XMCQDPT2-Fidelity Transfer-Learning Potentials and a Wavepacket Oscillation Model with Power-Law Decay for Ultrafast Photodynamics

Abstract

A central pursuit in theoretical chemistry is the accurate simulation of photochemical reactions, which are governed by nonadiabatic transitions through conical intersections. Machine learning has emerged as a transformative tool for constructing the necessary potential energy surfaces, but applying it to excited states faces a fundamental barrier: the cost of generating high-level quantum chemistry data. We overcome this challenge by developing machine-learning interatomic potentials (MLIPs) that achieve multi-state multi-reference perturbation theory accuracy through various techniques, such as transfer, multi-state, and $\Delta$-learning. Applied to the methaniminium cation, our highest-fidelity transfer-learning model uncovers its complete photodissociation landscape following S$_2$ photoexcitation. The comprehensive XMCQDPT2/SA(3)-CASSCF(12,12) electronic structure description captures all competing decay channels, including S$_1$ branching into photoisomerization and direct H$_2$-loss pathways. Our results show that the population dynamics generally depends on the MLIP model, correlating with its performance. At the same time, the introduction of MLIP-uncertainty corrections based on the predictions of an ensemble of models brings different approaches into agreement, validating this metric as essential for reliable dynamics. To interpret the population dynamics, we introduce a wavepacket oscillation model - a mechanistically transparent, power-law kinetics framework that extracts state-specific lifetimes directly from first-principles simulations. The model quantitatively reproduces the ultrafast decay, creating a direct link between quantum transition probabilities and classical rate constants. The kinetic fits yield channel-specific lifetimes, supporting the recently discovered photochemical pathway mediated by a novel $\sigma\pi^*/S_0$ conical intersection.