  We investigate the screening properties of Gaussian charge models of
electrolyte solutions by analysing the asymptotic behaviour of the pair
distribution functions. We use a combination of Monte-Carlo simulations with
the hyper-netted chain integral equation closure, and the random phase
approximation, to establish the conditions under which a screening length is
well defined and the extent to which it matches the expected Debye length. For
practical applications, for example in dissipative particle dynamics, we are
able to summarise our results in succinct rules-of-thumb which can be used for
mesoscale modeling of electrolyte solutions. We thereby establish a solid
foundation for future work, such as the systematic incorporation of specific
ion effects.
