We present an analytic ansatz to find the effective electrostatic potential and Coulomb correlations in multicenter problems, specifically homogeneous and doped clusters of metal atoms. The approach is based on a quasi-classical density-functional treatment. We focus on the interpretive aspect of our findings, particularly on extracting insight regarding the geometric effects of Coulomb correlations for any given spatial disposition of ionic cores. For singly-doped metallic clusters we obtain a

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... direct visualization of the variations of both screening and Coulomb correlations with changes of location of the dopant atom. This analysis provides a way to interpret recent observations of the variability of physical properties of metal clusters with changes of composition and geometry.