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In order to not miss crucial seed structures which ultimately led to the experimental structure, we found that the randomly generated initial population of structures must be sufficiently large. An initial population of size 300 was sufficient with a single generation size of 60. In total $\sim 700$ metastable structures were produced in 8 generations. In addition, spin polarization is crucial for the local relaxations performed within each USPEX generation in order to find the experimental structure. When non-spin-polarized DFT was used, we could not find some of the lowest energy materials (including the observed structure)  What causes To understand the behavior of  therelative shift in  energies as a  function of U? We $U$, we  first roughly grouped the structures by the behavior of the $E$ vs. $U-J$ curve, which we have indicated by colors in Fig.~\ref{fig:reordering}. For example, in red are a small The largest  group has a slope  of structures roughly $∆E \sim 0.3U$. A second subset has energies that a relatively constant $(∆E \sim const)$. The third group,  which are found appeared  to be have  the lowest energy structures energies  in paramagnetic LDA calculations, but which quickly shoot upwards the U = 0 run, rapidly increases  in energies as $U-J$ is increased. energy with $∆E \sim 0.7U$.  In order to the  rationalize this behavior, we Roughly, the correction depends on the occupation of the 3d orbitals to which U is applied, namely the energy difference between two states with occupations n1 and n2 is roughly $∆E \sim U(n1-1/2)(n2-n1)$. [Gabi, Ran, this is just my hypothesis. Ran, could you check this from the data?]  We can classify the candidate structures by the evolution of their energies as a function of U into roughly three groups. The largest group has a slope of roughly $∆E \sim 0.3U$. A second subset has energies that a relatively constant $(∆E \sim const)$. The third group, which appeared to have the lowest energies in the U = 0 run, rapidly increases in energy with $∆E \sim 0.7U$. We can rationalize this behavior begin  by [need to look at examining  thedata here — maybe it has to do with the local ligand environment of the Co atom, and maybe we won’t be able to rationalize it.]  There are several open questions. What is the effect of U on the energy landscape. Does U simply shift the local minima relative to one another, or does it create and destroy minima? Additionally, when is U necessary for correct reordering of the candidate energies? Perhaps U is only necessary for compound containing correlated atoms, or magnetic materials. Larger scale studies on multiple keystone compositions is necessary.  In conclusion, or proposed strategy for  structural prediction is as follows: first perform USPEX runs with spin-polarized DFT to generate the list of structures occupying local minima in the energy landscape. Then, apply LDA+U to the resulting structures to reorder the total energies to determine the true ground state structure. This is more economical than running USPEX motifs associated  with hundreds of calls to LDA+U, since LDA+U is more expensive than LDA. each group.