I am studying a material which was first discovered in the early 1960s. It was reported then that it crystallized in the hexagonal $P6_3/mmc$ space group. Recently the material was synthesized again and found that it posses $P6_3mc$ symmetry. My own DFT calculations and another published work find that the latter structure is more stable. Hence during the review of my work, the reviewer mentioned the original $P6_3/mmc$ structure as hypothetical.

How can the structure be called hypothetical if it was reported from experiments and corroborated by others?

Also in general, if an earlier experiment identifies a material with a crystal type and later its found (experiment and theory) that the material crystallizes with a different structure, is the original structure invalid?


2 Answers 2


Let's imagine we have two different structures for the same compound, and that structure 1 has the lower energy and structure 2 has the higher energy. If you consider the potential energy surface of all potential atomic configurations, then each of these structures sits at a local minimum, and the minimum associated with structure 1 is lower in energy than the minimum associated with structure 2. I am also going to assume, for simplicity, that structure 1 is the global minimum, so it is the ground state structure.

What does this mean regarding the experimental synthesis of these structures? Structure 1, which is the global minimum, is the most stable structure. What this means is that it will typically be easier to synthesize, and if you wait long enough, any structure of that compound will eventually turn into structure 1. However, it may still possible to synthesize structure 2 experimentally. Depending on your synthesis route, you can create structure 2, which is then "stuck" in that minimum and, even though the minimum of structure 1 is lower in energy, there is an energy barrier to get there. A very famous example of this is carbon structures. The ground state structure of carbon is graphite (my structure 1), but you can also find diamond (my structure 2). In this case, diamond is synthesized at high pressures (where it is actually the lowest energy structure), and then releasing pressure leaves it stuck at its local minimum of energy. Even though diamond is not the lowest energy structure at ambient pressure, it is a structure that carbon can adopt.

What does all this mean for your question? I guess there could be two things going on here:

  1. Both structures can be synthesized. The old experiment happened to synthesize a higher energy but locally stable structure (think diamond), and the new experiment has synthesized the true ground state (think graphite). In this case, I would not call any of the two structures hypothetical, as they have both been confirmed experimentally.

  2. Another option that always needs to be considered is that one of the experiments is wrong.

  • $\begingroup$ To say it differently: If the thermodynamics allow the reaction/transformation to happen that does not mean it will happen. The kinetics of that reaction/transformation should also be fast enough. If a particular experiment/analysis technique is not sufficiently advance then the future studies/analyses can add to those earlier findings. $\endgroup$
    – Sufyan
    Commented Jun 11, 2020 at 16:38

Sometime the experiments can also be interpreted incorrectly. Namely, not all kinds of experiments are unambiguous; some require computational modeling to extract the structure.

That is, even if the experiment were done correctly, the assignment can still be wrong if the interpretation is not correct.

(I'm not sure this applies to crystal structure modeling; if you have e.g. x-ray diffraction spectra the interpretation is quite straightforward. However, if your material contains hydrogens, x-ray diffraction spectroscopy can't usually locate the hydrogens and so your interpretations may again be limited. A full characterization tends to require both x-ray and neutron diffraction spectra.)

  • $\begingroup$ Crystal structure determination is not modeling. Also, if the structure was determined by single crystal x-ray diffraction, it's almost (99.9%?) that it's structure is correctly determined. I think that what we have here is just a polymorphism case. $\endgroup$
    – Camps
    Commented Jun 11, 2020 at 3:11
  • $\begingroup$ Molecular crystals aren't that easy, and it wasn't specified whether there is hydrogen in the system or not. Looks like crystal structure determination has advanced recently; a 2016 paper [1] claims that hydrogens can be located precisely but I get the feeling that the method is limited to small molecules. [1] advances.sciencemag.org/content/2/5/e1600192.full $\endgroup$ Commented Jun 11, 2020 at 7:52

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