A General Neural Network Potential for Energetic Materials with C, H, N, and O elements

Mingjie Wen; Jiahe Han; Wenjuan Li; Xiaoya Chang; Qingzhao Chu; Dongping Chen

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A General Neural Network Potential for Energetic Materials with C, H, N, and O elements

Mingjie Wen, Jiahe Han, Wenjuan Li, Xiaoya Chang, Qingzhao Chu, Dongping Chen

arXiv:2503.01932v1Mar 3, 2025cond-mat.mtrl-scics.LG

TL;DR

HEM discovery is limited by the computational expense and long development cycles of conventional simulation and experiment-driven approaches. This work develops a transfer-learned general NNP for C, H, N, and O HEMs, achieving accurate structural, mechanical, and decomposition predictions across 20 systems with reported low energy and force errors.

Problem
Conventional HEM simulation methods face high computational cost, long simulation times, and difficulty reproducing DFT-quality reaction energy surfaces for new molecules.
Method
The study fine-tunes a pre-trained NNP with transfer learning using DFT-derived energy and force data for C, H, N, and O HEMs.
Results
Energy errors below 65.2 meV/atom and force errors below 0.684 eV/Å were obtained over 300–4000 K, with equations of state consistent with DFT and decomposition distributions accurately predicted.
Takeaways & Limitations
The general NNP provides an efficient framework for predicting microscopic and macroscopic properties across C, H, N, O HEMs while reducing reliance on costly conventional calculations.
Takeaways & Limitations
AIMD remains constrained by high computational cost and long simulation times, while ReaxFF may not reproduce DFT-precision reaction energy surfaces for new molecules.

Abstract

from arXiv · show

The discovery and optimization of high-energy materials (HEMs) are constrained by the prohibitive computational expense and prolonged development cycles inherent in conventional approaches. In this work, we develop a general neural network potential (NNP) that efficiently predicts the structural, mechanical, and decomposition properties of HEMs composed of C, H, N, and O. Our framework leverages pre-trained NNP models, fine-tuned using transfer learning on energy and force data derived from density functional theory (DFT) calculations. This strategy enables rapid adaptation across 20 different HEM systems while maintaining DFT-level accuracy, significantly reducing computational costs. A key aspect of this work is the ability of NNP model to capture the chemical activity space of HEMs, accurately describe the key atomic interactions and reaction mechanisms during thermal decomposition. The general NNP model has been applied in molecular dynamics (MD) simulations and validated with experimental data for various HEM structures. Results show that the NNP model accurately predicts the structural, mechanical, and decomposition properties of HEMs by effectively describing their chemical activity space. Compared to traditional force fields, it offers superior DFT-level accuracy and generalization across both microscopic and macroscopic properties, reducing the computational and experimental costs. This work provides an efficient strategy for the design and development of HEMs and proposes a promising framework for integrating DFT, machine learning, and experimental methods in materials research. (To facilitate further research and practical applications, we open-source our NNP model on GitHub: https://github.com/MingjieWen/General-NNP-model-for-C-H-N-O-Energetic-Materials.)

1 Introduction

HEM research requires methods that retain high accuracy while reducing the computational cost and development time of predicting structural, mechanical, and decomposition properties. The paper addresses this need with a transferable general NNP for C, H, N, and O materials.

Research gap: Existing simulations struggle to balance prediction accuracy and computational efficiency for HEMs.AIMD provides high precision but incurs high computational costs and long simulation times, while ReaxFF may not reproduce DFT-quality reaction energy surfaces for new molecules.
Research gap: A general model must predict crystal structure, mechanical behavior, and decomposition while remaining efficient.These properties are central to evaluating HEMs across limited and extended systems.
Contribution: The resulting framework combines DFT-level precision with greater efficiency than traditional force fields and DFT calculations.The authors report accurate descriptions of mechanical, chemical, and thermal processes across systems and scales.
Approach: Transfer learning reduces the need for extensive training data while accelerating learning and improving performance.The approach is motivated by the computational and data demands of supervised learning for materials development.
Approach: The study develops a scalable general NNP by adapting a pre-trained model to condensed-phase C, H, N, O HEM chemistry.The framework uses a pre-trained NNP and transfer learning to move toward molecular dynamics with chemical accuracy.
Validation: The model predicts structural, mechanical, and decomposition properties for 20 HEMs and is compared with DFT and experimental reports.PCA is used to examine chemical activity space, while MD simulations assess microscopic and thermal behavior.

2 Methodology

The methodology constructs a broad C, H, N, O HEM dataset from DFT-based simulations and expands it through DP-GEN sampling. Transfer learning then identifies informative configurations for training and validates the resulting NNP across temperatures and molecular structures.

Dataset construction: The model covers 20 C, H, N, O HEMs grouped into ionic-salt, chain-like, cyclic-like, and cage-like structures.The study assumes these initial configurations encompass the main C, H, N, O HEMs considered.
Dataset construction: The foundational dataset uses AIMD simulations from 300 to 4000 K and contains 15,000 energy-and-force structures.Each of three HEMs contributes 5,000 snapshots generated across five temperatures and 2 ps simulations.
Dataset construction: Twenty-five percent of the configurations were randomly reserved as the test set.Ten configurations were additionally sampled from the test set to calculate training loss for each batch.
DP-GEN sampling: Configurations are classified as accurate, candidate, or failed using force-deviation thresholds of 0.05 and 0.15 eV/Å.Configurations between the thresholds are incorporated into the training set.
DP-GEN sampling: The DP-GEN process completed 45 iterations and generated 6900 configurations while reducing DFT computational cost.The workflow distinguishes accurate configurations from candidates and failed configurations before transfer-learning updates.

2.2 General NNP model training

The general NNP is trained by transfer learning from DFT-derived atomic coordinates, energies, and forces, using an energy decomposition into atomic contributions. Training combines energy and force errors, then applies the model to crystal and thermal-decomposition simulations.

Training procedure: Training uses atomic coordinates, energies, and forces as physical inputs for deep neural-network optimization.The model parameters are iteratively adjusted to reduce differences from reference data.
Model formulation: The model represents total potential energy as the sum of NNP-parameterized atomic energies.Each atomic energy depends on the atom’s local environment and chemical species.
Model architecture: The architecture uses embedded and fitting subnetworks with ResNet structure, a 6.0 Å cutoff, and a smoothly decaying descriptor.The embedding network is sized (25, 50, 100), while the fitting network is sized (240, 240, 240).
Training procedure: The loss function combines squared energy and force prediction differences, weighted by separate energy and force coefficients.Backpropagation computes gradients for model updates.
Applications: The trained NNP is evaluated through crystal-cell and equation-of-state tests and molecular-dynamics simulations of thermal decomposition.The MD workflow uses relaxation followed by thermal decomposition, with repeated simulations and product analysis.

3.1 Evaluation of general NNP model

The general NNP closely reproduces DFT energies and forces across 20 HEMs and remains stable within its data range. Transfer learning improves extrapolation, although performance remains less accurate for some systems outside the training distribution.

Validation: Energy and force predictions for 20 HEMs align closely with DFT, with most errors concentrated near ±0.1 eV/atom and ±5 eV/Å.The reported energy and force distributions show strong fitting across the evaluated systems.
Validation: 65.2 meV/atom and 0.684 eV/Å are the maximum reported MAEs for energy and force, observed in TKX-50 and TATB, respectively.The energy and force maxima correspond to different HEMs.
Extrapolation: 1.08 eV/atom and 0.97 eV/Å are the energy and force MAEs for TNT before it is added to the training set.TNT lies outside the pre-trained set, so the model does not accurately predict all C, H, N, and O HEMs without adaptation.
Extrapolation: Adding TNT and ADN to training reduces extrapolation errors for ADN to 0.632 eV/atom and 0.587 eV/Å, and for FOX-7 to 0.333 eV/atom and 0.553 eV/Å.The authors report improved extrapolation after including additional representative structures.
Stability: Below 0.2 eV/atom and 0.6 eV/Å are the average energy and force MAEs for existing data in the stability test.The authors characterize the model as stable for energy and force prediction within the evaluated data range.

3.2 Crystal properties

The NNP reproduces crystal structures and equations of state close to DFT and generally outperforms ReaxFF against experimental and DFT references. Its EOS predictions also remain accurate outside the training structures, with a noted BTF exception.

Cell parameters: 0%-6% are the absolute deviations of DFT-calculated crystal volumes from experiment, supporting the reliability of the training dataset.The NNP also shows good agreement with experimental crystal volumes.
Cell parameters: 1%-5% are the NNP’s average absolute deviations for crystallographic a/b/c dimensions from experiment and DFT, versus 3%-9% and 2%-8% for ReaxFF.NNP performs better for most HEMs, although BTF has larger NNP errors for cell and volume than ReaxFF.
Equation of state: The EOS test extrapolates mechanical behavior under compression ratios of 0.80-0.92 and tension ratios of 1.08-1.20.Shaded regions identify training structures, while points outside them represent NNP predictions.
Equation of state: NNP EOS curves reproduce DFT energy minima and perform well for structures outside the training set, unlike ReaxFF’s larger deviations.The comparison covers ionic, chain, cyclic, and cage HEM structures.
Mechanical behavior: Including atomic interaction forces in the loss function improves accuracy for microscopic mechanical behavior and extrapolated structures.The authors connect force-based training with the model’s mechanical predictions.

3.3 Thermal decomposition

The NNP predicts thermal decomposition products for ionic, chain, cyclic, and cage HEMs in agreement with DFT-based and experimental observations. Across representative materials, it also captures product differences that ReaxFF misses or underestimates.

Ionic salts: ADN decomposes mainly into H2O (37.4%), N2 (30.1%), NO2 (9.7%), OH (8.7%), and NO (8.0%), closely matching ReaxFF.The authors report only slight differences between the NNP and ReaxFF product quantities for ADN.
Ionic salts: TAGN produces CO2 (40.1%), H2O (30.0%), and N2 (12.8%), while its predicted decomposition temperature is 780.6 K versus an experimental ~580.28 K.ReaxFF shows premature structural breakdown below 500 K in these salts.
Chain HEMs: FOX-7 and NG predictions agree with AIMD or spectroscopy by capturing major products including N2, H2O, and CO2.For FOX-7, the NNP predicts N2 (32.8%), H2O (27.6%), and CO2 (22.8%); for NG, CO2 is 37.1% and H2O 28.9%.
Cyclic HEMs: RDX predictions closely match experiment, including N2 (32.7%), H2O (29.8%), and CO2 (19.7%).For DTTO-c1, the NNP predicts N2 (46.8%), N2O (18.9%), CO2 (16.8%), and NO (8.8%), consistent with DFT-MD observations.
Cage HEMs: For cage HEMs, NNP predictions agree with reported observations, including CL-20 products N2 (43.3%), CO2 (30.5%), and H2O (14.4%), and TEX products CO2 (48.7%) and H2O (17.1%).ReaxFF underestimates CO2 for both CL-20 and TEX.
Overall assessment: Across the tested HEM classes, the NNP is reported to agree with DFT and quantitatively reproduce experimental decomposition observations while reducing electronic-structure computational complexity.The authors frame this as narrowing the efficiency gap between classical force fields and DFT accuracy.

3.4 Formation mechanism of chemical activity space

PCA and correlation analyses show that the general NNP organizes 20 HEMs into chemically meaningful activity spaces shaped by structure, temperature, and decomposition products. These representations support coverage and generalization across related HEM configurations.

Chemical activity-space mapping: RDX, HMX, and CL-20 form distinct clusters whose strong mutual correlation reflects their related chemical structures.Their correlations with TNT, ADN, TKX-50, DNBF, BTF, TATB, TAGN, TNB, and HNS are lower, particularly for ionic salts.
Chemical activity-space mapping: Introducing structurally different HEMs such as TNT, ADN, and FOX-7 progressively fills the chemical activity space during iterative training.The expanding coverage supports predictions for HEMs and structurally similar substances within the training set.
Chemical activity-space mapping: PCA maps the 20 C, H, N, and O HEMs into a lower-dimensional representation of their high-dimensional chemical activity space.SOAP descriptors and Sklearn PCA reduce complex structural information while retaining chemically relevant organization.
Structure–decomposition relationships: HEMs containing similar functional groups can remain highly correlated despite structural differences, suggesting related physical properties or reaction mechanisms under specific conditions.Materials containing NO2 groups show especially high correlation with RDX, HMX, and CL-20.
Structure–decomposition relationships: The 20 HEMs cluster into C-N ring, phenyl ring, chain-like, and ionic-salt categories, with clustering patterns linked to decomposition behavior.C-N ring compounds cluster across low- and high-temperature product spaces, while ionic-salt separation reflects compositional differences such as NH4+ and carbon content.

4 Conclusions

The study develops a general C, H, N, O NNP through transfer learning and evaluates it against DFT, force-field, and experimental references. The model predicts structural, mechanical, and decomposition behavior across finite and extended HEM systems while capturing chemical activity and reaction mechanisms.

Model development: The work develops an accurate and efficient general NNP model for C, H, N, and O energetic materials using transfer learning from a pre-trained model.A small amount of new training data enhances generalization and predictive accuracy while reducing computational costs.
Model validation: Atomic-energy and force prediction errors across 300–4000 K were below 65.2 meV/atom and 0.684 eV/Å, respectively.Performance was evaluated against a DFT database spanning a wide temperature range.
Model validation: Cell parameters and equations of state were highly consistent with DFT results and outperformed the ReaxFF force field.This validates the model for mechanical-property prediction at the crystal-structure level.
Model validation: MD simulations accurately predicted major thermal-decomposition products for 20 HEMs in agreement with experimental data.The results support modeling decomposition behavior across the studied HEM systems.
Conclusions: The NNP describes crystal structural, mechanical, and decomposition properties in finite and extended systems with high precision.Its performance is attributed to capturing chemical activity, key atomic interactions, and reaction mechanisms during thermal decomposition.
Conclusions: By representing chemical activity space, the model supports analysis of HEM reactions under extreme conditions and future molecular and materials design.The authors connect this capability to modeling complex microstructures and macroscopic properties.

Declaration of competing interest

The authors report no known competing financial interests or personal relationships that could have influenced the work.

The authors declare no known competing financial interests or personal relationships that could have influenced the reported work.

Supplementary Material (SM)

The supplementary material documents the general NNP’s evaluation, structural comparisons, thermal-decomposition simulations, and chemical-space analyses across the HEM dataset.

Supplementary evaluations: The supplementary material includes the HEM types, crystallographic parameters, equation-of-state curves, and thermal-decomposition simulations evaluated with NNP, DFT, and ReaxFF methods.Table S2 compares crystallographic parameters using DFT, NNP, and ReaxFF; Fig. S4 compares equation-of-state curves, and Fig. S5 reports heating simulations from 300 K to 3000 K.
Model evaluation: Figures S1–S3 evaluate energy and force predictions by comparing the pre-trained or generalized NNP model with DFT calculations and MAE distributions.Energy is reported in eV/atom and force in eV/Å.
Experimental comparison: Table S2 uses experimental crystallographic values from the CCDC database and reports deviations as percentages in parentheses.The supplementary notes distinguish calculated results from experimental values and define the comparison conventions.
Reference methods: The supplementary material identifies DFT calculations as PBE/DZVP-MOLOPT computations using CP2K and ReaxFF values as taken from Liu et al.Dashed regions in the equation-of-state plots indicate data included in the training set.
Chemical-space analysis: Figures S6–S8 visualize the single-component and configuration spaces of the 20-HEM dataset at 300 K, 1500 K, and 3000 K using PCA and correlation heatmaps.These figures document chemical-space analysis during NNP model training across three temperatures.