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

TL;DR

This work develops XMCQDPT2‑fidelity interatomic potentials built via transfer learning and Δ‑learning to enable on‑the‑fly, multi‑state nonadiabatic dynamics of the methaniminium cation at a high active space (12e,12o). By coupling these potentials with an LZBL surface-hopping dynamics and an uncertainty-corrected ensemble, the authors map complete photodissociation channels and quantify state lifetimes, including a novel σπ*/S$_0$ conical-intersection pathway. To interpret the ultrafast population dynamics, they introduce a wavepacket oscillation model that yields channel‑specific lifetimes from first principles and reveals a power‑law kinetic regime arising from repeated conical-intersection passages. Across training strategies, uncertainty quantification improves cross‑model agreement, yielding robust predictions for hopping times and branching ratios, and the analysis provides mechanistic insight into photochemical pathways with broad applicability to excited-state dynamics and photochemistry modeling.

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 $Δ$-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 $σπ^*/S_0$ conical intersection.

Figures (4)

• Figure 1: Minimum-energy conical intersections (MECIs) located using an ensemble of the two best-performing SS-TL models (top) and the single best-performing SS-TL model (bottom). Structures shown from left to right are the $S_2/S_1$, $\pi\pi^*/S_0$, and $\sigma\pi^*/S_0$ MECIs.
• Figure 2: Time evolution of electronic state populations for dynamics initiated in the S$_2$ state, computed using the best SS-RI model (a) and an ensemble of the two best SS-TL models (b). The dashed lines show the average over 600 trajectories. The solid lines represent the average from the simulations corrected for the MLIP uncertainty.
• Figure 3: Branching ratios of the photodissociation channels after 100 fs, calculated using an ensemble of the two optimal SS-TL models (left) and the single best SS-TL model (right).
• Figure 4: Time evolution of electronic state populations following photoexcitation to S$_2$. The data points (circles) show the average from 600 nonadiabatic trajectories computed with the SS-TL model, corrected for the MLIP uncertainty. The solid lines are the fit obtained from the oscillating wavepacket cascade model, which accounts for branching in decay from S$_1$ to S$_0$.