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The title really explains what the issue is here. I would think that it has multicenter bonding akin to $(\ce{BeH2})_n$ polymer because they are pretty much iso-structural (although it shouldn't have $3c-2e^{-}$ bond but rather $3c-4e^{-}$ unlike $(\ce{BeH2})_n$.

J.D.Lee is a bit vague but it seems like it says there is no multicenter bonding in this polymer:

The anhydrous [Beryllium] halides are polymeric. Beryllium chloride vapour contains $\ce{BeCl2}$ and $(\ce{BeCl2})_2$, but the solid is polymerized. Though the structure of $(\ce{BeCl2})_n$ is similar to that for $(\ce{BeH2})_n$, the bonding is different. Both show clustering, but the hydride has three-center bonding. whereas the halides have halogen bridges, in which a halogen atom bonded to one atom uses a lone pair of electrons to form a coordinate bond to another beryllium atom.

I found another reference in Miessler & Tarr that is similarly vague about this issue:

Although beryllium halides $(\ce{BeX2})$ may be monomeric and linear in gas phase, in solid phase the molecules polymerize to form halogen-bridged chains with tetrahedral coordination around beryllium. Beryllium hydride ($\ce{BeH2}$) is also polymeric in solid with bridging hydrogens. The three-center bonding is involved in bridging by halogens, hydrogen and other atoms . .

Again here it is not explicitly mentioned here that halogens are involved in multicenter bonding for beryllium but are involved in general and it looks contradicting to what J.D.Lee says

enter image description here

Wikipedia cites this structure without any further comment. I would concur from this structure that it is involved in two seperate $2c-2e^{-}$ bonds. My instructor had noted that this is $3c-4e^{-}$ bond too which makes this matter rather confusing.

I would prefer if someone shows a primary citation with evidence for the type of bonding in this polymer (mentioned explicitly)

If there is no multicenter bonding like in the case of $(\ce{BeH2})_n$ then is there any qualitative reasoning as to why? (Any quantitative reasoning is also welcome albeit not preferred.)


Sources:

1) Concise Inorganic Chemistry by J.D.Lee (5th ed.)

2) Inorganic Chemistry by Gary L. Miessler and Donald A. Tarr (3rd ed.)

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  • $\begingroup$ IIRC, the Be-Cl bonds are equivalent. So, they are better considered as a 3c-4e bond (i.e. delocalised in a sense). The covalent Be-Cl and coordinate Cl->Be is just a Lewis model of the compound. If you are counting electrons, both give the same result, so it's a matter of the way of looking at things. IF one bond was covalent and the other was coordinate, you would be able to differentiate them, woudn't you? $\endgroup$
    – S R Maiti
    Jul 26 at 9:16
  • $\begingroup$ @SRMaiti . But are 3 orbitals (2 of be and 1 of cl) really overlapping? I would like to see some explicit reference. Also by delocalisation you mean resonance? If so why would J.D.Lee detail the bondings separately? If you have any sources please direct them to me. Thanks. $\endgroup$ Jul 26 at 9:23
  • $\begingroup$ Hmm I am not sure how the orbitals are overlapping. No, I didn't mean resonance, I was trying to say that the electrons are spread across two bonds, I couldn't find any other words except delocalisation. I think J D Lee wrote them separately because the Be-H-Be bonds are electron deficient, whereas Be-Cl-Be bonds are not. I don't have a reference right now, I am recalling something I read somewhere, so it might be wrong. $\endgroup$
    – S R Maiti
    Jul 26 at 9:27
  • $\begingroup$ I don't think there's any contradiction here between "two 2c/2e" and "one 3c/4e" descriptions. I believe the use of "three-center" is just to emphasize that the halogen has two bonds rather than the typical one. The 3c description also emphasizes the equivalence of the two bonds, even though the drawn Lewis structure necessarily makes one dative and one covalent. We could draw contributing resonance structures with each bond taking on covalent or dative character depending on the structure. $\endgroup$
    – Andrew
    Jul 26 at 13:01
  • $\begingroup$ @Andrew when I say 3c-4e I imagine that there are (atleast 3 orbitals overlapping (sort of the situation where in a venn diagram we see AnBnC and if AnBnC=0 then it is not 3 centre overlapping) I am still in high school so I don't know if currently this is a valid definition though. Also can you site me a source that refers to delocalisation and that 2 2c/2e and 3c/4e are really the same (Although it does seem plausible just to be sure). My main confusion is with what J.D.Lee was implying really. $\endgroup$ Jul 26 at 13:13

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