Merge pull request #909 from lammps/tablecut

\documentclass[12pt]{article}

\pagestyle{empty}

\begin{document}

\begin{eqnarray*}

        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{eqnarray*}

\end{document}

"nharmonic (o)"_dihedral_nharmonic.html,

"quadratic (o)"_dihedral_quadratic.html,

"spherical (o)"_dihedral_spherical.html,

"table (o)"_dihedral_table.html :tb(c=4,ea=c)

"table (o)"_dihedral_table.html,

"table/cut"_dihedral_table_cut.html :tb(c=4,ea=c)

:line

"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c

:link(lws,http://lammps.sandia.gov)

:link(ld,Manual.html)

:link(lc,Section_commands.html#comm)

:line

dihedral_style table/cut command :h3

[Syntax:]

dihedral_style table/cut style Ntable :pre

style = {linear} or {spline} = method of interpolation

Ntable = size of the internal lookup table :ul

[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 :pre

[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"_dihedral_coeff.html 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"_dihedral_coeff.html command as in the example

above.

style (aat)

cutoff prefactor

cutoff angle1

cutoff angle2

filename

keyword :ul

The cutoff dihedral style uses a tabulated dihedral interaction with a 

cutoff function:

:c,image(Eqs/dihedral_table_cut.jpg)

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.

:line

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  :pre

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 :pre

# Example 2: table of the potential. Forces omitted :pre

DIH_TABLE2

N 30 NOF CHECKU testU.dat CHECKF testF.dat :pre

1 -168.0 -1.40351172223

2 -156.0 -1.70447981034

3 -144.0 -1.62956100432

...

30 180.0 -0.707106781187 :pre

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"_dihedral_coeff.html 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"_dihedral_style.html 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_start.html#start_3

section for more info on packages.

[Related commands:]

"dihedral_coeff"_dihedral_coeff.html, "dihedral_style table"_dihedral_table.html

[Default:] none

:link(dihedralcut-Salerno)

[(Salerno)] Salerno, Bernstein, J Chem Theory Comput, --, ---- (2018).

   dihedral_quadratic

   dihedral_spherical

   dihedral_table

   dihedral_table_cut

   dihedral_zero

   dihedral_charmm

   dihedral_class2