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