Instanton theory for non-crossing potential energy surfaces

Nonadiabatic processes, such as nonradiative transitions between electronic states in large molecules, play a crucial role in many areas of chemical physics. Exact calculations of the timescale for these processes are challenging, even in simple molecular systems, often requiring highly idealized models such as a global harmonic approximation. We present a new semiclassical instanton theory that predicts the nonradiative lifetime of molecules with non-crossing potential energy surfaces (PES), which are common in such systems. Traditional approaches, including Marcus theory and standard golden-rule instanton formulations, assume that the surfaces cross, making them inapplicable to these scenarios. Our branch-point instanton approach bypasses this limitation, revealing a fundamentally different tunneling mechanism. We address the limitations of existing models, such as Jortner's energy gap law, which rely on oversimplified assumptions and are consequently less accurate. Our method broadens the applicability of instanton theory, providing a more general framework for studying nonadiabatic reactions in molecular systems.