Fang, Heller and Richardson extended golden-rule instanton theory to model nonadiabatic quantum tunnelling through a conical intersection (CI). Their formulation brings nuclear tunnelling, zero-point energy and geometric-phase effects into one rate-theory picture, with pathways that can pass through, bypass or wind around the intersection. They demonstrated the approach on charge transfer in the bis(methylene)-adamantyl cation, where heavy-atom tunnelling and geometric-phase effects compete.
Why a conical intersection complicates a tunnelling calculation
A conical intersection is a molecular geometry where two electronic states meet. Near that point, the molecule cannot be described adequately by following a single Born–Oppenheimer potential-energy surface: the electronic states are coupled, and nuclear motion can move the system between them.
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This makes a reaction involving a CI a nonadiabatic problem. A rate theory built around motion on just one electronic surface can miss important dynamics. Nuclear tunnelling and zero-point energy (ZPE) affect how nuclei move, while the geometric phase can alter the quantum-mechanical contribution from a nuclear pathway that goes around the intersection.
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1Repair Windows errors before they cause bigger problems2Fix the driver behind crashes, sound loss and screen glitches3Clear out junk files and repair common Windows errorsWhat the extended instanton theory adds
The 2023 method extends golden-rule instanton theory to a nonadiabatic reaction involving a CI. Instanton theory is a semiclassical approach to reaction rates: it represents quantum tunnelling through a pathway, or instanton, in nuclear configuration space. The extension incorporates tunnelling, ZPE and geometric-phase effects within the same rate calculation, alongside electronic-structure calculations.
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Rather than treating the CI as a point that every relevant trajectory must cross, the formulation allows several kinds of instanton pathway:
- Traverse the CI: a pathway passes through the intersection region.
- Bypass the CI: a pathway avoids the intersection.
- Wind around the CI: a pathway encircles it, making geometric-phase effects relevant.
That last class matters because the geometric phase is tied to how the nuclear pathway goes around the intersection. The 2024 review of nonadiabatic tunnelling methods likewise notes that the extension captures this effect when an instanton winds around a CI.
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What the bis(methylene)-adamantyl example showed
Fang and colleagues applied the method to electron transfer—charge transfer—in the bis(methylene)-adamantyl (BMA) cation using first-principles calculations. In this system, they found a strong competition between heavy-atom tunnelling and geometric-phase effects. In other words, nuclear motion involving heavy atoms and the phase associated with pathways around the CI both influence the calculated reaction picture.
This is a result for the BMA cation, not a general rule that tunnelling or geometric phase must dominate every reaction involving a CI. The study illustrates why both effects belong in the same calculation; it does not establish a universal balance across molecules.
What the method does—and does not—establish
The work is a semiclassical transition-state and rate-theory approach, not a claim to solve exact quantum dynamics for arbitrary molecular systems. Its contribution is to extend an instanton framework so that nonadiabatic pathways around a CI, nuclear tunnelling, ZPE and geometric phase can be considered together.
When the paper appeared in 2023, its authors described it as the first application of nonadiabatic instanton theory to a process involving a CI. That is a claim about the state of the field at the time of publication. The study demonstrates the method on one molecular system; the cited sources do not establish predictive accuracy across a broad range of reactions or indicate current software availability.
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Publication details
The paper by Wei Fang, Eric R. Heller and Jeremy O. Richardson was first published online in Chemical Science on 27 September 2023. It appeared in volume 14, issue 39, pages 10777–10785.
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