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<HTML>
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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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</CENTER>
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<HR>
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<H3>pair_style bop command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>pair_style bop keyword ...
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</PRE>
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<UL><LI>zero or more keywords may be appended
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<LI>keyword = <I>table</I> or <I>save</I> or <I>sigmaoff</I>
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<PRE> <I>table</I> = BOP potential file has tabulated form
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<I>save</I> = pre-compute and save some values
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<I>sigmaoff</I> = assume a_sigma = 0
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</PRE>
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>pair_style bop
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pair_coeff * * ../potentials/CdTe_bop Cd Te
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pair_style bop table save
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pair_coeff * * ../potentials/CdTe.bop.table Cd Te Te
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communicate single cutoff 14.70
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>The <I>bop</I> pair style computes Bond-Order Potentials (BOP) based on
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quantum mechanical theory incorporating both sigma and pi bondings.
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By analytically deriving the BOP from quantum mechanical theory its
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transferability to different phases can approach that of quantum
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mechanical methods. This particlular BOP is extremely effective at
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modeling III-V and II-VI compounds such as GaAs and CdTe. This
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potential is similar to the original BOP developed by Pettifor
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(<A HREF = "#Pettifor_1">Pettifor_1</A>, <A HREF = "#Pettifor_2">Pettifor_2</A>,
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<A HREF = "#Pettifor_3">Pettifor_3</A>) and later updated by Murdick, Zhou, and Ward
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(<A HREF = "#Murdick">Murdick</A>, <A HREF = "#Ward">Ward</A>).
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</P>
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<P>The BOP potential consists of three terms:
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</P>
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<CENTER><IMG SRC = "Eqs/pair_bop.jpg">
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</CENTER>
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<P>where phi_ij(r_ij) is a short-range two-body function representing the
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repulsion between a pair of ion cores, beta_(sigma,ij)(r_ij) and
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beta_(sigma,ij)(r_ij) are respectively sigma and pi bond ingtegrals,
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THETA_(sigma,ij) and THETA_(pi,ij) are sigma and pi bond-orders, and
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U_prom is the promotion energy for sp-valent systems.
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</P>
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<P>The detailed formulas for this potential are given in Ward
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(<A HREF = "#Ward">Ward</A>); here we provide only a brief description.
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</P>
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<P>The repulsive energy phi_ij(r_ij) and the bond integrals
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beta_(sigma,ij)(r_ij) and beta_(phi,ij)(r_ij) are functions of the
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interatomic distance r_ij between atom i and j. Each of these
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potentials has a smooth cutoff at a radius of r_(cut,ij). These
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smooth cutoffs ensure stable behavior at situations with high sampling
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near the cutoff such as melts and surfaces.
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</P>
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<P>The bond-orders can be viewed as environment-dependent local variables
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that are ij bond specific. The maximum value of the sigma bond-order
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(THETA_sigma) is 1, while that of the pi bond-order (THETA_pi) is 2,
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attributing to a maximum value of the total bond-order
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(THETA_sigma+THETA_pi) of 3. The sigma and pi bond-orders reflect the
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ubiquitous single-, double-, and triple- bond behavior of
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chemistry. Their analytical expressions can be derived from tight-
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binding theory by recursively expanding an inter-site Green's function
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as a continued fraction. To accurately represent the bonding with a
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computationally efficient potential formulation suitable for MD
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simulations, the derived BOP only takes (and retains) the first two
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levels of the recursive representations for both the sigma and the pi
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bond-orders. Bond-order terms can be understood in terms of molecular
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orbital hopping paths based upon the Cyrot-Lackmann theorem
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(<A HREF = "#Pettifor_1">Pettifor_1</A>). The sigma bond-order with a half-full
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valence band filling. This pi bond-order expression also contains
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also contains a three-member ring term that allows implementation of
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an asymmetric density of states, which helps to either stabilize or
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destabilize close-packed structures. The pi bond-order includes
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hopping paths of length 4. This enables the incorporation of dihedral
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angles effects.
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</P>
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<P>The cutoffs for the various interactions are defined in the BOP
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potential file.
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</P>
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<P>IMPORTANT NOTE: You must use the <A HREF = "communicate.html">communicate cutoff</A>
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command to insure ghost atoms are acquired at a distance 3x further
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than the largest BOP cutoff (for a particular pair of elements).
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E.g. if the BOP cutoff is 4.9 Angstroms, then the ghost atom
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communication needs to be 14.7 Angstroms or greater as in the example
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above. This is because the BOP formulation uses neighbors of
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neighbors of neighbors to enumerate all the required many-body
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interactions. LAMMPS will generate an error if you do not use an
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appropriate setting for the <A HREF = "communicate.html">communicate cutoff</A>
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command.
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</P>
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<P>Several options can be specified as keywords with the pair_style
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command.
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</P>
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<P>The <I>table</I> keyword tells LAMMPS what format the BOP potential file is
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in. The default is a non-tabulated form. If the <I>table</I> keyword is
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used, the file is in a tabulated form containing pre-tabulated pair
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functions for phi_ij(r_ij), beta_(sigma,ij)(r_ij), and
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beta_(pi,ij)(r_ij). This allows you to use your own functional
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form for various interactions.
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</P>
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<P>The <I>save</I> keyword gives you the option to calculate and store in
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advance a set of distances, angles, and derivatives of angles. The
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default is to not do this, but to calculate the various quantities
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on-the-fly each time they are needed. The former may be faster, but
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takes more memory. The latter requires less memory, but may be
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slower. It is best to test this option to see if it makes a
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difference on your machine for the specific problem you are modeling.
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</P>
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<P>The <I>sigmaoff</I> keyword optimizes the BOP equations for the case of
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a_sigma = 0. For some published BOP potentials, a_sigma = 0 and
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several terms in the BOP equationas drop out. If this is the case,
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specifying <I>sigmaoff</I> will typically speed up the BOP pair style.
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</P>
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<HR>
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<P>Only a single pair_coeff command is used with the <I>bop</I> style which
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specifies a BOP potential file, with parameters for all needed
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elements. These are mapped to LAMMPS atom types by specifying
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N additional arguments after the filename in the pair_coeff command,
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where N is the number of LAMMPS atom types:
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</P>
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<UL><LI>filename
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<LI>N element names = mapping of BOP elements to atom types
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</UL>
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<P>As an example, imagine the CdTe.bop file has BOP values for Cd
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and Te. If your LAMMPS simulation has 4 atoms types and you want the
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1st 3 to be Cd, and the 4th to be Te, you would use the following
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pair_coeff command:
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</P>
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<PRE>pair_coeff * * CdTe Cd Cd Cd Te
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</PRE>
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<P>The 1st 2 arguments must be * * so as to span all LAMMPS atom types.
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The first three Cd arguments map LAMMPS atom types 1,2,3 to the Cd
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element in the BOP file. The final Te argument maps LAMMPS atom type
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4 to the Te element in the BOP file. If a mapping value is specified
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as NULL, the mapping is not performed. This can be used when a
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<I>bop</I> potential is used as part of the <I>hybrid</I> pair style. The
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NULL values are placeholders for atom types that will be used with
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other potentials.
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</P>
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<P>BOP files in the <I>potentials</I> directory of the LAMMPS distribution
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have a ".bop" or ".bop.table" suffix, depending on whether they are of
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the non-tabulated or tabulated form, as described above.
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</P>
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<P>The parameters/coefficients format for the both kinds of BOP files are
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given below with variables matching the formulation of Ward
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(<A HREF = "#Ward">Ward</A>). Each header line containing a ":" is preceded by a
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blank line.
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</P>
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<UL><LI>Line 1: elements: (header)
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<LI>Line 2: #elements <I>N</I>
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</UL>
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<P>The first two lines are followed by N lines containing the atomic
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number and mass of each element.
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</P>
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<HR>
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<P><B>Non-tabulated potential file format</B>:
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</P>
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<P>Following the definition of the elements is the block of global
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variables for spline and quadratic fits of THETA_(S,ij) and its
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components THETA_0, THETA_1, and S.
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</P>
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<UL><LI>Line 1: global: (header)
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<LI>Line 2: delta_1-delta_7 (if all are not used in the particular
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formulation, set unused values to 0.0)
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<LI>Line 3: ncutoff, r_big, r_small (r_big and r_small are parameters for
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pairwise paramters gamma typically set to 0.99 and 0.01, respectively)
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<LI>Line 4: which, alpha, nfunc (these are options for the spline
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which=1.0 (means using a smooth function); which=2.0 (spline), alpha is
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a parameter in the spline, nfunc is the type of GSP function (f_ij)
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(nfunc=1 is the published equation from Ward (<A HREF = "#Ward">Ward</A>); nfunc=2
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f_ij(r_ij)=exp(n_ij*r_ij); nfunc=3 f_ij(r_ij)=1/(r_ij)^(n_ij)).
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<LI>Line 5: alpha_1, beta_1, gamma_1 (alpha_1=first coefficient for
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THETA_0; beta_1=first exponent for THETA_0; gamma_1=second exponent for
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THETA_0)
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<LI>Line 6: alpha_2, beta_2 (alpha_2=second coefficient for S; beta_2=first
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exponent for S)
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<LI>Line 7: alpha_3, beta_3 (alpha_3=first coefficient for THETA_1;
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beta_3=second coefficient for THETA_1)
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</UL>
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<P>The next block contains constants for the environment depend
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promotional energy for sp-valent systems, each of which are species
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dependent. Refer to Pettifor (<A HREF = "#Pettifor_3">Pettifor_3</A>) for constant
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definitions. As well as one species dependent parameter p_pi.
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</P>
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<UL><LI>Line 1: ptrs: (header)
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</UL>
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<P>Following the ptrs header there are N lines for e_1-e_N containing
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(A_ij)^(mu*nu), delta^mu, p_pi
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</P>
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<UL><LI>Line 2: (A_ij)^(mu*nu), delta^mu, p_pi (for e_1)
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<LI>Line 3: (A_ij)^(mu*nu), delta^mu, p_pi (for e_2 and continues to e_N)
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</UL>
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<P>The next block contains constants for the pair interactions.
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</P>
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<UL><LI>Line 1: pairs: (header)
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</UL>
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<P>Following the header the block contains a series of constants for the
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number of pair interaction types, the block will be broken up into
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parameters for e_i-e_j with i=0->N, j=i->N. Each single interaction
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section for this block will contain (see <A HREF = "#Ward">Ward</A> for parameter
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definitions):
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</P>
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<UL><LI>Line 2: r_0, r_c, r_1, r_cut (for e_1-e_2 interactions)
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<LI>Line 3: m, n, n_c
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<LI>Line 4: phi_0, beta_(sigma,0), beta_(pi,0)
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<LI>Line 5: a_sigma, c_sigma, delta_sigma (From complete formulation of 1/2
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full valance shell for this particular formulation delta_sigma=0)
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<LI>Line 6: a_pi, c_pi, delta_pi
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<LI>Line 7: f_sigma, k_sigma, delta_3 (This delta_3 is similar to that of
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the previous section but is interaction type dependent)
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<LI>Line 8: r_0, r_c, r_1, r_cut (for e_1-e_2 interactions and repeats as
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above)
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</UL>
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<P>The next block contains tris.
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</P>
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<UL><LI>Line 1: tris: (header)
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</UL>
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<P>Following the header there is a line for each three body interaction
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types as e_j-e_i-e_k with i->N, j->N, k=j->N
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</P>
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<UL><LI>Line 2: g_sigma0, g_sigma1, g_sigma2 (these are coefficients for
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g_(sigma,ijk)(theta_ijk) for e_1-e_1-e_1 interaction. <A HREF = "#Ward">Ward</A>
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contains the full expressions for the constants as functions of
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b_(sigma,ijk), p_(sigma,ijk), u(sigma,ijk)
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<LI>Line 3: g_sigma0, g_sigma1, g_sigma2 (for e_1-e_1-e_2)
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</UL>
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<P>This would be the end of the potential parameter file without pre-
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tabulated data.
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</P>
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<HR>
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<P><B>Tabulated potential file format</B>:
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</P>
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<P>The parameters/coefficients format for the BOP potentials input file
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containing pre-tabulated functions of is given below with variables
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matching the formulation of Ward (<A HREF = "#Ward">Ward</A>).
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</P>
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<UL><LI>Line 1: # elements N
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</UL>
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<P>The first two lines are followed by N lines containing the atomic
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number and mass of each element THETA_0 and THETA_1 (see
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<A HREF = "#Ward">Ward</A>).
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</P>
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<P>Following the definition of the elements several global variables for
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the tabulated functions are given.
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</P>
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<UL><LI>Line 1: nr, nBOt (nr is the number of divisions the radius is broken
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into for function tables and MUST be a factor of 5; nBOt is the number
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of divisions for the tabulated values of THETA_(S,ij)
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<LI>Line 2: delta_1-delta_7 (if all are not used in the particular
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<LI>formulation, set unused values to 0.0)
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</UL>
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<P>Following this N lines for e_1-e_N containing p_pi.
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</P>
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<UL><LI>Line 3: p_pi (for e_1)
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<LI>Line 4: p_pi (for e_2 and continues to e_N)
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</UL>
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<P>The next section contains several pair constants for the number of
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interaction types e_i-e_j, with i=1->N, j=i->N
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</P>
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<UL><LI>Line 1: r_cut (for e_1-e_1 interactions)
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<LI>Line 2: c_sigma, a_sigma, c_pi, a_pi
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<LI>Line 3: delta_sigma, delta_pi
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<LI>Line 4: f_sigma, k_sigma, delta_3 (This delta_3 is similar to that of
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the previous section but is interaction type dependent)
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</UL>
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<P>The next section contains a line for each three body interaction type
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e_j-e_i-e_k with i=0->N, j=0->N, k=j->N
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</P>
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<UL><LI>Line 1: g_(sigma0), g_(sigma1), g_(sigma2) (These are coefficients for
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g_(sigma,jik)(THETA_ijk) for e_1-e_1-e_1 interaction. <A HREF = "#Ward">Ward</A>
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contains the full expressions for the constants as functions of
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b_(sigma,ijk), p_(sigma,ijk), u_(sigma,ijk))
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<LI>Line 2: g_(sigma0), g_(sigma1), g_(sigma2) (for e_1-e_1-e_2)
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</UL>
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<P>The next section contains a block for each interaction type for the
|
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phi_ij(r_ij). Each block has nr entries with 5 entries per line.
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</P>
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<UL><LI>Line 1: phi(r1), phi(r2), phi(r3), phi(r4), phi(r5) (for the e_1-e_1
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interaction type)
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<LI>Line 2: phi(r6), phi(r7), phi(r8), phi(r9), phi(r10) (this continues
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until nr)
|
||||
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<LI>...
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||||
<LI>Line nr/5_1: phi(r1), phi(r2), phi(r3), phi(r4), phi(r5), (for the
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e_1-e_1 interaction type)
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</UL>
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<P>The next section contains a block for each interaction type for the
|
||||
beta_(sigma,ij)(r_ij). Each block has nr entries with 5 entries per
|
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line.
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</P>
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||||
<UL><LI>Line 1: beta_sigma(r1), beta_sigma(r2), beta_sigma(r3), beta_sigma(r4),
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beta_sigma(r5) (for the e_1-e_1 interaction type)
|
||||
|
||||
<LI>Line 2: beta_sigma(r6), beta_sigma(r7), beta_sigma(r8), beta_sigma(r9),
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||||
beta_sigma(r10) (this continues until nr)
|
||||
|
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<LI>...
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||||
<LI>Line nr/5+1: beta_sigma(r1), beta_sigma(r2), beta_sigma(r3),
|
||||
beta_sigma(r4), beta_sigma(r5) (for the e_1-e_2 interaction type)
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</UL>
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<P>The next section contains a block for each interaction type for
|
||||
beta_(pi,ij)(r_ij). Each block has nr entries with 5 entries per line.
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</P>
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||||
<UL><LI>Line 1: beta_pi(r1), beta_pi(r2), beta_pi(r3), beta_pi(r4), beta_pi(r5)
|
||||
(for the e_1-e_1 interaction type)
|
||||
|
||||
<LI>Line 2: beta_pi(r6), beta_pi(r7), beta_pi(r8), beta_pi(r9),
|
||||
beta_pi(r10) (this continues until nr)
|
||||
|
||||
<LI>...
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||||
|
||||
<LI>Line nr/5+1: beta_pi(r1), beta_pi(r2), beta_pi(r3), beta_pi(r4),
|
||||
beta_pi(r5) (for the e_1-e_2 interaction type)
|
||||
</UL>
|
||||
<P>The next section contains a block for each interaction type for the
|
||||
THETA_(S,ij)((THETA_(sigma,ij))^(1/2), f_(sigma,ij)). Each block has
|
||||
nBOt entries with 5 entries per line.
|
||||
</P>
|
||||
<UL><LI>Line 1: THETA_(S,ij)(r1), THETA_(S,ij)(r2), THETA_(S,ij)(r3),
|
||||
THETA_(S,ij)(r4), THETA_(S,ij)(r5) (for the e_1-e_2 interaction type)
|
||||
|
||||
<LI>Line 2: THETA_(S,ij)(r6), THETA_(S,ij)(r7), THETA_(S,ij)(r8),
|
||||
THETA_(S,ij)(r9), THETA_(S,ij)(r10) (this continues until nBOt)
|
||||
|
||||
<LI>...
|
||||
|
||||
<LI>Line nBOt/5+1: THETA_(S,ij)(r1), THETA_(S,ij)(r2), THETA_(S,ij)(r3),
|
||||
THETA_(S,ij)(r4), THETA_(S,ij)(r5) (for the e_1-e_2 interaction type)
|
||||
</UL>
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||||
<P>The next section contains a block of N lines for e_1-e_N
|
||||
</P>
|
||||
<UL><LI>Line 1: delta^mu (for e_1)
|
||||
<LI>Line 2: delta^mu (for e_2 and repeats to e_N)
|
||||
</UL>
|
||||
<P>The last section contains more constants for e_i-e_j interactions with
|
||||
i=0->N, j=i->N
|
||||
</P>
|
||||
<UL><LI>Line 1: (A_ij)^(mu*nu) (for e1-e1)
|
||||
<LI>Line 2: (A_ij)^(mu*nu) (for e1-e2 and repeats as above)
|
||||
</UL>
|
||||
<HR>
|
||||
|
||||
<P><B>Mixing, shift, table tail correction, restart</B>:
|
||||
</P>
|
||||
<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A>
|
||||
mix, 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>These pair styles are part of the MANYBODY package. They are only
|
||||
enabled if LAMMPS was built with that package (which it is by default).
|
||||
See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A> section for more
|
||||
info.
|
||||
</P>
|
||||
<P>These pair potentials require the <A HREF = "newton.html">newtion</A> setting to be
|
||||
"on" for pair interactions.
|
||||
</P>
|
||||
<P>The CdTe.bop and GaAs.bop potential files provided with LAMMPS (see the
|
||||
potentials directory) are parameterized for metal <A HREF = "units.html">units</A>.
|
||||
You can use the BOP potential with any LAMMPS units, but you would need
|
||||
to create your own BOP potential file with coefficients listed in the
|
||||
appropriate units if your simulation does not use "metal" units.
|
||||
</P>
|
||||
<P><B>Related commands:</B>
|
||||
</P>
|
||||
<P><A HREF = "pair_coeff.html">pair_coeff</A>
|
||||
</P>
|
||||
<P><B>Default:</B>
|
||||
</P>
|
||||
<P>non-tabulated potential file, a_0 is non-zero.
|
||||
</P>
|
||||
<HR>
|
||||
|
||||
<A NAME = "Pettofor_1"></A>
|
||||
|
||||
<P><B>(Pettifor_1)</B> D.G. Pettifor and I.I. Oleinik, Phys. Rev. B, 59, 8487
|
||||
(1999).
|
||||
</P>
|
||||
<A NAME = "Pettofor_2"></A>
|
||||
|
||||
<P><B>(Pettifor_2)</B> D.G. Pettifor and I.I. Oleinik, Phys. Rev. Lett., 84,
|
||||
4124 (2000).
|
||||
</P>
|
||||
<A NAME = "Pettofor_3"></A>
|
||||
|
||||
<P><B>(Pettifor_3)</B> D.G. Pettifor and I.I. Oleinik, Phys. Rev. B, 65, 172103
|
||||
(2002).
|
||||
</P>
|
||||
<A NAME = "Murdick"></A>
|
||||
|
||||
<P><B>(Murdick)</B> D.A. Murdick, X.W. Zhou, H.N.G. Wadley, D. Nguyen-Manh, R.
|
||||
Drautz, and D.G. Pettifor, Phys. Rev. B, 73, 45206 (2006).
|
||||
</P>
|
||||
<A NAME = "Ward"></A>
|
||||
|
||||
<P><B>(Ward)</B> D.K. Ward, X.W. Zhou, B.M. Wong, F.P. Doty, and J.A.
|
||||
Zimmerman, Phys. Rev. B, 85,115206 (2012).
|
||||
</P>
|
||||
</HTML>
|
||||
|
|
@ -0,0 +1,405 @@
|
|||
"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
|
||||
|
||||
pair_style bop command :h3
|
||||
|
||||
[Syntax:]
|
||||
|
||||
pair_style bop keyword ... :pre
|
||||
|
||||
zero or more keywords may be appended :ulb,l
|
||||
keyword = {table} or {save} or {sigmaoff} :l
|
||||
{table} = BOP potential file has tabulated form
|
||||
{save} = pre-compute and save some values
|
||||
{sigmaoff} = assume a_sigma = 0 :pre
|
||||
:ule
|
||||
|
||||
[Examples:]
|
||||
|
||||
pair_style bop
|
||||
pair_coeff * * ../potentials/CdTe_bop Cd Te
|
||||
pair_style bop table save
|
||||
pair_coeff * * ../potentials/CdTe.bop.table Cd Te Te
|
||||
communicate single cutoff 14.70 :pre
|
||||
|
||||
[Description:]
|
||||
|
||||
The {bop} pair style computes Bond-Order Potentials (BOP) based on
|
||||
quantum mechanical theory incorporating both sigma and pi bondings.
|
||||
By analytically deriving the BOP from quantum mechanical theory its
|
||||
transferability to different phases can approach that of quantum
|
||||
mechanical methods. This particlular BOP is extremely effective at
|
||||
modeling III-V and II-VI compounds such as GaAs and CdTe. This
|
||||
potential is similar to the original BOP developed by Pettifor
|
||||
("Pettifor_1"_#Pettifor_1, "Pettifor_2"_#Pettifor_2,
|
||||
"Pettifor_3"_#Pettifor_3) and later updated by Murdick, Zhou, and Ward
|
||||
("Murdick"_#Murdick, "Ward"_#Ward).
|
||||
|
||||
The BOP potential consists of three terms:
|
||||
|
||||
:c,image(Eqs/pair_bop.jpg)
|
||||
|
||||
where phi_ij(r_ij) is a short-range two-body function representing the
|
||||
repulsion between a pair of ion cores, beta_(sigma,ij)(r_ij) and
|
||||
beta_(sigma,ij)(r_ij) are respectively sigma and pi bond ingtegrals,
|
||||
THETA_(sigma,ij) and THETA_(pi,ij) are sigma and pi bond-orders, and
|
||||
U_prom is the promotion energy for sp-valent systems.
|
||||
|
||||
The detailed formulas for this potential are given in Ward
|
||||
("Ward"_#Ward); here we provide only a brief description.
|
||||
|
||||
The repulsive energy phi_ij(r_ij) and the bond integrals
|
||||
beta_(sigma,ij)(r_ij) and beta_(phi,ij)(r_ij) are functions of the
|
||||
interatomic distance r_ij between atom i and j. Each of these
|
||||
potentials has a smooth cutoff at a radius of r_(cut,ij). These
|
||||
smooth cutoffs ensure stable behavior at situations with high sampling
|
||||
near the cutoff such as melts and surfaces.
|
||||
|
||||
The bond-orders can be viewed as environment-dependent local variables
|
||||
that are ij bond specific. The maximum value of the sigma bond-order
|
||||
(THETA_sigma) is 1, while that of the pi bond-order (THETA_pi) is 2,
|
||||
attributing to a maximum value of the total bond-order
|
||||
(THETA_sigma+THETA_pi) of 3. The sigma and pi bond-orders reflect the
|
||||
ubiquitous single-, double-, and triple- bond behavior of
|
||||
chemistry. Their analytical expressions can be derived from tight-
|
||||
binding theory by recursively expanding an inter-site Green's function
|
||||
as a continued fraction. To accurately represent the bonding with a
|
||||
computationally efficient potential formulation suitable for MD
|
||||
simulations, the derived BOP only takes (and retains) the first two
|
||||
levels of the recursive representations for both the sigma and the pi
|
||||
bond-orders. Bond-order terms can be understood in terms of molecular
|
||||
orbital hopping paths based upon the Cyrot-Lackmann theorem
|
||||
("Pettifor_1"_#Pettifor_1). The sigma bond-order with a half-full
|
||||
valence band filling. This pi bond-order expression also contains
|
||||
also contains a three-member ring term that allows implementation of
|
||||
an asymmetric density of states, which helps to either stabilize or
|
||||
destabilize close-packed structures. The pi bond-order includes
|
||||
hopping paths of length 4. This enables the incorporation of dihedral
|
||||
angles effects.
|
||||
|
||||
The cutoffs for the various interactions are defined in the BOP
|
||||
potential file.
|
||||
|
||||
IMPORTANT NOTE: You must use the "communicate cutoff"_communicate.html
|
||||
command to insure ghost atoms are acquired at a distance 3x further
|
||||
than the largest BOP cutoff (for a particular pair of elements).
|
||||
E.g. if the BOP cutoff is 4.9 Angstroms, then the ghost atom
|
||||
communication needs to be 14.7 Angstroms or greater as in the example
|
||||
above. This is because the BOP formulation uses neighbors of
|
||||
neighbors of neighbors to enumerate all the required many-body
|
||||
interactions. LAMMPS will generate an error if you do not use an
|
||||
appropriate setting for the "communicate cutoff"_communicate.html
|
||||
command.
|
||||
|
||||
Several options can be specified as keywords with the pair_style
|
||||
command.
|
||||
|
||||
The {table} keyword tells LAMMPS what format the BOP potential file is
|
||||
in. The default is a non-tabulated form. If the {table} keyword is
|
||||
used, the file is in a tabulated form containing pre-tabulated pair
|
||||
functions for phi_ij(r_ij), beta_(sigma,ij)(r_ij), and
|
||||
beta_(pi,ij)(r_ij). This allows you to use your own functional
|
||||
form for various interactions.
|
||||
|
||||
The {save} keyword gives you the option to calculate and store in
|
||||
advance a set of distances, angles, and derivatives of angles. The
|
||||
default is to not do this, but to calculate the various quantities
|
||||
on-the-fly each time they are needed. The former may be faster, but
|
||||
takes more memory. The latter requires less memory, but may be
|
||||
slower. It is best to test this option to see if it makes a
|
||||
difference on your machine for the specific problem you are modeling.
|
||||
|
||||
The {sigmaoff} keyword optimizes the BOP equations for the case of
|
||||
a_sigma = 0. For some published BOP potentials, a_sigma = 0 and
|
||||
several terms in the BOP equationas drop out. If this is the case,
|
||||
specifying {sigmaoff} will typically speed up the BOP pair style.
|
||||
|
||||
:line
|
||||
|
||||
Only a single pair_coeff command is used with the {bop} style which
|
||||
specifies a BOP 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:
|
||||
|
||||
filename
|
||||
N element names = mapping of BOP elements to atom types :ul
|
||||
|
||||
As an example, imagine the CdTe.bop file has BOP values for Cd
|
||||
and Te. If your LAMMPS simulation has 4 atoms types and you want the
|
||||
1st 3 to be Cd, and the 4th to be Te, you would use the following
|
||||
pair_coeff command:
|
||||
|
||||
pair_coeff * * CdTe Cd Cd Cd Te :pre
|
||||
|
||||
The 1st 2 arguments must be * * so as to span all LAMMPS atom types.
|
||||
The first three Cd arguments map LAMMPS atom types 1,2,3 to the Cd
|
||||
element in the BOP file. The final Te argument maps LAMMPS atom type
|
||||
4 to the Te element in the BOP file. If a mapping value is specified
|
||||
as NULL, the mapping is not performed. This can be used when a
|
||||
{bop} potential is used as part of the {hybrid} pair style. The
|
||||
NULL values are placeholders for atom types that will be used with
|
||||
other potentials.
|
||||
|
||||
BOP files in the {potentials} directory of the LAMMPS distribution
|
||||
have a ".bop" or ".bop.table" suffix, depending on whether they are of
|
||||
the non-tabulated or tabulated form, as described above.
|
||||
|
||||
The parameters/coefficients format for the both kinds of BOP files are
|
||||
given below with variables matching the formulation of Ward
|
||||
("Ward"_#Ward). Each header line containing a ":" is preceded by a
|
||||
blank line.
|
||||
|
||||
Line 1: elements: (header)
|
||||
Line 2: #elements {N} :ul
|
||||
|
||||
The first two lines are followed by N lines containing the atomic
|
||||
number and mass of each element.
|
||||
|
||||
:line
|
||||
|
||||
[Non-tabulated potential file format]:
|
||||
|
||||
Following the definition of the elements is the block of global
|
||||
variables for spline and quadratic fits of THETA_(S,ij) and its
|
||||
components THETA_0, THETA_1, and S.
|
||||
|
||||
Line 1: global: (header) :ulb,l
|
||||
Line 2: delta_1-delta_7 (if all are not used in the particular
|
||||
formulation, set unused values to 0.0) :l
|
||||
Line 3: ncutoff, r_big, r_small (r_big and r_small are parameters for
|
||||
pairwise paramters gamma typically set to 0.99 and 0.01, respectively) :l
|
||||
Line 4: which, alpha, nfunc (these are options for the spline
|
||||
which=1.0 (means using a smooth function); which=2.0 (spline), alpha is
|
||||
a parameter in the spline, nfunc is the type of GSP function (f_ij)
|
||||
(nfunc=1 is the published equation from Ward ("Ward"_#Ward); nfunc=2
|
||||
f_ij(r_ij)=exp(n_ij*r_ij); nfunc=3 f_ij(r_ij)=1/(r_ij)^(n_ij)). :l
|
||||
Line 5: alpha_1, beta_1, gamma_1 (alpha_1=first coefficient for
|
||||
THETA_0; beta_1=first exponent for THETA_0; gamma_1=second exponent for
|
||||
THETA_0) :l
|
||||
Line 6: alpha_2, beta_2 (alpha_2=second coefficient for S; beta_2=first
|
||||
exponent for S) :l
|
||||
Line 7: alpha_3, beta_3 (alpha_3=first coefficient for THETA_1;
|
||||
beta_3=second coefficient for THETA_1) :l,ule
|
||||
|
||||
The next block contains constants for the environment depend
|
||||
promotional energy for sp-valent systems, each of which are species
|
||||
dependent. Refer to Pettifor ("Pettifor_3"_#Pettifor_3) for constant
|
||||
definitions. As well as one species dependent parameter p_pi.
|
||||
|
||||
Line 1: ptrs: (header) :ul
|
||||
|
||||
Following the ptrs header there are N lines for e_1-e_N containing
|
||||
(A_ij)^(mu*nu), delta^mu, p_pi
|
||||
|
||||
Line 2: (A_ij)^(mu*nu), delta^mu, p_pi (for e_1)
|
||||
Line 3: (A_ij)^(mu*nu), delta^mu, p_pi (for e_2 and continues to e_N) :ul
|
||||
|
||||
The next block contains constants for the pair interactions.
|
||||
|
||||
Line 1: pairs: (header) :ul
|
||||
|
||||
Following the header the block contains a series of constants for the
|
||||
number of pair interaction types, the block will be broken up into
|
||||
parameters for e_i-e_j with i=0->N, j=i->N. Each single interaction
|
||||
section for this block will contain (see "Ward"_#Ward for parameter
|
||||
definitions):
|
||||
|
||||
Line 2: r_0, r_c, r_1, r_cut (for e_1-e_2 interactions) :ulb,l
|
||||
Line 3: m, n, n_c :l
|
||||
Line 4: phi_0, beta_(sigma,0), beta_(pi,0) :l
|
||||
Line 5: a_sigma, c_sigma, delta_sigma (From complete formulation of 1/2
|
||||
full valance shell for this particular formulation delta_sigma=0) :l
|
||||
Line 6: a_pi, c_pi, delta_pi :l
|
||||
Line 7: f_sigma, k_sigma, delta_3 (This delta_3 is similar to that of
|
||||
the previous section but is interaction type dependent) :l
|
||||
Line 8: r_0, r_c, r_1, r_cut (for e_1-e_2 interactions and repeats as
|
||||
above) :l,ule
|
||||
|
||||
The next block contains tris.
|
||||
|
||||
Line 1: tris: (header) :ul
|
||||
|
||||
Following the header there is a line for each three body interaction
|
||||
types as e_j-e_i-e_k with i->N, j->N, k=j->N
|
||||
|
||||
Line 2: g_sigma0, g_sigma1, g_sigma2 (these are coefficients for
|
||||
g_(sigma,ijk)(theta_ijk) for e_1-e_1-e_1 interaction. "Ward"_#Ward
|
||||
contains the full expressions for the constants as functions of
|
||||
b_(sigma,ijk), p_(sigma,ijk), u(sigma,ijk) :ulb,l
|
||||
Line 3: g_sigma0, g_sigma1, g_sigma2 (for e_1-e_1-e_2) :l,ule
|
||||
|
||||
This would be the end of the potential parameter file without pre-
|
||||
tabulated data.
|
||||
|
||||
:line
|
||||
|
||||
[Tabulated potential file format]:
|
||||
|
||||
The parameters/coefficients format for the BOP potentials input file
|
||||
containing pre-tabulated functions of is given below with variables
|
||||
matching the formulation of Ward ("Ward"_#Ward).
|
||||
|
||||
Line 1: # elements N :ul
|
||||
|
||||
The first two lines are followed by N lines containing the atomic
|
||||
number and mass of each element THETA_0 and THETA_1 (see
|
||||
"Ward"_#Ward).
|
||||
|
||||
Following the definition of the elements several global variables for
|
||||
the tabulated functions are given.
|
||||
|
||||
Line 1: nr, nBOt (nr is the number of divisions the radius is broken
|
||||
into for function tables and MUST be a factor of 5; nBOt is the number
|
||||
of divisions for the tabulated values of THETA_(S,ij) :ulb,l
|
||||
Line 2: delta_1-delta_7 (if all are not used in the particular :l
|
||||
formulation, set unused values to 0.0) :l,ule
|
||||
|
||||
Following this N lines for e_1-e_N containing p_pi.
|
||||
|
||||
Line 3: p_pi (for e_1)
|
||||
Line 4: p_pi (for e_2 and continues to e_N) :ul
|
||||
|
||||
The next section contains several pair constants for the number of
|
||||
interaction types e_i-e_j, with i=1->N, j=i->N
|
||||
|
||||
Line 1: r_cut (for e_1-e_1 interactions) :ulb,l
|
||||
Line 2: c_sigma, a_sigma, c_pi, a_pi :l
|
||||
Line 3: delta_sigma, delta_pi :l
|
||||
Line 4: f_sigma, k_sigma, delta_3 (This delta_3 is similar to that of
|
||||
the previous section but is interaction type dependent) :l,ule
|
||||
|
||||
The next section contains a line for each three body interaction type
|
||||
e_j-e_i-e_k with i=0->N, j=0->N, k=j->N
|
||||
|
||||
Line 1: g_(sigma0), g_(sigma1), g_(sigma2) (These are coefficients for
|
||||
g_(sigma,jik)(THETA_ijk) for e_1-e_1-e_1 interaction. "Ward"_#Ward
|
||||
contains the full expressions for the constants as functions of
|
||||
b_(sigma,ijk), p_(sigma,ijk), u_(sigma,ijk)) :ulb,l
|
||||
Line 2: g_(sigma0), g_(sigma1), g_(sigma2) (for e_1-e_1-e_2) :l,ule
|
||||
|
||||
The next section contains a block for each interaction type for the
|
||||
phi_ij(r_ij). Each block has nr entries with 5 entries per line.
|
||||
|
||||
Line 1: phi(r1), phi(r2), phi(r3), phi(r4), phi(r5) (for the e_1-e_1
|
||||
interaction type) :ulb,l
|
||||
Line 2: phi(r6), phi(r7), phi(r8), phi(r9), phi(r10) (this continues
|
||||
until nr) :l
|
||||
... :l
|
||||
Line nr/5_1: phi(r1), phi(r2), phi(r3), phi(r4), phi(r5), (for the
|
||||
e_1-e_1 interaction type) :l,ule
|
||||
|
||||
The next section contains a block for each interaction type for the
|
||||
beta_(sigma,ij)(r_ij). Each block has nr entries with 5 entries per
|
||||
line.
|
||||
|
||||
Line 1: beta_sigma(r1), beta_sigma(r2), beta_sigma(r3), beta_sigma(r4),
|
||||
beta_sigma(r5) (for the e_1-e_1 interaction type) :ulb,l
|
||||
Line 2: beta_sigma(r6), beta_sigma(r7), beta_sigma(r8), beta_sigma(r9),
|
||||
beta_sigma(r10) (this continues until nr) :l
|
||||
... :l
|
||||
Line nr/5+1: beta_sigma(r1), beta_sigma(r2), beta_sigma(r3),
|
||||
beta_sigma(r4), beta_sigma(r5) (for the e_1-e_2 interaction type) :l,ule
|
||||
|
||||
The next section contains a block for each interaction type for
|
||||
beta_(pi,ij)(r_ij). Each block has nr entries with 5 entries per line.
|
||||
|
||||
Line 1: beta_pi(r1), beta_pi(r2), beta_pi(r3), beta_pi(r4), beta_pi(r5)
|
||||
(for the e_1-e_1 interaction type) :ulb,l
|
||||
Line 2: beta_pi(r6), beta_pi(r7), beta_pi(r8), beta_pi(r9),
|
||||
beta_pi(r10) (this continues until nr) :l
|
||||
... :l
|
||||
Line nr/5+1: beta_pi(r1), beta_pi(r2), beta_pi(r3), beta_pi(r4),
|
||||
beta_pi(r5) (for the e_1-e_2 interaction type) :l,ule
|
||||
|
||||
The next section contains a block for each interaction type for the
|
||||
THETA_(S,ij)((THETA_(sigma,ij))^(1/2), f_(sigma,ij)). Each block has
|
||||
nBOt entries with 5 entries per line.
|
||||
|
||||
Line 1: THETA_(S,ij)(r1), THETA_(S,ij)(r2), THETA_(S,ij)(r3),
|
||||
THETA_(S,ij)(r4), THETA_(S,ij)(r5) (for the e_1-e_2 interaction type) :ulb,l
|
||||
Line 2: THETA_(S,ij)(r6), THETA_(S,ij)(r7), THETA_(S,ij)(r8),
|
||||
THETA_(S,ij)(r9), THETA_(S,ij)(r10) (this continues until nBOt) :l
|
||||
... :l
|
||||
Line nBOt/5+1: THETA_(S,ij)(r1), THETA_(S,ij)(r2), THETA_(S,ij)(r3),
|
||||
THETA_(S,ij)(r4), THETA_(S,ij)(r5) (for the e_1-e_2 interaction type) :l,ule
|
||||
|
||||
The next section contains a block of N lines for e_1-e_N
|
||||
|
||||
Line 1: delta^mu (for e_1)
|
||||
Line 2: delta^mu (for e_2 and repeats to e_N) :ul
|
||||
|
||||
The last section contains more constants for e_i-e_j interactions with
|
||||
i=0->N, j=i->N
|
||||
|
||||
Line 1: (A_ij)^(mu*nu) (for e1-e1)
|
||||
Line 2: (A_ij)^(mu*nu) (for e1-e2 and repeats as above) :ul
|
||||
|
||||
:line
|
||||
|
||||
[Mixing, shift, table tail correction, restart]:
|
||||
|
||||
This pair style does not support the "pair_modify"_pair_modify.html
|
||||
mix, shift, table, and tail options.
|
||||
|
||||
This pair style does not write its information to "binary restart
|
||||
files"_restart.html, 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.
|
||||
|
||||
This pair style can only be used via the {pair} keyword of the
|
||||
"run_style respa"_run_style.html command. It does not support the
|
||||
{inner}, {middle}, {outer} keywords.
|
||||
|
||||
:line
|
||||
|
||||
[Restrictions:]
|
||||
|
||||
These pair styles are part of the MANYBODY package. They are only
|
||||
enabled if LAMMPS was built with that package (which it is by default).
|
||||
See the "Making LAMMPS"_Section_start.html#start_3 section for more
|
||||
info.
|
||||
|
||||
These pair potentials require the "newtion"_newton.html setting to be
|
||||
"on" for pair interactions.
|
||||
|
||||
The CdTe.bop and GaAs.bop potential files provided with LAMMPS (see the
|
||||
potentials directory) are parameterized for metal "units"_units.html.
|
||||
You can use the BOP potential with any LAMMPS units, but you would need
|
||||
to create your own BOP potential file with coefficients listed in the
|
||||
appropriate units if your simulation does not use "metal" units.
|
||||
|
||||
[Related commands:]
|
||||
|
||||
"pair_coeff"_pair_coeff.html
|
||||
|
||||
[Default:]
|
||||
|
||||
non-tabulated potential file, a_0 is non-zero.
|
||||
|
||||
:line
|
||||
|
||||
:link(Pettofor_1)
|
||||
[(Pettifor_1)] D.G. Pettifor and I.I. Oleinik, Phys. Rev. B, 59, 8487
|
||||
(1999).
|
||||
|
||||
:link(Pettofor_2)
|
||||
[(Pettifor_2)] D.G. Pettifor and I.I. Oleinik, Phys. Rev. Lett., 84,
|
||||
4124 (2000).
|
||||
|
||||
:link(Pettofor_3)
|
||||
[(Pettifor_3)] D.G. Pettifor and I.I. Oleinik, Phys. Rev. B, 65, 172103
|
||||
(2002).
|
||||
|
||||
:link(Murdick)
|
||||
[(Murdick)] D.A. Murdick, X.W. Zhou, H.N.G. Wadley, D. Nguyen-Manh, R.
|
||||
Drautz, and D.G. Pettifor, Phys. Rev. B, 73, 45206 (2006).
|
||||
|
||||
:link(Ward)
|
||||
[(Ward)] D.K. Ward, X.W. Zhou, B.M. Wong, F.P. Doty, and J.A.
|
||||
Zimmerman, Phys. Rev. B, 85,115206 (2012).
|
||||
Loading…
Reference in New Issue