Corrected effective medium method. II. N-body formulation

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Abstract
A general corrected effective medium (CEM) theory is presented which yields the interaction energy of an N‐atom system, in contrast to the previous version of the CEM theory which provides the energy of one atom interacting with the other (N−1) atoms acting as a host. The CEM method presented herein treats all N atoms on an equal basis without identifying all but one as a host, and is referred to by the acronym CEM‐N. The basis for this theory involves expressing the interaction energy for the real system in terms of the sum of the interaction energies for each atom embedded into a homogeneous electron gas with compensating positive background (i.e., the effective medium is jellium). Minimization of the difference in kinetic‐exchange‐correlation energy between the real and effective system, evaluated using density functionals and the approximation of superposition of atomic densities for the system density, yields the prescription for choice of the electron densities of each jellium system. The full interaction energy then consists of three terms: the embedding energy, Coulombic energy, and kinetic‐exchange‐correlation difference energy. Applications and tests for the C2 , N2, and O2 molecules are presented using the SCF‐LD embedding energies of Puska et al. The quality of these results illustrate the need for a new set of universal ‘‘covalent’’ embedding energies, which are constructed semiempirically in the present article.