The electrostatically embedded many-body expansion (EE-MB), previously applied to the total electronic energy, is here applied only to the electronic correlation energy (CE), combined with a Hartree–Fock calculation on the entire system. The separate treatment of the Hartree–Fock and correlation energies provides an efficient way to approximate correlation energy for extended systems. We illustrate this here by calculating accurate MØller-Plesset second-order perturbation theory (MP2) energies for a series of clusters ranging in size from 5 to 20 water molecules. In this new method, called EE-MB-CE, where MB is pairwise additive (PA) or three-body (3B), the full Hartree–Fock energy of a system of N monomers is calculated (i.e., the many-body expansion is carried out to N th order), while the EE-MB method is used to calculate the correlation energy of the system. We find that not only does this new method lead to better energetics than the original EE-MB method, but that one is able to obtain excellent agreement with full MP2 calculations by considering only a two-body expansion of the correlation energy, leading to a considerable savings in computational time as compared to the three-body expansion. Additionally, we propose the use of a cutoff to further reduce the number of two-body terms that must be calculated, and we show that if a cutoff of 6 Å is used one can eliminate up to 44 % of the pairs and still calculate energies to within 0.1 % of the net interaction energy of the full cluster. 2 1
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