DFT+U(R) for Accurate Energetics

Despite the importance of transition metals in a variety of biological and inorganic systems, density functional theory calculations often fail quantitatively in describing these systems. We first showed that a DFT+U approach improves upon standard density-functionals in transition metal systems of both small and large size over both standard pure and hybrid functionals. However, one major shortcoming of this approach remains: we must use a calculated average of the values of Hubbard U when comparing points along a potential energy surface. More recently, I developed an approach called DFT+U(R) that allows direct incorporation of variations of Hubbard U across coordinates for comparison of different geometries and coordination environments, further removing empiricism from the DFT+U approach. While this approach is always more rigorous than using an averaged value of U, it is only necessary to introduce this additional level of accuracy for key cases where coordination and electronic structure vary. Key examples include catalysis in molecules and at surfaces, where it is particularly critical to ensure accuracy in energetics as bonds rearrange. Current ongoing research is in the use of DFT+U(R) to improve binding energy estimates of small molecules on transition-metal oxide surfaces (e.g. for ceria and titania).