Flexible Framework for Surface Hopping: From Hybrid Schemes for Machine Learning to Benchmarkable Nonadiabatic Dynamics

TL;DR

This work presents a flexible, open-source framework in MLatom for nonadiabatic molecular dynamics that integrates FSSH and NAC-free curvature-driven schemes, aligning quantum chemistry, ML models, and trajectory analysis. It demonstrates three representative applications—fulvene, molecular ferro-wire, and methylenimmonium cation—to show custom-model workflows, benchmarking of curvature-driven schemes, and detailed trajectory analyses. A key finding is that LZSH generally outperforms TDBA in curvature-driven dynamics and that NACs can be efficiently incorporated via selective NAC computation using custom models, enabling faster benchmarking and ML development. Overall, the framework broadens access to NAMD, provides robust analysis tools, and supports accelerated ML-assisted dynamics within an open-source platform.

Abstract

Nonadiabatic molecular dynamics is a key technique for investigating a broad range of photochemical and photophysical processes. Among the established approaches, surface hopping schemes are widely used and can be easily integrated with various quantum chemistry programs or machine learning models. We present a flexible framework in MLatom that includes a newly implemented Tully's fewest-switches surface hopping algorithm and its time-dependent Baeck--An variant. The capabilities of this framework are demonstrated through three representative examples corresponding to typical stages of a surface hopping study. First, we focus on methods providing energy, energy gradients and nonadiabatic couplings. We show that the flexibility of user-defined custom models can save computational time and that it is useful for benchmarking machine learning models. Next, we compare curvature-driven surface hopping schemes and show that Landau--Zener approach outperforms the time-dependent Baeck--An scheme. Finally, we showcase easy-to-use analysis tools for both individual trajectories and trajectory ensembles. This framework enables accelerated development of machine learning models and provides deeper insight into nonadiabatic dynamics. It is available as a part of the open-source MLatom package.

Figures (9)

• Figure 1: The roadmap of NAMD development in MLatom. The highlighted methods in the interfaces section provide NACs and can be used in the FSSH scheme. The custom models, surface-hopping features, and analysis tools are presented in this work. The next step is the development of automated protocols integrated with AI agents.
• Figure 2: Code snippet example of accessing trajectory information. The molecular_trajectory instance contains a list of classical time steps. Each step instance contains all necessary data, such as interpolated potential energies, velocities, NACs, TDCs, state coefficients and their derivatives, phases, hopping probabilities and random numbers.
• Figure 3: A code snippet example of defining a custom class in MLatom, which combines QC method (CASSCF in Columbus) and ML model (MS-ANI model). The condition can be defined to use CASSCF to calculate NACs only in nonadiabatic region, e.g. when $\Delta E<0.5$ eV.
• Figure 4: Population comparison between different surface hopping schemes for 200 trajectories of the fulvene using custom models. The 95% confidence interval is shown for FSSH at SA-2-CASSCF(6,6)/6-31G* in Columbus (dark green). The MS-ANI model predicting energies and gradients, combined with CASSCF NACs (dark and light blue), referred to as PES@MS-ANI+NACs@CASSCF, agrees with the CASSCF reference, demonstrating the transferability of AL from LZSH to FSSH. Custom models can be easily modified to incorporate user-defined conditions, such as calculating NACs/TDCs only in a nonadiabatic region (light blue and orange). This approach can significantly speed up the simulations and provides an opportunity for benchmarking surface hopping schemes and ML models. The upper panel shows a typical FSSH PES@MS-ANI+NACs@CASSCF trajectory, where Columbus is called to calculate NACs only when the $S_1$ and $S_0$ states are closer than 0.5 eV (vertical grey lines). Comparing LZSH and TDBA to FSSH shows that LZSH (purple) lies within the confidence interval most of the time and outperforms TDBA (dark red), even when velocity rescaling is done along gradient difference $g_{ij}$ (soft orange) or when the condition to compute TDCs only in nonadiabatic region is applied (orange).
• Figure 5: Code snippet example of a molecular ferro-wire surface hopping trajectory simulation in MLatom. The initial condition is loaded from a JSON file, and the method providing the necessary information (OM2/MR-CISD in MNDO) is defined. The hopping_algorithm can be set to FSSH, TDBA, or LZSH, along with other simulation parameters such as time step, time step of state coefficients propagation, maximum propagation time, decoherence model, initial state or velocity rescaling direction.