulas 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.

These are the 2 coefficients for the $E_i$ formula:

-   $K$ (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.

For the $E_{aa}$ formula, each line in a
[improper_coeff](improper_coeff) command in the input script lists 7
coefficients, the first of which is *aa* to indicate they are AngleAngle
coefficients. In a data file, these coefficients should be listed under
a *AngleAngle Coeffs* heading and you must leave out the *aa*, i.e. only
list 6 coefficients after the improper type.

-   *aa*
-   $M_1$ (energy)
-   $M_2$ (energy)
-   $M_3$ (energy)
-   $\theta_1$ (degrees)
-   $\theta_2$ (degrees)
-   $\theta_3$ (degrees)

The $\theta$ values are specified in degrees, but LAMMPS converts them
to radians internally; hence the hence the various $M$ are 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](Speed_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](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](Run_options) when you invoke LAMMPS, or you can use the
[suffix](suffix) command in your input script.

See the [Accelerator packages](Speed_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 CLASS2
package. See the [Build package](Build_package) doc page for more info.

## Related commands

[improper_coeff](improper_coeff)

## Default

none

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

::: {#improper-Sun}
**(Sun)** Sun, J Phys Chem B 102, 7338-7364 (1998).
:::