The search for the most stable chemical ordering is typically carried out by iteratively permuting pairs of atoms such that the energy of the system decreases. Since the number of possible exchange pairs grows as O(N 2 ) in the number of atoms of the particle, a random selection of pairs of atoms to be permuted becomes inefficient for large particles. It is more convenient to instead select permutations based on "flip energies" E flip i , which we define as the energy change when replacing the atom type at a given site. We note that the most favorable exchanges correspond to those involving the most negative E flip i values. The energy change due to the exchange of two atoms i and j can then be approximated by ∆E ij ≈ E flip i + E flip j , which becomes exact in the case of eq. 1 if two non-neighboring atoms are considered. Obtaining the flip energies is straightforward due to the local nature of the Hamiltonian. Particularly, the local energy of an atom i is only dependent on the number of neighboring Au atoms (a) and Pt atoms (b), such that