# dihedral_style table/cut command

## Syntax

```
dihedral_style table/cut style Ntable
```

- style =
*linear*or*spline*= method of interpolation - Ntable = size of the internal lookup table

## Examples

```
dihedral_style table/cut spline 400
dihedral_style table/cut linear 1000
dihedral_coeff 1 aat 1.0 177 180 file.table DIH_TABLE1
dihedral_coeff 2 aat 0.5 170 180 file.table DIH_TABLE2
```

## Description

The *table/cut* dihedral style creates interpolation tables of length
*Ntable* from dihedral potential and derivative values listed in a
file(s) as a function of the dihedral angle “phi”. In addition, an
analytic cutoff that is quadratic in the bond-angle (theta) is applied
in order to regularize the dihedral interaction. The dihedral table
files are read by the dihedral_coeff command.

The interpolation tables are created by fitting cubic splines to the
file values and interpolating energy and derivative values at each of
*Ntable* dihedral 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 dihedral angle (phi) is used to find 2
surrounding table values from which an energy or its derivative is
computed by linear interpolation.

For the *spline* style, cubic spline coefficients are computed and
stored at each of the *Ntable* evenly-spaced values in the
interpolated table. For a given dihedral angle (phi), the appropriate
coefficients are chosen from this list, and a cubic polynomial is used
to compute the energy and the derivative at this angle.

The following coefficients must be defined for each dihedral type via the dihedral_coeff command as in the example above.

- style (aat)
- cutoff prefactor
- cutoff angle1
- cutoff angle2
- filename
- keyword

The cutoff dihedral style uses a tabulated dihedral interaction with a cutoff function:

The cutoff specifies an prefactor to the cutoff function. While this value would ordinarily equal 1 there may be situations where the value should change.

The cutoff angle1 specifies the angle (in degrees) below which the dihedral interaction is unmodified, i.e. the cutoff function is 1.

The cutoff function is applied between angle1 and angle2, which is the angle at which the cutoff function drops to zero. The value of zero effectively “turns off” the dihedral interaction.

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.

The format of a tabulated file is as follows (without the parenthesized comments). It can begin with one or more comment or blank lines.

```
# Table of the potential and its negative derivative
DIH_TABLE1 (keyword is the first text on line)
N 30 DEGREES (N, NOF, DEGREES, RADIANS, CHECKU/F)
(blank line)
1 -168.0 -1.40351172223 0.0423346818422
2 -156.0 -1.70447981034 0.00811786522531
3 -144.0 -1.62956100432 -0.0184129719987
...
30 180.0 -0.707106781187 0.0719306095245
# Example 2: table of the potential. Forces omitted
DIH_TABLE2
N 30 NOF CHECKU testU.dat CHECKF testF.dat
1 -168.0 -1.40351172223
2 -156.0 -1.70447981034
3 -144.0 -1.62956100432
...
30 180.0 -0.707106781187
```

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 dihedral_coeff 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.

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, the 3rd value is the energy (in energy units), and the 4th is -dE/d(phi) also in energy units). The 3rd term is the energy of the 4-atom configuration for the specified angle. The 4th term (when present) is the negative derivative of the energy with respect to the angle (in degrees, or radians depending on whether the user selected DEGREES or RADIANS). Thus the units of the last term are still energy, not force. The dihedral angle values must increase from one line to the next.

Dihedral table splines are cyclic. There is no discontinuity at 180
degrees (or at any other angle). Although in the examples above, the
angles range from -180 to 180 degrees, in general, the first angle in
the list can have any value (positive, zero, or negative). However
the *range* of angles represented in the table must be *strictly* less
than 360 degrees (2pi radians) to avoid angle overlap. (You may not
supply entries in the table for both 180 and -180, for example.) If
the user’s table covers only a narrow range of dihedral angles,
strange numerical behavior can occur in the large remaining gap.

**Parameters:**

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 dihedral_style table command.
Let *Ntable* is the number of table entries requested dihedral_style
command, and let *Nfile* be the parameter following “N” in the
tabulated file (“30” in the sparse example above). 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 (which are evenly spaced over a 360 degree range, even if the
angles in the file are not). The resulting tables of length *Ntable*
are then used as described above, when computing energy and force for
individual dihedral 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 nopreliminary
interpolation), you should set *Ntable* = *Nfile*. To insure the
nodal points in the user’s file are aligned with the interpolated
table entries, the angles in the table should be integer multiples of
360/*Ntable* degrees, or 2*PI/*Ntable* radians (depending on your
choice of angle units).

The optional “NOF” keyword allows the user to omit the forces (negative energy derivatives) from the table file (normally located in the 4th column). In their place, forces will be calculated automatically by differentiating the potential energy function indicated by the 3rd column of the table (using either linear or spline interpolation).

The optional “DEGREES” keyword allows the user to specify angles in degrees instead of radians (default).

The optional “RADIANS” keyword allows the user to specify angles in radians instead of degrees. (Note: This changes the way the forces are scaled in the 4th column of the data file.)

The optional “CHECKU” keyword is followed by a filename. This allows
the user to save all of the the *Ntable* different entries in the
interpolated energy table to a file to make sure that the interpolated
function agrees with the user’s expectations. (Note: You can
temporarily increase the *Ntable* parameter to a high value for this
purpose. “*Ntable*” is explained above.)

The optional “CHECKF” keyword is analogous to the “CHECKU” keyword. It is followed by a filename, and it allows the user to check the interpolated force table. This option is available even if the user selected the “NOF” option.

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 dihedral style can only be used if LAMMPS was built with the USER-MISC package. See the Making LAMMPS section for more info on packages.