On the Use of Normalized Metrics for Density Sensitivity Analysis in DFT

In the past years, there has been a discussion about how the errors in density functional theory might be related to errors in the self-consistent densities obtained from different density functional approximations. This, in turn, brings up the discussion about the different ways in which we can measure such errors and develop metrics that assess the sensitivity of calculated energies to changes in the density. It is important to realize that there cannot be a unique metric in order to look at this density sensitivity, simultaneously needing size-extensive and size-intensive metrics. In this study, we report two metrics that are widely applicable to any density functional approximation. We also show how they can be used to classify different chemical systems of interest with respect to their sensitivity to small variations in the density.

Automated summary

The study discusses the relationship between errors in density functional theory and errors in self-consistent densities obtained from different density functional approximations, as well as how to measure and evaluate density sensitivity. Two widely applicable metrics for any density functional approximation are reported, along with how they can be used to classify chemical systems based on their sensitivity to small variations in density.