First Principles (FP) methods are invoked to improve the accuracy of Bozzolo-Ferrante- Smith (BFS) model, one of the quantum-approximate modeling techniques for the computation of thermodynamic properties that involve a large number of particles. The BFS method calculates the energy of an atom in an alloy in two steps . A first term pertains to the structural contribution. A recent improvement  allows to calculate the strain energy depending on the local environment [1,2] and this involves only pure element properties of the different atomic species. In the second step, binary chemical interactions are taken into account. This was originally done by only two interaction parameters for each atom pair in an alloy. In contrast, the adaptable parameterization of Cluster Expansion Methods (CEM) routinely incorporates any number of FP data to describe ordering in alloy systems. But in standard CEM calculations, no explicit information on local atomic displacements is used. In this work, the BFS chemical energy term is successfully replaced by a CEM chemical term to combine the ability of BFS to account for local displacements and the ability of CEM to include as many FP results as needed for the correct evaluation of alloying effects.