Onsager-Thomas-Fermi diatomic confined molecules for the one-component plasma

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Abstract
The Onsager-Thomas-Fermi diatomic confined molecule for the one-component plasma (OCP) is composed of a pair of point ions, with separation r and a uniform neutralizing charge density of electrons. Its shape is determined by the (‘‘isolation’’) condition that the total electrostatic potential and field vanish outside its boundary. These uniquely defined objects are obtained variationally from the high-density (ρ→∞) solution of the hypernetted-chain (HNC) equation for an OCP in which certain ion pairs are constrained to have fixed separation r. The HNC variational problem is mapped on the Onsager ‘‘charge-smearing’’ optimization for obtaining the best lower bound for the interaction potential energy of the system. We outline the derivation of these ‘‘molecules’’ as natural generalizations of the ion-sphere Thomas-Fermi (TF) ‘‘atom.’’ Their shapes and self-energies are determined numerically and are compared with various approximations. The self-energies of these diatomic molecules provide excellent estimates of the short-range part of the OCP pair correlations and are rather insensitive to the optimization. Our results represent the ρ→∞ or T→∞ solution of the general confined-molecule TF equation, which is also solved at T=0 for finite but still high densities. Electron-screening contributions to the confined-molecule TF energies are interpreted in terms of the solution of the HNC integral equation for a Yukawa potential.