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Recent simulation results imply the lowering of the ground-state correlationenergy per counterion at a charged planar wall, compared with that of the 2Dand 3D one-component plasma systems. Our aim is to correctly evaluate theground-state energy of strongly-coupled counterion systems by considering aquasi-2D bound state where bound counterions are confined to a layer ofmolecular thickness. We use a variational approach based on theGibbs-Bogoliubov inequality for the lower-bound free energy so that theliquid-state theory can be incorporated into the formulations. The soft meanspherical approximation demonstrates that the lowered ground-state energy canbe reproduced by the obtained analytical form of a quasi-2D bound state.

Ground-state correlation energy of counterions at a charged planar wall: Gibbs-Bogoliubov lower-bound approach