"Adiabatic" Elastic Constants in Hubbard-Corrected Density-Functional Theory DFT+U: case UO$_2$

Abstract: Since in DFT+U there are multiple self-consistent electronic solutions, the so called metastable states, the elastic constants computed from stress-vs-strain will be incorrect if some of the strained configurations fall into a different local electronic minimum than the equilibrium non-strained state. So, it is crucial to carefully take steps to keep the same electronic Hubbard occupation branch when computing the stresses for small strained geometries. In this work, we have explained this "adiabatic" method of calculation for elastic constants and applied for UO$_2$ crystal described within two different unit cells of cubic 12-atom and tetragonal 6-atom basis sets. The calculation results for the two different unit cells are the same within 0.1 GPa, and agreement with experiment is excellent.