The Geometry of Chemical Reactivity

Chemical reactions often reorganise abruptly with small changes in solvent, catalyst, or excitation, yet such discontinuities are difficult to rationalise using potential energy surfaces alone. Here I show that reactivity is governed by the geometry of constraint‑defined state space. In this Boundary Theory (BT) framework, a chemical system occupies an admissible domain whose boundary (∂Ω) determines which reaction pathways exist. The contrast between tert -butyl chloride (S N 1) and methyl bromide (S N 2) shows how curvature on ∂Ω determines accessible pathways. Deformation of ∂Ω by external or internal constraints creates or eliminates continuous trajectories, providing a unified geometric explanation for S N 1/S N 2 switching, E1/E2/E1cB behaviour, rearrangement cascades, and pericyclic allowedness. Mechanisms correspond to accessible geodesics on ∂Ω rather than discrete stepwise sequences. By thinking of chemical reactivity in terms of boundary accessibility, BT offers a general geometric framework for predicting when reactions appear, vanish, or reorganise.