The magnetic and electronic properties of Ba${}_4$Ru${}_3$O${}_{10}$ were investigated by the ab initio and model calculations. It is shown that nonmagnetic ground state of the one-third Ru${}^{4+}$ ions is not due to the correlation effects. It is rather caused by the charge disproportionation between crystallographically different Ru and the molecular orbital formation in the Ru's trimer.

• Received 28 June 2012

DOI:https://doi.org/10.1103/PhysRevB.86.064429