A first-principles DFT+U functional for the flat-plane condition robust against stringent test cases*

The DFT+U method is an extremely popular tool for the prediction of Mott-Hubbard and Charge-Transfer insulators, thanks to its semi-local DFT cost. DFT+U-type functionals however, have been traditionally developed from the Hubbard model with use of ad-hoc double-counting correction schemes. 

We derive a DFT+U-type functional named BLOR [1], to explicitly enforce the flat plane condition on localized subspaces, dispensing with the need to invoke the Hubbard model or a double-counting correction scheme. BLOR by design corrects for Many-Electron Self-Ineraction Error (MSIE) and Static Correlation Error, two of the most notorious errors that plague practical DFT calculations. BLOR also corrects an additional energetic error we coin asymmetric-MSIE.

We use multireference homonuclear molecular test systems to compare the performance of BLOR to traditional functionals, with U & J parameters computed using the linear response methodology. We find that PBE and PBE+U (using Dudarev’s functional) yields relative energetic errors as high as 8% & 20.5% respectively, while BLOR yields errors below 0.6%.

We further show our recent work on constructing the energy versus spin-occupancy landscape of interacting fermionic systems [2], and how the flat-plane condition gives way to a more comprehensive ‘tilted plane’ condition. We will also highlight our recent proof of the long-assumed convexity condition of DFT [3].