<p>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.</p>
<p>The detailed formulas for this potential are given in Ward
(<a class="reference internal" href="#ward"><span>Ward</span></a>); here we provide only a brief description.</p>
<p>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.</p>
<p>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
(<span class="xref std std-ref">Pettifor_1</span>). The sigma bond-order with a half-full
valence shell is used to interpolate the bond-order expressiont that
incorporated explicite valance 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.</p>
<div class="admonition warning">
<p class="first admonition-title">Warning</p>
<p class="last">Note that unlike for other potentials, cutoffs for BOP
potentials are not set in the pair_style or pair_coeff command; they
are specified in the BOP potential files themselves. Likewise, the
BOP potential files list atomic masses; thus you do not need to use
the <a class="reference internal" href="mass.html"><em>mass</em></a> command to specify them. Note that for BOP
potentials with hydrogen, you will likely want to set the mass of H
atoms to be 10x or 20x larger to avoid having to use a tiny timestep.
You can do this by using the <a class="reference internal" href="mass.html"><em>mass</em></a> command after using the
<code class="xref doc docutils literal"><span class="pre">pair_coeff</span></code> command to read the BOP potential
file.</p>
</div>
<p>One option can be specified as a keyword with the pair_style command.</p>
<p>The <em>save</em> keyword gives you the option to calculate in advance and
store a set of distances, angles, and derivatives of angles. The
default is to not do this, but to calculate them 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 optimize the speed of BOP for your particular
system configuration.</p>
<hr class="docutils" />
<p>Only a single pair_coeff command is used with the <em>bop</em> 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:</p>
<ul class="simple">
<li>filename</li>
<li>N element names = mapping of BOP elements to atom types</li>
</ul>
<p>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:</p>
<div class="highlight-python"><div class="highlight"><pre>pair_coeff * * CdTe Cd Cd Cd Te
</pre></div>
</div>
<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
(<a class="reference internal" href="#ward"><span>Ward</span></a>) and Zhou (<a class="reference internal" href="pair_polymorphic.html#zhou"><span>Zhou</span></a>). Each header line containing a
<p>This pair style does not support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></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"><em>binary restart files</em></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"><em>run_style respa</em></a> command. It does not support the
Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/snide/sphinx_rtd_theme">theme</a> provided by <a href="https://readthedocs.org">Read the Docs</a>.