Bayesian error estimation in density functional theory

The principles behind the Bayesian error estimation functionals within density functional theory are reviewed and illustrated by selected applications. The functional construction involves the definition of a probability distribution in the space of exchange-correlation (xc) functionals which lead to the determination of an ensemble of xc-functionals.

The ensemble is then used to compute error bars on DFT-calculated properties. The probability distribution addresses the issue of insufficient model spaces, which do not include the theoretical exact xc-functional. The applications include calculation of cohesive energies, structural energy differences of solids, and the determination of the reaction rate for ammonia synthesis on metal catalysts.

Correlations in the functional ensemble are seen to play a major role for reliable error prediction. Finally, the approach is applied to identify systematic errors in calculation of binding energies of small organic molecules with generalized gradient approximation functionals.