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I am interesting in quantifying the coordination number of some atoms in metals and am curious what approaches to defining a coordination number are possible for an atom. In particular, I am curious if there are any continuous coordination number approaches that do not result in a hard change 12 to 11 for example when an atom moves just outside of the coordination shell.

It seems like the generalized coordination number solves this issue to some degree, but it is unclear to me if there are any better approaches. One requirement of this approach is that each atom should have its own coordination number assigned and not be an average value over the entire structure (as is seen in some liquid definitions).

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  • $\begingroup$ One possible option is the fractional coordination numbers defined in the DFT-D3 method: aip.scitation.org/doi/10.1063/1.3382344. However, I'm not sure if it has ever been shown that these coordination numbers can be safely used in contexts other than DFT-D. $\endgroup$
    – wzkchem5
    Jun 22 at 6:55
  • $\begingroup$ This looks along the right lines of what I was thinking of. $\endgroup$ Jun 22 at 16:58
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    $\begingroup$ @wzkchem5 If you spell out their definition, your comment is a complete answer. :) $\endgroup$
    – stafusa
    Jun 22 at 19:55

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