Quick tips: More about U
This month marked both the AIChE national meeting in San Francisco’s special symposium that I coorganized called “Applications of DFT+X in catalysis” as well as my first month as an assistant professor. The tutorials are likely to be archived and remain online but will no longer be updated as frequently. In Fall 2014, I will teach an elective in simulations at MIT, and some of this material may make its way to the tutorial page here. Here are a couple of quick tips related to questions that came up during the session and beyond:

Electron delocalization: if metallic character in a solid occurs upon vacancy formation in an oxide…this may be a common issue that is alleviated with a U, leading to differences in electronic states.

Using “ramping: For users of DFT+U with CP2K, “ramping” is encouraged. This is where low U values are used at first to ensure convergence to a specific electronic state. Note, using the potential from a previous SCF calculation is a useful tool for converging the same electronic state at a different value of U or with a different functional.

Unphysical values of “U”: When a manifold is nearly empty or nearly full, response functions from the linearresponse calculation of U become small. Inverting the bare and converged numbers may result in two large numbers that, when subtracted, will give a nonzero number that has little meaning.

Solid state vs. single site vs. slabs: In the solid state, a U calculation should be done in a matrix formalism, with each unique site getting its own U calculation (you can fill in the rest through symmetry). Single site calculations, we simply invert a number and subtract. For slab calculations (both pristine and decorated), it’s worthwhile to note that undercoordinated species often have different values of U than those in the bulk.

Selfconsistent U is most useful when the DFT(LDA/GGA) ground state is distinct from the state observed at nonzero U. This is particularly important for cases where the two states cannot both be selfconsistently achieved. For qualitatively equivalent electronic states, a linearresponse U is often sufficient. A more complete tutorial for calculating the selfconsistent U will be provided next month.
Hope you found these quick tips helpful. Stay tuned while tutorials shift gears and possibly go more back to basics while I address the needs of our new research group.