  Functional uncertainty quantification (FunUQ) was recently proposed to
quantify uncertainties in models and simulations that originate from input
functions, as opposed to parameters. This paper extends FunUQ to quantify
uncertainties originating from interatomic potentials in isothermal-isobaric
molecular dynamics (MD) simulations and to the calculation of defect formation
energies. We derive and verify a computationally inexpensive expression to
compute functional derivatives in MD based on perturbation theory. We show that
this functional derivative of the quantities of interest (average internal
energy, volume, and defect energies in our case) with respect to the
interatomic potential can be used to predict those quantities for a different
interatomic potential, without re-running the simulation. The codes and scripts
to perform FunUQ in MD are freely available for download. In addition, to
facilitate reproducibility and to enable use of best practices for the
approach, we created Jupyter notebooks to perform FunUQ analysis on MD
simulations and made them available for online simulation in nanoHUB. The tool
uses cloud computing resources and users can view, edit, and run end-to-end
workflows from a standard web-browser without the need to need to download or
install any software.
