(304f) Accurate Correction of DFT Delocalization Error in Transition Metal Catalysis
Semi-local density functional theory (DFT) suffers from delocalization error that prevents the accurate treatment of systems such as transition metal oxides in the solid state and transition metal complexes. Rigorously, delocalization error is defined as deviation from piecewise linearity of the energy with respect to fractional electron removal or addition. We will describe the extent to which popular approximate treatments for alleviating self-interaction error, such as global and range-separated hybrids as well as DFT+U, alleviate delocalization error and recover the derivative discontinuity. We recently showed for the first time that DFT+U eliminates delocalization error and recovers the derivative discontinuity, but not at the value of U typically employed in most simulations. Even when the former delocalization error is eliminated through DFT+U or exchange mixing in functionals, we have recently identified residual density delocalization error, when compared to accurate correlated wavefunction theory references. We will present recent extensions to this work on representative test cases in both catalytic transition metal complexes as well as in representative bulk and slab models of transition metal oxides. Although we identified DFT+U and Hartree-Fock exchange to equivalently alter properties of the density and energetics in molecules, we will present new, periodic-table-dependent, divergent behavior in the solid state. We describe the interplay between in models and quantities relevant for heterogeneous catalysis, including vacancy formation energies, adsorption energies, surface formation energies, and properties of the electron density. We identify where these functional tuning strategies provide improvements in properties consistently between DFT+U and hybrid exchange tuning and with respect to experiment. Finally, time permitting, we present new functional development strategies we have advanced that address both delocalization error due to fractional charge and fractional spin error. Prior methodological developments, including hybrid exchange and DFT+U, have eliminated delocalization error at the cost of increasing fractional spin error, which is correlated to increased errors in transition states in catalysis.