  We propose a simplified version of local molecular field (LMF) theory to
treat Coulomb interactions in simulations of ionic fluids. LMF theory relies on
splitting the Coulomb potential into a short-ranged part that combines with
other short-ranged core interactions and is simulated explicitly. The averaged
effects of the remaining long-ranged part are taken into account through a
self-consistently determined effective external field. The theory contains an
adjustable length parameter sigma that specifies the cut-off distance for the
short-ranged interaction. This can be chosen to minimize the errors resulting
from the mean-field treatment of the complementary long-ranged part. Here we
suggest that in many cases an accurate approximation to the effective field can
be obtained directly from the equilibrium charge density given by the Debye
theory of screening, thus eliminating the need for a self-consistent treatment.
In the limit sigma -> 0, this assumption reduces to the classical Debye
approximation. We examine the numerical performance of this approximation for a
simple model of a symmetric ionic mixture. Our results for thermodynamic and
structural properties of uniform ionic mixtures agree well with similar results
of Ewald simulations of the full ionic system. In addition we have used the
simplified theory in a grand-canonical simulation of a nonuniform ionic mixture
where an ion has been fixed at the origin. Simulations using short-ranged
truncations of the Coulomb interactions alone do not satisfy the exact
condition of complete screening of the fixed ion, but this condition is
recovered when the effective field is taken into account. We argue that this
simplified approach can also be used in the simulations of more complex
nonuniform systems.
