1 Introduction

Carbonyl compounds are widely spread atmospheric key components formed in the atmosphere by oxidation of volatile organic compounds (VOCs) emitted from biogenic and anthropogenic sources [1, 2]. They comprise a prominent class of organics released directly into the atmosphere. They are used in various industrial processes, including producing dyes, chloroform, fragrances, flavorings, and plastics, as well as solvents for resins, lacquers, and cellulose [3, 4]. They serve as fuel additives to lower soot emissions and fuel tracers for evaluating fuel qualities [5,6,7,8]. Volatile organic compounds (VOCs) are critical in the atmosphere because they directly connect with air quality and climate change [9,10,11]. Carbonyl compounds significantly affect urban air pollution and atmospheric chemistry. These carbonyl compounds extensively contribute to forming free radicals involved in the oxidation of hydrocarbons [12]. They are crucial intermediates in the creation of aerosols and serve as the building blocks for other oxidants like ozone, nitric acid, and peroxyacyl nitrates (PANs) [13].

Multifunctional ketones like hydroxyketones are hydroxyl and carbonyl group-containing compounds representing a significant class of oxygenated Volatile Organic Compounds (OVOCs) in the atmosphere. They are used in various industrial sectors, mainly in food [14], solvents, and pharmaceutical synthesis [15]. Hydroxyketones can either be released into the atmosphere as biogenic [16, 17] or anthropogenic pollutants [18] or formed by oxidation of alkanes, alkenes, and other oxygenated compounds [19, 20]. Like other carbonyl compounds, hydroxyketones are removed from the atmosphere in many possible ways like photolysis by solar radiation and oxidation by atmospheric oxidants like hydroxyl (OH), nitrate (NO3) radicals, ozone (O3) molecules, and. chlorine (Cl) atoms. The hydroxyl radical (OH) is the most reactive among these species, influencing various atmospheric chemical processes.

Therefore, studying OH radical reaction with hydroxyketones is necessary to assess their significance in air pollution. These hydroxyketones reactions have recently received significant attention from experimental and theoretical research groups. Following this, we have studied the oxidation reaction of 4-hydroxy-2-pentanone (4H2P) with OH radical. 4H2P was found to be a biomass-derived molecule produced significantly through a distinct method than other hydroxyketones [21]. Based on the literature survey, no theoretical or experimental study has been reported till now for the 4H2P + OH reaction.

This paper provides the results of the first theoretical investigation of the kinetics and mechanism of 4H2P + OH radical reactions. This work's main objective is to better understand the studied reaction's importance as a removal process of 4H2P in the atmosphere. Therefore, we used computational tools to study the plausible mechanism and thermochemistry and obtain rate coefficients of various pathways of the titled reaction in the 210–350 K temperature range. The rate coefficient value was then used to calculate the atmospheric lifetime of 4H2P. Additionally, secondary organic aerosols (SOAs), which negatively impact the climate and humans, are produced as a byproduct of the oxidation reaction of ketones like acetone and pentanone with atmospheric oxidants [22,23,24,25]. Therefore, the manuscript also discusses the subsequent reaction mechanisms of the product produced in the reaction's pathway and the formation of SOA.

2 Computational details

All reaction species involved in hydrogen abstraction pathways were optimized in gas-phase using second-order Møller–Plesset perturbation (MP2) [26] theory and hybrid meta-density functional, Becke-Half-and-Half-LYP (BH&HLYP) [27]. Dunning's correlation-consistent polarized valence triple zeta (cc-pVTZ) basis set was used for geometrical optimization purposes [28]. In the previous studies of hydrogen abstraction reactions, the BH&HLYP method is trustworthy for evaluating optimized geometries and frequencies of reaction species [29,30,31]. < S2 > values given in Table S5 in the Supplementary Information (SI) evince the absence of spin contamination in various reaction species at the BH&HLYP/cc-pVTZ level of theory. We performed computations at BH&HLYP and MP2 levels with cc-pVXZ basis sets and then extrapolated to the complete basis set (CBS) limit to refine energies. We used Helgaker relation [32, 33] to carry out CBS extrapolations, which are given as

$${E}_{X}= {E}_{CBS}+ A{X}^{-3}$$
(1)

where \({E}_{X}\) is the energy with X, that is 2, 3, 4, and 5 for cc-pVXZ basis sets, \({E}_{\mathrm{CBS}}\) is the CBS energy limit, and A is the fitting parameter. We did harmonic vibrational frequency analysis to understand the characteristics of stationary points on the potential energy diagram. Minima were defined as stationary points with only positive frequencies, and the appearance of one imaginary frequency verified the transition state. To validate the connectivity of transition states to their respective reactants and products, we performed intrinsic reaction coordinate (IRC) [34, 35] calculations at both theoretical methods. The minimum energy path (MEP) is obtained for further kinetic calculations at the BH&HLYP/cc-pVTZ level with a 0.1 Bohr gradient step size. Along the MEP, energy derivatives such as hessians and gradients are also calculated.

The rate coefficients depend on energy barriers, so higher theoretical calculations are performed to obtain barrier height values accurately. Using BH&HLYP/cc-pVTZ optimized geometries, we calculated single-point energy at coupled-cluster single-double and perturbative triples (CCSD(T)) [36] method with cc-pVTZ basis set to achieve a more accurate energetics. T1 diagnostic [37, 38] values given in Table S6 in the Supplementary Information (SI) are evaluated at the CCSD(T)/cc-pVTZ level and are clearly within the acceptable limit (0.045). Hence, the CCSD(T) single reference wave function is appropriate here. The IRC routes, vibrational movements, and molecular geometries were all visualized using the GaussView software [39]. Using the quantum chemistry code Gaussian16, all calculations involving electronic structure and energy were carried out [40].

All rate coefficient calculations were performed by utilizing the POLYRATE 2017-C program [41]. Utilizing variational transition state theory (VTST) and the interpolated single point energy (ISPE) method, the rate coefficients of each reaction pathway of the titled reaction are calculated. The rate coefficients are computed utilizing canonical variational transition state theory (CVT) in the 210–350 K temperature range [42,43,44]. For tunneling corrections, zero curvature tunneling (ZCT) [44,45,46,47,48] and small curvature tunneling (SCT) methods are employed [49, 50]. By minimizing the dividing surface s, the canonical variational theory rate coefficients\({(k}^{\mathrm{CVT}}\left(T\right)\)) [30, 51,52,53] are derived and can be written as:

$${k}^{\mathrm{CVT}}\left(T\right)=\mathrm{min}{k}^{GT}\left(T,s\right)$$
(2)
$${k}^{\mathrm{GT}}\left(T,s\right)= \frac{\sigma {k}_{B}T}{h}\frac{{Q}^{GT}(T,s)}{{\phi }^{R}(T)} \mathrm{exp}\left(-\frac{{V}_{\mathrm{MEP}}^{\mathrm{CVT}}(s)}{{k}_{B}T}\right)$$
(3)

where \({k}^{\mathrm{GT}}\left(T,s\right)\) denotes the generalized transition state theory rate coefficient at s, \({k}_{B}\) is the Boltzmann constant = 1.38 × 10–23 J K−1, T is the temperature, \(\mathrm{h}\) is the Planck's constant = 6.63 × 10–34 J Hz−1, and σ is the symmetry factor considered as unity. \({Q}^{\mathrm{GT}}(T,s)\) is the partition function of the generalized transition state at s. \({\phi }^{R}\left(T\right)\) is the partition function of reactants per unit volume and \({V}_{\mathrm{MEP}}^{\mathrm{CVT}}\left(s\right)\) is the potential energy at point s, along the minimum energy path. While calculating electronic partition functions, the 2Π3/2 and 2Π1/2 electronic states of the OH radical are taken into account with a splitting of 140 cm−1. By multiplying the CVT rate coefficient by a transmission coefficient \({\kappa }_{T}\), the tunneling effect is calculated. Transmission coefficient \({\kappa }_{T}\) is computed by using two semiclassical tunneling approximations. One is the minimum energy path semiclassical adiabatic ground state (MEPSAG) method, also called zero-curvature tunneling (ZCT) approximation. ZCT approximation assumes that the reaction path has negligible curvature, so the tunneling path coincides with it. It neglects the contribution of multidimensional reaction-path curvature.

Another tunneling approximation is the centrifugal dominant slight curvature semiclassical adiabatic ground state (CD-SCSAG) method. This method is also called small-curvature tunneling (SCT) approximation. When the reaction path possesses curvature, the tunneling occurs on the concave side of the MEP [54,55,56,57,58,59]. CD-SCSAG method is a generalization of the Marcus-Coltrin approximation [59] in which the tunneling path is distorted from the MEP out to a concave-side vibrational turning point in the direction of the internal centrifugal force [49]. This method is based on the vibrationally adiabatic assumption and the assumption that the curvature of the reaction path in inertial coordinates is small [60].

ZCT and SCT keywords are given in the POLYRATE input file to get the transmission coefficient \({\kappa }_{T}\) and tunneling corrected rate coefficients in the output file. Mainly geometries, frequencies, and force constants of reactants, transition states, and products, along with other keywords, are given in the POLYRATE input file and partition functions (\({Q}^{\mathrm{GT}}(T,s)\), and \({\phi }^{R}\left(T\right)\)), potential energy (\({V}_{\mathrm{MEP}}^{\mathrm{CVT}}\left(s\right)\)), transmission coefficients (\({\kappa }_{T}\)), and tunneling corrected rate coefficients (kCVT/ZCT and kCVT/SCT) are obtained in the POLYRATE output file along with other results. A brief explanation of how the POLYRATE program calculates partition functions (\({Q}^{\mathrm{GT}}(T,s)\), and \({\phi }^{R}\left(T\right)\)) and transmission coefficients (\({\kappa }_{T}\)) is given in the Supplementary Information (SI).

Modified Arrhenius equation is used to fit CVT/SCT rate coefficients in the temperature range of 210–350 K with the help of Origin2018 software [61].

$$k = {\text{AT}}^{{\text{n}}} {\text{exp}}\left( {\frac{{ - E_{{\text{a}}} }}{{{\text{RT}}}}} \right)$$
(4)

Here k = CVT/SCT rate coefficient values in the 210–350 K temperature range, T = 210–350 K, and R is the universal gas constant of 1.98 cal mol−1 s−1. With the help of these values, we fitted the modified Arrhenius equation in the Origin2018 software and got the values of Arrhenius prefactor (A), energy barrier (Ea), and temperature exponent (n). The temperature exponent n arises from the temperature dependence of the Arrhenius prefactor. In the case of the famous Arrhenius theory, n = zero and n = 1/2 in the collision theory of gases for bimolecular gas phase reactions. In transition state theory, n is one or greater depending on the number of reacting species involved in the geometry of the activated complex [62].

The VTST-ISPE approach is utilized to evaluate temperature-dependent rate coefficients [63]. In this method, frequencies, stationary point geometries, and first derivatives were computed at the BH&HLYP/cc-pVTZ theoretical level. Reaction energies and barrier heights were improved by performing computations at a higher CCSD(T)/cc-pVTZ level.

3 Results and discussion

3.1 Optimized structures of stationary points

Figure 1 shows the optimized geometries of all stationary points involved in five hydrogen abstraction pathways of the 4H2P + OH reaction. Bond lengths and angles at BH&HLYP/cc-pVTZ and MP2/cc-pVTZ levels are displayed in Fig. 1. These two theoretical approaches are used to calculate vibrational frequencies. Table S1 in the Supplementary Information (SI) illustrates scaled vibrational frequencies accompanying limited experimental values. Each transition state has an imaginary frequency corresponding to the stretching modes of coupling breaking and forming bonds.

Fig. 1
figure 1figure 1figure 1

Optimized geometries of reactants, reactant complexes, transition states, product complexes, and products of CH3C(O)CH2CH(OH)CH3 + OH reaction at BH&HLYP/cc-pVTZ and MP2/cc-pVTZ (in brackets) levels. Bond lengths are in angstroms, and angles are in degrees

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Hydrogen abstraction from –C(O)CH3 group (1), from –CH2 group (2), from –CH group (3), from –OH group (4), and from –CH3 group (5) comprises five reaction pathways of the 4H2P + OH reaction as follows:

CH3C(O)CH2CH(OH)CH3 + OH → CH2C(O)CH2CH(OH)CH3 + H2O (1)

CH3C(O)CH2CH(OH)CH3 + OH → CH3C(O)CHCH(OH)CH3 + H2O (2)

CH3C(O)CH2CH(OH)CH3 + OH → CH3C(O)CH2C(OH)CH3 + H2O (3)

CH3C(O)CH2CH(OH)CH3 + OH → CH3C(O)CH2CH(O)CH3 + H2O (4)

CH3C(O)CH2CH(OH)CH3 + OH → CH3C(O)CH2CH(OH)CH2 + H2O (5)

The abstraction reaction of 4H2P by OH radical starts by forming reactant complexes. Due to hydrogen bond interactions, all reactant complexes have lower energies than reactants, stabilizing them. The breaking C–H bond in TS1, TS2, TS3, and TS5 is lengthened by 13.24%, 13.47%, 18.48%, and 15.75% as compared to the equilibrium C–H bond distance in 4H2P, respectively. The dissociating O–H bond length in TS4 increases by 7.52% compared to the equilibrium O–H bond length in 4H2P. Compared to the equilibrium O–H bond length in free H2O molecule, the O–H bond in TS1, TS2, TS3, TS4, and TS5 is stretched by 34.41, 34.18, 51.92, 23.47, and 30.10%, respectively. It is evident from transition states TS1, TS2, TS3, TS4, and TS5 that establishing bonds elongate more than breaking bonds do. All transition states are reactant-like according to Hammond's postulate [64], and reactions will progress through early transition states. Product complexes (PC1, PC2, PC3, PC4, and PC5) are more energetically stable than their related products after overcoming potential barriers because of hydrogen bonding.

3.2 Reaction mechanisms and energetics

Figure 2 depicts the potential energy diagram for the 4H2P + OH reaction's five abstraction pathways. Reactants' energies are fixed to zero for reference. Relative energies are given in Table S3 in the Supplementary Information (SI). From Fig. 2, it can be visualized that the barrier height for reaction pathway 1 is 10.84 kcal/mol, 7.29 kcal/mol for reaction pathway 2, 2.84 kcal/mol for pathway 3, 11.73 kcal/mol for pathway 4, and 10.18 kcal/mol for pathway 5. Reaction pathway 3 has the lowest barrier height among all other reaction pathways. As a result, reaction pathway 3's rate coefficients will be higher than those of other reaction pathways.

Fig. 2
figure 2

Potential energy diagram of the 4H2P + OH reaction. Relative electronic energies (in kcal/mol) are computed at the CCSD(T)/cc-pVTZ//BH&HLYP/cc-pVTZ level

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The thermodynamic quantities like reaction enthalpies \(\left({\Delta H}_{298.15}^{^\circ }\right)\) and Gibbs free energies \(\left({\Delta G}_{298.15}^{^\circ }\right)\) of five reaction pathways are computed at the BH&HLYP/cc-pVTZ level of theory, and values are given in Table S4 in the Supplementary Information (SI). The reaction enthalpies values for 1, 2, 3, 4, and 5 reaction pathways are − 17.46, − 19.98, − 20.23, − 8.50, and − 10.54 kcal/mol, respectively. Based on these values, it can be gleaned that all reaction pathways are exothermic, with reaction pathway 3 being thermodynamically more favorable than the others. From \(\left({\Delta G}_{298.15}^{^\circ }\right)\) values given in Table S4, we can conclude that all reaction pathways (1, 2, 3, 4, and 5) are spontaneous, having \(\left({\Delta G}_{298.15}^{^\circ }\right)\) values − 18.35, − 21.97, − 21.90, − 10.41, and − 12.56 kcal/mol, respectively.

3.3 Rate coefficient calculations

Using canonical variational transition state theory (CVT), we estimated the 4H2P + OH reaction rate coefficients over the temperature range of 210–350 K. Zero curvature tunneling (ZCT) and small curvature tunneling (SCT) corrections are used to incorporate the tunneling effect. Figure 3a, b, c, d, and e displays the CVT, CVT/ZCT, and CVT/SCT rate coefficients of five abstraction pathways of the titled reaction. Tables S7-S11 in the Supplementary Information (SI) comprise all rate coefficient values.

Fig. 3
figure 3

CVT/SCT rate coefficients of reaction pathways 1 (3a), 2 (3b), 3 (3c), 4 (3d), 5 (3e) and overall reaction of 4H2P + OH (3f) at CCSD(T)/cc-pVTZ//BH&HLYP/cc-pVTZ level in the temperature range of 210–350 K

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The tunneling effect is defined as the ratio of CVT/SCT with CVT rate coefficients in Fig. 3a–e is significant for all reaction pathways across the temperature range. With temperature rise, the tunneling effect decreases. Figure 3f displays the CVT/SCT rate coefficients for each reaction pathway and the overall reaction, and Table S12 in the Supplementary Information (SI) provides the values. From Fig. 3f, we can conclude that reaction pathway 3 has faster rate coefficients than other reaction pathways. This outcome is compatible with energy barrier values, as reaction pathway 3's energy barrier is minimum among other reaction pathways.

Modified Arrhenius parameters utilizing CVT/SCT rate coefficients of the five abstraction pathways and overall 4H2P + OH reaction are given in Table 1. Figure 4 shows the fitted Arrhenius plot, demonstrating that CVT/SCT rate coefficients exhibit a positive temperature dependency in the 210–350 K temperature range.

Table 1 Fitted modified Arrhenius parameters (k = ATn exp(− Ea/RT)) of all reaction pathways and overall 4H2P + OH reaction utilizing CVT/SCT rate coefficients at CCSD(T)/cc-pVTZ//BH&HLYP/cc-pVTZ level over the temperature range of 210–350 K
Full size table
Fig. 4
figure 4

The fitted Arrhenius plot of overall reaction and all reaction pathways of 4H2P + OH over the temperature range of 210–350 K

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The negative and zero Ea values are found for all reaction pathways and overall reaction. Negative Ea values imply that reactants have attractive forces, and reaction initially proceeds via the formation of intermediate complexes [65]. This can be seen in the mechanism proposed for the titled reaction. Reactant complexes are found on the potential energy diagram in Fig. 2.

3.4 Branching ratio

The branching ratio is the ratio of the individual reaction pathway rate coefficient to the overall rate coefficient. We have calculated the branching ratio for all reaction pathways of the 4H2P + OH reaction, and values are given in Table S13 in the Supplementary Information (SI). The computed branching ratios for 1, 2, 3, 4, and 5 reaction pathway at 298 K are 0.06, 14.12, 85.30, 0.04, and 0.49%, respectively. From Fig. 5, it can be concluded that the branching ratios of reaction pathways 1, 4, and 5 are extremely low, and reaction pathway 3 is having highest branching ratio among all reaction pathways over the entire temperature range. The contribution from reaction pathway 3 is maximum, so it is the major pathway.

Fig. 5
figure 5

The 4H2P + OH reaction calculated branching ratios over the temperature range of 210–350 K utilizing CVT/SCT rate coefficients

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Table 2 provides an overview of the overall rate coefficients of the titled reaction and reactions of several similar hydroxyketones with OH radical at 298 K.

Table 2 Rate coefficients of the reactions of OH radicals with several ketones and hydroxyketones, including 4H2P at 298 K
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The oxidation reaction of 4H2P by OH radical is anticipated to occur through hydrogen abstraction, similar to other aliphatic ketones. According to our theoretical study, hydrogen abstraction advances mainly from the active methylene group (–CH group), i.e., reaction pathway (3), followed by the –CH2 group and methyl group (–CH3 group). Comparison of rate coefficients of 4H2P + OH reaction with that of other aliphatic ketones and hydroxyketones leads to the following trends:

⦁ The rate coefficients of hydroxyketones + OH reaction are more significant than their corresponding ketones. Because hydroxyketones react with OH primarily through hydrogen abstraction of the weakest C-H bond of the -CH(OH) group, which is activated by the -OH substituent group. 4H2P + OH, 3-Hydroxy-2-Butanone + OH, and hydroxyacetone + OH reactions follow this trend compared to their corresponding ketones.

⦁ Hydroxyketones with one tertiary hydrogen atom at the β position are more reactive toward OH oxidation than hydroxyketones with no β hydrogen atom. The OH functional group activates this tertiary hydrogen atom, which increases the rate coefficient value. This trend was followed by 4H2P when compared with 4-hydroxy-4-methyl-2-pentanone and 3-hydroxy-2-butanone when compared with 3-hydroxy-3-methyl-2-butanone.

⦁ The reactivity of hydroxyketones toward OH radical increases with chain length. At room temperature, the rate coefficient increases from hydroxyacetone, 3-hydroxy 2-butanone, to 4-hydroxy 2-pentanone. The increase in rate coefficient values is due to an increase in the number of abstractable hydrogens as chain length increases.

⦁ β-hydroxyketones are more reactive toward OH oxidation than α-hydroxyketones because of deactivating effect of the carbonyl group on α-carbon atoms. This trend can be seen in the case of 4-hydroxy-4-methyl-2-pentanone, as its rate coefficient values are higher than that of 3-hydroxy-3-methyl-2-butanone.

3.5 Secondary reactions of CH3C(O)CH2C·(OH)CH3 radical

Thermodynamic and kinetics results reveal that pathway 3 is the most favorable, producing alkyl radical CH3C(O)CH2C·(OH)CH3 and water. The degradation processes of CH3C(O)CH2C·(OH)CH3 were further studied and are shown in Scheme 1. In the oxygen-abundant atmosphere, alkyl radical forms peroxide radical CH3C(O)CH2C(OO·)(OH)CH3 (A) by reacting with O2 in the atmosphere through a barrierless pathway. Peroxide radicals are crucial in atmospheric chemistry. [10, 72,73,74,75]. The peroxide radical (A) undergoes a H-migration reaction to form acetonyl radical and peroxyacetic acid. Also, after reacting with HO2, peroxide radical (A) forms CH3C(O)CH2C(OOH)(OH)CH3 and O2 via TS11.

Scheme 1
scheme 1

Proposed mechanism of the consequent reactions of the CH3C(O)CH2C(OO·)(OH)CH3 radical

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According to Atkinson and Arey, the reaction of RO2 with NO occurs predominantly in the atmosphere compared to other radicals [10]. Generally, the RO2 + NO reaction produces alkoxy radicals and NO2. But in the present work, because of the poor stability of the alkoxy radical, while performing the NO2 elimination reaction, the C–C bond will break. The peroxide radical (A) reaction with NO results in the formation of peroxynitrite (B). This peroxynitrite (B) has two forms, namely IM1(cis-CH3C(O)CH2C(O2NO)(OH)CH3 and IM2 trans-CH3C(O)CH2C(O2NO)(OH)CH3). IM1 isomerizes to form IM2 through TS6. IM1 and IM2 yield acetonyl radical and stable product acetic acid through TS8 and TS9, respectively, by eliminating NO2. The acetonyl radical, after reacting with HO2, yields acetone and oxygen molecule.

Secondary organic aerosols (SOA) account for the majority of aerosol mass present in the atmosphere. These SOA seriously affect air quality, atmospheric chemistry, and human health [22,23,24,25]. IM1 do tautomerization via TS7 to form IM3 (CH3C(O)CH2C(ONO2)(OH)CH3) which is an SOA that influences climate and people's life adversely.

The relative energies of various species are obtained at the CCSD(T)/cc-pVTZ//BH&HLYP/cc-pVTZ level. The transition state TS10 of the H-migration reaction has a barrier height of 45.86 kcal/mol. The enthalpy and Gibbs free energy associated with the H-migration reaction are 5.48 kcal/mol and − 8.73 kcal/mol, respectively, implying this reaction is endothermic and spontaneous. Transition state TS11 involved in A's reaction with HO2 has a barrier height of 16.57 kcal/mol. This reaction has a − 34.27 kcal/mol ΔH value and − 32.46 kcal/mol ΔG value, demonstrating this reaction to be exothermic and spontaneous. The potential energy surface for the A + NO reaction is shown in Fig. 6. The < S2 > and T1 diagnostic values of the A + NO reaction species are listed in Tables S14 and S15 in the Supplementary Information (SI).

Fig. 6
figure 6

Schematic potential energy diagram for the consequent pathways of the A + NO reaction at the CCSD(T)/cc-pVTZ//BH&HLYP/cc-pVTZ level

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After reacting with NO, the peroxide radical (A) forms peroxynitrites IM1 and IM2, which have binding energies of − 26.25 and − 24.59 kcal/mol, respectively. IM1 can be transformed into IM2 and IM3 via TS6 and TS7 transition states with a barrier height of 20.77 and 13.41 kcal/mol, respectively. Barrier height values imply that IM1 and IM2 conversion is easier than IM1 and nitrate ester IM3 conversion. With respect to reactants, the energy of nitrate ester IM3 is -50.43 kcal/mol, and the exothermicity of this reaction is –38.83 kcal/mol, implying this reaction is exothermic. In addition, IM2 nitrite undergoes C–C and O–O bond scission via TS9 to form acetonyl radical, acetic acid, and NO2. The barrier height of this reaction is 47.91 kcal/mol with a − 42.96 kcal/mol ΔH value, and ΔG for this reaction is − 44.50 kcal/mol. However, IM1 generates the same product via TS8 with an energy barrier of 38.62 kcal/mol. Hence, cis-form generates NO2 more easily than trans-form. Therefore, acetone, NO2, and oxygen are the final products of OH-initiated atmospheric oxidation of 4H2P.

4 Atmospheric implications

The atmospheric lifetimes of volatile organic compounds generally depend on the atmosphere's many physical and chemical processes. However, oxidizing species, including OH radicals, Cl atoms, O3 molecules, and NO3 radicals, are primarily responsible for removing volatile organic chemicals from the atmosphere. As OH radicals are considered the atmosphere's detergent, the reaction of 4H2P with OH radicals plays a significant role in determining atmospheric lifetime. So the atmospheric lifetime of 4H2P (τeff) can be calculated by assuming that it is removed from the atmosphere primarily by reaction with OH radicals and is given as:

$$\frac{1}{{\uptau }_{\mathrm{eff}}}=\frac{1}{{\tau }_{OH}}$$
(5)

where τeff ≈\({\tau }_{\mathrm{OH}}={\left( {k}_{\mathrm{OH}} \times \left[\mathrm{OH}\right]\right)}^{-1},\) where \({\tau }_{\mathrm{OH}}\) is the lifetime of 4H2P with OH radicals, \({k}_{\mathrm{OH}}\) is the rate coefficient of 4H2P with OH radicals, equal to 3.70 × 10–11 cm3 molecule−1 s−1, and [OH] concentration = 2.0 × 106 molecules cm−3 [76]. By utilizing all these values, the calculated lifetime for 4H2P is 3.75 h.

5 Conclusions

This work comprises the first mechanistic and chemical kinetic study of the 4H2P + OH reaction using density functional theory and canonical variational transition state theory. We have constructed the potential energy diagram of the titled reaction at the CCSD(T)/cc-pVTZ//BH&HLYP/cc-pVTZ level. All five pathways are exothermic and spontaneous as all have negative \(\left({\Delta H}_{298.15}^{^\circ }\right)\) and \(\left({\Delta G}_{298.15}^{^\circ }\right)\) values. The energy barrier for reaction pathway 3 is minimum among five possible pathways, so it is expected to have faster rate coefficients than other reaction pathways. In the temperature range of 210–350 K, rate coefficients were computed using canonical variational transition state theory (CVT) with small-curvature tunneling (SCT) correction. For all five reaction pathways, it is found that the tunneling effect exists significantly over the whole temperature range. The overall rate coefficient of the 4H2P + OH reaction at 298 K is calculated to be 3.70 × 10–11 cm3 molecule−1 s−1. The calculated atmospheric lifetime of tested molecule 4H2P is very short (3.75 h). Both energetic and kinetic calculations reveal that the attack of OH radical occurs predominantly at the –CH position of the tested 4H2P molecule. Based on the thermodynamic study, it is also proposed that the hydrogen abstraction from the –CH group of the 4H2P molecule (reaction pathway 3) is the most favorable pathway to occur. The branching ratio study indicated that reaction pathway 3 has the maximum contribution to the overall rate coefficient as the branching ratio for reaction pathway 3 (85.30%) is the highest among other reaction pathways. Hence, it is the major reaction pathway. We hope our theoretical study of the titled reaction will provide helpful information for future experimental studies.