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I am reading the paper "Twenty five years of Finnis-Sinclair potentials" by Graeme Ackland, Adrian Sutton, and Vasek Vitek, Philosophical Magazine 2009, 89, 3111-3116. It is a review-type article describing the notion that pair potentials are inadequate for describing bonding in metals. But it turns out that if the attractive interaction is "described by the square root of a sum of pair interactions to neighbors, centered on each atom in the solid," metallic bonding can be described reasonably well. The authors point out:

The novelty is entirely in the square root. The square root captures the dependence of atomic interactions on the local density: as the number of neighbors of an atom decreases, the strength of the remaining bonds increases. This immediately predicts an inward relaxation at metallic free surfaces with a tensile surface stress, both of which are widely observed but not predicted by models in which the cohesive energy is just a sum of pair potentials.

My question is, is it true for metals that "as the number of neighbors of an atom decreases, the strength of the remaining bonds increases"? Is there any way that I can understand this, either in a qualitative or quantitative way? Also, when it says "the strength of the remaining bonds increases," is this referring to the energy per bond?

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