<p>The <em>bop</em> 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 potential is similar to the original BOP
developed by Pettifor (<aclass="reference internal"href="#pettifor-1"><spanclass="std std-ref">Pettifor_1</span></a>,
<aclass="reference internal"href="#pettifor-2"><spanclass="std std-ref">Pettifor_2</span></a>, <aclass="reference internal"href="#pettifor-3"><spanclass="std std-ref">Pettifor_3</span></a>) and later updated
by Murdick, Zhou, and Ward (<aclass="reference internal"href="#murdick"><spanclass="std std-ref">Murdick</span></a>, <aclass="reference internal"href="#ward"><spanclass="std std-ref">Ward</span></a>).
Currently, BOP potential files for these systems are provided with
LAMMPS: AlCu, CCu, CdTe, CdTeSe, CdZnTe, CuH, GaAs. A sysstem with
only a subset of these elements, including a single element (e.g. C or
Cu or Al or Ga or Zn or CdZn), can also be modeled by using the
appropriate alloy file and assigning all atom types to the
singleelement or subset of elements via the pair_coeff command, as
<p>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.</p>
<p>BOP files in the <em>potentials</em> directory of the LAMMPS distribution
have a ”.bop” suffix. The potentials are in tabulated form containing
pre-tabulated pair functions for phi_ij(r_ij), beta_(sigma,ij)(r_ij),
and beta_pi,ij)(r_ij).</p>
<p>The parameters/coefficients format for the different kinds of BOP
files are given below with variables matching the formulation of Ward
(<aclass="reference internal"href="#ward"><spanclass="std std-ref">Ward</span></a>) and Zhou (<aclass="reference internal"href="pair_polymorphic.html#zhou"><spanclass="std std-ref">Zhou</span></a>). Each header line containing a
<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 (<aclass="reference internal"href="#ward"><spanclass="std std-ref">Ward</span></a>). This format also
assumes the angular functions have the formulation of (<aclass="reference internal"href="pair_polymorphic.html#zhou"><spanclass="std std-ref">Zhou</span></a>).</p>
<ulclass="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>
<ulclass="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>
<ulclass="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>
<ulclass="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>
<ulclass="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
<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 (<aclass="reference internal"href="#ward"><spanclass="std std-ref">Ward</span></a>). This format also
assumes the angular functions have the formulation of (<aclass="reference internal"href="pair_polymorphic.html#zhou"><spanclass="std std-ref">Zhou</span></a>).</p>
<ulclass="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>
<ulclass="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>
<ulclass="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>
<ulclass="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>
<ulclass="simple">
<li>Line 1: g(theta1), g(theta2), g(theta3), g(theta4), g(theta5) (for the e_1-e_1-e_1
<p>This pair style does not support the <aclass="reference internal"href="pair_modify.html"><spanclass="doc">pair_modify</span></a>
mix, shift, table, and tail options.</p>
<p>This pair style does not write its information to <aclass="reference internal"href="restart.html"><spanclass="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
<aclass="reference internal"href="run_style.html"><spanclass="doc">run_style respa</span></a> command. It does not support the
Built with <ahref="http://sphinx-doc.org/">Sphinx</a> using a <ahref="https://github.com/snide/sphinx_rtd_theme">theme</a> provided by <ahref="https://readthedocs.org">Read the Docs</a>.