Automated AFGL quantum number assignment for CO$_2$ isotopologues using a graph neural network

Abstract

Accurate quantum number assignment for calculated molecular energy levels is a critical bottleneck in generating line broadening parameters for comprehensive line lists for radiative transfer applications. We present an automated pipeline for assigning Air Force Geophysics Laboratory (AFGL) quantum numbers to CO2 calculated rovibrational states lying below 15,000cm$^{-1}$ across all 12 stable isotopologues. A GraphSAGE graph neural network is trained transductively on empirical (MARVEL) energy levels, exploiting inter-isotopologue perturbation chains and intra-isotopologue rotational ladder edges to propagate assignment information to unlabelled calculated states. Physical uniqueness is enforced locally by a Hungarian algorithm solver operating within groups of states sharing the same polyad, rotational quantum number, and parity. A five-generation bootstrap loop iteratively promotes high-confidence predictions into the training set, expanding coverage without additional labelling effort. The pipeline assigns 224,650 previously unlabelled states over 12 isotopologues, accounting for 10.7$\%$ of all available states (including MARVEL-derived levels), with coverage now increased to 97.4$\%$ below 5000cm$^{-1}$. The pipeline includes a novel decision tree method for converting AFGL to Herzberg notation in asymmetric isotopologues, while the architecture and Hungarian uniqueness enforcement are applicable beyond CO2, any molecular system with a conserved polyad-like quantum number and a large body of unlabelled computed states is a natural target for this approach, suggesting a pathway toward automated quantum number annotation for the next generation of large-scale computed line lists.