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improper_style class2 command :h3

[Syntax:]

improper_style class2 :pre

[Examples:]

improper_style class2
improper_coeff 1 100.0 0 :pre

[Description:]

The {class2} improper style uses the potential

:c,image(Eqs/improper_class2.jpg)

where Ei is the improper term and Eaa is an angle-angle term.  The 3 X
terms in Ei 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.html command) are ordered I,J,K,L.  X_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 X_KJLI and X_LJIK.
Note that atom J appears in the common bonds (JI, JK, JL) of all 3 X
terms.  Thus J (the 2nd atom in the quadruplet) is the atom of
symmetry in the 3 X 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.  Theta1,
theta2, theta3 are the equilibrium positions of those angles.  Again,
atom J (the 2nd 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)"_#Sun for a description of the COMPASS class2 force field.

The following coefficients must be defined for each improper type via the
"improper_coeff"_improper_coeff.html command as in the example above, or in
the data file or restart files read by the "read_data"_read_data.html
or "read_restart"_read_restart.html commands:

For this style, coefficients for the Ei formula can be specified in
either the input script or data file.  These are the 2 coefficients:

K (energy/radian^2)
X0 (degrees) :ul

X0 is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of K are in energy/radian^2.

Coefficients for the Eaa formula can only be specified in the data
file.  For the Eaa formula, the coefficients are listed under a
"AngleAngle Coeffs" heading and each line lists 6 coefficients:

M1 (energy/distance)
M2 (energy/distance)
M3 (energy/distance)
theta1 (degrees)
theta2 (degrees)
theta3 (degrees) :ul

The theta values are specified in degrees, but LAMMPS converts them to
radians internally; hence the units of M are in energy/radian^2.

[Restrictions:]

This improper style can only be used if LAMMPS was built with the
"class2" package.  See the "Making LAMMPS"_Section_start.html#2_3
section for more info on packages.

[Related commands:]

"improper_coeff"_improper_coeff.html

[Default:] none

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:link(Sun)
[(Sun)] Sun, J Phys Chem B 102, 7338-7364 (1998).
