= Solution
The filled <alkene> $\pi$ <molecular orbital> donates into a vacant <metal> acceptor orbital directed toward the center of the C=C bond. In the reverse direction, a filled <metal> $d$ orbital can overlap with the <alkene> $\pi^*$ <antibonding molecular orbital>. These are the donation and <pi backbonding> components of the <Dewar-Chatt-Duncanson model>, illustrated in the lower part of the bonding schematic. The <alkene> is an $\eta^2$ <alkene ligand>, attached through both carbons. Increasing backbonding weakens and lengthens C=C and can push the bonding toward a metallacyclopropane description.
\b[Zr(IV) is $d^0$, so <alkene>-to-<metal> donation predominates.] It has suitable empty orbitals but no occupied <metal> $d$ set to provide substantial conventional backbonding. An <electron>-deficient cationic zirconocene can consequently bind and activate an <alkene> largely through its Lewis acidity; it should not be drawn as a strongly backbonded late-<metal> <alkene> merely because its formal coordination mode is $\eta^2$.
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