<p>where rho_i is the density at atom I, theta_jik is the angle between
atoms J, I, and K centered on atom I. The five functions Phi, U, rho,
f, and g are represented by cubic splines.</p>
<p>The cutoffs and the coefficients for these spline functions are listed
in a parameter file which is specified by the
<aclass="reference internal"href="pair_coeff.html"><spanclass="doc">pair_coeff</span></a> command. Parameter files for different
elements are included in the “potentials” directory of the LAMMPS
distribution and have a ”.meam.spline” file suffix. All of these
files are parameterized in terms of LAMMPS <aclass="reference internal"href="units.html"><spanclass="doc">metal units</span></a>.</p>
<p>Note that unlike for other potentials, cutoffs for spline-based MEAM
potentials are not set in the pair_style or pair_coeff command; they
are specified in the potential files themselves.</p>
<p>Unlike the EAM pair style, which retrieves the atomic mass from the
potential file, the spline-based MEAM potentials do not include mass
information; thus you need to use the <aclass="reference internal"href="mass.html"><spanclass="doc">mass</span></a> command to
specify it.</p>
<p>Only a single pair_coeff command is used with the <em>meam/spline</em> style
which specifies a 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>
<ulclass="simple">
<li>filename</li>
<li>N element names = mapping of spline-based MEAM elements to atom types</li>
</ul>
<p>See the <aclass="reference internal"href="pair_coeff.html"><spanclass="doc">pair_coeff</span></a> doc page for alternate ways
to specify the path for the potential file.</p>
<p>As an example, imagine the Ti.meam.spline file has values for Ti. If
your LAMMPS simulation has 3 atoms types and they are all to be
treated with this potentials, you would use the following pair_coeff
command:</p>
<preclass="literal-block">
pair_coeff * * Ti.meam.spline Ti Ti Ti
</pre>
<p>The 1st 2 arguments must be * * so as to span all LAMMPS atom types.
The three Ti arguments map LAMMPS atom types 1,2,3 to the Ti element
in the potential file. If a mapping value is specified as NULL, the
mapping is not performed. This can be used when a <em>meam/spline</em>
potential is used as part of the <em>hybrid</em> pair style. The NULL values
are placeholders for atom types that will be used with other
potentials.</p>
<divclass="admonition note">
<pclass="first admonition-title">Note</p>
<pclass="last">The <em>meam/spline</em> style currently supports only single-element
MEAM potentials. It may be extended for alloy systems in the future.</p>
</div>
<hrclass="docutils"/>
<p>Styles with a <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
functionally the same as the corresponding style without the suffix.
They have been optimized to run faster, depending on your available
hardware, as discussed in <aclass="reference internal"href="Section_accelerate.html"><spanclass="doc">Section_accelerate</span></a>
of the manual. The accelerated styles take the same arguments and
should produce the same results, except for round-off and precision
issues.</p>
<p>These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,
USER-OMP and OPT packages, respectively. They are only enabled if
LAMMPS was built with those packages. See the <aclass="reference internal"href="Section_start.html#start-3"><spanclass="std std-ref">Making LAMMPS</span></a> section for more info.</p>
<p>You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the <aclass="reference internal"href="Section_start.html#start-7"><spanclass="std std-ref">-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
use the <aclass="reference internal"href="suffix.html"><spanclass="doc">suffix</span></a> command in your input script.</p>
<p>See <aclass="reference internal"href="Section_accelerate.html"><spanclass="doc">Section_accelerate</span></a> of the manual for
more instructions on how to use the accelerated styles effectively.</p>
<p>The current version of this pair style does not support multiple
element types or mixing. It has been designed for pure elements only.</p>
<p>This pair style does not support the <aclass="reference internal"href="pair_modify.html"><spanclass="doc">pair_modify</span></a>
shift, table, and tail options.</p>
<p>The <em>meam/spline</em> 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 an external
potential parameter file. Thus, you need to re-specify the pair_style
and pair_coeff commands in an input script that reads a restart file.</p>
<p>The <em>meam/spline</em> 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. They do not support the
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