  The problem of the calculation of equilibrium thermodynamic properties and
the establishment of statistical-thermodynamically-consistent finite
bound-state partition functions in nonideal multi-component plasma systems is
revised within the chemical picture. The present exploration accompanied by the
introduction of a generalized accurate formulation, in terms of the solution of
the inverse problem, clears ambiguities and gives a better understanding of the
problem on top of pointing out weaknesses and inaccuracies/inconsistencies
buried in widely used models in the literature.
