(478f) DFT+U(R) for Better Ab Initio Surface Catalysis: The Cases of Ceria, Platinum, and Titania

Computational, electronic structure descriptions of transition metals that are key for catalysis have benefited greatly over the past twenty years from the development of Hubbard U augmented density functional approaches, known as DFT+U. While these methods are primarily employed in the solid state, we have also more recently shown that they have incredible potential for improving descriptions of transition metal complexes and molecules as well.  Importantly, the U term used in DFT+U is calculated self-consistently and from linear response for every system we study, and is not a fitting parameter.  However, typical studies using DFT+U still average U over all relevant intermediates and states because the energetics at different values of U cannot be compared directly.  We recently introduced a new DFT+U(R) approach that incorporates variations in the value of self-consistently calculated, linear-response U with changes in geometry.  This approach not only overcomes the one major shortcoming of previous DFT+U studies, i.e. the use of an averaged Hubbard U when comparing energies for different points along a potential energy surface is no longer required, but it also permits a quantification of how much U is changing with changes in coordinates. We now employ this approach to improve descriptions for binding events of small molecules to catalytically-relevant, transition-metal surfaces. This position-dependent DFT+U(R) provides a significant two- to four-fold improvement over DFT+U predictions. It also ameliorates previous failings of DFT+U in balancing accurate descriptions of oxidation and spin states of transition metals while maintaining accurate descriptions of binding strengths of small organic molecules to transition metal surfaces.  We highlight several key cases including ceria and platinum where both standard DFT and DFT+U approaches fail to produce a picture of small molecule binding preferences consistent with experiment.  Now, thanks to the improvements afforded by DFT+U(R) a fully consistent theoretical picture of catalysis on transition metal surfaces is well within reach.