Accurate prediction of formation energy for RHEAs using computational methods is of critical importance to accurately calculate the phase separation and microstructure evolution. This effort requires: (1) studying a crystal structure with a sufficiently large number of atoms to capture the effect of the configurational entropy, (2) reduce the boundary effect on the prediction of the formation energy, and (3) include effect of temperature. State of the-art density functional theory (DFT) based approaches used to compute the formation energy on large crystal structures are very expensive and typically only focus on static crystal structures at 0 Kelvin. This makes questionable the use of DFT based approaches to compute the formation energy for several atomic configurations that span multiple chemical compositions for several temperature. Additionally, the material space described by all the possible chemical composition and atomic disorders for the crystal structure of the high entropy alloy is high dimensional. The dimensionality of the material space increases exponentially with the number of pure elements mixed and the number of atoms in the crystal structure. Computation of ground-state structures of a binary alloy requires calculating the total energy for all possible configurations of placing atoms A and B on N sites of the underlying Bravais lattice. As the number of possible configurations 2 N is extremely high, even for relatively low values of N, it is computationally unfeasible to calculate the energy quantum mechanically for an exhaustive set of configurations even using state-of-the-art leadership class supercomputing facilities.