Atom Addition Formation of Thionylimide (HNSO) on Interstellar Dust Grains: Chemical Routes Requiring Oxygen and Nitrogen Atom Surface Diffusion

TL;DR

This paper explores how the molecule HNSO forms on interstellar dust grains through reactions involving oxygen and nitrogen atoms.

Contribution

The study identifies a new chemical route for HNSO formation involving surface diffusion of oxygen and nitrogen atoms.

Findings

HNSO is efficiently produced on grain surfaces via reactions with atomic oxygen and nitrogen.

The cis conformer of HNSO is favored over the metastable trans form under interstellar conditions.

Solid HNSO abundances can rival those of OCS in interstellar ices.

Abstract

We investigate the formation of the recently detected
HNSO molecule
using quantum chemical calculations on ices and astrochemical models
in tandem. Our results indicate that HNSO is efficiently produced
on grain surfaces through reactions involving atomic oxygen and nitrogen
atoms with the radicals NS and SO, forming NSO as a key intermediate.
Subsequent hydrogenation of NSO leads to HNSO, with a clear preference
for the lowest energy cis conformer, while the trans form is metastable and may be short-lived under typical
interstellar conditions. The models predict that solid HNSO can reach
abundances comparable to icy OCS, placing it among the major sulfur-bearing
species in interstellar ices. Gas-phase abundances, in contrast, remain
lower than those of OCS. The implementation of a multibinding scheme
in our models clarifies the role of diffusive chemistry in the production
of HNSO at early times, improving agreement with observations. These
findings suggest that reactions involving diffusing O and N atoms
on icy grains contribute significantly to sulfur chemistry and beyond
in dense clouds and motivate further searches for molecules containing
simultaneously H, N, O, and S in other astronomical environments.

Figures

Examples of the three binding sites on the cluster model of amorphous solid water (ASW) considered in this work. Red dotted lines indicate the hydrogen-bond network. The SO molecule is shown as a representative adsorbate.

Spin density of the NSO radical obtained with an isovalue of 0.02 au.

Eckart corrected isomerization rate constants for the gas phase cis-trans isomerization.

Astrochemical model results for Models A–C see Table . In all models, the abundance of gas trans-HNSO is below 10–19 due to spontaneous tunneling conversion. The black horizontal bar represents the observed abundance of HNSO while the red one represents the gaseous OCS abundance, both in in G+0.693. We note that a good agreement with observations of G+0.693 does not imply that the physical description of the cloud is accurate, see text.

Tables

1. Reaction Energies and Activation Energies, when Applicable, of the Nitrogen and Oxygen Atom Addition Reactions Studied in This Work

reaction	binding site	ΔH ○, R	ΔH ○, A
SO + N → NSO	pocket	–70.8	BL
	dH	–71.9	BL
	pentamer	–71.3	BL
SO + N → NOS	pocket	–37.8	14.7
	dH	–16.6	16.1
	pentamer	–41.1	15.6
NS + O → NSO	pocket	–80.4	–0.3
	dH	–82.1	BL
	pentamer	–79.7	BL
NS + O → ONS	pocket	–78.7	BL
	dH	–78.0	BL
	pentamer	–77.3	BL

2. Binding Energies (BE; in kcal mol–1 and K in Parentheses) of the Species Involved in the Atom Addition Reactions Shown in Section

species	binding site	BE
SO	pocket	5.5 (2755)
	dH	2.7 (1368)
	pentamer	5.1 (2755)
average SO:		4.4 (2222) ± 1.5
NS	pocket	6.0 (3007)
	dH	4.1 (2038)
	pentamer	6.2 (3108)
average NS:		5.4 (2717) ± 1.2
NSO	pocket	6.6 (3330)
	dH	4.8 (2438)
	pentamer	7.3 (3682)
average NSO:		6.3 (3150) ± 1.3
NOS	dH	1.9 (971)
ONS	pocket	4.7 (2364)
	dH	2.1 (1039)
	pentamer	3.4 (1727)
average ONS:		3.4 (1710) ± 1.3

4. Elemental Abundances (with Respect to Hydrogen Nuclei) at the Beginning of Each Chemical Model

element	fractional abundance
H2	0.5
H	1(−5)
He	9(−2)
N	6.2(−5)
O	2.4(−4)
C+	1.7(−4)
S+	1.5(−5)
Si+	1.8(−6)
Fe+	1.0(−8)
Na+	2.3(−7)
Mg+	2.3(−6)
Cl+	1.0(−9)
P+	7.8(−8)

6. Reactions Added to the Modified Garrod Reaction Network

reaction	type	α	β	γ
SO(i) + N(i) → NSO(i)	two body surface	1.00	0.00	0.00
NS(i) + O(i) → NSO(i)	two body surface	0.50	0.00	0.00
NS(g) + OH(g) → NSO(g) + H(g)	neutral–neutral gas	1.00(−11)	0.00	0.00
NSO(i) + H(i) → cis-HNSO(i)	two body surface	0.66	0.00	0.00
NSO(i) + H(i) → trans-HNSO(i)	two body surface	0.33	0.00	0.00
NSO(i) + N(i) → SO(i) + N2(i)	two body surface	1.00	0.00	0.00
SO(g) + NH2(g) → cis-HNSO(g) + H(g)	neutral–neutral gas	5.00(−12)	0.00	0.00
SO(g) + NH2(g) → trans-HNSO(g) + H(g)	neutral–neutral gas	5.00(−12)	0.00	0.00
NSO(g) + H(g) → HNO(g) + S(g)	neutral–neutral gas	1.00(−11)	0.00	0.00
NSO(g) + N(g) → SO(g) + N2(g)	neutral–neutral gas	1.00(−11)	0.00	0.00
NSO(g) + C+(g) → NSO+(g) + C(g)	ion–molecule gas	1.00(−9)	0.00	0.00
NSO(g) + He+(g) → NSO+(g) + He(g)	ion–molecule gas	1.00(−9)	0.00	0.00
HNSO+(g) + NH3(g) → NSO(g) + NH4 +(g)	ion–molecule gas	1.00(−9)	0.00	0.00
NSO+(g) + H2 → HNSO+(g) + H(g)	ion–molecule gas	1.00(−9)	0.00	0.00
NSO(g) + HCO+(g) → HNSO+(g) + CO(g)	ion–molecule gas	1.00(−9)	0.00	0.00
NSO(g) + H3 +(g) → HNSO+(g) + H2(g)	ion–molecule gas	1.00(−9)	0.00	0.00
NSO(g) + N2H+(g) → HNSO+(g) + N2(g)	ion–molecule gas	1.00(−9)	0.00	0.00
HNSO+(g) + H2(g) → H2NSO+(g) + H(g)	ion–molecule gas	1.00(−9)	0.00	0.00
HNSO+(g) + e– → NSO(g) + H(g)	dissociative recombination	1.00(−7)	0.00	0.00
cis-HNSO(g) + C+(g) → HNSO+(g) + C(g)	ion–molecule gas	1.80(−9)	–3.68(−1)	–3.30(−1)
trans-HNSO(g) + C+(g) → HNSO+(g) + C(g)	ion–molecule gas	4.97(−9)	–4.60(−1)	–9.90(−2)
cis-HNSO(g) + He+(g) → NSO+(g) + H(g) + He(g)	ion–molecule gas	2.95(−9)	–3.69(−1)	–3.30(−1)
trans-HNSO(g) + He+(g) → NSO+(g) + H(g) + He(g)	ion–molecule gas	8.11(−9)	–4.60(−1)	–9.90(−2)
cis-HNSO(g) + HCO+(g) → H2NSO+(g) + CO(g)	ion–molecule gas	1.29(−9)	–3.69(−1)	–3.30(−1)
trans-HNSO(g) + HCO+(g) → H2NSO+(g) + CO(g)	ion–molecule gas	3.54(−9)	–4.60(−1)	–9.90(−2)
cis-HNSO(g) + N2H+(g) → H2NSO+(g) + N2(g)	ion–molecule gas	1.29(−9)	–3.69(−1)	–3.30(−1)
trans-HNSO(g) + N2H+(g) → H2NSO+(g) + N2(g)	ion–molecule gas	3.54(−9)	–4.60(−1)	–9.90(−2)
cis-HNSO(g) + H3 +(g) → H2NSO+(g) + H2(g)	ion–molecule gas	3.39(−9)	–3.69(−1)	–3.30(−1)
trans-HNSO(g) + H3 +(g) → H2NSO+(g) + H2(g)	ion–molecule gas	9.30(−9)	–4.60(−1)	–9.90(−2)
H2NSO+(g) + e– → cis-HNSO(g) + H(g)	dissociative recombination	3.33(−8)	0.00	0.00
H2NSO+(g) + e– → trans-HNSO(g) + H(g)	dissociative recombination	3.33(−8)	0.00	0.00
H2NSO+(g) + e– → NSO(g) + H2(g)	dissociative recombination	3.33(−8)	0.00	0.00
H2NSO+(g) + NH3(g) → cis-HNSO(g) + NH4 +(g)	ion–molecule gas	5.00(−10)	0.00	0.00
H2NSO+(g) + NH3(g) → trans-HNSO(g) + NH4 +(g)	ion–molecule gas	5.00(−10)	0.00	0.00
NSO + hν → N + SO	photodissociation interstellar field	2.13(−9)	0.00	2.00
NSO(g) + hν → NS(g) + O(g)	photodissociation interstellar field	2.13(−9)	0.00	2.00
NSO(g) + hν → N(g) + SO(g)	photodissociation cosmic-ray photon	2.77(3)	0.00	0.00
NSO(g) + hν → NS(g) + O(g)	photodissociation cosmic-ray photon	2.77(3)	0.00	0.00
NSO+(g) + hν → N(g) + SO+(g)	photodissociation interstellar field	3.43(−10)	0.00	2.00
NSO+(g) + hν → O(g) + NS+(g)	photodissociation interstellar field	3.43(−10)	0.00	2.00
NSO+(g) + hν → N(g) + SO+(g)	photodissociation cosmic-ray photon	2.30(2)	0.00	0.00
NSO+(g) + hν → O(g) + NS+(g)	photodissociation cosmic-ray photon	2.30(2)	0.00	0.00
cis/trans-HNSO(g) + hν → NSO(g) + H(g)	photodissociation interstellar field	1.42(−9)	0.00	2.00
cis/trans-HNSO(g) + hν → NSO(g) + H(g)	photodissociation cosmic-ray photon	1.85(3)	0.00	0.00
cis/trans-HNSO(g) + hν → SO(g) + NH(g)	photodissociation interstellar field	1.42(−9)	0.00	2.00
cis/trans-HNSO(g) + hν → SO(g) + NH(g)	photodissociation cosmic-ray photon	1.85(3)	0.00	0.00
cis/trans-HNSO(g) + hν → NS(g) + OH(g)	photodissociation interstellar field	1.42(−9)	0.00	2.00
cis/trans-HNSO(g) + hν → NS(g) + OH(g)	photodissociation cosmic-ray photon	1.85(3)	0.00	0.00
HNSO+(g) + hν → H(g) + NSO+(g)	photodissociation interstellar field	6.86(−10)	0.00	2.00
HNSO+(g) + hν → H(g) + NSO+(g)	photodissociation cosmic-ray photon	4.60(2)	0.00	0.00
H2NSO+(g) + hν → H2(g) + NSO+(g)	photodissociation interstellar field	3.43(−10)	0.00	0.00
H2NSO+(g) + hν → H2(g) + NSO+(g)	photodissociation cosmic-ray photon	2.30(2)	0.00	2.00
H2NSO+(g) + hν → H(g) + HNSO+(g)	photodissociation interstellar field	3.43(−10)	0.00	2.00
H2NSO+(g) + hν → H(g) + HNSO+(g)	photodissociation cosmic-ray photon	2.30(2)	0.00	0.00
cis-HNSO(g) → trans-HNSO(g)	unimolecular isomerization	1.12(−1)	0.00	1.69(3)
trans-HNSO(g) → cis-HNSO(g)	unimolecular isomerization	6.92(−4)/2.26(−3)	0.00	0.00

7. Dipole Moments (μ, in Debye) and Diagonal Components of the Polarizability Tensor (α ii , in Å3) for cis-HNSO and trans-HNSO

species	μ	α xx	α yy	α zz
cis-HNSO	0.91	1.41	1.75	2.60
trans-HNSO	3.50	1.41	1.71	2.66

8. Binding Energies (BE, in kcal mol–1 and K in Parentheses) of Species Different than the Ones in Table of the New Species Included in the Modified Garrod Reaction Network

species	binding site	BE
cis-HNSO	pocket	8.2 (4121)
	dH	4.6 (2326)
	pentamer	6.6 (3313)
average cis-HNSO:		6.5 (3253) ± 1.8
trans-HNSO	dH	5.4 (2703)
	pentamer	10.4 (5220)
average trans-HNSO:		7.9 (3962) ± 3.5

Full text

Introduction

1

One of the main points of consensus that the astrochemical community needs to reach amid the current surge of new interstellar molecule detections is the definition of what constitutes a complex interstellar molecule. In 2009, and referring specifically to complex organic molecules (COMs), Herbst and Van Dishoeck? defined them as species containing at least one carbon atom, and more than five atoms in total. This definition encompasses a wide range of chemical compounds. like PAHs, or prebiotic compounds However, in order to understand the chemical complexity in the interstellar medium (ISM) it is necessary to understand the formation of molecules that do not strictly fit this definition.

The molecule subject of this study, thionylimide (HNSO), is certainly not organic, as it lacks a carbon atom in its structure, nor is it complex since it contains only four atoms in total. Nevertheless, it displays a remarkable diversity of heteroatoms, simultaneously harboring N, S, and O, three key elements for the development of life, a rare occurrence in interstellar chemical inventories. HNSO was recently discovered toward the Galactic Center molecular cloud G+0.693–0.027 (hereafter G+0.693)? as part of an ultradeep molecular line survey conducted with the Yebes 40 m and IRAM 30 m radio telescopes. ?,? Interestingly, G+0.693 hosts one of the richest chemical inventories in our Galaxy. Its chemistry is governed by large-scale low-velocity shocks, which facilitate the release of material from the icy mantles of dust grains, thereby providing access to grain-surface chemistry. ?,? This makes G+0.693 a unique astrochemical niche for the discovery of new interstellar species. ?,?,?,? The detection of HNSO opened the door to a completely new family of interstellar chemistry, as it is the first interstellar molecule ever detected containing the NSO moiety, thus representing a promising link between the chemistry of these three elements in space. Within Earth’s biosphere, NSO chemistry plays a key role in cellular and intercellular signaling processes, linking the biochemistries of two essential biological messengers, nitric oxide (NO) and hydrogen sulfide (H_2_S). ?−? ? ? ? NO, recognized as the first gasotransmitter, is involved in regulating vascular tone and cardiac function, while H_2_S contributes to antioxidative stress defense and inflammation control. ?,? Moreover, NSO-bearing compounds hold valuable geological and geochemical information,? effectively recording biotic and palaeoenvironmental signatures,? reinforcing their relevance in astrobiological research even further.

In light of the discussion above and the growing evidence that grain processes are viable initiators of chemical complexity in G+0.693, it is natural to examine non-hydrogenative grain chemistry alongside the well-established hydrogenation pathways. ?−? ? ? ? ? ? ? ? ? Hydrogen additions are favored because H atoms possess unique properties, such as rapid diffusion on amorphous solid water (ASW) surfaces ?−? ? and the ability to tunnel through activation barriers. However, hydrogenation alone cannot account for the formation of HNSO, since its immediate precursor, NSO, contains no hydrogen. Moreover, the NSO radical has not yet been detected nor characterized in the laboratory, and its chemistry is missing from current astrochemical models and databases such as KIDA? and UMIST.? Consequently, understanding the formation of HNSO first requires elucidating how NSO itself is produced. Combinatorially, three elementary reactions can, in principle, yield NSO on grains:

$$[eqn]$$ $$[eqn]$$ $$[eqn]$$

where the Reaction ? was originally suggested in Sanz-Novo et al.? Elemental two-body processes are assumed for reactions on grains because the ice matrix effectively acts as a third body. ?−? ? Among these candidates, the route starting from NO

• S is considered unfavorable, as it would require a significant heavy-atom rearrangement to place sulfur in the central position. This assessment is consistent with previous thermochemical studies showing that isomers with an NSO structural motif are more stable than those with an SNO motif, owing to the ability of the central sulfur atom to effectively expand its valency.? In contrast, the NS + O and SO + N channels are, in principle, plausible. Both NS and SO are well-established interstellar radicals ?−? ? ? ? also abundant in G+0.693,? that can encounter diffusing O and N atoms (of which N is faster due to the lower binding energy on ASW), which have been shown to migrate on ASW at 10 K, ?−? ? ? ? ? ? although more slowly than H. The feasibility of such heavy-atom diffusion arises from the wide distribution of adsorption sites on ASW, a heterogeneity that astrochemical models have only recently begun to represent in a general way. ?,?

The interstellar detection of HNSO is therefore timely in several respects. First, it establishes a new benchmark for the chemical complexity of small interstellar molecules, as it contains four different elements and exhibits a relatively high abundance, 6 × 10^–10^ with respect to H_2_, i.e., only a factor ∼5 lower than the ubiquitous SO_2_ molecule in G+0.693. Second, its formation cannot be explained solely through hydrogenation chemistry and instead requires the inclusion of heavy-atom reactions to account for its synthesis. Third, HNSO serves as an excellent molecule to test the impact of multibinding approaches in astrochemical models,? as its reaction network is small enough to be treated in a controlled manner.

The aim of this work is to understand, from an astrochemical perspective, how HNSO forms, to explain its presence in G+0.693, and to evaluate to what extent its chemistry and detectability may apply to other interstellar environments. The article is structured as follows. Section presents the quantum chemical calculations used to determine the surface parameters implemented in our astrochemical models, with the results of such investigation shown in Section. Section introduces the modeling framework, describes the resulting chemical abundances, and discusses their astrophysical implications. Finally, Section summarizes the main findings derived from both the quantum chemical and astrochemical modeling analyses.

Computational Methodology

2

Reactivity on Dust Grains

2.1

We performed density functional theory (DFT) calculations to investigate the reactivity leading to the formation of the title molecule. Specifically, we adopted a dual-level approach: geometry optimizations and vibrational frequency (Hessian) calculations were carried out at the ωB97M-D4-gCP/def2-SVP level of theory, ?−? ? ? ? and single-point energy refinements were performed using ωB97M-D4/def2-TZVPPD. The latter energy refinement is not gCP corrected, owing to the significantly larger based set used in the computations. Further improvements through high-level single-determinant wave function methods were deemed unfeasible due to the pronounced multiconfigurational character of many of the reactions studied. Likewise, multireference calculations become prohibitively expensive when explicit water molecules are included. Consequently, a broken-symmetry DFT approach? was employed to describe the low-spin reactive channels, providing a practical balance between accuracy and computational cost. Trabelsi et al.? previously characterized the electronic structure of radical NSO and SNO by means of multireference methods, providing one-dimensional cuts of the potential energy surface. These do not show any appreciable barriers along the reaction coordinate, a behavior that we can duplicate with our broken symmetry DFT approach. Since most of the reactions investigated are either barrierless or involve low activation barriers, this level of theory is adequate for our purposes. All calculations were performed with the Orca program package, employing resolution-of-identity and seminumerical techniques for efficient evaluation of the Coulomb (RIJ) and exchange (Chain-of-Spheres, COSX) terms. ?−? ? ?

We explored the formation pathways of HNSO on amorphous solid water (ASW) using a representative cluster of 33 water molecules, previously employed in related studies. ?−? ? The first step in modeling these reactions consisted of placing the SO and NS radicals on three distinct binding sites of the ASW cluster. Each of these sites, labeled Pocket, dH, and Pentamer, each represent a characteristic hydrogen-bonding environment within the ASW structure, as illustrated in Figure and its caption. From the totally optimized structures, we derived the binding energies of the species as

$$[eqn]$$

where H represents the enthalpy at zero kelvin, that is, the sum of the electronic and zero-point energies (ZPE). The protocol involves placing the radicals on top of the preoptimized water cluster, and relaxing the structure, taking H adsorbate (the remaining term) from a gas phase calculation. Once the adsorption minima were located, we investigated atom-addition reactions at each site. We began with Reactions ? and ?, deliberately excluding competing processes, which will be discussed in the following sections. Attacks on both atomic centers of each diatomic molecule were considered, resulting in 12 distinct reactions (3 adsorption sites × 2 reactants, SO and NS, × 2 atomic addition sites per reactant). The binding energies of the distinct products of reactions are obtained similarly, with the optimized structures of the reaction serving as H cluster+adsorbate. We must note, however, that the calculation arising from three binding sites should not be confused with a rigorous characterization of the binding energy distribution, although our values fall within it.

Examples of the three binding sites on the cluster model of amorphous solid water (ASW) considered in this work. Red dotted lines indicate the hydrogen-bond network. The SO molecule is shown as a representative adsorbate.

The protocol used to study these reactions was the same in all cases. First, starting from the adsorption minima, the N or O atom was placed at an initial distance of approximately 4.0 Å from the adsorbate to mimic coadsorption of both species. Second, the broken-symmetry wave function for the reactant complex was obtained and subsequently used as input to ensure continuity along the relaxed potential energy surface (PES) scans performed for each of the 12 reaction coordinates. The resulting scans were then analyzed to determine whether the reactions were barrierless. For those showing a barrier, the transition state was located through conventional saddle-point optimization. Finally, the end points of each scan were fully optimized to yield the reference reactant and product states, and their ZPEs were obtained from Hessian calculations. Reaction and activation energies, when applicable, were then computed as

$$[eqn]$$ $$[eqn]$$

where PS, RS, and TS stand for product state, reactant state and transition state, respectively.

A second set of reactions was examined starting from the products of the previous ones, as described in Sections and 3.3. For these reactions, the general protocol remained nearly identical, although specific details are discussed in the corresponding sections.

Quantum Chemical Treatment of Isomerism

2.2

A key feature of HNSO is its conformational flexibility. So far, only the cis form has been detected in the ISM,? but the trans conformer could also be present in space, as observed for other high-energy stereoisomers, ?−? ? yet it lacks available rotational data to enable its astronomical search. To assess the possibility of cis–trans isomerization, we performed exploratory simulations of tunneling-mediated interconversion. ?,? For this purpose, we evaluated the feasibility of isomerization in the gas phase by computing the isomerization rate constant, k ^iso^, as

$$[eqn]$$

The trans/cis isomerization rate constants and times were recently determined by Jiang et al.? and, as shown in Section their values are retained owing to their high precision. In the above expression, and for cis/trans isomerization, ΔG ^‡^ represents the free energy barrier, obtained from electronic structure calculations. These were performed at the CCSD­(T)-F12/VTZ-F12//ωB97M-D4-gCP/def2-SVP level of theory,? while we did not consider isomerization on the surface, as we discuss in Section. The parameter κ denotes the tunneling transmission coefficient, which can be evaluated with different levels of sophistication. Since our calculations consistently indicate cis/trans conversion is intrinsically slow and only weakly dependent on the tunneling model employed, we report rate constants using the computationally efficient asymmetric Eckart approximation, expressed as

$$[eqn]$$

where P(E) is the tunneling probability calculated through an asymmetric Eckart barrier, whose analytic form can be consulted, for example at Johnston and Heicklen? or the original reference.?

Quantum Chemical Results

3

Nitrogen and Oxygen Addition

3.1

To explore potential grain-surface pathways for the formation of HNSO, we first identified small interstellar species that are both abundant and capable of forming an −S– moiety. Within these constraints, SO and NS emerge as the most plausible candidates, as described in Section. The adsorption of SO and NS on ASW results in physisorbed species with average binding energies of 4.4 ± 1.5 kcal mol^–1^ (2222 K) for SO and 5.4 ± 1.2 kcal mol^–1^ (2717 K) for NS (see Table). The reported uncertainties correspond to the standard deviation of the individual values. These results indicate that the diffusion of SO and NS is unlikely to compete with that of atomic N and O, which have binding energies of approximately 720 or 400 K depending on the literature, ?,? and 1300 K,? respectively. This supports the conclusion that N and O diffusion are the main processes driving Reactions ? and ?.

The 4N + 3SO Route

3.1.1

We begin our exploration of the HNSO reaction network by examining the addition of an N atom to SO. The SO molecule, in its electronic ground state (^3^Σ), was placed on the three adsorption binding sites, and the two possible attack directions of a (^4^ S)-N atom were analyzed in the doublet channel, assuming antiparallel spins between SO and N. Reactions proceeding through the high-spin (sextet) configuration, which could lead to abstraction channels such as SO + N → NS + O or SO + N → NO + S, must be endothermic because they produce electronically excited fragments. The quartet state, although potentially reactive, shows pronounced multiconfigurational character, making DFT inadequate for its reliable description. As this study focuses on low-spin channels that promote radical coupling, the investigation of the quartet potential energy surface (PES) is deferred to future work.

The doublet state was generated using a broken-symmetry electronic wave function: first, the high-spin state was converged, and then the low-spin wave function was obtained by explicitly enforcing a spin configuration corresponding to separated spins on SO and N.? The same computational protocol was applied to Reaction ?. The results for the two possible additions, namely Reaction ? and:

$$[eqn]$$

are shown in the first two entries of Table.

1: Reaction Energies and Activation Energies, when Applicable, of the Nitrogen and Oxygen Atom Addition Reactions Studied in This Work

The results for both reactions are summarized in Table, together with the binding energies (BE) of all sulfur-bearing species involved, listed in Table. Reaction ? is consistently exothermic and barrierless across all binding sites, making it highly favorable. In contrast, Reaction ? exhibits significant activation barriers at all sites, with little variation among them. Notably, the formation of NOS shows some dependence of ΔH ^○^, R on the binding site. This arises because NOS is unstable on certain sites and spontaneously dissociates into NO + S, with the sulfur atom in the singlet state chemisorbing onto water.? However, in the dH site, NOS remains stable. Despite this, the large activation barrier and the lack of quantum tunneling render the nitrogen-addition to the oxygen atom pathway highly improbable and ultimately irrelevant under astrophysical conditions. Consequently, the formation of NOS will not be considered in subsequent discussions.

2: Binding Energies (BE; in kcal mol–1 and K in Parentheses) of the Species Involved in the Atom Addition Reactions Shown in Section

Given the barrierless and exothermic nature of Reaction ?, we conclude that it is the most favorable pathway within the present network for the SO + N reaction and model it with a branching ratio (α) of 1.0. Finally, although not further considered in this work, the BE of the NOS radical in the sites where it is stable is found to be 1.9 kcal mol^–1^ (Table).

The 3O + 2NS Route

3.1.2

The second possible route to form the parent radical NSO is through the addition of an O atom to NS. As in Reaction ?, two possible attack directions were considered, both Reaction ? and

$$[eqn]$$

Both reactions are exothermic, with comparable ΔH ^○,R ^ values. Moreover, both channels are barrierless, in contrast with the results presented in the previous subsection, indicating that their occurrence depends mainly on the relative orientation of the NS molecule and the incoming O atom, which can be considered random on an anisotropic potential such as that of ASW surfaces. In this work, we focus on the chemistry leading to HNSO formation and do not examine in detail the reaction network stemming from the ONS radical. A preliminary analysis of the spin density of ONS suggests that further radical–radical H-addition reactions could yield undetected interstellar species such as NSOH and N­(SH)­O, owing to the delocalized nature of the unpaired spin. This behavior contrasts with that of NSO, where the spin population is largely localized on the nitrogen atom, favoring the predominant formation of HNSO (Section). However, a more detailed investigation would be necessary before reaching firm conclusions.

For the modeling of Reaction ? (Section), we adopt a branching ratio of α = 0.5 to represent the competition between the NS

• O → NSO and NS + O → ONS channels. It should be noted that this treatment corrects only for the potential overproduction of NSO from the NS + O reaction, but does not account for the sulfur sink in NOS and related species, which slightly increases the sulfur available for other compounds. Finally, as in the case of the NOS radical, the ONS radicalalthough not considered in subsequent analyseshas a binding energy of 3.4 kcal mol^–1^.

Hydrogenation of NSO

3.2

The next step in the formation of HNSO is the addition of a hydrogen atom to the NSO radical. The evolution of the NOS and ONS radicals is not considered as already mentioned. Other channels are included, when relevant, only indirectly, as they influence the formation efficiency of the target molecule in the astrochemical models. The NSO + H reaction can proceed through five competing pathways:

$$[eqn]$$ $$[eqn]$$ $$[eqn]$$ $$[eqn]$$ $$[eqn]$$

In the above reactions, competition among the different channels makes it difficult to isolate individual processes, as both barrierless and activated pathways coexist within a relatively narrow orientational space (given that NSO is a small radical). To investigate these reactions, we followed a strategy similar to that described by Ferrero et al.? In their approach, barrierless pathways are identified by monitoring the spontaneous conversion of a prereactive complex into products during a force minimization, starting from a configuration in which the reactants are initially placed at a large separation distance.

We start the protocol placing H atoms in various relative orientations with respect to the NSO radical and at different binding sites. Additionally, we slightly extended the protocol of Ferrero et al.? by performing a constrained geometry optimization of the prereactant complex, fixing the distance between the H atom and the nearest atom of the NSO molecule at 3.0 Å. After this constrained step, the H atom was released, and a full geometry optimization was carried out to determine whether the reaction proceeded without an activation barrier. The results of this analysis are summarized in Table.

3: Energetic Parameters for All NSO + H Reactions Studied in This Work, as a Function of the Binding Site

Overall, we find that cis-HNSO, the isomer detected in the ISM, is consistently formed across all binding sites and over a wide range of initial orientations. For instance, cis-HNSO is produced when the H atom approaches the N end of the NSO molecule in the cis conformation, but also when approaching the O end in the same orientation, or even in less favorable configurations such as the O–trans end at the Pentamer site. This clearly indicates that cis-HNSO is the most favored isomer, a preference that can be rationalized in terms of both electronic and geometric effects. As shown in Figure, the spin density of the NSO radical at the Pentamer site is mainly localized at the N end. Combined with the bent, V-shaped geometry of the molecule, this facilitates the formation of cis-HNSO even when the initial approach occurs near the O atom.

Spin density of the NSO radical obtained with an isovalue of 0.02 au.

The second product that forms without activation barriers on the ASW surface is trans-HNSO, which arises when the H atom approaches the N end of the NSO molecule in the trans configuration. However, in our limited sampling, there are cases where cis-HNSO is still preferred over trans-HNSO. For example, at the Pocket site, no accessible orientation leads to trans-HNSO formation, making cis-HNSO the only viable product. Attacks at the O end generally involve sizable activation barriers and are therefore expected to contribute less to the overall product distribution, similar to attacks at the S site. Interestingly, the barriers for the latter are considerably lower, suggesting that the formation of N­(SH)­O, while rare, cannot be entirely ruled out. Nevertheless, to maintain the chemical model presented in Section tractable and to avoid introducing additional species with poorly characterized chemistry, these alternative products are not explicitly included in the reaction network. Finally, we note an interesting case involving hydrogenation at the S site of the Pentamer configuration, which leads to the formation of trans-NSOH instead of N­(SH)­O. This unconventional outcome results from a favorable hydrogen-bond arrangement that facilitates a proton relay following initial N­(SH)O formation. We expect this mechanism could occur more frequently when considering additional binding sites, offering an alternative route to produce trans-NSOH. However, as discussed above, and for the purposes of this work, cis-HNSO remains the clearly preferred product of the NSO + H reaction.

Other Reactions

3.3

In order to complete the reaction network surrounding NSO and HNSO we have investigated a number of additional reactions to be later included in our rate equation models. In particular, we considered reactions of NSO with other atoms (N,O), and H-abstraction reactions from HNSO.

In the first place, we studied the NSO + O reaction in the low-spin channel following the same method that we used for the previous hydrogenation in the Pocket site, not finding any appreciable reactivity. On the contrary, the reaction with N atoms on the same site spontaneously (barrierless) forms N_2_ through the following reaction:

$$[eqn]$$

with a ΔH ^○,^ * ^R^

• of −155.4 kcal mol^–1^, i.e., an enormous reaction energy, following the formation of the very stable N_2_ molecule. This route acts a promising competing route to hydrogenation, reducing the abundance of HNSO.

Finally, we complete the trifecta of studied reactions with the H-abstraction in HNSO:

$$[eqn]$$ $$[eqn]$$

Interestingly, this reaction is sensitive to the isomeric form of HNSO, with gas-phase reaction energies of 1.3 kcal mol^–1^ (endothermic) and −1.5 kcal mol^–1^ exothermic when starting from cis-HNSO and trans-HNSO, respectively. We did not further investigate the endothermic channel. For Reaction ?, its study on the model ice yields an activation enthalpy of ΔH ^○,A ^ ∼ 13 kcal mol^–1^, corresponding to a very high barrier that precludes its viability. While quantum tunneling might be invoked as a driver for the reactions, the barriers are probably too high to be competitive with H diffusion away of the reaction center. Moreover, given that the almost null exothermicity of the reaction, one could also invoke the back reactions as viable, as they would be equally affected by tunneling, ultimately making H-abstraction of HNSO an irrelevant chemical process in the HNSO network. Therefore, among the additional reactions considered in this section, only Reaction ? is relevant to the chemistry of HNSO and is the one included in our astrochemical models.

Alternative formation routes of HNSO by means of direct combination reaction such as NH + SO → HNSO, SH + NO → HNSO, and NS + OH → HNSO are not considered in our study. Hassani et al.? studied these pathways by means of different single- and multi–reference computational methods. Reactions SH + NO → HNSO and NS + OH → HNSO involve the barrierless formation of HSNO and HOSN, respectively. In both cases, the hydrogen atom must subsequently rearrange through a series of intermediate steps to yield the desired product HNSO (either the cis or trans isomer). These intermediate steps involve a series of energy barriers that, considering the icy grain as a third body, will not be overcome. The remaining alternative (NH + SO), though reported exothermic and barrierless, would necessarily involve the diffusion of NH on the grain surfaces, whose higher diffusion energy (e.g., Molpeceres et al.?) makes this route less competitive, at least on H_2_O ice and under cold, thermalized, conditions.

cis/trans-HNSO Isomerization

3.4

We conclude our quantum chemical investigation of HNSO reactivity by examining its possible isomerization, both in the gas phase and on the ASW surface. For the latter, we focus on the dH binding site, where both isomers can form. In the gas phase, the energy difference between the two isomers is 2.8 kcal mol^–1^ (1413 K), with cis-HNSO being the most stable form. This separation is smaller than typical values reported for other interstellar imines.? The isomerization barriers between the cis and trans forms are, however, very high: 14.5 kcal mol^–1^ (7305 K) for the cis → trans process and 11.7 kcal mol^–1^ (5892 K) for the reverse. On the ASW surface, these barriers remain similar, at 12.9 kcal mol^–1^ (6495 K) and 10.9 kcal mol^–1^ (5502 K), respectively.

These computed energetics are consistent with those reported by Jiang et al.,? who found trans–cis barriers of approximately 10 kcal mol^–1^. Based on their experimental results, we derive a trans-HNSO → cis-HNSO rate constant of 6.92 × 10^–4^ s^–1^ at 3 K, corresponding to a half-life of about 16 min.? This extremely short lifetime challenges the presence of trans-HNSO under interstellar conditions provided that cis/trans isomerization is slow as demonstrated in the next paragraphs.

Previous studies of isomerization reactions on ice surfaces ?,? have shown that direct isomerization is often hindered by hydrogen bonding, which restricts molecular motion and can raise the effective activation barrier by several orders of magnitude despite a marginal decrease in the activation energies. It is unclear whether this effect also applies to trans-HNSO or if spontaneous isomerization could occur on grains. In this work, we assume that surface isomerization does not take place, since reproducing the calculations of Jiang et al.? on ices would be computationally prohibitive. Nevertheless, this assumption does not affect our conclusions regarding the detectability of trans-HNSO, as its very short gas-phase half-life at near-zero temperature already makes its detection challenging. Therefore, for astrochemical modeling, the cis → trans isomerization channel is also considered. We computed its rate constants using an Eckart tunneling model as indicated in Section. The results, shown in Figure, confirm that the process is intrinsically slow. Therefore, in our astrochemical model, we adopt the experimental rate constant from Jiang et al.? in the 10–90 K temperature range and the instanton rate constant reported in their Supporting Information above 90 K for the trans-HNSO → cis-HNSO reaction, and fit our own derived rate constants for the cis-HNSO → trans-HNSO reaction constant to a modified Arrhenius expression (see Section).

Eckart corrected isomerization rate constants for the gas phase cis-trans isomerization.

Chemical Model and Astrophysical Implications

4

Description of the Chemical Model

4.1

To evaluate the astrochemical relevance of the quantum chemical results presented in the previous sections, we performed exploratory simulations of HNSO formation under different interstellar conditions. The specific models employed are described later in this section. For this purpose, we used the three-phase gas–grain code Rokko,? coupled to the latest version of our modified chemical network,? which is greatly based on the three-phase reaction network developed by Garrod.? A list of the modifications and additions to the Garrod? network on which our work builds can be found in Appendix A of Molpeceres et al.;? here, we briefly summarize only the features specific to this study. As we will show during this section, our model does not fully include a full sulfur chemistry network pertaining G+0.693, nor it includes several of the important physical processes characteristic of this cloud. Therefore, the agreement between the models and observations can be regarded as qualitative, with significant uncertainties still needed to be resolved in the gas–gas and gas-grain interplay of HNSO and more generally, sulfur chemistry in G+0.693.

A distinctive aspect of this work is the incorporation of the full set of reactions relevant to HNSO, including those discussed above as well as standard gas-phase and grain-surface processes. The details of these new reactions and their implementation are provided in Section. We reiterate here that our models are essentially exploratory and the rate constants for the gas-phase processes are included for completeness of the reaction network and might significantly vary from the actual values. Nevertheless, the chemistry of HNSO in our models is dominated by grain-surface processes, which were constrained through the quantum chemical calculations presented in Section.

The three models introduced below share the same initial abundances. We adopt as starting abundances the high-metallicity values proposed by Wakelam et al.,? with all elements except hydrogen assumed to be in their atomic form, either neutral or ionized depending on their ionization potentials (see Table). Hydrogen is considered predominantly molecular (H_2_), with a small atomic fraction (1 × 10^–5^) included to represent the steady-state abundance of H atoms produced by cosmic-ray–induced H_2_ dissociation.?

4: Elemental Abundances (with Respect to Hydrogen Nuclei) at the Beginning of Each Chemical Model

Sulfur is assumed to be less depleted on dust grains at the start of the simulations, consistent with previous observations toward galactic center clouds and recent theoretical modeling on S-bearing chemistry toward G+0.693. ?,?,? A visual extinction of 10 mag is imposed in all cases, representing a cloud well shielded from the interstellar radiation field. The models incorporate several nonthermal desorption mechanisms, namely cosmic-ray–induced heating, photodesorption (with a yield of 1 × 10^–3^), and chemical desorption. For the latter, a constant efficiency of 1% per reactive event is used.

In addition to the common initial conditions described above and elsewhere,? we varied several physical parameters to progressively introduce additional complexity into the models. Three chemical models were run, designed to explore the influence of a multibinding treatment of the binding energies? and of a set of more energetic physical conditions as elevated cosmic-ray ionization rates and temperatures. The differing parameters among the three models are summarized in Table. Model A represents the simplest case, employing a single binding energy per species and cold gas and dust temperatures. Model B introduces a multibinding treatment of the binding energies while maintaining the same cold temperatures as Model A. Finally, Model C features a higher cosmic-ray ionization rate (1.3 × 10^–16^ s^–1^), a warmer gas temperature (100 K), and increased dust temperature (15 K). The physical environment in G+0.693 where HNSO is found is surely more energetic, but the here presented models cannot reproduce these conditions. For example, we tested higher ζ in our exploratory single binding model, finding a significant decrease of all our considered species and an overall very poor agreement with observations. We attribute this to the inability of our model to fully account for the Central Molecular Zone particularities, like shock induced desorption, radiolysis, or mantle chemistry. Therefore, an increase of 1 order of magnitude in ζ is sufficient to evaluate the impact of this parameter on molecular abundances, postponing (and strongly advocating for) a more detailed modeling of G+0.693 to future works.

5: Differing Conditions in the Three Astrochemical Models Studied in This Work

The inclusion of a multibinding treatment in Models B and C accounts for the variability in binding energies arising from different adsorption sites on ASW surfaces, as discussed in Section. In this work, the multibinding approach was applied to O, N, and S atoms, using the standard binding energies from Garrod? (1320, 720, and 2600 K, respectively) and assuming a distribution with a full width at half-maximum of 0.2 relative to the mean value. We also tested initial conditions with reduced average binding energies for the N atom approximately 400 K, ?,? but found no significant effect on the resulting abundances, as the multibinding scheme naturally encompasses these variations at low temperatures. All other species in the reaction network are treated using a single binding energy. Overall, the multibinding approach provides a more realistic representation of grain-surface chemistry compared to the single binding energy assumption used in Model A.

Input Parameters Used in the Chemical Model

4.2

The most significant additions to the chemical models used in this work are the reactions involving NSO and HNSO, particularly the heavy-atom addition processes described in Section. A summary of the newly included reactions is provided in Table. As noted in the caption, the table does not list all the physical processes implemented in the model but focuses primarily on the newly incorporated chemical reactions.

6: Reactions Added to the Modified Garrod Reaction Network

Gas Phase Reactions: ion–molecule,

Unimolecular Conversion and Photorates

4.2.1

Although our quantum chemical investigation focuses exclusively on grain-surface chemistry, we also incorporated gas-phase processes into our chemical models, albeit with a lower level of detail and using effective rate theories with assumed products and branching ratios. To construct the gas-phase reaction network, we distinguished five classes of reactions: neutral–neutral, ion–molecule, dissociative electron recombination, photodissociation (driven by both the interstellar radiation field and cosmic-ray–induced photons), and unimolecular isomerization.

For the first three categories, and as a general rule, rate constants were taken as the collisional rate divided by the number of available reaction channels. We adopted collisional rate constants of 1 × 10^–11^ cm^3^ s^–1^ for neutral–neutral reactions, 1 × 10^–9^ cm^3^ s^–1^ for ion–molecule reactions, and 1 × 10^–7^ cm^3^ s^–1^ for dissociative recombination. The different rates obey to conventional choices in the astrochemical literature and the differences in orders of magnitude between the different processes stem from the different physicochemical forces driving the reactive collision, e.g., dipole–induced dipole, ion-dipole/induced dipole or ion-electron recombination. An exception to this general treatment is the ion–molecule reactivity of the cis- and trans-HNSO stereoisomers, as it is well established that the relative abundances of stereoisomers are influenced by their differing destruction reactivities, a concept known as the Relative Dipole Principle (RDP).? For these processes we explicitly computed the Su–Chesnavich capture rate.?

$$[eqn]$$ $$[eqn]$$

where

$$[eqn]$$ $$[eqn]$$

Here, μ_D_ denotes the total dipole moment of the neutral reactant, α its scalar polarizability, μ the reduced mass of the reactants, and e the elementary charge. The dipole moments and diagonal components of the polarizability tensors for cis-HNSO and trans-HNSO were obtained at the ωB97M-D4/def2-TZVPPD level of theory, and the corresponding values are listed in Table. For ease of implementation in every astrochemical model, instead of directly using eqs and ?, we fitted the rate constants derived from these expressions to a modified Arrhenius equation; the resulting parameters are given in Table.

7: Dipole Moments (μ, in Debye) and Diagonal Components of the Polarizability Tensor (α ii , in Å3) for cis-HNSO and trans-HNSO

In the absence of specific photochemical data for NSO derivatives, we adopt photodissociation rates by analogy: SO rates for neutral species and SH^+^ rates for cations, scaled by the number of available photodissociation channels in each case. Rates are taken from the Leiden database (https://home.strw.leidenuniv.nl/~ewine/photo).[?](#ref84) This uniform treatment removes any possibility of preferential photodestruction among isomers and will certainly overestimate or underestimate absolute photodissociation rates. Nevertheless, when assessing the total destruction rates for all species included in the additional reactions considered here, we find that photodissociation is several orders of magnitude less relevant than ion–molecule pathways under the shielded conditions adopted (A V = 10 mag). Consequently, uncertainties in the assumed photorates have a negligible impact on our results.

Finally, we included the rate constants obtained in Section for the isomerization of cis-HNSO and trans-HNSO. In the model, we only included isomerization in the gas phase, as the effect of an ice matrix reduces the rate constants as discussed in Section and the chemical time scale of species is dominated by hydrogenation rather than by isomerization. For reference a H atom accretes on average at a rate of one atom per day at canonical ζ (1.3 × 10^–17^ s^–1^).? We note that Jiang et al.? only report rate constants up to 90 K, and therefore for the inclusion on the models, we recommend to use the rate constants at 90 K for temperatures above this value. Caution is advised when determining cis-HNSO/trans-HNSO ratios at high temperatures, where the rate constants should be extrapolated above the validity range of our fit and trans-cis rate constants are not available.

Surface Reactions

4.2.2

We constructed an NSO/HNSO reaction network based on the results presented in Section. In brief, we added two-body surface reactions following the Langmuir–Hinshelwood formalism described by Hasegawa and Herbst? and Ruaud et al.,? assuming reaction–diffusion competition for processes with activation barriers. Though the Eley–Rideal gas-grain formalism could also be considered, as all the here considered reactions would be viable, the low coverage of NO and NS on the ice would make the total reaction rate constant very small. Our quantum chemical calculations indicate that the hydrogenation of SO and NS proceeds through distinct numbers of reactive channels. Based on our sampling, we assume that the reaction between SO and N forms NSO with 100% efficiency, whereas the reaction between NS and O produces NSO and ONS in a 2:1 ratio. The ONS radical is not explicitly included in the model, as its chemistry remains largely unexplored; its presence is instead implicitly accounted for by the reduced efficiency of the NS + O → NSO reaction. Additionally, we included the destruction of NSO through Reaction ?. The hydrogenation of NSO leading to HNSO was also implemented, with a 2:1 branching ratio for the formation of cis-HNSO and trans-HNSO, respectively, based on the results summarized in Table. No further reactions involving HNSO, such as hydrogen abstraction, whose was deemed uninmportant in Section or additional hydrogenation to form more complex species like H_2_NSO, were included. Nevertheless, their investigation constitutes a promising direction for future studies.

Average Binding Energies

4.2.3

The binding energies of sulfur-bearing species on ASW have been the subject of increasing attention in recent years, both for common S-bearing molecules? and for sulfur allotropes.? Among the species considered in this work, and for the chemical models discussed in Section, we determined the binding energies that were still missing from our data set, namely those of cis-HNSO and trans-HNSO, in addition to the values presented in Table. In this section, we consider important to reiterate that our reported binding energies come only from an average over three binding sites, without explicit knowledge of the site population on ASW. Therefore, from the limited sampling we cannot extract reliable binding energy distributions where dedicated works are needed. ?−? ? ?

8: Binding Energies (BE, in kcal mol–1 and K in Parentheses) of Species Different than the Ones in Table of the New Species Included in the Modified Garrod Reaction Network

Although the binding energies of both cis- and trans-HNSO are sufficiently high to make thermal desorption unlikely under typical dense-cloud conditions, it is worth noting the close similarity between the two isomers. This behavior is consistent with our previous findings for formic acid,? where the binding energy distributions of the trans and cis isomers were found to be essentially equivalent in terms of their adsorption strength.

Chemical Model Results: Astrophysical Implications

4.3

The results of the astrochemical models discussed in the previous section are presented in Figure, highlighting several key points. One of the most surprising aspects of the interstellar detection of HNSO by Sanz-Novo et al.? is the relatively high abundance of such a complex molecule (complex in terms of chemical composition rather than size), despite its small dipole moment of ∼0.90 D, as in cis-HNSO. This abundance suggests either highly efficient formation routes, routes that start from very abundant precursors, or a combination of both. These conditions are, in principle, difficult to reconcile with a molecular formula containing H, N, S, and O. Our quantum chemical calculations reveal that efficient grain-surface chemistry can arise from the simplest precursors, namely atomic oxygen and nitrogen. We also tested sulfur-atom diffusion as a potential driver of chemistry, considering that the NS or SO production could be enhanced by S-atom diffusion, but its contribution was found to be lower than that of O and N, owing to its reduced mobility. The models shown in Figure clearly indicate that the increase in HNSO abundance occurs after the freeze-out of SO and NS, around 10^3^ years, when the main routes leading to the formation of solid SO and NS originate from the gas phase. This behavior resembles that of icy H_2_S (brown line), which in our model forms primarily through the direct hydrogenation of atomic sulfur at all times. H_2_S is the most abundant sulfur-bearing molecule on ices in our simulations, in good agreement with observational constraints,? with modeled abundances of 0.5–2.0% relative to water in the 10^4^–10^5^ yr range. In contrast, OCS formation is largely independent of SO and NS, as it proceeds mainly through the gas-phase reaction HCS + O → OCS + H (where HCS originates from S + CH_2_ → HCS + H) and the grain-surface reaction S + CO → OCS at all times. The dual gas-phase and surface chemistry allows OCS, one of the only icy sulfur-bearing molecules unambiguously identified in space to date,? to form via routes that do not compete with those of HNSO, ultimately leading to comparable abundances between the two species. This is likely the most important conclusion of the present work. On ices, our models predict an HNSO abundance comparable to that of OCS, positioning HNSO as a primary sulfur reservoir under typical molecular cloud conditions. Gas-phase abundances of OCS and HNSO (both isomers), on the other hand, are not comparable, which is expected since gas-phase formation of OCS remains one of the dominant channels. These results strongly motivate further searches for HNSO in other astronomical environments, as this molecule may represent a key player in the sulfur chemistry of the interstellar medium.

Astrochemical model results for Models A–C see Table . In all models, the abundance of gas trans-HNSO is below 10–19 due to spontaneous tunneling conversion. The black horizontal bar represents the observed abundance of HNSO while the red one represents the gaseous OCS abundance, both in in G+0.693. We note that a good agreement with observations of G+0.693 does not imply that the physical description of the cloud is accurate, see text.

We would like to emphasize the differences arising from the distinct approaches employed in our models. Although the general conclusions discussed above hold for all three models at steady or near–steady state (around 10^6^ years), both ice and gas abundances are significantly affected at earlier times, particularly between 10^4^ and 10^5^ years when the multibinding scheme is applied. This treatment directly influences the gas-phase abundance of HNSO, bringing the modeled values into good agreement with the observational constraints (horizontal line in Figure), especially in Model C. This model, which represents the actual astrochemical history of the molecule a bit better, allows HNSO to reach the same ice abundance as OCS at early times, thereby enhancing its subsequent release into the gas phase. It is important to reiterate, however, that the nonthermal desorption mechanisms responsible for releasing HNSO into the gas phase remain poorly constrained, limiting our ability to accurately predict its detectability in conventional dark clouds. Nevertheless, our model, despite its significant simplifications, is able to reproduce the formation of HNSO in Model C, and it encourages extending the chemistry leading to HNSO to other interstellar molecules that could form through O or N diffusion on grains, in addition to the more typical hydrogenation pathways. Finally, we tested models incorporating a higher sulfur depletion factor, but these did not reproduce the observed abundances satisfactorily either, reinforcing the idea that sulfur is not severely depleted in energetic environments.? From a methodological perspective, our results demonstrate the effectiveness of the multibinding approach for modeling grain-surface chemistry in astrochemical simulations, consistent with the benchmark study of Furuya,? where a similar enhancement of ice CO_2_ abundances was reported.

Finally, we observe that in all models, both at low and high gas temperatures, the trans–cis isomerization makes the abundance of trans-HNSO negligibly small. This is due to the fast spontaneous interconversion between conformers due to quantum tunneling,? suggesting that detecting this species will be extremely challenging unless additional isomerization mechanisms operate in the region. For comparison, it is known that photon-driven isomerization can bring the abundance of cis-HCOOH to parity with that of the low-energy isomer trans-HCOOH in warm photodissociation regions,? where the high-energy form would otherwise be only residual.? By analogy, if the low-lying electronic states of cis-HNSO are favorable for photoisomerization to trans-HNSO, the latter might be detectable in photodissociation regions, making it a potential tracer of the local photon field. Although this remains speculative, deriving photoisomerization cross sections represents a plausible line of future work, particularly given that the proposed formation mechanism under Earth conditions of trans-HNSO involves UV irradiation at 254 nm? of cis-HNSO. In the solid phase, our models predict that the abundance of trans-HNSO is comparable to that of cis-HNSO. The reliability of this later prediction, however, depends on two key approximations in our modeling. First, mantle chemistry is not included, meaning that any molecule buried by subsequent ice growth is effectively protected from further reactions. Second, unimolecular isomerizations are neglected in the ice, as molecular motions responsible for isomerism are assumed to be hindered in the solid phase. These two simplifications may overestimate the amount of trans-HNSO on grains. Nonetheless, they do not affect the conclusions of this work, which rest on the gas-phase abundance of cis-HNSO and the total HNSO abundance in the ice mantle.

Conclusions

5

In summary, our results suggest that the formation of HNSO can follow a grain-surface pathway. The combination of quantum chemical and astrochemical modeling allows us to extract several key conclusions, summarized below:

• Additions of atomic oxygen and nitrogen to the interstellar radicals NS and SO efficiently produce the HNSO precursor, NSO. Our calculations also show that the positional isomer ONS can form from the NS + O reaction with a comparable branching ratio to Reaction ?. In contrast, formation of the metastable NOS radical involves prohibitively high activation barriers and is therefore unlikely.
• Hydrogenation of NSO readily yields HNSO, with a clear preference for the cis (cis-HNSO) conformer on ice surfaces. The trans form (trans-HNSO) can also be produced, together with small amounts of radicals such as N­(SH)O and NSOH. Once formed, HNSO, regardless of the conformer, is resistant to hydrogen abstraction.
• We evaluated the spontaneous isomerization of trans-HNSO to cis-HNSO based on the available literature.? Our findings confirm that trans-HNSO is a metastable species under an astronomical prism, that rapidly converts to the more stable cis-HNSO via quantum tunneling. The reverse process (cis-HNSO → trans-HNSO) is extremely slow, making the cis-HNSO ⇌ trans-HNSO equilibrium almost completely displaced to cis-HNSO at low temperatures, and implying that astronomical detection of trans-HNSO will be very difficult.
• Our exploratory astrochemical models, which explicitly include the chemistry of NSO and HNSO, predict that the abundance of HNSO in ices is comparable to that of OCS, a sulfur-bearing molecule unambiguously detected in interstellar ices. This result suggests that HNSO could be a major sulfur reservoir in the solid phase. In the gas phase, however, the presence of efficient gas-phase routes for OCS competing with its destruction and the lack of those for HNSO results in HNSO abundances much lower than those of OCS.
• Incorporating a multibinding treatment in our astrochemical models substantially modifies the time evolution of both ice and gas-phase HNSO, increasing its abundance at earlier evolutionary stages of dark clouds and improving agreement with observations. This effect is expected to extend to other molecules formed via oxygen or nitrogen diffusion, as shown by Furuya? for icy CO_2_.

Future work should explore the broader chemical landscape accessible from the HNSO molecular formula. This includes not only successive hydrogen additions but also the potential formation of high-energy isomers along the hydrogenation sequence, involving reactions of H atoms with transient radicals such as N­(SH)O or NSOH, which are not yet incorporated into current chemical networks. From an astrochemical standpoint, targeted searches for HNSO in other star-forming regions would be particularly valuable, given the relatively high abundances predicted by our models. In addition, a significantly improved characterization of the energetic chemistry of HNSO in G+0.693, where it is ultimately detected.