265 lines
10 KiB
ReStructuredText
265 lines
10 KiB
ReStructuredText
.. index:: dihedral_style table
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.. index:: dihedral_style table/omp
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.. index:: dihedral_style table/cut
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dihedral_style table command
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============================
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Accelerator Variants: *table/omp*
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dihedral_style table/cut command
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================================
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Syntax
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""""""
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.. code-block:: LAMMPS
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dihedral_style style interpolation Ntable
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* style = *table* or *table/cut*
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* interpolation = *linear* or *spline* = method of interpolation
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* Ntable = size of the internal lookup table
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Examples
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""""""""
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.. code-block:: LAMMPS
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dihedral_style table spline 400
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dihedral_style table linear 1000
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dihedral_coeff 1 file.table DIH_TABLE1
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dihedral_coeff 2 file.table DIH_TABLE2
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dihedral_style table/cut spline 400
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dihedral_style table/cut linear 1000
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dihedral_coeff 1 aat 1.0 177 180 file.table DIH_TABLE1
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dihedral_coeff 2 aat 0.5 170 180 file.table DIH_TABLE2
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Description
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"""""""""""
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The *table* and *table/cut* dihedral styles create interpolation tables
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of length *Ntable* from dihedral potential and derivative values listed
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in a file(s) as a function of the dihedral angle "phi". The files are
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read by the :doc:`dihedral_coeff <dihedral_coeff>` command. For
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dihedral style *table/cut* additionally an analytic cutoff that is
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quadratic in the bond-angle (theta) is applied in order to regularize
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the dihedral interaction.
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The interpolation tables are created by fitting cubic splines to the
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file values and interpolating energy and derivative values at each of
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*Ntable* dihedral angles. During a simulation, these tables are used
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to interpolate energy and force values on individual atoms as
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needed. The interpolation is done in one of 2 styles: *linear* or
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*spline*\ .
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For the *linear* style, the dihedral angle (phi) is used to find 2
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surrounding table values from which an energy or its derivative is
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computed by linear interpolation.
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For the *spline* style, cubic spline coefficients are computed and
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stored at each of the *Ntable* evenly-spaced values in the
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interpolated table. For a given dihedral angle (phi), the appropriate
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coefficients are chosen from this list, and a cubic polynomial is used
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to compute the energy and the derivative at this angle.
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For dihedral style *table* the following coefficients must be defined
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for each dihedral type via the :doc:`dihedral_coeff <dihedral_coeff>`
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command as in the example above.
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* filename
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* keyword
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The filename specifies a file containing tabulated energy and derivative
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values. The keyword specifies which section of the file to read. The
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format of this file is the same for both dihedral styles and described
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below.
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For dihedral style *table/cut* the following coefficients must be
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defined for each dihedral type via the :doc:`dihedral_coeff
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<dihedral_coeff>` command as in the example above.
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* style (= aat)
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* cutoff prefactor (unitless)
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* cutoff angle1 (degrees)
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* cutoff angle2 (degrees)
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* filename
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* keyword
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The cutoff dihedral style uses a tabulated dihedral interaction with a
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cutoff function:
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.. math::
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f(\theta) & = K \qquad\qquad\qquad\qquad\qquad\qquad \theta < \theta_1 \\
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f(\theta) & = K \left(1-\frac{(\theta - \theta_1)^2}{(\theta_2 - \theta_1)^2}\right) \qquad \theta_1 < \theta < \theta_2
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The cutoff includes a prefactor *K* to the cutoff function :math:`f(\theta)`.
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While this value would ordinarily be 1, there may be situations where the value
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could be different.
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The cutoff :math:`\theta_1` specifies the angle (in degrees) below which
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the dihedral interaction is unmodified, i.e. the cutoff function is 1.
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The cutoff function is applied between :math:`\theta_1` and
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:math:`\theta_2`, which is the angle at which the cutoff function drops
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to zero. The value of zero effectively "turns off" the dihedral
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interaction.
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The filename specifies a file containing tabulated energy and derivative
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values. The keyword specifies which section of the file to read. The
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format of this file is the same for both dihedral styles and described
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below.
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----------
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Suitable tables for use with this dihedral style can be created using
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the Python code in the ``tools/tabulate`` folder of the LAMMPS source
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code distribution.
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The format of a tabulated file is as follows (without the
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parenthesized comments). It can begin with one or more comment
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or blank lines.
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.. parsed-literal::
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# Table of the potential and its negative derivative
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DIH_TABLE1 (keyword is the first text on line)
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N 30 DEGREES (N, NOF, DEGREES, RADIANS, CHECKU/F)
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(blank line)
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1 -168.0 -1.40351172223 0.0423346818422
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2 -156.0 -1.70447981034 0.00811786522531
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3 -144.0 -1.62956100432 -0.0184129719987
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...
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30 180.0 -0.707106781187 0.0719306095245
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# Example 2: table of the potential. Forces omitted
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DIH_TABLE2
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N 30 NOF CHECKU testU.dat CHECKF testF.dat
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1 -168.0 -1.40351172223
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2 -156.0 -1.70447981034
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3 -144.0 -1.62956100432
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...
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30 180.0 -0.707106781187
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A section begins with a non-blank line whose first character is not a
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"#"; blank lines or lines starting with "#" can be used as comments
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between sections. The first line begins with a keyword which
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identifies the section. The line can contain additional text, but the
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initial text must match the argument specified in the
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:doc:`dihedral_coeff <dihedral_coeff>` command. The next line lists (in
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any order) one or more parameters for the table. Each parameter is a
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keyword followed by one or more numeric values.
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Following a blank line, the next N lines list the tabulated values. On
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each line, the first value is the index from 1 to N, the second value is
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the angle value, the third value is the energy (in energy units), and
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the fourth is -dE/d(phi) also in energy units). The third term is the
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energy of the 4-atom configuration for the specified angle. The fourth
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term (when present) is the negative derivative of the energy with
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respect to the angle (in degrees, or radians depending on whether the
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user selected DEGREES or RADIANS). Thus the units of the last term
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are still energy, not force. The dihedral angle values must increase
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from one line to the next.
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Dihedral table splines are cyclic. There is no discontinuity at 180
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degrees (or at any other angle). Although in the examples above, the
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angles range from -180 to 180 degrees, in general, the first angle in
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the list can have any value (positive, zero, or negative). However
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the *range* of angles represented in the table must be *strictly* less
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than 360 degrees (2pi radians) to avoid angle overlap. (You may not
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supply entries in the table for both 180 and -180, for example.) If
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the user's table covers only a narrow range of dihedral angles,
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strange numerical behavior can occur in the large remaining gap.
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**Parameters:**
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The parameter "N" is required and its value is the number of table
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entries that follow. Note that this may be different than the N
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specified in the :doc:`dihedral_style table <dihedral_style>` command.
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Let *Ntable* is the number of table entries requested dihedral_style
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command, and let *Nfile* be the parameter following "N" in the
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tabulated file ("30" in the sparse example above). What LAMMPS does
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is a preliminary interpolation by creating splines using the *Nfile*
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tabulated values as nodal points. It uses these to interpolate as
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needed to generate energy and derivative values at *Ntable* different
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points (which are evenly spaced over a 360 degree range, even if the
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angles in the file are not). The resulting tables of length *Ntable*
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are then used as described above, when computing energy and force for
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individual dihedral angles and their atoms. This means that if you
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want the interpolation tables of length *Ntable* to match exactly what
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is in the tabulated file (with effectively nopreliminary
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interpolation), you should set *Ntable* = *Nfile*\ . To ensure the
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nodal points in the user's file are aligned with the interpolated
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table entries, the angles in the table should be integer multiples of
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360/\ *Ntable* degrees, or 2\*PI/\ *Ntable* radians (depending on your
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choice of angle units).
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The optional "NOF" keyword allows the user to omit the forces
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(negative energy derivatives) from the table file (normally located in
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the fourth column). In their place, forces will be calculated
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automatically by differentiating the potential energy function
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indicated by the third column of the table (using either linear or
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spline interpolation).
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The optional "DEGREES" keyword allows the user to specify angles in
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degrees instead of radians (default).
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The optional "RADIANS" keyword allows the user to specify angles in
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radians instead of degrees. (Note: This changes the way the forces
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are scaled in the fourth column of the data file.)
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The optional "CHECKU" keyword is followed by a filename. This allows
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the user to save all of the *Ntable* different entries in the
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interpolated energy table to a file to make sure that the interpolated
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function agrees with the user's expectations. (Note: You can
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temporarily increase the *Ntable* parameter to a high value for this
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purpose. "\ *Ntable*\ " is explained above.)
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The optional "CHECKF" keyword is analogous to the "CHECKU" keyword.
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It is followed by a filename, and it allows the user to check the
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interpolated force table. This option is available even if the user
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selected the "NOF" option.
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Note that one file can contain many sections, each with a tabulated
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potential. LAMMPS reads the file section by section until it finds one
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that matches the specified keyword.
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----------
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.. include:: accel_styles.rst
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Restart, fix_modify, output, run start/stop, minimize info
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"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
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These dihedral styles write the settings for the "dihedral_style table"
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or "dihedral_style table/cut" command to :doc:`binary restart files
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<restart>`, so a dihedral_style command does not need to specified in an
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input script that reads a restart file. However, the coefficient
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information loaded from the table file(s) is not stored in the restart
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file, since it is tabulated in the potential files. Thus, suitable
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dihedral_coeff commands do need to be specified in the restart input
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script after reading the restart file.
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Restrictions
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""""""""""""
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The *table* dihedral style can only be used if LAMMPS was built with the
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MOLECULE package. The *table/cut* dihedral style can only be used if
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LAMMPS was built with the EXTRA-MOLECULE package. See the
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:doc:`Build package <Build_package>` doc page for more info.
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Related commands
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""""""""""""""""
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:doc:`dihedral_coeff <dihedral_coeff>`
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Default
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"""""""
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none
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