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Phase separation of the ultrasoft restricted primitive model (URPM) withGaussian charges is re-investigated in the random phase approximation(RPA)---the 'Level A' approximation discussed by Nikoubashman, Hansen and Kahl[J. Chem. Phys. 137, 094905 (2012)]. We find that the RPA predicts a region oflow temperature vapour-liquid coexistence, with a critical density much lowerthan that observed in either simulations or more refined approximations (wealso remark that the RPA critical point for a related model with Bessel chargescan be solved analytically). This observation suggests that the hierarchy ofapproximations introduced by Nikoubashman et al. should be analogous to thoseintroduced by Fisher and Levin for the restricted primitive model [Phys. Rev.Lett. 71, 3826 (1993)], which makes the inability of these approximations tocapture the observed URPM phase behaviour even more worthy of investigation.

Phase behaviour and the random phase approximation for ultrasoft restricted primitive models