We decompose the energy error of any variational density functional theory calculation into a contribution due to the approximate functional and that due to the approximate density. Typically, the functional error dominates, but in many interesting situations the density-driven error dominates. Examples range from calculations of electron affinities to preferred geometries of ions and radicals in solution. In these abnormal cases, the error in density functional theory can be greatly reduced by using a more accurate density. A small orbital gap often indicates a substantial density-driven error.

Standard density functional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected density functional theory (DC-DFT), certain classes of density functional theory calculations are significantly improved by using densities more accurate than the self-consistent densities. We discuss how to identify such cases, and how DC-DFT applies more generally. To illustrate, we calculate potential energy surfaces of HO·Cl(-) and HO·H2O complexes using various common approximate functionals, with and without this density correction. Commonly used approximations yield wrongly shaped surfaces and/or incorrect minima when calculated self consistently, while yielding almost identical shapes and minima when density corrected. This improvement is retained even in the presence of implicit solvent.

All-electron fixed-node diffusion Monte Carlo provides benchmark spin gaps for four Fe(II) octahedral complexes. Standard quantum chemical methods (semilocal DFT and CCSD(T)) fail badly for the energy difference between their high- and low-spin states. Density-corrected DFT is both significantly more accurate and reliable and yields a consistent prediction for the Fe-Porphyrin complex.

We review the role of self-consistency in density functional theory. We apply a recent analysis to both Kohn-Sham and orbital-free DFT, as well as to Partition-DFT, which generalizes all aspects of standard DFT. In each case, the analysis distinguishes between errors in approximate functionals versus errors in the self-consistent density. This yields insights into the origins of many errors in DFT calculations, especially those often attributed to self-interaction or delocalization error. In many classes of problems, errors can be substantially reduced by using 'better' densities. We review the history of these approaches, many of their applications, and give simple pedagogical examples.

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements

We present a colloidal route for the synthesis of ultrathin ZrS(2) (UT-ZrS(2)) nanodiscs that are ~1.6 nm thick and consist of approximately two unit cells of S-Zr-S. The lateral size of the discs can be tuned to 20, 35, or 60 nm while their thickness is kept constant. Under the appropriate conditions, these individual discs can self-assemble into face-to-face-stacked structures containing multiple discs. Because the S-Zr-S layers within individual discs are held together by weak van der Waals interactions, each UT-ZrS(2) disc provides spaces that can serve as host sites for intercalation. When we tested UT-ZrS(2) discs as anodic materials for Li(+) intercalation, they showed excellent nanoscale size effects, enhancing the discharge capacity by 230% and greatly improving the stability in comparison with bulk ZrS(2). The nanoscale size effect was especially prominent for their performance in fast charging/discharging cycles, where an 88% average recovery of reversible capacity was observed for UT-ZrS(2) discs with a lateral diameter of 20 nm. The nanoscale thickness and lateral size of UT-ZrS(2) discs are critical for fast and reliable intercalation cycling because those dimensions both increase the surface area and provide open edges that enhance the diffusion kinetics for guest molecules.

Density-corrected DFT is a method that cures several failures of self-consistent semilocal DFT calculations by using a more accurate density instead. A novel procedure employs the Hartree-Fock density to bonds that are more severely stretched than ever before. This substantially increases the range of accurate potential energy surfaces obtainable from semilocal DFT for many heteronuclear molecules. We show that this works for both neutral and charged molecules. We explain why and explore more difficult cases, for example, CH(+), where density-corrected DFT results are even better than sophisticated methods like CCSD. We give a simple criterion for when DC-DFT should be more accurate than self-consistent DFT that can be applied for most cases.

Parkinson's disease (PD), one of the most common neurodegenerative disorders, is characterised by the loss of dopaminergic neurons in the substantia nigra pars compacta (SNpc) to the striatum (ST), and involves oxidative stress. Mulberry fruit from Morus alba L. (Moraceae) is commonly eaten, and has long been used in traditional oriental medicine. It contains well-known antioxidant agents such as anthocyanins. The present study examined the protective effects of 70 % ethanol extract of mulberry fruit (ME) against neurotoxicity in in vitro and in vivo PD models. In SH-SY5Y cells stressed with 6-hydroxydopamine (6-OHDA), ME significantly protected the cells from neurotoxicity in a dose-dependent manner. Other assays demonstrated that the protective effect of ME was mediated by its antioxidant and anti-apoptotic effects, regulating reactive oxygen species and NO generation, Bcl-2 and Bax proteins, mitochondrial membrane depolarisation and caspase-3 activation. In mesencephalic primary cells stressed with 6-OHDA or 1-methyl-4-phenylpyridinium (MPP þ), pre-treatment with ME also protected dopamine neurons, showing a wide range of effective concentrations in MPP þ -induced toxicity. In the sub-acute mouse PD model induced by 1-methyl-4-phenyl-1,2,3, 6-tetrahydropyridine (MPTP), ME showed a preventative effect against PD-like symptoms (bradykinesia) in the behavioural test and prevented MPTP-induced dopaminergic neuronal damage in an immunocytochemical analysis of the SNpc and ST. These results indicate that ME has neuroprotective effects in in vitro and in vivo PD models, and that it may be useful in preventing or treating PD.