The common example of back-donation is the interaction of a CO molecule with a metal center (d-orbitals) on a surface.

Can a similar mechanism occur between CO and a non-metal center, like oxygen on a surface (like in an oxide)? Can the p-orbitals of the surface oxygen be involved in such an interaction?

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    $\begingroup$ It is a matter of perspective: back donation of pi-electrons is not limited to M-CO interactions. The more important question would be whether you would like to define it that way and look at it that way or not, and whether or not it will have a stabilising effect. (Related negative hyperconjugation) Carbon suboxide can certainly be explained that way: $\ce{O#C\bond{->}C\bond{<-}C#O <-> O=C=C=C=O}$ $\endgroup$ May 8, 2019 at 15:19
  • $\begingroup$ Pi back-donation can and often does occur in all-nonmetal molecules. See this answer in relation to chalcogen halides, where pi back-donation affects the stoichiimetry we see. $\endgroup$ Dec 2, 2022 at 10:41

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Yes. This is a hot topic in main group chemistry, and has been used to explain stable CO complexes with main group elements. Here is a very nice open-access article by Sergeieva et al. where they look at the pi-back donation with some state-of-the-art computational chemistry. Here's a graphical demonstration of the Si←CO σ-donation and Si→CO π-back donation.

enter image description here Figure 2 Plot of deformation densities Δρ1–3 (isovalue=0.003) of the pairwise orbital interaction and shape of the most important occupied and vacant orbitals (isovalue=0.03) in silylene−carbonyl complex 1 with the orbital interaction energies ΔEorb (in kcal/mol) and their eigenvalues ν (in e). For the deformation densities, the direction of the charge flow is red→blue. The eigenvalues ν indicate the amount of donated (negative numbers) and accepted charge (positive numbers). The occupied orbitals are shown in yellow and blue for the different phases, while the unoccupied orbitals are in cyan and orange. Reproduced with permission according to CC BY 4.0 license.

The references contained therein detail the long history of Si--CO backbonding in particular.

There is nothing to stop back-donation to non-metal centers, but it is much rarer with main group elements. This is likely just because it happens to be that the overlap is more likely to occur with metals due to, e.g., ionic radius, d-orbital shape, etc..

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    $\begingroup$ Good discussion, but pi back-donation is not rare at all with main-group elements. It's just more subtle. For example, we can draw a structure for disulfur dichloride without pi back-donation, but that interaction accounts for $\ce{S2Cl2}$ being favored over $\ce{SCl2}$. $\endgroup$ Dec 2, 2022 at 10:54

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