Comparison of SMC and OMC results in determining the ground-state and meta-stable states solutions for UO2 in the DFT+U method

Correct prediction of the behavior of UO2 crystal, which is an anti-ferromagnetic system with strongly correlated electrons, is possible by using a modified density functional theory, the DFT+U method. In the context of DFT+U, the energy of the crystal turns out to be a function with several local minima, the so-called meta-stable states, and the lowest energy state amongst them is identified as the ground state. OMC was a method that was used in DFT+U to determine the ground state. The SMC method, by leveraging only the oxygen electronic spin-polarization degrees of freedom, has indeed uncovered the multi-minima energy structure within  the DFT+U approach and produced results consistent  with the experimental data. In this work, we compare the SMC and OMC results and show that although the ground states of the two methods have similar energies and geometries, the electronic structures have significant differences. Moreover, we show that the GS obtained from SMC is by 0.0022 Ry/(formula unit) above that of OMC. The discrepancy in  GS results between the two methods suggests that they explore minimum-energy states across different electron densities subspaces. Neither method alone is sufficient to identify the global minimum energy state. Therefore, to obtain the global-minimum state of energy one has to search over larger subspaces that involve both occupation matrices of U atoms and starting magnetization of O atoms.