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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
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<HTML>
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<HEAD>
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<META NAME="Generator" CONTENT="Cosmo Create 1.0.3">
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</HEAD>
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<BODY>
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<H2>
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LAMMPS Force Fields</H2>
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<P>
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<A HREF="README.html">Return</A> to top-level of LAMMPS documentation</P>
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<P>
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This file outlines the force-field formulas used in LAMMPS. Read this
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file in conjunction with the <A HREF="data_format.html">data_format</A>
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and <A HREF="units.html">units</A> file.</P>
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<P>
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The sections of this page are as follows:</P>
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<UL>
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<LI>
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<A HREF="#_cch3_930957465">Nonbond Coulomb</A>
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<LI>
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<A HREF="#_cch3_930957471">Nonbond Lennard-Jones</A>
|
||||
<LI>
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||||
<A HREF="#_cch3_930957478">Mixing Rules for Lennard-Jones</A>
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||||
<LI>
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<A HREF="#_cch3_930957482">Bonds</A>
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<LI>
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<A HREF="#_cch3_930957488">Angles</A>
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||||
<LI>
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<A HREF="#_cch3_930957509">Dihedrals</A>
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||||
<LI>
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<A HREF="#_cch3_930957513">Impropers</A>
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<LI>
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<A HREF="#_cch3_930957527">Class II Force Field</A>
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</UL>
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<HR>
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<H3>
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<A NAME="_cch3_930957465">Nonbond Coulomb</A></H3>
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<P>
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Whatever Coulomb style is specified in the input command file, the
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short-range Coulombic interactions are computed by this formula,
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modified by an appropriate smoother for the smooth, Ewald, and PPPM
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styles.</P>
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<PRE>
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E = C q1 q2 / (epsilon * r)
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r = distance (computed by LAMMPS)
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C = hardwired constant to convert to energy units
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||||
q1,q2 = charge of each atom in electron units (proton = +1),
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||||
specified in "Atoms" entry in data file
|
||||
epsilon = dielectric constant (vacuum = 1.0),
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set by user in input command file
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</PRE>
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||||
<HR>
|
||||
<H3>
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<A NAME="_cch3_930957471">Nonbond Lennard-Jones </A></H3>
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<P>
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The style of nonbond potential is specified in the input command file. </P>
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<H4>
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(1) lj/cutoff </H4>
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<PRE>
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E = 4 epsilon [ (sigma/r)^12 - (sigma/r)^6 ]
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standard Lennard Jones potential
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r = distance (computed by LAMMPS)
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coeff1 = epsilon (energy)
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coeff2 = sigma (distance)
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2 coeffs are listed in data file or set in input script
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1 cutoff is set in input script
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</PRE>
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<H4>
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(2) lj/switch </H4>
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<PRE>
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E = 4 epsilon [ (sigma/r)^12 - (sigma/r)^6 ] for r < r_inner
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= spline fit for r_inner < r < cutoff
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= 0 for r > cutoff
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switching function (spline fit) is applied to standard LJ
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within a switching region (from r_inner to cutoff) so that
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energy and force go smoothly to zero
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spline coefficients are computed by LAMMPS
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so that at inner cutoff (r_inner) the potential, force,
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and 1st-derivative of force are all continuous,
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and at outer cutoff (cutoff) the potential and force
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both go to zero
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r = distance (computed by LAMMPS)
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coeff1 = epsilon (energy)
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coeff2 = sigma (distance)
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2 coeffs are listed in data file or set in input script
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||||
2 cutoffs (r_inner and cutoff) are set in input script
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||||
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</PRE>
|
||||
<H4>
|
||||
(3) lj/shift </H4>
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||||
<PRE>
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||||
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E = 4 epsilon [ (sigma/(r - delta))^12 - (sigma/(r - delta))^6 ]
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same as lj/cutoff except that r is shifted by delta
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r = distance (computed by LAMMPS)
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coeff1 = epsilon (energy)
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coeff2 = sigma (distance)
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||||
coeff3 = delta (distance)
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||||
|
||||
3 coeffs are listed in data file or set in input script
|
||||
1 cutoff is set in input script
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||||
|
||||
</PRE>
|
||||
<H4>
|
||||
(4) soft </H4>
|
||||
<PRE>
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||||
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E = A * [ 1 + cos( pi * r / cutoff ) ]
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useful for pushing apart overlapping atoms by ramping A over time
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||||
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r = distance (computed by LAMMPS)
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coeff1 = prefactor A at start of run (energy)
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||||
coeff2 = prefactor A at end of run (energy)
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||||
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2 coeffs are listed in data file or set in input script
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||||
1 cutoff is set in input script
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||||
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||||
</PRE>
|
||||
<H4>
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||||
(5) class2/cutoff </H4>
|
||||
<PRE>
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||||
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E = epsilon [ 2 (sigma/r)^9 - 3 (sigma/r)^6 ]
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used with class2 bonded force field
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r = distance (computed by LAMMPS)
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coeff1 = epsilon (energy)
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coeff2 = sigma (distance)
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||||
|
||||
2 coeffs are listed in data file or set in input script
|
||||
1 cutoff is set in input script
|
||||
</PRE>
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||||
<HR>
|
||||
<H3>
|
||||
<A NAME="_cch3_930957478">Mixing Rules for Lennard-Jones</A></H3>
|
||||
<P>
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The coefficients for each nonbond style are input in either the data
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file by the "read data" command or in the input script using
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the "nonbond coeff" command. In the former case, only one set
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||||
of coefficients is input for each atom type. The cross-type coeffs are
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computed using one of three possible mixing rules: </P>
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||||
<PRE>
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||||
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geometric: epsilon_ij = sqrt(epsilon_i * epsilon_j)
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sigma_ij = sqrt(sigma_i * sigma_j)
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arithmetic: epsilon_ij = sqrt(epsilon_i * epsilon_j)
|
||||
sigma_ij = (sigma_i + sigma_j) / 2
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||||
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||||
sixthpower: epsilon_ij =
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(2 * sqrt(epsilon_i*epsilon_j) * sigma_i^3 * sigma_j^3) /
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(sigma_i^6 + sigma_j^6)
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||||
sigma_ij= ((sigma_i**6 + sigma_j**6) / 2) ^ (1/6)
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</PRE>
|
||||
<P>
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||||
The default mixing rule for nonbond styles lj/cutoff, lj/switch,
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lj/shift, and soft is "geometric". The default for nonbond
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||||
style class2/cutoff is "sixthpower". </P>
|
||||
<P>
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||||
The default can be overridden using the "mixing style"
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command. The one exception to this is for the nonbond style soft, for
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||||
which only an epsilon prefactor is input. This is always mixed
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||||
geometrically. </P>
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||||
<P>
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Also, for nonbond style lj/shift, the delta coefficient is always mixed
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||||
using the rule </P>
|
||||
<UL>
|
||||
<LI>
|
||||
delta_ij = (delta_i + delta_j) / 2
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||||
</UL>
|
||||
<HR>
|
||||
<H3>
|
||||
<A NAME="_cch3_930957482">Bonds</A></H3>
|
||||
<P>
|
||||
The style of bond potential is specified in the input command file.</P>
|
||||
<H4>
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||||
(1) harmonic </H4>
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||||
<PRE>
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||||
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E = K (r - r0)^2
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standard harmonic spring
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||||
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r = distance (computed by LAMMPS)
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coeff1 = K (energy/distance^2) (the usual 1/2 is included in the K)
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||||
coeff2 = r0 (distance)
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||||
|
||||
2 coeffs are listed in data file or set in input script
|
||||
|
||||
</PRE>
|
||||
<H4>
|
||||
(2) FENE/standard </H4>
|
||||
<PRE>
|
||||
|
||||
E = -0.5 K R0^2 * ln[1 - (r/R0)^2] +
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4 epsilon [(sigma/r)^12 - (sigma/r)^6] + epsilon
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||||
|
||||
finite extensible nonlinear elastic (FENE) potential for
|
||||
polymer bead-spring models
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||||
see Kremer, Grest, J Chem Phys, 92, p 5057 (1990)
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r = distance (computed by LAMMPS)
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coeff1 = K (energy/distance^2)
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coeff2 = R0 (distance)
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||||
coeff3 = epsilon (energy)
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coeff4 = sigma (distance)
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1st term is attraction, 2nd term is repulsion (shifted LJ)
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1st term extends to R0
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2nd term only extends to the minimum of the LJ potential,
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a cutoff distance computed by LAMMPS (2^(1/6) * sigma)
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4 coeffs are listed in data file or set in input script
|
||||
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</PRE>
|
||||
<H4>
|
||||
(3) FENE/shift </H4>
|
||||
<PRE>
|
||||
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E = -0.5 K R0^2 * ln[1 - ((r - delta)/R0)^2] +
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4 epsilon [(sigma/(r - delta))^12 - (sigma/(r - delta))^6] + epsilon
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||||
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same as FENE/standard expect that r is shifted by delta
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r = distance (computed by LAMMPS)
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coeff1 = K (energy/distance^2)
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coeff2 = R0 (distance)
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coeff3 = epsilon (energy)
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coeff4 = sigma (distance)
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||||
coeff5 = delta (distance)
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||||
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||||
1st term is attraction, 2nd term is repulsion (shifted LJ)
|
||||
1st term extends to R0
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||||
2nd term only extends to the minimum of the LJ potential,
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||||
a cutoff distance computed by LAMMPS (2^(1/6) * sigma + delta)
|
||||
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||||
5 coeffs are listed in data file or set in input script
|
||||
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||||
</PRE>
|
||||
<H4>
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||||
(4) nonlinear </H4>
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||||
<PRE>
|
||||
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||||
E = epsilon (r - r0)^2 / [ lamda^2 - (r - r0)^2 ]
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non-harmonic spring of equilibrium length r0
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with finite extension of lamda
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see Rector, Van Swol, Henderson, Molecular Physics, 82, p 1009 (1994)
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r = distance (computed by LAMMPS)
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coeff1 = epsilon (energy)
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coeff2 = r0 (distance)
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coeff3 = lamda (distance)
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||||
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3 coeffs are listed in data file or set in input script
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||||
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||||
</PRE>
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||||
<H4>
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(5) class2 </H4>
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<PRE>
|
||||
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||||
E = K2 (r - r0)^2 + K3 (r - r0)^3 + K4 (r - r0)^4
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||||
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r = distance (computed by LAMMPS)
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||||
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coeff1 = r0 (distance)
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coeff2 = K2 (energy/distance^2)
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coeff3 = K3 (energy/distance^3)
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coeff4 = K4 (energy/distance^4)
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4 coeffs are listed in data file - cannot be set in input script
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</PRE>
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<HR>
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<H3>
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<A NAME="_cch3_930957488">Angles </A></H3>
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<P>
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||||
The style of angle potential is specified in the input command file. </P>
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<H4>
|
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(1) harmonic </H4>
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||||
<PRE>
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E = K (theta - theta0)^2
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theta = radians (computed by LAMMPS)
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coeff1 = K (energy/radian^2) (the usual 1/2 is included in the K)
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||||
coeff2 = theta0 (degrees) (converted to radians within LAMMPS)
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2 coeffs are listed in data file
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</PRE>
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<H4>
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(2) class2 </H4>
|
||||
<PRE>
|
||||
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E = K2 (theta - theta0)^2 + K3 (theta - theta0)^3 +
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K4 (theta - theta0)^4
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theta = radians (computed by LAMMPS)
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coeff1 = theta0 (degrees) (converted to radians within LAMMPS)
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||||
coeff2 = K2 (energy/radian^2)
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coeff3 = K3 (energy/radian^3)
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coeff4 = K4 (energy/radian^4)
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4 coeffs are listed in data file
|
||||
</PRE>
|
||||
<HR>
|
||||
<H3>
|
||||
<A NAME="_cch3_930957509">Dihedrals </A></H3>
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<P>
|
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The style of dihedral potential is specified in the input command file. </P>
|
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<H4>
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(1) harmonic </H4>
|
||||
<PRE>
|
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E = K [1 + d * cos (n * phi) ]
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phi = radians (computed by LAMMPS)
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coeff1 = K (energy)
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coeff2 = d (always +1 or -1)
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coeff3 = n (1,2,3,4,6)
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Cautions when comparing to other force fields:
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||||
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||||
some force fields reverse the sign convention on d so that
|
||||
E = K [1 - d * cos(n*phi)]
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||||
some force fields divide/multiply K by the number of multiple
|
||||
torsions that contain the j-k bond in an i-j-k-l torsion
|
||||
some force fields let n be positive or negative which
|
||||
corresponds to d = 1,-1
|
||||
in the LAMMPS force field, the trans position = 180 degrees, while
|
||||
in some force fields trans = 0 degrees
|
||||
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3 coeffs are listed in data file
|
||||
</PRE>
|
||||
<H4>
|
||||
(2) class2 </H4>
|
||||
<PRE>
|
||||
|
||||
E = SUM(n=1,3) { K_n [ 1 - cos( n*Phi - Phi0_n ) ] }
|
||||
|
||||
phi = radians (computed by LAMMPS)
|
||||
|
||||
coeff1 = K_1 (energy)
|
||||
coeff2 = Phi0_1 (degrees) (converted to radians within LAMMPS)
|
||||
coeff3 = K_2 (energy)
|
||||
coeff4 = Phi0_2 (degrees) (converted to radians within LAMMPS)
|
||||
coeff5 = K_3 (energy)
|
||||
coeff6 = Phi0_3 (degrees) (converted to radians within LAMMPS)
|
||||
|
||||
6 coeffs are listed in data file
|
||||
</PRE>
|
||||
<HR>
|
||||
<H3>
|
||||
<A NAME="_cch3_930957513">Impropers</A></H3>
|
||||
<P>
|
||||
The style of improper potential is specified in the input command file. </P>
|
||||
<H4>
|
||||
(1) harmonic </H4>
|
||||
<PRE>
|
||||
|
||||
E = K (chi - chi0)^2
|
||||
|
||||
chi = radians (computed by LAMMPS)
|
||||
|
||||
coeff1 = K (energy/radian^2) (the usual 1/2 is included in the K)
|
||||
coeff2 = chi0 (degrees) (converted to radians within LAMMPS)
|
||||
|
||||
in data file, listing of 4 atoms requires atom-1 as central atom
|
||||
some force fields (AMBER,Discover) have atom-2 as central atom - it is really
|
||||
an out-of-plane torsion, may need to treat as dihedral in LAMMPS
|
||||
|
||||
2 coeffs are listed in data file
|
||||
</PRE>
|
||||
<H4>
|
||||
(2) class2 </H4>
|
||||
<PRE>
|
||||
|
||||
same formula, coeffs, and meaning as "harmonic" except that LAMMPS
|
||||
averages all 3 angle-contributions to chi
|
||||
in class II this is called a Wilson out-of-plane interaction
|
||||
|
||||
2 coeffs are listed in data file
|
||||
</PRE>
|
||||
<HR>
|
||||
<H3>
|
||||
<A NAME="_cch3_930957527">Class II Force Field</A></H3>
|
||||
<P>
|
||||
If class II force fields are selected in the input command file,
|
||||
additional cross terms are computed as part of the force field.</P>
|
||||
<H4>
|
||||
Bond-Bond (computed within class II angles) </H4>
|
||||
<PRE>
|
||||
|
||||
E = K (r - r0) * (r' - r0')
|
||||
|
||||
r,r' = distance (computed by LAMMPS)
|
||||
|
||||
coeff1 = K (energy/distance^2)
|
||||
coeff2 = r0 (distance)
|
||||
coeff3 = r0' (distance)
|
||||
|
||||
3 coeffs are input in data file
|
||||
</PRE>
|
||||
<H4>
|
||||
Bond-Angle (computed within class II angles for each of 2 bonds) </H4>
|
||||
<PRE>
|
||||
|
||||
E = K_n (r - r0_n) * (theta - theta0)
|
||||
|
||||
r = distance (computed by LAMMPS)
|
||||
theta = radians (computed by LAMMPS)
|
||||
|
||||
coeff1 = K_1 (energy/distance-radians)
|
||||
coeff2 = K_2 (energy/distance-radians)
|
||||
coeff3 = r0_1 (distance)
|
||||
coeff4 = r0_2 (distance)
|
||||
|
||||
Note: theta0 is known from angle coeffs so don't need it specified here
|
||||
|
||||
4 coeffs are listed in data file
|
||||
</PRE>
|
||||
<H4>
|
||||
Middle-Bond-Torsion (computed within class II dihedral) </H4>
|
||||
<PRE>
|
||||
|
||||
E = (r - r0) * [ F1*cos(phi) + F2*cos(2*phi) + F3*cos(3*phi) ]
|
||||
|
||||
r = distance (computed by LAMMPS)
|
||||
phi = radians (computed by LAMMPS)
|
||||
|
||||
coeff1 = F1 (energy/distance)
|
||||
coeff2 = F2 (energy/distance)
|
||||
coeff3 = F3 (energy/distance)
|
||||
coeff4 = r0 (distance)
|
||||
|
||||
4 coeffs are listed in data file
|
||||
</PRE>
|
||||
<H4>
|
||||
End-Bond-Torsion (computed within class II dihedral for each of 2
|
||||
bonds) </H4>
|
||||
<PRE>
|
||||
|
||||
E = (r - r0_n) * [ F1_n*cos(phi) + F2_n*cos(2*phi) + F3_n*cos(3*phi) ]
|
||||
|
||||
r = distance (computed by LAMMPS)
|
||||
phi = radians (computed by LAMMPS)
|
||||
|
||||
coeff1 = F1_1 (energy/distance)
|
||||
coeff2 = F2_1 (energy/distance)
|
||||
coeff3 = F3_1 (energy/distance)
|
||||
coeff4 = F1_2 (energy/distance)
|
||||
coeff5 = F2_3 (energy/distance)
|
||||
coeff6 = F3_3 (energy/distance)
|
||||
coeff7 = r0_1 (distance)
|
||||
coeff8 = r0_2 (distance)
|
||||
|
||||
8 coeffs are listed in data file
|
||||
</PRE>
|
||||
<H4>
|
||||
Angle-Torsion (computed within class II dihedral for each of 2 angles) </H4>
|
||||
<PRE>
|
||||
|
||||
E = (theta - theta0) * [ F1_n*cos(phi) + F2_n*cos(2*phi) + F3_n*cos(3*phi) ]
|
||||
|
||||
theta = radians (computed by LAMMPS)
|
||||
phi = radians (computed by LAMMPS)
|
||||
|
||||
coeff1 = F1_1 (energy/radians)
|
||||
coeff2 = F2_1 (energy/radians)
|
||||
coeff3 = F3_1 (energy/radians)
|
||||
coeff4 = F1_2 (energy/radians)
|
||||
coeff5 = F2_3 (energy/radians)
|
||||
coeff6 = F3_3 (energy/radians)
|
||||
coeff7 = theta0_1 (degrees) (converted to radians within LAMMPS)
|
||||
coeff8 = theta0_2 (degrees) (converted to radians within LAMMPS)
|
||||
|
||||
8 coeffs are listed in data file
|
||||
</PRE>
|
||||
<H4>
|
||||
Angle-Angle-Torsion (computed within class II dihedral) </H4>
|
||||
<PRE>
|
||||
|
||||
E = K (theta - theta0) * (theta' - theta0') * (phi - phi0)
|
||||
|
||||
theta,theta' = radians (computed by LAMMPS)
|
||||
phi = radians (computed by LAMMPS)
|
||||
|
||||
coeff1 = K (energy/radians^3)
|
||||
coeff2 = theta0 (degrees) (converted to radians within LAMMPS)
|
||||
coeff3 = theta0' (degrees) (converted to radians within LAMMPS)
|
||||
|
||||
Note: phi0 is known from dihedral coeffs so don't need it specified here
|
||||
|
||||
3 coeffs are listed in data file
|
||||
|
||||
</PRE>
|
||||
<H4>
|
||||
Bond-Bond-13-Torsion (computed within class II dihedral) </H4>
|
||||
<PRE>
|
||||
|
||||
(undocumented)
|
||||
|
||||
</PRE>
|
||||
<H4>
|
||||
Angle-Angle (computed within class II improper for each of 3 pairs of
|
||||
angles) </H4>
|
||||
<PRE>
|
||||
|
||||
E = K_n (theta - theta0_n) * (theta' - theta0_n')
|
||||
|
||||
theta,theta' = radians (computed by LAMMPS)
|
||||
|
||||
coeff1 = K_1 (energy/radians^2)
|
||||
coeff2 = K_2 (energy/radians^2)
|
||||
coeff3 = K_3 (energy/radians^2)
|
||||
coeff4 = theta0_1 (degrees) (converted to radians within LAMMPS)
|
||||
coeff5 = theta0_2 (degrees) (converted to radians within LAMMPS)
|
||||
coeff6 = theta0_3 (degrees) (converted to radians within LAMMPS)
|
||||
|
||||
6 coeffs are listed in data file
|
||||
</PRE>
|
||||
</BODY>
|
||||
</HTML>
|
||||
Reference in New Issue
Block a user