deletions | additions       diff --git a/bacoso.tex b/bacoso.tex  index 3781669..7133e0b 100644  --- a/bacoso.tex  +++ b/bacoso.tex 
...
\subsection{BaCoSO} \section{BaCoSO}  \label{bacoso} Illustrates the need for Ran’s reshuffling.  % Illustrates the need for Ran’s reshuffling. U.  % Illustrates the need for U.  % Outcome, a material that was found slightly earlier experimentally. For structure prediction, it has been commonly assumed that LDA/GGA is sufficient. Whereas comparisons between compounds with differing compositions certainly require the corrections detailed above, it is assumed that the systematic errors in LDA/GGA energies should cancel for differing structures of a *single* given composition. We argue this is not the case. In fact, correlations are important for comparison of energetics among structures for a single composition.  We use USPEX to sample the local minima in the energy landscape of the Ba-Co-S-O system with the elements in a 1:1:1:1 ratio. We allow two formula units in a unit cell. We use VASP as our DFT engine. We use spin-polarized LDA/GGA and do not include U corrections. Around 300 k-points are used, with convergence criteria EDIFF=1e-6, NELM=40.  To capture the relevant local minima, we retain all candidate structures produced in any of the USPEX generations that lie within 0.5eV/(unit cell) of the final lowest energy structure. Wedevised a structure matching algorithm to  group together similar structures structure using the criterion  that differ by only small shifts in internal atomic coordinates their symmetry groups are identical  and cell geometry [Ran, fill in any details here]. their computed energies are less than 3meV apart.  The energies of this set of structures is are  then examined as a function of U, which we plot in Fig. 2. We do not structurally relax the structures. We find that the inclusion of even a very small U-J ~ 1eV causes a clear separation of a single structure from the remaining minima, which we term the “ground state". The energy gap between the next-best structure and the ground state widens significantly as U-J increases. This ground state, as it turns out, is indeed the experimentally observed structure.  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. We found that an An  initial population of size 300 was insufficient and that sufficient with  a single generation size 80 was necessary. of 60.  In total ~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 the relative shift in energies as function of U? 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 ~ U(n1-1/2)(n2-n1). [Gabi, Ran, this is just my hypothesis. Ran, could you check this from the data?] 
...
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 a more economical way to find the ground state than running USPEX with LDA+U, since LDA+U is more expensive than LDA.