This repository contains the complete analysis code, datasets, and supplementary materials for the paper "Bayesian Uncertainty Quantification and Sensitivity Analysis for the H₂ + OH → H₂O + H Reaction: A Comprehensive Comparison of Ten Kinetic Studies" (Rababah, 2025).
The H₂ + OH → H₂O + H reaction is fundamental to hydrogen combustion, atmospheric chemistry, and clean energy systems. This study provides the first comprehensive Bayesian uncertainty quantification and sensitivity analysis for this critical elementary reaction.
- Bayesian uncertainty quantification with hierarchical decomposition of measurement vs. inter-study variability
- Sensitivity analysis identifying which Arrhenius parameters dominate at different temperatures
- Machine learning validation confirming modified Arrhenius form captures true physics
- Application-specific recommendations for atmospheric chemistry, combustion, and high-T applications
- Complete open-source workflow for reproducible chemical kinetics analysis
| Aspect | Details |
|---|---|
| Studies Analyzed | 10 independent investigations (1981–2021) |
| Temperature Range | 200–3044 K (span: 2844 K) |
| Methods | Bayesian inference, sensitivity analysis, ML validation |
| Data Source | NIST Chemical Kinetics Database |
| Average Uncertainty | 14.6% (range: 10.0%–21.2%) |
| Best Agreement Zone | Combustion (800–2000 K): CV < 6% |
| Temperature | Posterior Mean k | 95% CI | Uncertainty | N Studies |
|---|---|---|---|---|
| 300 K | 6.85 × 10⁻¹⁵ | ± 1.42 × 10⁻¹⁵ | 20.7% | 7 |
| 500 K | 1.33 × 10⁻¹³ | ± 1.35 × 10⁻¹⁴ | 10.0% | 4 |
| 750 K | 6.61 × 10⁻¹³ | ± 1.40 × 10⁻¹³ | 21.2% | 4 |
| 1000 K | 2.09 × 10⁻¹² | ± 2.33 × 10⁻¹³ | 5.8% | 5 |
| 1500 K | 7.21 × 10⁻¹² | ± 7.27 × 10⁻¹³ | 10.1% | 4 |
| 2000 K | 1.56 × 10⁻¹¹ | ± 2.12 × 10⁻¹² | 13.7% | 3 |
| 2500 K | 2.66 × 10⁻¹¹ | ± 4.86 × 10⁻¹² | 18.3% | 2 |
Units: cm³ molecule⁻¹ s⁻¹
| Temperature | Measurement | Inter-study | Total | Dominant Source |
|---|---|---|---|---|
| 300 K | 3.2% | 17.5% | 20.7% | Inter-study |
| 500 K | 8.9% | 1.1% | 10.0% | Measurement |
| 1000 K | 2.1% | 3.7% | 5.8% | Balanced |
| 2000 K | 5.1% | 8.6% | 13.7% | Inter-study |
Key Insight: Inter-study variability dominates at most temperatures, indicating systematic differences between experimental methods.
| Temperature | Dominant Parameter | |S_Ea| | |S_n| | |S_A| |
|---|---|---|---|---|
| 300 K | Activation Energy (Ea) | 6.8 | 0.0 | 1.0 |
| 700 K | Transition | 3.2 | 1.7 | 1.0 |
| 1500 K | Temperature Exponent (n) | 2.1 | 2.7 | 1.0 |
| 2500 K | Temperature Exponent (n) | 1.3 | 3.4 | 1.0 |
Practical Implications:
- Atmospheric chemistry (T < 500 K): Prioritize accurate Ea measurements
- Combustion (800–2000 K): All three parameters matter; balanced accuracy needed
- High-T applications (T > 2000 K): Temperature exponent n is critical
| Model | R² (Test) | MAPE (%) | Parameters |
|---|---|---|---|
| Polynomial Ridge | 0.9993 | 6.0 | 56 |
| Random Forest | 0.9985 | 8.6 | 100+ |
| Gradient Boosting | 0.9983 | 8.9 | 100+ |
| Neural Network | 0.9917 | 22.2 | 2,500+ |
| Modified Arrhenius | 0.9981 | 10.3 | 3 |
Conclusion: ML models provide minimal improvement over 3-parameter Arrhenius (ΔR² < 0.002), confirming physical appropriateness of the traditional form.
Ten kinetic studies spanning 200–3044 K showing excellent agreement at combustion temperatures and greater scatter at extremes.
Posterior estimates with 95% credible intervals showing U-shaped uncertainty pattern with minimum at 1000 K.
Activation energy dominates at low T; temperature exponent becomes critical above 1500 K.
Application-specific recommendations with data coverage and uncertainty by temperature zone.
ML models confirm modified Arrhenius captures true physics—additional complexity provides minimal benefit.
# Clone the repository
git clone https://github.com/YourUsername/H2-OH-Bayesian-Kinetics.git
cd H2-OH-Bayesian-Kinetics
# Install dependencies
pip install -r code/requirements.txt
# Run main analysis (generates all figures and data)
python code/H2_OH_comprehensive_analysis.pyimport numpy as np
# Modified Arrhenius function
def modified_arrhenius(T, A, n, Ea, R=8.314472e-3):
"""Calculate rate constant k(T) = A × (T/298)^n × exp(-Ea/RT)"""
return A * (T / 298.0)**n * np.exp(-Ea / (R * T))
# Yang et al. (2021) - Recommended for combustion modeling
k_1000K = modified_arrhenius(1000, A=1.54e-12, n=1.64, Ea=13.72)
print(f"k(1000 K) = {k_1000K:.2e} cm³ molecule⁻¹ s⁻¹")
# Output: k(1000 K) = 2.16e-12 cm³ molecule⁻¹ s⁻¹- Replace
data/arrhenius_parameters.csvwith your reaction's data - Update temperature ranges in configuration
- Run the same analysis pipeline
- Get Bayesian uncertainties for your system!
Hierarchical Uncertainty Decomposition:
σ²_total = σ²_measurement + σ²_inter-study
where:
• σ²_measurement = posterior variance from inverse-variance weighting
• σ²_inter-study = empirical variance between studies
Normalized sensitivity coefficients for modified Arrhenius k(T) = A × (T/298)ⁿ × exp(-Ea/RT):
S_A = 1 (constant)
S_n = ln(T/298) (increases with T)
S_Ea = -Ea/(RT) (decreases with T)
Purpose: Confirm Arrhenius form captures physics
Logic: If data followed a different functional form, ML models would show much better R² than Arrhenius. Since the improvement is minimal (<0.2%), the Arrhenius form is physically appropriate.
| Application | Temperature | Recommended Study | Rate Expression |
|---|---|---|---|
| Atmospheric Chemistry | 200–450 K | Atkinson et al. (2004) | k = 7.70×10⁻¹² exp(-2100/T) |
| Combustion Modeling | 800–2000 K | Yang et al. (2021) | k = 1.54×10⁻¹² (T/298)^1.64 exp(-1651/T) |
| High-Temperature | 2000–3044 K | Hong et al. (2010) | k = 8.79×10⁻¹³ (T/298)^2.08 exp(-1771/T) |
Note: Exponential term shown as exp(-Ea/R/T) where Ea/R values are: 2100 K (17.46 kJ/mol), 1651 K (13.72 kJ/mol), 1771 K (14.72 kJ/mol)
numpy>=1.21.0
pandas>=1.3.0
scipy>=1.7.0
matplotlib>=3.4.0
seaborn>=0.11.0
scikit-learn>=1.0.0
If you use this analysis, code, or data in your research, please cite:
@article{rababah2025bayesian,
title={Bayesian Uncertainty Quantification and Sensitivity Analysis for the
H₂ + OH → H₂O + H Reaction: A Comprehensive Comparison of Ten Kinetic Studies},
author={Rababah, Anfal},
journal={ChemRxiv},
year={2025},
doi={10.26434/chemrxiv-2025-rd9v8},
url={https://doi.org/10.26434/chemrxiv-2025-rd9v8}
}APA Format:
Rababah, A. (2025). Bayesian uncertainty quantification and sensitivity analysis for the H₂ + OH → H₂O + H reaction: A comprehensive comparison of ten kinetic studies. ChemRxiv. https://doi.org/10.26434/chemrxiv-2025-rd9v8
- NIST Chemical Kinetics Database: https://kinetics.nist.gov/
- Original Publications: See Table 1 in paper for complete references (10 studies, 1981–2021)
This work is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
You are free to share and adapt this material for any purpose with appropriate attribution.
Anfal Rababah
- 📧 Email: Anfal0Rababah@gmail.com
- 🔬 ORCID: 0009-0003-7450-8907
- Chemical Kinetics Community for four decades of meticulous experimental work (1981–2021)
- NIST for maintaining the Chemical Kinetics Database
- Research Groups: Ravishankara, Pirraglia, Baulch, Old, Sutherland, Demissy & Lesclaux, Atkinson, Hong, Varga, and Yang
- Claude (Anthropic) for assistance with code development and manuscript preparation
Bayesian Methods • Chemical Kinetics • Open Science
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