We introduce a method for the estimation of uncertainties in density-functional-theory (DFT) calculations for atomistic systems. The method is based on the construction of an uncertainty-aware functional distribution (UAFD) in a space spanned by a few different exchange-correlation functionals and is illustrated at the level of generalized-gradient-approximation functionals. The UAFD provides reliable estimates of errors—compared to experiments or higher-quality calculations—in calculations performed self-consistently with the Perdew-Burke-Ernzerhof functional. The scheme furthermore allows for a decomposition of the error into a systematic bias and a reduced error. The approach is applied to four different properties: molecular atomization energies, cohesive energies, lattice constants, and bulk moduli of solids. The probability distribution can be tailored to optimize the prediction of a single property or for several properties simultaneously.

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• Crystalline systems
• Nanostructures
• Bayesian methods
• Density functional theory
• Density functional theory development