Bayesian error estimation in density-functional theory

Phys Rev Lett. 2005 Nov 18;95(21):216401. doi: 10.1103/PhysRevLett.95.216401. Epub 2005 Nov 15.


We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities such as binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude for different systems in good agreement with existing experience.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Bayes Theorem*
  • Models, Biological
  • Models, Chemical