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The many-body perturbation theory of Brueckner and Goldstone is used to calculate the electron correlation energy among the $n=3$ and $n=4$ electrons of FeI. The results is - 0.7155 a.u. Combined with a semiempirical estimate of correlations from the (1s)²(2s)²(2p)⁶ core, the total correlation energy of FeI is - 1.165 a.u.
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Kelly et al. (1971) studied this question.
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