OH model adopted in this work. (a) X²Π and A² Σ⁺ electronic levels split into vibrational levels and further split into rotational levels labeled by N (left ladder corresponding the OH(X²Π)(v = 0) state). The red line indicates the dissociation energy of OH(X²Π). (b) Structure of the rotational ladders of OH(X²Π) within a vibrational state that gives rise to mid- and far-IR lines. Each N level is split by the spin-orbit coupling and the Λ-doubling. The two spin-orbit states are labeled by the Ω quantum number and the Λ-doubling states are labeled by their ϵ = e∕f spectroscopic parity. Radiative transitions included in our model and emerging from the four N-levels are also depicted by arrows. There are three kinds of transitions: intra-ladder rotational transitions (blue and red arrows), cross-ladder transitions (green, with ΔN = − 1, and orange, with ΔN = 0, −2), and Λ-doubling transitions (purple). (c) Optically thin LTE spectrum of OH at T_K = 750 K. The color code is the same as panel b) and is repeated in Figs. 4 and 9. The upper N level is indicated for some transitions. The Λ-doubling lines are too weak and at longer radio wavelengths to appear in this spectrum. Ro-vibrational lines are at shorter wavelengths than shown here (λ ≲ 2.7 μm).