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Energy current density correlation function. I. Frequency sum rules

Expressions for zeroth-, second- and fourth-frequency sum rules of energy current density correlation function have been derived. These exact expressions involve static correlation functions of up to five particles. Because of the non-availability of any information about triplet and higher-particle correlation functions, the authors use a low-order decoupling approximation for these. The resulting expressions for the frequency sum rules, which now contain only a static pair correlation function and an inner-atomic potential, are suitable for applications. Numerical results for these frequency sum rules have been obtained for Lennard-Jones fluids over a wide range of densities and temperatures. The density and temperature dependence and the relative importance of higher-particle correlation contributions to the frequency sum rules have been discussed.