  Using the evolutionary algorithm USPEX and DFT+U calculations, we predicted a
high-symmetry geometric structure of bare Ti8O12 cluster composed of 8 Ti atoms
forming a cube, which O atoms are at midpoints of all of its edges, in
excellent agreement with experimental results. Using Natural Bond Orbital
analysis, Adaptive Natural Density Partitioning algorithm, electron
localization function and partial charge plots, we find the origin of the
particular stability of bare Ti8O12 cluster: unique chemical bonding where
eight electrons of Ti atoms interacting with each other in antiferromagnetic
fashion to lower the total energy of the system. The bare Ti8O12 is thus an
unusual molecule stabilized by d-orbital antiferromagnetic coupling.
