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			<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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			<H3>pair_style tersoff command
			</H3>
			<P><B>Syntax:</B>
			</P>
			<PRE>pair_style tersoff
			</PRE>
			<P><B>Examples:</B>
			</P>
			<PRE>pair_style tersoff
			pair_coeff * * si.tersoff Si
			pair_coeff * * SiC.tersoff Si C Si
			</PRE>
			<P><B>Description:</B>
			</P>
			<P>The <I>tersoff</I> style computes a 3-body Tersoff potential
			<A HREF = "#Tersoff_1">(Tersoff_1)</A> for the energy E of a system of atoms as
			</P>
			<CENTER><IMG SRC = "Eqs/pair_tersoff_1.jpg">
			</CENTER>
			<P>where f_R is a two-body term and f_A includes three-body interactions.
			The summations in the formula are over all neighbors J and K of atom I
			within a cutoff distance = R + D.
			</P>
			<P>Only a single pair_coeff command is used with the <I>tersoff</I> style
			which specifies a Tersoff potential file with parameters for all
			needed elements. These are mapped to LAMMPS atom types by specifying
			N additional arguments after the filename in the pair_coeff command,
			where N is the number of LAMMPS atom types:
			</P>
			<UL><LI>filename
			<LI>N element names = mapping of Tersoff elements to atom types
			</UL>
			<P>As an example, imagine the SiC.tersoff file has Tersoff values for Si
			and C. If your LAMMPS simulation has 4 atoms types and you want the
			1st 3 to be Si, and the 4th to be C, you would use the following
			pair_coeff command:
			</P>
			<PRE>pair_coeff * * SiC.tersoff Si Si Si C
			</PRE>
			<P>The 1st 2 arguments must be * * so as to span all LAMMPS atom types.
			The first three Si arguments map LAMMPS atom types 1,2,3 to the Si
			element in the Tersoff file. The final C argument maps LAMMPS atom
			type 4 to the C element in the Tersoff file. If a mapping value is
			specified as NULL, the mapping is not performed. This can be used
			when a <I>tersoff</I> potential is used as part of the <I>hybrid</I> pair style.
			The NULL values are placeholders for atom types that will be used with
			other potentials.
			</P>
			<P>Tersoff files in the <I>potentials</I> directory of the LAMMPS distribution
			have a ".tersoff" suffix. Lines that are not blank or comments
			(starting with #) define parameters for a triplet of elements. The
			parameters in a single entry correspond to coefficients in the formula
			above:
			</P>
			<UL><LI>element 1 (the center atom in a 3-body interaction)
			<LI>element 2 (the atom bonded to the center atom)
			<LI>element 3 (the atom influencing the 1-2 bond in a bond-order sense)
			<LI>m
			<LI>gamma
			<LI>lambda3 (1/distance units)
			<LI>c
			<LI>d
			<LI>costheta0 (can be a value < -1 or > 1)
			<LI>n
			<LI>beta
			<LI>lambda2 (1/distance units)
			<LI>B (energy units)
			<LI>R (distance units)
			<LI>D (distance units)
			<LI>lambda1 (1/distance units)
			<LI>A (energy units)
			</UL>
			<P>The n, beta, lambda2, B, lambda1, and A parameters are only used for
			two-body interactions. The m, gamma, lambda3, c, d, and costheta0 parameters
			are only used for three-body interactions. The R and D parameters
			are used for both two-body and three-body interactions. The
			non-annotated parameters are unitless.
			</P>
			<P>The Tersoff potential file must contain entries for all the elements
			listed in the pair_coeff command. It can also contain entries for
			additional elements not being used in a particular simulation; LAMMPS
			ignores those entries.
			</P>
			<P>For a single-element simulation, only a single entry is required
			(e.g. SiSiSi). For a two-element simulation, the file must contain 8
			entries (for SiSiSi, SiSiC, SiCSi, SiCC, CSiSi, CSiC, CCSi, CCC), that
			specify Tersoff parameters for all permutations of the two elements
			interacting in three-body configurations. Thus for 3 elements, 27
			entries would be required, etc.
			</P>
			<P>As annotated above, the first element in the entry is the center atom
			in a three-body interaction and it is bonded to the 2nd atom and the
			bond is influenced by the 3rd atom. Thus an entry for SiCC means Si
			bonded to a C with another C atom influencing the bond. Thus
			three-body parameters for SiCSi and SiSiC entries will not, in
			general, be the same. The parameters used for the two-body
			interaction come from the entry where the 2nd element is repeated.
			Thus the two-body parameters for Si interacting with C, comes from the
			SiCC entry. By symmetry, the twobody parameters in the SiCC and CSiSi
			entries should thus be the same. The parameters used for a particular
			three-body interaction come from the entry with the corresponding
			three elements. The parameters used only for two-body interactions
			(n, beta, lambda2, B, lambda1, and A) in entries whose 2nd and 3rd
			element are different (e.g. SiCSi) are not used for anything and can
			be set to 0.0 if desired.
			</P>
			<P>We chose the above form so as to enable users to define all commonly
			used variants of the Tersoff potential. In particular, our form
			reduces to the original Tersoff form when m = 3 and gamma = 1, while
			it reduces to the form of <A HREF = "#Albe">Albe et al.</A> when beta = 1 and m = 1.
			Tersoff used a slightly different but equivalent form for alloys,
			which we will refer to as Tersoff_2 potential
			<A HREF = "#Tersoff_2">(Tersoff_2)</A>.
			</P>
			<P>LAMMPS parameter values for Tersoff_2 can be obtained as follows.
			The parameters for species i and j can be calculated
			using the Tersoff_2 mixing rules:
			</P>
			<CENTER><IMG SRC = "Eqs/pair_tersoff_2.jpg">
			</CENTER>
			<P>Values not shown are determined by the first atom type. Finally, the
			Tersoff_2 parameters R and S must be converted to the LAMMPS
			parameters R and D (R is different in both forms), using the following
			relations: R=(R'+S')/2 and D=(S'-R')/2, where the primes indicate the
			Tersoff_2 parameters.
			</P>
			<P>In the potentials directory, the file SiCGe.tersoff provides the
			LAMMPS parameters for Tersoff's various versions of Si, as well as his
			alloy paramters for Si, C, and Ge. This file can be used for pure Si,
			(three different versions), pure C, pure Ge, binary SiC, and binary
			SiGe. LAMMPS will generate an error if this file is used with any
			combination involving C and Ge, since there are no entries for the GeC
			interactions (Tersoff did not publish parameters for this
			cross-interaction.) Tersoff files are also provided for the SiC alloy
			(SiC.tersoff) and the GaN (GaN.tersoff) alloys.
			</P>
			<P>Many thanks to Rutuparna Narulkar, David Farrell, and Xiaowang Zhou
			for helping clarify how Tersoff parameters for alloys have been
			defined in various papers.
			</P>
			<HR>

			<P><B>Mixing, shift, table, tail correction, restart, rRESPA info</B>:
			</P>
			<P>For atom type pairs I,J and I != J, where types I and J correspond to
			two different element types, mixing is performed by LAMMPS as
			described above from values in the potential file.
			</P>
			<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A>
			shift, table, and tail options.
			</P>
			<P>This pair style does not write its information to <A HREF = "restart.html">binary restart
			files</A>, since it is stored in potential files. Thus, you
			need to re-specify the pair_style and pair_coeff commands in an input
			script that reads a restart file.
			</P>
			<P>This pair style can only be used via the <I>pair</I> keyword of the
			<A HREF = "run_style.html">run_style respa</A> command. It does not support the
			<I>inner</I>, <I>middle</I>, <I>outer</I> keywords.
			</P>
			<HR>

			<P><B>Restrictions:</B>
			</P>
			<P>This pair style is part of the "manybody" package. It is only enabled
			if LAMMPS was built with that package (which it is by default). See
			the <A HREF = "Section_start.html#2_3">Making LAMMPS</A> section for more info.
			</P>
			<P>This pair style requires the <A HREF = "newton.html">newton</A> setting to be "on"
			for pair interactions.
			</P>
			<P>The Tersoff potential files provided with LAMMPS (see the potentials
			directory) are parameterized for metal <A HREF = "units.html">units</A>. You can
			use the Tersoff potential with any LAMMPS units, but you would need to
			create your own Tersoff potential file with coefficients listed in the
			appropriate units if your simulation doesn't use "metal" units.
			</P>
			<P><B>Related commands:</B>
			</P>
			<P><A HREF = "pair_coeff.html">pair_coeff</A>
			</P>
			<P><B>Default:</B> none
			</P>
			<HR>

			<A NAME = "Tersoff_1"></A>

			<P><B>(Tersoff_1)</B> J. Tersoff, Phys Rev B, 37, 6991 (1988).
			</P>
			<A NAME = "Albe"></A>

			<P><B>(Albe)</B> J. Nord, K. Albe, P. Erhartand K. Nordlund, J. Phys.:
			Condens. Matter, 15, 5649(2003).
			</P>
			<A NAME = "Tersoff_2"></A>

			<P><B>(Tersoff_2)</B> J. Tersoff, Phys Rev B, 39, 5566 (1989)
			</P>
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