= Solution
A useful strongly bound limit is \b[Zr(IV), $d^0$, and Ta(V), $d^0$, with an aryne dianion in each complex]. Charge balance uses two Cp$^-$ ligands for <zirconium>, and Cp\*$^-$ plus two <methyl ligands> for <tantalum>:
$$
x_{\rm Zr}-2-2=0,\qquad x_{\rm Ta}-1-2-2=0.
$$
Equivalently, an unreduced neutral-aryne description starts from Zr(II) and Ta(III), both $d^2$, and transfers that pair strongly into the aryne acceptor. These are alternative bookkeeping limits for the same covalent interaction; saying that a formal $d^0$ assignment has no available <electrons> must not erase the strong <metal>–<carbon> bonds in the reduced-ligand description.
Both ligands have therefore lost much of the extra in-plane C–C bonding of free <benzyne> and approach the same reduced, approximately double-bond-length C1–C2 framework. \b[Their identical $1.364\,\text{Å}$ C–C distances are consistent with similar aryne reduction in both complexes.] The distance is intermediate in a delocalized ring, so it should not be converted into an exact integer bond order.
The M–C distances depend additionally on <metal> size, effective nuclear attraction and <orbital overlap>. The high formal charge of Ta(V), the size effects associated with the <lanthanide contraction>, and effective $5d$ covalent bonding favour shorter Ta–C contacts than Zr–C contacts. This is consistent with $2.075$ versus $2.250\,\text{Å}$. Different coordination envelopes and ancillary ligands also contribute, so this pair is not a controlled measurement of a radius or a <metal>–<carbon> bond energy. \b[Similar internal ligand bond order can coexist with different <metal>–ligand distances.]
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