Past exam of the chemistry A course of the University of Cambridge / 2024 / Paper 1 / A5 / a / ii

Let $d_{\mu ,A}$ and $d_{\mu ,B}$ be corresponding real 4d orbitals on the upper and lower metals, with identical global-axis phases. Their symmetry-adapted linear combinations arewith the normalization shown in the negligible-overlap approximation; including overlap changes the denominator but not the symmetry. Inversion exchanges the centres and each local d orbital has even intrinsic parity, so the plus combinations are gerade and the minus combinations ungerade.The reversal of bonding phase for $d_{xz},d_{yz}$ is important: the facing lobes have opposite signs when the two atomic orbitals share the same global phase convention, so their difference is bonding. Each $e$ irrep is two-dimensional. Thuswith total dimension ten. Rotating $x,y$ by $45^{\circ }$ interchanges the names of the two delta families; all labels here retain the chloride-aligned axes fixed above.