Mechanistic insights and atmospheric implications of the degradation reaction of 3-methoxy-1-propanol by reaction with hydroxyl radicals and identification of the end products in the presence of O₂/NO

Abstract

The study investigated the degradation of 3-methoxy-1-propanol (3M1P) by OH^• using the M06-2X/6-311++G(d, p) level, with CCSD(T) single-point corrections. We focused on hydrogen atom abstraction from various alkyl groups within the molecule. The rate coefficient for 3M1P degradation was calculated from the sum of the rate coefficients corresponding to the removal of H-atoms from primary (–CH₃), secondary (–CH₂–), tertiary (–CH< ), and alcohol (–ΟH) groups. The primary attack by hydroxyl radicals occurs at the hydrogen atom bonded to carbon atoms adjacent to the oxygen atom in the ether group, leading to the formation of alkyl radicals. The computed overall rate constant is 1.85 × 10^‒11 cm³ molecule^‒1 sec^‒1 at atmospheric pressure and room temperature, which is consistent with the experimental value of (2.15 ± 0.28)×10^‒11 cm³ molecule^‒1 sec^‒1. This strong agreement confirms the reliability of the computational approach, which provides insights into the atmospheric reactivity and degradation pathways of 3M1P. The tropospheric lifetime of 3M1P is around 15 h, indicating rapid degradation in the atmosphere, potentially contributing to photochemical smog formation. The average ozone production from 3M1P emissions is ~ 2.1 ppb, with estimated photochemical ozone creation potential (POCP) values of 44 and 43 for north-west European and USA-urban conditions, respectively. These values indicate a moderate risk of photochemical smog production and potential harm to human health and the environment due to 3M1P emissions. Successive pathways involve the addition of molecular oxygen to the energized adducts [3M1P]^•, forming [3M1P–O₂]^• peroxy radicals, which primarily react with nitric oxide to produce nitrogen dioxide and the [3M1P–O]^• alkoxy radicals. The major degradation products include methyl formate, 3-hydroxypropyl formate, glycolaldehyde, and 3-methoxypropanal.

Introduction

Oxygenated volatile organic compounds (OVOCs) are found in the troposphere¹, and can be released into the atmosphere by biogenic and anthropogenic processes, as well as gas-phase oxidation of parent hydrocarbons^2,3. While natural OVOC emissions dominate globally, anthropogenic sources provide a major contribution to ambient concentrations, especially near industrialized regions^2,4. The complex degradation of OVOCs produces secondary pollutants like ozone, secondary organic aerosols (SOAs)^5,6,7, and highly oxidized VOCs^2,8, which can negatively impact human health, climate change, and air quality².

Glycol-ethers (GEs), such as 3-methoxy-1-propanol (3M1P), are an important family of OVOCs that are largely released into the atmosphere by human sources^2,8,9,10,11. They are widely employed as solvents in writing inks, dyes, and resins, as well as in the production of surface coatings, cleaning products, and grease removers. However, glycol ethers are prone to atmospheric release, contributing to photochemical air pollution in both urban and regional areas¹². Without proper safety measures, significant quantities can accumulate in the atmosphere¹³. Once released, OVOCs like GEs undergo various physical and chemical degradation processes, having a substantial influence on local, regional, and global environments¹⁴. Due to their extensive applications, OVOCs are prone to atmospheric losses through evaporation, which can influence the ozone balance and contribute to the formation of secondary organic pollutants¹⁵.

Glycol ethers, classified as hazardous air pollutants by the US Environmental Protection Agency (EPA) under the 1990 Clean Air Act Amendments, are the dominant precursors of secondary organic aerosols (SOA)¹⁶. They contribute ~ 1% of the current SOA from mobile sources and are expected to play a more significant role in future SOA formation. In the United States, these compounds are tracked as part of the toxic release inventory, with total releases fluctuating around 3000 tons annually in industrial sectors. In California, emissions of glycol ethers are projected to exceed 13 tons per day by 2020, predominantly from industrial and solvent use sectors, as reported by the California Air Resources Board¹⁷.

Glycol ethers significantly impact air quality and human health, causing acute and chronic effects like narcosis, pulmonary edema, liver and kidney damage, fatigue, nausea, tremors, and anemia¹⁸. In Korea, 2-methoxyethanol emissions were estimated at 8880 and 8950 kg/year in 2006 and 2007, respectively, while 2-ethoxyethanol emissions were 84,442 and 55,816 kg/year in 2006 and 2007, respectively¹⁹. They enter humans through breathing, skin contact, and polluted water or foods, and are removed through urine and breathing²⁰.

The 3M1P as an industrial solvent, is likely present in measurable quantities in the atmosphere due to its moderate volatility and extensive industrial applications. Although specific atmospheric concentration data for 3M1P are not available, its structural similarities in urban and industrial environments suggest potential emissions. Further investigation into its degradation mechanisms is needed to better understand its environmental and atmospheric impacts.

Theoretical and experimental studies have assessed the negative effects of OVOCs on atmospheric oxidants, including chlorine atoms, ozone (O₃), as well as hydroxyl and nitrate radicals². Most investigations focus on glycol ethers’ reactivity with hydroxyl radicals^{13,21,22,23,24,25,26,27} with limited research on their reactions with NO₃ radicals and chlorine atoms, and only one published study addresses ozone reactivity. Understanding these interactions is crucial for avoiding potential negative effects associated with OVOCs¹³. Therefore, assessing the environmental impact of the 3M1P molecule after its atmospheric release requires an understanding of its atmospheric lifetimes, environmental acceptability indices, photochemical ozone creation potential, and degradation products.

Barrera et al.²⁸ experimentally studied the gas-phase reaction between hydroxyl radicals and 3M1P molecule at T = (298 ± 2) K and atmospheric pressure. They employed the flash photolysis-resonance fluorescence technique, using ultra-pure N₂ or synthetic air as the bath gas. The reported kinetic rate constant for the oxidation process was (2.15 ± 0.28)×10⁻¹¹ cm³ molecule⁻¹ s⁻¹.²⁸ However, this study did not consider removing hydrogen atoms from the methyl group neighboring the ether group, which is crucial for accurately computing the total rate coefficient and assessing the product distribution. Previous studies on similar compounds have highlighted the significance of this reaction pathway, demonstrating its importance in determining the overall rate constant.

Du et al.²⁹ recently investigated the degradation reaction of 3M1P initiated by OH radicals using the BH&HLYP/6-311++G(d,p) level of theory^30,31. They calculated the rate constant employing conventional transition state theory (TST)^{32,33,34,35,36,37} along with Eckart’s tunneling correction, reporting a value of 1.5 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ at T = 298 K. Their study revealed that abstractions at the three –CH₂– groups (α, β, and γ-position) of 3M1P play a significant role in the oxidation mechanisms, leading to the formation of three different intermediates: CH₃OCH₂CH₂C^•HOH, CH₃OCH₂C^•HCH₂OH, and CH₃OC^•HCH₂CH₂OH.

The 3M1P molecule, containing both ether (–O–) and alcohol (–OH) functional groups, features two oxygen atoms separated by three carbon atoms. These functional groups are expected to enhance their reactivity, necessitating a thorough risk assessment of their oxidation processes in complex environments involving NO and molecular O₂⁵. This structure can enhance reaction rates with OH radicals, driven by the activating effects of these functional groups. Previous studies suggest that an intermediate adduct, formed through hydrogen bonding between the oxygen atoms and OH radicals, offers an alternative reaction to the direct hydrogen abstraction process seen in alkanes^6,8,28,38. The degradation reaction with hydroxyl radicals is also evident in the case of 3-methoxy-1-butanol^23,28, 2-methoxy ethanol^23,24,25, and 3-methoxy-1-propanol²⁸, with kinetic rate coefficients of 2.37 × 10⁻¹¹, 1.2 × 10⁻¹¹, and 2.15 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹, respectively, as per various studies.

The primary objective of our work is to reinvestigate the OH-addition pathway through a detailed analysis of the kinetic rate constants reported in the experimental work by Barrera et al.²⁸ on the reaction of 3M1P initiated by OH radicals. To achieve this, we will examine the four reaction pathways 1–4 depicted in Fig. 1.

Fig. 1

The proposed mechanism for atmospheric degradation reactions of 3M1P with OH radicals. (Structures in red boxes correspond to closed-shell products).

The proposed initial reaction mechanism is according to the tropospheric reactivity principles and is supported by several studies on the reactions between hydroxy ether and OH^• radicals^{9,24,25,26,39,40,41,42,43}. This mechanism involves OH^• attacking hydrogen atoms connected to carbon atoms neighboring the O-atom of the alcohol or ether groups [channels 1–4], resulting in the formation of the related alkyl radicals (see Fig. 1).

The alkyl radicals produced in channels 1–4 react with molecular oxygen to form peroxy radicals, which can undergo various processes. These include forming alkoxy radicals that can react with O₂ or undergo unimolecular isomerization and decomposition under tropospheric conditions⁴⁴. The dominant pathway for the RC(O^•)OR′ alkoxy radical involves unimolecular decomposition through C–C bond cleavage, with C–O bond cleavage being a minor pathway^9,40,45. Reaction of the alkoxy radical with molecular oxygen and unimolecular isomerization is also possible but considered less important^{26,28,39,40,43,45}. Isomerization in channels 2 and 3, involving the abstraction of an H-atom from the C_β and C_γ positions, can theoretically proceed via three pathways. However, only those occurring through a five-membered ring transition state are considered here due to their enhanced stability.

Under typical “polluted” atmospheric conditions, where 3M1P emissions are likely to have a significant impact, the fate of RO₂ radicals is dominated by reactions with NO rather than with HO₂ or other RO₂ radicals. Additionally, the study assessed the environmental impacts of 3M1P by estimating average ozone production [O₃] and its POCP. This involved examining rate coefficients for the reactions between 3M1P and OH^• under atmospheric conditions. This information helps assess the role of 3M1P in air quality and its potential contribution to ozone formation, particularly under urban atmospheric conditions.

Computational methods

In this work, we utilized the Gaussian 16 software program⁴⁶ for computations, the ChemCraft program⁴⁷ for molecular structure analysis, and Density functional theory (DFT)⁴⁸ for geometry optimization and vibrational frequency calculations, using the M06-2X functional⁴⁹ along with the 6-311++G(d, p) basis set⁵⁰. This combination includes sufficient polarization and diffuse functions to ensure accuracy. This method ensures accuracy in predicting mechanisms and kinetics of atmospheric reactions^{51,52,53,54,55,56}, providing reliable results without increasing computational cost, making it a reliable choice for thermochemistry and kinetics⁵⁷. The harmonic vibrational frequencies at the M06-2X/6-311++G(d, p) level were scaled by a factor of 0.983⁵⁸. The vibrational frequency calculations were conducted to confirm the stationary points with positive frequencies for the local minimum and one imaginary frequency for the transition states. The CCSD(T) method⁵⁹ along with the aug-cc-pVTZ basis set were used to refine energies and obtain more accurate thermodynamic data. To ensure accuracy, T₁-diagnostic values⁶⁰ were evaluated at the ROCCSD/6–31 + G(d′) level. According to Lee and Taylor (1989), T₁-diagnostic values greater than 0.02 indicate a multi-reference nature of the wave functions^60,61. However, the T₁-diagnostic values for pre-RCs, TSs, and post-RCs are around 0.014, 0.019, and 0.015, respectively (see Table 1). These values indicate that the electronic wave functions are well-described by single-reference methods.

Table 1 Energetic and thermodynamic parameters of the species involved in reaction pathways 1–4 as well as T₁-diagnostic values. All calculations were performed under standard conditions (P = 1 atm, T = 298 K).

The study used the M06-2X approach to perform intrinsic reaction coordinate (IRC) calculations^62,63 along the examined channels, confirming the identification of reactants and products for each transition state^64,65,66. Kinetic rate coefficients at the high-pressure limits were obtained using TST with activation energies (E_a) estimated using the M06-2X method with CCSD(T) single-point corrections, including contributions from zero-point vibrational energy (ZPVE), as described in^67,68,69,70

$${k_{{\text{TST}}}}=\kappa (T)\frac{{\sigma {k_B}T}}{h}{V_m}(T)\frac{{Q_{{TS}}^{\dag }}}{{{Q_A} \times {Q_B}}}\exp \left( { - {{{E_a}} \mathord{\left/ {\vphantom {{{E_a}} {RT}}} \right. \kern-0pt} {RT}}} \right){\text{ (bimolecular reactions)}}$$

(1)

$${k_{{\text{TST}}}}=\kappa (T)\frac{{\sigma {k_B}T}}{h}\frac{{Q_{{TS}}^{\dag }}}{{{Q_A}}}\exp \left( { - {{{E_a}} \mathord{\left/ {\vphantom {{{E_a}} {RT}}} \right. \kern-0pt} {RT}}} \right){\text{ (unimolecular reactions)}}$$

(2)

The definitions of all the parameters used in the above equations have been explained in our previous papers^{51,52,53,54,55,56}. Tunneling corrections were computed using the asymmetric Eckart approximation^71,72, κ(T) is a widely utilized method for incorporating tunneling effects in reaction rate calculations based on TST. The rate constants were determined using the Eyringpy package^73,74.

Results and discussion

The atmospheric degradation of 3M1P begins with an initial attack by hydroxyl radicals on H-atoms bonded to carbon atoms located at various positions relative to the ether (–O–) and alcohol (–OH) functional groups. The removal of a hydrogen atom can occur from primary (–CH₃), secondary (–CH₂–), tertiary (–CH< ), and alcohol (–OH) groups. These abstraction reactions lead to the production of water molecules and related alkyl radicals, which are highly reactive intermediates. The specific products and pathways depend on which hydrogen atom is abstracted, as illustrated in Fig. 1.

Properties of the stationary points’ structure

The 3M1P molecule contains various types of hydrogen atoms, enabling distinct degradation reactions, but all H-atoms bonded to each carbon atom are identical. However, these pathways are believed to involve pre-reactive complexes (pre-RCs) due to long-range Coulomb interactions between the isolated reactants.

Our study focuses exclusively on hydrogen abstraction from various alkyl groups, rather than the removal of a hydrogen atom from the hydroxyl group within 3M1P at 298 K, for several reasons. First, the O–H bond in alcohol groups generally has a higher bond dissociation energy (BDE) compared to the C–H bonds in alkyl groups, making hydrogen abstraction from the alkyl chains more favorable under atmospheric conditions. Second, atmospheric reactions initiated by hydroxyl radicals typically target sites with lower activation energy, with the C–H bonds in alkyl groups being more accessible and kinetically favored for abstraction than the O–H bond. This trend aligns with observed degradation pathways of similar molecules in ambient environments. Third, hydrogen abstraction from the O–H bond is more common in high-temperature conditions (such as combustion), where additional thermal energy can overcome the higher BDE. In contrast, under atmospheric conditions, OH radicals preferentially abstract hydrogens from weaker C–H bonds. Finally, since our study focuses on ambient or low-temperature atmospheric degradation mechanisms, investigating hydrogen abstraction from alkyl groups better aligns with the dominant pathways contributing to radical formation and subsequent oxidation processes.

The study found that pre-RCs are bound by up to 7.26 [5.45] kcal mol⁻¹ with respect to the isolated reactants, at the M06-2X [CCSD(T)] level. The new interacting H…O bond distances in pre-RC1α, pre-RC1β, pre-RC1γ, and pre-RC1_OR (see Fig. 2) are characterized by H_α–O, H_β–O, H_γ–O, and H_OR–O bond distances of 2.645, 2.491, 2.793, and 3.194 Å, respectively, indicating weak interactions at the M06-2X level. The C–H and H–O bond lengths in transition states (TSs) are elongated compared to the equilibrium structure, with the C–H bond experiencing less stretching than the H–O bond, suggesting TS structures are more similar to the initial reactants than final products, aligning with Hammond’s postulate⁷⁵. This postulate will be further examined to validate our findings. Table 1 shows the energies and thermodynamic characteristics of the optimized stationary points in the reactions between 3M1P and hydroxyl radicals along channels 1–4 [R1–R4], which are selected according to the atom labels in Fig. 3. The computations were conducted at the M06-2X/6-311++G(d, p) level, providing critical information for understanding the overall reaction kinetics. The Cartesian coordinates as well as the energetic and thermodynamic parameters of all species can be found in Table S1 of the Supplementary Information, SI. It is noted that all examined channels follow an indirect approach, with pre-RC species forming at the entry reaction.

Fig. 2

Potential energy profile for the initial steps of the reactions between 3M1P and OH^• as calculated using the CCSD(T)//M06-2X level.

The first reaction (R1) involves a hydroxyl attack on the H-atom bonded to the C_α-position, forming a pre-RC1α species. This weakly bonds the oxygen atom to the hydrogen atom, forming a 2.645 Å bond length. This produces energized adducts, post-RC1α by forming the TS1α structure, with a change in bond length from 1.564 to 0.961 Å in the post-RC1α species. The second reaction (R2) includes OH radicals attacking the hydrogen atom linked to the C_β-position via the formation of pre-RC1β species. This causes the formation of post-RC1β species, forming the TS1β species. The bond distance between the OH radical and the hydrogen atom changes from 1.372 to 0.965 Å in the post-RC1β species. In pathway R3, hydrogen atoms linked to the C_γ-carbon are abstracted by OH^• radicals, forming the pre-RC1γ complex. This results in an elongation of the C–H bond by 0.05 Å compared to the optimized bond length in 3M1P. Finally, in pathway R4, hydrogen atoms bonded to the carbon adjacent to the ether group are abstracted by hydroxyl radicals, forming the pre-RC1_OR species. The TS1_OR structure shows significant C–H bond elongation, breaking by 1.156 Å.

Fig. 3

Different reactions are involved in the reactions between 3M1P and OH radicals. (All reaction energy and energy barrier calculated at the M06-2X/6-311++G(d, p) level are given in kcal mol⁻¹).

Energetic and thermodynamic parameters

Table 1 presents the calculated total internal energies, enthalpies, and Gibbs free energies for all species involved in the studied channels between 3M1P and OH radicals, including ZPVE corrections. The TS structures are all submerged (below the separated reactants in energy, though not in free energy). The CCSD(T)/6-311++G(d, p)//BH&HLYP/6-311++G(d,p) data obtained by Du et al.²⁹ are reported in Table 1, where they can be compared with our newly supplied DFT data.

The formation of water molecules and the corresponding energized adducts (IM1α, IM1β, IM1γ, and IM1_OR) through hydrogen abstraction transition states (TS1 –TS4) is exothermic, with ΔH_298K values of −22.82, −17.88, −22.54, and −20.68 kcal mol⁻¹, respectively. These reactions are also exoergic, indicating thermodynamic spontaneity under standard conditions, with ΔG_298K values of − 24.02, − 19.70, − 23.92, and − 21.92 kcal mol⁻¹. The post-reactive complexes (post-RC1α, post-RC1β, post-RC1γ, and post-RC1_OR) serve as intermediates, eventually leading to the final degradation products through subsequent reactions (described below). Among the reactions investigated, hydrogen abstraction from the C_α and C_γ positions (corresponding to reactions R1 and R3) exhibit more negative ΔH_298K and ΔG_298K values compared to the other reactions, indicating these pathways are more thermodynamically favorable. However, the activation barrier for reaction R1 is higher than for other pathways, indicating that reactions R1 and R3 are thermodynamically preferred, and they require greater energy input to proceed.

The –OH group in the 3M1P molecule has a strong electron-donating effect, increasing electron density on adjacent atoms, particularly hydrogens bonded to the carbon atom directly next to the –OH group (α-carbon). This makes the hydrogen atoms in the methylene group (–CH₂–) more nucleophilic, making them more susceptible to abstraction by OH radicals.

As shown in Table 1, the transition state TS1α in reaction 1 has a barrier height of around 1.26 [1.80] kcal mol⁻¹ relative to the pre-RC1α species, based on calculations using the M06-2X/6–311++G(d, p) and CCSD(T)/aug-cc-pVTZ//M06-2X/6–311++G(d, p) levels of theory. For reaction 2, the energy barrier is about 4.91 [5.42] kcal mol⁻¹ at the M06-2X [CCSD(T)] level, relative to the pre-RC1β species. The reaction products, specifically H₂O and the CH₃OCH₂C^•HCH₂OH adduct, have energies of approximately − 18.40 [− 16.47] kcal mol⁻¹ using the M06-2X [CCSD(T)] method.

The difference in energy barriers across the hydrogen abstraction pathways for the reaction 3M1P + OH^•→ H₂O + P_i ,(i = α, β, γ, OR) suggests that the formation of the post-RC1γ species has the lowest Gibbs free energy of activation (ΔG^† = 5.79 kcal mol⁻¹), as shown in Table 1. This makes pathway R3 kinetically favored and suggests it is the dominant degradation pathway for 3MP1 under standard conditions.

The energy calculations using the M06-2X/6-311++G(d, p) level are generally consistent with the CCSD(T)/aug-cc-pVTZ//M06-2X/6-311++G(d, p) method, although discrepancies of up to 1.94 kcal mol⁻¹ were observed. Specifically, the CCSD(T) method predicts slightly higher energy levels for TS1α and TS1β species compared to their respective pre-reactive complexes, influencing the routes’ relative energy profiles. Figure S1 in the Supplementary Information shows the optimized structures of all species involved in the degradation processes.

We observe that the exchange-correlation functionals employed predict notable differences in the relative energies of the identified stationary points. As reported by Du et al. in ref.²⁹, the CCSD(T)/6-311++G(d, p)//BH&HLYP/6-311++G(d,p) approach overestimates the computed reaction energies by up to 1.6 kcal mol⁻¹ compared to the M06-2X functional. In contrast, the computed activation energies differ by no more than 1.2 kcal mol⁻¹. While these differences may lead to significant variations in the calculated rate constants, the branching ratios exhibit only a limited dependence on the choice of exchange-correlation functional. This suggests that the overall reaction pathways remain consistent across different computational methods.

Hammond’s postulate⁷⁵ suggests that the TS structure resembles the species with the closer free energy, with the parameter L, defined here as the ratio of the elongation of the C–H bond and the H–O bond indicating whether the TS structure is closer to the reactants or the products.

$$L=\frac{{\delta r\left( {{\text{C}} - {\text{H}}} \right)}}{{\delta r\left( {{\text{H}} - {\text{O}}} \right)}}$$

(3)

The TS structures for pathways 1–4 were evaluated by examining their proximity to either the reactants or the final products using the parameter L; a parameter L greater than 1 (L > 1) indicates a closer TS to the products, while a parameter L less than 1 (L < 1) suggest that the TS structure is closer to the reactants⁷⁶. For pathways 1–4, the L values for the H-abstraction process range from 0.73 to 0.86, indicating that the TS structures are closer to the reactants than to the resulting alkyl radicals.

Kinetic parameters

The study investigates the removal of H-atoms from 3M1P by OH^• using the mechanism proposed by Singleton and Cvetanovic⁷⁷. This reaction is assumed to proceed by a two-step mechanism⁷⁸, involving a rapid pre-equilibrium between the reactants and a pre-RC species, followed by the elimination of an H-atoms, leading to the formation of a post-RC species and the final products:

$$\begin{aligned} & {\text{3M1P + OH}}^{ \bullet } \underset{{k_{{-1}} }}{\overset{{k_{1} }}{\rightleftharpoons}} \left[ {{\text{3M1P}} \cdots {\text{OH}}} \right]^{ \bullet } \\ & \left[ {{\text{3M1P}} \cdots {\text{OH}}} \right]^{ \bullet } \xrightarrow{{k_{2} }}{\text{ H}}_{{\text{2}}} {\text{O}} + \left[ {{\text{3M1P}}} \right]^{ \bullet } \\ \end{aligned}$$

The scheme uses k₁ and k_–1 as the rate coefficients for the forward and reverse channels, respectively, and k₂ for the second step. A steady-state analysis of the overall pathway is provided by Singleton and Cvetanovic⁷⁷, and yields the following expression

$${k_{{\text{overall}}}}=\frac{{{k_1}\,{k_2}}}{{{k_{ - 1}}+{k_2}}}$$

(4)

Even though the energy barrier for k₋₁ is similar to that for k₂, the entropy alteration for the reverse reaction (IM1i → 3M1P + OH) is significantly larger than that for product formation (IM1i→P). As a result, k₋₁ is expected to be much larger than k₂⁷⁷. Therefore, the overall rate constant can be expressed as

$${k_{{\text{overall}}}}={K_{{\text{eq}}}} \times {k_2}$$

(5)

Here, K_eq is the equilibrium constant for pre-RC formation, and k₂ is computed using TST (Eq. 2).

The rate constants computed for each channel can then be used to calculate the branching ratios (BRs) for pathways 1–4:

$$BR(i)={{{k_i}(T)} \mathord{\left/ {\vphantom {{{k_i}(T)} {\sum\limits_{{i=1}}^{4} {{k_i}(T)} }}} \right. \kern-0pt} {\sum\limits_{{i=1}}^{4} {{k_i}(T)} }};\quad (i=1 - 4)$$

(6)

where k_i is the rate constant for pathway i. Using the CCSD(T)–corrected M06-2X method as described above, the rate constants k_α, k_β, k_γ, and k_OR for the initial steps of pathways 1–4 at 298 K were calculated as 2.07 × 10⁻¹², 4.81 × 10⁻¹³, 1.13 × 10⁻¹¹, and 4.69 × 10⁻¹² cm³ molecule⁻¹ s⁻¹, respectively. Based on the results reported by Du et al. (ref.²⁹), the corresponding rate constants under atmospheric conditions, calculated using the CCSD(T)/6-311++G(d, p)// BHandHLYP/6-311++G(d, p) level, were 4.39 × 10⁻¹², 9.92 × 10⁻¹³, 7.41 × 10⁻¹², and 9.89 × 10⁻¹³ cm³ molecule⁻¹ s⁻¹, respectively²⁹. The overall rate constant (1.85 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹) calculated using CCSD(T)/aug-cc-pVTZ//M06-2X/6-311++G(d, p) energetics is about 1.23 times greater than that the value obtained by Du et al.²⁹ (1.5 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹) using CCSD(T)/6-311++G(d, p)//BHandHLYP energetics. Notably, our result is closer to the experimental value of (2.15 ± 0.28) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ reported by Barrera et al.²⁸ This comparison between two computational approaches highlights the advantages of the M06-2X over BHandHLYP, as employed in Du et al.‘s study. M06-2X exhibits superior performance for predicting thermochemical properties, reaction kinetics, and transition state energies in hydroxyl radical degradation. It is designed for main-group thermochemistry and kinetics, making it ideal for modeling H abstraction and other key reactions. It handles open-shell systems and spin states, and its empirical dispersion corrections enhance non-covalent interactions between radicals and intermediates. In contrast, BHandHLYP is a computationally less demanding method, overestimates reaction barriers and lacks dispersion corrections, leading to potential inaccuracies in complex systems. M06-2X is preferred for detailed mechanistic investigations and precise pathway predictions. The CCSD(T)/aug-cc-pVTZ//M06-2X/6-311++G(d, p) approach is particularly useful for studying the degradation of 3M1P by OH radicals. The combination of the “gold-standard” CCSD(T) method with the aug-cc-pVTZ basis set ensures highly reliable single-point energetics, while M06-2X provides accurate geometries and transition states. Although BHandHLYP is computationally cheaper, it sacrifices accuracy in describing radical reactions and transition states. Thus, for detailed and precise mechanistic studies, the CCSD(T)/aug-cc-pVTZ//M06-2X/6-311++G(d, p) level remains the preferred choice.

Furthermore, the calculated rate constants were compared with the available k_SAR values^79,80, estimated using the structure-activity relationship (SAR) method developed by Kwok and Atkinson⁸⁰. For hydrogen atom abstraction, the k_SAR values for the primary (–CH₃), secondary (–CH₂–), tertiary (–CH< ) groups, and alcohol (–OH) group were 1.4 × 10⁻¹³, 9.3 × 10⁻¹³, 1.94 × 10⁻¹², and 1.4 × 10⁻¹³ cm³ molecule⁻¹ s⁻¹, respectively. Notably, the calculated rate constant (k_calc = 1.85 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹) exhibits excellent agreement with the SAR-derived value²⁸ (k_SAR = 1.8 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹) compared to the value obtained by Du et al. (k_SAR = 1.5 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹).

The study analyzed the reactivity trends of 3M1P and its analogous with OH radicals, comparing their rate constants with those of related alkane and alcohol. It was found that the degradation reaction primarily involves H-atom abstraction from the C–H bonds of their alkyl groups. The C–H abstraction process is thermochemically favored⁸, and H-abstraction from the alcohol group is a minor reaction channel in OH radical reactions^6,81. This highlights the predominant role of alkyl C–H bond reactivity in determining the degradation pathway of 3M1P in the atmosphere. The kinetic data for the reactions of OH + 1-butanol and n-butane with OH radicals reveal that the substitution of a hydrogen atom by a hydroxyl group in n-butane increases the reactivity of 1-butanol towards OH radicals. This increase is partly due to the decrease in the C–H bond strength of the carbon atom bound to the O-atom of the alcohol group^8,81. The insertion of an ether linkage (–Ο–) into 1-butanol increases the reactivity of the resulting 3M1P towards OH radicals (see Table 2). The presence of the O-atom of the ether functional group has an activating effect felt at a distance of up to about three carbon atoms from the ether group⁶, indicating that abstraction at carbon atoms remote from the ether group is more facile than expected. The increase in reactivity due to the long-range activating effect of the alcohol and ether group cannot be explained in terms of bond energy or inductive effects alone and indicates an alternative pathway to the direct H-atom abstraction mechanism for n-butane^6,81,82. The formation of an intermediate adduct, where the OH radical is weakly bound to the O-atom of the alcohol or ether group via a hydrogen bond, could explain the possible long-range activation effects in the degradation reaction^8,38. In conclusion, the presence of the alcohol (–OH) and ether (–O–) functional groups in the 3M1P molecule has a key role in the reactivity of 3M1P towards OH radicals.

Table 2 Comparison of the rate constants (units of cm³ molecule⁻¹ s⁻¹) for the reaction of OH radicals with 3M1P and its corresponding alkane and alcohol at 298 K.

The calculated percentages of hydroxyl radical reactions involving hydrogen abstraction from various C–H bonds in CH₃OCH₂CH₂CH₂OH are 11.2%, 2.6%, 60.9%, and 25.3%, respectively, from the terminal carbon to the hydroxyl group. The two most reactive sites are the carbon atoms adjacent to the ether (–O–) group, contributing to over 86% of the total OH radical reactions. This suggests that these positions dominate the degradation pathways of 3M1P. The oxygen atom in the ether group plays a crucial role by weakening the adjacent C–H bonds. This weakening occurs due to the electron-withdrawing effect of the oxygen, which transfers electron density through π-electron delocalization to the neighboring carbon atoms, lowering the activation energy required for H-abstraction. Consequently, these carbon sites become more reactive toward OH^• attack. This activating effect explains why the C_γ and C_OR positions are more reactive in the attendance of OH^•. Hydrogen abstraction from these carbons forms alkyl-type radicals, which rapidly react with oxygen to form RO₂^• peroxy radicals^83,84. Similarly, the removal of H-atoms from other C–H bonds, such as those in the terminal CH₂ group, results in the production of CH₃OC^•HCH₂CH₂OH alkyl radicals, which also quickly react with O₂ to produce RO₂^• species. These peroxy radicals can then react with NO, producing alkoxy radicals (RO^•) and NO₂^83,84.

The M06-2X energy profiles show that the Eckart’s tunneling correction values for the second reaction step [pre-RCi→H₂O + Pi] in pathways 1–4 at T = 298 K are 1.19 (α), 2.71 (β), 1.74 (γ) and 1.89 (methyl group). These values indicate modest tunneling effects, especially in pathway 2 (β-position), which cannot be neglected if accurate results are desired. While the energy barrier difference between hydrogen abstraction from the C_γ position and the C_OR position is relatively small (~ 0.86 kcal mol⁻¹), the difference in rate constants (2.4 times faster for C_γ hydrogen abstraction) at ambient temperature implies that factors beyond the intrinsic energy barrier are influencing the reaction kinetics. Steric effects in the transition state could explain this discrepancy. If the C_OR position is more sterically hindered than the C_γ position, it would be more difficult for the abstracting species (e.g., a radical) to access the C_OR site, leading to a less favorable transition state. Consequently, despite the small difference in energy barriers, the steric hindrance at the C_OR position could reduce the reaction rate compared to the C_γ position. Furthermore, as shown in Table 1, the activation entropies for the transition state leading to the IM1γ and IM1_OR species are −27.97 and −28.52 cal mol⁻¹ K⁻¹, respectively. The slightly higher activation entropy for TS1_OR indicates a greater entropy penalty when forming this transition state compared to TS1γ, and supports the hypothesis that steric effects contribute to the observed differences in reaction rates.

Furthermore, the bond dissociation energies of the C–H bonds show a slightly lower BED for the hydrogen atom at the C_γ position (93.56 kcal mol⁻¹) compared to the C_OR position (95.41 kcal mol⁻¹), which could also facilitate hydrogen abstraction at the C_γ site. Although this difference in BDE minimizes the overall energy barrier, variations in the transition state could magnify this effect, further explaining the observed rate differences (see Fig. 4).

Fig. 4

BDE values (in kcal mol⁻¹) for different C–H bonds in the 3-methoxy-1-propanol molecule, were calculated using the M06-2X/6-311++G(d, p) level.

Atmospheric implications

The atmospheric lifetime (τ) of the 3M1P molecule with respect to oxidation by hydroxyl radicals can be calculated using the following expression:

$$\tau \,=\frac{1}{{{k_{({\text{3M1P}}+{\text{OH}})}} \times [{\text{OH}}]}}$$

(7)

where [OH] represents the global atmospheric concentration of hydroxyl radicals, typically taken as 1 × 10⁶ molecule cm⁻³ (12-hr average)⁸⁵, and k is the rate coefficient for the reaction. The Stockholm Convention⁸⁶ classifies organic pollutants as persistent organic pollutants (POPs) if they persist in the environment for more than two days. The calculated atmospheric lifetime of 3M1P is ~ 15 h, which is slightly longer than the 13-hour experimental value reported by Barrera et al.. Given its estimated atmospheric lifetime of only 15 h, 3M1P does not meet this criterion.

Another concern regarding the 3M1P emissions is its potential contribution to greenhouse warming, which can be evaluated using its global warming potential (GWP). The atmospheric lifetime plays a crucial role in determining GWP. As the lifetime of 3MP1 is shorter than the threshold recommended by the World Meteorological Organization (WMO)⁸⁷, it is unlikely to contribute to the greenhouse effect. 3M1P’s lifetime is shorter than the 0.5-year threshold, making it unlikely to significantly contribute to the greenhouse effect⁸⁸. However, it may contribute to ozone formation in areas near its emission sources. To assess this potential contribution, the POCP index was estimated using a modeling technique developed by Jenkin et al.⁸⁹ to assess the impact of 3M1P on local ozone levels.

Photochemical ozone formation potential

Another important parameter for evaluating a compound’s atmospheric impact is its role in tropospheric ozone formation, which can harm human health, materials, and vegetation⁹⁰. The POCP index is used to assess this impact by quantifying the additional ozone formed from increased emissions of a compound, using ethene emissions as a reference^89,91.

Wallington et al. established that POCP values of VOCs are based on ethane, with a value of 100⁹². The POCP index is determined using atmospheric boundary layer models that simulate the degradation chemistry of VOCs, considering regional and urban-scale scenarios^89,91. Jenkin et al. devised a technique for estimating POCP values using a VOC’s chemical structure and OH reactivity, which was employed to evaluate the POCP of 3M1P in USA-urban and north-west European conditions:⁸⁹

$${\text{POCP}}=A \times {\gamma _s} \times R \times S \times F$$

(8)

where γ_s, R, and S are core parameters used for all VOCs, and parameter A acts as a multiplier. The parameter F is utilized only for particular groups of compounds, otherwise, it defaults to a value of 1. The parameter γ_R represents the reactivity-based index, while γ_S refers to the structure-based index for ozone formation⁹³. The formulas for calculating γ_s and γ_R are given by⁹³

$${\gamma _s}=\frac{{{n_B}}}{M} \times \frac{{28}}{6}$$

(9)

$${\gamma _R}=\frac{{{k_{{\text{OH}}}}}}{{{n_{\text{B}}}}} \times \frac{6}{{k_{{{\text{OH}}}}^{{{\text{ethane}}}}}}$$

(10)

where k_OH is the total rate constant of the studied reaction, M denotes the molecular weight, n_C represents the number of carbon atoms, and n_B is the total number of C–H and C–C bonds in 3M1P. The reference rate constant for the reactions between ethene and OH^• radicals under atmospheric conditions is $k_{{{\text{OH}}}}^{{{\text{ethane}}}}=8.64 \times {10^{ - 12}}$ cm³ molecule⁻¹s⁻¹.⁹⁴ Jenkin et al.⁷¹ define the R parameter, which is associated with the OH-reactivity of the 3M1P molecule, as follows:

$$R=1 - {\left( {B \times {\gamma _R}+1} \right)^{ - 1}}$$

(11)

where B is a constant that indicates how POCP dependency changes with k_OH for the studied conditions. The parameter S, which reflects the size of the VOC, is given by⁸⁹

$$S=\left( {1 - \alpha } \right) \times \exp \left( { - C \times n_{c}^{\beta }} \right)+\alpha$$

(12)

The POCP values for 3M1P were calculated to be 42.63 and 43.96 for USA-urban and north-west European conditions, which are fairly close to experimental values of 47.2 and 46.6, respectively²⁸. The small discrepancy is likely due to the γ_R parameter (see Eq. 10), as the calculated rate constant (k_OH), which directly influences the γ_R value. 3M1P has the potential to contribute to ozone formation, but its impact is lower than most alkenes, which have higher POCP values ranging from 50 to 170⁸⁹. This indicates that while 3M1P can contribute to ozone formation, its impact is relatively lower than that of most alkenes.

During hydrocarbon degradations, peroxy radicals oxidize NO to NO₂, producing tropospheric ozone. The photochemical decomposition of each NO₂ molecule generates one ozone molecule, meaning that the amount of ozone formed is directly related to the number of NO₂ molecules generated from a hydrocarbon⁹⁵. Bufalini et al.⁹⁶ developed a method to estimate ozone formation potential, predicting larger molecules tend to produce more ozone. Its hydrogen and carbon atoms influence the maximum number of ozone molecules from a single hydrocarbon molecule. Generally, larger hydrocarbons have a greater potential to produce ozone through their degradation process. A study estimated the concentration of ozone ([O₃]) (in ppb) during the reactions between hydroxyl radicals and VOCs, which is crucial for understanding how VOCs contribute to ozone formation, a significant concern for human health and air quality.

$${{\text{O}}_3}=\frac{{n^{\prime}{{\left( {k[{\text{OH}}]} \right)}^2}}}{{4.6\left( {2.7 \times {{10}^{ - 5}} - k[{\text{OH}}]} \right)}} \times \left( {\frac{1}{{k[{\text{OH}}]}} - \frac{{1 - {e^{{{ - 1.24 \times {{10}^{ - 4}}} \mathord{\left/ {\vphantom {{ - 1.24 \times {{10}^{ - 4}}} {k[{\text{OH}}]}}} \right. \kern-0pt} {k[{\text{OH}}]}}}}}}{{2.7 \times {{10}^{ - 5}}}}} \right)$$

(13)

where [OH] represents the global average daytime concentration of OH radicals, k denotes the rate constant for the studied reaction, and n′ is the maximum number of ozone molecules produced from one molecule of 3M1P (molecular formula: C₄H₁₀O₂) determined by the number of carbon and hydrogen (n_C+n_H) atoms in the studied molecule. For 3M1P, n′ is 14 (n_C+n_H = 14). The average ozone concentration produced by 1 ppm of 3M1P with OH^• is calculated to be 2.09 ppm, lower than the 3.30 ppm generated by ethene. The degradation of 3M1P makes a negligible contribution to atmospheric ozone formation due to factors such as the overall emission levels (of 3M1P compared to other VOCs) and the efficiency of its pathways in producing ozone. Therefore, while the specific ozone yield from 3M1P degradation is slightly higher, its overall impact on atmospheric ozone levels remains minimal.

Subsequent reactions of the alkyl radicals

As shown in Fig. 1, the OH radical reactions produce alkyl radicals (labeled IM1i, where i denotes the α, β, γ, and methyl group), which subsequently add molecular oxygen (O₂) to form peroxy radicals (labeled IM2i). We did not find any barriers for the O₂ addition reactions and also found them to be highly exothermic (See Table S4 in the Supplementary Information for full data on the studied pathways). The IM2α species, an alpha-hydroxy peroxy radical, undergoes the unimolecular elimination of the HO₂ radical, forming 3-methoxypropanal²⁸. The other IM2 radicals, in polluted conditions, primarily react with NO, contributing to ozone (O₃) formation (as discussed in the previous section). This NO reaction is also barrierless and exothermic for all three remaining cases, leading to alkoxy radicals (IM3i). The subsequent reactions of the IM3i differ from each other. The IM3_OR radical predominantly reacts with O₂, forming methyl 3-hydroxypropanoate, while IM3β and IM3γ radicals may undergo both O₂ addition and C–C bond cleavage reaction channels, as illustrated in Fig. 1.

In all studied pathways (see Fig. 1 and Table S4 in the Supplementary Information), the reaction between the IM1i and molecular oxygen results in the formation of IM2i peroxy species, which is exothermic with ΔG_r values ranging from −18.42 to −26.51 kcal mol⁻¹. For the IM2α peroxy radicals, HO₂ elimination can occur immediately without alkoxy radical formation, leading to the 3-methoxypropanal formation. In contrast, other IM2 species react with NO radicals to form a vibrationally excited intermediate [IM1i-O₂–NO]^•, which can decompose into an alkoxy radical [IM1i–O]^• (denoted as IM3i) through three different reaction channels at the C_β and C_γ positions.

Previous studies^{9,26,28,40,43,45} have identified that the primary degradation pathway for alkoxy radicals involves unimolecular decomposition through C–C bond cleavage, while C–O bond cleavage is less significant. Thus, reactions between the IM3i alkoxy radical and O₂, as well as potential unimolecular isomerization, contribute minimally to the overall degradation process.

As shown in Fig. 1, Fig. S1, and Table S4 of the Supplementary Information, the CH₃OCH₂CH(O^•)CH₂OH alkoxy radicals (denoted as IM3β) can be categorized into three reaction channels: (i) IM3β species react with O₂ to form 1-hydroxy-3-methoxyacetone, which is not commercially available for identification purposes; (ii) IM3β decomposing through C_α–C_β bond cleavage, producing 2-methoxy acetaldehyde and ^•CH₂OH radicals (denoted as IM4β) via the TS5β species, elongating the C_α–C_β bond from 1.538 Å to 2.103 Å; (iii) breaking the C_β–C_γ bond, producing glycolaldehyde and the ^•CH₂OCH₃ radical (denoted as IM5β) via the TS6β species, which elongates the C_β–C_γ bond from 1.521 Å to 2.181 Å. The IM5β is expected to react quickly with O₂ and NO radicals through the TS7β species (a reaction that is exothermic and spontaneous with ΔH_r = −47.19 and ΔG_r = −36.87 kcal mol⁻¹), leading to the production of the IM6β species, which finally produces a stable product (methyl formate) and releasing an unstable, highly reactive hydroperoxyl (HO₂) radical⁹⁷. This reaction occurs via transition state TS8β cleaving the C–H bond and forming the O–H bond with bond lengths of 1.265 and 1.489 Å, correspondingly.

Similarly, the CH₃OCH(^•O)CH₂CH₂OH alkoxy radical (denoted as IM3γ) can follow three possible reaction routes: (i) IM3γ can react with O₂ to form methyl 3-hydroxypropanoate, a thermodynamically highly exothermic and spontaneous process, with ΔH_r = −46.59 and ΔG_r = −47.43 kcal mol⁻¹; (ii) IM3γ radicals can undergo scission at the O–C_γ bond, producing 3-hydroxypropanal along with the ^•OCH₃ radical (denoted as IM4γ) via the TS5γ species, with an energy barrier of 21.95 kcal mol⁻¹ (see Table S4 of the Supplementary Information). In this TS structure, the O–C_γ bond distance elongates to 1.837 Å compared to 1.395 Å in IM3γ species; (iii) If the scission in IM3γ radicals occurs at the C_β–C_γ bond, it produces methyl formate along with ^•CH₂CH₂OH radicals (denoted as IM5γ) via the TS6γ species, causing the C_β–C_γ bond to elongate to 1.967 Å compared to 1.517 Å in IM3γ species (see Fig. S1 of the Supplementary Information). The ^•CH₂CH₂OH radical (IM5γ) then reacts with molecular oxygen, followed by a reaction with NO radicals, producing the IM6γ species in a highly exothermic and spontaneous reaction, with ΔH_r = −44.80 and ΔG_r = −33.81 kcal mol⁻¹. The IM6γ radicals can then isomerize via a five-membered ring transition state (TS8γ), resulting in the elimination of HO₂ and the formation of 2-hydroxyacetaldehyde as the final product. In the TS8γ species, C–H bond cleavage and O–H bond formation occur with bond distances of 1.274 Å and 1.406 Å, correspondingly (see Fig. S1 and Table S4 of the Supplementary Information).

By inspecting Figs. 1, 5 and 6, and Table S4 in the Supplementary Information, it is observed that the relative energy for forming the IM2β species is −31.79 kcal mol⁻¹ compared to the IM1β alkyl radical and O₂, while the energy for forming the IM2γ peroxy radical from the IM1γ alkyl radical is −35.79 kcal mol⁻¹, indicating that the production of the IM2γ species is thermodynamically more favorable than that of the IM2β species. Notably, the energy barriers for reactions involving the IM2β and IM2γ radicals are −0.49 and −5.49 kcal mol⁻¹, correspondingly (Table 1). In the existence of NO radicals, the relative energies for IM3β and IM3γ species formation are −11.62 and −10.43 kcal mol⁻¹, respectively. Additionally, the energy barrier for the cleavage of the C_β–C_γ bond at the TS6γ species is 7.35 kcal mol⁻¹, while the energy barrier at the TS6β structure is slightly lower, at 6.45 kcal mol⁻¹. This suggests that the production of the IM5β species is energetically more favorable than the formation of the IM5γ species. The calculated energy barriers at TS6β and TS6γ indicate that the decomposition of the IM3β, is kinetically faster than that of the IM3γ species, as illustrated in Figs. 5 and 6. Consistent with these results, the spontaneous decomposition reactions of IM3β and IM3γ radicals have Gibbs free energies of −5.01 and −15.89 kcal mol⁻¹, respectively. Finally, the IM6β and IM6γ species produce methyl formate and 2-hydroxyacetaldehyde via the TS8β and TS8γ species, with energy barriers of 9.29 and 10.88 kcal mol⁻¹, respectively. As a result, it can be concluded that the production of methyl formate and HO₂ species is more favorable both thermodynamically and kinetically.

Fig. 5

Potential energy profile for the degradation pathway of the IM1β species along with the relative energies calculated at the M06-2X/6-311++G(d, p) level of theory.

Fig. 6

Potential energy profile for the degradation pathway of the IM1γ species along with the relative energies calculated at the M06-2X/6-311++G(d, p) level of theory.

Conclusion

The study optimized geometries and analyzed vibrational frequencies of stationary points on the potential energy surfaces involved in the degradation of 3-methoxy-1-propanol (3M1P) by hydroxyl radicals using the M06-2X/6-311++G(d, p) level of theory, and single-point energy calculations at the CCSD(T)/aug-cc-pVTZ theoretical level. The process initiates with the removal of H-atoms from the alkyl groups, followed by O₂ addition to form [3M1P–O₂]^• peroxy radicals, which subsequently convert to [3M1P–O]^• alkoxy radicals except for alpha position that it may eliminate HO₂ radicals immediately (no alkoxy step). The atmospheric degradation produces several VOCs, which can affect tropospheric chemistry and air quality.

The results show that the primary degradation pathway involves the removal of H-atoms from the carbon atoms adjacent to the ether linkage (–O–). The γ-carbon (C_γ) position is kinetically more favorable due to its lower bond dissociation energy and electron-withdrawing effects of the ether group. Major degradation products include 3-hydroxypropyl formate, methyl formate, 3-hydroxypropyl formate, and glycolaldehyde, which contribute to the atmosphere’s oxidative capacity and secondary pollutants, like ozone and peroxyacyl nitrates (PANs), particularly under conditions in the presence of NO_x. The computed reaction rate coefficient was 1.85 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹, which is within the error margins of a previous experimental study. This corresponds to a lifetime of approximately 15 h. The photochemical ozone creation potential of 3M1P was also assessed and found to be relatively modest.