Potassium-doped barium bismuth oxide (\(Ba_{1-x}K_{x}BiO_{3}\)), is a famous high temperature superconductor, discovered in the late 1980s \cite{Sleight_1975, Cava_1988}. Its parent compound, BaBiO\({}_{3}\), has a distorted perovskite structure, with a band gap of \(\sim 0.2\) eV \cite{Sleight_1975}. Doping the material, with K for example, suppresses the structural distortions and makes the material superconducting, with a transition temperature of nearly 30 K at optimal doping. DFT does not describe the insulating character of the parent compound. Additionally, DFT estimates of the electron phonon coupling \(\lambda\) within Migdal-Eliasberg theory give a value of 0.34 in the doped compound, too small to account for its superconductivity \cite{Meregalli_1998}.

Examining the effect of correlations, we found that \(\lambda\) is substantially enhanced relative to its DFT estimate to a value of nearly \(1.0\), and that this enhancement is responsible for superconductivity in doped BaBiO\({}_{3}\) \cite{Yin_2013}. We argue that correlations similarly enhance the electron phonon coupling in other materials proximate to an insulating state, accounting for superconductivity in systems such as HfNCl, borocarbides and buckminsterfullerenes. For these materials, the most important type of correlation that must be captured is the static contribution, and a GW or hybrid DFT calculation is sufficient to correct the electronic structure. After these calculations are done, one is left with a strongly-coupled electron-phonon system with \(\lambda\sim 1\). This coupling induces a large dynamical self energy, which accounts for the observed anomalous optical properties of this system \cite{Nourafkan_2012} at energies below 1 eV.

By analogy, we searched for other materials in this class: materials where the parent compound would be strongly mixed valent and the electron-phonon coupling would be understimated by LDA. We propose these would be candidate high temperature superconductors. We describe the steps in the workflow:

Electronic structure. In this material static correlations are very important, they thus require GW or hybrid DFT to make correct predictions (for example, the large electron phonon coupling and the tendency towards valence disproportionation) and it’s a case that LDA is not a good guide to the electronic strucure. Identification of the level and the nature of the correlations is thus very important for a successful material design problem.

Structural prediction The structural design proceeded by analogy with BaBiO\({}_{3}\) and the local stability was checked by computing phonon modes with LDA. However experiments revealed another allotropes. It would be interesting to see if these would show up in more general searches as detailed in the Section \ref{sec:bacoso}.

Global stability The parent compound was succesfully synthesized, and the prediction realized, because it is likely that its total energy lied well below the the convex hull. The indications come from the energetics of a few reaction pathways were computed and they turned out to be exothermic.