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From my conjecture, I think it's a mix between valence electron and the principal energy state, but I'm not sure.

For example, C, N, O and F can only make a maximum of four bonds, as they can only have up to sp3 hybrid orbitals.

For Si, P, S and Cl, they can make a maximum of nine bonds, as they can have sp3d5 hybrid orbitals.

That's what I think, but I'm probably incorrect in some aspect.

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    $\begingroup$ You should expand on your statement since it doesn't provide your reason. $\endgroup$
    – LDC3
    Commented Jan 3, 2015 at 18:27
  • $\begingroup$ LDC3 is right. I can't see how these should get "mixed". $\endgroup$
    – M.A.R.
    Commented Jan 3, 2015 at 18:35
  • $\begingroup$ >For Si, P, S and Cl, they can make a maximum of nine bonds, as they can have sp3d5 hybrid orbitals. || nope, they can have 4 bonds at most as well. $\endgroup$
    – permeakra
    Commented Jan 3, 2015 at 19:42
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    $\begingroup$ @LtotheV $\ce{PCl5}$ molecule can be very roughly described as resonance hybrid (i.e. half-sum in this case) of two symmetrical structure. Three Cl atoms are contently bound to P atom, forming a flat triangle with the P atom in the center. one of the remaining electrons of P atom is transferred to one of the remaining Cl atoms, while another electron is used to form a covalent bond with remaining chlorine atom. Another resonance structure is a mirror opposite of described one, with roles of two last Cl atoms reversed. $\endgroup$
    – permeakra
    Commented Jan 3, 2015 at 21:38
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    $\begingroup$ @Dissenter Are you sure it is not 3-center, 4-electron bonding? link.springer.com/article/10.1007/s00897010525a $\endgroup$
    – DavePhD
    Commented Jan 5, 2015 at 16:26

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Considering the number of other atoms a central atom can be bonded to, "hybridization [is] irrelevant" and "the coordination number ... is not restricted by the number of hybrid orbitals that the atom can form", quoting On the role of d orbitals in sulfur hexafluoride J. Am. Chem. Soc., 1986, 108 (13), pp 3586–3593.

Examples such as $\ce{CLi6}$ and $\ce{TeF8^{2-}}$ are cited and emphasis is placed upon the ionic character of the bonding by the cited reference.

In my opinion, the main limiting factor is how many atoms can simultaneously be close to the central atom, this increasing with increasing radius of the central atom and with decreasing radius of the surrounding atoms.

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    $\begingroup$ +1 Agreed. There are plenty of examples with known crystal structures where there appear to be 5, 6, or even 7 interactions between Carbon atoms and neighboring ligands. Certainly 3rd row TM and actinide complexes more readily show large coordination numbers. $\endgroup$
    – Geoff Hutchison
    Commented Jan 5, 2015 at 19:24

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