The uncertainty pyramid for electronic-structure methods

Abstract Electronic-structure methods predict material behavior mostly without prior knowledge and are therefore often considered an absolute standard. Nevertheless, hidden assumptions and approximations inevitably introduce uncertainty. This chapter focuses on density-functional theory (DFT), a popular approach to determine electronic structures from first principles. A crucial ingredient is the exchange-correlation functional, for which different functional forms possess varying degrees of uncertainty. However, DFT uncertainties are much wider than the exchange-correlation functional alone and range from numerical effects to intrinsic deficiencies in the atomic-scale description of macroscopic phenomena. The accumulation of these uncertainties leads to an inverse uncertainty pyramid. We discuss this uncertainty pileup by means of two case studies: (1) equation-of-state predictions with different DFT codes and (2) the ductility of a W–Re alloy. These two case studies demonstrate some best practices with respect to the use of DFT-related error bars, as well as identify future challenges for DFT uncertainty quantification.