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We demonstrate the applicability of an extended cluster expansion (CE) technique, variable-lattice CE (VLCE), enabling configurational energetics on multiple lattices to be modeled. For application in real systems, the general conditions of determining interactions in VLCE is derived. As an example, VLCE was applied to a boron nitride (BN) binary system on two-dimensional lattices. VLCE successfully predicted the energy of structures, not only on lattices that are used to obtain interactions, but also of structures on those not used to obtain interactions. VLCE reasonably predicts the stable structure of BN on a honeycomb lattice from information about other lattices. These facts indicate that VLCE opens the door to effectively searching for stable as well as metastable structures on multiple lattices for unknown given systems, which has not been achieved by the current CE

Modeling configurational energetics on multiple lattices through extended cluster expansion