Diffusion quantum Monte Carlo calculations of SrFeO${_3}$ and LaFeO${_3}$

The equations of state, formation energy and migration energy barrier of the oxygen vacancy in SrFeO${_3}$ and LaFeO${_3}$ were calculated with the diffusion quantum Monte Carlo (DMC) method. Calculations were also performed with various Density Functional Theory (DFT) approximations for comparison. DMC reproduces the measured cohesive energies of these materials with errors below 0.23(5) eV and the structural properties within 1% of the experimental values. The DMC formation energies of the oxygen vacancy in SrFeO${_3}$ and LaFeO${_3}$ under oxygen-rich conditions are 1.3(1) and 6.24(7) eV, respectively. Similar calculations with semi-local DFT approximations for LaFeO$_3$ yielded vacancy formation energies 1.5 eV lower. Comparison of charge density evaluated with DMC and DFT approximations shows that DFT tends to overdelocalize the electrons in defected SrFeO${_3}$ and LaFeO${_3}$. Calculations with DMC and LDA yield similar vacancy migration energy barriers, indicating that steric/electrostatic effects mainly determine migration barriers in these materials.