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This is a particular aspect I'm interested in, from the more generic question "Does the thermal evolution of chemical structures critically affect the validity of the calculated physical properties?". Generic, as well as particular answers will be welcomed.

Materials modelling is commonly performed starting from the single-crystal X-ray crystallography, whenever it is available. Theoretically determined structures are compared with this reference structure to assess the validity of the chosen method to estimate the physical property under study. A conceptual problem with this approach is that the theoretical structure corresponds to the bottom of the potential energy well, while the experimental structure is often determined at relatively high temperatures (e.g. 100 K or even 300 K). This means that we have experimental access to the thermally averaged coordinates, which may or may not coincide with the low-temperature energy minimum.

A related conceptual problem is that the higher temperature properties are often estimated from this bottom-of-the-well theoretical structure.

While it seems clear that there is a fundamental conceptual problem with this approach, since it implicitly assumes that the low temperature structure and the high temperature structures are the same, my question is how serious this problem is, in practice? How much of an error is expected to be introduced by this approximation?

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Not always the research pipeline is from experimental to theory. The group of Professor Artem Oganov had very interesting results where they started predicting theoretical structures (at extreme conditions) and then synthetize them in the lab. to confirm the predictions. One of their results is about $Na_3Cl$, $Na_2Cl$, $Na_3Cl_2$, $NaCl_3$, and $NaCl_7$.

About the errors to considered calculations at 0K for other temperatures, take a look at this answer this a similar question.

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