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Fang, Heller and Richardson extended golden-rule instanton theory to describe nonadiabatic quantum tunnelling in a reaction involving a conical intersection (CI). Their approach brings nuclear tunnelling, zero-point energy and geometric-phase effects into one rate-theory framework, and allows the calculated tunnelling pathway to pass through, bypass or wind around the intersection. They demonstrated it for charge transfer in the bis(methylene)-adamantyl cation.
Why a conical intersection challenges ordinary rate theory
A conical intersection is a molecular geometry where electronic states meet. Near it, nuclear motion can involve transitions between electronic states, so describing the reaction on just one Born–Oppenheimer surface misses important nonadiabatic behavior. Nuclear tunnelling and geometric phase can also affect how the reaction proceeds.
Instanton theory provides a semiclassical way to describe tunnelling contributions to reaction rates. The 2023 work extends its golden-rule form—the rate-theory framework used for transitions between electronic states—to include a conical intersection and the associated nonadiabatic pathways. It is a rate-theory method paired with electronic-structure calculations, not an exact quantum-dynamics solution for arbitrary molecules.
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Nuclear tunnelling and zero-point energy
The formulation incorporates nuclear tunnelling and zero-point energy (ZPE), allowing nuclear quantum effects to contribute to the rate description rather than treating the reaction as motion over a purely classical barrier.
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Geometric phase and multiple pathways
The theory accounts for geometric-phase effects (GPEs) and represents distinct instanton pathways in relation to the CI: a path can traverse the intersection, bypass it, or wind around it. Winding matters because the geometric phase can affect the tunnelling contribution along such a path. A 2024 review of nonadiabatic tunnelling methods likewise notes that the CI extension captures the geometric-phase effect when an instanton winds around the intersection.
These ingredients are considered together in the nonadiabatic rate picture: the pathway is not defined only by whether nuclei tunnel, but also by how it relates geometrically to the intersection.
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What the bis(methylene)-adamantyl example showed
The authors applied the method to charge transfer in the bis(methylene)-adamantyl (BMA) cation using first-principles calculations. In this system, they found competition between heavy-atom tunnelling and geometric-phase effects. As the authors put it, “Our study reveals a strong competition between heavy-atom tunnelling and geometric-phase effects.”
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1Scan for outdated or missing drivers - takes under a minute2Repair Windows errors before they cause bigger problems3Fix the driver behind crashes, sound loss and screen glitchesThis is a result for the studied BMA reaction, not evidence that heavy-atom tunnelling or geometric phase always dominates reactions involving conical intersections. The example demonstrates how the extended framework can bring both effects into the same analysis.
What the result establishes—and what it does not
When the paper appeared in 2023, its authors described it as the first application of nonadiabatic instanton theory to a process involving a conical intersection. That is a claim about the state of the field at publication, not a statement of present-day priority.
The work establishes a way to formulate and illustrate CI-related tunnelling pathways, including geometric-phase effects. The cited study and 2024 review do not establish accuracy across a broad range of molecular systems, rank this approach against alternative methods, or show that it is available in a particular software package. Those questions require evidence beyond this example.
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Publication details
Wei Fang, Eric R. Heller and Jeremy O. Richardson published the paper in Chemical Science, volume 14, issue 39, pages 10777–10785. The journal lists its first online publication as 27 September 2023. PubMed records 11 October 2023; that is the database publication date, not the journal’s online-first date.
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