  Correct prediction of the behavior of UO2 crystal, which is an
antiferromagnetic 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 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 were used in
DFT+U to determine the ground state. Recently the SMC method was proposed which
using only the oxygen electronic spin-polarization degrees of freedom also
revealed the multi-minima structure of energy in the DFT+U approach and led to
results in good agreement with experiment. 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 different GS results from the two
methods implies that they search for the minimum-energy state over different
subspaces of electron densities and each method alone is not capable to locate
the global minimum of the energy. 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.
