Thermodynamically Consistent Theory of Classical Liquid Structure and Inverse Problem of Extracting Pair Potential

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Abstract The direct correlation function c(r) is divided into two parts, following the work of Kumar et al. One part, c(r) potential [tbnd] c p(r), contributes the entire compressibility and decays at large r as-φ(r)/KBT, with φ(r) the density independent pair potential. The definition of c p(r) as–φ(r)/KBT{(1/6ρr 2)∂2/∂ρ∂r[ρ2 r 3 g(r)]{ is motivated by the condition of thermodynamic consistency, and for a hard core liquid leads to c p(r) small inside an atomic diameter. The second part c(r) cooperative [tbnd] cc(r) is not expressible simply in terms of φ(r) and the pair function g(r), and is expected to differ in range between condensed rare gases and liquid metals say. Also, for a given liquid like argon, cc(r) can be shorter or longer range than c p(r) depending whether one is near the triple point, or near critical conditions. At the critical point, or alternatively in the presence of a collective mode as in liquid Rb, the long-range behaviour of cc(r) can be dominated by cooperative effects. To illus...