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562 lines
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<li>pair_style bop command</li>
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<div class="section" id="pair-style-bop-command">
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<span id="index-0"></span><h1>pair_style bop command</h1>
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<div class="section" id="syntax">
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<h2>Syntax</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">pair_style</span> <span class="n">bop</span> <span class="n">keyword</span> <span class="o">...</span>
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</pre></div>
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</div>
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<ul class="simple">
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<li>zero or more keywords may be appended</li>
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<li>keyword = <em>save</em></li>
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</ul>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">save</span> <span class="o">=</span> <span class="n">pre</span><span class="o">-</span><span class="n">compute</span> <span class="ow">and</span> <span class="n">save</span> <span class="n">some</span> <span class="n">values</span>
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</pre></div>
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</div>
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</div>
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<div class="section" id="examples">
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<h2>Examples</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">pair_style</span> <span class="n">bop</span>
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<span class="n">pair_coeff</span> <span class="o">*</span> <span class="o">*</span> <span class="o">../</span><span class="n">potentials</span><span class="o">/</span><span class="n">CdTe_bop</span> <span class="n">Cd</span> <span class="n">Te</span>
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<span class="n">pair_style</span> <span class="n">bop</span> <span class="n">save</span>
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<span class="n">pair_coeff</span> <span class="o">*</span> <span class="o">*</span> <span class="o">../</span><span class="n">potentials</span><span class="o">/</span><span class="n">CdTe</span><span class="o">.</span><span class="n">bop</span><span class="o">.</span><span class="n">table</span> <span class="n">Cd</span> <span class="n">Te</span> <span class="n">Te</span>
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<span class="n">comm_modify</span> <span class="n">cutoff</span> <span class="mf">14.70</span>
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</pre></div>
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</div>
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</div>
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<div class="section" id="description">
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<h2>Description</h2>
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<p>The <em>bop</em> 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 potential is similar to the original BOP
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developed by Pettifor (<a class="reference internal" href="#pettifor-1"><span class="std std-ref">Pettifor_1</span></a>,
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<a class="reference internal" href="#pettifor-2"><span class="std std-ref">Pettifor_2</span></a>, <a class="reference internal" href="#pettifor-3"><span class="std std-ref">Pettifor_3</span></a>) and later updated
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by Murdick, Zhou, and Ward (<a class="reference internal" href="#murdick"><span class="std std-ref">Murdick</span></a>, <a class="reference internal" href="#ward"><span class="std std-ref">Ward</span></a>).
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Currently, BOP potential files for these systems are provided with
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LAMMPS: AlCu, CCu, CdTe, CdTeSe, CdZnTe, CuH, GaAs. A sysstem with
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only a subset of these elements, including a single element (e.g. C or
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Cu or Al or Ga or Zn or CdZn), can also be modeled by using the
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appropriate alloy file and assigning all atom types to the
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singleelement or subset of elements via the pair_coeff command, as
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discussed below.</p>
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<p>The BOP potential consists of three terms:</p>
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<img alt="_images/pair_bop.jpg" class="align-center" src="_images/pair_bop.jpg" />
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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.</p>
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<p>The detailed formulas for this potential are given in Ward
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(<a class="reference internal" href="#ward"><span class="std std-ref">Ward</span></a>); here we provide only a brief description.</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.</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 class="reference internal" href="#pettifor-1"><span class="std std-ref">Pettifor_1</span></a>). The sigma bond-order with a half-full
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valence shell is used to interpolate the bond-order expressiont that
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incorporated explicite valance band filling. This pi bond-order
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expression also contains also contains a three-member ring term that
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allows implementation of an asymmetric density of states, which helps
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to either stabilize or destabilize close-packed structures. The pi
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bond-order includes hopping paths of length 4. This enables the
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incorporation of dihedral angles effects.</p>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">Note that unlike for other potentials, cutoffs for BOP
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potentials are not set in the pair_style or pair_coeff command; they
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are specified in the BOP potential files themselves. Likewise, the
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BOP potential files list atomic masses; thus you do not need to use
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the <a class="reference internal" href="mass.html"><span class="doc">mass</span></a> command to specify them. Note that for BOP
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potentials with hydrogen, you will likely want to set the mass of H
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atoms to be 10x or 20x larger to avoid having to use a tiny timestep.
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You can do this by using the <a class="reference internal" href="mass.html"><span class="doc">mass</span></a> command after using the
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<a class="reference internal" href="pair_coeff.html"><span class="doc">pair_coeff</span></a> command to read the BOP potential
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file.</p>
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</div>
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<p>One option can be specified as a keyword with the pair_style command.</p>
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<p>The <em>save</em> keyword gives you the option to calculate in advance and
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store a set of distances, angles, and derivatives of angles. The
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default is to not do this, but to calculate them on-the-fly each time
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they are needed. The former may be faster, but takes more memory.
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The latter requires less memory, but may be slower. It is best to
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test this option to optimize the speed of BOP for your particular
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system configuration.</p>
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<hr class="docutils" />
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<p>Only a single pair_coeff command is used with the <em>bop</em> 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:</p>
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<ul class="simple">
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<li>filename</li>
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<li>N element names = mapping of BOP elements to atom types</li>
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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:</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">pair_coeff</span> <span class="o">*</span> <span class="o">*</span> <span class="n">CdTe</span> <span class="n">Cd</span> <span class="n">Cd</span> <span class="n">Cd</span> <span class="n">Te</span>
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</pre></div>
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</div>
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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.</p>
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<p>BOP files in the <em>potentials</em> directory of the LAMMPS distribution
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have a ”.bop” suffix. The potentials are in tabulated form containing
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pre-tabulated pair functions for phi_ij(r_ij), beta_(sigma,ij)(r_ij),
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and beta_pi,ij)(r_ij).</p>
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<p>The parameters/coefficients format for the different kinds of BOP
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files are given below with variables matching the formulation of Ward
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(<a class="reference internal" href="#ward"><span class="std std-ref">Ward</span></a>) and Zhou (<a class="reference internal" href="pair_polymorphic.html#zhou"><span class="std std-ref">Zhou</span></a>). Each header line containing a
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”:” is preceded by a blank line.</p>
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<hr class="docutils" />
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<p><strong>No angular table file format</strong>:</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 g is given below with variables
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matching the formulation of Ward (<a class="reference internal" href="#ward"><span class="std std-ref">Ward</span></a>). This format also
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assumes the angular functions have the formulation of (<a class="reference internal" href="#ward"><span class="std std-ref">Ward</span></a>).</p>
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<ul class="simple">
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<li>Line 1: # elements N</li>
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</ul>
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<p>The first line is followed by N lines containing the atomic
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number, mass, and element symbol of each element.</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.</p>
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<ul class="simple">
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<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)</li>
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<li>Line 2: delta_1-delta_7 (if all are not used in the particular</li>
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<li>formulation, set unused values to 0.0)</li>
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</ul>
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<p>Following this N lines for e_1-e_N containing p_pi.</p>
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<ul class="simple">
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<li>Line 3: p_pi (for e_1)</li>
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<li>Line 4: p_pi (for e_2 and continues to e_N)</li>
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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</p>
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<ul class="simple">
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<li>Line 1: r_cut (for e_1-e_1 interactions)</li>
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<li>Line 2: c_sigma, a_sigma, c_pi, a_pi</li>
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<li>Line 3: delta_sigma, delta_pi</li>
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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)</li>
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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</p>
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<ul class="simple">
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<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 class="reference internal" href="#ward"><span class="std std-ref">Ward</span></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))</li>
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<li>Line 2: g_(sigma0), g_(sigma1), g_(sigma2) (for e_1-e_1-e_2)</li>
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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.</p>
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<ul class="simple">
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<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)</li>
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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)</li>
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<li>...</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)</li>
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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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beta_(sigma,ij)(r_ij). Each block has nr entries with 5 entries per
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line.</p>
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<ul class="simple">
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<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>
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<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)</li>
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<li>...</li>
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<li>Line nr/5+1: beta_sigma(r1), beta_sigma(r2), beta_sigma(r3),
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beta_sigma(r4), beta_sigma(r5) (for the e_1-e_2 interaction type)</li>
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</ul>
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<p>The next section contains a block for each interaction type for
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beta_(pi,ij)(r_ij). Each block has nr entries with 5 entries per line.</p>
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<ul class="simple">
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<li>Line 1: beta_pi(r1), beta_pi(r2), beta_pi(r3), beta_pi(r4), beta_pi(r5)
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(for the e_1-e_1 interaction type)</li>
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<li>Line 2: beta_pi(r6), beta_pi(r7), beta_pi(r8), beta_pi(r9),
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beta_pi(r10) (this continues until nr)</li>
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<li>...</li>
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<li>Line nr/5+1: beta_pi(r1), beta_pi(r2), beta_pi(r3), beta_pi(r4),
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beta_pi(r5) (for the e_1-e_2 interaction type)</li>
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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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THETA_(S,ij)((THETA_(sigma,ij))^(1/2), f_(sigma,ij)). Each block has
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nBOt entries with 5 entries per line.</p>
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<ul class="simple">
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<li>Line 1: THETA_(S,ij)(r1), THETA_(S,ij)(r2), THETA_(S,ij)(r3),
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THETA_(S,ij)(r4), THETA_(S,ij)(r5) (for the e_1-e_2 interaction type)</li>
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<li>Line 2: THETA_(S,ij)(r6), THETA_(S,ij)(r7), THETA_(S,ij)(r8),
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THETA_(S,ij)(r9), THETA_(S,ij)(r10) (this continues until nBOt)</li>
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<li>...</li>
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<li>Line nBOt/5+1: THETA_(S,ij)(r1), THETA_(S,ij)(r2), THETA_(S,ij)(r3),
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THETA_(S,ij)(r4), THETA_(S,ij)(r5) (for the e_1-e_2 interaction type)</li>
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</ul>
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<p>The next section contains a block of N lines for e_1-e_N</p>
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<ul class="simple">
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<li>Line 1: delta^mu (for e_1)</li>
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<li>Line 2: delta^mu (for e_2 and repeats to e_N)</li>
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</ul>
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<p>The last section contains more constants for e_i-e_j interactions with
|
|
i=0->N, j=i->N</p>
|
|
<ul class="simple">
|
|
<li>Line 1: (A_ij)^(mu*nu) (for e1-e1)</li>
|
|
<li>Line 2: (A_ij)^(mu*nu) (for e1-e2 and repeats as above)</li>
|
|
</ul>
|
|
<hr class="docutils" />
|
|
<p><strong>Angular spline table file format</strong>:</p>
|
|
<p>The parameters/coefficients format for the BOP potentials input file
|
|
containing pre-tabulated functions of g is given below with variables
|
|
matching the formulation of Ward (<a class="reference internal" href="#ward"><span class="std std-ref">Ward</span></a>). This format also
|
|
assumes the angular functions have the formulation of (<a class="reference internal" href="pair_polymorphic.html#zhou"><span class="std std-ref">Zhou</span></a>).</p>
|
|
<ul class="simple">
|
|
<li>Line 1: # elements N</li>
|
|
</ul>
|
|
<p>The first line is followed by N lines containing the atomic
|
|
number, mass, and element symbol of each element.</p>
|
|
<p>Following the definition of the elements several global variables for
|
|
the tabulated functions are given.</p>
|
|
<ul class="simple">
|
|
<li>Line 1: nr, ntheta, nBOt (nr is the number of divisions the radius is broken
|
|
into for function tables and MUST be a factor of 5; ntheta is the power of the
|
|
power of the spline used to fit the angular function; nBOt is the number
|
|
of divisions for the tabulated values of THETA_(S,ij)</li>
|
|
<li>Line 2: delta_1-delta_7 (if all are not used in the particular</li>
|
|
<li>formulation, set unused values to 0.0)</li>
|
|
</ul>
|
|
<p>Following this N lines for e_1-e_N containing p_pi.</p>
|
|
<ul class="simple">
|
|
<li>Line 3: p_pi (for e_1)</li>
|
|
<li>Line 4: p_pi (for e_2 and continues to e_N)</li>
|
|
</ul>
|
|
<p>The next section contains several pair constants for the number of
|
|
interaction types e_i-e_j, with i=1->N, j=i->N</p>
|
|
<ul class="simple">
|
|
<li>Line 1: r_cut (for e_1-e_1 interactions)</li>
|
|
<li>Line 2: c_sigma, a_sigma, c_pi, a_pi</li>
|
|
<li>Line 3: delta_sigma, delta_pi</li>
|
|
<li>Line 4: f_sigma, k_sigma, delta_3 (This delta_3 is similar to that of
|
|
the previous section but is interaction type dependent)</li>
|
|
</ul>
|
|
<p>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</p>
|
|
<ul class="simple">
|
|
<li>Line 1: g0, g1, g2... (These are coefficients for the angular spline
|
|
of the g_(sigma,jik)(THETA_ijk) for e_1-e_1-e_1 interaction. The
|
|
function can contain up to 10 term thus 10 constants. The first line
|
|
can contain up to five constants. If the spline has more than five
|
|
terms the second line will contain the remaining constants The
|
|
following lines will then contain the constants for the remainaing g0,
|
|
g1, g2... (for e_1-e_1-e_2) and the other three body
|
|
interactions</li>
|
|
</ul>
|
|
<p>The rest of the table has the same structure as the previous section
|
|
(see above).</p>
|
|
<hr class="docutils" />
|
|
<p><strong>Angular no-spline table file format</strong>:</p>
|
|
<p>The parameters/coefficients format for the BOP potentials input file
|
|
containing pre-tabulated functions of g is given below with variables
|
|
matching the formulation of Ward (<a class="reference internal" href="#ward"><span class="std std-ref">Ward</span></a>). This format also
|
|
assumes the angular functions have the formulation of (<a class="reference internal" href="pair_polymorphic.html#zhou"><span class="std std-ref">Zhou</span></a>).</p>
|
|
<ul class="simple">
|
|
<li>Line 1: # elements N</li>
|
|
</ul>
|
|
<p>The first two lines are followed by N lines containing the atomic
|
|
number, mass, and element symbol of each element.</p>
|
|
<p>Following the definition of the elements several global variables for
|
|
the tabulated functions are given.</p>
|
|
<ul class="simple">
|
|
<li>Line 1: nr, ntheta, nBOt (nr is the number of divisions the radius is broken
|
|
into for function tables and MUST be a factor of 5; ntheta is the number of
|
|
divisions for the tabulated values of the g angular function; nBOt is the number
|
|
of divisions for the tabulated values of THETA_(S,ij)</li>
|
|
<li>Line 2: delta_1-delta_7 (if all are not used in the particular</li>
|
|
<li>formulation, set unused values to 0.0)</li>
|
|
</ul>
|
|
<p>Following this N lines for e_1-e_N containing p_pi.</p>
|
|
<ul class="simple">
|
|
<li>Line 3: p_pi (for e_1)</li>
|
|
<li>Line 4: p_pi (for e_2 and continues to e_N)</li>
|
|
</ul>
|
|
<p>The next section contains several pair constants for the number of
|
|
interaction types e_i-e_j, with i=1->N, j=i->N</p>
|
|
<ul class="simple">
|
|
<li>Line 1: r_cut (for e_1-e_1 interactions)</li>
|
|
<li>Line 2: c_sigma, a_sigma, c_pi, a_pi</li>
|
|
<li>Line 3: delta_sigma, delta_pi</li>
|
|
<li>Line 4: f_sigma, k_sigma, delta_3 (This delta_3 is similar to that of
|
|
the previous section but is interaction type dependent)</li>
|
|
</ul>
|
|
<p>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</p>
|
|
<ul class="simple">
|
|
<li>Line 1: g(theta1), g(theta2), g(theta3), g(theta4), g(theta5) (for the e_1-e_1-e_1
|
|
interaction type)</li>
|
|
<li>Line 2: g(theta6), g(theta7), g(theta8), g(theta9), g(theta10) (this continues
|
|
until ntheta)</li>
|
|
<li>...</li>
|
|
<li>Line ntheta/5+1: g(theta1), g(theta2), g(theta3), g(theta4), g(theta5), (for the
|
|
e_1-e_1-e_2 interaction type)</li>
|
|
</ul>
|
|
<p>The rest of the table has the same structure as the previous section (see above).</p>
|
|
<hr class="docutils" />
|
|
<p><strong>Mixing, shift, table tail correction, restart</strong>:</p>
|
|
<p>This pair style does not support the <a class="reference internal" href="pair_modify.html"><span class="doc">pair_modify</span></a>
|
|
mix, shift, table, and tail options.</p>
|
|
<p>This pair style does not write its information to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></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 <em>pair</em> keyword of the
|
|
<a class="reference internal" href="run_style.html"><span class="doc">run_style respa</span></a> command. It does not support the
|
|
<em>inner</em>, <em>middle</em>, <em>outer</em> keywords.</p>
|
|
</div>
|
|
<hr class="docutils" />
|
|
<div class="section" id="restrictions">
|
|
<h2>Restrictions</h2>
|
|
<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 class="reference internal" href="Section_start.html#start-3"><span class="std std-ref">Making LAMMPS</span></a> section for more
|
|
info.</p>
|
|
<p>These pair potentials require the <a class="reference internal" href="newton.html"><span class="doc">newtion</span></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 class="reference internal" href="units.html"><span class="doc">units</span></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>
|
|
</div>
|
|
<div class="section" id="related-commands">
|
|
<h2>Related commands</h2>
|
|
<p><a class="reference internal" href="pair_coeff.html"><span class="doc">pair_coeff</span></a></p>
|
|
</div>
|
|
<div class="section" id="default">
|
|
<h2>Default</h2>
|
|
<p>non-tabulated potential file, a_0 is non-zero.</p>
|
|
<hr class="docutils" />
|
|
<p id="pettifor-1"><strong>(Pettifor_1)</strong> D.G. Pettifor and I.I. Oleinik, Phys. Rev. B, 59, 8487
|
|
(1999).</p>
|
|
<p id="pettifor-2"><strong>(Pettifor_2)</strong> D.G. Pettifor and I.I. Oleinik, Phys. Rev. Lett., 84,
|
|
4124 (2000).</p>
|
|
<p id="pettifor-3"><strong>(Pettifor_3)</strong> D.G. Pettifor and I.I. Oleinik, Phys. Rev. B, 65, 172103
|
|
(2002).</p>
|
|
<p id="murdick"><strong>(Murdick)</strong> 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>
|
|
<p id="ward"><strong>(Ward)</strong> D.K. Ward, X.W. Zhou, B.M. Wong, F.P. Doty, and J.A.
|
|
Zimmerman, Phys. Rev. B, 85,115206 (2012).</p>
|
|
<p id="zhou"><strong>(Zhou)</strong> X.W. Zhou, D.K. Ward, M. Foster (TBP).</p>
|
|
</div>
|
|
</div>
|
|
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|
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</div>
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