Physics-Informed Neural Networks (PINNs) for the determination of Vibrational Energy Levels of the HCl molecule

Abstract

Understanding vibrational spectra is essential in molecular physics, as they reveal the anharmonic behavior of molecular vibrations and the underlying interatomic forces in diatomic molecules. Analysis of vibrational transitions
provides valuable information about molecular potentials and bonding characteristics. In this work, a Physics-Informed Neural Networks (PINNs) approach is employed to determine the vibrational energy levels of the hydrogen chloride (HCl) molecule using the Morse potential. The vibrational dynamics are described by theone-dimensional time independent Schr¨odinger equation, with the fundamental physical laws directly incorporated into the neural network training. The PINNs framework simultaneously learns the vibrational wavefunctions, energy
eigenvalues, and Morse potential parameters by minimizing a composite loss function that enforces the Schr¨odinger equation residual, normalization, orthogonality, and physical dissociation constraints. The predicted vibrational energy levels and optimized potential parameters show strong agreement with experimental and theoretical values, demonstrating the accuracy and reliability of the proposed method.
These results establish PINNs as a powerful and data-efficient framework for molecular spectroscopy and computational quantum chemistry.