 Solution

The three $d_{xz}$ orbitals are in the Ru–O plane and can overlap directly along the Ru–Ru edges. Their locally rotated lobes have nonzero edge-directed overlap, producing metal–metal bonding and antibonding combinations; a simple triangle model resolves the three orbitals into a singlet and a doublet. The phases and ordering depend on the chosen local basis, so the important feature is the complete set of three combinations.

In the occupancy obtained in (i), this $d_{xz}$ set contains six electrons. All three combinations are filled: the stabilization of the bonding combinations is offset by occupation of their antibonding partners. Equivalently, the sum of the three eigenvalues of a pure off-diagonal interaction matrix is zero. Hence there is no net Ru–Ru bond order from this filled set in the stated model. Overlap alone is not evidence of a net metal–metal bond. This conclusion neglects higher-order mixing and the interactions explicitly excluded from the qualitative diagram.