There are many examples of metallic clusters that distort from the structure predicted by Wade's rules to a more 'spherical', closo-like arrangement. For example,

  1. $\ce{Bi8^2+}$ is a square antiprism (WR predict an arancho-derivative of a bicappped square antiprism, with 1 capping and 1 adjacent to an open-face atoms removed, instead of 2 capping atoms)
  2. $\ce{Bi9^5+}$ is a tricapped prism (WR predict a capped antiprism)
  3. $\ce{Ge8R6}$ is a square prism (WR predict an arachno-derivative of a bicapped square antiprism)
  4. $\ce{Ge9R3^-}$ is a tricapped trigonal prism (WR predict a capped square antiprism, i.e. expect nido but get closo)

My lecture notes (not available online) say that

Wade's rules are much less effective at predicting structures of metallic elements because intact polyhedra (spherical arrangements of metal atoms) tend to be a lot more stable for the more metallic elements, as compared to boron.

Could someone please explain why intact polyhedra are more stable for these elements.


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