  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. 
Functional uncertainty quantification for isobaric molecular dynamics   simulations and defect formation energies