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More than half of a century has passed since the free energy of classicalfluids defined by second Legendre transform was derived as a functional ofdensity-density correlation function. It is now becoming an increasinglysignificant issue to develop the correlation functional theory that encompassesthe liquid state theory, especially for glassy systems where out of equilibriumcorrelation fields are to be investigated. Here we have formulated a fieldtheoretic perturbation theory that incorporates two-body fields (both ofdensity-density correlation field and its dual field playing the role oftwo-body interaction potential) into a density functional integralrepresentation of the Helmholtz free energy. Quadratic density fluctuations areonly considered in the saddle-point approximation of two-body fields as well asdensity field. We have obtained a set of self-consistent field equations withrespect to these fields, which simply reads a modified mean-field equation ofdensity field where the bare interaction potential in the thermal energy unitis replaced by minus the direct correlation function given in the meanspherical approximation. Such replacement of the interaction potential in themean-field equation belongs to the same category as the local molecular fieldtheory proposed by Weeks and co-workers. Notably, it has been shown that eventhe mean-field part of the free energy functional given by the self-consistentfield theory includes information on short-range correlations between fluidparticles, similarly to the formulation of the local molecular field theory.The advantage of our field theoretic approach is not only that the modifiedmean-field equation can be improved systematically, but also that fluctuationsof two-body fields in nonuniform fluids may be considered, which would berelevant especially for glass-forming liquids.

A self-consistent field theory of density correlations in classical fluids