\(\renewcommand{\AA}{\text{Å}}\)

# angle_style table command

Accelerator Variants: *table/omp*

## Syntax

```
angle_style table style N
```

style =

*linear*or*spline*= method of interpolationN = use N values in table

## Examples

```
angle_style table linear 1000
angle_coeff 3 file.table ENTRY1
```

## 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
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 command as in the example above.

filename

keyword

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.

Suitable tables for use with this angle style can be created by LAMMPS
itself from existing angle styles using the angle_write command. This can be useful to have a template file for
testing the angle style settings and to build a compatible custom file.
Another option to generate tables is 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):

```
# Angle potential for harmonic (one or more comment or blank lines)
HAM (keyword is the first text on line)
N 181 FP 0 0 EQ 90.0 (N, FP, EQ parameters)
(blank line)
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
```

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 angle_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.

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 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 second 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 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 first value is the index from 1 to N, the second value is the angle value (in degrees), the third value is the energy (in energy units), and the fourth is -dE/d(theta) (also in energy units). The third 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.

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

This angle style writes the settings for the “angle_style table” command to binary restart files, so a angle_style command does not need to specified in an input script that reads a restart file. However, the coefficient information is not stored in the restart file, since it is tabulated in the potential files. Thus, angle_coeff commands do need to be specified in the restart input script.

## Restrictions

This angle style can only be used if LAMMPS was built with the MOLECULE package. See the Build package doc page for more info.

## Default

none