HCL in Chemistry and Machine Learning

• HCL is a term that denotes both hydrogen chloride, a polar covalent molecule key to spectroscopy and astrochemical studies, and advanced ML methodologies.
• In chemistry, HCl’s well-characterized rotational, vibrational, and pressure-induced phase transitions provide insights into atmospheric, interstellar, and corrosion processes.
• In machine learning, HCL represents frameworks such as Hierarchical Contrastive Learning and heterogeneous causal structure learning, enhancing graph representations and clustering accuracy.

HCL denotes distinct entities across the contemporary research literature. In chemistry, planetary science, and astrophysics it most commonly denotes hydrogen chloride, a polar covalent molecule whose rotational and vibrational spectra, reaction kinetics, and phase behavior make it a key chlorine-bearing species from dense clouds to planetary atmospheres and high-pressure solids (Zeng et al., 2015). In machine learning, HCL also denotes “Hierarchical Contrastive Learning,” a graph representation framework, and “Interpretable Causal Mechanism-Aware Clustering with Adaptive Heterogeneous Causal Structure Learning,” an unsupervised method for mixed observational data (Wang et al., 2022, Li et al., 4 Sep 2025).

1. Chemical identity, spectroscopy, and pressure-induced structural diversity

Hydrogen chloride is described as a “textbook” example of a polar covalent molecule (Zeng et al., 2015). Its fundamental rotational transition lies near $626$ GHz: the $J=1\!\to\!0$ lines occur at $625.918756$ GHz for H$^ {35}$Cl and $624.977821$ GHz for H$^ {37}$Cl, and the chlorine nuclear spin splits each line into three hyperfine components. For H$^ {35}$Cl, the outer components lie at $-6.35$ and $+8.22$ km s$^{-1}$ relative to the strongest central component; for H$J=1\!\to\!0$0Cl, the separations are $J=1\!\to\!0$1 and $J=1\!\to\!0$2 km s$J=1\!\to\!0$3 (Peng et al., 2010). In the infrared, the fundamental vibration–rotation band $J=1\!\to\!0$4 spans $J=1\!\to\!0$5–$J=1\!\to\!0$6m, and both $J=1\!\to\!0$7- and $J=1\!\to\!0$8-branch lines of H$J=1\!\to\!0$9Cl and H$625.918756$0Cl have been observed in absorption toward CRL 2136 (Goto et al., 2013).

Under compression, the H–Cl system exhibits pressure-stable stoichiometries beyond HCl itself. Variable-composition ab initio searches from ambient pressure to $625.918756$1 GPa identified HCl, H$625.918756$2Cl, H$625.918756$3Cl, H$625.918756$4Cl, and H$625.918756$5Cl$625.918756$6 as stable in different pressure windows. HCl is stable from $625.918756$7 to $625.918756$8 GPa and again above $625.918756$9 GPa, but unstable between $^ {35}$0 and $^ {35}$1 GPa, where it decomposes into H$^ {35}$2Cl and H$^ {35}$3Cl$^ {35}$4. The molecular $^ {35}$5 phase transforms to $^ {35}$6 near $^ {35}$7–$^ {35}$8 GPa as zigzag chains symmetrize, and a metallic $^ {35}$9 layered phase becomes stable above $624.977821$0 GPa (Zeng et al., 2015).

2. Interstellar, protostellar, and circumstellar HCl

In gas where H$624.977821$1 dominates, chlorine chemistry predicts HCl to be a principal halogen reservoir, yet observations show strong depletion in dense molecular material. A Galactic survey of the HCl $624.977821$2 transition toward $624.977821$3 sources found HCl emission in $624.977821$4, absorption in $624.977821$5, $624.977821$6 marginal emission detections, and $624.977821$7 non-detections. RADEX modeling yielded $624.977821$8–$624.977821$9 cm$^ {37}$0, $^ {37}$1–$^ {37}$2 cm$^ {37}$3 in typical emission sources, and $^ {37}$4 relative to H$^ {37}$5, corresponding to chlorine depletion factors up to $^ {37}$6. The same survey found localized $^ {37}$7 ratios from $^ {37}$8 to $^ {37}$9, generally below the terrestrial value of $^ {35}$0 (Peng et al., 2010).

Absorption studies sharpened this picture. Along the line of sight to W31C, HCl was detected in diffuse molecular clouds with a total column density of $^ {35}$1 cm$^ {35}$2, and HCl accounted for about $^ {35}$3 of the total gas-phase chlorine, exceeding theoretical model predictions by a factor of $^ {35}$4 (Monje et al., 2013). In the protostellar core OMC-2 FIR 4, NLTE modeling with newly computed HCl–H$^ {35}$5 hyperfine rate coefficients gave $^ {35}$6, only $^ {35}$7 of the volatile elemental chlorine abundance. Gas–grain chemistry indicated that at least $^ {35}$8 of the volatile chlorine is sequestered as HCl ice, with gas-phase HCl characterized as “the tip of the chlorine iceberg” (Kama et al., 2014).

In shocked gas, HCl behaves differently from many grain-released species. The first detection of HCl toward a protostellar shock, L1157-B1, yielded $^ {35}$9 cm$-6.35$0, $-6.35$1–$-6.35$2 cm$-6.35$3, $-6.35$4–$-6.35$5 K, and $-6.35$6–$-6.35$7. The abundance is consistent with values in low- and high-mass protostars rather than being shock-enhanced, suggesting either that HCl is not the main gas-phase chlorine reservoir or that the elemental chlorine abundance is low in L1157-B1 (Codella et al., 2011).

Circumstellar and hot-core detections show that HCl can nevertheless be abundant in warm, dense environments. In IRC+10216, Herschel/SPIRE and PACS detected HCl from $-6.35$8 to $-6.35$9, and LVG modeling placed its origin in the innermost circumstellar envelope with an abundance relative to H$+8.22$0 of $+8.22$1, extending to the photodissociation zone (Cernicharo et al., 2010). Toward CRL 2136, the fundamental band of HCl was detected in absorption for the first time in a dense cloud environment, with $+8.22$2 K, $+8.22$3 cm$+8.22$4, $+8.22$5, and approximately $+8.22$6 of elemental chlorine residing in gaseous HCl (Goto et al., 2013).

3. Comets and Mars

Searches for HCl in Solar System bodies have emphasized depletion and heterogeneous loss. Herschel/HIFI observations of comets 103P/Hartley 2 and C/2009 P1 (Garradd) targeted the $+8.22$7 lines of HCl near $+8.22$8 GHz. HCl was not detected in either comet, yielding $+8.22$9 s$^{-1}$0 for 103P/Hartley 2 and $^{-1}$1 s$^{-1}$2 for Garradd. Relative to water, the abundance limits are $^{-1}$3 and $^{-1}$4, implying depletion factors $^{-1}$5 and $^{-1}$6 with respect to the solar Cl/O ratio. The authors concluded that HCl was not the main reservoir of chlorine in the regions of the solar nebula where these comets formed (Bockelée-Morvan et al., 2014).

For Mars, early submillimetre observations produced only upper limits. Herschel/HIFI observations of the H$^{-1}$7Cl $^{-1}$8 hyperfine multiplet near $^{-1}$9 GHz on 16 April 2010 yielded a disk-averaged upper limit of $J=1\!\to\!0$00 ppt, and the study concluded that there was no evidence for current volcanic HCl emission at that time (Hartogh et al., 2010).

Later orbital observations overturned the assumption of persistent non-detection. ACS onboard ExoMars TGO found gas-phase HCl in the Martian atmosphere during perihelion season, with maximum volume mixing ratios up to $J=1\!\to\!0$01 ppbv in the Southern Hemisphere, followed by a rapid drop to undetectable levels below $J=1\!\to\!0$02 ppbv. Simultaneous measurements of HCl and water ice showed detached HCl-rich layers at “ice-hole” altitudes, and associated chemistry indicated that H$J=1\!\to\!0$03O ice becomes the most effective sink for HCl above $J=1\!\to\!0$04 km, with characteristic times shorter than $J=1\!\to\!0$05 hours (Luginin et al., 2023). A subsequent 3D Mars Planetary Climate Model with heterogeneous chlorine chemistry reproduced ACS detections and $J=1\!\to\!0$06 of ACS non-detections in Mars Years 34 and 35, found HCl lifetimes of a few sols, and showed that modeled HCl is correlated with water vapour, airborne dust, and temperature, and anticorrelated with water ice (Benne et al., 23 Jun 2025).

4. Collisional physics, ionic recombination, and corrosion chemistry

Because HCl is the dominant atmospheric reservoir of chlorine, high-fidelity line-shape parameters are required for remote sensing. Fully quantum calculations for the HCl($J=1\!\to\!0$07)–O$J=1\!\to\!0$08($J=1\!\to\!0$09) system, based on a new UCCSD(T)-F12b potential energy surface, were used to derive collision-induced line-shape parameters for the O$J=1\!\to\!0$10-perturbed H$J=1\!\to\!0$11Cl $J=1\!\to\!0$12 $J=1\!\to\!0$13 line at $J=1\!\to\!0$14 GHz. At $J=1\!\to\!0$15 K the recommended parameters are $J=1\!\to\!0$16 MHz/Torr, $J=1\!\to\!0$17 MHz/Torr, $J=1\!\to\!0$18 MHz/Torr, $J=1\!\to\!0$19 MHz/Torr, $J=1\!\to\!0$20 MHz/Torr, and $J=1\!\to\!0$21 MHz/Torr, with an estimated total combined uncertainty corresponding to about $J=1\!\to\!0$22 relative RMSE in the simulated line shape at $J=1\!\to\!0$23 K (Olejnik et al., 2023).

Ion–electron chemistry places HCl$J=1\!\to\!0$24 at a central kinetic bottleneck. Merged-beams measurements of the dissociative recombination of HCl$J=1\!\to\!0$25 at the TSR storage ring covered collision energies from $J=1\!\to\!0$26 to $J=1\!\to\!0$27 eV and produced a plasma rate coefficient for $J=1\!\to\!0$28–$J=1\!\to\!0$29 K. Relative to the “typical diatomic” DR rate adopted previously, the new data imply that earlier values underestimate the plasma rate coefficient by a factor of $J=1\!\to\!0$30 at $J=1\!\to\!0$31 K and overestimate it by a factor of $J=1\!\to\!0$32 at $J=1\!\to\!0$33 K. Because HCl$J=1\!\to\!0$34 is the primary ionic intermediate on the way to H$J=1\!\to\!0$35Cl$J=1\!\to\!0$36 and ultimately neutral HCl, the revised DR kinetics partly explain discrepancies between observed abundances of chlorine-bearing molecules and astrochemical models (Novotný et al., 2013).

In high-temperature corrosion, HCl acts not as a trace spectroscopic species but as an aggressive gas-phase reactant. A study of laser-clad Kanthal APMT exposed FeCrAl coatings at $J=1\!\to\!0$37C for $J=1\!\to\!0$38 h in air and in a synthetic biomass flue gas containing $J=1\!\to\!0$39 ppm HCl and $J=1\!\to\!0$40 O$J=1\!\to\!0$41. The experiments showed that HCl allowed chlorine-based corrosion to occur, suggesting interaction from the gas phase. When both HCl and KCl were present, the mass gain was reduced relative to KCl in air, but the interpretation was not reduced corrosion: the paper attributed the lower mass gain to hindered KCl dissociation and enhanced formation of volatile chromium chlorides (Reddy et al., 2018).

5. HCL as “Hierarchical Contrastive Learning” in graph representation learning

In graph machine learning, HCL denotes “Hierarchical Contrastive Learning,” a self-supervised framework designed to address the limitations of single-scale graph contrastive learning (Wang et al., 2022). The method constructs a hierarchy of graph topologies with an adaptive “Learning to Pool” module, L2Pool, and uses a multi-channel pseudo-siamese network to maximize DGI-style mutual information at each scale. In the reported default configuration, HCL uses hidden dimension $J=1\!\to\!0$42, Adam with learning rate $J=1\!\to\!0$43, two non-weight-sharing encoder channels, and three recursive pooling scales with ratios $J=1\!\to\!0$44, $J=1\!\to\!0$45, and $J=1\!\to\!0$46, together with $J=1\!\to\!0$47 attention heads and a $J=1\!\to\!0$48-layer GCNII inside L2Pool. On node classification, the model achieved $J=1\!\to\!0$49 on Cora, $J=1\!\to\!0$50 on Citeseer, and $J=1\!\to\!0$51 on Pubmed; with a diffusion matrix variant, HCL* improved these to $J=1\!\to\!0$52, $J=1\!\to\!0$53, and $J=1\!\to\!0$54. On graph classification it reported $J=1\!\to\!0$55 on REDDIT-B, and ablations showed that both the multi-scale and multi-channel components contributed to the performance gains (Wang et al., 2022).

6. HCL as heterogeneous causal structure learning

A second machine-learning use of HCL is “Interpretable Causal Mechanism-Aware Clustering with Adaptive Heterogeneous Causal Structure Learning,” an unsupervised framework for mixed-type observational data (Li et al., 4 Sep 2025). This HCL jointly infers latent clusters and their associated DAGs without requiring temporal ordering, environment labels, interventions, or other prior knowledge. The model introduces a representation $J=1\!\to\!0$56 derived from posterior expectations of exogenous components under a shared causal backbone, alternates between Bayesian Gaussian-mixture clustering in $J=1\!\to\!0$57-space and NOTEARS-style structure learning, and regularizes cluster-specific graphs with backbone-aware penalties that balance universality and specificity. The optimization includes an acyclicity term such as $J=1\!\to\!0$58, while merging decisions are based on normalized SHD. In synthetic experiments, HCL reached ARI $J=1\!\to\!0$59 at $J=1\!\to\!0$60 and $J=1\!\to\!0$61 at $J=1\!\to\!0$62, maintained ARI $J=1\!\to\!0$63 under class imbalance ratios of $J=1\!\to\!0$64, $J=1\!\to\!0$65, and $J=1\!\to\!0$66, and did not hallucinate heterogeneity at $J=1\!\to\!0$67, where ARI $J=1\!\to\!0$68. On the Sachs single-cell perturbation data, it recovered three mechanistic clusters with ARI $J=1\!\to\!0$69, compared with $J=1\!\to\!0$70 for a Dirichlet-process baseline (Li et al., 4 Sep 2025).