Beilstein Arch. 2026, 202639. https://doi.org/10.3762/bxiv.2026.39.v1
Published 27 Oct 2026
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 (SN1) and methyl bromide (SN2) 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 SN1/SN2 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.
Keywords: Boundary Theory, Chemical Reactivity, Reaction Mechanisms, Chemical Space, Pathway Accessibility, Mechanistic Switching
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Gibbons, S. Beilstein Arch. 2026, 202639. doi:10.3762/bxiv.2026.39.v1
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© 2026 Gibbons; licensee Beilstein-Institut.
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