Machine learning isotope shifts in molecular energy levels

TL;DR

This paper introduces a machine learning framework to improve molecular energy level predictions for isotopologues, enhancing spectroscopic accuracy for exoplanet atmospheric studies.

Contribution

It develops neural network models and transfer learning techniques to correct and generalize isotope shift predictions across different molecules.

Findings

Neural network reduces MAE for CO2 energy levels by over 87%.

Transfer learning improves MAE in CO isotopologues by over 93%.

Updated line lists for 11 CO2 isotopologues are provided.

Abstract

Recent advances in the use of High-Resolution Cross-Correlation Spectroscopy (HRCCS) to detect molecular species in exoplanet atmospheres, presents a new challenge for the accuracy of reference spectroscopic line lists. While parent isotopologues of key atmospheric tracers are often well-characterized, minor isotopologues, crucial for diagnosing planetary formation histories and evolution, suffer from a scarcity of experimental data, often leading to reliance on less accurate theoretical predictions. In this work, a comprehensive machine learning framework is designed to mitigate these inaccuracies by modelling the residual errors of the isotopologue extrapolation (IE) method used within the ExoMol project. A fully connected neural network architecture for carbon dioxide (CO$_2$) is shown to predict energy corrections with high fidelity, reducing the mean absolute error (MAE) relative to the original IE approach for more than 87\% of the levels when benchmarked against empirical (\Marvel) energies. Furthermore, development of a novel hybrid, molecule-aware transfer learning architecture is presented that successfully propagates correction patterns from the data-rich CO$_2$ system to the data-poor carbon monoxide (CO) system. This transfer learning approach yields MAE improvements in over 93\% of CO samples, demonstrating that physical correction factors related to isotopic substitution can be generalized across chemically related molecular systems. Updated and improved line lists are presented for 11 CO$_2$ isotopologues and energy levels for excited states of CO isotopologues are predicted. The methodology establishes a scalable, data-driven paradigm for refining molecular line lists, helping to bridge the gap between theoretical calculations and experimental precision.