Atomistic Modeling of Methyl Formate and Glycolaldehyde Formation on Interstellar Dirty Ice Mantles via a “Radical + Ice” Mechanism

Abstract

Methylformate (MF) and glycolaldehyde (GA) are two primogenital organic molecules detected in both cold and warm regions of the interstellar medium (ISM). Both gas‐phase and grain‐surface pathways have been proposed to explain their abundances, yet uncertainties remain, since prevailing grain‐surface mechanisms favor the formation of GA over MF, which mismatch observations in different ISM regions. In this work, MF and GA synthetic reactions are atomistically modeled on surfaces containing variable HO and CO percentages (interstellar dirty ices), in which one of the reactants coming from the gas phase reacts with an icy CO, thus adopting the following two‐step "radical + ice" mechanism: for MF, OCH + ${\mathrm{CO}}_{\left(\mathrm{ice}\right)}$ $\to$ COOCH + H $\to$ HCOOCH; for GA, CHOH + ${\mathrm{CO}}_{\left(\mathrm{ice}\right)}$ $\to$ COCHOH + H $\to$ HCOCHOH. Calculations show that the first step presents an energy barrier (32–38 kJ mol for MF and 17–20 kJ mol for GA), while the second step is nearly barrierless. Although the energetics favor GA formation, the observed abundances are better explained by desorption phenomena rather than reaction barriers are argued. Specifically, the weaker binding energies of MF (16.8–46.1 kJ mol) than GA (28.4–90.2 kJ mol) support its higher abundance in the ISM.

The presence of interstellar complex organic molecules (COMs) has been baffling astrochemists for a long time. Methyl formate and glycolaldehyde are widely detected but their abundances mismatch kinetic astrochemical model predictions. Here, the formation of these two COMs is characterized onto a mixed ice surface, highlighting the importance of considering both formation and desorption of these species in the astrochemical models.

1. Introduction

Among the approximately 330 molecules that have been detected in the interstellar medium (ISM),¹(https://cdms.astro.uni‐koeln.de/classic/molecules), about one‐third are interstellar complex organic molecules (COMs). COMs are defined as species that contain at least six atoms, among which one or more are carbon atoms combined with heteroatoms.^{[ 1 ]} They represent a subject of primary interest in astrochemistry because i) they could be related to the emergence of prebiotic chemistry and subsequently life, [e.g.],^{[ 2 , 3 ]} and ii) their synthesis in the ISM represents a long‐standing challenge, as explained below.^{[ 4 ]}

Two prevailing paradigms have been suggested to explain the formation and presence of COMs in the ISM: one considering them as products of gas‐phase reactions involving radicals with closed‐shell species or ions with molecules,^{[ 5 , 6 ]} the other assuming them to be products of grain‐surface reactions.^{[ 7 ]} Both approaches seem necessary to explain the unexpectedly complex chemistry of the ISM rather than one dominating over the other, leaving the debate still open in present days.^{[ 8 , 9 ]}

Both paradigms start from dust grain surfaces covered in ices, predominantly of HO, but also of other volatile species (CO, CO, NH, CHOH, and CH). In the coldest (T $\approx$10 K), starless interstellar environments, these ices form by successive adsorption of gaseous species on the grains (like the case of CO) or in situ surface reactions (like hydrogenation of O, N, and CO, forming HO, NH, and CHOH). The gas‐phase paradigm postulates that ices are desorbed through thermal or nonthermal mechanisms, and their components are subjected to a series of gas‐phase processes transforming them into COMs. In contrast, the grain‐surface chemistry paradigm is based on three elementary steps: i) the ice mantle components are processed by UV radiation and/or cosmic rays, leading to their homolytic dissociation forming radicals; ii) at temperatures around 30 K (achieved during the birth of a protostar), radicals on the surfaces acquire mobility and start to diffuse; and iii) once radicals encounter one to each other, radical–radical coupling reactions take place leading to the formation of COMs. They are subsequently released to the gas phase during later stages of star formation, as the temperature of the environment rises.^{[ 7 , 10 ]}

However, identification of COMs in cold environments (where T $\approx$ 10 K such that diffusive chemistry is not allowed), alongside the continuous detection of new COMs both in the gas phase and on the icy surface of dust grains,^{[ 11 , 12 ]} motivated the research of additional mechanisms to encompass the number of reactions involving their formation. Accordingly, alternative pathways have been proposed in recent years, such as nondiffusive mechanisms^{[ 13 ]} and cosmic‐ray driven reactions.^{[ 14 ]} Dedicated efforts have been done to investigate the former one, deriving schemes based on the condensation of atomic C,^{[ 15} , ¹⁶ , ^{17 – 18 ]} the insertion of excited O‐atoms,^{[ 19 , 20 ]} the formation of HCO radicals on ice surfaces as the parent precursors of other COMs,^{[ 21} , ^{22 – 23 ]} and the “radical + ice” mechanism, in which the icy grain‐surface participates in the reaction by providing a reactant.^{[ 24 , 25 ]}

The latter scheme was recently investigated theoretically showing successful results in the formation of formamide (${\mathrm{NH}}_2\mathrm{CHO}$)^{[ 24 ]} and ethanol (${\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{OH}$)^{[ 25 ]} through reaction of $\mathrm{CN}+{\mathrm{H}}_2{\mathrm{O}}_{(\mathrm{ice})}$ and $\mathrm{CCH}+{\mathrm{H}}_2{\mathrm{O}}_{(\mathrm{ice})}$, followed by atomic H additions. However, this was not the case for acetaldehyde ${\mathrm{CH}}_3\mathrm{CHO}$ formation via the reaction of ${\mathrm{CH}}_3+{\mathrm{CO}}_{(\mathrm{ice})}$, followed by atomic H addition.^{[ 26 ]} In this work, we aim to extend the study of this “radical + ice” mechanism to the formation of methyl formate (MF, ${\mathrm{HCOOCH}}_3$) and glycolaldehyde (GA, ${\mathrm{HCOCH}}_2\mathrm{OH}$).

MF and GA are ${\mathrm{C}}_2{\mathrm{H}}_4{\mathrm{O}}_2$ structural isomers and have been detected in diverse astrophysical environments. The most stable conformer of MF (cis‐${\mathrm{HCOOCH}}_3$) was observed in cold molecular clouds (interstellar regions called TMC‐1 and L1544),^{[ 27 , 28 ]} in the prestellar core L1689B,^{[ 29 ]} in the cold core B1‐b,^{[ 30 ]} and in some protoplanetary disks.^{[ 31 ]} Very recently, the higher‐energy conformer trans‐${\mathrm{HCOOCH}}_3$ was detected for the first time toward the Galactic center molecular cloud G + 0.693–0.027 and the protostellar shock L1157‐B1.^{[ 32 ]} The difference between the two MF conformers is in the orientation of the $\mathrm{O}[chemistry\; single\; bond\; solid\; line]{\mathrm{CH}}_3$ moiety with respect to the $\mathrm{H}[chemistry\; single\; bond\; solid\; line]\mathrm{C}[chemistry\; double\; bond\; solid\; lines]\mathrm{O}$ group. At variance, GA has four conformers: syn, cis‐, anti, cis‐, gauche, trans‐, and anti, trans‐GA (an overview of the structures is available in the Supporting Information (SI), Figure S1). In this classification, cis/trans refers to the orientation of the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{OH}$ bond with respect to the $\mathrm{H}[chemistry\; single\; bond\; solid\; line]\mathrm{C}[chemistry\; double\; bond\; solid\; lines]\mathrm{O}$ group, while syn/gauche/anti defines the orientation of the $\mathrm{O}[chemistry\; single\; bond\; solid\; line]\mathrm{H}$ bond with respect to $\mathrm{H}[chemistry\; single\; bond\; solid\; line]\mathrm{C}[chemistry\; double\; bond\; solid\; lines]\mathrm{O}$ group. Among the four conformers, syn, cis‐GA is the most stable, due to the intramolecular H‐bond between the carbonyl and the hydroxyl groups.^{[ 33 ]} Syn, cis‐GA was detected in hot cores (G31.41 + 0.31),^{[ 34 ]} in class 0 and class I protostars of the Perseus region,^{[ 35 ]} in shock regions (L1157‐B1)^{[ 36 ]} and in comets (Lovejoy and 67P/C‐G).^{[ 37 , 38 ]} Additionally, the simultaneous presence of MF and GA was documented in diverse interstellar, suggesting similar formation pathways. Usually, MF is more abundant than GA, with MF:GA ratios up to 8:1, as found in the hot molecular core Sgr B2(N2) and in the low‐mass protostar IRAS16293B.^{[ 39 , 40 ]}

The interest toward these two species stems from GA being the simplest sugar, and accordingly serving as a potential precursor of more complex sugar molecules,^{[ 41 ]} such as ribose and deoxyribose, which are fundamental components of RNA and DNA. Meanwhile, MF is related to the synthesis of key biomolecule precursors, such as formamide^{[ 42 ]} and glycine.^{[ 43 ]}

The gas‐phase and grain‐surface reactivity of MF and GA in the ISM has been extensively investigated, both from a theoretical and an experimental point of view. Among the experimental surface chemistry studies, the work of Chuang et al.^{[ 44 ]} showed that GA, alongside with MF and ethylene glycol (${\mathrm{HOCH}}_2{\mathrm{CH}}_2\mathrm{OH}$) are produced in mixed CO, ${\mathrm{H}}_2\mathrm{CO}$, and ${\mathrm{CH}}_3\mathrm{OH}$ ices via nonenergetic radical–radical recombination (i.e., without the need of UV photolysis or cosmic rays as external triggers), highlighting the pivotal role of H addition and abstraction reactions in developing a rich chemistry. The role of radiochemistry in MF and GA synthesis was also investigated, such as the formation of MF via cosmic ray irradiation of ${\mathrm{CH}}_3\mathrm{OH}$:CO ice mantles.^{[ 45 ]} The inclusion of radiolysis in kinetic astrochemical models was tested by monitoring the efficiency of grain‐surface reactions, such as HCO + ${\mathrm{OCH}}_3$ $\to$ MF and HCO + ${\mathrm{CH}}_2\mathrm{OH}$ $\to$ GA, showing how their abundances increase as a consequence of nonthermal chemistry induced by cosmic rays.^{[ 46 ]}

In the gas phase, dimethylether (DME, ${\mathrm{CH}}_3{\mathrm{OCH}}_3$) was suggested to be the parent species of MF,^{[ 5 , 15 ]} which results from a two‐step process: the addition of atomic O to the ${\mathrm{CH}}_3{\mathrm{OCH}}_2$ DME radical, followed by the release of an H atom yielding MF.^{[ 47 ]} At variance, GA was proposed to be a product of gas‐phase ethanol processing, occurring via H abstraction followed by O‐addition.^{[ 6 ]} Alternatively, the formation of GA via formose reaction was thoroughly investigated, both theoretically and experimentally.^{[ 48 , 49 ]} However, the process does not appear to be efficient in the gas phase, while grain‐surface formation routes seem to be promising.^{[ 50} , ^{51 – 52 ]}

Among ice chemical processes, the “radical + closed‐shell” reaction HCO + ${\mathrm{H}}_2\mathrm{CO}$ (+ H) $\to$ MF and GA was recently investigated on small water clusters.^{[ 53 ]} Several radical–radical coupling reactions on water ice clusters were characterized by Enrique–Romero et al. 2022,^{[ 54 ]} which revealed the presence of small barriers for the coupling and side reactions competing with the formation of the desired product. In this specific case, the HCO radical can couple with ${\mathrm{OCH}}_3$ and ${\mathrm{CH}}_2\mathrm{OH}$ radicals forming H${\mathrm{COOCH}}_3$ and H${\mathrm{COCH}}_2\mathrm{OH}$, respectively, or can undergo an H abstraction yielding CO + ${\mathrm{CH}}_3\mathrm{OH}$ and ${\mathrm{H}}_2\mathrm{CO}$ + ${\mathrm{H}}_2\mathrm{CO}$, reducing the efficiency of the COM formation. More extended surface models were adopted by Martínez–Bachs et al.,^{[ 55 ]} where a number of gas‐phase reactions were simulated onto the ice surface to test their feasibility. Among the targeted COMs, the process yielding MF showed an energy barrier, the reaction requiring tunneling effects to progress. The latest published computational study simulates the formation of MF via the nucleophilic substitution HCOOH + ${\mathrm{CH}}_3\mathrm{OH}$ $\to$ MF +${\mathrm{H}}_2\mathrm{O}$.^{[ 56 ]}

Considering the state of the art, in this work, we characterized the synthesis of MF and GA via the following stepwise processes:

$${\mathrm{OCH}}_3+{\mathrm{CO}}_{(\mathrm{ice})}\to {\mathrm{COOCH}}_3$$ (1)

$$\mathrm{H}+{\mathrm{COOCH}}_3\to {\mathrm{HCOOCH}}_3$$ (2)

and

$${\mathrm{CH}}_2\mathrm{OH}+{\mathrm{CO}}_{(\mathrm{ice})}\to {\mathrm{COCH}}_2\mathrm{OH}$$ (3)

$$\mathrm{H}+{\mathrm{COCH}}_2\mathrm{OH}\to {\mathrm{HCOCH}}_2\mathrm{OH}$$ (4)

We aim to assess the feasibility and efficiency (namely, without competitive H abstractions) of the “radical + dirty ice” mechanism successfully adopted for the synthesis of formamide^{[ 24 ]} and ethanol,^{[ 25 ]} and characterize the reactivity of CO molecules embedded in the interstellar dirty ices.

Grain‐surface reactions can occur via four different mechanisms: i) Langmuir–Hinshelwood (LH),^{[ 57 , 58 ]} which requires the previously adsorbed reactants to diffuse on the surface of the grains to react^{[ 59 ]}; ii) Eley–Rideal (ER),^{[ 60 ]} in which species from the gas phase directly react with surface molecules, thus avoiding diffusion^{[ 15 ]}; iii) Harris–Kasemo (or hot atom) mechanism, in which high‐energy species have enough energy to overcome the diffusion barriers and travel on the surface, a condition that is not feasible in cold environments^{[ 61 ]}; and iv) reactions promoted by suprathermal species, which result from the excitation and/or ionization caused by cosmic ray bombardment.^{[ 14 , 46 , 62 ]} Here, the LH and ER mechanisms were considered in the simulation of (Equation (1)–(4) ).

2. Results and Discussion

2.1. Gas‐Phase Benchmark Study

To determine the most appropriate density functional theory (DFT) method with which performing the simulations, we conducted a benchmark analysis of Equation ( (1)–(4) ) in the gas phase (i.e., in the absence of the icy surfaces). The first reaction step consists of a radical species (${\mathrm{OCH}}_3$ or ${\mathrm{CH}}_2\mathrm{OH}$) attacking the carbon atom of the closed‐shell CO molecule. In the case of MF, both cis and trans‐conformers were considered, while for GA the syn, cis‐, and gauche, trans‐conformers were taken into account because they are the structures resulting from its formation on the ice surface (see below). For simplicity, Table  1 and Figure  1 report the benchmark results for the most stable conformers (cis‐MF and syn, cis‐GA). The complete information, including the less stable conformers, is available in the SI (Table S1 and Figure S1–S4, Supporting Information).

Table 1.

Relative energies (in kJ mol) of gas‐phase methyl formate (MF) and glycolaldehyde (GA) formation calculated at BHLYP‐D3(BJ) and MPWB1K‐D3(BJ) for benchmarking purposes. PRC (pre–reactant complex) corresponds to the OCHCO and ${\mathrm{CH}}_2\mathrm{OH}$ $\dots$CO, in which the radical and CO are interacting. TS indicates the transition state structure of the reaction. The given error pertains to each DFT energy in comparison with the corresponding CCSD(T)‐F12 single point energy (computed on the optimized geometry of the previous DFT column). The structures can be found in Figure 1.

Structure	BHLYP‐D3(BJ)	CCSD(T)‐F12	Error	MPWB1K‐D3(BJ)	CCSD(T)‐F12	Error
MF
cis‐PRC	0.0	0.0	–	0.0	0.0	–
cis‐TS	29.6	19.2	54%	20.7	22.1	6%
cis‐${\mathrm{COOCH}}_3$	−66.9	−79.7	16%	−88.8	−79.6	12%
cis‐${\mathrm{HCOOCH}}_3$	−431.4	−442.3	2%	−435.5	−442.3	2%
GA
syn,cis‐PRC	0.0	0.0	–	0.0	0.0	–
syn,cis‐TS	19.8	25.4	17%	12.6	23.3	46%
syn,cis‐${\mathrm{COCH}}_2\mathrm{OH}$	−35.2	−20.4	11%	−49.1	−31.7	55%
syn,cis‐${\mathrm{HCOCH}}_2\mathrm{OH}$	−399.3	−407.2	2%	−403.3	−407.3	1%

Figure 1.

Stationary points of Equation (1) and (2) yielding the most stable cis‐MF conformer, computed at MPWB1K‐D3(BJ)/6‐31G(d, p) theory level, and Equation (3) and (4) yielding the most stable syn, cis‐GA conformer, computed at BHLYP‐D3(BJ)/6‐31G(d, p) level of theory. PRC stands for prereactant complex and TS for transition state. Distances are given in Å. The energetics can be found in Table 1.

In the cis‐${\mathrm{COOCH}}_3$ formation, the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{O}$ distance in the prereactive complex (PRC) and transition state (TS) structure is 2.956 and 1.901 Å at the MPWB1K‐D3(BJ) level of theory, respectively, resulting in a barrier of 20.7 kJ mol, which is slightly underestimated with respect to CCSD(T)‐F12 (22.1 kJ mol). Conversely, at the BHLYP‐D3(BJ) level of theory, the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{O}$ distance is 2.865 Å in the PRC and 1.838 Å in the TS structure, giving rise to an energy barrier of 29.6 kJ mol, 54% larger than the one at CCSD(T)‐F12 (19.2 kJ mol). The shorter $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{O}$ distance in the TS with respect to MPWB1K‐D3(BJ) probably leads to a repulsive interaction when computing the single‐point energy of the system at the CCSD(T)‐F12 level of theory.

For cis‐${\mathrm{COCH}}_2\mathrm{OH}$ formation, the opposite behavior is observed: there is a large discrepancy between the barrier computed at MPWB1K‐D3(BJ) and the corresponding single‐point energy at CCSD(T)‐F12 (12.6 against 23.3 kJ mol, respectively, with an error amounting to 46%), while the barrier computed at BHLYP‐D3(BJ) deviates only by 17% from the CCSD(T)‐F12 reference value (18.9 against 25.4 kJ mol, respectively).

The second reaction step is the hydrogenation of cis‐${\mathrm{COOCH}}_3$ and cis‐${\mathrm{COCH}}_2\mathrm{OH}$, which yields the final MF and GA products. These processes are radical–radical couplings, which are barrierless in the gas phase. The two tested functionals are suitable to describe the reaction energies, with only 1–2% error. For this reason, we determined the most suitable methodology considering the performance of the functionals in the energy barrier of the first step. Accordingly, we can conclude that the MPWB1K‐D3(BJ) functional is the most suitable method to characterize the formation of ${\mathrm{HCOOCH}}_3$, whereas BHLYP‐D3(BJ) is the most suitable for ${\mathrm{HCOCH}}_2\mathrm{OH}$ formation. At this point, we have two alternatives to proceed with the simulations: i) make a compromise and choose one of the two methods, sacrificing the accuracy for one of the two reactions; and ii) chose the best method for each separate case, sacrificing the direct comparability between the two cases. We choose the second option in order to keep both cases as close as possible to the best CCSD(T)‐F12, ensuring the confrontability of the two cases at the CCSD(T)‐F12 level.

2.2. Grain‐Surface Reactions: LH Mechanism

2.2.1. Adsorption of the Radicals on the ${\mathit{H}}_{\mathit{2}}\mathit{O}$:CO Dirty Ice

The ${\mathrm{OCH}}_3$ and ${\mathrm{CH}}_2\mathrm{OH}$ radicals were adsorbed at four different positions on each surface, two on the top face and two on the bottom face, in proximity of CO molecules exposing their C‐side, to sample different representative surface binding sites and identify suitable locations to simulate the first reaction step.

The BH(0)s (binding enthalpy, i.e., zero‐point energy (ZPE)‐corrected binding energies (BEs)) of ${\mathrm{OCH}}_3$ and ${\mathrm{CH}}_2\mathrm{OH}$ adsorbed on dirty ice surfaces are summarized in Table  2 , which also provides the nomenclature adopted for the binding sites. For ${\mathrm{OCH}}_3$, the BH(0) ranges from 8.3 to 42.1 kJ mol, depending on its interaction with the surface, which is established through the oxygen atom or the methyl group (perpendicular) or via the whole radical in case it lies parallel to the surface (an overview of all adsorption complexes is available in SI, Figure S5 and S6, Supporting Information). The weakest interaction is found for the ${\mathrm{CH}}_3$‐side at approximately 2.5 Å above the surface, the interaction being driven by only weak dispersion forces (BH(0) = 8.3 kJ mol). In contrast, the strongest interaction (BH(0) = 42.1 kJ mol) is due to the inclusion of ${\mathrm{OCH}}_3$ within a surface cavity, thus maximizing either H‐bond and dispersion interactions.

Table 2.

ZPE‐corrected BEs (BH(0), in kJ mol) of ${\mathrm{OCH}}_3$ and ${\mathrm{CH}}_2\mathrm{OH}$ adsorbed on the (100), (010), and (001) HO:CO surfaces. The nomenclature of each binding site refers to the C atom index of the CO molecule close to which the radicals were manually adsorbed.

Surface Site	BH(0) ${\mathrm{OCH}}_3$	BH(0) ${\mathrm{CH}}_2\mathrm{OH}$
14	25.5	10.7
15	9.9	23.4
178	7.8	10.4
184	17.6	14.4
32	14.8	14.2
37	8.3	3.7
178	29.7	14.3
179	20.5	19.7
14	42.1	54.3
15	34.2	5.5
171	39.1	62.5
205	28.5	75.4

For ${\mathrm{CH}}_2\mathrm{OH}$, the BH(0) ranges from 3.7 to 75.4 kJ mol, broader than for ${\mathrm{OCH}}_3$. The weakest BH(0) corresponds to a conformation, in which the molecule lies almost perpendicular to the surface at approximately 3 Å from its first neighbor, where very weak dispersion interactions between the ${\mathrm{CH}}_2$ moiety and the top‐layer CO molecules are established. The highest BH(0) values, found specifically for the (100) surface, result from the significant rearrangement of the CO molecules surrounding the adsorbate, which allows the formation of H‐bonds between ${\mathrm{CH}}_2\mathrm{OH}$ and the surface. In particular, the strongest interaction (BH(0) =75.4 kJ mol) is due to ${\mathrm{CH}}_2\mathrm{OH}$ donating a H‐bond to the C‐side of the nearest CO, and receiving a H‐bond from an underlying ${\mathrm{H}}_2\mathrm{O}$ molecule.

A key feature in determining the adsorption strength is the high mobility of external CO molecules, as a consequence of the weak interactions with water and with other CO molecules, as discussed in Perrero et al.^{[ 26 ]} The mixed ${\mathrm{H}}_2\mathrm{O}$:CO ice surface models exhibit a clathrate‐like network, revealing the tendency of CO to segregate from water, also observed in other works dealing with similar ice surface models.^{[ 63 ]} By assessing the atomistic ice models, one can identify orientations in which cage‐like structures, formed by H‐bonded water molecules, enclose CO molecules. Additionally, the central network of water molecules is covered by a more or less dense layer of CO molecules on both the top and bottom surfaces. The external CO molecules interact very weakly with the underlying water, making them highly mobile.

During geometry optimisations of the molecule/ice adsorption complexes, surface reconstruction can occur, giving rise to the discovery of previously unexplored local minima on the potential energy surface (PES). As a result, the BE may be exceptionally high, part of the contribution arising from the adsorption process itself and part from the energy gained by the surface due to structural reorganization of the external layers.

2.2.2. LH: 1) ${\mathit{OCH}}_{\mathit{3}}$ + ${\mathit{CO}}_{(\mathit{ice})}$ and 3) ${\mathit{CH}}_{\mathit{2}}\mathit{OH}$ + ${\mathit{CO}}_{(\mathit{ice})}$

The identification of the initial geometry for the characterization of Equation (1) and (3) was made considering both a large BH(0) of the radicals and their position, ensuring that its reactive moiety was oriented toward the C‐side of a nearby CO molecule. The latter criterion is necessary to guarantee the formation of the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{O}$ bond in Equation (1) and of the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{C}$ bond in Equation (3) . From this analysis, we selected one complex per surface: 184, 37, and 205 for ${\mathrm{OCH}}_3$, and 184, 32, and 14 for ${\mathrm{CH}}_2\mathrm{OH}$. For each structure, we performed a relaxed scan calculation along the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{O}$ and $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{C}$ distances defined by the atoms involved in the formation of $\mathrm{OC}[chemistry\; single\; bond\; solid\; line]{\mathrm{OCH}}_3$ and $\mathrm{OC}[chemistry\; single\; bond\; solid\; line]{\mathrm{CH}}_2\mathrm{OH}$ bonds, respectively, obtaining a pseudo‐potential energy surface (pPES) constrained along the bond lengths of interest.

Following the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{O}$ and $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{C}$ distance decreases, each pPES was characterized by i) the presence of a small potential well corresponding to a new adsorption minimum, in which the radical is closer to the surface; ii) a sudden increase in the energy of the system, indicative of the presence of an energy barrier, and iii) a steep decrease in the potential energy of the system, corresponding to the formation of the chemical bond. The structures corresponding to these three features of the PES were optimized as stationary points to determine the reactant (R), transition state (TS) and product (P) geometries, and hence derive the actual PES. Results are given in Table  3 and Figure  2 ,  3 .

Table 3.

ZPE‐corrected energy barriers ($\Delta H_{\mathrm{TS}}$) and reaction energies ($\Delta H_{\mathrm{R}}$) of ${\mathrm{COOCH}}_3$ and ${\mathrm{COCH}}_2\mathrm{OH}$ formation, complemented with gas‐phase values for the sake of comparison. ZPE‐corrected BEs (BH(0)) of the products ${\mathrm{COOCH}}_3$, ${\mathrm{COCH}}_2\mathrm{OH}$, ${\mathrm{HCOOCH}}_3$, ${\mathrm{HCOCH}}_2\mathrm{OH}$ are also provided. All energies are given in kJ mol.

${\mathrm{OCH}}_3$ + ${\mathrm{CO}}_{\left(\mathrm{ice}\right)}$
Surface Site	$\Delta H_{\mathrm{TS}}$	$\Delta H_{\mathrm{R}}$	BH(0) ${\mathrm{COOCH}}_3$	BH(0) ${\mathrm{HCOOCH}}_3$
184	38.4	−69.8	21.7	37.0
37	32.2	−68.9	15.8	11.7
205	32.6	−68.6	8.3	43.8
Gas phase	27.4	−66.9
${\mathrm{CH}}_2\mathrm{OH}$ + ${\mathrm{CO}}_{\left(\mathrm{ice}\right)}$
Surface Site	$\Delta H_{\mathrm{TS}}$	$\Delta H_{\mathrm{R}}$	BH(0) ${\mathrm{COCH}}_2\mathrm{OH}$	BH(0) H${\mathrm{COCH}}_2\mathrm{OH}$
184	20.3	−28.0	79.1	83.8
32	17.5	−28.5	31.3	52.5
14	17.6	−23.1	27.9	27.4
Gas phase	19.8–29.0	−24.0– −35.2

Figure 2.

Reactants (R), transition states (TS), and products (P) of Equation ( (1) ) ${\mathrm{OCH}}_3+\mathrm{CO}$ on the (001), (010), and (100) HO:CO surfaces computed at MPWB1K‐D3(BJ)/6‐31G(d, p). Distances are in Å. The ZPE‐corrected energy barriers ($\Delta H_{\mathrm{TS}}$) and reaction energies ($\Delta H_{\mathrm{R}}$) of each reaction with respect to the reactants are also provided in kJ mol.

Figure 3.

Reactants (R), transition states (TS), and products (P) of Equation (3) ${\mathrm{CH}}_2\mathrm{OH}+\mathrm{CO}$ on the (001), (010), and (100) HO:CO surfaces computed at BHLYP‐D3(BJ)/6‐31G(d, p). Distances are in Å. The ZPE‐corrected energy barriers ($\Delta H_{\mathrm{TS}}$) and reaction energies ($\Delta H_{\mathrm{R}}$) of each reaction with respect to the reactants are also provided, in kJ mol.

From the relative orientation of the radical and the CO in the TS structure, we can already foresee which conformer will be obtained as a product: trans‐${\mathrm{COOCH}}_3$ only and both syn, cis‐${\mathrm{COCH}}_2\mathrm{OH}$ (in complex 14) and gauche, trans‐${\mathrm{COCH}}_2\mathrm{OH}$ (in complexes 184 and 32). The energy barriers ($\Delta$ $H_{\mathrm{TS}}$, accounting for ZPE corrections) computed at different surface sites span a narrow range from 32.2 to 38.4 kJ mol for ${\mathrm{OCH}}_3$ +${\mathrm{CO}}_{(\mathrm{ice})}$ (vs. 27.5 kJ mol for trans‐${\mathrm{COOCH}}_3$ in the gas phase) and from 17.5 to 20.3 kJ mol for ${\mathrm{CH}}_2\mathrm{OH}$ + ${\mathrm{CO}}_{(\mathrm{ice})}$ (vs. 19.8 and 29.0 kJ mol for syn, cis‐ and gauche, trans‐${\mathrm{COCH}}_2\mathrm{OH}$ in the gas phase, respectively). The actual contribution of the surface to promote these reactions is manifold: i) it provides one of the reactants (CO), ii) it acts as reactant concentrator, favoring the encounter probability of the radicals with CO, iii) it imposes geometrical constraints, directing which conformers form, and iv) as a third body by dissipating the energy released in the formation of a chemical bond and stabilizing the newly formed products, as it has been reported in recent studies.^{[ 23 , 64 , 65 ]}

From the computed energy barriers, it emerges that the one for ${\mathrm{COCH}}_2\mathrm{OH}$ formation is almost half of that computed for ${\mathrm{COOCH}}_3$ formation. This aligns with the findings of a theoretical investigation focused on the “radical + closed‐shell” reaction $\mathrm{HCO}+{\mathrm{H}}_2\mathrm{CO}$,^{[ 53 ]} which yields MF and GA precursors depending on their orientation in the TS. Similarly to what we observe in this work, the study showed that GA formation is energetically more favorable than MF due to the lower energy barrier of the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{C}$ bond formation compared to $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{O}$.

A further factor to be considered is the effect of the icy water molecules on the reactants. In principle, both ${\mathrm{OCH}}_3$ and ${\mathrm{CH}}_2\mathrm{OH}$ can interact with the surface via H‐bonds. However, ${\mathrm{OCH}}_3$ forms a long and weak H‐bond (2.556 Å) with water only in one case (complex 37), yet the energy barrier at this site remains comparable to that in complex 205, where radical–surface interactions are stronger. In contrast, ${\mathrm{CH}}_2\mathrm{OH}$ can both donate and accept H‐bonds through its hydroxyl group, as observed in complex 184, contributing to its large BH(0). Nevertheless, this interaction does not hamper its reactivity, as the ${\mathrm{CH}}_2$ moiety remains free to rotate toward CO. Thus, for both ${\mathrm{CH}}_2\mathrm{OH}$ and ${\mathrm{OCH}}_3$, H‐bonds do not prevent the formation of the ${\mathrm{COOCH}}_3$ and ${\mathrm{COCH}}_2\mathrm{OH}$ radicals and the differences in the reaction barriers are due to the effects of the surface on the reactant geometries.

Finally, we computed the BH(0)s of the ${\mathrm{COOCH}}_3$ and ${\mathrm{COCH}}_2\mathrm{OH}$ radicals obtained from the first reaction step. Since one of the CO molecules of each original surface becomes part of the reaction product, we defined as a reference slab the optimized surface obtained after removal of the radical. The BH(0) values are listed in Table 3. ${\mathrm{COOCH}}_3$ interacts weakly with the surface (BH(0) = 8.3–21.7 kJ mol), in contrast to ${\mathrm{COCH}}_2\mathrm{OH}$, whose BH(0) values range from 27.9 to 79.1 kJ mol. In particular, the complex 184 is characterized by the largest BH(0) due to two H‐bonds established with the water molecules of the ice (see bottom panel of Figure 3). Cis‐${\mathrm{COCH}}_2\mathrm{OH}$ is the conformer with the weakest BH(0), due to its preference for an intramolecular H‐bond, which causes the molecule to interact only through weak forces with the surface.

The large variability in these BH(0) values is partially due to the fact that the ice model is relatively labile, as mentioned above. Its optimization, subsequent to the removal of one of the external CO molecules, causes surface rearrangements that could alter the final BH(0) obtained for ${\mathrm{COOCH}}_3$ and ${\mathrm{COCH}}_2\mathrm{OH}$.

2.2.3. LH: 2) H + ${\mathit{COOCH}}_{\mathit{3}}$ and 4) H + ${\mathit{COCH}}_{\mathit{2}}\mathit{OH}$

After the formation of the ${\mathrm{COOCH}}_3$ and ${\mathrm{COCH}}_2\mathrm{OH}$ radicals, one H atom addition is required to obtain the final products. As shown in Figure  4 , atomic H is initially placed at the surface near the radical species. To prevent the direct reaction between the H atom and the radical, the complex was first optimized in the triplet electronic state and subsequently as an open‐shell singlet, which allows but does not force the coupling of the two unpaired electrons in the same orbital.

Figure 4.

Top view of the positions where the H atom was adsorbed on the (010) surface for the H + COOCH reaction (top panel) and for the H + ${{\mathrm{COCH}}_2\mathrm{OH}}_{(ice)}$ reaction (bottom panel).

A careful study of the hydrogenation reaction was conducted on the 37 (MF) and 14 (GA) complexes. The choice was based on taking structures that show the smallest $\Delta$ $H_{\mathrm{TS}}$ in the first reaction step and that has the CO moiety more exposed toward the exterior of the surface to facilitate the reaction with the H atom. Hydrogen was initially adsorbed on five different positions surrounding ${\mathrm{COOCH}}_3$ and ${\mathrm{COCH}}_2\mathrm{OH}$ in order to examine whether or not the formation of the product is barrierless (as in the gas phase).

The hydrogenation step resulted in the spontaneous formation of MF and GA in 3 and 2 out of 5 cases, respectively, as summarized in Table  4 . Initially, the H atom was located in the surroundings of the carbonyl moiety of ${\mathrm{COOCH}}_3$ and ${\mathrm{COCH}}_2\mathrm{OH}$, and the system was optimized in the triplet state, this way Pauli repulsion determining the distance between the two radicals (listed in Table 4).

Table 4.

Outcomes of the H addition to ${\mathrm{COOCH}}_3$ and ${\mathrm{COCH}}_2\mathrm{OH}$. The surface site number is referred to Figure 4. The $\mathrm{C}–\mathrm{H}$ distances of the optimized triplet and open‐shell singlet electronic spin state complexes are given in Å. The energy difference between the triplet and the singlet state ($\Delta$ $E_{(\mathrm{s}–\mathrm{t})}$, in kJ mol) is provided: a number close to zero is indicative of no reaction.

H + ${\mathrm{COOCH}}_{3\left(\mathrm{ice}\right)}$ 37
Surface Site	Barrier	$\mathrm{C}–\mathrm{H}$ Triplet	$\mathrm{C}–\mathrm{H}$ Singlet	$\Delta$ $E_{(\mathrm{s}–\mathrm{t})}$
1	NO	3.666	1.098	−440.1
2	YES	4.044	4.043	−0.1
3	YES	4.360	4.354	−0.1
4	NO	4.100	1.102	−417.6
5	NO	4.470	1.101	−420.3
H + ${{\mathrm{COCH}}_2\mathrm{OH}}_{\left(\mathrm{ice}\right)}$ 14
Surface Site	Barrier	$\mathrm{C}–\mathrm{H}$ Triplet	$\mathrm{C}–\mathrm{H}$ Singlet	$\Delta$ $E_{(\mathrm{s}–\mathrm{t})}$
1	NO	3.207	1.098	−392.2
2	YES	3.857	3.824	−0.2
3	YES	3.915	3.839	−0.3
4	NO	3.578	1.099	−393.6
5	YES	4.596	4.715	−0.5

Subsequent open‐shell singlet optimization yields the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{H}$ bond formation but only in those situations where the two partners have a favorable orientation. Two factors concur to determine such a condition: the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{H}$ distance and the eventual presence of an obstacle between the H atom and the reactive center. For this reason, for $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{H}$ distances larger than and 3.6 Å (for GA) there is no formation of the product during the geometry optimization process, while it is not possible to define a distance threshold for the formation of MF. This is in agreement with the previous findings of Perrero et al.,^{[ 26 ]} where ${\mathrm{CH}}_3\mathrm{CHO}$ was formed spontaneously on the same surfaces for H atoms located at a maximum distance of 3.5 Å from the carbonyl moiety of ${\mathrm{CH}}_3\mathrm{CO}$. Relaxed scan calculations along the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{H}$ distance were performed on the complexes, in which no spontaneous formation of MF and GA was observed, which indicated the presence of small diffusion barriers (less than 4 kJ mol, below the chemical accuracy). This is due to the flat PES, a direct consequence of the weak interaction between the H atom and the surface (the BE ranging from 0.7 to 1.6 kJ mol at MPWB1K‐D3(BJ) and from 2.7 to 4.4 kJ mol at BHLYP‐D3(BJ) level of theory). Therefore, we can conclude that there is not actually a barrier for the second step of the reaction.

Table 4 also reports the energy difference between the biradical system in the electronic spin state of open‐shell singlet and triplet ($\Delta$ $E_{(\mathrm{s}-\mathrm{t})}$). An energy close to zero is indicative of no reaction, while in case of $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{H}$ bond formation, the value corresponds to $\Delta$ $H_{\mathrm{R}}$. The $\Delta$ $E_{(\mathrm{s}-\mathrm{t})}$ computed for MF formation comprises between $-$420 and $-$440 kJ mol, in agreement with the gas phase $\Delta$ $H_{\mathrm{R}}$ = $-$435.5 kJ mol. Similarly, for the GA formation, we obtained $\Delta$ $E_{(\mathrm{s}-\mathrm{t})}$ $\approx$ $-$395 kJ mol, which agrees with the $\Delta$ $H_{\mathrm{R}}$ = $-$399.3 kJ mol of the gas‐phase reaction. These values comply with the typical reaction energies of radical–radical couplings.^{[ 54 ]}

Similarly to what was done with the products of the first reaction step, we provided the BH(0)s of the MF and GA obtained on the reactive surface sites (an overview of the structures is available in SI, Figure S7, Supporting Information). The BH(0)s, computed after defining as a reference slab the optimized surface obtained after removal of the product, are presented in Table 3.

The BH(0)s of ${\mathrm{HCOOCH}}_3$ span a range from 11.7 kJ mol (interaction through weak forces) to 43.8 kJ mol (MF accepts a H‐bond from a neighbor water molecule) and are slightly larger than those of ${\mathrm{COOCH}}_3$. We observe a similar moderate increase for ${\mathrm{HCOCH}}_2\mathrm{OH}$, where the syn, cis conformer has the weakest BH(0) = 24.7 kJ mol (no H‐bond formation is observed), while for gauche, trans‐GA BH(0) = 52.5 and 83.8 kJ mol due to forming 2 and 3 H‐bonds with the water molecules of the surface, respectively. The presence of $\mathrm{O}[chemistry\; single\; bond\; solid\; line]\mathrm{H}$ and $\mathrm{H}[chemistry\; single\; bond\; solid\; line]\mathrm{C}[chemistry\; double\; bond\; solid\; lines]\mathrm{O}$ moieties in the final products offers the chance to establish H‐bonds that, however, depend on the chemical environment of the surface. The absence or presence of neighboring water molecules alters the strength of the interaction with the adsorbate, resulting in wide BH(0) ranges. However, the few structures available for the determination of the BEs of the products do not allow the definition of a BH(0) distribution, which would be more appropriate for a thorough and accurate characterization of the interaction between the adsorbate and the surface. Nevertheless, the computation of the BEs is not the primary aim of this work.

In the literature, no other estimation of the BH(0)s of these species on a dirty ice model has been documented. However, trapping and desorption experiments of GA and MF adsorbed on or in water ices at 20 K showed that MF desorbs at lower temperatures (and thus interacts more weakly with the ice) than GA,^{[ 66 ]} confirming the behavior we observed in our calculations. Additionally, the BEs computed on both crystalline and amorphous pure water ice surfaces report BH(0)s = 21–66 kJ mol for cis‐${\mathrm{HCOOCH}}_3$ and BH(0)s = 31–99 kJ mol for anti, trans‐${\mathrm{HCOCH}}_2\mathrm{OH}$.^{[ 67 ]} While the range spanned by the BH(0)s of GA is very similar to that of this work (despite the different conformers considered), the BH(0)s of MF on pure ${\mathrm{H}}_2\mathrm{O}$ ice cover a broader range, with the lowest ends slightly shifted toward larger values. This is understandable as i) a pure water ice model offers stronger binding sites than the dirty H₂O:CO ice used in this work, and ii) distinct conformations may establish different interactions with the ice surface, due to their geometry. Despite the different composition of the two ice models, the similar BH(0) ranges are due to the presence of weak binding sites offered either by neighboring CO molecules (this work) or by weakly polar regions of the amorphous water ice model.^{[ 67 ]}

2.3. Grain‐Surface Reactions: ER Mechanism

2.3.1. ER: 1) ${\mathit{OCH}}_{\mathit{3}}$ + ${\mathit{CO}}_{(\mathit{ice})}$ and 3) ${\mathit{CH}}_{\mathit{2}}\mathit{OH}$ + ${\mathit{CO}}_{(\mathit{ice})}$

In the ER mechanism, gas‐phase species approach the surface and directly react with one of its components. To simulate the fall of a radical toward the surface, several geometries, in which the distance between the gaseous species (${\mathrm{OCH}}_3$ or ${\mathrm{CH}}_2\mathrm{OH}$) and the targeted icy CO progressively decreases, were generated.

The reactions were simulated on the same surface sites where the LH reactions were previously characterized: 37 for MF and 14 for GA formation. The top panel of Figure  5 reports the relaxed scans of ${\mathrm{OCH}}_3+{\mathrm{CO}}_{\left(\mathrm{ice}\right)}$ and ${\mathrm{CH}}_2\mathrm{OH}$ + ${\mathrm{CO}}_{\left(\mathrm{ice}\right)}$ obtained by decreasing the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{O}$ and $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{C}$ distances, respectively. In both cases, there is first a slight stabilization due to the intermolecular interaction between the two partners. Indeed, both processes are characterized by a wide and shallow potential well ($\approx$ –5 kJ mol for ${\mathrm{OCH}}_3$ and $\approx$ –9 kJ mol for ${\mathrm{CH}}_2\mathrm{OH}$) located approximately at 3.0 Å from the ${\mathrm{CO}}_{\left(\mathrm{ice}\right)}$. The maximum of the ${\mathrm{OCH}}_3$ + ${\mathrm{CO}}_{\left(\mathrm{ice}\right)}$ energy curve is located at 1.861 Å and corresponds to the transition state of $\mathrm{OC}[chemistry\; single\; bond\; solid\; line]{\mathrm{OCH}}_3$ formation. The $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{O}$ distance agrees well with that found in the LH mechanism (1.870–1.891 Å) and in the gas phase (1.877 Å). The energy barrier of the ER pathway ($\Delta$E = 28.6 kJ mol) almost corresponds to the average value in the range computed in the LH process ($\Delta E$ = 26.3–32.0 kJ mol) and is very close to that of the gas‐phase reaction ($\Delta E$ = 27.4 kJ mol), as expected due to the absence of diffusion in both the ER and the gas‐phase mechanism.

Figure 5.

Relaxed scans along selected bond distances of the ER formation of MF (red line) and GA (blue line). The top panel is for the first reaction step (formation of $\mathrm{OC}-{\mathrm{OCH}}_3$ and $\mathrm{OC}-{\mathrm{CH}}_2\mathrm{OH}$), while the bottom panel is for the hydrogen addition step (formation of $\mathrm{H}-{\mathrm{COOCH}}_3$ and $\mathrm{H}-{\mathrm{COH}}_2\mathrm{OH}$).

Similarly, the maximum of ${\mathrm{CH}}_2\mathrm{OH}$ + ${\mathrm{CO}}_{\left(\mathrm{ice}\right)}$ potential energy curve is located at 2.189 Å, the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{C}$ distance in the TS geometry being slightly larger than in the LH mechanism (2.085–2.139 Å) and in the gas phase reaction (2.104 Å). The energy barrier of the ER process $\Delta$ $E_{\mathrm{TS}}$ = 16.7 kJ mol is located between that of LH mechanism ($\Delta$ $E_{\mathrm{TS}}$ = 11.8–14.7 kJ mol) and that of the gas‐phase reaction ($\Delta$ $E_{\mathrm{TS}}$ = 19.8 k mol).

After the maximum energy point is reached, the potential energy of the system decreases, indicating that the formation of the chemical bond is energetically favored. The $\Delta$ $E_{\mathrm{R}}$ extracted from Figure 5 ($\Delta$ $E_{\mathrm{R}}$ $\approx$ $-$130 kJ mol for ${\mathrm{COOCH}}_3$ and $\approx$ $-$85 kJ mol for ${\mathrm{COCH}}_2\mathrm{OH}$) is larger than those computed in both the LH and the gas‐phase mechanism ($\Delta$ $E_{\mathrm{R}}$ $\approx$ $-$90 kJ mol for ${\mathrm{COOCH}}_3$ and $\approx$ $-$40 kJ mol for ${\mathrm{COCH}}_2\mathrm{OH}$). The difference between the $\Delta$ $E_{\mathrm{R}}$ is approximately comparable with the BH(0) of the radical (${\mathrm{OCH}}_3$ or ${\mathrm{CH}}_2\mathrm{OH}$) that in the LH mechanism is adsorbed on the surface, while in the ER process, it comes from the gas phase.

The agreement between the gas‐phase and the surface (LH and ER) mechanisms in the energetics computed for the first reaction step does not imply that the ER reaction mechanism can effectively yield the desired product. In fact, the ER mechanism is only efficient when the reaction proceeds without an energy barrier^{[ 15 ]}: this is true for some radical–radical couplings and for reactions such as those between atomic carbon and water.^{[ 18 ]} In contrast, when in the presence of a reaction barrier, a van der Waals complex between the gas‐phase species and the surface may form, and energy dissipation causes the stabilization of the complex.^{[ 15 ]} From here, the reactivity would then follow the LH mechanism, which is what we expect based on the relaxed scan computed for $\mathrm{OC}[chemistry\; single\; bond\; solid\; line]{\mathrm{OCH}}_3$ and $\mathrm{OC}[chemistry\; single\; bond\; solid\; line]{\mathrm{CH}}_2\mathrm{OH}$ formation. Nevertheless, for completeness, we also simulated the ER hydrogenation step.

2.3.2. ER: 2) H + ${\mathit{COOCH}}_3$ and 4) H + ${\mathit{COCH}}_{\mathit{2}}\mathit{OH}$

Both H + ${\mathrm{COOCH}}_{3\left(\mathrm{ice}\right)}$ and H + ${{\mathrm{COCH}}_2\mathrm{OH}}_{\left(\mathrm{ice}\right)}$ reaction steps are characterized by a decrease in the electronic energy of the system, as the $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{H}$ distance is reduced (see the bottom panels of Figure 5). Concurrently, the electronic spin state of the system changes from open‐shell singlet (at large distances) to closed‐shell singlet (at short distances), once the H atom is located at $<$2.0 Å from the CO moiety.

As expected from a radical–radical coupling, the reaction is barrierless. The energy liberated by the formation of the product is $\approx$400 kJ mol for ${\mathrm{HCOCH}}_2\mathrm{OH}$ and slightly higher for ${\mathrm{HCOOCH}}_3$, in accordance with the energies computed in the gas‐phase processes ($\Delta$ $H_{\mathrm{R}}$=$-$414 kJ mol and $\Delta$ $H_{\mathrm{R}}$=$-$399 kJ mol for ${\mathrm{HCOOCH}}_3$ and ${\mathrm{HCOCH}}_2\mathrm{OH}$, respectively). Additionally, these data agree with the $\Delta$ $H_{\mathrm{R}}$ presented in Table 4 for the LH mechanism.

Despite the presence of several species that could be hydrogenated on the surface, the large quantity of H atoms freezing out on the surface of dust grains ensures that ${\mathrm{COOCH}}_3$ and ${\mathrm{COCH}}_2\mathrm{OH}$ will eventually undergo hydrogenation. Nevertheless, several distinct H additions and H abstraction processes could occur on the surface. The most important is the hydrogenation of CO, which is the most abundant species of the dirty ice surfaces here considered after water. The formation of $\mathrm{HCO}$ ^{[ 23 ]} should not be considered as a competitive reaction, since its radical coupling with ${\mathrm{OCH}}_3$ and ${\mathrm{CH}}_2\mathrm{OH}$ may yield MF and GA, respectively.^{[ 54 ]} The same reactants could also lead to the formation of CO + ${\mathrm{CH}}_3\mathrm{OH}$ and ${\mathrm{H}}_2\mathrm{CO}$ + ${\mathrm{H}}_2\mathrm{CO}$ that, when included in a network of H abstraction and H addition reactions, could newly produce the radicals needed to form the final COMs. To better untangle this strictly linked reaction network, more calculations should be performed.

2.4. Astrochemical Implications

In this work, the synthesis of MF and GA was characterized adopting two different reaction mechanisms, i.e., via LH and ER mechanisms. Calculations showed that $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{C}$ and $\mathrm{C}[chemistry\; single\; bond\; solid\; line]\mathrm{O}$ bond formations are characterized by energy barriers, as expected when an open‐shell species reacts with a closed‐shell molecule. At variance, the hydrogenation of ${\mathrm{COOCH}}_3$ and ${\mathrm{COCH}}_2\mathrm{OH}$ radicals was almost barrierless, as radical couplings usually are.

Despite a few exceptions, e.g.,^{[ 32 , 56 , 68 ]} the computational literature does not explicitly deal with the MF and GA conformers. However, it is possible to identify them by checking the structures presented in these studies. Radical–radical coupling pathways yield the trans‐conformer of both MF and GA,^{[ 54 ]} whereas the cis conformer arises from “radical + closed‐shell” reactions.^{[ 53 ]} In this work, both syn, cis‐ and gauche, trans‐GA conformers are formed via the grain‐surface reaction between CO and ${\mathrm{CH}}_2\mathrm{OH}$. The interconversion barrier from gauche, trans‐ to syn, cis‐GA is 10.0 kJ mol (see SI, Figures 4, Supporting Information), compared to the BH(0) = 52.5–83.8 kJ mol. Therefore, if the species has sufficient kinetic energy to break the interaction with the surface, then it desorbs retaining most of the energy excess to itself (it cannot be dissipated by the surface), which can be used for internal rearrangements of the species such as the interconversion from gauche, trans‐ to syn, cis‐GA, the most stable and usually detected conformer. In contrast to the finding of ref. [32], only the trans‐MF conformer was formed on the ice surface. According to the literature, the reaction between HCOOH and ${\mathrm{CH}}_3\mathrm{OH}$ yields both cis‐ and trans‐MF conformers.^{[ 56 ]} The authors propose that interconversion between MF conformers is unlikely to occur in the ISM once the products desorb into the gas phase, due to the large interconversion barrier. In this work, we computed a barrier of 35.5 kJ mol for the trans‐to‐cis interconversion, which is within the BH(0) = 11.7–43.8 kJ mol range. In this case, thus, much more residual kinetic energy would be required for internal rearrangements with respect to gauche, trans‐GA, making a less probable, but not completely excluding the interconversion to cis‐MF. Thus, two hypotheses could contribute to the widespread detection of the cis conformer compared to the singular observation of trans‐MF^{[ 32 ]}: the two conformers may originate from distinct reaction pathways,^{[ 68 , 69 ]} or the trans‐conformer may rearrange to the cis‐one after desorption.

The prevalence of reaction pathways favoring GA formation over MF contrasts with observations, as MF is the most abundant ${\mathrm{C}}_2{\mathrm{H}}_4{\mathrm{O}}_2$ isomer. Nevertheless, some star‐forming regions exhibit a low MF/GA ratio, suggesting that the local stellar environment influences the abundances of ${\mathrm{C}}_2{\mathrm{H}}_4{\mathrm{O}}_2$ isomers. This suggests that a distinct chemical network operates in those regions, in contrast to high‐mass star‐forming environments, where the MF/GA ratio is significantly higher.^{[ 70 ]}

However, when considering surface reactions, one should not limit the discussion to the reaction energy barriers alone, but also consider the fate of the reaction products. Observations determine the gas‐phase abundances of COMs, thus requiring the products to desorb from the surface. Desorption is governed by the BH(0)s, which were computed for both the radicals ${\mathrm{COOCH}}_3$ and ${\mathrm{COCH}}_2\mathrm{OH}$ (8.3–21.7 and 27.9–79.1 kJ mol, respectively), as well as for the products ${\mathrm{HCOOCH}}_3$ and ${\mathrm{HCOCH}}_2\mathrm{OH}$ (11.7–43.8 and 24.7–83.8 kJ mol, respectively). Methyl formate and its precursor interact weaker with the surface than gauche, trans‐glycolaldehyde (BH(0) = 52.5–83.8 kJ mol), which instead spans a wide range of BH(0)s, exceeding that of water (14.2–61.6 kJ mol, peaking at 35.2 kJ mol).^{[ 71 ]} In contrast, syn, cis‐glycolaldehyde (BH(0) =24.7 kJ mol) is weakly bound to the ice surface, due to the intramolecular H‐bond that prevents the molecule from engaging in other interactions with the water molecules of the surface. Therefore, we expect syn, cis‐GA and MF to desorb prior to water, while gauche, trans‐GA will remain adsorbed on the grains until the large majority of water has desorbed. This could explain why, despite the most efficient grain‐surface production of GA, MF is the most abundant ${\mathrm{C}}_2{\mathrm{H}}_4{\mathrm{O}}_2$ isomer in the gas phase.

3. Conclusion

This work is a computational study on the formation of MF and GA on HO:CO slab models, mimicking the surfaces of interstellar ice mantles. The investigated pathway consists of two steps. The first is based on the “radical + ice” mechanism, in which a radical species reacts with one of the ice components, here CO; the second is an H addition emulating a radical–radical coupling reaction.

The reaction between ${\mathrm{OCH}}_3$ and ${\mathrm{CO}}_{\left(\mathrm{ice}\right)}$ is characterized by an energy barrier of around 32–38 kJ mol, while that between ${\mathrm{CH}}_2\mathrm{OH}$ and ${\mathrm{CO}}_{\left(\mathrm{ice}\right)}$ has a smaller energy barrier of 17–20 kJ mol. Compared to the gas‐phase process, the presence of the surface promotes the formation of GA, while it hinders that of MF. The explanation for such effect resides in the atomistic details of the interaction between the radical and the ice surface, which has a direct consequence on the energetics of the system. The same processes simulated via the ER mechanism show similar energy barriers. Atomic H additions are instead barrierless via both LH and ER mechanisms. Therefore, considering interstellar conditions, these processes are not feasible due to presenting exceedingly high energy barriers.

Despite this, our simulations provide useful astrochemical insights. They suggest that the formation of GA is energetically more favored than that of MF. This is in agreement with previous studies, but strikes with the MF/GA ratio observed in a number of sources, for which the abundance of MF is similar or greater to that of GA. In fact, the BEs of ${\mathrm{COOCH}}_3$ and ${\mathrm{HCOOCH}}_3$ indicate that these species are less bounded to the ice compared to ${\mathrm{COCH}}_2\mathrm{OH}$ and ${\mathrm{HCOCH}}_2\mathrm{OH}$, and therefore, MF can desorb at lower temperatures than GA. This could offer an explanation to the larger abundance of MF compared to GA as detected in astrophysical environments. Nevertheless, alternative reaction pathways remain to be explored in order to better constrain the formation and destruction of these species in the ISM.

4. Computational Methods

Simulations were performed with crystal23 ^{[ 72 ]} (periodic DFT calculations) and ORCA 6.0.1^{[ 73 ]} (molecular post‐Hartree–Fock calculations). Visualization and manipulation of structures were executed with MOLDRAW.^{[ 74 ]}

Formation of ${\mathrm{HCOOCH}}_3$ and ${\mathrm{HCOCH}}_2\mathrm{OH}$ was initially simulated in the gas phase with the aim of selecting the most suitable DFT functional to be applied to extended surface models. The performance of BHLYP^{[ 75 , 76 ]} and MPWB1K^{[ 77 ]} with Grimme's D3 Becke–Johnson dispersion correction,^{[ 78 , 79 ]} combined with the Pople‐based 6‐31G(d, p)^{[ 80 ]} basis set was tested against a higher reference level of theory. The geometrical counterpoise correction was accounted for in the geometry optimisations, in order to correct for both intermolecular and intramolecular basis set superposition errors (BSSE), which are expected to be significant due to the small basis set useda in the calculations.^{[ 81 , 82 ]} As a reference methodology, the explicitly correlated variant of the coupled‐cluster approach with single‐, double‐, and perturbative triple‐excitations, CCSD(T)‐F12, was selected.^{[ 83 , 84 ]} This post‐Hartree–Fock method requires the use of correlation‐consistent basis sets. In our case, aug‐cc‐pVTZ was employed as the main basis set, while cc‐pVTZ‐F12, cc‐pVTZ‐F12‐CABS, and aug‐cc‐pVQZ/C were added as auxiliary basis sets.^{[ 85} , ^{86 – 87 ]}

The periodic ice surface models adopted here were characterized in a previous publication.^{[ 26 ]} Briefly, one every four ${\mathrm{H}}_2\mathrm{O}$ molecules of a crystalline P‐ice model were substituted with CO, generating a dirty ice bulk. Lately, three amorphous‐like surfaces cut along the (001), (010), and (100) planes from the bulk were fully optimized, resulting in amorphous‐like slabs, each with a different percentage of CO. In this work, each surface was fully relaxed at the level of theory selected for the specific reaction, prior to the adsorption of the radicals. In the following calculations, only the atomic positions were optimized, while the cell parameters were kept fixed.

The sampling of the reciprocal space was conducted with a Monkhorst–Pack mesh, with the shrinking factor of (2 2 1), which generates four irreducible k points in the first Brillouin zone. Truncation criteria for bielectronic integrals were set to 10, 10, 10, 10, and 10 through the tolinteg keyword. The self‐consistent field iterative procedure was converged to a tolerance in total energy of $\Delta E$ = 10 a.u. for single energy point calculations, $\Delta E$ = 10 a.u. for geometry optimisations, and $\Delta E$ = 10 a.u. for frequency calculations.

Geometry optimisations were performed with default convergence criteria (root mean square, RMS, of the gradient to 0.0003 a.u. and RMS of the displacement 0.0012 a.u.) in all cases, with the exception of transition state structure optimisations (in which they were set to one third of the default value). Scan calculations aimed at characterizing the PES along a specific bond length were characterized by steps of 0.1 Å and loose convergence criteria (RMS of the gradient to 0.0009 a.u. and RMS of the displacement 0.0036 a.u.), since the aim was to generate guess structures that would undergo successive refinements.

Vibrational frequency calculations within the harmonic approximation were calculated at the $\mathrm{\Gamma }$ point. Each Hessian matrix element was computed numerically by means of the three‐point formula based on one displacement of 0.001 Å from the minimum along each Cartesian coordinate of the whole system for adsorption complexes. At variance, the calculation was restricted to the atoms involved in the reaction for the structures related to the reaction mechanism. The small size of the fragment here considered allowed the use of the more accurate six‐point formula based on two displacements along each Cartesian coordinate of each atom. This strategy was validated by our research group in the past and was shown to be satisfactory.^{[ 63 , 88 , 89 ]} The ZPE correction was computed with the standard rigid rotor/harmonic oscillator formalism. Reactants and products are confirmed to be linked to the transition states structures through a SCANMODE calculation, which follows the eigenvector of the selected mode (the imaginary frequency of the transition state structure), in a similar fashion to an intrinsic reaction coordinate simulation. The optimized endpoints of the SCANMODE result in the previously modeled reactants and the products.

The strength of the interaction between the radical and the surface was measured by calculating the BE, following the scheme adopted in previous publications.^{[ 26 , 90 ]} In this case, the use of the geometrical counterpoise in the calculation yields BSSE‐free adsorption geometries, and therefore, the calculated BEs are intrinsically corrected for the BSSE. We defined BH(0) as the BE corrected for the $\Delta$ZPE at 0 K

$$\begin{array}{ccc}\mathrm{BE}& =& -\Delta E_{\mathrm{ads}}\\ \Delta E_{\mathrm{ads}}& =& E_{\mathrm{complex}}-E_{\mathrm{surface}}-E_{\mathrm{radical}}\\ \mathrm{BH}\left(0\right)& =& \mathrm{BE}-\mathrm{\Delta ZPE}\end{array}$$ (5)

where $\Delta E_{\mathrm{ads}}$ represents the adsorption energy; and $E_{\mathrm{complex}}$, $E_{\mathrm{surface}}$, and $E_{\mathrm{radical}}$ are the absolute potential energies of the adsorption complex, the bare surface, and the gas‐phase adsorbate, respectively.

Radical–radical reactions were modeled using the broken‐(spin)‐symmetry ansatz to correctly describe the open‐shell singlet state of the biradical system, allowing two unpaired electrons with opposite spin to occupy different orbitals, thereby avoiding to force the recombination between the two radicals.^{[ 91 , 92 ]}

The geometries needed to simulate the ER reaction mechanism were generated via a Python script, which is provided in Supporting Information. In order to obtain the PES along the bond distance of interest, only the atomic coordinates of the gas‐phase radical were optimized, thus preventing the radical from falling onto the surface. The coordinates of the atoms belonging to the surface, as well as the distance between the two atoms involved in bond formation, were kept frozen. This strategy was adopted to overcome the limitation of a classic scan calculation, in which only the distance between two atoms is kept fixed. This condition defines a hemisphere of points, where the incoming species can be located (due to the presence of the underlying surface), including points that are close to the surface. This would immediately cause any species approaching from the gas phase to fall onto the surface as the energy of the interacting system would be lower than the noninteracting one (provided that the BE of the species on the surface is a positive quantity).

Conflict of Interest

The authors declare no conflict of interest.

Author Contributions

Jessica Perrero: conceptualization, data curation, formal analysis, investigation, methodology, software, resources, writing—original draft, writing—review & editing. Albert Rimola: conceptualization, funding acquisition, project administration, resources, supervision, validation, writing—review & editing. Stefano Pantaleone: methodology, resources, supervision, writing—review & editing. Piero Ugliengo: validation, writing—review & editing.

Supporting information

Supplementary Material

Perrero Jessica, Pantaleone Stefano, Ugliengo Piero, Rimola Albert, ChemPlusChem 2025, 90, e202500324. 10.1002/cplu.202500324

Data Availability Statement

The Supplementary Material is freely available in Zenodo at https://doi.org/10.5281/zenodo.15268445.