Determining ground states of alloy by a symmetry-based classification

Herein, we demonstrate that the generalized Hamiltonian can be described by the atom classification model (ACM) based on symmetry, generating competent candidates for the first-principles calculations to determine ground states of alloy directly. The candidates can be obtained in advance through solving the convex hull step by step because the correlation functions of the ACM can be divided into various subspace according to the defined index l.