\(\renewcommand{\AA}{\text{Å}}\)

# dihedral_style table command

Accelerator Variants: table/omp

# dihedral_style table/cut command

## Syntax

    dihedral_style style interpolation Ntable

- style = table or table/cut

- interpolation = linear or spline = method of interpolation

- Ntable = size of the internal lookup table

## Examples

    dihedral_style table spline 400
    dihedral_style table linear 1000
    dihedral_coeff 1 file.table DIH_TABLE1
    dihedral_coeff 2 file.table DIH_TABLE2

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

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.

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

- filename

- keyword

The filename specifies a file containing tabulated energy and derivative values. The keyword specifies which section of the file to read. The format of this file is the same for both dihedral styles and described below.

For dihedral style table/cut the following coefficients must be defined for each dihedral type via the dihedral_coeff command as in the example above.

- style (= aat)

- cutoff prefactor (unitless)

- cutoff angle1 (degrees)

- cutoff angle2 (degrees)

- filename

- keyword

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

\[\begin{split}f(\theta) & = K \qquad\qquad\qquad\qquad\qquad\qquad \theta < \theta_1 \\ f(\theta) & = K \left(1-\frac{(\theta - \theta_1)^2}{(\theta_2 - \theta_1)^2}\right) \qquad \theta_1 < \theta < \theta_2\end{split}\]

The cutoff includes a prefactor K to the cutoff function \(f(\theta)\). While this value would ordinarily be 1, there may be situations where the value could be different.

The cutoff \(\theta_1\) 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 \(\theta_1\) and \(\theta_2\), 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 which section of the file to read. The format of this file is the same for both dihedral styles and described below.

Suitable tables for use with this dihedral style can be created using the Python code in the `tools/tabulate` folder of the LAMMPS source code distribution.

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 first 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 first value is the index from 1 to N, the second value is the angle value, the third value is the energy (in energy units), and the fourth is -dE/d(phi) also in energy units). The third term is the energy of the 4-atom configuration for the specified angle. The fourth 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 ensure 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 fourth column). In their place, forces will be calculated automatically by differentiating the potential energy function indicated by the third 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 fourth column of the data file.)

The optional “CHECKU” keyword is followed by a filename. This allows the user to save all of 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.

Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Accelerator packages page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page for more info.

You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

## Restart, fix_modify, output, run start/stop, minimize info

These dihedral styles write the settings for the “dihedral_style table” or “dihedral_style table/cut” command to binary restart files, so a dihedral_style command does not need to specified in an input script that reads a restart file. However, the coefficient information loaded from the table file(s) is not stored in the restart file, since it is tabulated in the potential files. Thus, suitable dihedral_coeff commands do need to be specified in the restart input script after reading the restart file.

## Restrictions

The table dihedral style can only be used if LAMMPS was built with the MOLECULE package. The table/cut dihedral style can only be used if LAMMPS was built with the EXTRA-MOLECULE package. See the Build package doc page for more info.

## Related commands

dihedral_coeff

## Default

none