Reaction Mechanisms & Kinetics — formula sheet

Stable / unstable are thermodynamic words. They describe the position of equilibrium — how far downhill the products lie. They are quantified by ΔG°, by K, by the formation constants β_n of Part 7.Labile / inert are kinetic words. They describe the height of the barrier — how quickly the system gets to equilibrium. They are quantified by rate constants and by ΔG‡.

Taube’s criterion. A complex is labile if its substitution reactions are essentially complete within about one minute at 25 °C for solutions around 0.1 M. If they take appreciably longer, it is inert.

Crystal field activation energy (CFAE): the loss of crystal field stabilisation energy on going from the ground-state geometry to the transition-state geometry.CFAE = CFSE(octahedral reactant) − CFSE(transition state).A large positive CFAE means an extra barrier and predicts inertness. A zero or negative CFAE predicts lability.

D — dissociative. X leaves first, completely. A five-coordinate intermediate of reduced coordination number is genuinely formed and survives long enough to be a chemical species. Y then adds to it.A — associative. Y adds first. A seven-coordinate intermediate of increased coordination number is genuinely formed. X then leaves.I — interchange. Bond breaking and bond making happen in one concerted step. There is no intermediate at all. X and Y trade places through a single transition state.

I_d — dissociative interchange. Concerted, but at the transition state bond breaking has run ahead of bond making. The metal has essentially lost X before it has appreciably gained Y.I_a — associative interchange. Concerted, but bond making has run ahead of bond breaking. The metal has appreciably gained Y before it has lost X.

Acid hydrolysis (or aquation): replacement of a ligand by a water molecule from the solvent, under neutral or acidic conditions where [OH⁻] is negligible.

Anation: replacement of a coordinated water molecule by an anion — the reverse of acid hydrolysis.

k₂[Y] — the direct path. Y attacks the metal itself. Second order overall; the slope depends strongly on which Y is used.k₁ — the solvent path. A molecule of solvent attacks the metal, giving a solvento complex, which then loses solvent rapidly to whatever Y is around. Because the solvent concentration is fixed, this appears as a concentration-independent term; in truth k₁ = k_S[S].

trans effect: the ability of a coordinated ligand T to increase the rate at which the ligand trans to it is substituted. It is a kinetic phenomenon — a statement about ΔG‡ and therefore about the transition state.

trans influence: the extent to which a coordinated ligand T weakens the bond trans to it in the ground state. It is a thermodynamic / structural property of the molecule as it sits, measurable without any reaction taking place at all.

Outer-sphere electron transfer: the electron passes from one complex to another with both coordination spheres remaining intact. No bond is broken, no bond is made, no ligand is transferred. The two complexes merely approach, the electron tunnels, and they separate.

Franck–Condon principle, applied to electron transfer: an electron moves in about 10⁻¹⁵ s, while nuclei move in about 10⁻¹³ s. On the electron’s timescale the nuclei are frozen. Therefore the electron must transfer between two states that already have the same nuclear geometry and the same energy. The nuclei have to get themselves into that configuration first, and that costs energy.

Reorganisation energy λ: the energy required to distort the reactants into the equilibrium nuclear geometry of the products, without transferring the electron. It splits into two parts:λ_in (inner-sphere): changes in bond lengths and angles within the two complexes.λ_out (outer-sphere): re-orientation of the solvent molecules around them.

Inner-sphere electron transfer: the two metal centres become bonded to a common bridging ligand before the electron moves. The electron travels through that ligand. Both coordination spheres are therefore altered during the reaction, and a ligand is very often transferred from one metal to the other.

Requirements on a bridging ligand: it must have at least one lone pair beyond the one used to bind the first metal, and it must be able to reach the second metal. Good bridges: halides (F⁻, Cl⁻, Br⁻, I⁻), OH⁻, N₃⁻, SCN⁻, CN⁻, carboxylates, oxalate, pyrazine and other bridging N-heterocycles. Poor or impossible bridges: NH₃, H₂O in practice, py, and chelating amines — none has an accessible spare lone pair suitably placed.

Resonance (superexchange) transfer: the electron never resides on the bridge. The bridge orbitals mix into the donor and acceptor states and mediate the coupling. The bridge is a conduit.Chemical (stepwise, radical) transfer: the electron is genuinely accepted by the bridging ligand first, producing a radical intermediate, and is passed on in a second step. The bridge is a relay station.

Complementary reaction: the number of electrons lost by each reductant molecule equals the number gained by each oxidant molecule — a one-electron reductant meeting a one-electron oxidant, or a two-electron reductant meeting a two-electron oxidant.Non-complementary reaction: the two do not match — for example a two-electron oxidant meeting a one-electron reductant.

The central idea of photochemistry: an electronically excited molecule is a different chemical species from its ground state. It has its own structure, its own lifetime and its own reactions. It is not simply a hot ground state.

Adamson’s rules for Cr(III) photosubstitution.Rule 1. Consider the six ligands as three trans pairs defining three axes. The axis with the weakest average ligand field is the one labilised.Rule 2. If the two ligands on that axis are different, the one with the greater ligand-field strength is the one preferentially lost.