Localized orbital corrections for density functional calculations on transition metal containing systems

We describe a method that improves density functional theory (DFT) calculations for transition metal containing systems via a set of empirical localized orbital corrections applied to the d-electron manifold of the metal (DBLOC). The method is an extension of the localized orbital approach that we have developed for first and second row atoms (DFT-LOC) which has demonstrated considerable success in correcting errors in gradient corrected and hybrid functionals. The most effective set of corrections are constructed using the B3LYP functional (B3LYP-DBLOC) but we have also investigated other functionals, which are similarly improved by the methodology. The method has initially been applied to benchmark data sets of octahedral complexes, which are used to calibrate the empirical correction parameters. For these data sets, mean unsigned errors of B3LYP-DBLOC are on the order of 1 kcal/mol for metal-ligand bond energies (as compared to 3.7 kcal/mol for uncorrected B3LYP), 2 kcal/mol for spin splittings (as compared to 10 kcal/mol for uncorrected B3LYP), and 0.12 eV for redox potentials (as compared to 0.40 eV for uncorrected B3LYP). The underlying rationale for the success of the LOCs, based on transferability of errors in DFT calculations for localized chemical groups across different molecules, is discussed, and the results for the various property calculations enumerated above are summarized. Applications to a number of complex systems, including titanium dioxide nanoparticles and several metalloenzymes, are presented, which demonstrate that the correction terms improve agreement with experiment in these systems.