\(\renewcommand{\AA}{\text{Å}}\)

# improper_style class2 command

Accelerator Variants: class2/omp, class2/kk

## Syntax

    improper_style class2

## Examples

    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

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

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 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 three 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) 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 command as in the example above, or in the data file or restart files read by the read_data or 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 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 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.

## Symmetry convention

For the class2 improper style, the second 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 CLASS2 package. See the Build package doc page for more info.

## Related commands

improper_coeff

## Default

none

(Sun) Sun, J Phys Chem B 102, 7338-7364 (1998).