While I haven't had a chance to do any experiments with this molecule, I can offer some a priori observations at least. Many of the observations are probably more appropriate for an aqueous system, but some of the observations should translate to the polar organic solvents that you mentioned, at least in part. The structure of astaxanthin (assuming I found the correct structure) contains two ring structures that with alpha-hydroxycarbonyl donor groups and an extensively-conjugated backbone separating the potential donor groups.
I would think there's a decent possibility that the molecule could bind to a metal ion, but it seems most likely that it would only be able to bind one donor group per molecule to the metal center (so, 1:1, 1:2, and 1:3 M:L complexes), and it might not be that strong of a binding interaction. It looks like the molecule could pretty easily delocalize electron density to the donor groups, producing a dihydroxy donor group, which is able to bind metal ions, but depending on the strength of the interaction, it might get beaten out by the protonation of the hydroxyl groups on the molecule (which I'd think might be a bigger issue. Sterics would likely prevent the formation of 2:3 M:L or 2:2 complexes. Further, the rigidity of the backbone looks like it would prevent the molecule from bending around and forming a tetracoordinate complex. It would be pretty cool if it could form a polymeric structure or a lattice structure, but that's just conjecture on my part (and it's possible that the organic solvent might help with that).
I hope some of these observations are helpful, and I'd love to hear from others who might have some thoughts!
Thanks James for your useful input. I share with you the view of some weak binding with the metal ion, the solvent polarity would have a decisive influence to the stability of the coordinated system and the metal ion size for the number of possible coordinates. Experimental data eventually could show that.
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