Although the many-body expansion (MBE) approach is widely applied to estimate the energy of large systems containing weak interactions, it is inapplicable to calculating the energies of covalent or metal clusters. In this work, we propose an interaction many-body expansion (IMBE) to calculate the energy of atomic clusters containing covalent bonds. In this approach, the energy of a system is expressed as the sum of the energy of atoms and the interaction energy between the atom and its surrounding atoms. The IMBE method is first applied to calculate the energies of nitrogen clusters, in which the interatomic interactions are truncated to four-body terms. The results show that the IMBE approach could significantly reduce the energy error for nitrogen clusters compared with the traditional MBE method. The weak size and structure dependence of the IMBE error with respect to DFT calculations indicates the IMBE method has good potential application in estimating energy of large covalent systems.
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