Unit 5.3 - Benzene and Polymorphism

[@bigproton]

Thank you so much for taking the time to answer, Frank. It is greatly appreciated. What I meant is that if the molecule retains, for example, its center of inversion in the crystal (ie the benzene retains its inversion center in the crystal) then it should necessarily crystallize in a centro symmetric space group (and the asymmetric unit, of course would be just part of the benzene) or it could still crystalline in a non centrosymmetric space group because even though the benzene is centrosymmetric this "local" center of inversion is not compatible with the overall symmetry of the crystal. My guess is that it should crystallize necessarily in a centro symmetric space group but I am not sure since I know that a non symmetric molecule can crystallize in a centro symmetric space group. Thanks again for your time and kind answers, Frank.

[@FrankHoffmann1000]

Your interesting question raised my curiosity and therefore I've done a small literature survey. I found this very interesting article "Why do crystal structures waste molecular inversion symmetry?" by Andrew D. Bond. doi.org/10.1039/C001341B Here, a very few examples of molceules are listed that have an inversion center but crystallize in a non-centrosymmetric space group! But none of them have such a high symmetry as benzene! If you do not have access to the article, write me an eMail ([e-mail]). Best! Frank

[@bigproton]

Great Video. I have two questions. (1) Regarding the primitive lattice, I don't see that it is a primitive one rather than a centered one. Is it related to the fact that the motif is based on several molecules (since it should be a single motif in the whole primitive unit cell)? (2) Could benzene crystallize in any space group? For instance, P1? Benzene is very symmetrical so I don't know if it could crystallize in a space group with no symmetry. If so, it is related to the fact that the symmetry has to be consistent with the translational symmetry?

[@FrankHoffmann1000]

Hi proton! (Don't know, why your user pictire and name is gone, but anyway...) (1) "Is it related to the fact that the motif is based on several molecules (since it should be a single motif in the whole primitive unit cell)?" --> No, th ereason is not the motif are comprised of several molecules, but rather that not all of them have the exact same orientation in space! Note that a centering is merely a translation operation! (2) "Could benzene crystallize in any space group?" --> No. Or maybe a better answer would be: Probably not. A molecule can crystallize in several space groups, depending on the conditions (pressure, temperature), but not in all space groups, or to say the minimum: it it not very likely. Ice for instance exists in 18(!) polymorphs and maybe in the future some more will be discovered, but I think it can be ruled out that a total of 230 polymorphs will be found.

[@bigproton]

@@FrankHoffmann1000 Thank you very much for your kind answers. Regarding my second one, I guess we cannot rule out that benzene can crystalize in P1, right?. However, I don´t see how this could be the case since benzene is very symmetrical and has several mirror planes and an inversion center. it is related to the fact that the symmetry has to be consistent with the translational symmetry? I find difficult to see that it could crystalize in a non centro symmetric space group while bencene is centrosymmetric itself. Thanks a lot, Frank!

[@FrankHoffmann1000]

@@bigproton Hi again proton! I would agree that we cannot rule out that benzene crystallize in P1 at certain conditions. But in this context I have some difficulties to understand your sentence "it is related to the fact that the symmetry has to be consistent with the translational symmetry?". Well, yes, the translational symmetry _is_ simply present in every case, because that is the unique and characteristic feature of crystals par excellence :-) But that doesn't touch upon the relation between the symmetry of the constituent of a crystal (i.e., in a molecular crystal the molecule) and the symmetry of the packing so to speak. However, I would agree that very symmetrical molecules tend to crystallize in a packing that also has some additional symmetry elements other than pure translation. Nevertheless, I would not rule out P1, because I could imagine, for example, that the benzene molecules could 'fold' at very high pressures and are no longer planar, so that many intrinsic symmetry elements are not present any more. It would be quite interesting to investigate which molecular crystals crystallise in P1 and which intrinsic symmetry the corresponding molecules have.

[@DiAoyUdAoprOtEctOr]

Hi prof, how to hide the hydrogen atoms like you did at about 1:42?

[@FrankHoffmann1000]

See 6.2.11 in this manual: www.ccdc.cam.ac.uk/support-and-resources/ccdcresources/mercury.pdf