[Paper Review] Advancing Nonadiabatic Molecular Dynamics Simulations for Solids: Achieving Supreme Accuracy and Efficiency with Machine Learning

Changwei Zhang, Zhong Yang+8 more|arXiv (Cornell University)|Aug 13, 2024

Machine Learning in Materials ScienceMaterials Science3 citations

TL;DR

This paper introduces N²AMD, a machine learning framework that uses an E(3)-equivariant deep neural Hamiltonian to achieve state-of-the-art accuracy and efficiency in nonadiabatic molecular dynamics (NAMD) simulations for solids. By directly computing electronic Hamiltonians with symmetry-preserving neural networks, N²AMD enables large-scale, accurate simulations of electron-hole recombination in semiconductors, including defective systems where conventional methods fail.

ABSTRACT

Non-adiabatic molecular dynamics (NAMD) simulations have become an indispensable tool for investigating excited-state dynamics in solids. In this work, we propose a general framework, N$^2$AMD which employs an E(3)-equivariant deep neural Hamiltonian to boost the accuracy and efficiency of NAMD simulations. The preservation of Euclidean symmetry of Hamiltonian enables N$^2$AMD to achieve state-of-the-art performance. Distinct from conventional machine learning methods that predict key quantities in NAMD, N$^2$AMD computes these quantities directly with a deep neural Hamiltonian, ensuring supreme accuracy, efficiency, and consistency. Furthermore, N$^2$AMD demonstrates excellent generalizability and enables seamless integration with advanced NAMD techniques and infrastructures. Taking several extensively investigated semiconductors as the prototypical system, we successfully simulate carrier recombination in both pristine and defective systems at large scales where conventional NAMD often significantly underestimates or even qualitatively incorrectly predicts lifetimes. This framework not only boosts the efficiency and precision of NAMD simulations but also opens new avenues to advance materials research.

Motivation & Objective

• Address the high computational cost and accuracy limitations of conventional nonadiabatic molecular dynamics (NAMD) simulations in solids.
• Overcome the reliance on approximate exchange-correlation functionals and their self-interaction errors in predicting nonradiative recombination.
• Develop a machine learning framework that directly predicts the full electronic Hamiltonian with Euclidean symmetry preservation to ensure physical consistency.
• Enable accurate, scalable simulations of electron-hole recombination in both pristine and defective semiconductors, including large-scale systems.
• Achieve seamless integration with advanced NAMD techniques such as the DISH algorithm and phase correction for decoherence effects.

Proposed method

• Propose N²AMD, a general framework that employs an E(3)-equivariant deep neural Hamiltonian to model the full electronic structure of solids with exact Euclidean symmetry preservation.
• Use a two-stage training process for the Hamiltonian model: first minimizing mean absolute error of real-space Hamiltonian matrices, then adding a regularization term for band energy error to improve transferability.
• Train the Hamiltonian model using HamGNN with five interaction layers and a 20 Bohr cutoff, leveraging datasets of 1000–2000 structures across multiple materials including TiO₂, GaAs, MoS₂ bilayers, and silicene.
• Integrate the learned Hamiltonian into the Hefei-NAMD code for ab initio NAMD with time-dependent Schrödinger equation propagation and nonadiabatic coupling calculations.
• Apply phase correction and the DISH algorithm to account for decoherence in electron-hole recombination dynamics.
• Use concatenated microcanonical MD trajectories (up to 5000 fs) and ensemble averaging over 20 initial configurations and 200 trajectories per configuration to simulate long-time recombination.

Experimental results

Research questions

• RQ1 Can a machine learning model that directly predicts the full electronic Hamiltonian outperform conventional methods in accuracy and efficiency for nonadiabatic dynamics in solids?
• RQ2 To what extent does preserving Euclidean symmetry in the Hamiltonian model improve physical consistency and transferability in NAMD simulations?
• RQ3 Can the framework accurately simulate electron-hole recombination lifetimes in defective semiconductors where standard DFT functionals fail qualitatively?
• RQ4 How does the two-stage training strategy with band energy regularization enhance the stability and transferability of the Hamiltonian model across diverse materials?
• RQ5 Can the framework enable large-scale NAMD simulations of complex systems like twisted bilayer MoS₂ and silicon nanotubes with high fidelity?

Key findings

• N²AMD achieves state-of-the-art accuracy in NAMD simulations by directly computing the electronic Hamiltonian via an E(3)-equivariant deep neural network, ensuring physical consistency and symmetry preservation.
• The framework successfully simulates electron-hole recombination in both pristine and defective TiO₂, GaAs, twisted MoS₂ bilayers, and silicon nanotubes at large scales where conventional NAMD methods significantly underestimate or qualitatively mispredict recombination lifetimes.
• For stoichiometric TiO₂, the N²AMD-predicted recombination dynamics matched reference HONPAS results, validating the method’s accuracy across 5000 fs microcanonical trajectories.
• The use of a two-stage training process with band energy regularization reduced Hamiltonian prediction errors and improved transferability across materials with varying strain and stacking configurations.
• The model demonstrated robust performance across diverse systems, including a 252-atom, 3×√3 orthogonal supercell of a 38.2° twisted MoS₂ bilayer, enabling recombination dynamics at the Γ point.
• Simulations at 50 K for the unstable silicon nanotube showed that N²AMD maintained numerical stability and provided reliable recombination dynamics, highlighting its capability for challenging systems.