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<journal-id journal-id-type="publisher-id">Front. Chem.</journal-id>
<journal-title>Frontiers in Chemistry</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Chem.</abbrev-journal-title>
<issn pub-type="epub">2296-2646</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
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<article-id pub-id-type="publisher-id">1615586</article-id>
<article-id pub-id-type="doi">10.3389/fchem.2025.1615586</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Chemistry</subject>
<subj-group>
<subject>Original Research</subject>
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</article-categories>
<title-group>
<article-title>Computational prediction for the formation of amides and thioamides in the gas phase interstellar medium</article-title>
<alt-title alt-title-type="left-running-head">Akbar Ali and Thripati</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fchem.2025.1615586">10.3389/fchem.2025.1615586</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Akbar Ali</surname>
<given-names>Mohamad</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
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<contrib contrib-type="author">
<name>
<surname>Thripati</surname>
<given-names>Sorakayala</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
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<xref ref-type="aff" rid="aff2">
<sup>2</sup>
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<aff id="aff1">
<sup>1</sup>
<institution>Department of Chemistry</institution>, <institution>Khalifa University of Science and Technology</institution>, <addr-line>Abu Dhabi</addr-line>, <country>United Arab Emirates</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Center for Catalysis and Separations</institution>, <institution>Khalifa University of Science and Technology</institution>, <addr-line>Abu Dhabi</addr-line>, <country>United Arab Emirates</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/426903/overview">Leonardo Bernasconi</ext-link>, University of Pittsburgh, United States</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/344057/overview">Georgios Papamokos</ext-link>, University of Ioannina, Greece</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2640778/overview">Steven Maley</ext-link>, Wilfrid Laurier University, Canada</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Mohamad Akbar Ali, <email>akbar.mohamad@ku.ac.ae</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>30</day>
<month>06</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>13</volume>
<elocation-id>1615586</elocation-id>
<history>
<date date-type="received">
<day>21</day>
<month>04</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>04</day>
<month>06</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2025 Akbar Ali and Thripati.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Akbar Ali and Thripati</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Amino acids and amide bonds (&#x2212;C(O)&#x2212;NH&#x2212;) are the essential components of proteins, which serve as the foundation of life on Earth. As a result, molecules containing peptide bonds are of great interest in studies related to the origin of life and are central to both terrestrial and prebiotic chemistry. Despite this, our understanding of how nitrogen-containing compounds like formamide and urea, along with their sulfur analogs thioformamide and thiourea, form in the cold interstellar medium (ISM) remains incomplete. The chemistry underlying their formation is largely elusive, making the elucidation of their mechanism in the ISM and EA a topic of ongoing interest. This study employs <italic>ab initio</italic>//density functional theory (DFT) calculations to predict the possible formation routes of amides and thioamides. The rate constants (<italic>k</italic>) for barrierless reactions were determined using statistical rate theory, such as microcanonical variational transition state theory (&#xb5;VTST) and Rice&#x2013;Ramsperger&#x2013;Kassel&#x2013;Marcus (RRKM)/master equation (ME) simulations, to understand their kinetic behavior. Using basic interstellar precursors&#x2014;CO, CS, NH<sub>2</sub>, H<sub>2</sub>, and NH<sub>3</sub>&#x2014;we assessed gas-phase formation routes for amides and thioamides. The data reveal that thioamides (HCSNH<sub>2</sub>, NH<sub>2</sub>CSNH<sub>2</sub>) may form under ISM conditions, while amides (HCONH<sub>2</sub>, NH<sub>2</sub>CONH<sub>2</sub>) are less likely due to their relatively high energy barriers (&#x3e;5&#xa0;kcal/mol). In this work, we suggest the potential detection of four new molecules in ISM environments based on enthalpy and rate constant calculations: (i) &#x00B7;CSNH<sub>2</sub>, (ii) HCSN&#x00B7;H, (iii) HCSNH<sub>2</sub>, and (iv) NH<sub>2</sub>CSNH<sub>2</sub>. Furthermore, organosulfur-bearing molecules are identified as potential precursors to iron-sulfide grains and astrobiologically significant compounds, such as the amino acids methionine and cysteine. Understanding these mechanisms is crucial for linking the chemistries of carbon, nitrogen, oxygen, and sulfur in deep space, thereby expanding our knowledge of the sulfur cycle within the Galaxy.</p>
</abstract>
<abstract abstract-type="graphical">
<title>Graphical Abstract</title>
<p>
<graphic xlink:href="FCHEM_fchem-2025-1615586_wc_abs.tif">
<alt-text content-type="machine-generated">Diagram illustrating molecular structures in a starry background labeled &#x201C;Cold Interstellar Medium.&#x201D;; Carbon sulfide combines with another molecule to form thioformamide and thiourea, showing chemical reactions with white arrows indicating the transformation pathways.</alt-text>
</graphic>
</p>
</abstract>
<kwd-group>
<kwd>astrochemistry</kwd>
<kwd>interstellar chemical reactions</kwd>
<kwd>reactive intermediates</kwd>
<kwd>amino acids</kwd>
<kwd>peptide bonds</kwd>
<kwd>thioamides</kwd>
<kwd>
<italic>ab initio</italic>
</kwd>
</kwd-group>
<contract-sponsor id="cn001">Khalifa University of Science, Technology and Research<named-content content-type="fundref-id">10.13039/501100004070</named-content>
</contract-sponsor>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Theoretical and Computational Chemistry</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>The formation of unknown and complex chemical species in the interstellar and circumstellar envelopes (CSEs) has contributed to the limited exploration of gas-phase astrochemical compounds. More than 300 molecules have been observed in the interstellar medium (ISM), with nitrogen and sulfur-bearing species accounting for a notable portion, around 96 and 33, respectively. (<xref ref-type="bibr" rid="B64">Koln Database, 2024</xref>; <xref ref-type="bibr" rid="B112">Woon, 2004</xref>). As key components of proteins, amino acids and peptide linkages (&#x2212;C(O)&#x2212;NH&#x2212;) are integral to terrestrial life and have become focal points in studies of prebiotic and biochemical evolution, (<xref ref-type="bibr" rid="B32">Damodaran and Parkin, 2017</xref>; <xref ref-type="bibr" rid="B43">Frenkel-Pinter et al., 2020</xref>; <xref ref-type="bibr" rid="B14">Awata et al., 2020</xref>; <xref ref-type="bibr" rid="B92">Ruiz-Mirazo et al., 2014</xref>; <xref ref-type="bibr" rid="B110">Wieland and Bodanszky, 2012</xref>), and have garnered significant attention in terrestrial and prebiotic chemistry. (<xref ref-type="bibr" rid="B66">Kubyshkin and Budisa, 2019</xref>; <xref ref-type="bibr" rid="B70">Ma, 2014</xref>; <xref ref-type="bibr" rid="B34">Das, 2022</xref>; <xref ref-type="bibr" rid="B47">Gomes and Rautureau, 2021</xref>; <xref ref-type="bibr" rid="B61">Kerkeni and Simmie, 2023</xref>; <xref ref-type="bibr" rid="B69">Ligterink et al., 2022</xref>). Despite the lack of confirmed amino acid detections in the ISM remains unconfirmed, several peptide-containing molecules have already been identified.</p>
<p>Peptide-like molecules, such as formamide (NH<sub>2</sub>CHO) (<xref ref-type="bibr" rid="B91">Rubin et al., 1971</xref>), urea [NH<sub>2</sub>C(O)NH<sub>2</sub>] (<xref ref-type="bibr" rid="B23">Belloche et al., 2019</xref>) acetamide (CH<sub>3</sub>CONH<sub>2</sub>) (<xref ref-type="bibr" rid="B55">Hollis et al., 2006</xref>), N-methylformamide (CH<sub>3</sub>NHCHO) (<xref ref-type="bibr" rid="B24">Belloche et al., 2017</xref>) and propionamide (C<sub>2</sub>H<sub>5</sub>CONH<sub>2</sub>) (<xref ref-type="bibr" rid="B68">Li et al., 2021</xref>) have been tentatively observed. Such observations indicate that peptide-containing species may be more prevalent in space than previously thought, indicating their relevance to prebiotic chemistry and life&#x2019;s origins. Some of these molecules serve as precursors for the formation of adenine, guanine, cytosine, and uracil. Additionally, compounds such as urea and cyanoacetylene are promising candidates as the reactants for prebiotic cytosine synthesis.</p>
<p>Formamide, an important building block of life, was the first peptide-like molecule detected in space, as reported by Rubin et al. in Sagittarius B2. (<xref ref-type="bibr" rid="B91">Rubin et al., 1971</xref>). Despite its widespread presence in the ISM, the formation of interstellar complex organic molecules (iCOMs) like formamide remains an active area of research. Various experiments have sought to elucidate how NH<sub>2</sub>CHO forms, considering mechanisms occurring in the gas phase as well as on interstellar grain surfaces. (<xref ref-type="bibr" rid="B54">Herbst and Van Dishoeck, 2009</xref>; <xref ref-type="bibr" rid="B27">Charnley et al., 1992</xref>; <xref ref-type="bibr" rid="B16">Balucani et al., 2015</xref>; <xref ref-type="bibr" rid="B106">Vasyunin and Herbst, 2013</xref>; <xref ref-type="bibr" rid="B45">Garrod and Herbst, 2006</xref>; <xref ref-type="bibr" rid="B75">&#xd6;berg et al., 2009</xref>; <xref ref-type="bibr" rid="B90">Ruaud et al., 2015</xref>; <xref ref-type="bibr" rid="B109">Watanabe and Kouchi, 2002</xref>; <xref ref-type="bibr" rid="B88">Rimola et al., 2014</xref>). Hubbard et al. were among the first to suggest that photolysis of CO and NH<sub>3</sub> under Martian atmospheric conditions could lead to NH<sub>2</sub>CHO formation. (<xref ref-type="bibr" rid="B56">Hubbard et al., 1975</xref>; <xref ref-type="bibr" rid="B41">Ferris et al., 1974</xref>; <xref ref-type="bibr" rid="B59">Kakumoto et al., 1985</xref>; <xref ref-type="bibr" rid="B58">Jones et al., 2011</xref>; <xref ref-type="bibr" rid="B71">Mason et al., 2014</xref>; <xref ref-type="bibr" rid="B60">Ka&#x148;uchov&#xe1; et al., 2016</xref>; <xref ref-type="bibr" rid="B25">Bredeh&#xf6;ft et al., 2017</xref>; <xref ref-type="bibr" rid="B38">Dulieu et al., 2019</xref>). Kakumoto et al. analyzed the formation of NH<sub>2</sub>CHO in their shock tube experiments. (<xref ref-type="bibr" rid="B59">Kakumoto et al., 1985</xref>). Kaiser and co-workers (<xref ref-type="bibr" rid="B58">Jones et al., 2011</xref>) performed surface studies on formamide formation, while Mason et al. utilized electron-induced irradiation of CH<sub>3</sub>OH and NH<sub>3</sub>. (<xref ref-type="bibr" rid="B71">Mason et al., 2014</xref>). Strazzulla&#x2019;s team carried out irradiation experiments on frozen gas mixtures (<xref ref-type="bibr" rid="B60">Ka&#x148;uchov&#xe1; et al., 2016</xref>), and <xref ref-type="bibr" rid="B25">Bredeh&#xf6;ft et al. (2017)</xref> explored the formation of NH<sub>2</sub>CHO from mixtures carbon monoxide and ammonia. Dulieu and colleagues, on the other hand, investigated the simultaneous hydrogenation of nitric acid (HNO<sub>3</sub>) and formaldehyde (CH<sub>2</sub>O). (<xref ref-type="bibr" rid="B38">Dulieu et al., 2019</xref>).</p>
<p>The use of quantum chemical techniques has become widespread in conjunction with experimental studies, providing crucial mechanistic insights. (<xref ref-type="bibr" rid="B76">Oie et al., 1982</xref>; <xref ref-type="bibr" rid="B33">Darla and Sitha, 2019</xref>; <xref ref-type="bibr" rid="B96">Spezia et al., 2016</xref>; <xref ref-type="bibr" rid="B87">Rimola et al., 2018</xref>; <xref ref-type="bibr" rid="B107">Vazart et al., 2016</xref>; <xref ref-type="bibr" rid="B21">Barone et al., 2015</xref>). Earlier work has highlighted the formation of NH<sub>2</sub>CO, driven by reactions between closed-shell species, including HCOOH and NH<sub>3.</sub>
<sup>36</sup> Other studies, such as those by <xref ref-type="bibr" rid="B33">Darla and Sitha (2019)</xref>, proposed a reaction between CO and NH<sub>3</sub>, while Spezia et al. (<xref ref-type="bibr" rid="B96">Spezia et al., 2016</xref>) investigated the reaction of HCHO and ammonium hydroxide (NH<sub>4</sub>OH). <xref ref-type="bibr" rid="B87">Rimola et al. (2018)</xref> investigated various formation pathways of formamide (NH<sub>2</sub>CHO) on interstellar ices. They studied the radical&#x2013;radical recombination reaction HCO (ice) &#x2b; NH<sub>2</sub> (ice) &#x2192; HCONH<sub>2</sub> (ice), which was found to be exothermic and barrierless, suggesting it can proceed efficiently even under the cold conditions of the interstellar medium. Their study employed a cluster model consisting of 33 H<sub>2</sub>O molecules to simulate water-rich amorphous ices and evaluate the atomistic mechanisms leading to formamide formation. Some theoretical works have employed a combination of radical molecule approaches. For example, Rimola et al. (<xref ref-type="bibr" rid="B87">Rimola et al., 2018</xref>) studied CN radical &#x2b; H<sub>2</sub>O, while <xref ref-type="bibr" rid="B107">Vazart et al. (2016)</xref> and <xref ref-type="bibr" rid="B21">Barone et al. (2015)</xref> examined NH<sub>2</sub> radicals &#x2b; HCHO reaction. In another theoretical work, <xref ref-type="bibr" rid="B40">Enrique-Romero et al. (2019)</xref>, explored radical-radical reactions, such as those between HCO and NH<sub>2</sub>, which suggested the formation of NH<sub>2</sub>CHO. Additionally, some studies investigated reactions between ionic compounds, such as NH<sub>4</sub>
<sup>&#x2b;</sup> and NH<sub>2</sub>OH<sup>&#x2b;</sup> and metal ions, mediated with HCHO to form NH<sub>2</sub>CO. (<xref ref-type="bibr" rid="B84">Redondo et al., 2014</xref>; <xref ref-type="bibr" rid="B83">Redondo et al., 2013</xref>; <xref ref-type="bibr" rid="B102">Thripati et al., 2021</xref>).</p>
<p>Urea is another important compound with the unique characteristic of having two N&#x2013;C bonds. It plays a significant role in the origin of life and serves as a precursor for the production of cytosine and uracil. (<xref ref-type="bibr" rid="B95">Shapiro, 1999</xref>; <xref ref-type="bibr" rid="B72">Menor-Salv&#xe1;n, 2018</xref>; <xref ref-type="bibr" rid="B93">Saladino et al., 2004</xref>; <xref ref-type="bibr" rid="B89">Robertson and Miller, 1995</xref>; <xref ref-type="bibr" rid="B108">Wang and Bowie, 2012</xref>). Despite numerous studies on urea, many uncertainties remain regarding its formation in ISM. Previous laboratory and theoretical studies have suggested isocyanic acid (HNCO) as a possible precursor to urea. (<xref ref-type="bibr" rid="B82">Raunier et al., 2004</xref>). <xref ref-type="bibr" rid="B82">Raunier et al. (2004)</xref> were the first to propose that HNCO could serve as a building block for urea (NH<sub>2</sub>CONH<sub>2</sub>) by subjecting pure HNCO ice to vacuum ultraviolet irradiation at 10&#xa0;K, which resulted in the formation of ammonium cyanate (NH<sub>4</sub>
<sup>&#x2b;</sup>, OCN<sup>&#x2212;</sup>), NH<sub>2</sub>COH, and NH<sub>2</sub>CONH<sub>2</sub>. Another hypothesis, reported by <xref ref-type="bibr" rid="B42">F&#xf6;rstel et al. (2016)</xref>, suggested that NH<sub>2</sub>COH could be a precursor to NH<sub>2</sub>CONH<sub>2</sub>, in which NH<sub>3</sub>:CO ices were initially irradiated first to produce formamide and urea. More recently, <xref ref-type="bibr" rid="B79">Perrero and Rimola (2024)</xref> studied the reaction between HNCO and NH<sub>3</sub> on an 18 H<sub>2</sub>O molecule ice cluster model, which mimics interstellar ice mantles.</p>
<p>Despite these prior studies, the formation pathways of N-bearing molecules such as formamide and urea (amides) through chemical reactions remain largely unknown. However, the formation of S-bearing molecules, thioformamide (NH<sub>2</sub>CSH) and thiourea (thioamides, NH<sub>2</sub>CSNH<sub>2</sub>), is entirely unexplored and has yet to be actively investigated. Currently, no known chemical reactions have been identified that can produce thioformamide and thiourea in the ISM.</p>
<p>Carbon monosulfide (CS) was the first sulfur-containing molecule discovered in the ISM, identified in 1971. From a biochemical perspective, sulfur, along with H, C, O, N, and P, is considered one of the six elements for the foundation of life. (<xref ref-type="bibr" rid="B13">Aversa et al., 2016</xref>; <xref ref-type="bibr" rid="B44">Frieden, 1972</xref>; <xref ref-type="bibr" rid="B111">Williams, 2002</xref>; <xref ref-type="bibr" rid="B35">Da Silva and Williams, 2001</xref>; <xref ref-type="bibr" rid="B94">Sanz-Novo et al., 2024</xref>). It is found in various biomolecules, including nucleic acids, amino acids, vitamins and sugars. As suggested in the literature, two sulfur-containing amino acids -methionine (C<sub>5</sub>H<sub>11</sub>NO<sub>2</sub>S) and cysteine (C<sub>3</sub>H<sub>7</sub>NO<sub>2</sub>S)- play vital roles in protein synthesis. (<xref ref-type="bibr" rid="B1">Ahmad et al., 2017</xref>; <xref ref-type="bibr" rid="B29">Colovic et al., 2018</xref>; <xref ref-type="bibr" rid="B97">Stipanuk, 2020</xref>; <xref ref-type="bibr" rid="B36">Doddipatla et al., 2020</xref>). Additionally, organosulfur-bearing molecules are considered potential precursors to iron-sulfide grains. (<xref ref-type="bibr" rid="B36">Doddipatla et al., 2020</xref>).</p>
<p>The purpose of this study is to investigate how formamides (formamide and urea) and thioamides (thioformamide and thiourea) can form under interstellar conditions. In this context, several intriguing questions arise:<list list-type="simple">
<list-item>
<p>(i) How do these precursors (CO, NH<sub>2</sub>, NH<sub>3</sub>, and H<sub>2</sub>) undergo feasible pathways to form formamide and urea?</p>
</list-item>
<list-item>
<p>(ii) Can these precursors (CS, NH<sub>2</sub>, NH<sub>3</sub>, and H<sub>2</sub>) lead to the formation of thioformamide and thiourea ?</p>
</list-item>
<list-item>
<p>(iii) What are the differences in reactivity between CO and CS with the NH<sub>2</sub> radical, and most importantly, how feasible are these interstellar chemical reactions?</p>
</list-item>
</list>
</p>
<p>In <xref ref-type="scheme" rid="sch1">Scheme 1</xref> below, we explore the possibility of interstellar gas-phase formation of amides (HCONH<sub>2</sub>, NH<sub>2</sub>CONH<sub>2</sub>) and formation of thioamides (HCSNH<sub>2</sub>, NH<sub>2</sub>CSNH<sub>2</sub>) through interaction between CO, CS, NH<sub>3</sub>, and H<sub>2</sub> and the NH<sub>2</sub> radical.</p>
<fig id="sch1" position="float">
<label>SCHEME 1</label>
<caption>
<p>Proposed formation pathways for <bold>(a)</bold> amides (HCONH<sub>2</sub> and NH<sub>2</sub>CONH<sub>2</sub>) (<xref ref-type="bibr" rid="B91">Rubin et al., 1971</xref>; <xref ref-type="bibr" rid="B23">Belloche et al., 2019</xref>) and <bold>(b)</bold> thioamides (HCSNH<sub>2</sub> and NH<sub>2</sub>CSNH<sub>2</sub>) from plausible interstellar precursors&#x2014;CO, CS, NH<sub>2</sub>, H<sub>2</sub>, and NH<sub>3</sub>. (<xref ref-type="bibr" rid="B85">Rickard et al., 1975</xref>; <xref ref-type="bibr" rid="B51">Henkel and Bally, 1985</xref>; <xref ref-type="bibr" rid="B105">van Dishoeck et al., 1993</xref>; <xref ref-type="bibr" rid="B98">Thompson et al., 1978</xref>; <xref ref-type="bibr" rid="B28">Cheung et al., 1968</xref>; <xref ref-type="bibr" rid="B74">Motiyenko et al., 2020</xref>).</p>
</caption>
<graphic xlink:href="FCHEM_fchem-2025-1615586_wc_sch1.tif">
<alt-text content-type="machine-generated">illustrates the formation of amides and thioamides. Panel (a) shows carbon monoxide reacting with an amine group to form formamide and urea, aided by hydrogen gas or ammonia. Panel (b) depicts carbon sulfide reacting with an amine group to produce thioformamide and thiourea, also involving hydrogen gas or ammonia.</alt-text>
</graphic>
</fig>
<p>To investigate the formation of NH<sub>2</sub>CO, NH<sub>2</sub>CONH<sub>2</sub>, NH<sub>2</sub>CS, and NH<sub>2</sub>CSNH<sub>2</sub>, we employed <italic>ab initio</italic>//Density Functional Theory (DFT) calculations in combination with statistical rate theory-based predictions. This study explores an alternative stepwise mechanism involving the reaction of NH<sub>2</sub> with CO, followed by H<sub>2</sub> addition&#x2014;a pathway that may be relevant under conditions where CO is abundant and NH<sub>2</sub> is produced via ammonia photodissociation. For thioformamide and thiourea, the proposed mechanisms&#x2014;based on NH<sub>2</sub> &#x2b; CS reactions&#x2014;represent, to our knowledge, the first detailed gas-phase pathways suggested for these species under interstellar conditions. Our analysis includes structural, energetic, and kinetic details, providing key chemical insights. Finally, we discuss the astrochemical significance, of these findings and present our conclusions.</p>
</sec>
<sec id="s2">
<title>2 Computational details</title>
<sec id="s2-1">
<title>2.1 <italic>Ab initio//DFT</italic> calculations</title>
<p>Gaussian 16 quantum chemical software was employed for all the <italic>ab initio</italic>//DFT calculations. (<xref ref-type="bibr" rid="B46">Gaussian 16 et al., 2016</xref>). We employed the unrestricted double-hybrid density functional method, specifically the B2PLYP functional, (<xref ref-type="bibr" rid="B49">Grimme, 2006</xref>), with augmented triple-zeta basis sets (<xref ref-type="bibr" rid="B39">Dunning, 1989</xref>) (aug-cc-pVTZ and aug-cc-pV (T&#x2b;d)Z, the latter used only for the sulfur system) to optimize the structures of reactants, pre-reactive complex, intermediates, transition states, and products. The B2PLYP functional was supplemented with Grimme&#x2019;s DFT-D3 zero-damping correction to address long-range London dispersion interactions. (<xref ref-type="bibr" rid="B50">Grimme et al., 2011</xref>). The B2PLYP-D3 double-hybrid functional is particularly well-suited for investigating noncovalent interactions in transition states, intermediates, and post-intermediates, especially in systems involving hydrogen bonding, as suggested in the earlier study. (<xref ref-type="bibr" rid="B107">Vazart et al., 2016</xref>). Several research groups have successfully used this method to predict the astrochemical formation of nitrogen-containing compounds such as methylamine and formyl cyanide<sup>.</sup> (<xref ref-type="bibr" rid="B103">Tonolo et al., 2020</xref>; <xref ref-type="bibr" rid="B80">Puzzarini et al., 2020</xref>). To confirm the nature of the saddle point, frequency analysis was performed, revealing a single imaginary frequency for the transition states and all positive frequencies for the reactants, intermediates and products. Vibrational analysis was performed for each optimized species to include the zero-point vibrational energy (ZPE). Energy accuracy was improved by performing single-point calculations at the CCSD(T) (<xref ref-type="bibr" rid="B81">Raghavachari et al., 1989</xref>)/aug-cc-pVTZ basis set, using geometries optimized at the B2PLYP-D3 level. The combination of CCSD(T) and B2PLYP-D3-optimized methods has been used previously, achieving accuracy within &#x223c;1&#xa0;kcal/mol. (<xref ref-type="bibr" rid="B15">Ballotta et al., 2021</xref>). The zero-point energies (ZPEs) obtained using the B2PLYP-D3 functional are suitable for interstellar medium (ISM) chemistry; however, there may be an uncertainty of 1&#x2013;2&#xa0;kcal/mol in the computed energies, which can affect predictions for low-temperature kinetics. B2PLYP-D3 was selected over more conventional hybrid functionals because it offers a consistent and well-established balance between accuracy and computational cost, particularly for systems where both dynamical and static correlation are non-negligible. (<xref ref-type="bibr" rid="B49">Grimme, 2006</xref>; <xref ref-type="bibr" rid="B39">Dunning, 1989</xref>). The double-hybrid nature of B2PLYP, which includes a perturbative second-order correlation component, improves the description of subtle electronic effects that are critical for accurately modeling low-frequency vibrational modes and tunneling pathways. Furthermore, B2PLYP-D3 has demonstrated superior performance in reproducing vibrational frequencies and barrier heights in similar systems compared to standard hybrid functionals, especially in the presence of non-covalent interactions and anharmonic contributions. (<xref ref-type="bibr" rid="B107">Vazart et al., 2016</xref>; <xref ref-type="bibr" rid="B21">Barone et al., 2015</xref>). This aligns with the objectives of our study, which emphasize the accurate characterization of low-frequency vibrational modes associated with quantum tunneling. Earlier work by Papamokos and Demetropoulos supports the use of the hybrid functional PW91XC for amide systems and addresses low-frequency vibrational issues, as discussed in their study. (<xref ref-type="bibr" rid="B77">Papamokos and Demetropoulos, 2004a</xref>; <xref ref-type="bibr" rid="B78">Papamokos and Demetropoulos, 2004b</xref>). The increased accuracy offered by double-hybrid methods such as B2PLYP-D3 makes them particularly suitable for the current investigation, which focuses on low-temperature tunneling-relevant vibrational features and dispersion corrected zero-point energies. Our choice thus reflects a targeted effort to improve the reliability of both geometries and harmonic frequencies in a regime where conventional hybrid functionals may not be sufficiently accurate.</p>
<p>To investigate how the single-reference wave function qualitatively contributes, T1 diagnostic calculations were done at the CCSD(T)/aug-cc-pVTZ level. The resulting T1 diagnostic values were &#x2264;0.03, which is within the accepted range (&#x2264;0.04) for a single-reference wave function. (<xref ref-type="bibr" rid="B86">Rienstra-Kiracofe et al. 2000</xref>). To evaluate spin contamination, the spin expectation value &#x27e8;S<sup>2</sup>&#x27e9; was calculated, yielding values in the range of &#x223c;0.75&#x2013;0.77, indicating that spin contamination is negligible.</p>
</sec>
<sec id="s2-2">
<title>2.2 Chemical kinetics calculations</title>
<p>All chemical kinetics calculations were performed using the MultiWell program suite. (<xref ref-type="bibr" rid="B17">Barker, 2001</xref>; <xref ref-type="bibr" rid="B18">Barker, 2009</xref>; <xref ref-type="bibr" rid="B19">Barker et al., 2016</xref>). The rate constants were calculated using RRKM/ME theory, where the energy- and angular momentum-dependent unimolecular rate coefficient, <italic>k(E, J)</italic> (<xref ref-type="bibr" rid="B17">Barker, 2001</xref>; <xref ref-type="bibr" rid="B18">Barker, 2009</xref>; <xref ref-type="bibr" rid="B19">Barker et al., 2016</xref>) is given by <xref ref-type="disp-formula" rid="e1">Equation 1</xref>:<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>J</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mi>L</mml:mi>
<mml:mo>&#x2260;</mml:mo>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mi>G</mml:mi>
<mml:mo>&#x2260;</mml:mo>
</mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>J</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mi>J</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3c1;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>J</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
</p>
<p>Here, <italic>L</italic>
<sup>
<italic>&#x2b;</italic>
</sup> is the reaction path degeneracy, <italic>h</italic> is Planck&#x2019;s constant, <italic>&#x3c1;(E,J)</italic> is the rovibrational density of states of the reactant, <italic>G</italic>
<sup>
<italic>&#x2b;</italic>
</sup>
<italic>(E - E</italic>
<sub>
<italic>0</italic>
</sub>
<italic>,J, J)</italic> is the transition state sum of states, and <italic>E</italic>
<sub>
<italic>0</italic>
</sub>
<italic>,J</italic> represents the critical energy threshold for the reaction, which is angular momentum-dependent. The reaction path degeneracy was determined from symmetry considerations and optical isomer counts. The DenSum module within MultiWell was used to compute these sums and densities of states as discussed in the MultiWell manual. (<xref ref-type="bibr" rid="B17">Barker, 2001</xref>; <xref ref-type="bibr" rid="B18">Barker, 2009</xref>; <xref ref-type="bibr" rid="B19">Barker et al., 2016</xref>). For efficiency, the two-dimensional terms were integrated over angular momentum to yield one-dimensional forms (<xref ref-type="disp-formula" rid="e1">Equations 2</xref>, <xref ref-type="disp-formula" rid="e3">3</xref>):<disp-formula id="e2">
<mml:math id="m2">
<mml:mrow>
<mml:msup>
<mml:mi>G</mml:mi>
<mml:mo>&#x2260;</mml:mo>
</mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>J</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>J</mml:mi>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:mrow>
<mml:msup>
<mml:mi>G</mml:mi>
<mml:mo>&#x2260;</mml:mo>
</mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>J</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mi>J</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
<disp-formula id="e3">
<mml:math id="m3">
<mml:mrow>
<mml:mi>&#x3c1;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>J</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>J</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>J</mml:mi>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>J</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
</p>
<p>The 1-D rate constants <italic>k</italic>(<italic>E</italic>) were calculated as given in <xref ref-type="disp-formula" rid="e4">Equation 4</xref>:<disp-formula id="e4">
<mml:math id="m4">
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mi>L</mml:mi>
<mml:mo>&#x2260;</mml:mo>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mi>G</mml:mi>
<mml:mo>&#x2260;</mml:mo>
</mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3c1;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>where <italic>E</italic>
<sub>
<italic>0</italic>
</sub>
<italic>,</italic>
<sub>
<italic>0</italic>
</sub> includes zero-point energy and J &#x3d; 0 centrifugal corrections. Rotational motion was modeled using the symmetric top approximation (<italic>A &#x3e; B &#x3d; C</italic>), treating the <italic>K</italic>-rotor as active and the perpendicular 2D-rotor (<italic>B &#x3d; C</italic>) as adiabatic. The rotational constants were derived from <italic>B2PLYP-D3/aug-cc-pVTZ</italic> optimized geometries and vibrational frequencies, and the Stein&#x2013;Rabinovitch version of the Beyer&#x2013;Swinehart algorithm was employed for statistical summations. To calculate the pressure-dependent rate constants, N<sub>2</sub> bath gases were used with an approximate value of the energy transfer process <inline-formula id="inf1">
<mml:math id="m5">
<mml:mrow>
<mml:mo>&#x3c;</mml:mo>
<mml:mo>&#x394;</mml:mo>
<mml:mi>E</mml:mi>
<mml:msub>
<mml:mo>&#x3e;</mml:mo>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>w</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>200</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>300</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>0.85</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> cm<sup>&#x2212;1</sup>. (<xref ref-type="bibr" rid="B5">Ali and Balaganesh, 2023</xref>) In the MultiWell software, master equation simulations utilized double arrays containing 500 elements, each representing energy intervals of 10&#xa0;cm<sup>&#x2212;1</sup>. The quasi-continuum region was modeled up to an energy limit of 85,000&#xa0;cm<sup>-1</sup>. Simulations at each specified temperature and pressure began with a chemical activation energy distribution, which is particularly suited for modeling recombination processes. A total of 10<sup>6</sup> stochastic trials were performed, with each trial simulating a time span equivalent to the average duration of 1,000 molecular collisions. The pressure-dependent forward total rate constants, k<sub>
<italic>f</italic>
</sub> for CS &#x2b; NH<sub>2</sub> reactions, have been computed using,<disp-formula id="e5">
<mml:math id="m6">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>f</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">&#x393;</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msubsup>
<mml:mi>k</mml:mi>
<mml:mi>&#x221e;</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi mathvariant="italic">PR</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>
</p>
<p>The <italic>&#x393;</italic> Eckart asymmetric tunneling (EAT) correction was applied as implemented in the MultiWell master equation (ME) code, with the tight transition state explicitly calculated, <italic>f</italic> is the fraction of the chemical reaction going back to the respective reactive species, and <inline-formula id="inf2">
<mml:math id="m7">
<mml:mrow>
<mml:msubsup>
<mml:mi>k</mml:mi>
<mml:mi>&#x221e;</mml:mi>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> is the rate constant at the high-pressure limit.</p>
<p>The chemical kinetics of the pre-reactive complex (PRC) formation CS&#x2026;.NH<sub>2</sub>, which is assumed to play an important role in ISM condition, has not been investigated. The rate constants for CS &#x2b; NH<sub>2</sub> were calculated using a combination of variational transition state theory (VTST) and &#xb5;VTST. (<xref ref-type="bibr" rid="B5">Ali and Balaganesh, 2023</xref>; <xref ref-type="bibr" rid="B12">Ali et al., 2016</xref>; <xref ref-type="bibr" rid="B6">Ali et al., 2021</xref>). The variational transition state theory (VTST) was used to calculate the rate constants as given in <xref ref-type="disp-formula" rid="e6">Equation 6</xref> and <xref ref-type="disp-formula" rid="e7">Equation 7</xref>:<disp-formula id="e6">
<mml:math id="m8">
<mml:mrow>
<mml:msup>
<mml:mi>k</mml:mi>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mi>L</mml:mi>
<mml:mo>&#x2260;</mml:mo>
</mml:msup>
<mml:mo>&#xd7;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mi>h</mml:mi>
</mml:mfrac>
<mml:mfrac>
<mml:mrow>
<mml:msubsup>
<mml:mi>Q</mml:mi>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mo>&#x2260;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mi>R</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mi mathvariant="italic">exp</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>E</mml:mi>
<mml:mi>P</mml:mi>
</mml:mrow>
</mml:msub>
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</inline-formula> is the zero-point corrected barrier height. Based on VTST calculations, &#xb5;VTST calculations were carried out as discussed in our previous work. (<xref ref-type="bibr" rid="B5">Ali and Balaganesh, 2023</xref>; <xref ref-type="bibr" rid="B12">Ali et al., 2016</xref>; <xref ref-type="bibr" rid="B6">Ali et al., 2021</xref>) The <italic>ktools</italic> module within the MultiWell program was used to perform the VTST and &#xb5;VTST calculations, as described in the MultiWell manual. (<xref ref-type="bibr" rid="B17">Barker, 2001</xref>; <xref ref-type="bibr" rid="B18">Barker, 2009</xref>; <xref ref-type="bibr" rid="B19">Barker et al., 2016</xref>) The equilibrium constant (<italic>K</italic>
<sub>
<italic>eq</italic>
</sub>) for the formation of bimolecular complexes were calculated using THERMO code as given in <xref ref-type="disp-formula" rid="e8">Equation 8</xref>:<disp-formula id="e8">
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</disp-formula>
</p>
</sec>
</sec>
<sec sec-type="results|discussion" id="s3">
<title>3 Results and discussion</title>
<p>Here, we initially highlight our computational findings on the formation of formamide, urea, thioformamide, and thiourea under interstellar conditions. Consistent with the previous work research, (<xref ref-type="bibr" rid="B102">Thripati et al., 2021</xref>; <xref ref-type="bibr" rid="B101">Thripati and Ramabhadran, 2017</xref>; <xref ref-type="bibr" rid="B48">Gopalsamy et al., 2019</xref>; <xref ref-type="bibr" rid="B99">Thripati, 2022</xref>; <xref ref-type="bibr" rid="B100">Thripati et al., 2023</xref>)<sup>,</sup> we used zero-point corrected energies rather than free energies. This approach prevents any inferences based on the predominance of Boltzmann distributions, which may not consistently hold true in all regions of the ISM. Additionally, this study references all energies, including those of minimized energy structures and transition states, relative to the energy of individual monomers when they are infinitely separated, which is considered the baseline energy of zero. Our previous investigation employed a similar paradigm, which remains valid for gas-phase processes occurring in the ISM under low-density conditions. Therefore, the negligible significance of collisional deactivation&#x2014;more relevant to solution-phase processes on Earth&#x2014;supports our selection of the zero-reference state.</p>
<sec id="s3-1">
<title>3.1 Methods validation</title>
<p>Barrier heights are important parameters for determining astrochemical reactions in the ISM. To ensure consistency with other theoretical methods, several <italic>ab initio</italic> and DFT calculations (B2PLYP-D3 (<xref ref-type="bibr" rid="B49">Grimme, 2006</xref>; <xref ref-type="bibr" rid="B50">Grimme et al., 2011</xref>), B3LYP (<xref ref-type="bibr" rid="B22">Becke, 1993</xref>; <xref ref-type="bibr" rid="B67">Lee et al., 1988</xref>), M06-2X (<xref ref-type="bibr" rid="B113">Zhao and Truhlar, 2008</xref>), and &#x3c9;B97XD (<xref ref-type="bibr" rid="B26">Chai and Head-Gordon, 2008</xref>)) were performed using the CCSD(T)/aug-cc-pVTZ//B2PLYP-D3/aug-cc-pVTZ, CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ, CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ, and CCSD(T)/aug-cc-pVTZ//&#x3c9;B97XD/aug-cc-pVTZ methods for both amide and thioamide schemes. A combination of CCSD(T) and several DFT-based optimization methods has been successfully used in our past work, showing good consistency with experimental findings for similar systems. (<xref ref-type="bibr" rid="B4">Ali and Balaganesh, 2022</xref>; <xref ref-type="bibr" rid="B7">Ali et al., 2019</xref>; <xref ref-type="bibr" rid="B8">Ali et al., 2018</xref>; <xref ref-type="bibr" rid="B3">Ali, 2020</xref>; <xref ref-type="bibr" rid="B10">Ali et al., 2022</xref>; <xref ref-type="bibr" rid="B2">Ali, 2019</xref>; <xref ref-type="bibr" rid="B11">Ali and Saswathy, 2024</xref>; <xref ref-type="bibr" rid="B9">Ali and Barker, 2015</xref>). The results in <xref ref-type="table" rid="T1">Table 1</xref> show that our calculations align with different levels of theory, with a deviation of less than 0.5&#xa0;kcal/mol for the pre-reactive complex and transition state. The energy analysis in <xref ref-type="table" rid="T1">Table 1</xref> clearly indicates that CCSD(T)//B2PLYP-D3 values are accurate compared to the other three DFT methods. As suggested in previous work, (<xref ref-type="bibr" rid="B80">Puzzarini et al., 2020</xref>), CCSD(T)//B2PLYP-D3 provides accurate energies compared to the &#x201c;Cheap&#x201d; composite method. Therefore, all minimum energy pathway (MEP) and kinetics calculations were performed at the CCSD(T)//B2PLYP-D3 level.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Comparison of the energy barriers &#x394;E<sup>&#x2260;</sup> (kcal/mol) with different level of theories on representative TSs with respect to Reactants.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Formamide and urea</th>
<th align="center">
<sup>a</sup>CCSD(T)//B2PLYP-D3</th>
<th align="center">
<sup>a</sup>CCSD(T)//&#x3c9;B97XD</th>
<th align="center">
<sup>a</sup>CCSD(T)//B3LYP</th>
<th align="center">
<sup>a</sup>CCSD(T)//M06-2X</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">TS-1</td>
<td align="center">5.5</td>
<td align="center">5.4</td>
<td align="center">5.2</td>
<td align="center">5.5</td>
</tr>
<tr>
<td align="center">TS-2</td>
<td align="center">&#x2212;0.4</td>
<td align="center">&#x2212;0.5</td>
<td align="center">&#x2212;0.6</td>
<td align="center">&#x2212;0.8</td>
</tr>
<tr>
<td align="center">TS-3</td>
<td align="center">34.2</td>
<td align="center">34.4</td>
<td align="center">34.1</td>
<td align="center">34.3</td>
</tr>
<tr>
<td align="center">TS-4</td>
<td align="center">12.1</td>
<td align="center">12.3</td>
<td align="center">12.2</td>
<td align="center">12.1</td>
</tr>
<tr>
<td align="center">TS-5</td>
<td align="center">13.4</td>
<td align="center">13.8</td>
<td align="center">13.4</td>
<td align="center">13.5</td>
</tr>
<tr>
<td align="center">TS-6</td>
<td align="center">22.1</td>
<td align="center">22.3</td>
<td align="center">21.9</td>
<td align="center">22.2</td>
</tr>
</tbody>
</table>
<table>
<thead valign="top">
<tr>
<th align="left">&#xa0;Thioforamamide and Thiourea</th>
<th align="center">
<sup>b</sup>CCSD(T)//B2PLYP-D3</th>
<th align="center">
<sup>b</sup>CCSD(T)//&#x3c9;B97XD</th>
<th align="center">
<sup>b</sup>CCSD(T)//B3LYP</th>
<th align="center">
<sup>b</sup>CCSD(T)//M06-2X</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">TS-1<sub>s</sub>
</td>
<td align="center">&#x2212;1.4</td>
<td align="center">&#x2212;1.49</td>
<td align="center">&#x2212;1.4</td>
<td align="center">&#x2212;1.7</td>
</tr>
<tr>
<td align="center">TS-2<sub>s</sub>
</td>
<td align="center">&#x2212;35.9</td>
<td align="center">&#x2212;36.2</td>
<td align="center">&#x2212;36.1</td>
<td align="center">&#x2212;36.2</td>
</tr>
<tr>
<td align="center">TS-3<sub>s</sub>
</td>
<td align="center">&#x2212;3.3</td>
<td align="center">&#x2212;3.21</td>
<td align="center">&#x2212;3.5</td>
<td align="center">&#x2212;3.4</td>
</tr>
<tr>
<td align="center">TS-4<sub>s</sub>
</td>
<td align="center">&#x2212;27.1</td>
<td align="center">&#x2212;27.4</td>
<td align="center">&#x2212;27.0</td>
<td align="center">&#x2212;27.7</td>
</tr>
<tr>
<td align="center">TS-5<sub>s</sub>
</td>
<td align="center">&#x2212;25.7</td>
<td align="center">&#x2212;25.8</td>
<td align="center">&#x2212;25.8</td>
<td align="center">&#x2212;26.1</td>
</tr>
<tr>
<td align="center">TS-6<sub>s</sub>
</td>
<td align="center">&#x2212;26.3</td>
<td align="center">&#x2212;26.2</td>
<td align="center">&#x2212;26.4</td>
<td align="center">&#x2212;26.6</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Where &#x394;E<sup>&#x2260;</sup> &#x3d; E<sub>TS</sub>&#x2013;<inline-formula id="inf6">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">E</mml:mi>
<mml:mi>&#x221e;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> separated reactants. The energy values (including zero-point corrections) are provided in kcal/mol. basis set a:aug-cc-pVTZ; b: aug-cc-pV (T&#x2b;d)Z.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>To further validate our results on the formation of PRC in the sulfur system, we employed several quantum composite methods, including CBS-QB3 (<xref ref-type="bibr" rid="B73">Montgomery et al., 2000</xref>), G4 (<xref ref-type="bibr" rid="B30">Curtiss et al., 2007</xref>), and W1BD (<xref ref-type="bibr" rid="B20">Barnes et al., 2009</xref>) methods were employed (see ESI <xref ref-type="sec" rid="s12">Supplementary Figure SI,13</xref>). These calculations indicate that our results are consistent across different levels of theory, with a difference of less than 0.5&#xa0;kcal/mol for the pre-reactive complex and transition state. Therefore, we believe the results presented in this paper are reasonably accurate for astrochemical implications.</p>
</sec>
<sec id="s3-2">
<title>3.2 Formation of amides [&#x2013;(C&#x3d;O)&#x2013;NH&#x2013;]</title>
<p>Possible reaction pathways for the formamide (Path 1 and Path 2), urea (Path 3), and protonated urea (Path 4) are shown in <xref ref-type="scheme" rid="sch2">Scheme 2</xref>.</p>
<fig id="sch2" position="float">
<label>SCHEME 2</label>
<caption>
<p>Possible reaction pathways for the formamide (Path 1 and Path 2), urea (Path 3), and protonated urea (Path 4).</p>
</caption>
<graphic xlink:href="FCHEM_fchem-2025-1615586_wc_sch2.tif">
<alt-text content-type="machine-generated">Four chemical reaction pathways depict the formation of formamide and urea. Path 1 (red) starts with carbon monoxide and ammonia, forming intermediates and resulting in formamide. Path 2 (green) involves different intermediates and also ends with formamide. Path 3 (blue) uses intermediates to produce urea. Path 4 (purple) details a separate process ending with protonated urea. Each path involves multiple intermediate steps with labels indicating intermediate and transition states.</alt-text>
</graphic>
</fig>
<p>
<xref ref-type="fig" rid="F1">Figure 1</xref> displays the PES for formamide and urea formation. The optimized structures of reactants, pre-reactive complex, intermediates, transition states and products, along with energy values, are shown in ESI <xref ref-type="sec" rid="s12">Supplementary Figure S1</xref>. The Cartesian coordinates for all these species are tabulated in ESI <xref ref-type="sec" rid="s12">Supplementary Table S1</xref>. When the <sup>&#x00B7;</sup>NH<sub>2</sub> radical attacks the carbon atom of CO, a pre-reactant complex (OC&#x00B7; &#x00B7;&#x00B7;NH<sub>2</sub>) is formed (see ESI <xref ref-type="sec" rid="s12">Supplementary Figure S1</xref>). The computed energy for the formation of PRC is nearly &#x2212;0.2&#xa0;kcal/mol (at CCSD(T)/aug-cc-pVTZ//B2PLYP-D/aug-cc-pVTZ), which is in good agreement with the energy computed energy at CCSD(T)/aug-cc-pVTZ//&#x3c9;B97X-D/aug-cc-pVTZ level. This result is attributed to a weak interaction between C and N atoms. To form a C&#x2013;N bond between N of <sup>&#x00B7;</sup>NH<sub>2</sub> and C of CO, both molecules come closer to each other via a transition state (TS-1), incurring a significant energy penalty. The barrier height for C-N bond formation is approximately &#x223c;6&#xa0;kcal/mol, leading to the formation of the intermediate Int-1 (<sup>&#x00B7;</sup>CONH<sub>2</sub>). The energy value is well-supported by calculations performed at the CCSD(T)/aug-cc-pVTZ level using &#x3c9;B97X-D optimized geometries. The Int-1 (<sup>&#x00B7;</sup>CONH<sub>2</sub>) can react with hydrogen molecules to form Int-2 (H-H &#x2026; CONH<sub>2</sub>), with an energy barrier of 16.6&#xa0;kcal/mol, ultimately dissociates via transition state TS-2 to produce formamide (HCONH<sub>2</sub>) &#x2b; H. As shown in path-2, Int-1 can undergo isomerization via H migration, forming Int-3 (HCONH) through a transition state (TS-3), which has a high barrier of 51.5&#xa0;kcal/mol relative to Int-1 (<sup>&#x22C5;</sup>CONH<sub>2</sub>). Additionally, the transition state (TS-4) involves the addition of hydrogen molecules to form Int-4 (H-H &#x2026; CONH<sub>2</sub>). Due to the high energy barrier and the formation of endothermic intermediates, Path-2 is less feasible compared to Path-1, making such a reaction more relevant under combustion conditions rather than ISM environments.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Zero-point corrected potential energy surface (in kcal/mol) for the formation of formamide and urea from CO, NH<sub>2</sub>, H<sub>2</sub>, and NH<sub>3</sub>, computed at the CCSD(T)/aug-cc-pVTZ//B2PLYP-D3/aug-cc-pVTZ level of theory.</p>
</caption>
<graphic xlink:href="fchem-13-1615586-g001.tif">
<alt-text content-type="machine-generated">Reaction energy diagram showing four pathways: Path 1 (red) for formamide, Path 2 (green) for formamide, Path 3 (blue) for urea, and Path 4 (purple) for protonated urea. Each path details the transition states and intermediates through reaction coordinates and energy levels. Key intermediates and products are marked at specific energy values, revealing the reaction energetics for different products along each path.</alt-text>
</graphic>
</fig>
<p>As shown in <xref ref-type="fig" rid="F1">Figure 1</xref>, the <sup>&#x00B7;</sup>NH<sub>2</sub> radical reacts with CO to form Int-1 (<sup>&#x00B7;</sup>CONH<sub>2</sub>), which then reacts with H<sub>2</sub> to produce formamide (HCONH<sub>2</sub>), following a sequential two-body process. In this study, we consider that in the presence of H<sub>2</sub>, CO, and <sup>&#x00B7;</sup>NH<sub>2</sub> molecules, simultaneous three-body collisions are highly unlikely. Instead, the reaction is expected to proceed through the formation of two-body complexes, which subsequently collide with a third species to form three-body complexes and products. A sequential two-body collision mechanism is therefore proposed, as illustrated in <italic>ESI Page S18</italic>. Such reaction hypotheses for the ISM and EA will be validated through kinetic calculations and <italic>vice versa.</italic>
</p>
<p>To understand the formation of urea (NH<sub>2</sub>CONH<sub>2</sub>), Int-1 can also react with NH<sub>3</sub> molecules to form CONH<sub>2</sub>&#x00B7; &#x00B7;NH<sub>3</sub> (Int-5), which is more stable than Int-1. This increased stability is due to the formation of two hydrogen bonds from ammonia molecules (see ESI <xref ref-type="sec" rid="s12">Supplementary Figure SI,1</xref>). As shown in <xref ref-type="fig" rid="F1">Figure 1</xref>, the Int-5 involves two pathways, Path 3 and Path 4, to generate NH<sub>2</sub>CONH<sub>2</sub> molecules. Path 3 involves the formation of a second&#xa0;C-N bond of Int-5, which then dissociates via transition state TS-5, leading to the production of NH<sub>2</sub>CONH<sub>2</sub> and H radical with a barrier of 37.1&#xa0;kcal/mol. Another possibility involves the simultaneous formation of a C &#x336; N bond and protonation of CONH<sub>2</sub>, resulting in the formation of the protonated urea (Product-4). The increased stability of this product is due to the formation of three hydrogen bonds. Based on the barrier height calculations, which are relatively high in all four proposed pathways, we believe the formation of NH<sub>2</sub>COH and NH<sub>2</sub>COH<sub>2</sub> is unlikely to occur in the gas-phase ISM.</p>
</sec>
<sec id="s3-3">
<title>3.3 Formation of thioamides [&#x2013;(C&#x3d;S)&#x2013;NH&#x2013;]</title>
<p>Possible reaction pathways for the thioformamide (Path 1 and 2), thiourea (Path 3), and protonated thiourea (Path 4) are shown in <xref ref-type="scheme" rid="sch3">Scheme 3</xref>.</p>
<fig id="sch3" position="float">
<label>SCHEME 3</label>
<caption>
<p>Possible reaction pathways for the thioformamide (Path 1 and 2), thiourea (Path 3), and protonated thiourea (Path 4).</p>
</caption>
<graphic xlink:href="FCHEM_fchem-2025-1615586_wc_sch3.tif">
<alt-text content-type="machine-generated">Chemical reaction pathway illustrating four different reaction paths for the formation of thioformamide and thiourea. Path 1 (red) shows steps from isothiocyanate and ammonia leading to thioformamide. Path 2 (green) details a progression through intermediates to thioformamide. Path 3 (blue) displays conversion steps to thiourea. Path 4 (purple) depicts the formation of protonated thiourea. Each path involves multiple intermediate steps with labels indicating intermediate and transition states.</alt-text>
</graphic>
</fig>
<p>
<xref ref-type="fig" rid="F2">Figure 2</xref> displays the PES for the formation of thioformamide (NH<sub>2</sub>CSH) and thiourea (NH<sub>2</sub>CSNH<sub>2</sub>), including zero-point energy corrections. Carbon sulfide (CS) is the S-analog of carbon monoxide (CO), with the primary difference between them arising from their dipole moments. The C&#x3d;S (&#x3bc; &#x3d; 1.912 D) has a significantly higher dipole moment than the C&#x3d;O (&#x3bc; &#x3d; 0.113 D), which is reflected in the longer bond length of CS (1.52&#xa0;&#xc5;) than CO 1.12&#xa0;&#xc5;. The formation of a pre-reactant complex (CS&#x00B7;&#x00B7;&#x00B7;&#x00B7;NH<sub>2</sub>, PRC<sub>s</sub>) is a barrierless process with an energy of &#x2212;1.7&#xa0;kcal/mol (w.r.t. Reactants). This stationary point is 0.3&#xa0;kcal/mol lower than that of the transition state TS-1<sub>s</sub> to form a submerged barrier relative to the reactants at infinite separation, facilitating N-S bond formation. This is because carbon sulfide has a higher dipole moment, bond length, and polarizability, leading to more reactivity with NH<sub>2</sub> radicals.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Zero-point corrected potential energy surface (in kcal/mol) for the formation of thioformamide and thiourea from CS, NH<sub>2</sub>, H<sub>2</sub>, and NH<sub>3</sub>, computed at the CCSD(T)/aug-cc-pV (T&#x2b;d)Z//B2PLYP-D3/aug-cc-pV (T&#x2b;d)Z level of theory.</p>
</caption>
<graphic xlink:href="fchem-13-1615586-g002.tif">
<alt-text content-type="machine-generated">Energy profile diagram displaying four reaction pathways. Path 1 (red) and Path 2 (green) lead to thioformamide formation. Path 3 (blue) and Path 4 (purple) involve thiourea and protonated thiourea, respectively. Transitions and intermediates with energy levels are marked, showing progression through different states.</alt-text>
</graphic>
</fig>
<p>The Int-1<sub>s</sub> (<sup>&#x00B7;</sup>CSNH<sub>2</sub>) can react with hydrogen molecules to form Int-2<sub>s</sub> (H<sub>2</sub> &#x2026; CSNH<sub>2</sub>) which then dissociates via transition state TS-2<sub>s</sub> to produce thioformamide (HCSNH<sub>2</sub>) &#x2b; H radical, with an energy barrier of 17.7&#xa0;kcal&#xa0;mol<sup>-1</sup>, as seen in Path 1. In Path 2, Int-1 (see ESI <xref ref-type="sec" rid="s12">Supplementary Figure S2</xref>) undergoes isomerization to form Int-3<sub>s</sub> (HCSN&#x00B7;H), which then undergoes hydrogenation, followed by breaking the H-H bond, resulting in the formation of thioformamide and a H radical. As shown in ESI <xref ref-type="sec" rid="s12">Supplementary Figure SI,2</xref>, Path 3 and Path-4 lead to two different transition states (TSs) for thiourea (TS-5<sub>s</sub>) and protonated thiourea (TS-6<sub>s</sub>). In this process, ammonia reacts with C of Int-1<sub>s</sub>, forming thiourea and a H radical. Another possible reaction pathway (Path 4) involves Int-5<sub>s</sub> reacting with an ammonia molecule, simultaneously leading to C&#x2013;N bond formation and protonation (H<sup>&#x2b;</sup>) of Int-1<sub>s</sub>. This reaction results in the formation of protonated thiourea, which is more stable than thiourea. As shown in <xref ref-type="fig" rid="F2">Figure 2</xref>, since the first barrier is low, the other barriers are relatively lower, and the exothermic nature of the products, Path 1, Path 3, and Path 4, is likely to be feasible under ISM conditions. On the other hand, Path 2 has a barrier height of &#x223c;50&#xa0;kcal/mol, making this pathway infeasible under ISM conditions.</p>
<p>The dipole moment is a crucial parameter for detecting molecules in the ISM, as it can be analyzed using microwave spectroscopy (<xref ref-type="bibr" rid="B65">Kroto, 1981</xref>) and quantum chemical calculations. Molecules with smaller dipole moments exhibit weak emissions and are difficult to detect, even if they are abundant in the ISM. The dipole moments (in debye) for stable amide species are as follows: CO (0.113), CONH<sub>2</sub> (3.693), HCONH (3.388), HCOONH<sub>2</sub> (3.975), and NH<sub>2</sub>CONH<sub>2</sub> (4.384). For stable thioamide species, the values are CS (1.912), Int-1<sub>s</sub> (<sup>&#x00B7;</sup>CSNH<sub>2</sub>) (3.786), Int-3<sub>s</sub> (<sup>&#x00B7;</sup>HCSNH) (2.209), thioformamide (HCSNH<sub>2</sub>) (4.528), and thiourea (NH<sub>2</sub>CSNH<sub>2</sub>) (5.586). Molecules with higher dipole moments are more likely to be detected in the ISM. Therefore, sulfur-containing compounds such as Int-1<sub>s</sub> (<sup>&#x00B7;</sup>CSNH<sub>2</sub>), thioformamide (HCSNH<sub>2</sub>), and thiourea (NH<sub>2</sub>CSNH<sub>2</sub>) may also be present. However, experimental evidence is needed to confirm this prediction.</p>
</sec>
<sec id="s3-4">
<title>3.4 Rate constants for CS &#x2b; NH<sub>2</sub> reaction</title>
<p>To identify the transition state for the CS&#x22ef;NH<sub>2</sub> &#x2192; CS &#x2b; NH<sub>2</sub> dissociation, the minimum energy path (MEP) was computed by performing constrained optimizations along the bond distance, incorporating zero-point energy corrections for the vibrational modes orthogonal to the forming bond, as illustrated in <xref ref-type="fig" rid="F3">Figure 3</xref>. The MEP was determined using the B2PLYP-D3/aug-cc-pVTZ level of theory, performing constrained optimization at S-N distances ranging from 3.8&#xa0;&#xc5; to 9.0&#xa0;&#xc5; in increments of 0.1&#xa0;&#xc5;.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Zero-point corrected potential energy surface (in kcal/mol) as a function of bond distance for the dissociation of CS&#x22ef;NH<sub>2</sub> &#x2192; CS &#x2b; NH<sub>2</sub>, computed at the CCSD(T)/aug-cc-pVTZ//B2PLYP-D3/aug-cc-pVTZ level of theory.</p>
</caption>
<graphic xlink:href="fchem-13-1615586-g003.tif">
<alt-text content-type="machine-generated">Graph showing the relationship between energy (in kcal/mol) and the distance \( r_{N...S} \) (in &#x00C5;ngstr&#x00F6;ms) from 4 to 9 &#x00C5;. Molecule diagrams are depicted along the x-axis at various distances. The energy increases sharply from 4.0 &#x00C5; and levels out past 6.0 &#x00C5;. The y-axis ranges from 0 to 1.2 kcal/mol.</alt-text>
</graphic>
</fig>
<p>The reaction path illustrated in <xref ref-type="fig" rid="F3">Figure 3</xref> was used to calculate VTST rate constants across a temperature range of 10&#xa0;K&#x2013;100&#xa0;K are shown in <xref ref-type="fig" rid="F4">Figure 4</xref>.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Rate constants as a function of bond distance for the dissociation of CS&#x22ef;NH<sub>2</sub> &#x2192; CS &#x2b; NH<sub>2</sub>, calculated at the CCSD(T)/aug-cc-pVTZ//B2PLYP-D3/aug-cc-pVTZ level of theory.</p>
</caption>
<graphic xlink:href="fchem-13-1615586-g004.tif">
<alt-text content-type="machine-generated">Chart displaying reaction rate constant \( k(s^{-1}) \) as a function of distance \( r(S...N) \) in angstroms. Data series represent temperatures from ten Kelvin to one hundred Kelvin, showing a decrease in rate constant with increasing distance across all temperatures. Logarithmic scale used for \( k \).</alt-text>
</graphic>
</fig>
<p>Based on the VTST calculation, the &#xb5;VTST rate constants range from approximately 10<sup>&#x2013;8</sup> to 10<sup>&#x2013;11</sup>&#xa0;cm<sup>3</sup> molecule<sup>&#x2212;1</sup> s<sup>-1</sup> between 10K and 100K, as shown in <xref ref-type="fig" rid="F5">Figure 5</xref>. The tabulated rate constant values are provided in ESI <xref ref-type="sec" rid="s12">Supplementary Table SI,7</xref>. As highlighted in earlier research, barrierless reactions can exhibit a negative temperature dependence, which supports a capture-type mechanism facilitated by long-range intermolecular forces. These forces grow more influential at lower temperatures as thermal energy diminishes. Our results reflect a similar trend, comparable to the NH<sub>2</sub> &#x2b; NO reaction. (<xref ref-type="bibr" rid="B62">Klemperer, 2006</xref>).</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>The capture rate constants associated with the entrance channels were computed using the microcanonical variational transition state theory method.</p>
</caption>
<graphic xlink:href="fchem-13-1615586-g005.tif">
<alt-text content-type="machine-generated">Graph showing the relationship between rate constant \(k_0\) and temperature. The plot is a downward curve from 10 to 100 Kelvin on the x-axis, with the y-axis representing \(k_0\) in cubic centimeters per molecule per second, ranging from \(10^{-8}\) to \(10^{-11}\). Data points are marked with black circles connected by a red dashed line.</alt-text>
</graphic>
</fig>
<p>
<xref ref-type="fig" rid="F6">Figure 6</xref> presents the rate constants for the CS &#x2b; NH<sub>2</sub> reaction over a pressure range from 10<sup>&#x2013;7</sup>&#xa0;bar&#x2013;1&#xa0;bar at various temperatures. The figure reveals that the greatest disparity between the two limits occurs around 90&#xa0;K, with a difference of nearly three orders of magnitude. In contrast, at 10&#xa0;K, the difference between the two regimes is approximately a factor of 5. To gain a deeper understanding of the formation of thioformamide and thiourea, the rate constants for these channels were also calculated for temperatures ranging from 10&#xa0;K to 30&#xa0;K at a very low pressure of approximately 10<sup>&#x2013;10</sup>&#xa0;bar. Our calculations show that at low temperatures (&#x3c;30&#xa0;K) and very low pressures, Int-1<sub>s</sub> forms efficiently. However, at high pressures (&#x3e;10<sup>&#x2013;7</sup>&#xa0;bar) and temperatures (&#x3e;30&#xa0;K), the reaction tends to revert to the reactants, making the formation of thioformamide and thiourea nearly negligible. Our analysis suggests that thioformamide (NH<sub>2</sub>CS) and thiourea (NH<sub>2</sub>CSNH<sub>2</sub>) can be formed from Int-1<sub>s</sub> &#x2b; H<sub>2</sub> and Int-1<sub>s</sub> &#x2b; NH<sub>3</sub>, respectively, under conditions of very low temperature and pressure. We also considered the role of competitive reactions, such as Radiative Association (RA), which are significant in interstellar medium (ISM) conditions. The forward reaction rates at low temperatures and very low pressures are faster than typical RA reactions, which generally exhibit rate constants well below &#x223c;10<sup>&#x2013;11</sup>&#xa0;cm<sup>3</sup> molecules<sup>-1</sup> s<sup>-1</sup>. In other words, the reactive intermediate (Int-1<sub>s</sub>) will interact with &#x201c;third body&#x201d; species such as H<sub>2</sub> or NH<sub>3</sub>, leading to the formation of NH<sub>2</sub>CSH and NH<sub>2</sub>CSNH<sub>2</sub>. From the data in <xref ref-type="fig" rid="F6">Figure 6</xref>, the low-pressure analysis (10<sup>&#x2013;7</sup>&#xa0;bar, typical of experimental conditions) shows that under ISM-like pressures (P &#x3c; 10<sup>&#x2013;14</sup>&#xa0;bar, corresponding to a molecular density of approximately 10<sup>6</sup> molecules/cm<sup>3</sup>), the reactive intermediate (Int-1<sub>s</sub>) can still form effectively. This is because the pressure effect is almost negligible.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Temperature- and pressure-dependent total rate constants for the CS &#x2b; NH<sub>2</sub> &#x2192; Int-1<sub>s</sub> reaction were calculated using RRKM/master equation (RRKM/ME) simulations.</p>
</caption>
<graphic xlink:href="fchem-13-1615586-g006.tif">
<alt-text content-type="machine-generated">Graph showing rate constants (k) in cm&#x00B3; per molecule per second against pressure in bars. Curves for temperatures 10K, 30K, 50K, 70K, and 90K are plotted, each labeled and distinct with different colors and line styles. The rate constant decreases as temperature increases.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-5">
<title>3.5 Chemistry of ISM</title>
<p>In the case of formamide (HCONH<sub>2</sub>) and urea (NH<sub>2</sub>CONH<sub>2</sub>) formation, all the precursor molecules, such as CO, <sup>&#x00B7;</sup>NH<sub>2</sub>, H<sub>2</sub>, and NH<sub>3</sub>, have been detected in ISM. However, all transition states (TS-1 to TS-6) involved in Path 1 and Path 2 (formamide formation), Path 3 (urea formation), and Path 4 (protonated urea formation) are infeasible due to the energy barriers. For thioformamide and thiourea formation, it is important to note that the precursors used in this study, CS, <sup>&#x00B7;</sup>NH<sub>2</sub>, H<sub>2</sub>, and NH<sub>3,</sub> have been observed in the ISM. However, intermediates such as Int-1<sub>s</sub> (<sup>&#x00B7;</sup>CSNH<sub>2</sub>) and Int-3<sub>s</sub> (HCSN&#x00B7;H), as well as products like thioformamide (HCSNH<sub>2)</sub> and urea (NH<sub>2</sub>CSNH<sub>2</sub>), have not yet been detected. The transition states (TS-1<sub>s</sub> to TS-6<sub>s</sub>) involved in Path 1 (thioformamide formation), Path-3 (thiourea formation), and Path 4 (Protonated thiourea formation) are feasible under interstellar conditions due to their lower barrier heights and kinetic feasibilities (see <xref ref-type="fig" rid="F2">Figures 2</xref>, <xref ref-type="fig" rid="F6">6</xref>).</p>
<p>Following the approach suggested in previous studies (<xref ref-type="bibr" rid="B15">Ballotta et al., 2021</xref>; <xref ref-type="bibr" rid="B63">Klippenstein et al., 1996</xref>), the effective association reaction in the low-pressure limit was calculated as <inline-formula id="inf7">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>f</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>f</mml:mi>
</mml:msub>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>b</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula> , where k<sub>
<italic>f</italic>
</sub> is the forward association rate constant (cm<sup>3</sup> molecule<sup>&#x2212;1</sup> s<sup>-1</sup>), k<sub>r</sub> (s<sup>-1</sup>) is the radiative stabilization rate constant and k<sub>b</sub> (s<sup>-1</sup>) is the back-dissociation rate constant. To assess the accuracy of radiative stabilization, the forward rate constant was calculated using the &#xb5;VTST_RRKM/ME method, as discussed in <xref ref-type="sec" rid="s3-4">section 3.4</xref>. k<sub>f</sub> varies from 10<sup>&#x2013;8</sup>&#xa0;cm<sup>3</sup> molecule<sup>&#x2212;1</sup> s<sup>-1</sup> to 10<sup>&#x2013;11</sup>&#xa0;cm<sup>3</sup> molecule<sup>&#x2212;1</sup> s<sup>-1</sup> from the temperature range of 10&#x2013;100K. As suggested in previous studies (<xref ref-type="bibr" rid="B31">Dalgarno, 1987</xref>; <xref ref-type="bibr" rid="B104">Van Dishoeck, 2014</xref>; <xref ref-type="bibr" rid="B37">Douglas et al., 2024</xref>), and anticipated in our calculation, the k<sub>r</sub> is expected to be higher than the backward reaction (k<sub>b</sub>). In that case, the effective association rate for this process is almost expected to be the same as the forward reaction (k<sub>r</sub> &#x3e;&#x3e; k<sub>b</sub>, the <inline-formula id="inf8">
<mml:math id="m16">
<mml:mrow>
<mml:msub>
<mml:mi>k</mml:mi>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mi>f</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> This analysis also agrees with the literature value of similar ISM product formation under low temperature and low-pressure conditions, which is in the range of 10<sup>&#x2013;9</sup> to 10<sup>&#x2013;11</sup>&#xa0;cm<sup>3</sup> molecule<sup>&#x2212;1</sup> s<sup>-1</sup>. (<xref ref-type="bibr" rid="B81">Raghavachari et al., 1989</xref>; <xref ref-type="bibr" rid="B63">Klippenstein et al., 1996</xref>; <xref ref-type="bibr" rid="B31">Dalgarno, 1987</xref>).</p>
<p>The above analysis is further supported by the high dipole moments of each species in the sulfur system. The ISM is characterized by extremely low density (10<sup>2</sup>&#x2013;10<sup>6</sup> atoms, molecules, and ions per cm<sup>3</sup>) and temperatures ranging from 10K to 100&#xa0;K). (<xref ref-type="bibr" rid="B62">Klemperer, 2006</xref>). Due to these conditions, chemical reactions in the ISM are typically barrierless (or involve submerged TSs) and lead to exothermic products. (<xref ref-type="bibr" rid="B104">Van Dishoeck, 2014</xref>; <xref ref-type="bibr" rid="B37">Douglas et al., 2024</xref>; <xref ref-type="bibr" rid="B57">Jensen, 2007</xref>). On Earth, gas phase reactions typically involve the formation of pre-reactive complexes through weak interactions between reactants, often via two-body collisions, with occasional involvement of a third body. However, in interstellar chemistry, three-body collisions are highly improbable due to the extremely low number density, cold temperatures, and long reaction time scales. (<xref ref-type="bibr" rid="B52">Herbst, 1985</xref>). For a dense interstellar cloud with a number density of 10<sup>5</sup>&#xa0;cm<sup>&#x2212;3</sup>, the typical chemical reaction timescales are: reactions involving &#x201c;inert&#x201d; neutral species &#x223c;10<sup>5</sup> years (or even longer in some cases), reactions of reactive neutral species &#x223c;100 years, reactions of molecular ions, 1 hour&#x2013;100 years. This aspect has been well-documented in the literature for several years. (<xref ref-type="bibr" rid="B53">Herbst and Klemperer, 1976</xref>).</p>
<p>We estimated the timescale for the formation of Int-1s using an approximate association rate of k&#x223c;10<sup>&#x2013;8</sup> to 10<sup>&#x2013;13</sup>&#xa0;cm<sup>3</sup>&#xa0;s<sup>-1</sup> over a temperature range of 10&#x2013;100&#xa0;K, under extremely low-pressure conditions. from 10&#xa0;K to 100K at extremely low pressure for the formation of Int-1s. These calculations assume particle densities ranging from 10<sup>2</sup> to 10<sup>6</sup>&#xa0;cm<sup>&#x2212;3</sup>, representative of diffuse and molecular clouds.&#x201d;.</p>
<p>At 10&#xa0;K, &#x3c4;&#x223c;1/(k&#x22c5;n<sub>reactant)</sub> &#x3d; (10<sup>&#x2013;8</sup>&#xa0;cm<sup>3</sup>&#xa0;s<sup>-1</sup>&#x2a;10<sup>2</sup>&#xa0;cm<sup>-3</sup>) &#x3d; 10<sup>6</sup>&#xa0;sec &#x3d; &#x223c; 12&#xa0;days.</p>
<p>At 100K &#x3c4;&#x223c;1/(k&#x22c5;n<sub>reactant)</sub> &#x3d; (10<sup>&#x2013;13</sup>&#xa0;cm<sup>3</sup>&#xa0;s<sup>-1</sup>&#x2a;10<sup>6</sup>&#xa0;cm<sup>-3</sup>) &#x3d; 10<sup>7</sup>&#xa0;sec &#x3d; 115&#xa0;days.</p>
<p>Based on the above facts, we believe the reaction mechanism proposed in this work aligns with the current understanding of interstellar gas-phase chemistry.</p>
</sec>
<sec id="s3-6">
<title>3.6 Astrochemical implications and limitations</title>
<p>We explicitly acknowledge that, to date, neither thioformamide nor thiourea has been detected in the interstellar medium (ISM). Although our quantum chemical and kinetic calculations indicate that their formation is feasible under cold gas-phase conditions, there is currently no observational spectroscopic confirmation. This limitation is now clearly emphasized, and our study is framed as a theoretical foundation to motivate targeted astronomical searches&#x2014;particularly in sulfur-rich interstellar environments. Our proposed reaction mechanisms assume either radiative stabilization or sufficiently long-lived intermediates to permit subsequent reactions under the ultra-low-pressure conditions of the ISM. While we apply RRKM/master equation (RRKM/ME) simulations where applicable, significant uncertainties remain, especially in estimating radiative association rates and the stability of reactive complexes. These assumptions are now explicitly discussed, and we underscore the need for both experimental and theoretical investigations into the dynamics and energetics of such stabilization pathways. We note that ion&#x2013;molecule and grain-surface reactions are known to play crucial roles in the formation of prebiotic species such as formamide. While our current work focuses exclusively on neutral&#x2013;neutral gas-phase pathways, we now recognize the potential importance of alternative routes, including ion-mediated reactions and grain-surface processes such as HCO &#x2b; NH<sub>2</sub> coupling on dust grains. Given the large permanent dipole moments predicted for both thioformamide and thiourea, we strongly recommend laboratory rotational spectroscopy studies to provide reference spectra for radioastronomical detection. Finally, we highlight the need for astrochemical modeling using our computed rate constants to evaluate the viability and relative importance of these proposed formation pathways across a range of ISM environments.</p>
</sec>
</sec>
<sec sec-type="conclusion" id="s4">
<title>4 Conclusion</title>
<p>This study provides a comprehensive theoretical investigation into the gas-phase formation pathways of amides and thioamides in the interstellar medium (ISM), employing high-level quantum chemical methods [CCSD(T)//B2PLYP] along with &#xb5;VTST and RRKM/ME simulations. While reaction pathways for formamide and urea formation via NH<sub>2</sub> &#x2b; CO and subsequent hydrogenation and ammoniation appear unfavorable in the gas phase due to significant energy barriers, alternative routes on interstellar ices remain promising and warrant further exploration. In contrast, the formation of thioamides such as thioformamide (HCSNH<sub>2</sub>) and thiourea (NH<sub>2</sub>CSNH<sub>2</sub>) emerges as kinetically and thermodynamically viable under ISM conditions, with exothermic and largely barrierless reaction profiles. Importantly, we propose the existence and potential detectability of four novel sulfur-containing species&#x2014;&#x00B7;CSNH<sub>2</sub>, HCSN&#x00B7;H, HCSNH<sub>2</sub>, and NH<sub>2</sub>CSNH<sub>2</sub>&#x2014;which have not yet been conclusively observed in the ISM. Among these, thioformamide and thiourea are highlighted as particularly promising due to their feasible gas-phase formation pathways and strong binding energies. This study presents, for the first time, detailed gas-phase mechanisms for these molecules, especially involving NH<sub>2</sub> &#x2b; CS and urea-thione analogues, emphasizing their astrochemical relevance. Our findings serve as a foundation for future astronomical searches, laboratory spectroscopic studies, and astrochemical modeling efforts focused on sulfur-bearing prebiotic molecules. By improving our understanding of sulfur chemistry in the ISM, this work contributes to the broader quest to unravel the molecular origins of life and the chemical complexity of the universe.</p>
</sec>
<sec id="s5">
<title>5 Supporting Information</title>
<p>The Cartesian coordinates of formamide, urea, thioformamide, and thiourea are provided for the pre-reactant, transition state (TS), and products. The optimized geometries and their energy barriers are compared using different DFT methods on representative TSs. The study explains how different sequences of two-body reactions lead to the same highly stabilized pre-reaction complex. The energy differences between the products and reactants of formamide, urea, thioformamide, and thiourea are analyzed. Additionally, the TS energy barriers of formamide, urea, thioformamide, and thiourea are compared using different methods for representative molecules. The electronic energies for all investigated compounds (in Hartrees) are reported. The Cartesian coordinates of formamide, urea, thioformamide, and thiourea are provided for the pre-reactant, transition state (TS), and product complex. ZPE corrected energies of PRC and TS-1 for CS &#x2b; NH2 at different levels of theory. The equilibrium constant and rate constants (in cm<sup>3</sup> molecule<sup>&#x2212;1</sup> s<sup>-1</sup>) for the reaction CS &#x2b; NH<sub>2</sub> &#x2192; CS &#x2026; NH<sub>2</sub> is also presented.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s6">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/<xref ref-type="sec" rid="s12">Supplementary Material</xref>, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec sec-type="author-contributions" id="s7">
<title>Author contributions</title>
<p>AM: Funding acquisition, Project administration, Visualization, Formal Analysis, Conceptualization, Resources, Validation, Data curation, Supervision, Methodology, Software, Writing &#x2013; review and editing, Investigation, Writing &#x2013; original draft. ST: Software, Methodology, Conceptualization, Writing &#x2013; original draft, Formal Analysis.</p>
</sec>
<sec sec-type="funding-information" id="s8">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research and/or publication of this article. The work is supported by Faculty Startup Grant &#x23; 8474000461 at Khalifa University of Science and Technology Abu Dhabi UAE. ST and MAA also thank the Center for Catalysis and Separations, Khalifa University of Science and Technology, for their support. ST thanks Raghunath O Ramabhadran for valuable discussions.</p>
</sec>
<ack>
<p>MAA and ST gratefully acknowledge the computational resources at the High-Performance Computer Facility at Khalifa University of Science and Technology Abu Dhabi.</p>
</ack>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="ai-statement" id="s10">
<title>Generative AI statement</title>
<p>The author(s) declare that no Generative AI was used in the creation of this manuscript.</p>
</sec>
<sec sec-type="disclaimer" id="s11">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec sec-type="supplementary-material" id="s12">
<title>Supplementary material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fchem.2025.1615586/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fchem.2025.1615586/full&#x23;supplementary-material</ext-link>
</p>
<supplementary-material xlink:href="DataSheet1.docx" id="SM1" mimetype="application/docx" xmlns:xlink="http://www.w3.org/1999/xlink"/>
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