A Possible Additional Formation Pathway for the Interstellar Diatomic SiS (2024)

Ryan C. FortenberryDepartment of Chemistry & Biochemistry, University of Mississippi,
University, Mississippi, 38677, United StatesBrett A. McGuireDepartment of Chemistry, Massachusetts Institute of Technology,
Cambridge, Massachusetts, 02139, United States

(May 20, 2024)

Abstract

The formation of silicon monosulfide (SiS) in space appears to be a difficultprocess, but the present work is showing that a previously excluded pathway maycontribute to its astronomical abundance. Reaction of the radicals SH +SiH produces SiS with a submerged transition state and generates a stabilizingH₂ molecule as a product to dissipate the kinetic energy. Such is a textbookchemical reaction for favorable gas-phase chemistry. While previously proposedmechanisms reacting atomic sulfur and silicon with SiH, SH, and H₂S willstill be major contributors to the production of SiS, an abundance of SiS incertain regions could be a marker for the presence of SiH where it haspreviously been unobserved. These quantum chemically-computed reactionprofiles imply that the silicon-chalcogen chemistry of molecular clouds, shockedregions, or protoplanetary disks may be richer than previously thought.Quantum chemical spectral data for the intermediate $cis$ - and $trans$ -HSiSH are also provided in order to aid in their potential spectroscopiccharacterization.

Astrochemistry (75) — Interdisciplinary astronomy (804) —Neutral-neutral reactions (2265) — Quantum-chemical Calculations (2232)

1 Introduction

Silicon monosulfide (SiS) has been observed in a variety of astronomicalenvironments since it was first observed in the circ*mstellar environment of the evolved carbon star IRC+10216 in 1975 (Morris etal., 1975).Currently, SiS is believed to be created from the following set of reactions with their percent contributions given for SiS formation over $t=1\times 10^{3}$ yr assuming a molecular cloud with $T=10$ K, $n(\mathrm{H}_{2})=2\times 10^{4}$ cm^-3 and a cosmic ray ionisation rate of $1.3\times 10^{-17}$ s^-1 (Mendoza etal., 2024):

$\displaystyle\mathrm{Si}+\mathrm{SH}\rightarrow\mathrm{H}+\mathrm{SiS}\hskip 1%4.22636pt$	$\displaystyle 30.6\%$	(1)
$\displaystyle\mathrm{S}+\mathrm{SiC}\rightarrow\mathrm{C}+\mathrm{SiS}\hskip 1%4.22636pt$	$\displaystyle 26.5\%$	(2)
$\displaystyle\mathrm{Si}+\mathrm{SO}\rightarrow\mathrm{O}+\mathrm{SiS}\hskip 1%4.22636pt$	$\displaystyle 23.8\%$	(3)
$\displaystyle\mathrm{HSiS}^{+}+e^{-}\rightarrow\mathrm{H}+\mathrm{SiS}\hskip 1%4.22636pt$	$\displaystyle 18.3\%$	(4)
$\displaystyle\mathrm{Si}+\mathrm{H}_{2}\mathrm{S}\rightarrow\mathrm{H}_{2}+%\mathrm{SiS}\hskip 14.22636pt$	$\displaystyle 0.70\%$	(5)

The above reactions are built upon a large body of work from several theoretical and experimental groups (Willacy & Cherchneff, 1998; Paiva etal., 2018; Lai etal., 2001; Doddipatla etal., 2021). The last of these above contributions to the formation of SiS (Reaction 5) shows that even minor contributors can have a role to play in the overall chemical modeling for any potential reaction mechanism. While other mechanisms have been suggested (Rosi etal., 2018; Zanchet etal., 2018; Campanha etal., 2022), the above have risen to the top as the most viable mechanisms for current models that are in line with current observations of SiS (Mendoza etal., 2024). However, other reactions could still be present as contributions to SiS abunance, and these have exciting correlations with currently hypothesized but as-of-yet undetected molecules.

Recent work has shown that isolated molecule reaction pathways starting fromwater and metal hydrides can lead to both simple, diatomic metal oxides as wellas larger clusters of inorganic oxides (Grosselin & Fortenberry, 2022; Flint & Fortenberry, 2023; Firth etal., 2024);a similar case is also present for aluminum hydride plus ammonia(Palmer & Fortenberry, 2024). These reactions exhibit barrierless entrance intermediates, showcase submerged reaction barriers, and generate ubiquitous H₂ as a stabilizing leaving group. Such molecular behavior allows for the question as to whetheror not silicon may perform in a related fashion in the same way as its periodictable third-row mates aluminum and magnesium will. Additionally, the questionis also open if hydrogen sulfide or SH can replace water or the hydroxyl radicalin similar reactions. AlO can form from AlH + OH (Firth etal., 2024), and such leads to the suggestion thatradical-radical reactions extrapolated to SiH + SH may proceed to SiS.

Hence, the present discussion will examine the reactions of silicon and sulfur hydrides and dihydrides with one another in order to explore additionalmeans for formation of SiS beyond those reactions with atomic species:

	$\displaystyle\mathrm{SiH}+\mathrm{SH}$	$\displaystyle\rightarrow\mathrm{H}_{2}+\mathrm{SiS}$			(6)
	$\displaystyle\mathrm{SiH}_{2}+\mathrm{H}_{2}\mathrm{S}$	$\displaystyle\rightarrow 2\mathrm{H}_{2}+\mathrm{SiS}.$			(7)

Again, H₂S is known in astronomical regions(Thaddeus etal., 1972) as is the SH radical(Neufeld etal., 2012). The SiH radical has been observed inthe Sun (Wöhl, 1971) implying that it could be present elsewhere(Yurchenko etal., 2017). While clues have been given to show that SiH may bepresent in the ISM (Schilke etal., 1997), conclusive detection has yet to be reported (McGuire, 2022). However, ifthis molecule contributes to the formation of the known SiS molecule, renewedattempts for detection of silicon monohydride are warranted. SiH₂, however, has yet to beobserved despite searches for it (Avery etal., 1994), but its inclusion is retainedherein in order to see what, if any, role it could play in the formation of SiS. Regardless, a more expansive set of possibilities will be generated forthe creation of SiS.

2 Computational Details

All minima are optimized and real harmonic frequencies confirmed with coupledcluster theory (Crawford & Schaefer III, 2000; Shavitt & Bartlett, 2009) at the singles, doubles, andperturbative triples level (Raghavachari etal., 1989) under the F12 explicitly correlatedframework (Adler etal., 2007; Knizia etal., 2009) with a correlation consistent triple- $\zeta$ basis set (Dunning, 1989; Peterson etal., 2008) giving the CCSD(T)-F12b/cc-pVTZ-F12 (orjust F12-TZ) level of theory within the MOLPRO2022.1 quantum chemistry program(Werner etal., 2022, 2012). Transition states are optimized at theB3LYP/aug-cc-pVTZ level within Gaussian16 (Becke, 1993; Yang etal., 1986; Lee etal., 1988; Frisch etal., 2016), butF12-TZ single point energies are computed at these geometries to provideconsistent energetic profiles and to address any potential pitfalls in energyB3LYP could generate. All relative energies are computed including harmoniczero-point energy corrections from the optimized geometries and thecorresponding level of theory.

The spectral data for the $trans$ - and $cis$ -HSiSH conformers are providedherein. These are computed from the so-called F12-TcCR (Watrous etal., 2021)quartic forice field (QFF). The QFF is a fourth-order Taylor series expansionof the internuclear Hamiltonian and has been discussed in detail for itsrelevance for astrochemical spectroscopic reference data(Fortenberry & Lee, 2019, 2022; Fortenberry, 2024). The energysurface defining the QFF is comprised of F12-TZ energies inclusive of coreelectron correlation as well as canonical CCSD(T) with Douglas-Kroll scalarrelativity included. The QFFs are computed via normal coordinates in anautomated fashion and fed through an updated second-order vibrationalperturbation theory (VPT2) code (Watson, 1977; Mills, 1972; Papousek & Aliev, 1982) written inRust called pbqff (Westbrook & Fortenberry, 2023) built upon the existingSpectro code (Gaw etal., 1991).

3 Results & Discussion

3.1 SiS Formation

A Possible Additional Formation Pathway for the Interstellar Diatomic SiS (1)

The additionally suggested formation pathways of ${}^{1}\Sigma^{+}$ SiS are shown in Fig.1. Firstof all, the new reaction of SH + SiH defines the zero of energy here for thesestarting materials. The association of these two molecules can proceed toeither a $trans$ - or $cis$ -HSiSH intermediate. If the lower-energy $trans$ -HSiSH (-88.7 kcal mol^-1) conformer is formed first, it canisomerize into the $cis$ over a submerged and relatively small barrier. Oncethe two hydrogen atoms are on the same side of the molecule, they can associateinto a transition state (TS2) at -57.2 kcal mol^-1 below the startingmaterials where the H $-$ H bond forms. This is nearly identical to the behaviornoted for aluminum/magnesium hydrides plus water/OH and in corroboration, inpart, with Lai etal. (2001). At this point, the hydrogen molecule leaves producingSiS at -93.8 kcal mol^-1 below the starting materials, and the expulsion ofthe hydrogen molecule will stabilize the system as it can dissipate the excessenergy kinetically. Such a reaction profile, especially from the SH + SiHstarting materials through $cis$ -HSiSH has one barrier to overcome that iswell-submerged below the starting materials and follows a similar pattern asthat suggested for formation of the known ethynyl cyclopropenylidene(Cernicharo, J. etal., 2021; Fortenberry, 2021). The climb from the $cis$ -HSiSHminimum intermediate to TS2 is 29.1 kcal mol^-1, but this would benefit fromthe -86.3 kcal mol^-1 energy gained in the association in the first placelikely rendering such an up-hill pathway from $cis$ -HSiSH to TS2 moot.

Additionally, Fig.1 also explores the reaction of H₂S with SiH₂in spite of the lack of SiH₂ observation. While this process forms a stableintermediate (H₂S-SiH₂) resulting from a dative bond between a lone pairon the sulfur and the empty $p$ orbital on the silicon as shown in related work(Grosselin & Fortenberry, 2022; Flint & Fortenberry, 2023; Palmer & Fortenberry, 2024; Firth etal., 2024), the creation of TS1 where anH₂ molecule is prepared for departure from the system is barely exothermiclying -0.9 kcal mol^-1 below the pair of dihydride starting materials. Whilethis would once more produce H₂, the effective “solvent of the universe”(Woon, 2023; Fortenberry, 2024), the barrier is likely too close to thereactants for any population to traverse this saddle. However, shocks, disks,or regions with effective temperatures at or above 100 K could begin to see somepopulation of H₂ and $trans$ -HSiSH form in this manner, but, again, thiswould require enough SiH₂ to be on hand in the first place likely reducingthe role that this reaction would play. If H₂S + SiH₂ could traverse TS1and form $trans$ -HSiSH, it would initially kick off an H₂ in the processwhich would dissipate the kinetic energy and stabilize HSiSH. However, TS2 ishigher than TS1 implying that at best this reaction would form $trans$ -HSiSH andmaybe would isomerize to $cis$ -HSiSH. It would be highly unlikely to contributeto any formation of SiS.

Finally, the reaction of SiH + H₂S $\rightarrow$ SiSH + H₂ $\rightarrow$ SiS + H₂ + H has also been computed in this work but is not shown inFig.1. The reason is that while this reaction is net exothermic, thefirst TS for creation of H₂ in the first step has an energy of -0.8 kcalmol^-1 relative to the reactants. Within the accuracies of the approach,this is too close to say that it would confidently be a submerged barrier.Additionally, the breaking of the S $-$ H bond to form the products puts the finalenergy at only -3.7 kcal/mol, again, not low enough for this to be confidentlyexothermic. Even if exothermic, such a small value would make this reactionrelatively slow and would likely be a minor contributor to formation of SiS atbest.

3.2 Spectral Characterization of $trans$ - and $cis$ -HSiSH

	$trans$ -HSiSH	$cis$ -HSiSH
$\omega_{1}$ (a’)	2700.1 (1)	2713.6 (1)
$\omega_{2}$ (a’)	2070.1 (232)	2066.8 (245)
$\omega_{3}$ (a’)	920.6 (35)	813.7 (54)
$\omega_{4}$ (a’)	637.1 (17)	666.2 (8)
$\omega_{5}$ (a”)	633.1 (1)	541.9 (15)
$\omega_{6}$ (a’)	526.4 (43)	516.6 (51)
$\nu_{1}$ (a’)	2586.4 (1)	2600.2 (1)
$\nu_{2}$ (a’)	1982.1 (234)	1987.8 (249)
$\nu_{3}$ (a’)	896.9 (34)	794.1 (50)
$\nu_{4}$ (a’)	606.5 (17)	651.0 (7)
$\nu_{5}$ (a”)	615.1 (1)	508.8 (15)
$\nu_{6}$ (a’)	511.8 (43)	499.5 (51)
Zero-point	3691.5	3610.5
$A_{e}$	4.293204	4.322487
$B_{e}$	0.243442	0.239242
$C_{e}$	0.230379	0.226694
$A_{0}$	4.259478	4.299109
$B_{0}$	0.242050	0.238045
$C_{0}$	0.228762	0.225278
$\Delta_{J}$ ( $\times 10^{-6}$ )	0.186	0.182
$\Delta_{K}$ ( $\times 10^{-6}$ )	65.255	69.300
$\Delta_{JK}$ ( $\times 10^{-6}$ )	2.125	3.065
$\delta_{J}$ ( $\times 10^{-6}$ )	0.010	0.009
$\delta_{K}$ ( $\times 10^{-6}$ )	1.464	1.783
$\Phi_{J}$ ( $\times 10^{-14}$ )	-6.772	-9.574
$\Phi_{K}$ ( $\times 10^{-7}$ )	-3.171	-1.141
$\Phi_{JK}$ ( $\times 10^{-7}$ )	-1.579	-0.761
$\Phi_{KJ}$ ( $\times 10^{-7}$ )	5.318	2.588
$\phi_{J}$ ( $\times 10^{-14}$ )	15.576	13.870
$\phi_{JK}$ ( $\times 10^{-7}$ )	17.405	12.703
$\phi_{K}$ ( $\times 10^{-7}$ )	479.536	390.488
$\mu$	0.59	1.04

^aComputed at the B3LYP/aug-cc-pVTZ level.

While the lifetimes of the HSiSH intermediates will likely be too short for astrophysical observation stemming from the reaction of SiH + SH, they are the products of SiH₂ + H₂S. Hence, the presence of either form of HSiSH could indicate some abundance of SiH₂. Even so, high-resolution laboratory experiments could be able to observe $cis$ - or $trans$ -HSiSH during its brief epochs of existence in either reaction.

As such and in order to aid in potential observation or laboratory characterization of anyreaction pathway leading to SiS as described in Fig.1, detectablespectral features must be provided for the molecular species involved.Notably, this includes $trans$ - and $cis$ -HSiSH (Table 1) which havenot been analyzed in significant detail, yet, in the literature unlike theirH₂SiS isomer (McCarthy etal., 2011). Both conformers are rotationally active,but their dipole moments are not so large as to indicate that they wouldimmediately be targets of radioastronomical searches. The $trans$ conformerdipole moment of 0.59 D is lower than the $cis$ at 1.04 D implying that thehigher-energy $cis$ conformer would be more observable akin to recent observationsof carbonic acid (Sanz-Novo etal., 2023). Neither conformer has any contribution to thedipole moment from the coordinate largely defined from the vector of the Si $-$ Sbond; all of the dipole moment vector effectively is perpendicular to it. Both conformers have verysimilar rotational constants owing to the fact that both are dominated by themuch more massive Si and S atoms regardless of the orientation of the muchsmaller hydrogen atoms. Case in point, both conformers are near prolate with $k=-0.99$ for each. The full set of principal ( $A_{0}$ , $B_{0}$ , & $C_{0}$ ), quartic ( $\Delta$ / $\delta$ ), and sextic ( $\Phi$ / $\phi$ ) rotational constants are given in Table 1.

This similarity is continued in the fundamental vibrational frequencies alsogiven in Table 1. The S-H and Si-H stretches ( $\nu_{1}$ & $\nu_{2}$ ,respectively) are within 15 cm^-1 or less of one another between isomers,and $\nu_{4}$ & $\nu_{6}$ differ between isomers by a little more. However, $\nu_{3}$ & $\nu_{5}$ are more than 100 cm^-1 apart between isomers. Theselast two modes correspond to the “symmetric” bend as well as the out-of-planebend, respectively. While not totally “symmetric,” the normal modecoordinates for $\nu_{3}$ show both hydrogen-terminated bond angles changingsimultaneously. Even though this is a free motion in the $trans$ -HSiSH isomer, the twohydrogen atoms hinder one another significantly in the $cis$ form explaining thereduction in frequency therein. This is also present in the $\nu_{5}$ $a^{\prime\prime}$ frequency where the $cis$ conformer is more hindered in its rotation.

With the launch of JWST, the IR features of such molecules may becomenotable for observation, the $\nu_{2}$ Si-H stretch most notably for theseconformers of HSiSH. This intensity of $\sim 240$ km mol^-1 is more thanthree times the antisymmetric stretch in water giving it a large transitiondipole making it potentially observeable even if interstellar lifetimes of HSiSH in either conformer are relatively short. These frequencies correspond to $\sim 5.05$ $\mu$ m right at the edge ofwhat JWST’s NIRSpec instrument can observe, but first-look spectra indicatefeatures in this region and slightly beyond (Boersma etal., 2023) that are presentin JWST observations. In using IR spectra to distinguish conformers most likely to be createdin the laboratory, the $\nu_{3}$ frequencies would be the best option, again, dueto their separation, but also because they have notable intensities, in line withwhat would be expected for IR features of organic molecules.

3.3 Astrochemical Implications

While SiS is not a rare interstellar species, it is certainly not widely observed and has, thus far, primarily been identified in evolved stars (e.g. IRC+10216; Gong etal. 2017). This diatomic molecule is seen in a small selection of other locations, including massive protostars (e.g. Orion Src I; Wright etal. 2020), shock-associated molecular outflows in a few star-forming regions and protostellar sources (e.g. L1157-B1; Podio etal. 2017), and very recently in protoplanetary disks, potentially surrounding protoplanets (Law etal., 2023). SiS emission appears to be associated with shocked regions in these sources. Yet, as pointed out by Podio etal. (2017), the spatial distribution of SiS differs from that of SiO, suggesting different formation pathways. SiO is associated with the strongest shocked regions, while SiS is found offset from these locations.

This may suggest that SiS is formed in a delayed fashion from material not directly generated by the shock, but rather from a second generation of products formed from these. One such second-generation product is SiH, which according to Schilke etal. (1997) can form from the successive dehydrogenation of silane (\ceSiH4):

\ce{SiH4+H->SiH3+H2}

(8)

\ce{SiH3+H->SiH2+H2}

(9)

\ce{SiH2+H->SiH+H2}.

(10)

Reaction8 is endothermic by $\sim$ 1400 K, meaning that this can likely only proceed in the very high temperatures of the post-shocked gas. Such high-temperature chemistry, resulting in chemical abundance peaks delayed in time from the shock event itself, has been shown to be viable in chemical shock models (Burkhardt etal., 2019).

As noted in the introduction, however, the definitive presence of SiH in the interstellar medium or circ*mstellar environments has yet to be confirmed (McGuire, 2022). A tentative detection of SiH was made toward Orion-KL by Schilke etal. (2001), but further searches for the molecule by Siebert etal. (2020) failed to identify it using SOFIA data. Given the work presented here that shows SiS can be efficiently formed from SiH via Reaction11

\ce{SiH+SH->SiS+H2},

(11)

this suggests a straightforward set of observational tests that can be performed to assess the importance of this pathway. If Reaction11 is indeed dominant, then it is reasonable to expect we should be able to detect the reactants, SH and SiH, co-located with the SiS emission. Because this is likely to be in relatively compact spatial regions concentrated around shocked gas, interferometric observations are likely mandatory. The molecular outflow in Orion Src I is perhaps best-suited to this task. It is well-observed, and the spatial structure of SiS is well-constrained (Wright etal., 2020).

4 Conclusions

An additional pathway to SiS through SH + SiH (Reaction 6) is shown here to have many advantages for gas-phase chemistry: a large exothermicity, submerged barriers, and the formation of H₂ as a leaving group. While Reactions 1 through 5 certainly cannot be discounted for their roles in creation of SiS, this additional pathway may help to further explain SiS abundance in observed regions augmenting recent work (Mendoza etal., 2024).Reaction 6 (SiH + SH) is dependent upon a high enough population of SiH to be present in regions where SH is also found, but such coupling between SiS abundance and the presence of SiH would give evidence for the existence of the currently undetected SiH diatomic. Hence, if higher abundance of SiS is present, such could imply the presence of SiH if the proposed, additonal mechanism for SiS is a contributor. Orion Src I would be a logical target for further examination of the presence of SiH. Regardless, the present work is showing that this additional mechanism (Reaction 6) should be included in reaction networks where SiS is produced.

H₂S + SiH₂ likely will have little-to-no role in the formation of SiS. H₂S + SiH will have even less. Warmer or denser regions couldalter this, and the former could lead to HSiSH formation making this a possiblemolecule for future astronomical detection. Even so, H₂S + SiH₂ stillrequires the presence of the elusive SiH₂. SiH has been difficult to observesave for the closest of stars. SiH₂ would presumably be moreso. IR androtational spectral data are also provided for the HSiSH intermediate conformersin order to aid in possible experimental or observational characterization ofthese molecules and any reaction pathways in which they may participate.Microwave observation would likely favor the $cis$ conformer, but bothconformers exhibit a large intensity for the Si-H stretch in the 5 $\mu$ m range.

5 Acknowledgments

This work is supported by NASA Grant NNH22ZHA004C and by the University ofMississippi’s College of Liberal Arts. The Mississippi Center forSupercomputing Research provided the computational resources for this work andis funded in part by NSF Grant OIA-1757220. RCF would also like to acknowledge Dr.Vincent J.Esposito of the NASA Ames Research Center for useful discussions related to this work. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

References

Adler etal. (2007)Adler, T.B., Knizia, G., & Werner, H.-J. 2007, J. Chem. Phys., 127, 221106
Avery etal. (1994)Avery, L.W., Bell, M.B., Cunningham, C.T., etal. 1994, Astrophys.J., 426, 737, doi:10.1086/174110
Becke (1993)Becke, A.D. 1993, J. Chem. Phys., 98, 5648
Boersma etal. (2023)Boersma, C., Allamandola, L.J., Maragkoudakis, A., etal. 2023, Astrophys.J., 959, 74
Burkhardt etal. (2019)Burkhardt, A.M., Shingledecker, C.N., Gal, R.L., etal. 2019, TheAstrophysical Journal, 881, 32, doi:10.3847/1538-4357/ab2be8
Campanha etal. (2022)Campanha, D.R., Mendoza, E., Silva, M.X., etal. 2022, Monthly Notices ofthe Royal Astronomical Society, 515, 369, doi:10.1093/mnras/stac1647
Cernicharo, J. etal. (2021)Cernicharo, J., Agúndez, M., Cabezas, C., etal. 2021, Astron.Astrophys., 649, L15
Crawford & Schaefer III (2000)Crawford, T.D., & Schaefer III, H.F. 2000, in Reviews in ComputationalChemistry, ed. K.B. Lipkowitz & D.B. Boyd, Vol.14 (New York: Wiley),33–136
Doddipatla etal. (2021)Doddipatla, S., Galimova, G.R., Wei, H., etal. 2021, Science Advances, 7,eabd4044, doi:10.1126/sciadv.abd4044
Dunning (1989)Dunning, T.H. 1989, J. Chem. Phys., 90, 1007
Firth etal. (2024)Firth, R.A., Bell, K.M., & Fortenberry, R.C. 2024, ACS Earth Space Chem.
Flint & Fortenberry (2023)Flint, A.R., & Fortenberry, R.C. 2023, ACS Earth Space Chem., 7, 2119
Fortenberry (2021)Fortenberry, R.C. 2021, Astrophys. J., 921, 132
Fortenberry (2024)—. 2024, J. Phys. Chem. A, doi:10.1021/acs.jpca.3c07601
Fortenberry & Lee (2019)Fortenberry, R.C., & Lee, T.J. 2019, Ann. Rep. Comput. Chem., 15, 173
Fortenberry & Lee (2022)—. 2022, in Vibrational Dynamics of Molecules, ed. J.M. Bowman (Singapore:World Scientific), 235–295
Frisch etal. (2016)Frisch, M.J., Trucks, G.W., Schlegel, H.B., etal. 2016, Gaussian16Revision C.01
Gaw etal. (1991)Gaw, J.F., Willets, A., Green, W.H., & Handy, N.C. 1991, in Advances inMolecular Vibrations and Collision Dynamics, ed. J.M. Bowman & M.A. Ratner(Greenwich, Connecticut: JAI Press, Inc.), 170–185
Gong etal. (2017)Gong, Y., Henkel, C., Ott, J., etal. 2017, The Astrophysical Journal, 843,54, doi:10.3847/1538-4357/aa7853
Grosselin & Fortenberry (2022)Grosselin, D., & Fortenberry, R.C. 2022, ACS Earth Space Chem., 6, 18
Knizia etal. (2009)Knizia, G., Adler, T.B., & Werner, H.-J. 2009, J. Chem. Phys., 130, 054104
Lai etal. (2001)Lai, C.-H., Su, M.-D., & Chu, S.-Y. 2001, Int. J. Quantum Chem., 82, 14
Law etal. (2023)Law, C.J., Booth, A.S., & Öberg, K.I. 2023, The Astrophysical Journal,952, L19, doi:10.3847/2041-8213/acdfd0
Lee etal. (1988)Lee, C., Yang, W.T., & Parr, R.G. 1988, Phys. Rev. B., 37, 785
McCarthy etal. (2011)McCarthy, M.C., Gottlieb, C.A., Thaddeus, P., Thorwirth, S., & Gauss, J.2011, J. Chem. Phys., 134, 034306
McGuire (2022)McGuire, B.A. 2022, The Astrophysical Journal Supplement Series, 259, 30,doi:10.3847/1538-4365/ac2a48
Mendoza etal. (2024)Mendoza, E., Costa, S. F.M., Carvajal, M., etal. 2024, New SiS destructionand formation routes via neutral-neutral reactions and their fundamental rolein interstellar clouds at low and high metallicity values.https://arxiv.org/abs/2404.07406
Mills (1972)Mills, I.M. 1972, in Molecular Spectroscopy - Modern Research, ed. K.N. Rao& C.W. Mathews (New York: Academic Press), 115–140
Morris etal. (1975)Morris, M., Gilmore, W., Palmer, P., Turner, B.E., & Zuckerman, B. 1975,Astrophys. J., 199, L47
Neufeld etal. (2012)Neufeld, D.A., Falgarone, E., Gerin, M., etal. 2012, Astron. Astrophys.,542, L6
Paiva etal. (2018)Paiva, M. A.M., Lefloch, B., & Galvão, B. R.L. 2018, Monthly Notices of theRoyal Astronomical Society, 481, 1858, doi:10.1093/mnras/sty2382
Palmer & Fortenberry (2024)Palmer, C.Z., & Fortenberry, R.C. 2024, Astrophys. J.
Papousek & Aliev (1982)Papousek, D., & Aliev, M.R. 1982, Molecular Vibration-Rotation Spectra(Amsterdam: Elsevier)
Peterson etal. (2008)Peterson, K.A., Adler, T.B., & Werner, H.-J. 2008, J. Chem. Phys., 128,084102
Podio etal. (2017)Podio, L., Codella, C., Lefloch, B., etal. 2017, Monthly Notices of theRoyal Astronomical Society: Letters, 470, L16, doi:10.1093/mnrasl/slx068
Raghavachari etal. (1989)Raghavachari, K., Trucks, G.W., Pople, J.A., & Head-Gordon, M. 1989, Chem.Phys. Lett., 157, 479
Rosi etal. (2018)Rosi, M., Mancini, L., Skouteris, D., etal. 2018, Chemical Physics Letters,695, 87, doi:10.1016/j.cplett.2018.01.053
Sanz-Novo etal. (2023)Sanz-Novo, M., Rivilla, V.M., Jiménez-Serra, I., etal. 2023, Astrophys.J., 950, 3
Schilke etal. (2001)Schilke, P., Benford, D.J., Hunter, T.R., Lis, D.C., & Phillips, T.G.2001, The Astrophysical Journal Supplement Series, 132, 281,doi:10.1086/318951
Schilke etal. (1997)Schilke, P., Walmsley, C.M., Pineaudes Forets, G., & Flower, D.R. 1997,Astronomy and Astrophysics, 321, 293.https://ui.adsabs.harvard.edu/abs/1997A&A...321..293S
Shavitt & Bartlett (2009)Shavitt, I., & Bartlett, R.J. 2009, Many-Body Methods in Chemistry andPhysics: MBPT and Coupled-Cluster Theory (Cambridge: Cambridge UniversityPress)
Siebert etal. (2020)Siebert, M.A., Simon, I., Shingledecker, C.N., etal. 2020, TheAstrophysical Journal, 901, 22, doi:10.3847/1538-4357/abac0e
Thaddeus etal. (1972)Thaddeus, P., Kutner, M.L., Penzias, A.A., Wilson, R.W., & Jefferts, K.B.1972, Astrophys. J., 176, L73
Watrous etal. (2021)Watrous, A.G., Westbrook, B.R., & Fortenberry, R.C. 2021, J. Phys. Chem. A,125, 10532
Watson (1977)Watson, J. K.G. 1977, in Vibrational Spectra and Structure, ed. J.R. During(Amsterdam: Elsevier), 1–89
Werner etal. (2012)Werner, H.-J., Knowles, P.J., Knizia, G., Manby, F.R., & Schütz, M.2012, WIREs Comput. Mol. Sci., 2, 242
Werner etal. (2022)Werner, H.-J., Knowles, P.J., Knizia, G., etal. 2022
Westbrook & Fortenberry (2023)Westbrook, B.R., & Fortenberry, R.C. 2023, J. Chem. Theory Comput., 19, 2606
Willacy & Cherchneff (1998)Willacy, K., & Cherchneff, I. 1998, Astronomy and Astrophysics, 330, 676.https://ui.adsabs.harvard.edu/abs/1998A&A...330..676W
Wöhl (1971)Wöhl, H. 1971, Sol. Phys., 16, 362, doi:10.1007/BF00162477
Woon (2023)Woon, D.E. 2023, Mon. Not. Royal Astron. Soc., 527, 1357,doi:10.1093/mnras/stad3242
Wright etal. (2020)Wright, M., Plambeck, R., Hirota, T., etal. 2020, The Astrophysical Journal,889, 155, doi:10.3847/1538-4357/ab5864
Yang etal. (1986)Yang, W.T., Parr, R.G., & Lee, C.T. 1986, Phys. Rev. A, 34, 4586
Yurchenko etal. (2017)Yurchenko, S.N., Sinden, F., Lodi, L., etal. 2017, Mon. Not. Royal Astron.Soc., 473, 5324, doi:10.1093/mnras/stx2738
Zanchet etal. (2018)Zanchet, A., Roncero, O., Agúndez, M., & Cernicharo, J. 2018, TheAstrophysical Journal, 862, 38, doi:10.3847/1538-4357/aaccff