1.. index:: improper_style cossq
2.. index:: improper_style cossq/omp
3
4improper_style cossq command
5============================
6
7Accelerator Variants: *cossq/omp*
8
9Syntax
10""""""
11
12.. code-block:: LAMMPS
13
14   improper_style cossq
15
16Examples
17""""""""
18
19.. code-block:: LAMMPS
20
21   improper_style cossq
22   improper_coeff 1 4.0 0.0
23
24Description
25"""""""""""
26
27The *cossq* improper style uses the potential
28
29.. math::
30
31   E = \frac{1}{2} K \cos^2{\left(\chi - \chi_0\right)}
32
33where :math:`\chi` is the improper angle, :math:`\chi_0` is its
34equilibrium value, and :math:`K` is a prefactor.
35
36If the 4 atoms in an improper quadruplet (listed in the data file read
37by the :doc:`read_data <read_data>` command) are ordered I,J,K,L then
38:math:`\chi` is the angle between the plane of I,J,K and the plane of J,K,L.
39Alternatively, you can think of atoms J,K,L as being in a plane, and
40atom I above the plane, and :math:`\chi` as a measure of how far
41out-of-plane I is with respect to the other 3 atoms.
42
43Note that defining 4 atoms to interact in this way, does not mean that
44bonds necessarily exist between I-J, J-K, or K-L, as they would in a
45linear dihedral.  Normally, the bonds I-J, I-K, I-L would exist for an
46improper to be defined between the 4 atoms.
47
48The following coefficients must be defined for each improper type via
49the :doc:`improper_coeff <improper_coeff>` command as in the example
50above, or in the data file or restart files read by the
51:doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
52commands:
53
54* :math:`K` (energy)
55* :math:`\chi_0` (degrees)
56
57----------
58
59.. include:: accel_styles.rst
60
61----------
62
63Restrictions
64""""""""""""
65
66This improper style can only be used if LAMMPS was built with the
67MOLECULE package.  See the :doc:`Build package <Build_package>` doc
68page for more info.
69
70Related commands
71""""""""""""""""
72
73:doc:`improper_coeff <improper_coeff>`
74
75Default
76"""""""
77
78none
79