<p>where the prime on each summation sign indicates the exclusion of all
self-interaction terms from the summation. The leading volume term
E_vol as well as the two-ion central-force pair potential v_2 and the
three- and four-ion angular-force potentials, v_3 and v_4, depend
explicitly on the atomic volume Omega, but are structure independent
and transferable to all bulk ion configurations, either ordered or
disordered, and with of without the presence of point and line
defects. The simplified model GPT or MGPT (<aclass="reference internal"href="#moriarty2"><spanclass="std std-ref">Moriarty2</span></a>,
<aclass="reference internal"href="#moriarty3"><spanclass="std std-ref">Moriarty3</span></a>), which retains the form of E_tot and permits
more efficient large-scale atomistic simulations, derives from the GPT
through a series of systematic approximations applied to E_vol and the
potentials v_n that are valid for mid-period transition metals with
nearly half-filled d bands.</p>
<p>Both analytic (<aclass="reference internal"href="#moriarty2"><spanclass="std std-ref">Moriarty2</span></a>) and matrix
(<aclass="reference internal"href="#moriarty3"><spanclass="std std-ref">Moriarty3</span></a>) representations of MGPT have been developed.
In the more general matrix representation, which can also be applied
to f-band actinide metals and permits both canonical and non-canonical
d/f bands, the multi-ion potentials are evaluated on the fly during a
simulation through d- or f-state matrix multiplication, and the forces
that move the ions are determined analytically. Fast matrix-MGPT
algorithms have been developed independently by Glosli
(<aclass="reference internal"href="#glosli"><spanclass="std std-ref">Glosli</span></a>, <aclass="reference internal"href="#moriarty3"><spanclass="std std-ref">Moriarty3</span></a>) and by Oppelstrup
<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
needs 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
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