# Machine Learning Nonadiabatic Dynamics: Eliminating Phase Freedom of Nonadiabatic Couplings with the State-Intraction State-Averaged Spin-Restricted Ensemble-Referenced Kohn-Sham Approach

arXiv: https://arxiv.org/abs/2410.22801 · HTML: https://mlsanity.com/paper/2410.22801/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 79 references that are in the map.
- First posted on arXiv 30 Oct 2024.

## Builds on (most cited first, 8 of 8)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Combining SchNet and SHARC: The SchNarc machine learning approach for excited-state dynamics](https://mlsanity.com/paper/2002.07264/) (2020)
- [Excited state, non-adiabatic dynamics of large photoswitchable molecules using a chemically transferable machine learning potential](https://mlsanity.com/paper/2108.04879/) (2021)

## Built on by (most cited first, 1 of 1)

- [A Descriptor Is All You Need: Accurate Machine Learning of Nonadiabatic Coupling Vectors](https://mlsanity.com/paper/2505.23344/) (2025)

## Abstract (arXiv)

Excited-state molecular dynamics (ESMD) simulations near conical intersections (CIs) pose significant challenges when using machine learning potentials (MLPs). Although MLPs have gained recognition for their integration into mixed quantum-classical (MQC) methods, such as trajectory surface hopping (TSH), and their capacity to model correlated electron-nuclear dynamics efficiently, difficulties persist in managing nonadiabatic dynamics. Specifically, singularities at CIs and double-valued coupling elements result in discontinuities that disrupt the smoothness of predictive functions. Partial solutions have been provided by learning diabatic Hamiltonians with phaseless loss functions to these challenges. However, a definitive method for addressing the discontinuities caused by CIs and double-valued coupling elements has yet to be developed. Here, we introduce the phaseless coupling term, Delta2, derived from the square of the off-diagonal elements of the diabatic Hamiltonian in the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS, briefly SSR)(2,2) formalism. This approach improves the stability and accuracy of the MLP model by addressing the issues arising from CI singularities and double-valued coupling functions. We apply this method to the penta-2,4-dieniminium cation (PSB3), demonstrating its effectiveness in improving MLP training for ML-based nonadiabatic dynamics. Our results show that the Delta2 based ML-ESMD method can reproduce ab initio ESMD simulations, underscoring its potential and efficiency for broader applications, particularly in large-scale and long-timescale ESMD simulations.