| Abstract
| - We examine the origin of the orbital localization requirement, commonly imposed on effective potentialimplementations of the Perdew−Zunger (PZ) self-interaction correction (SIC). We demonstrate that thecondition arises because of the presence of irreducible off-diagonal Lagrangian multipliers in the coupled PZeigenequations. Thus, this condition is essential for obtaining an energy-minimizing solution. Further, wereport on an implementation of PZ SIC for the generalized gradient approximation (GGA) to the exchange-correlation energy within density functional theory (DFT). The implementation relies on the Krieger−Li−Iafrate (KLI) approximation to the optimized effective potential (OEP), simplifying the evaluation of molecularproperties, such as the NMR chemical shifts. We examine several approaches toward incorporating the frozencore orbitals within the SIC−KLI−OEP scheme. To achieve an accurate description of both the energeticand magnetic properties, core orbitals must be included in the KLI potential on an equal footing with thevalence orbitals. Implementation of the frozen core orbitals enables incorporation of relativistic effects viathe quasirelativistic Pauli Hamiltonian. As the first application of the SIC−GGA approach, we examine 31PNMR chemical shifts of 18 representative small molecules, as well as the previously reported C, H, N, O,and F SIC-LDA (local density approximation) test set. For C, N, O, and F NMR chemical shifts, SIC−GGAperforms similarly to SIC−LDA, whereas a significant improvement is observed for hydrogen. Almost identicalresults, both for the chemical shifts and absolute shieldings, are obtained with different parent GGAs. For the31P test set, SIC−revPBE (revised Perdew−Burke−Ernzerhof functional of Zhang and Yang) leads to anroot-mean-square (RMS) residual error of 23 ppm, compared to 54 ppm for its parent GGA, and 40 ppm forthe SIC−VWN (Vosko−Wilk−Nusair) LDA functional. In particular, SIC−revPBE correctly reproducesthe experimental trends in the PF3−PCl3−PBr3−PI3 series, which is described qualitatively incorrectly byVWN, revPBE, and SIC−VWN calculations. A similar improvement is observed for the 31P shielding tensorcomponents. The spurious self-interaction, in modern approximate DFT, appears to be a major, and so farlargely overlooked, source of errors in calculations of the NMR shielding tensors.
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