The angles theta and phi are the standard spherical polar angles
defining the direction of the bond vector <em>rij</em>.
The second equation defines <em>Ql</em>, which is a
rotationally invariant scalar quantity obtained by summing
over all the components of degree <em>l</em>.</p>
<p>The optional keyword <em>cutoff</em> defines the distance cutoff
used when searching for neighbors. The default value, also
the maximum allowable value, is the cutoff specified
by the pair style.</p>
<p>The optional keyword <em>nnn</em> defines the number of nearest
neighbors used to calculate <em>Ql</em>. The default value is 12.
If the value is NULL, then all neighbors up to the
specified distance cutoff are used.</p>
<p>The optional keyword <em>degrees</em> defines the list of order parameters to
be computed. The first argument <em>nlvalues</em> is the number of order
parameters. This is followed by that number of integers giving the
degree of each order parameter. Because <em>Q</em>2 and all odd-degree
order parameters are zero for atoms in cubic crystals
(see <aclass="reference internal"href="#steinhardt"><spanclass="std std-ref">Steinhardt</span></a>), the default order parameters
are <em>Q</em>4, <em>Q</em>6, <em>Q</em>8, <em>Q</em>10, and <em>Q</em>12. For the
FCC crystal with <em>nnn</em>=12, <em>Q</em>4 = sqrt(7/3)/8 = 0.19094....
The numerical values of all order parameters up to <em>Q</em>12
for a range of commonly encountered high-symmetry structures are given
in Table I of <aclass="reference internal"href="#mickel"><spanclass="std std-ref">Mickel et al.</span></a>.</p>
<p>The value of <em>Ql</em> is set to zero for atoms not in the
specified compute group, as well as for atoms that have less than
<em>nnn</em> neighbors within the distance cutoff.</p>
<p>The neighbor list needed to compute this quantity is constructed each
time the calculation is performed (i.e. each time a snapshot of atoms
is dumped). Thus it can be inefficient to compute/dump this quantity
too frequently.</p>
<divclass="admonition note">
<pclass="first admonition-title">Note</p>
<pclass="last">If you have a bonded system, then the settings of
<aclass="reference internal"href="special_bonds.html"><spanclass="doc">special_bonds</span></a> command can remove pairwise
interactions between atoms in the same bond, angle, or dihedral. This
is the default setting for the <aclass="reference internal"href="special_bonds.html"><spanclass="doc">special_bonds</span></a>
command, and means those pairwise interactions do not appear in the
neighbor list. Because this fix uses the neighbor list, it also means
those pairs will not be included in the order parameter. This
difficulty can be circumvented by writing a dump file, and using the
<aclass="reference internal"href="rerun.html"><spanclass="doc">rerun</span></a> command to compute the order parameter for
snapshots in the dump file. The rerun script can use a
<aclass="reference internal"href="special_bonds.html"><spanclass="doc">special_bonds</span></a> command that includes all pairs in
the neighbor list.</p>
</div>
<p><strong>Output info:</strong></p>
<p>This compute calculates a per-atom array with <em>nlvalues</em> columns, giving the
<em>Ql</em> values for each atom, which are real numbers on the range 0 <= <em>Ql</em><= 1.</p>
<p>These values can be accessed by any command that uses
per-atom values from a compute as input. See <aclass="reference internal"href="Section_howto.html#howto-15"><spanclass="std std-ref">Section 6.15</span></a> for an overview of LAMMPS output
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