trans influence

Two people pulling on opposite ends of the same rope share a single tug-of-war: the harder one pulls, the less rope the other has to grip. A metal atom in a complex is a bit like that rope. A ligand bonding strongly on one side draws the metal's bonding capacity toward itself, leaving the bond on the directly opposite side weaker and longer. The trans influence is exactly this ground-state weakening of the bond trans to a strongly bonding ligand.

Unlike the trans effect, which is about reaction rates, the trans influence is a static, thermodynamic, ground-state property — you see it in the molecule sitting still, before any reaction. It shows up as a measurably longer metal-ligand bond directly opposite a strong sigma-donor, and as shifts in spectroscopic signals (such as smaller metal-ligand coupling constants in NMR) for that trans bond. The cause is competition for the same metal orbital: a ligand and its trans partner both want to bond using the metal's orbital that points along their shared axis. A strong sigma-donor monopolizes that orbital, so the trans partner gets a weaker share and its bond lengthens. The order of trans influence largely follows sigma-donor strength: hydride and alkyl and phosphines are strong, while halides and amines are weak.

The trans influence and the trans effect are easy to confuse because they overlap and share the word trans, but they are genuinely different ideas. Trans influence is thermodynamic and structural (how strong and long is the ground-state bond), trans effect is kinetic (how fast does substitution happen). They march together for sigma-donor ligands, since a ligand that weakens the trans bond in the ground state also tends to make it easier to break. But they part ways for pi-acceptors like CO and ethene: those are powerful trans-effect directors because they stabilize the transition state, yet they exert only a modest trans influence on the ground-state bond.