The More O'Ferrall–Jencks Diagram: Mapping Concerted vs Stepwise Mechanisms

What It Is and Where It Applies

A More O'Ferrall–Jencks diagram is a 2D contour map of a potential energy surface (PES) for a reaction in which two bonds change simultaneously. Because a single reaction coordinate cannot describe two independent bond motions, More O'Ferrall recognized that you need a surface, not a curve — but you can view that surface from directly above and read it like a topographic map.

• Each axis runs from 0 to 1, representing the fractional progress of one bond change (e.g. C–H cleavage on x, C–leaving-group cleavage on y).
• The four corners are true local minima: reactants, products, and the two possible stepwise intermediates.
• Energy projects out of the page; the transition state is the lowest saddle point on the ridge separating reactants from products.

It applies wherever a mechanism can slide between concerted and stepwise limits: β-eliminations (E1/E2/E1cb), general acid–base catalyzed additions to carbonyls, ester and phosphate hydrolysis, and even SN2-vs-SN1 borderline cases. Its power is qualitative-predictive: it tells you which way the transition state moves when you perturb the system.

Building the Diagram Step by Step

Take a β-elimination, H–C–C–LG → C=C. Two bonds break: the C–H (proton removed by base) and the C–LG (leaving group departs). Assign one to each axis.

• Top-left (reactant): both bonds intact.
• Bottom-right (product): both bonds broken — the alkene.
• Bottom-left: only C–LG broken → a carbocation (the E1 intermediate).
• Top-right: only C–H broken → a carbanion (the E1cb intermediate).

A perfectly concerted E2 follows the diagonal from top-left to bottom-right, its transition state a saddle point at the center. Now the key move: raising or lowering the energy of a corner deforms the surface and slides the saddle point. Chemists resolve any shift into two orthogonal components: the parallel effect (along the reaction diagonal, governed by the Hammond postulate — the TS moves toward whatever is raised in energy) and the perpendicular effect (across the diagonal, governed by the Thornton / anti-Hammond rule — the TS moves away from a raised corner toward a lowered one). Vector-add the two to find where the transition state ends up.

Characteristic Numbers and a Worked Example

The diagram is qualitative, but it is grounded in measurable quantities. Consider making the leaving group better (e.g. going from –Cl to –Br, or –Br to –OTs) in a substrate that eliminates by E2.

• A better LG lowers the two right-hand-to-bottom corners where C–LG is broken (product and carbocation), stabilizing them.
• Parallel (Hammond): product is lowered, so the TS moves earlier, toward reactants — an earlier, more reactant-like transition state.
• Perpendicular (anti-Hammond): the carbocation corner is lowered, so the TS slides toward it — more C–LG breaking, less C–H breaking. The mechanism gains E1 character.

This is read out experimentally through the kinetic isotope effect. Central, symmetric E2 transition states show maximal primary k(H)/k(D) ≈ 6–8 at 25 °C for C–H cleavage; a shift toward the carbocation corner (less C–H breaking at the TS) drops the KIE toward ~2–3. Hammett ρ values on the leaving-group aryl and Brønsted β for the base similarly track the TS position — a β near 0.5 signals a central, E2-like TS, while β → 1 signals an E1cb-like, carbanion-shifted transition state.

How the Diagram Is Measured and Used

You never observe the saddle point directly; you triangulate its position from linear free-energy relationships and isotope effects, then map those onto the square.

• Brønsted coefficients (α, β): the slope of log k vs pKa of the catalyzing acid or base. β measures how far proton transfer has progressed at the TS — a direct read of one axis (0 → 1).
• Hammett ρ: log(k/k₀) = ρσ, from substituted aryl leaving groups or aryl-substituted substrates; a large positive ρ means substantial negative charge (carbanion character) at the TS.
• Primary and secondary KIEs: the extent of C–H and C–LG bond change.
• Cross-interaction / interaction coefficients: p(xy) = ∂β/∂(σ of LG) = ∂ρ/∂(pKa) — the mixed second derivative. Its sign tells you the curvature of the surface and whether the TS shifts along or across the diagonal.

In practice, physical-organic chemists (and increasingly DFT computations that locate real saddle points on the true PES) use MOJ diagrams to rationalize why one enzyme's phosphoryl transfer is concerted while a solution analog is stepwise, or to design substrates that force a desired mechanism — e.g. an E1cb-driven prodrug release or a clean E2 for stereospecific alkene synthesis.

MOJ vs Related Diagrams and Concepts

The MOJ diagram is one member of a family of mechanistic maps, and it is easy to confuse with its relatives.

• vs a simple reaction-coordinate diagram: a 1D energy-vs-progress plot handles only one bond change and cannot show a mechanism sliding between concerted and stepwise. The MOJ is its 2D generalization.
• vs the Hammond postulate: Hammond gives only the parallel (along-diagonal) shift — TS resembles the nearer, higher-energy species. MOJ adds the crucial, counterintuitive perpendicular (anti-Hammond) shift that Hammond alone misses.
• vs Marcus theory: Marcus quantifies a single coordinate's barrier from λ (reorganization) and ΔG°. MOJ is the 2D, two-coordinate qualitative cousin; the two are complementary, and Marcus intersecting-parabola logic underlies each edge of the square.
• vs a Jencks 'bifurcation' or 'reaction cube' (3D): when three bonds change (e.g. some acyl transfers), the square becomes a cube. The 2D MOJ is the workhorse; the cube is the rare extension.

Exceptions, Limits, and Famous Cases

The diagram's greatest triumph is Jencks' 1972 rule on enforced concertedness: if a putative stepwise intermediate would be so unstable that it cannot exist for the time of a bond vibration (lifetime < ~10⁻¹³ s), the corresponding corner is inaccessible and the reaction is forced to be concerted. This explains why general-acid-catalyzed additions of weakly basic nucleophiles to carbonyls proceed concertedly — the oxocarbenium/alkoxide corner is simply too high.

• Limit: the axes assume the two bond changes are separable and orthogonal; strongly coupled motions distort the map and make quantitative placement unreliable.
• Limit: it is a topological/qualitative tool. Corner energies are estimates; only DFT/ab initio surfaces give true saddle-point coordinates.
• Caution: perpendicular effects are genuinely anti-Hammond and routinely trip up students who expect the TS to always move toward the destabilized species.

Famous applications include the E1cb-vs-E2 borderline in base-induced eliminations, the mechanism of the Kemp elimination, phosphoryl-transfer 'concerted vs stepwise' debates central to enzymology (kinases, phosphatases), and Jencks' analysis of carbonyl hydration — the work that made the diagram a permanent fixture of physical organic chemistry.

The four corners of a β-elimination MOJ diagram and the mechanisms they anchor

Corner	Species	C–H bond	C–LG bond	Mechanism at that edge
Top-left	Reactant (H–C–C–LG)	Intact	Intact	Starting material
Bottom-right	Product (alkene + H⁺ + LG⁻)	Broken	Broken	Fully eliminated
Bottom-left	Carbocation (C⁺)	Intact	Broken	E1 (rate-limiting LG loss)
Top-right	Carbanion (C⁻)	Broken	Intact	E1cb (rate-limiting deprotonation)
Center / diagonal	Concerted TS (saddle)	Partial	Partial	E2 (single step)