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<div>
<div>
<p>We extend the framework for polarizable force fields to include the case where
the electrostatic multipoles are not determined by a variational minimization of the
electrostatic energy. Such models formally require that the polarization response is
calculated for all possible geometrical perturbations in order to obtain the energy
gradient required for performing molecular dynamics simulations.
</p><div>
<div>
<div>
<p>By making use
of a Lagrange formalism, however, this computational demanding task can be re-
placed by solving a single equation similar to that for determining the electrostatic variables themselves. Using the recently proposed bond capacity model that describes
molecular polarization at the charge-only level, we show that the energy gradient for
non-variational energy models with periodic boundary conditions can be calculated
with a computational effort similar to that for variational polarization models. The
possibility of separating the equation for calculating the electrostatic variables from
the energy expression depending on these variables without a large computational
penalty provides flexibility in the design of new force fields.
</p><div><div><div>
</div>
</div>
</div>
<p>
</p><div>
<div>
<div>
<p>variables themselves. Using the recently proposed bond capacity model that describes
molecular polarization at the charge-only level, we show that the energy gradient for
non-variational energy models with periodic boundary conditions can be calculated
with a computational effort similar to that for variational polarization models. The
possibility of separating the equation for calculating the electrostatic variables from
the energy expression depending on these variables without a large computational
penalty provides flexibility in the design of new force fields.
</p>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
Periodic Boundary Conditions for Dislocation Dynamics Simulations in Three Dimensions