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Current ab initio methods may not be able to predict the electronic transport properties of cuprate superconductors but can they be used to predict their crystal structure? Furthermore those materials are typically polycrystalline and tend to brittle, can ab initio methods predict the details of those properties?

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Check the USPEX method which is mainly a crystal structure prediction code. It uses the evolutionary algorithm to find the global minimum on the potential energy surface of a material, thereby predicting its crystal structure in the equilibrium state. It works with even a bare-minimum input like the composition of the material.

This dissertation (Esfahani, M.M.D., 2017. Novel Superconducting Phases of Materials under Pressure by Evolutionary Algorithm USPEX (Doctoral dissertation, State University of New York at Stony Brook)) seems useful.

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Yes, indeed it's done by using plane-wave ultrasoft pseudo-potential technique and GGA exchange-correlation. See here: https://www.tandfonline.com/doi/pdf/10.1080/23311940.2016.1231361?needAccess=true . Particularly in this paper authors were able to calculate mechanical properties of Barium cuprate ($\text{BaCuO}_{2}$) superconductor and they find indeed it's brittle based on the definition of $\frac{G}{B} > 0.5$ where $G$ is shear modulus and $B$ is the bulk modulus both of them calculated from DFT.

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    $\begingroup$ Great answer @Alone Programmer. $\endgroup$ – Peter Morgan May 3 at 14:35

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