Exploring the role of a single water molecule in the tropospheric reaction of glycolaldehyde with an OH radical: a mechanistic and kinetics study

Abstract

The mechanism, thermochemistry and kinetics of hydrogen abstraction pathways in the atmospheric reaction of glycolaldehyde with a hydroxyl radical, in the absence and presence of a single-water molecule under tropospheric conditions, are investigated. The pathways are explored through high-level quantum mechanical computations employing a global reaction route mapping method at the levels of coupled-cluster and density-functional theories employing BHandHLYP and M06-2X exchange–correlation functionals. The reaction is found to be dominated by the hydrogen abstraction pathways involving the aldehydic site in glycolaldehyde, both in the presence and absence of water. The spin-density from the natural orbital analysis and molecular orbitals predict that a few of the pathways, water-free as well as with water, proceed through a proton-coupled electron-transfer mechanism rather than the conventional free radical mechanism. The overall rate constant for the water-free reaction at room temperature, calculated using the transition state theory, at the CCSD(T)//BHandHLYP level, is found to be in good agreement with the experimental results, though the rate constants corresponding to the water-assisted reaction are found to be smaller by several orders of magnitude, but M06-2X was observed to overestimate the rate constants. However, contrary to the negative temperature-dependence exhibited by the rate constants observed in the case of the water-free reaction, the water-assisted rate constants exhibit a correct Arrhenius behavior with significant tunneling at low temperatures. Notably, cis–trans interconversion in glycolaldehyde is observed to be feasible along the water-assisted pathways contrary to that along the water-free pathways. Besides this, the present work also explored an addition reaction pathway for the addition of a hydroxy radical to the carbonyl group of glycolaldehyde which can result in species like hydroxyl-formaldehyde, hydroxyl-methyl and a dihydroxy radical.

---

1. Introduction

The assistance by a single-water molecule in the atmospheric reactions of a hydroxyl radical with various volatile organic molecules has attracted significant scientific interest in recent years.^1–11 These reactions mainly proceed through pre-reaction complexes (PRCs) which get transformed into the respective product complexes (PCs) via the transition states (TSs).^1–13 The hydrogen-bonded co-operation from a single-water molecule in the binary pre-reaction complexes, between the hydroxyl radical and the respective organic molecule, can result into a ternary complex (with water) which may be more stabilized than the binary pre-reaction complex, thereby lowering the reaction barrier.^1,2,5,6

However, as far as the kinetics of such reactions is concerned, it is not necessary that a single-water molecule can always accelerate the reaction, particularly, under the atmospheric conditions.^3,7,9 The formation of pre-reaction complexes with water can involve a significant loss of entropy due to the complexation, which in some cases may be so huge that the decrease of energy-barrier is no more relevant, and the Gibbs free-energy of activation may become even more significant. For example, in a recent study,⁶ on the reaction of formaldehyde with OH radical under the “tropospheric” conditions, the quantum-mechanically computed rate constant for the water-assisted reaction was found to be an order of magnitude less than that for the water-free reaction, even though a single-water molecule considerably lowered the reaction barrier.⁶ The lower rate constant for the water-assisted reaction than that of the water-free reaction was attributed to the low concentration of the reactant complex with water under the “tropospheric” conditions, besides the factors arising from the loss of entropy and quantum tunneling.^3,7

In fact, a similar observation was made in a previous study carried out by Iuga et al.,³ on the reaction of acetaldehyde with hydroxyl radical, under the atmospheric conditions. However, this is contrary to the experimental work reported by Vöhringer-Martinez et al.,⁴ in which the authors measured the effect of water leading to enhanced rate constant of this reaction in a laval-nozzle expansion at low temperature, which was further supported by the quantum mechanical calculations.⁴ However, a subsequent detailed quantum mechanical studies by Iuga et al.,³ revealed that the role of water has been overestimated in the study by Vöhringer-Martinez et al.⁴ Such controversies highlight the importance of further detailed theoretical investigations of such chemical reactions. Other reactions of this type in which the rate enhancement does not occur by incorporation of a single-water molecule is the reaction of glyoxal and acetone with hydroxyl radical.^7,9

The focus of the present study is the quantum mechanical analysis of a reaction relevant to the atmospheric chemistry: the water-catalyzed gas phase reaction of hydroxyl radical with glycolaldehyde. Hydroxyl radical generally abstracts hydrogen atoms from the glycolaldehyde to form water. There are three possible hydrogen-abstraction sites in the glycolaldehyde: the possibility of abstraction from the aldehydic site is 80%, whereas it is 20% for methylinic but negligible for the alcoholic site.¹² To investigate the catalytic effect of a single-water molecule in this reaction, the present work explores various possible water formation pathways of this reaction in the presence and absence of a single-water molecule. Previously, Galano et al.,¹² and Ochando-Pardo et al.,¹³ had studied the mechanism and kinetics of this reaction, but in the absence of water. Galano et al.,¹² reported the relative energy values of various stationary points modeled in their work, which revealed that the reactant complexes are stabilized with respect to the separated reactants. They also found that the interaction of these reactant complexes with a single-water molecule can further stabilize them,¹² but in this study, the effect of water catalysis and/or water-assistance on the complete reaction pathways of the system has not been investigated. The present work reports the detailed analysis on the assistance by a single-water molecule in the reaction of glycolaldehyde with OH radical. It should further be noted that the stationary points, to determine the reaction pathway, were intuitively located in the study by Galano et al., whereas the present work explores the reaction pathways by mapping the potential energy surface (PES) through a global reaction route mapping (GRRM)^14–20 methodology (described in the next section), thereby, providing new pre-reaction complexes, and hence, new pathways for hydrogen abstraction.

Further, the hydrogen abstraction reactions of the OH radical are known to follow mainly either a conventional free-radical hydrogen atom transfer (HAT)²¹ mechanism or proton-coupled electron-transfer (PCET)²² mechanism though a double-proton transfer mechanism can also be feasible.²¹ The net result of both the processes is same as that of HAT, however, in PCET, the proton and the electron to be transferred may come from different orbitals. To unravel the detailed mechanism followed during the abstraction of hydrogen in glycolaldehyde, a natural bond orbital (NBO)²³ analysis has also been carried out in the present work besides a molecular orbital analysis.

More importantly, the present work analyses the reaction rate constants using the transition state theory,²⁴ and compares with those known from the previous studies considering the effect of quantum tunneling.^3,7 Previously, Galano et al.,¹² had reported rate coefficients of this reaction using an approach based on the canonical variational theory with small-curvature tunneling (CVT/SCT),^25–27 combined with the quantum-mechanical calculation, where the calculated overall rate constant was determined to be 7.29 × 10⁻¹² cm³ per molecule per s, compared to an experimental known value of (1 ± 0.2) × 10⁻¹¹ cm³ per molecule per s reported in a study by Niki et al.,²⁸ using acetaldehyde as reference. In an another study by Bacher et al.,²⁹ using propene and acetaldehyde as reference, the corresponding experimental rate constants for the title reaction were found to be (1.28 ± 0.08) × 10⁻¹¹ and (1.65 ± 0.20) × 10⁻¹¹ cm³ per molecule per s respectively. Lately, using a pulsed laser technique, Karunanandan et al.,³⁰ estimated the rate coefficient to be (8.0 ± 0.8) × 10⁻¹² cm³ per molecule per s which is found to remain constant in the temperature range of 240–362 K, contrary to the theoretical studies of Galano et al.,¹² and Ochando-Pardo et al.,¹³ where a negative temperature dependence of the rate constants is predicted.

The paper is organized as follows: next section describes the details on the computational methodology, including the GRRM strategy, utilized for this work to trace the hydrogen abstraction pathways in glycolaldehyde. This is followed by the section on the Results and discussion which analyses the detailed mechanism and kinetics of the hydrogen abstraction pathways traced during this study both in the absence and presence of a single-water molecule under the tropospheric conditions, and their comparison with the previously known results. The last section makes a few concluding remarks.

2. Computational details

In the present work, various reaction pathways were explored through the GRRM method,^14–20 which works on the basic principle that whenever a reaction system goes towards the transition state or the dissociation channel, there is some distortion from the harmonic potential (around the equilibrium reaction species) in the downward direction, which is termed as anharmonic downward distortion (ADD).^14–20 Following these ADDs, GRRM can systematically explore the equilibrium structures (EQs), transition states (TSs) and the dissociation channels (DCs) on the PES of the reaction system, automatically elucidating the possible reaction pathways. GRRM deploys a combination of an uphill-walking technique based on a scaled hypersphere search (SHS)¹⁸ method to locate the TS, and a downhill-walking technique like IRC to obtain the equilibrium structures. Moreover, the ADD-following (ADDF) strategy in the GRRM can also be used for associative studies through a two-point SHS (2PSHS)³¹ algorithm, which can be deployed to locate the transition states connecting the reactants and products without any inceptive assumption of the TS.³¹ Recently, we have utilized GRRM to explore isomerization pathways in exotic radical species such as C₆H,³² and C₆N,³³ radicals as well as in metastable molecular anions of poly-deprotonated benzenes.³⁴ Besides this, stereochemical pathways of chiral molecules like 2-aminopropionitrile,³⁵ L-serine,³⁶ and water catalytic pathways in the reaction of hydroxyl radical with thioformic acid (TFA),¹ dithioformic acid² and mechanistic investigations of water-migration in the water-complexes of TFA,³⁷ and L-proline,³⁸ have also been successfully carried out using the GRRM.

In this work, through the GRRM, we had carried out the exploration for the reaction pathways of cis- and trans- isomers of glycolaldehyde reacting with the OH radical, in the presence as well as in the absence of a single-water molecule. The two most stable conformations of glycolaldehyde, depicted in Fig. 1, are OO-s-cis (I) and OO-s-trans (II).¹² The initial search for locating the reactant complexes or the pre-reaction complexes (PRCs) for the reaction of cis-glycolaldehyde with OH radical, in the absence as well as in the presence of a single-water molecule, was carried out at the DFT/BHandHLYP/6-31G level of theory using a hybrid Becke-half-and-half-Lee–Yang–Parr (BHandHLYP),³⁹ exchange–correlation (XC) functional of the density functional theory (DFT) and a 6-31G Gaussian basis set. All the computations reported in this work were carried out using GRRM in assistance with Gaussian 03 (ref. 40) and 09 (ref. 41) quantum mechanical software packages.

Fig. 1 BHandHLYP/6-311++G(d,p) optimized geometries, with bond lengths depicted in angstroms, for the two conformers of glycolaldehyde. The numerical values represent relative energies, with respect to cis-isomer (I) calculated at the CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) level of the theory. The total energy including (ZPE) of isolated cis-isomer (I) at the M06-2X/6-311++G(d,p), BHandHLYP/6-31G, BHandHLYP/6-311++G(d,p) and CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) levels of the theory, respectively, is −228.9585 (0.0621), −228.7587 (0.0635) a.u., −228.9261 (0.0633) a.u. and −228.5835 (0.0633) a.u.

The default GRRM exploration, which employs a full-ADDF search, automatically locates all the possible EQs, TSs and DCs, however, it is computationally quite expensive. Moreover, locating all the stationary points of each kind is not always necessary, for example, in the present study, locating reactant complexes is the primary requirement. For this purpose, GRRM provides an option of carrying out a restrictive search using “EQOnly” keyword.⁴² This saves computational time as well as computational resources since the transition states will be located only for those equilibrium states which are relevant to the abstraction pathways. Moreover, a full-ADD search explores even those pathways which lie quite high in energy and therefore, may be irrelevant. In view of this, only the low energy-barrier pathways of any chemical reaction are important. For the present work, only five-lowest energy pathways were searched using largest-ADD option (LADD = 5) in the GRRM.⁴²

The initial search at the BHandHLYP/6-31G level of the theory for the reaction of cis-glycolaldehyde with OH radical resulted in only one abstraction pathway corresponding to hydroxyl abstraction (see discussions later). Besides this, an equilibrium structure, PRC11 (depicted in ESI Fig. S1†) was also located which could be involved in a probable methylinic abstraction but a complete pathway corresponding to this could not be traced using GRRM. For cis-isomer, a PRC corresponding to aldehydic abstraction could not be obtained, though the exploration for the reaction pathways of trans-isomer provided two pathways for the aldehydic abstraction but no PRCs for hydroxy and methylinic abstraction were located for the trans-isomer. These aldehydic pathways traced are further depicted in Fig. 2. Since a PRC corresponding to the methylinic abstraction was not obtained from either cis- or trans-isomer, therefore, pathways corresponding to both cis- as well as trans-isomers, were intuitively located which resembled with those reported by Galano et al.,¹² and are depicted in Fig. 3.¹² The transition states (TSs) and the product complexes (PCs), for all the above mentioned pathways, depicted in Fig. 2–4, were obtained by the 2PSHS and IRC computations, respectively.

Fig. 2 Hydrogen abstraction pathways (path 1 and 2 at the aldehydic site) in the reaction of glycolaldehyde with OH radical, in the absence of water. The geometries, with bond lengths depicted in angstroms, are optimized at the BHandHLYP/6-311++G(d,p) level of the theory. The numerical values, with and without parentheses, respectively, represent the Gibbs free-energy change and relative energy, in kcal mol⁻¹, with respect to the isolated reactants R1, at the BSSE uncorrected CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) and BHandHLYP/6-311++G(d,p) levels of the theory, respectively. For path 2 transition-state, TS2*, relative energy value is at the BSSE corrected level, the corresponding BSSE uncorrected CCSD(T) single-point relative energy value is −2.45 kcal mol⁻¹ which is even lower than that of PRC2 by 0.13 kcal mol⁻¹.

Fig. 3 Same as Fig. 2 but for the hydrogen abstraction at the methylinic site in glycolaldehyde, through path 3 and 4, involving cis- and trans-isomers, respectively.

Fig. 4 Same as Fig. 2 but for the hydrogen abstraction at the hydroxyl site in glycolaldehyde, through water-free pathway (path 5) and water-assisted pathway (path 6), involving hydroxyl group in cis and trans conformations, respectively. * The numerical values, within square brackets for path 6, represent the relative energy, in kcal mol⁻¹, with respect to the isolated reactants R3, at the CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) level of the theory, except for TS6 which could not be refined at the specified level (see Table S1†).

For the water-assisted pathways of the reaction of cis-glycolaldehyde with OH radical in the presence of a single-water molecule, 192 minima were located utilizing the aforementioned options in the GRRM method at the same level of the theory. In this search, the relevant product complexes, PC7 to PC10 (depicted in Fig. 5 and 6), were obtained for the aldehydic and methylinic hydrogen atom abstractions, and the reactant complex PRC6, depicted in Fig. 4, was located for the abstraction at the hydroxy site. It should be noted that the binary complexes of glycolaldehyde with water (referred as BCs in Fig. 4–6) were obtained by re-optimization of the binary complexes obtained by the removal of OH radical from the ternary reactant complexes. The latter were located through a GRRM exploration on the reaction of OH radical with glycolaldehyde in the presence of a single-water molecule. The located transition states through 2PSHS computations were further saddle optimized, and to confirm the connection between the reactant and product complexes, IRC computations of the located TSs were carried out at the same level of the theory.

Fig. 5 Same as Fig. 2, but for the water-assisted hydrogen abstraction pathways at the aldehydic site in glycolaldehyde, through pathways 7 [H₂O] and 8 [H₂O], respectively, involving aldehydic group in cis and trans conformations. The relative energy and the Gibbs free energy change, in kcal mol⁻¹, are with respect to the isolated reactants R3.

Fig. 6 Same as Fig. 2, but for the water-assisted hydrogen abstraction pathways at the methylinic site in glycolaldehyde, through pathways 9 [H₂O] and 10 [H₂O], both resulting in the cis-conformation. The relative energies and the Gibbs free energy change, in kcal mol⁻¹, are with respect to the isolated reactants R3.

Further, the geometries of all the stationary points: EQs (reactants, products, reactant- and product-complexes) and TSs were refined at the BHandHLYP/6-311++G(d,p), and M06-2X/6-311++G(d,p) level using a meta-hybrid M06-2X⁴³ exchange–correlation functional of the DFT. The frequency calculations at the same level were carried out for each stationary point to ascertain that whether the given stationary point corresponds to minima (with no imaginary frequency) or to a transition state (first-order saddle point with one imaginary frequency). This also provided the zero-point energy (ZPE) correction. The energies of all the stationary points relevant to the abstraction pathways, re-optimized at BHandHLYP/6-311++G(d,p), were finally refined through the coupled-cluster (CC)⁴⁴ calculations at the CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) level of the theory. For the radical species, to take care of the odd electron, the unrestricted wavefunction at the UBHandHLYP/6-311++G(d,p) and UCCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) level was utilized during re-optimization and single-point energy calculations, respectively. The single point energy values (listed in Table S1, ESI†) calculated at the CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) level of the theory are further corrected for the basis set superposition error (BSSE) using the counterpoise method.⁴⁵ However, the BSSE correction seems to result in the overestimation of energy barriers, and its use may be erroneous as had been observed by other studies.^46,47 Therefore, to check the effect of basis set in the CCSD(T) computations, the single-point energy values were also calculated, using cc-pVTZ basis set, at the CCSD(T)/cc-pVTZ//BHandHLYP/6-311++G(d,p) level of the theory for one of the pathways explored in the present work (see Table S8, ESI†). But even using cc-pVTZ basis set, the BSSE corrected values remained overestimated.

Besides this, the relative energy values are also compared with those obtained with the zero-point energies, included in CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p), scaled with a scaling factor 0.9540.⁴⁸ The ZPE corrected energies of all the reactant complexes, transition states, product complexes and the separated products relative to the separated reactants are provided in Table S1 (ESI†), both for the water-free and water-assisted reaction, at the M06-2X/6-311++G(d,p), BHandHLYP/6-31G, BHandHLYP/6-311++G(d,p), CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p), levels of the theory, with and without BSSE correction. Further, to check for the spin contamination⁴⁹ in the open-shell species, the 〈S²〉 values at the BHandHLYP/6-31G, BHandHLYP/6-311++G(d,p) and CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) levels of the theory are analyzed in Table S2 (ESI†). It should be noted that except for the transition state TS10, various pre-reaction complexes and transition-states explored along the pathways were found to be insignificantly affected by the spin contamination (after allowing 10% of variation), though a few of the product complexes (PCs) are significantly affected. The affected species were further investigated using the restricted open-shell (RO) methodology at the ROCCSD(T)/6311++G(d,p)//BHandHLYP/6-311++G(d,p) level of the theory, but as evident in Table S1,† we did not observed any significant change in the energy of affected transition state, TS10, and hence, in the computed rate constants (see later).

Further, the thermodynamic as well as kinetic control in the abstraction pathways was also analyzed in terms of the Gibbs free-energy change (ΔG) from PRCs to PCs, and activation energy barrier (ΔE_A) from PRCs to TSs, respectively at different temperatures, as analyzed in Fig. 7–9 and Table S3 (ESI†). For a general abstraction pathway,

Reactants → PRC → TS → PC → products, (1)

the ΔG and ΔE_A is estimated, including ZPEs, respectively, as,

ΔG = G_PC − G_PRC, (2)

ΔE_A = E_TS − E_PRC, (3)

where G and E, respectively, refers to the Gibbs free-energy and total electronic energy of involved species i.e., PRC, TS and PC. Since in the present study, the reactant complexes and the product complexes are the main intermediates involved, therefore, PRCs and PCs have been used for deciding the feasibility, instead of separated reactants and separated products (see later). For a reaction to be thermodynamically feasible, ΔG has to be significantly negative, whereas a small reaction barrier (ΔE_A) will make it kinetically favorable though the overall rate constant may present a different picture. To provide further details into the reaction mechanism, the NBO spin density distribution and molecular orbitals are analyzed in Fig. 10 and Table S4 (ESI†), respectively. It should further be noted that the OH radical is known to participate only in the hydrogen abstraction in glycolaldehyde, it cannot add to the carbonyl group. However, in the present work, some reaction routes (depicted in ESI Fig. S2†) were explored in which the OH radical adds to the carbonyl carbon. The energy values of stationary points relevant to addition pathways are given in Table S12.†

Fig. 7 (a) Gibbs free-energy profile at the level of BHandHLYP/6-311++G(d,p) method, and (b) relative energy profile, at the CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) (BSSE uncorrected) level of theory, for the aldehydic abstraction pathways 1, 2, 7 and 8 depicted in Fig. 2 and 5, for the reaction of glycolaldehyde with the OH radical (R: separated reactants; BC: Binary Complexes; PRC: pre-reaction complexes; TS: Transition States; PC: Product Complexes; P: separated products).

Fig. 8 Same as Fig. 7, but for the methylinic hydrogen abstraction pathways 3, 4, 9 and 10 depicted in Fig. 3 and 6.

Fig. 9 Relative Gibbs free energy and relative energy profiles; all at the BHandHLYP/6-311++G(d,p) level of the theory, for water-free and water-assisted, respectively of pathways 5 and 6, for the hydroxyl abstraction in the reaction of glycolaldehyde with hydroxyl radical.

Fig. 10 Surface plots (isovalue = 0.02) of molecular orbitals depicting a probable PCET mechanism in the transition states TS2, TS3, TS4, TS5 and TS7, and HAT mechanism in TS1, TS6, TS8, TS9 and TS10 at the DFT/UBHandHLYP/6-311++G(d,p) level of the theory. The plots correspond to highest singly occupied β molecular orbitals (for labels on the atoms, see ESI Table S4†).

3. Results and discussion

Water assistance can greatly affect the reaction being investigated because of the possibility of hydrogen bonding interactions, therefore, mechanistic and kinetics details are discussed in this section to reveal the role of a single-water molecule in the hydrogen abstraction pathways. We will first consider the pathways traced in the absence of water.

3.1 Water-free pathways: mechanism

Through the reactant complexes explored for the water-free reaction of glycolaldehyde with hydroxyl radical, five possible pathways (depicted in Fig. 2–4) have been traced; two each for the abstraction at the aldehydic and methylinic sites, and one for the abstraction from hydroxy site. Each of the traced pathways, their thermodynamic feasibility and kinetics are discussed below.

3.1.1 Aldehydic hydrogen abstraction in the absence of water. For the aldehydic abstraction, pathways 1 and 2, depicted in Fig. 2, were traced out. Along pathway 1, the interaction of trans-glycolaldehyde with the OH radical, results into a pre-reaction complex, PRC1. This complex further changes to the product complex PC1 via the transition state TS1. As evident from Fig. 2 and 7, the product complex PC1 is though energetically more stable than the separated trans-product and a molecule of water, mainly through the hydrogen-bonding interaction, but due to the entropy loss in this hydrogen-bonded complex, the separated products P1 are more stable (in terms of the Gibbs free-energy change) than the complex PC1. Note that the aldehydic abstraction pathways for cis-isomer could not be located.

Along pathway 2, the reactant complex PRC2 was traced for the aldehydic abstraction in the reaction of trans-glycolaldehyde with OH radical. The transition state TS2, along this pathway, has also been located in a previous study,¹² but the corresponding reactant and product complexes are found to be different in the present work. With the trans-reactant, the final product complex (PC2) is found to be energetically more stable than the complex PC1 along pathway 1. However, the reactant complex PRC1 is more stabilized than PRC2 in terms of the Gibbs free energy change whereas the transition states TS1 corresponding to pathway 1, and TS2 along pathway 2, seem to be equally stabilized. Note that the BSSE uncorrected CCSD(T) relative energy value for TS2 is −2.45 kcal mol⁻¹ which is even lower than PRC2 by 0.13 kcal mol⁻¹. Further, from Table S3,† it is obvious that at the DFT/BHandHLYP/6-311++G(d,p) level of the theory, the ΔG from PRC1 to PC1 is −22.78 kcal mol⁻¹ whereas it is −24.85 kcal mol⁻¹ for change from PRC2 to PC2. These values suggest that path 2 is thermodynamically more feasible. Further, the energy barrier (ΔE_A), of −0.13 kcal mol⁻¹, is found to be lower for TS2 than for TS1 (0.75 kcal mol⁻¹), suggesting path 2 to be kinetically also more favorable (see the rate constants discussed later).

A further inspection of the structure of pre-reaction complex, PRC1, along pathway 1 suggests that the hydroxyl radical is in the plane of the glycolaldehyde molecule. In the corresponding transition state TS1 along this pathway, the radical is in such an orientation that it interacts with the aldehydic hydrogen to give a 3-centre 3-electron bond, and results in an overall hydrogen atom transfer following the HAT mechanism. This is further supported by the (unpaired) spin density values in Table S4,† obtained from the NBO analysis. It is evident that at the carbon atom C(4) of the glycolaldehyde, the spin density increases from −0.0010e in PRC1 to −0.2126e in TS1, and at atom O(12) of the OH radical, it decreases from −1.0240e in PRC1 to −0.7009e in TS1, clearly indicating the interaction of C(4)–H(5) with the unpaired electron of O(12) during the hydrogen abstraction. This is further supported by the plots of highest occupied molecular orbital (HOMO) of TS1, depicted in Fig. 10. Similarly, the PRC2 and TS2 are analyzed to predict the hydrogen-abstraction mechanism followed along pathway 2. This pathway, however, may follow PCET mechanism as evident from the MO plot of TS2 which clearly depicts the overlapping of the orbitals of atom O(12) of the OH radical with that of the atom O(7) in glycolaldehyde. Along this pathway, while the lone pair of electrons present on the O(12) abstracts the aldehydic proton H(5), the electron may come from O(7). The orientation of hydroxyl radical is also such that the atom O(12) points towards the hydroxy oxygen O(7) of the glycolaldehyde. But the spin density values, which are more or less same at O(6) and O(7), do not support the involvement of any of the oxygen atom. The spin density value at O(12) decreases from −0.9921e to −0.7278e, in moving from PRC2 to TS2. But it should be noted that not only the orbitals of O(7) and O(12) are overlapped, but also both of these are overlapping with the carbonyl carbon, C(4), as well. Therefore, there can be a concerted movement of the single electron in three steps resulting in the obtained spin density values: initially, the electron may go from O(7) to O(12) giving net unpaired electron density at O(7). Since, atom C(4) after removal of H(5) is left with two electrons, so in the second step, one electron may go from C(4) to O(7), leaving net unpaired electron density at C(4). Finally, there will be a shift of an electron from O(12) to C(4). From the MO plots, it can be seen that the orientation of hydroxyl radical along path 1 is such that the interaction of hydroxyl radical is not possible with the carbonyl or hydroxy oxygen whereas along path 2, the hydroxyl oxygen O(12) lays towards the hydroxy moiety of the glycolaldehyde, and obviously far enough from the carbonyl.

3.1.2 Methylinic hydrogen abstraction in the absence of water. The pathways, depicted in Fig. 3, for the methylinic abstraction were located intuitively. It should be noted that no planar pre-reaction complex has been detected in this study corresponding to methylinic abstraction through GRRM. Although PRC11 (shown in ESI Fig. S1†) has been located by the GRRM which resembles with the reactant complex for methylinic abstraction modeled by Ochando et al.¹³ But numerous attempts to trace the complete path corresponding to PRC11 failed in the present work. Despite of the fact that in the present work, the pre-reaction complexes are located for the five lowest energy barriers; the water-free pathway corresponding to the methylinic hydrogen abstraction could not be searched by the GRRM.

As depicted in Fig. 3 and 8, pathway 3 corresponding to cis-isomer seem to be more probable, since the reactant complex PRC3 and transition state TS3 along path 3, are more stabilized than PRC4 and TS4, respectively, along pathway 4 for trans-isomer. In terms of Gibbs free energy change, the formation of PRC3 is more facile than PRC4 making path 3 thermodynamically and kinetically more feasible than path 4. As far as the mechanism along these pathways is concerned, the net unpaired electron spin-density values, for PRC3 and TS3, provided in Table S4† corresponds to HAT mechanism. But the possibility of PCET mechanism also arises because there is some overlapping of electron density at O(6), O(7) and O(12) as evident from the HOMO of TS3 in Fig. 10. Similarly, from the HOMO of TS4, the overlapping of O(6) with O(12) indicates a possible PCET mechanism along path 4.

3.1.3 Hydroxy hydrogen abstraction in the absence of water. The hydrogen abstraction at the hydroxyl site in glycolaldehyde could be located only for the cis-isomer as depicted in Fig. 4. Along pathway 5, the interaction of hydroxyl radical with glycolaldehyde leads to a reactant complex PRC5, which was also previously reported in the study by Galano et al.¹² PRC5 contains the characteristic H-bonding interactions of the hydroxyl radical with the carbonyl oxygen and hydroxy hydrogen result in the formation of a seven-membered ring, with H-bonding distances of 1.942 and 2.029 Å, respectively. In the transition state TS5 along path 5, the distance between the carbonyl oxygen and hydroxyl hydrogen increases to 2.126 Å while that between the hydroxy hydrogen of glycolaldehyde and the hydroxyl oxygen decreases to 1.174 Å. Moreover, there is an elongation of the O–H bond of the glycolaldehyde from 0.958 Å to 1.157 Å, resulting in the product complex PC5, and finally into the separated cis products P4.

The pre-reaction complex PRC5 involved along pathway 5, is relatively unstable than the pre-reaction complexes along the aldehydic and methylinic hydrogen abstraction pathways. Therefore, the hydroxyl hydrogen abstraction from glycolaldehyde seems to be least probable. This path is likely to follow either HAT or PCET mechanism. The MO diagram for TS3, in Fig. 10, clearly shows the overlapping of atoms O(6), O(7) and O(12), while the lone pair of O(12) abstracts the hydroxyl proton H(8), the unpaired electron of it may interact with the O(6). After this, an electron may move from O(7) to O(6), giving a net unpaired electron spin density on O(7). The HAT mechanism would be followed if the electron goes directly from O(7) to O(12) but PCET may also be followed in case the electron goes to O(12) from O(7) via O(6) in two steps. However, the spin-density values indicate a free radical mechanism only, since the spin-density on O(6) is same in PRC5 and TS5, it only shifts from O(12) to O(7).

3.1.4 Addition reactions of hydroxyl radical to the carbonyl. Besides the aforementioned water-free hydrogen abstraction pathways, the present exploration on the PES of investigated reaction system using the GRRM strategy was able to trace pathways that revealed the addition of hydroxyl radical to the carbonyl group of glycolaldehyde. Four routes, pathways 12–15 depicted in the ESI Fig. S2,† have been traced but all in the absence of water. Notably, this is the first study reporting such addition reactions of the hydroxyl radical with glycolaldehyde. Out of the four pathways traced, path 13 is likely to be the most feasible. This pathway suggests a decomposition of glycolaldehyde into formic acid and the hydroxymethyl radical. Along pathways 12 and 13, the formation of equilibrium structures PRC12 and PRC13, seems to be also feasible via the mechanism shown in Fig. S3.† Interestingly, PRC12 or PRC13, being a hydroxymethoxymethyl radical, may undergo self-recombination,⁵⁰ to yield 1,2-bis(hydroxymethoxy)ethane-1,2-diol or can also combine with the hydroxymethyl radical to provide 1-(hydroxymethoxy)ethane-1,2-diol i.e., vicinal diols. Not only this, these intermediate species can act as precursors for the formaldehyde resin synthesis.⁵¹ The other pathways correspond to the formation of peroxy-radical, PC15 along path 15, whereas path 14 represents the conversion of peroxy-radical (PRC14) to the oxy-radical (PC14) via the transition state TS14. However, both these pathways seem to be infeasible as the reactant complexes as well as the product complexes are highly unstable.

3.2 Water-free pathways: kinetics

The generalized reaction for the water-free hydrogen abstraction in glycolaldehyde by the OH radical can be represented as,¹²where k₁ and k₋₁, respectively, are the rate constant for the forward and backward reactions in the pre-equilibrium first step. The formation of pre-reaction complex, [HOCH₂CHO⋯OH], is believed to be reversible,¹² and k₂ is the rate constant for the dissociation of PRC into the products. An application of the steady-state approximation to the reaction scheme (4) leads to an overall rate constant (k) for the water-free pathways as,⁵²

k = K_eqk₂, K_eq = k₁/k₋₁ (5)

where K_eq is the equilibrium constant for the first step. The rate constants for all the aforementioned hydrogen abstraction water-free pathways have been calculated using the conventional transition state theory (TST), following a partition function approach,^6,53 as well as incorporating a correction for quantum tunneling,^3,7,12,54 and symmetry factor^12,53 (see later). Within this, the equilibrium constant K_eq can be given as,and k₂, the rate constant for the second step as,where Q_reactants, Q_PRC and Q_TS are the overall the partition functions per unit volume, E_reactants, E_PRC and E_TS are the scaled ZPE-corrected energies of the reactant, pre-reaction complex and the transition state, respectively, whereas k_B, h, R and T refer to the Boltzmann's constant, Planck's constant, universal gas constant and temperature, respectively. It should be noted that since the energy values (Es) employed for the reaction barrier in the aforementioned calculations are already ZPE corrected, therefore, the partition functions were determined from the lowest vibrational level, not from the bottom of the potential-energy well, though usually, bottom of the potential-energy well is chosen as a reference for zero of the energy. However, same results are obtained if the ZPE-excluded energies for the reaction barrier are used along with the partition function determined from the bottom of the well. It should also be noted that from a computation through quantum mechanical software like Gaussian,⁵⁵ the partition functions obtained are dimensionless. Therefore, in order to appropriately obtain the rate constant (for a second order reaction) in the units of cm³ per molecule per s, the volume and number of molecules (in terms of Avagadro's number) has to be appropriately accounted during the calculation.

Further, it has been observed that such reactions are significantly affected by the quantum tunneling and symmetry factors, therefore, an effective rate constant is further calculated as,

where σ is the symmetry factor accounting for the reaction path degeneracy which for the abstractions at the aldehydic and hydroxyl sites is taken to be 1, and for the methylinic, its value is taken to be 2 since there are two equivalent methylic hydrogen available for the abstraction. To include the quantum effects arising from the tunneling of light particles (proton or hydrogen atom in the present work), the rate coefficients calculated using the TST are further corrected with the transmission coefficient (κ), determined using a widely used Eckart tunneling potential.⁵⁶ The latter was calculated using an interactive program, KisThelp.⁵⁷ Since tunneling correction from other methods like small curvature tunneling (SCT) is available for the investigated system from a previous study by Galano et al., the rate constants reported using the same are further compared with the rate constant calculated in the present work but employing the Eckart tunneling correction (see discussions below). The calculated rate constants using the aforementioned equations for the water-free pathways are analyzed in Table 1.

Table 1 Calculated rate constants, k and k_eff (both in cm³ per molecule per s), k₂ (in s⁻¹) and equilibrium constant (K_eq) (in cm³ per molecule), at 298.15 K, along various pathways of the water-free reaction of glycolaldehyde with hydroxyl radical, at ZPE scaled CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) level of the theory. The rate constant k_eff includes corrections for the symmetry factor (σ) and Eckart tunneling correction (κ)

Pathway	Keq	k2	k = Keqk2	κ	keff = κσk
1	5.20 × 10^−23	5.19 × 10^11	2.70 × 10^−11	3.53	9.37 × 10^−11
2	1.10 × 10^−22	8.05 × 10^10	8.86 × 10^−12	1.28	1.13 × 10^−11
3	2.15 × 10^−21	3.34 × 10^8	7.18 × 10^−13	3.79	5.44 × 10^−12
4	1.04 × 10^−22	1.36 × 10^9	1.41 × 10^−13	14.64	4.14 × 10^−12
5	5.50 × 10^−25	4.51 × 10^7	2.48 × 10^−17	1637.61	4.07 × 10^−14

---

Further, following the previous work of Galano et al.,¹² the overall rate constant accounting for all the water-free hydrogen abstraction pathways, is calculated including the symmetry factor and tunneling correction, as:

k_overall = p_cisk_cis + p_transk_trans (9)

where p_cis and p_trans are the fractions of cis- and trans-glycolaldehyde at a particular temperature, and k_cis and k_trans are the rate constants of all the hydrogen abstraction pathways, respectively, involving cis- and trans-glycolaldehyde. As discussed before, for cis-glycolaldehyde, pathways 3 and 5 have been obtained, whereas for the trans-glycolaldehyde, pathways 1, 2 and 4 has been traced, therefore, using the rate constants along the respective pathways, the rate constants for cis-and trans-isomers were determined as,

k_cis = k₃ + k₅ & k_trans = k₁ + k₂ + k₄ (10)

Using eqn (9) and (10), the overall rate constant (k_overall) has been calculated as listed in Table 1. These rate constants in the temperature range 200–500 K for overall abstraction pathways are further compared, in Table 2 and Fig. 11, with the rate constants reported in the previous study by Galano et al.¹² The values of rate constants for aldehydic abstraction in path 2, and cis-hydroxy abstraction in path 5 have also been compared with the previously known values as reported in the ESI Tables S5 and S6,† respectively.

Table 2 Overall rate constant, k_overall calculated for the water-free reaction, k^water_overall for the water-assisted reaction (all in cm³ per molecule per s), and their comparison with water-free rate constants (k_{overall,Galano}) previously reported in the literature [ref. 12], within the temperature range of 200–500 K. The known experimental value of the rate constant is (1 ± 0.2) × 10⁻¹¹ cm³ per molecule per s at 298 K [ref. 28]. k_overall is calculated in terms of rate constants, k_cis and k_trans, along the pathways involving cis- and trans-glycolaldehyde. p_cis and p_trans are the fractions of cis- and trans-glycolaldehyde at particular temperature, as taken from ref. 12 (also see Table 3, and ESI Tables S5, S6 and S9–S11)

Temperature (K)	kcis (×10^−12)	ktrans (×10^−11)	pcis	ptrans	koverall (×10^−12)	koverall,Galano (×10^−12)	k^watereff,overall (×10^−14)	keff,overall (×10^−11)
200	44.72	298.18	0.98	0.02	103.46	30.6	—	302.65
220	20.93	110.46	0.98	0.02	42.60	19.6	—	112.55
240	12.36	50.48	0.97	0.03	27.13	13.9	1.54	51.72
260	8.48	26.82	0.96	0.04	18.87	10.5	—	27.67
270	7.36	20.42	0.95	0.05	17.20	9.40	—	21.16
280	6.47	16.06	0.95	0.05	14.18	8.50	1.24	16.70
290	5.80	12.84	0.94	0.06	13.16	7.77	1.26	13.42
298.15	5.43	10.90	0.94	0.06	11.64	7.29	1.30	11.44
300	5.32	10.50	0.94	0.06	11.31	7.18	1.31	11.03
310	4.91	8.75	0.93	0.07	10.70	6.70	1.37	9.24
320	4.61	7.39	0.93	0.07	9.47	6.30	1.44	7.86
330	4.35	6.35	0.92	0.08	9.08	5.97	1.53	6.78
340	4.15	5.49	0.92	0.08	8.21	5.68	1.63	5.91
350	3.97	4.85	0.91	0.09	7.98	5.44	1.74	5.25
360	3.84	4.30	0.90	0.10	7.75	5.22	1.86	4.68
370	3.75	3.85	0.90	0.10	7.22	5.04	2.00	4.23
380	3.65	3.49	0.89	0.11	7.08	4.88	2.12	3.85
390	3.58	3.11	0.88	0.12	6.88	4.73	2.28	3.46
400	3.50	2.91	0.88	0.12	6.57	4.60	2.42	3.27
420	3.43	2.51	0.87	0.13	6.24	4.37	2.74	2.85
440	3.38	2.19	0.85	0.15	6.16	4.18	3.09	2.53
460	3.37	1.96	0.84	0.16	5.97	4.02	3.49	2.30
480	3.38	1.78	0.83	0.17	5.83	3.89	3.90	2.12
500	3.43	1.65	0.82	0.18	5.77	3.77	4.37	1.99

---

Fig. 11 Arrhenius plot, log k vs. 1/T, in the temperature range of 200–500 K, for the rate constants k_overall and k^water_eff,overall calculated in the present work, respectively for the water-free and water-assisted reaction of glycolaldehyde with OH radical, at the CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) (BSSE uncorrected) level of the theory. These are further compared with the known experimental rate constant, 8 × 10⁻¹² cm³ per molecule per s of Karunanandan et al. [ref. 30], which is taken to be constant (while ignoring any uncertainty) in the temperature range of 240–362 K (and extrapolated to 500 K), and also with a value of 1 × 10⁻¹¹ cm³ per molecule per s of Niki et al. [ref. 28], at room temperature (depicted as * in the middle of the plot). The CVT/SCT rate constants, k_{overall,Galano}, compared are taken from Galano et al. [ref. 12]. Note that k_overall from present work is computed in the same fashion as in ref. 12, but employing Eckart tunneling correction.

At the room temperature, the maximum rate constant is calculated to be 9.37 × 10⁻¹¹ cm³ per molecule per s along the aldehydic abstraction path 1, and the overall rate constant (k_overall) for water-free pathways, is determined to be 1.16 × 10⁻¹¹ cm³ per molecule per s, which is in an excellent agreement with the known experimental values of (1.1 ± 0.3) × 10⁻¹¹ and (1.0 ± 0.2) × 10⁻¹¹ cm³ per molecule per s,^28,29 though with a negative temperature dependence similar to that reported in the previous studies.¹² Note that the overall rate constant (k_overall) was calculated assuming that the hydrogen abstraction pathways for cis and trans glycolaldehyde are different, and no cis–trans interconversion occurs along the pathways. The calculated overall rate constant at different temperatures, as analyzed in Table 2, may become temperature-independent at low temperatures as had been observed in the study of Karunanandan et al.³⁰ Note that, Table 2 also compares the overall rate constant (k_eff,overall) calculated assuming cis–trans interconversion to be feasible along the pathways (see discussions later), but this is observed to be an order of magnitude larger than the k_overall.

As further evident in Table 2, Eckart tunneling correction is applied for the estimation of rate constants, and it is found to range between 3.53 and 1637.61 along various water-free pathways at 298.15 K, compared to the tunneling corrections of 2.18 to 110.66 determined using small curvature tunneling (SCT) in the study by Galano et al.,¹² along similar pathways. The maximum tunneling was observed along the pathway corresponding to the hydrogen abstraction at hydroxy site which though contribute least to the overall rate constant. As further evident in Fig. 11 depicting Arrhenius plot (log k vs. 1/T), it can be seen that the curve corresponding to both k_{overall,Galano} determined by Galano et al., and k_overall determined in the present work exhibit significant curvature, though at the room temperature, present work exhibits a very good agreement with the experimental rate constant, yet in both the cases, the activation energy (E_act) is found to be negative. Notably, as evident from Table 2, the rate constant (k_overall) at low-temperatures, calculated in the present work with Eckart tunneling, for example at 200 K, are an order of magnitude larger than the k_{overall,Galano} determined using SCT. However, experimental rate constant determined by Karunanandan et al.,³⁰ remain temperature-independent in the temperature range of 240–362 K. Moreover, the negative temperature-dependence of the rate constant predicted for the water-free reaction is questionable,³⁰ therefore, it would be interesting to see (as discussed below) how the water-assisted rate constant compares with the experimental rate constant in the event of significant quantum tunneling.

As discussed, the overall rate constant in water-free reaction estimated using the CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) level of the theory is found to be in very good agreement with the experimental value at the room temperature. To check the validity of the applied theory, rate constants were also calculated at M06-2X/6-311++G(d,p) level using M06-2X exchange–correlation functional of the DFT, and are compared with the rate constant values at BHandHLYP/6-311++G(d,p) and CCSD(T)/6-311++G(d,p)//BHandhLYP/6-311++G(d,p) levels (in ESI Table S11†). For the water-free reaction, there is no significant change in the overall rate constant estimated using M06-2X, though it slightly overestimates the rates.

3.3 Water-assisted pathways: mechanism

For water-assisted reaction, a total of five pathways were traced out: two each for the aldehydic and methylinic abstractions, and one for the hydroxy abstraction. Each pathway along with its mechanism is discussed in detail as follows:

3.3.1 Aldehydic hydrogen abstraction in the presence of water. As discussed in the previous sections, for the aldehydic abstraction in the absence of water, only the trans product was obtained, however, as evident from pathways 7 and 8 and also illustrated in Fig. 5, with the addition of a single-water molecule, both cis- and trans-products can result. Glycolaldehyde is pretty much soluble in water,²⁹ so in the presence of both a single-water molecule and hydroxyl radical, it will prefer to form a binary complex with water, which then interacts with the hydroxyl radical to give a more stabilized ternary complex. For example, along pathway 7 or 8, the binary complexes BC7 or BC8 is formed initially by the interaction of cis-isomer of glycolaldehyde with the water molecule, which are further stabilized significantly with the incorporation of the hydroxyl radical to give a ternary reactant complex PRC7 or PRC8, respectively. Although in PRC7, the alignment of the hydroxyl radical is in such a way that the hydroxyl oxygen can be seen interacting with the hydrogen of the water molecule, and the hydroxyl hydrogen is interacting with the carbonyl oxygen. However, in the transition state TS7 along this pathway, two processes occur simultaneously: first, the rotation of C–C bond, which results in the change of configuration of glycolaldehyde from cis to trans, and second, the hydroxyl radical adjusts itself in such a way that the oxygen of the hydroxyl interacts with the aldehydic hydrogen as well as the hydrogen of the water molecule. Subsequently, this transition state changes to the product complex PC7, which finally dissociates into the separated products P6 but as trans product and a water molecule. Similarly, along path 8, cis-product is formed via TS8 and PC8.

However, as depicted in Fig. 7, the Gibbs free-energy of activation for conversion from pre-reaction complexes to transition state (PRC to TS), was found to be 6.40 and 11.92 kcal mol⁻¹, respectively, for trans and cis aldehydic abstraction in the presence of water molecule, which is significantly higher when compared to 4.08 and 5.71 kcal mol⁻¹ for the respective water-free abstraction pathways 1 and 2, though the corresponding product complexes are equally stable, whereas the reactant complexes are destabilized. It is quite clear that the presence of a single-water molecule increases the Gibbs free-energy barrier, however, it should be noted that the presence of a single-water molecule has made the cis abstraction feasible. This is probably because of the fact that water molecule provides flexibility to the reactant complex. Moreover, the reversal of conformation is not necessary for the hydrogen bonding interactions to occur when water molecule is participating in the reaction, which is contrary to the previous case.

Further as evident in Table S3,† and Fig. 5 and 7, among the water-assisted pathways, path 7 is likely to be kinetically more probable than path 8. A further comparison of the water-assisted pathways with the water-free pathways 1 and 2, as analyzed in Fig. 7, suggests that considering the thermodynamically feasibility of pre-reaction complexes, paths 2 & 8 are equally probable whereas path 7 is least probable. The water-free pathway 1 leading to the trans-abstracted product is kinetically the most feasible as suggested by the standard Gibbs free energy of activation. Moreover, instead of lowering the thermodynamic barriers, the TSs corresponding to the water-assisted pathways lay higher, in terms of Gibbs free-energy of activation, than those along the more feasible water-free pathways. Hence, it may be inferred that though in the presence of a single-water molecule, the PRCs are energetically more stabilized but the respective pathways may not be more feasible than the water-free pathways, indicating a significant role of entropy loss during complexation. Though Fig. 7b suggests that there is a considerable lowering of the PES in the presence of a single-water molecule, however, Fig. 7a, in which entropy is taken into account, clearly reveals that the presence of water molecule results in the increase in the thermodynamic barrier in terms of Gibbs free-energy of activation. Note that the formation of pre-reaction binary complexes as well as ternary complexes is accompanied by positive free-energy change, although during this process, the H-bonding interactions are occurring which should stabilize the complexes, however, this first step is entropy forbidden (as also evident in ESI Table S7†).

Coming to the mechanism of aforementioned water-assisted pathways, the orientation of hydroxyl radical in PRC7 and TS7, along path 7, is in such a way that atom O(6) of glycolaldehyde cannot interact with the oxygen atom O(12) of hydroxyl radical. In TS7, a 3-center 3-electron bond is formed among O(12), H(5) and C(4) which may lead to the HAT mechanism. This is further supported by the spin-density distribution values given in Table S4† which decreases on O(12) from −1.0267e in PRC6 to −0.8003e in TS7, and increases on C(4) from 0.0006e in PRC6 to −0.1121e in TS7. But examination of the MO of TS7, depicted in Fig. 10, also indicates a probability of PCET mechanism. It clearly shows the overlapping of O(12) with O(7). Similar to the water-free path 2, here again, the movement of the electron may occur in concerted manner, from O(7) to O(12) followed by a shift of electron from C(4) to O(7). On the contrary, the other water-assisted pathway 8 strictly follows the free radical mechanism because of the orientation of hydroxyl radical is such that its interaction with the O(6) or O(7) is not possible. This is further supported by the MO for TS8, in Fig. 10, which reveals that the O(12)–H(13) bond lays anti-parallel to C(4)=O(6) bond, ruling out the probability of interaction between O(6) and O(12). Though these two groups seems to be in parallel orientation, but the carbonyl oxygen O(6) is out of the plane of hydroxyl and thereby, rendering the orbital overlap almost impossible, and hence eliminating the possibility of PCET mechanism. Moreover, the hydroxyl oxygen O(12), carbonyl carbon C(4) and the aldehydic hydrogen H(5) are very much in plane to give a 3-center 3-electron bond leading to HAT mechanism, with no involvement of O(7).

3.3.2 Methylinic hydrogen abstraction in the presence of water. As evident in Fig. 6, the abstraction of hydrogen from the methylinic site of the glycolaldehyde in the presence of water may occur in two ways: (i) along pathway 9, where water molecule in the binary complex interacts with the hydroxy group of the glycolaldehyde such that the aldehydic moiety does not interact at all, (ii) along pathway 10, where aldehydic moiety of glycolaldehyde takes part in the hydrogen-bond formation leading to binary reactant complex PRC10. Both the possibilities seem to be almost equally probable and lead to the trans products. The Gibbs free energy values analyzed in Table S4† and Fig. 8 suggest that path 9 is thermodynamically more feasible than path 10. Moreover, the effect of a single-water molecule on the abstraction of methylinic hydrogen from the glycolaldehyde, is found to be the same as aldehydic abstraction.

As far as the mechanism for the water-assisted hydrogen abstraction from the methylinic site is concerned, the structures of PRC9 and PRC10 are such that the unpaired electron of the hydroxyl radical cannot interact with the lone pair of electrons of any of the oxygen atom present in the system suggesting that the conventional hydrogen atom transfer (HAT) mechanism is being followed. This is further supported by a 3-center 3-electron bond in TS9 and TS10 as depicted in the respective MOs (as in Fig. 10) as well as by the spin density values given in Table S4 (ESI†).

Table 3 Calculated rate constants, k^water and k^water_eff (both in cm³ per molecule per s), equilibrium constants (K^°_eq0 and K^°_eq1) (both in cm³ per molecule), and k^°₂ (in s⁻¹) at 298 K, along various pathways of the water-assisted reaction of glycolaldehyde with hydroxyl radical in the presence of a single-water molecule, at ZPE scaled CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) level of the theory, except for pathway 6 (also see ESI Table S10). The value of water concentration [H₂O], at 298 K is taken as 7.70 × 10¹⁷ molecules cm⁻³ [ref. 24]

Pathway	K^°eq0	K^°eq1	k^°2	k^water = K^°eq0K^°eq1k^°2[H2O]	κ	k^watereff = κσk^water
6 [H2O]	6.54 × 10^−24	1.29 × 10^−19	3.13 × 10^2	2.04 × 10^−22	7065.40	1.44 × 10^−18
7 [H2O]	8.18 × 10^−23	1.47 × 10^−20	4.07 × 10^9	3.76 × 10^−15	1.11	4.17 × 10^−15
8 [H2O]	6.98 × 10^−22	2.41 × 10^−21	3.38 × 10^8	4.37 × 10^−16	19.58	8.57 × 10^−15
9 [H2O]	5.56 × 10^−22	9.53 × 10^−22	2.34 × 10^7	9.56 × 10^−18	1.32	2.52 × 10^−17
10 [H2O]	3.19 × 10^−23	1.50 × 10^−21	5.76 × 10^8	2.13 × 10^−17	15.37	6.54 × 10^−16

---

3.3.3 Hydroxy hydrogen abstraction in the presence of water. As depicted in Fig. 3, only one pathway, path 6, has been located for the hydroxyl hydrogen abstraction in the presence of a single-water molecule, with the end product having the trans configuration. Similar to the pathways discussed before, here again, a binary complex BC6, which upon interaction with hydroxyl radical, gives the ternary complex PRC6. The latter dissociates into separated products P5 via the transition state TS6 and the product complex PC6. It should be noted that the single-point energy of TS6 could not be refined using the CCSD(T), therefore, the comparison of this pathway with water-free pathway (path 5) is done at BHandHLYP/6-311++G(d,p) level of the theory, as presented in Fig. 9. It is evident that the water-free pathway 5 is thermodynamically more favorable one though the water-assisted pathway, path 6, is kinetically the most favorable one (see the next section).

However, it should also be noted that the GRRM search in the absence of water provided the reactant complexes as equilibrium structures whereas the search in the presence of water molecule gives the product complexes as the equilibrium structures except for the case of hydroxy abstraction for which the search resulted in PRC6 not PC6. This is another evidence which further confirms that the hydroxy abstraction is not as feasible as aldehydic and methylinic abstractions. Further, the structures of the pre-reaction complex PRC6, transition state TS6, and the spin density distribution analysis confirms the HAT as a probable mechanism for this pathway.

From the aforementioned discussion on the Gibbs free-energy profiles presented in Fig. 7–9, it is clear that the hydrogen abstraction reaction may occur easily in the absence of a single-water molecule than in presence of a single-water molecule, though the TSs involved along all the pathways are considerably stabilized energetically by the H-bonding interactions with the participation of a single-water molecule. However, the corresponding Gibbs free-energy change follow the opposite trend, indicating a significant role and importance of entropy factor in such reactions as evident from the entropy change as well as the enthalpy change analyzed in Table S7 (ESI†).

3.4 Water-assisted pathways: kinetics

For the water-assisted reaction, three steps are involved which can be depicted as:

Following the eqn (5)–(8) for the water-free pathways, the rate constant for the water-assisted pathways, with and without correction for symmetry and tunneling, can be respectively, determined as,

k^water = K^°_eq0K^°_eq1k^°₂[H₂O] (12)

k^water_eff = κσK^°_eq0k^°₂[H₂O] (13)

where the two equilibrium constants (K^°_eq0 and K^°_eq1) corresponds to the first two equilibrium steps, and [H₂O] is the maximum possible water concentration (corresponding to 100% humidity) under tropospheric conditions, taken from the existing literature.^58,59 Using these equations, the calculated rate constants for various water-assisted pathways are provided in Table 3. The overall rate constant, k^water_eff,overall, is further estimated as the sum of all the rate constants corresponding to the water-assisted pathways 6–10.

The overall rate constant calculated for the water-assisted reaction, at 298.15 K, is 1.30 × 10⁻¹⁴ cm³ per molecule per s, which is ∼10³ times less than that for the water-free pathways for which the calculated rate constant is 1.16 × 10⁻¹¹ cm³ per molecule per s as discussed in the previous sections. From the comparison of the rate-constants of water-free and water-assisted pathways in Tables 1 and 3, it is evident that at 298 K, the tunneling correction in both the cases is found to be quite large for the pathway involving hydrogen abstraction at the hydroxyl site though its contribution to the overall rate constant is insignificant. This is similar to that observed in the previous study by Galano et al., on the water-free reaction, where the tunneling correction (from SCT) was found to be in the range of 2–3 for the most dominating pathways except for the pathway involving hydrogen abstraction at the hydroxyl site where it was computed to be as much as 8200 in the temperature range of 200–500 K. The water-assisted rate constants estimated using the CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) level of the theory (without employing tunneling correction) were further compared with those estimated using M06-2X/6-311++G(d,p), as analyzed in the ESI Table S11.† For the water-assisted reaction, meta-hybrid M06-2X exchange–correlation functional of the DFT seems to significantly overestimate the rate constant contrary to that in the case of water-free reaction.

The rate constants for the water-free and water-assisted reactions are also compared in the temperature range of 240–500 K as analysed in Fig. 11 and Table 2. It is evident that the calculated rate constants, k^water_eff,overall, for the water-assisted reaction follow a correct Arrhenius behavior contrary to a negative temperature-dependence of the rate-constants observed in the case of water-free reaction discussed before. Besides this, in the low temperature range, the water-assisted rate constants show a significant curvature akin to a significant quantum tunneling. It should be noted that along the water-assisted pathways, cis–trans interconversion takes place contrary to that observed for the water-free pathways. Since the rate-constant for water-free pathways, in the present work as well as in the previous study, correlates with the experimental rate constants, therefore, one may infer that the reaction of OH radical with glycolaldehyde is not assisted by a single-water molecule, however, provided that no cis–trans interconversion occurs in glycolaldehyde along the pathways. However, if cis–trans interconversion occurs in glycolaldehyde along the water-free pathways than the rate constants (calculated as effective overall rate constant k_eff,overall, listed in Table 2) will significantly exceed the experimental value. In that case, the plausibility of water-free pathways is doubtful. It should be noted that glycolaldehyde posses an energy barrier for isomerization (as analyzed in Fig. 12). From Fig. 2–6, it is obvious that the PRCs and TSs corresponding to water-assisted pathways show flexibility and may allow cis–trans isomerization, but the PRCs and TSs along water-free pathways are quite rigid and hinder the isomerization. It means that the presence of hydroxyl radical does not alter the situation but the incorporation of a molecule of water into the system provides flexibility, making the C–C bond rotation in glycolaldehyde feasible. To analyze this quantitatively, transition states for the cis–trans isomerization were located for both glycolaldehyde and its complex with hydroxyl radical, as depicted in Fig. 12. It is evident from Fig. 12 that the barrier for the gas-phase cis–trans isomerization in glycolaldehyde is smaller than that in its complex with hydroxyl radical with the latter having a relatively lower barrier, and the rate constants for the two isomerization pathways were found to be 4.62 s⁻¹ and 5.77 s⁻¹, respectively. This indicates that the cis–trans interconversion along water-free pathways does not contribute, contrary to that observed along the water-assisted pathways, which can significantly influence the kinetics of the investigated reaction.

Fig. 12 (a) Pathways depicting cis–trans isomerization: (i) between cis- & trans-glycolaldehyde (GLH), (ii) between cis- & trans-GLH⋯OH binary complex. The structures are optimized at the BHandHLYP/6-311++G(d,p) level of the theory, with bond lengths depicted in angstroms. The values depicted with and without parentheses represent the Gibbs free energy and total energy, respectively. Note that cis–trans isomerisation in the corresponding water complexes is already depicted in Fig. 4–6. (b) Relative Gibbs free-energy profile for cis–trans isomerization of glycolaldehyde (GLH) and its complex with hydroxyl radical (GLH⋯OH) at the BHandHLYP/6-311++G(d,p) level of the theory.

4. Conclusions

In this work, the assistance of a single-water molecule, along the hydrogen abstraction pathways, in the reaction of glycolaldehyde with hydroxyl radical, was analyzed mainly at the CCSD(T)/6-311++G(d,p)//BHandHLYP/6-311++G(d,p) level of the theory. The detailed mechanism along both the water-free and water-assisted pathways was revealed, and a few of the proposed pathways were observed to follow the PCET mechanism. The rate constants for the reaction in the absence of water are found to follow a negative temperature dependence as also observed in the previous study, however, a correct Arrhenius behavior is exhibited by the reaction in the presence of a single-water molecule under the tropospheric conditions, though with a significant curvature at low temperatures indicating the role of quantum tunneling in the water-assisted reaction. However, the calculated rate constant only for the water-free reaction, at room temperature, correlates with the experimental results, though those calculated using the meta-hybrid M06-2X exchange–correlation functional of the DFT are significantly overestimated, particularly for the water-assisted reaction. Besides this, the present work also revealed the possibility of a pathway involving addition of hydroxyl radical to the carbonyl group of glycolaldehyde.

This work suggests that though a single-water molecule significantly lowers the reaction barrier, however, to the contrary, it raises the free-energy barrier even more significantly resulting in a decelerated reaction compared to the water-free reaction. This mainly results due to the atmospheric concentration of water in the troposphere, and to the entropy loss resulting from the complexation of glycolaldehyde and hydroxy radical with the water molecule though the latter stabilizes the complex by hydrogen bonding interactions. However, contrary to the water-free pathways, cis–trans interconversion in glycolaldehyde is observed along the water-assisted pathways, significantly affecting the kinetics of the investigated atmospheric reaction.

Acknowledgements

One of the authors, RK, thanks Council of Scientific and Industrial Research (CSIR), New Delhi (India) for providing financial support in the form of SRF(NET) fellowship. The authors are also grateful to Prof. Koichi Ohno for providing GRRM program and to Dr Neetu Goel and the Department of Chemistry, Panjab University, Chandigarh for providing other computational software and resources.

References

1. G. Kaur and Vikas, J. Phys. Chem. A, 2014, 118, 4019–4029.
2. G. Kaur and Vikas, R. Soc. Chem. Adv., 2015, 5, 50989–50998.
3. C. Iuga, J. R. Alvarez-Idaboy, L. Reyes and A. Vivier-Bunge, J. Phys. Chem. Lett., 2010, 1, 3112–3115.
4. E. Vöhringer-Martinez, B. Hansmann, H. Hernandez, J. S. Francisco, J. Troe and B. Abel, Science, 2007, 315, 497–501.
5. Y. Luo, S. Maeda and K. Ohno, Chem. Phys. Lett., 2009, 469, 57–61.
6. W. Zhang, B. Du and Z. Qin, J. Phys. Chem. A, 2014, 118, 4797–4807.
7. C. Iuga, J. R. Alvarez-Idaboy and A. Vivier-Bunge, Chem. Phys. Lett., 2010, 501, 11–15.
8. B. Long, X.-F. Tan, D.-S. Ren and W.-J. Zhang, J. Mol. Struct.: THEOCHEM, 2010, 956, 44–49.
9. C. Iuga, J. R. Alvarez-Idaboy and A. Vivier-Bunge, Theor. Chem. Acc., 2011, 129, 209–217.
10. D. L. Thomsen, T. Kurten, S. Jorgensen, T. J. Wallington, S. B. Baggesen, C. Aalling and H. G. Kjaergaard, Phys. Chem. Chem. Phys., 2012, 14, 12992–12999.
11. A. M. Kosmas, D. K. Papayannis and E. Tsiaras, Comput. Theor. Chem., 2013, 1019, 18–22.
12. A. Galano, J. R. Alvarez-Idaboy, M. E. Ruiz-Santoyo and A. Vivier-Bunge, J. Phys. Chem. A, 2005, 109, 169–180.
13. M. Ochando-Pardo, I. Nebot-Gil, A. Gonzalez-Lafont and J. M. Lluch, J. Phys. Chem. A, 2004, 108, 5117–5125.
14. K. Ohno and S. Maeda, Phys. Scr., 2008, 78, 058122.
15. K. Ohno and S. Maeda, Chem. Lett., 2006, 35, 492–493.
16. K. Ohno, S. Maeda and K. Morokuma, Phys. Chem. Chem. Phys., 2013, 15, 3683–3701.
17. K. Ohno and S. Maeda, J. Phys. Chem. A, 2006, 110, 8933–8941.
18. S. Maeda, T. Taketsugu, K. Morokuma and K. Ohno, Bull. Chem. Soc. Jpn., 2014, 87, 1315–1334.
19. K. Ohno and S. Maeda, Chem. Phys. Lett., 2004, 384, 277–282.
20. S. Maeda, T. Taketsugu, K. Ohno and K. Morokuma, J. Am. Chem. Soc., 2015, 137, 3433–3445.
21. J. M. Anglada, S. Olivella and A. Solé, J. Phys. Chem. A, 2006, 110, 1982–1990.
22. J. M. Mayer, Annu. Rev. Phys. Chem., 2004, 55, 363–390.
23. F. Weinhold, J. Comput. Chem., 2012, 33, 2363–2379.
24. B. Du and W. Zhang, J. Phys. Chem. A, 2013, 117, 6883–6892.
25. D.-h Lu, T. N. Truong, V. Melissas, G. C. Lynch, Y.-P. Liu, B. C. Garrett, R. Steckler, A. D. Isaacson, S. N. Rai, G. C. Hancock, J. G. Lauderdale, T. Joseph and D. G. Truhlar, Comput. Phys. Commun., 1992, 71, 235–262 , and references cited therein.
26. T. N. Truong, D.-h. Lu, G. C. Lynch, Y.-P. Liu, V. S. Melissas, J. J. P. Stewart, R. Steckler, B. C. Garrett, A. D. Isaacson, A. Gonzalez- Lafont, S. N. Rai, G. C. Hancock, T. Joseph and D. G. Truhlar, Comput. Phys. Commun., 1993, 75, 143–159.
27. Y.-P. Liu, G. C. Lynch, T. N. Truong, D.-h. Lu, D. G. Truhlar and B. C. Garrett, J. Am. Chem. Soc., 1993, 115, 2408–2415.
28. H. Niki, P. D. Maker, C. M. Savage and M. D. Hurley, J. Phys. Chem., 1987, 91, 2174–2178.
29. C. Bacher, G. S. Tyndall and J. J. Orlando, J. Atmos. Chem., 2001, 39, 171–189.
30. R. Karunanandan, D. Hollscher, T. J. Dillon, A. Horowitz and J. N. Crowley, J. Phys. Chem. A, 2007, 111, 897–908.
31. S. Maeda and K. Ohno, Chem. Phys. Lett., 2005, 404, 95–99.
32. Vikas and G. Kaur, J. Chem. Phys., 2013, 139, 224311 , Erratum 2014, 141, 039901.
33. G. Kaur and Vikas, J. Comput. Chem., 2014, 35, 1568–1576.
34. P. Sangwan and Vikas, Theor. Chem. Acc., 2015, 134, 99.
35. R. Kaur and Vikas, J. Chem. Phys., 2015, 142, 074307.
36. G. Kaur and Vikas, Tetrahedron Lett., 2015, 56, 142–145.
37. G. Kaur and Vikas, Phys. Chem. Chem. Phys., 2014, 16, 24401–24416.
38. G. Kaur and Vikas, R. Soc. Chem. Adv., 2015, 5, 82587–82604.
39. A. D. Becke, J. Chem. Phys., 1993, 98, 1372–1377.
40. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman Jr, J. A. Montgomery, T. Vreven, K. N. Kudin and J. C. Burant, et al., Gaussian 03, Revision E.01, Gaussian, Inc., Wallingford, CT, 2004.
41. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci and G. A. Petersson, et al., Gaussian 09, Revision D.01, Gaussian, Inc., Wallingford CT, 2013.
42. S. Maeda, Y. Osada, K. Morokuma and K. Ohno, GRRM 11 user manual, 2011, http://grrm.chem.tohoku.ac.jp/GRRM/.
43. Y. Zhao and D. G. Truhlar, Theor. Chem. Acc., 2008, 120, 215–241.
44. K. Raghavachari, G. W. Trucks, J. A. Pople and M. Head-Gordon, Chem. Phys. Lett., 1989, 157, 479–483.
45. S. F. Boys and F. Bernardi, Mol. Phys., 1970, 19, 553–566.
46. J. R. Alvarez-Idaboy and A. Galano, Theor. Chem. Acc., 2010, 126, 75–85.
47. H. G. Wallnoefer, T. Fox, K. R. Liedl and C. S. Tautermann, Phys. Chem. Chem. Phys., 2010, 12, 14941–14949.
48. J. P. Merrick, D. Moran and L. Radom, J. Phys. Chem. A, 2007, 111, 11683–11700.
49. M. W. Wong and L. Radom, J. Phys. Chem., 1995, 99, 8582–8588.
50. K. Kanjana, J. A. Walker and D. M. Bartels, J. Phys. Chem. A, 2015, 119, 1830–1837.
51. Q.-N. Sun, C.-Y. Hse and T. F. Shupe, J. Appl. Polym. Sci., 2014, 40644.
52. D. L. Singleton and R. J. Cvetanovic, J. Am. Chem. Soc., 1976, 98, 6812–6819.
53. J. M. Anglada and V. M. Domingo, J. Phys. Chem. A, 2005, 109, 10786–10792.
54. W. T. Duncan, R. L. Bell and T. N. Truong, J. Comput. Chem., 1998, 19, 1039–1052.
55. J. W. Ochterski, Thermochemistry in Gaussian, 2000, http://www.gaussian.com/g_whitepap/thermo.htm.
56. C. Eckart, Phys. Rev., 1930, 35, 1303–1309.
57. S. Canneaux, F. Bohr and E. Hénon, J. Comput. Chem., 2014, 35, 82–93.
58. W. Wagnera and A. Pruß, J. Phys. Chem. Ref. Data, 2002, 31, 387–535.
59. D. M. Murphy and T. Koop, Q. J. R. Meteorol. Soc., 2005, 131, 1539–1565.

---

Footnote

† Electronic supplementary information (ESI) available: Tables S1–S12, comparing the rate constant from the present work with those known from the previous studies, along with Cartesian coordinates of the PRCs located in this work. Fig. S1 depicts PRC11 explored along the pathways as discussed in the text. Fig. S2 and S3 respectively represent addition pathways and mechanism involved in addition reactions for the title reaction. See DOI: 10.1039/c6ra01299j

---