lammps/doc/angle_table.txt

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angle_style table command :h3

[Syntax:]

angle_style table style N :pre

style = {linear} or {spline} = method of interpolation
N = use N values in table :ul

[Examples:]

angle_style table linear 1000
angle_coeff 3 file.table ENTRY1 :pre

[Description:]

Style {table} creates interpolation tables of length {N} from angle
potential and derivative values listed in a file(s) as a function of
angle The files are read by the "angle_coeff"_angle_coeff.html
command.

The interpolation tables are created by fitting cubic splines to the
file values and interpolating energy and derivative values at each of
{N} angles.  During a simulation, these tables are used to interpolate
energy and force values on individual atoms as needed.  The
interpolation is done in one of 2 styles: {linear} or {spline}.

For the {linear} style, the angle is used to find 2 surrounding table
values from which an energy or its derivative is computed by linear
interpolation.

For the {spline} style, a cubic spline coefficients are computed and
stored at each of the {N} values in the table.  The angle is used to
find the appropriate set of coefficients which are used to evaluate a
cubic polynomial which computes the energy or derivative.

The following coefficients must be defined for each angle type via the
"angle_coeff"_angle_coeff.html command as in the example above.

filename
keyword :ul

The filename specifies a file containing tabulated energy and
derivative values.  The keyword specifies a section of the file.  The
format of this file is described below.

:line

The format of a tabulated file is as follows (without the
parenthesized comments):

# Angle potential for harmonic (one or more comment or blank lines) :pre

HAM                           (keyword is the first text on line)
N 181 FP 0 0 EQ 90.0          (N, FP, EQ parameters)
                              (blank line)
N 181 FP 0 0                  (N, FP parameters)
1 0.0 200.5 2.5               (index, angle, energy, derivative)
2 1.0 198.0 2.5
...
181 180.0 0.0 0.0 :pre

A section begins with a non-blank line whose 1st character is not a
"#"; blank lines or lines starting with "#" can be used as comments
between sections.  The first line begins with a keyword which
identifies the section.  The line can contain additional text, but the
initial text must match the argument specified in the
"angle_coeff"_angle_coeff.html command.  The next line lists (in any
order) one or more parameters for the table.  Each parameter is a
keyword followed by one or more numeric values.

The parameter "N" is required and its value is the number of table
entries that follow.  Note that this may be different than the {N}
specified in the "angle_style table"_angle_style.html command.  Let
Ntable = {N} in the angle_style command, and Nfile = "N" in the
tabulated file.  What LAMMPS does is a preliminary interpolation by
creating splines using the Nfile tabulated values as nodal points.  It
uses these to interpolate as needed to generate energy and derivative
values at Ntable different points.  The resulting tables of length
Ntable are then used as described above, when computing energy and
force for individual angles and their atoms.  This means that if you
want the interpolation tables of length Ntable to match exactly what
is in the tabulated file (with effectively no preliminary
interpolation), you should set Ntable = Nfile.

The "FP" parameter is optional.  If used, it is followed by two values
fplo and fphi, which are the 2nd derivatives at the innermost and
outermost angle settings.  These values are needed by the spline
construction routines.  If not specified by the "FP" parameter, they
are estimated (less accurately) by the first two and last two
derivative values in the table.

The "EQ" parameter is also optional.  If used, it is followed by a the
equilibrium angle value, which is used, for example, by the "fix
shake"_fix_shake.html command.  If not used, the equilibrium angle is
set to 180.0.

Following a blank line, the next N lines list the tabulated values.
On each line, the 1st value is the index from 1 to N, the 2nd value is
the angle value (in degrees), the 3rd value is the energy (in energy
units), and the 4th is -dE/d(theta) (also in energy units).  The 3rd
term is the energy of the 3-atom configuration for the specified
angle.  The last term is the derivative of the energy with respect to
the angle (in degrees, not radians).  Thus the units of the last term
are still energy, not force.  The angle values must increase from one
line to the next.  The angle values must also begin with 0.0 and end
with 180.0, i.e. span the full range of possible angles.

Note that one file can contain many sections, each with a tabulated
potential.  LAMMPS reads the file section by section until it finds
one that matches the specified keyword.

[Restrictions:]

This angle style can only be used if LAMMPS was built with the
MOLECULAR package (which it is by default).  See the "Making
LAMMPS"_Section_start.html#start_3 section for more info on packages.

[Related commands:]

"angle_coeff"_angle_coeff.html

[Default:] none