.. index:: improper_style class2 improper_style class2 command ============================= improper_style class2/omp command ================================= improper_style class2/kk command ================================ Syntax """""" .. code-block:: LAMMPS improper_style class2 Examples """""""" .. code-block:: 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 .. math:: 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) where :math:`E_i` is the improper term and :math:`E_{aa}` is an angle-angle term. The 3 :math:`\chi` terms in :math:`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 :doc:`read_data ` command) are ordered I,J,K,L. :math:`\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 :math:`\chi_{kjli}` and :math:`\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 :math:`\chi` angles. The subscripts on the various :math:`\theta`\ s refer to different combinations of 3 atoms (I,J,K,L) used to form a particular angle. E.g. :math:`\theta_{ijl}` is the angle formed by atoms I,J,L with J in the middle. :math:`\theta_1`, :math:`\theta_2`, :math:`\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 :ref:`(Sun) ` for a description of the COMPASS class2 force field. Coefficients for the :math:`E_i` and :math:`E_{aa}` formulas must be defined for each improper type via the :doc:`improper_coeff ` command as in the example above, or in the data file or restart files read by the :doc:`read_data ` or :doc:`read_restart ` commands. These are the 2 coefficients for the :math:`E_i` formula: * :math:`K` (energy) * :math:`\chi_0` (degrees) :math:`\chi_0` is specified in degrees, but LAMMPS converts it to radians internally; hence :math:`K` is effectively energy per radian\^2. For the :math:`E_{aa}` formula, each line in a :doc:`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* * :math:`M_1` (energy) * :math:`M_2` (energy) * :math:`M_3` (energy) * :math:`\theta_1` (degrees) * :math:`\theta_2` (degrees) * :math:`\theta_3` (degrees) The :math:`\theta` values are specified in degrees, but LAMMPS converts them to radians internally; hence the hence the various :math:`M` are effectively energy per radian\^2. ---------- .. include:: accel_styles.rst ---------- Restrictions """""""""""" This improper style can only be used if LAMMPS was built with the CLASS2 package. See the :doc:`Build package ` doc page for more info. Related commands """""""""""""""" :doc:`improper_coeff ` **Default:** none ---------- .. _improper-Sun: **(Sun)** Sun, J Phys Chem B 102, 7338-7364 (1998).