Integrating the Asymptotic Iteration Method with Machine Learning for Predicting Vibrational Energy Levels of Diatomic Molecules

Abstract

Aim: This study integrates the Asymptotic Iteration Method (AIM) with Machine Learning (ML) models to enhance the prediction of vibrational energy levels in diatomic molecules. Traditional quantum mechanical methods, while accurate, are computationally demanding. This study aims to determine whether ML models can approximate these calculations efficiently while maintaining high accuracy. Methodology: The vibrational energy levels of Li₂, CN, and CO molecules were computed using AIM within the Morse potential framework. Three ML models—Random Forest (RF), Gradient Boosting (GB), and Support Vector Regression (SVR)—were trained using AIM-derived datasets. The models were evaluated using Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and R² score to assess their predictive performance. Results: SVR demonstrated the highest predictive accuracy, achieving a R² score of 0.999650, the lowest MAE and RMSE values of 0.124391 and 0.158412 respectively, outperforming RF and GB. The results indicate that ML models, particularly SVR, can effectively approximate AIM calculations with minimal error. Furthermore, 3D potential energy surface visualizations confirmed the strong agreement between ML and AIM predictions, validating the reliability of ML-based approaches. Conclusions: This study demonstrates that ML can serve as an efficient and scalable alternative to traditional quantum mechanical methods for predicting vibrational energy levels. The findings have implications for computational chemistry, spectroscopy, and materials science by reducing reliance on computationally intensive calculations. However, the study is limited by data generalization, as accuracy depends on the diversity of the training dataset. Future work should focus on expanding datasets, integrating deep learning techniques, and exploring hybrid AIM-ML models to improve generalizability and predictive robustness.