Abstract
A formula for the Helmholtz free energy of a one-component fluid, classical or quantum, is obtained in terms of the radial distribution function, by attaching a coupling contant to the pair interaction potential. Compatibility of the formula is discussed in connection with the formula derived in paper II, leading to the condition to be satisfied by the radial distribution function. It is shown that the condition for compatibility is equivalent in a classical fluid to the one discussed in paper I. The present formula is applied to deal with the hyper-netted chain approximation and the condition for compatibility is shown to be satisfied in this case. The formula is generalized to a multicomponent fluid and also to the case of a grand canonical ensemble.
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