  Computationally-guided material discovery is being increasingly employed
using a descriptor-based screening through the calculation of a few properties
of interest. A precise understanding of the uncertainty associated with first
principles density functional theory calculated property values is important
for the success of descriptor-based screening. Bayesian error estimation
approach has been built-in to several recently developed exchange-correlation
functionals, which allows an estimate of the uncertainty associated with
properties related to the ground state energy, for e.g. adsorption energies.
Here, we propose a robust and computationally efficient method for quantifying
uncertainty in mechanical properties, which depends on the derivatives of the
energy. The procedure involves calculating the energy around the equilibrium
cell volume with different strains and fitting the obtained energies to the
corresponding energy-strain relationship. At each strain, we use instead of a
single energy, an ensemble of energies, giving us an ensemble of fits and
thereby, an ensemble of mechanical properties associated with each fit, whose
spread can be used to quantify its uncertainty. The generation of ensemble of
energies is only a post-processing step involving a perturbation of parameters
of the exchange-correlation functional and solving for the energy non-self
consistently. The proposed method is computationally efficient and provides a
more robust uncertainty estimate compared to the approach of self-consistent
calculations employing several different exchange-correlation functionals. We
demonstrate the method by calculating the uncertainty bounds for Si using the
developed method. We show that the calculated uncertainty bounds the property
values obtained using three different GGA functionals: PBE, PBEsol and RPBE.
