The composition functionality of the mixture energy parameter, a(M), used in the Gibbs-Helmholtz Constrained (GHC) equation of state is studied. An analysis is presented that shows that a(M) for liquid mixtures is approximately quadratic in composition. All non-quadratic behavior is due solely to ln(T-CM) in the GHC up-scaling equation. If a mean value approximation of this term is used, then a(M)(L) is quadratic, but non symmetric, in composition. For vapors, non-quadratic behavior is coupled to the molar volume of the mixture through the term beta(M) = (V-M + b(M))/V-M. It is shown that the difference between beta(M) and some average beta(M) is very small and a(M)(V) is quadratic in composition. Sensitivity analyses of a(M) and resulting molar density to these approximations are also presented. Finally, the non-symmetric composition functionality of a(M) is discussed along with GHC predictions of mixture second virial coefficients. Numerical examples are presented to support all claims. (C) 2016 Elsevier Ltd. All rights reserved.