dihedral_style table/cut command
dihedral_style table/cut style Ntable
- style = linear or spline = method of interpolation
- Ntable = size of the internal lookup table
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
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
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.
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.
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.