Determining a Mechanism — The Physical Organic Toolkit — formula sheet

A reaction mechanism: a description of the sequence of elementary steps by which reactants become products, specifying for each step which bonds break and form, the structure and energy of its transition state, and the structure, energy and lifetime of every intermediate between steps.

The fundamental rule of kinetics: the rate law of a multi-step reaction contains the concentrations of every species that appears in the rate-determining transition state, together with everything consumed in any equilibrium before it. It contains no information whatsoever about anything that happens after the rate-determining step.

Rate-determining (rate-limiting) step: the step whose transition state is the highest point on the free-energy profile relative to the reactants, and hence the step whose rate constant most strongly controls the overall rate. More rigorously, the step with the largest degree of rate control: the fractional change in the overall rate produced by a fractional change in that step’s rate constant, all others held fixed.

Catalyst: a species that increases the rate of a reaction by providing a pathway of lower activation free energy, and is regenerated unchanged at the end. It cannot alter the position of equilibrium, because it must accelerate the forward and reverse reactions by exactly the same factor — both pass over the same lowered barrier.

Specific acid catalysis: the rate depends only on the concentration of the solvated proton, H₃O⁺ — that is, only on pH. The substrate is protonated in a fast, reversible pre-equilibrium and the protonated substrate then reacts in the rate-determining step.General acid catalysis: the rate depends on the concentration of every acid present, including undissociated buffer acids HA. The proton is in flight in the rate-determining transition state.

Principle of non-perfect synchronisation (PNS): when a product-stabilising feature develops later along the reaction coordinate than the bond change to which it is coupled, the intrinsic barrier is raised and LFER exponents are distorted — they may fall outside the range 0 to 1. Conversely, a stabilising feature that develops early lowers the intrinsic barrier.

Kinetic isotope effect (KIE): the ratio of rate constants for two isotopically substituted versions of the same reactant, k_light/k_heavy, most commonly k_H/k_D. A primary KIE arises when the bond to the isotopically substituted atom is being broken or formed in the rate-determining step; a secondary KIE arises when it is not, and reports on a change in the environment of that atom instead.

Linear free-energy relationship (LFER): an empirical linear correlation between the logarithm of a rate or equilibrium constant for one reaction series and the logarithm of the corresponding constant for a different, reference series, when the same structural variation is applied to both. Because log K is proportional to ΔG° and log k to ΔG‡, the correlation is a proportionality between free-energy changes.

The reaction constant ρ: a measure of how sensitive the reaction is to electronic change at the reaction centre, and of the sign of the charge that develops there on the way to the transition state. By definition ρ = 1.00 for the ionisation of benzoic acids in water at 25 °C.

σ⁺: the substituent constant appropriate when a positive charge at the reaction centre is directly conjugated to the substituent. Defined from the solvolysis of substituted 2-aryl-2-chloropropanes (cumyl chlorides) in 90% aqueous acetone.σ⁻: the mirror image, for a negative charge directly conjugated to the substituent. Defined from the ionisation of substituted phenols (or anilinium ions in some compilations).

Crossover experiment: run the reaction on a mixture of two differently labelled substrates and look at the products. If no crossed products appear, the migrating group never left its own molecule and the reaction is intramolecular. If crossed products appear in statistical amounts, the group became free and the reaction is intermolecular.