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We present an algorithm that combines quantum scattering calculations with probabilistic machine-learning models to predict quantum dynamics rate coefficients for a large number of state-to-state transitions in molecule–molecule collisions much faster than with direct solutions of the Schrödinger equation. By utilizing the predictive power of Gaussian process regression with kernels, optimized to make accurate predictions outside of the input parameter space, the present strategy reduces the computational cost by about 75%, with an accuracy within 5%. Our method uses temperature dependences of rate coefficients for transitions from the isolated states of initial rotational angular momentum j, determined via explicit calculations, to predict the temperature dependences of rate coefficients for other values of j. The approach, demonstrated here for rovibrational transitions of SiO due to thermal collisions with H2, uses different prediction models and is thus adaptive to various time and accuracy requirements. The procedure outlined in this work can be used to extend multiple inelastic molecular collision databases without exponentially large computational resources required for conventional rigorous quantum dynamics calculations. 

Context.One of the main problems in astrochemistry is determining the amount of sulfur in volatiles and refractories in the interstellar medium. The detection of the main sulfur reservoirs (icy H₂S and atomic gas) has been challenging, and estimates are based on the reliability of models to account for the abundances of species containing less than 1% of the total sulfur. The high sensitivity of theJames WebbSpace Telescope provides an unprecedented opportunity to estimate the sulfur abundance through the observation of the [SI] 25.249 µm line. Aims.Our aim is to determine the amount of sulfur in the ionized and warm molecular phases toward the Orion Bar as a template to investigate sulfur depletion in the transition between the ionized gas and the molecular cloud in HII regions. Methods.We used the [S III] 18.7 µm, [S IV] 10.5 µm, and [S l] 25.249 µm lines to estimate the amount of sulfur in the ionized and molecular gas along the Orion Bar. For the theoretical part, we used an upgraded version of the Meudon photodissociation region (PDR) code to model the observations. New inelastic collision rates of neutral atomic sulfur with ortho-and para- molecular hydrogen were calculated to predict the line intensities. Results.The [S III] 18.7 µm and [S IV] 10.5 µm lines are detected over the imaged region with a shallow increase (by a factor of 4) toward the HII region. This suggests that their emissions are partially coming from the Orion Veil. We estimate a moderate sulfur depletion, by a factor of ~2, in the ionized gas. The corrugated interface between the molecular and atomic phases gives rise to several edge-on dissociation fronts we refer to as DF1, DF2, and DF3. The [S l] 25.249 µm line is only detected toward DF2 and DF3, the dissociation fronts located farthest from the HII region. This is the first ever detection of the [S l] 25.249 µm line in a PDR. The detailed modeling of DF3 using the Meudon PDR code shows that the emission of the [S l] 25.249 µm line is coming from warm (>40 K) molecular gas located atA_V~1–5 mag from the ionization front. Moreover, the intensity of the [S l] 25.249 µm line is only accounted for if we assume the presence of undepleted sulfur. Conclusions.Our data show that sulfur remains undepleted along the ionic, atomic, and molecular gas in the Orion Bar. This is consistent with recent findings that suggest that sulfur depletion is low in massive star-forming regions because of the interaction of the UV photons coming from the newly formed stars with the interstellar matter. 

ABSTRACT Rate coefficients for rotational transitions in HD induced by H2 impact for rotational levels of HD j ≤ 8 and temperatures 10 K ≤ T ≤ 5000 K are reported. The quantum mechanical close-coupling (CC) method and the coupled-states (CS) decoupling approximation are used to obtain the cross-sections employing the most recent highly accurate H2–H2 potential energy surface (PES). Our results are in good agreement with previous calculations for low-lying rotational transitions The cooling efficiency of HD compared with H2 and astrophysical applications are briefly discussed.