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Chuck-Hou Yee added section_BaCoSO_For_structure_prediction__.tex
almost 8 years ago
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\section{BaCoSO}
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. [Ran, please fill in technical details here — how many k-points, convergence criteria, population sizes, etc.].
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. We devised a structure matching algorithm to group together similar structures that differ by only small shifts in internal atomic coordinates and cell geometry [Ran, fill in any details here]. The energies of this set of structures is 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 [XXX] was insufficient and that a population of [XXX] is necessary. 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 find [Ran, can you elaborate on the details here?]
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?]
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 ~ 0.3U. A second subset has energies that a relatively constant (∆E ~ const). The third group, which appeared to have the lowest energies in the U = 0 run, rapidly increases in energy with ∆E ~ 0.7U. We can rationalize this behavior by [need to look at the data 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.
