Quantum-defect analysis of $np$ and $nd$ ${\mathrm{H}}_3$ Rydberg energy levels

In this work, Rydberg energy levels of the triatomic hydrogen molecule (${\mathrm{H}}_3$) are studied with multichannel quantum-defect theory. We extract the body-frame p-wave quantum defects from highly accurate \emph{ab initio} electronic potential surfaces and calculate the quantum defects of higher momentum states by using the long-range multipole potential model. To obtain laboratory-frame quantum defects, we perform a rovibrational-frame transformation with accurate rovibrational states of ${\mathrm{H}}_3^{+}$. Finally, we use the laboratory-frame quantum defects to calculate Rydberg energy levels for the fundamental neutral triatomic molecule ${\mathrm{H}}_3$.