A theoretical study on the reaction mechanism and

MOLECULAR PHYSICS,  http://dx.doi.org/./..

RESEARCH ARTICLE

A theoretical study on the reaction mechanism and kinetics of allyl alcohol (CH = CHCH OH) with ozone (O ) in the atmosphere C. Elakiyaa , R. Shankara , S. Vijayakumarb and P. Kolandaivela a

Department of Physics, Bharathiar University, Coimbatore, India; b Department of Medical Physics, Bharathiar University, Coimbatore, India

ABSTRACT

ARTICLE HISTORY

Volatile organic compounds (VOCs) play a major role in the physical and chemical process of the tropospheric chemical reactions in both polluted and remote environments. A theoretical work has been presented on the VOC of allyl alcohol with O3 molecule is investigated using density functional theory methods. The reaction profile is initiated through the cycloaddition of ozone which leads to the formation of primary ozonide with minimal relative energy barrier of 1.31 kcal/mol which decomposes to form carbonyl molecule and carbonyl oxide. Carbonyl oxide, i.e. criegee intermediates reacts with various atmospheric species to produce more hazardous and toxic end products to the environment. The condensed form of Fukui function was calculated to predict reactive sites of the primary and secondary reaction profile. The rate coefficient using CVT with SCT over the temperature range of 258–358K is analysed and also to study the atmospheric effects of allyl alcohol in the atmosphere. The predicted rate coefficient for the favourable reaction pathway of kp1 found to be 1.190 × 10−15 cm3 /molecule/sec and comparable with the experimental result at 298 K. The atmospheric lifetime of allyl alcohol was found to be around 10 hours in addition to that global warming potentials are compared with the CO2.

Received  November  Accepted  January 

1. Introduction Ozonolysis is one of the common oxidation pathways for the unsaturated hydrocarbons in the atmosphere and plays a major role in urban and rural areas [1]. The oxygenated volatile organic compounds (OVOCs) play a main role in the physical and chemical process of the tropospheric chemical reactions in both polluted and remote environment [2,3]. Large scale of OVOCs emitted into the atmosphere and turns hazardous for all living things from a wide number of anthropogenic and biogenic sources. The natural and man-made sources such as forest fire, volcano eruption, oxidation of hydrocarbons, emission

Allyl alcohol; ozone; criegee intermediate; rate constant; atmospheric implications

from biological sources, incomplete combustion, fuels used in the industrial process, motor vehicle exhaust, etc. [4–8] contribute to the emission of OVOC. Hence, the emission of OVOC is one of the major problems in the present world which is harmful to human health [9]. The present work deals with the allyl alcohol (CH2 = CHCH2 OH), which is colourless toxic liquid, flammable and high reactive rather than its alcoholic derivatives. It is widely used in large amount in a variety of drug industries and domestic industries such as in the manufacture of drugs, fabrication of glycerine, organic chemicals, plastics, perfumes and in fire retardants [4–10]. Allyl alcohol

CONTACT R. Shankar [email protected] Supplemental data for this article can be accessed at http://dx.doi.org/./... ©  Informa UK Limited, trading as Taylor & Francis Group

KEYWORDS

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C. ELAKIYA ET AL.

is one of the top 20 VOC emissions and the total emission is 7.99 kilo tones in U.K. in 2010 [2]. Ozone is an inorganic molecule, a powerful oxidising reagent which reacts with other chemical compounds to make more toxic oxides in the troposphere. It is released naturally in the troposphere by plants, soil and because of the human activities such as automobiles, industries and also it is a secondary pollutant, one that is formed by reaction of primary pollutant [11]. Hence, it is very important to study the reaction between the unsaturated alcohol with ozone and its role in the atmospheric chemistry and the impact on the environment. The reaction mechanism of unsaturated alcohol with OH, O3 , NO3 radicals and Cl atoms was studied and reported [12–16]. Voukides et al. [17] and Wang et al. [18] investigated the reaction of ozone with aldehydes which is one of the most irreducible reaction sequences in the atmospheric chemistry. Lots of investigations have been carried out for the mechanism of allyl alcohol with OH radical, in order to explore the kinetic data and properties of allyl alcohol, both experimentally and theoretically [11,19–22]. The reaction of allyl alcohol with OH radicals and ozone has been investigated experimentally by Le Person et al. [11] and at the room temperature, the kinetic data for allyl alcohol with OH radical and ozone was found to be kOH = (5.7 ± 0.2) × 10−12 cm3 molecule−1 s−1 and kO3 = (1.8 ± 0.2)× 10−17 cm3 molecule−1 s−1 , respectively and also confirmed that it has a short atmospheric lifetime of one day. The importance of the computational calculations has been increased during the past decades and it is useful for the reaction system theoretical calculations than experimental studies [23–26] especially for the analysis of short-lived reactive species and highly reactive atmospheric compounds. Therefore, with this importance, the complete reaction mechanism for the decomposition of allyl alcohol by ozone is studied using quantum chemical methods. To the best of our knowledge, based on the available literature, there are no proper theoretical results to know about the thermodynamic properties and reaction kinetics of ozone molecule with allyl alcohol. The reactions of allyl alcohol with O3 proceed through the intermediates and transition states, which is initiated by the cycloaddition of alkene group to the C = C bond forming the primary ozonide (P1). In the atmosphere, this primary ozonide undergoes decomposition, which leads to form a carbonyl molecule and carbonyl oxide known as criegee intermediate (CI1 , CI2 ) as shown in Scheme 1. It is a key reaction mechanism for the above-mentioned reaction scheme [27]. The criegee intermediate (CI), known as carbonyl oxide, is formed and undergoes unimolecular decomposition and most of the CIs in the troposphere are produced by ozonolysis which is one of the common

oxidation paths for the unsaturated hydrocarbons in the atmosphere [1,28,29]. In the secondary reactions, the stabilised CI reacts with various atmospheric species like formic acid, aldehyde, ozone, NOX, SOX , carbonyl oxides, etc. and tends to form more hazardous atmospheric radicals [30–32]. Most of the secondary reactions of criegee intermediates are of zwitterionic character with the biradical character [31,33]. Moreover, in the present work, the rate coefficient and atmospheric implications of the reaction are determined using canonical variational transition state theory (CVT) with small curvature tunnelling corrections (SCT) over the temperature range from 258 to 358 K for the most favourable reactions. Moreover, the experimental study provides only the rate constants that are difficult to predict the thermochemistry [34]. The new Natural Orbital Fukui Function (NOFF) suggests that the orbital can donate or accept electrons when attacked by a nucleophilic or an electrophilic concept [35–37]. When the length of the C–H bond usually increases, it leads to a red shift of the infrared C–H stretching frequency and an increase in the IR intensity of the corresponding band. When the C–H bond length decreases, a blue shift of the C–H stretching frequency is observed. The unscaled factor has been scaled by multiplying the unscaled value with the value of 0.98 according to the level of theory [38].

2. Computational details of the present work Recent literature survey shows that the meta-hybrid density functional method M06-2X has been proved to perform better for the thermodynamics and atmospheric reaction mechanism [39,40]. In the present study, the geometries of the reactants, intermediates, transition states and the products on the ground state potential energy surface of the allyl alcohol + O3 reaction system are performed using meta-hybrid density functional theory (DFT) method M06-2X with the basis set 6-311++G(d,p). For more regress energies, the geometries of the stationary points are also fully re-optimised using coupled cluster level of theory with single–double and non-iterative excitation CCSD(T) [41] calculation on post Hartree–Fock method with the Dunning correction consistent double zeta basis set cc-pVDZ [42,43]. CCSD(T)/cc-pVDZ method was used to calculate the single-point energies on the basis of the M06-2X/6-311++G(d,p) optimised geometry. Harmonic vibrational frequencies have been calculated for all the optimised geometries to determine the nature of the stationary points (minima or first-order saddle points). All the reactants and products possess real frequencies, whereas the transition state possess single imaginary

MOLECULAR PHYSICS

H2C=CH-CH2OH

+

3

O3

Allyl alcohol

TS1

Pathway 1

O O

O

Primary ozonide (P1) CH2OH

Pathway 2 TS2

+

C

CI1

Unimolecular decomposition

H

OH CH2 Glycolaldehyde

H

CO+H2O CO2+H2

(Uni2)

UTS3

HCOOH

(Uni3)

O

C CH2OH

H O

Stabilization (SCI1)

O

Formaldehyde

(Uni1)

UTS2

+

H

Pathway 3 UTS1

H

O

C

HC

Unimolecular decomposition

O

O

O

H

Pathway 5

C

CI2

Pathway 6 UTS4

O2+OHCH=CH2 (Uni4)

O Stabilization (SCI2)

H O

C CH2OH

H

TS9

TS14

TS10

+Gly

+HCOOH

+C2H4

+SO2

+Gly TS7

+HCHO

TS4

+CH2OO

Pathway 7

+HCHO

+HCOOH

Pathway 4

TS11

+SO2

O

TS3

TS12 CH2OH

OH

O

O

CH

H2C

O H2C

O

TS5

O + CH2

CH2 O

(P2)

O

O

O

H2C

CH2

O

(P5)

O

C H2

HO

(I3) TS6

CH2OH

O

TS8

O

O

(P7)

OH O O O O H O HC CH CH2OH O CH2OH

(P8)

(P9)

(P10)

TS13

O C + SO3 CH2OH

(P11)

O O H2C

HCHO+HCOOH

(P3)

HCHO+CO+H2O

(P4)

CH2

HCHO+SO3

O O

(P6)

(P12)

Scheme . The proposed reaction scheme of allyl alcohol + O .

frequency. Frequency calculations were performed to check whether the obtained equilibrium structures are local minima or saddle points. Using intrinsic reaction coordinate calculations, the connections between the transition state structures and their corresponding reactant and product were confirmed at the M06-2X/6311++G(d,p) level of theory [44,45]. The standard enthalpy, entropy and Gibbs free energy values were also calculated at the temperature of 298.15 K and 1 atm of pressure. The theoretical rate constants for the most favourable reactions of allyl alcohol + O3 were calculated using canonical variational transition state theory (CVT) [46,47] from the rate constant at the temperature T is

given by the formula:   T, SCVT (T ) kCVT (T ) = kGT (T, s) = kGT c c c

(1)

where kGT (T, s) is the generalised transition state theory rate constant, given by kGT (T, s) =

  σkB T QGT c (T, s) exp −βV MEP (s) (2) R h φ (T )

Here, kB is the Boltzmann constant, Ò» is the Planck’s constant, QGT c (T, s) is the classical mechanical generalised transition state partition function, QR (T, s) is the

4

C. ELAKIYA ET AL.

reaction partition function per unit volume and V MEP (s) is the generalised transition state theory rate constant on the minimum energy path at s. The rate constant calculations are carried out using GAUSSRATE 2009A, [48] which is an interface between the GAUSSIAN 09 and POLYRATE 2010A programs [49]. All the calculations have been carried out using the GAUSSIAN 09 set of program [50].

2.1. Fukui functional analysis Fukui function is one of the widely used local density functional descriptors to model chemical reactivity and selectivity. The Fukui function of the system defines the more reactive regions in a molecule, the reactivity indices are directly concerned with the selectivity of the molecule towards specific chemical events. It is a non-dimensional one and also has no units. Using Mulliken atomic charges of neutral, cation and anion states of present molecule, Fukui functions( fk+ , fk− , fk0 ), are calculated using the following equations: fk+ = qk (n + 1) − qk (n) for nucleophilic attack (3) fk− = qk (n) − qk (n − 1) for electrophilic attack

(4) 1 fk0 = qk (n + 1) − qk (n − 1) for radical attack (5) 2 where fk− and fk+ describe the ability of an atom to accommodate an extra electron or a loss of an electron, fk0 is considered an indicator for radial reactivity, qk (n + 1), qk (n − 1) and qk (n) are the Mulliken charges of the anionic, cationic and neutral system corresponding to (n + 1), (n − 1) and n electron states, respectively [37,51–54]. Recently, a new form of the condensed Fukui function based on the natural bond orbital (nbo) theory was introduced. The natural atomic bond orbitals may be used to define the condensed forms of the Fukui function:  ∂nnbo N = nN+1 nbo − nnbo ∂N   ∂nnbo = nNnbo − nN−1 = nbo ∂N

+ = fnbo − fnbo



(6) (7)

Both Equations (6) and (7) are only approximate, but + they are believed to be reasonably accurate [35]. fnbo − and fnbo are the nbo to characterise nucleophilic and N−1 electrophilic attack on the reagent. nNnbo , nN+1 nbo and nnbo describe the nbo occupancy corresponding to the N, N + 1 and N − 1 electron systems, where N is the total number of electrons in the molecule.

3. Results and discussion 3.1. Reaction mechanism and path The proposed reaction scheme for the possible primary and secondary degradation pathways of allyl alcohol with ozone molecule (O3 ) is shown in Scheme 1. The optimised electronic structures of the transition state, intermediate involved in the above-mentioned reaction scheme are calculated at M06-2X/6-311++G(d,p) level of theory is shown in Supplementary Figure S8. In the present study, the standard enthalpy, Gibbs free energy and energy barriers calculated at M06-2X/6311++G(d,p) level of theory and for more regress energies, single-point energy have been calculated at CCSD(T)/cc-pVDZ level of theory and the corresponding energies are presented in Tables 1 and 2. Based on the previous literature, the reaction energy barriers (E) calculated at the M06-2X level of theory are comparable with the corresponding results obtained from the CCSD(T) level of theory [55]. In the present investigation, the selected geometrical parameters of the optimised structures of the primary and secondary reaction pathways are calculated at M06-2X/6-311++G(d,p) level of theory and the corresponding results compared with the CCSD (T)/cc-pVDZ level of theory are summarised in Tables 3.1–3.3. The condensed Fukui function values of allyl alcohol with O3 molecules and their corresponding primary and secondary reaction profile values are listed in Supplementary Table S1.1–S1.18. In addition to that, the new form of Fukui function calculations helps to identify the electrophilic and nucleophilic nature of a specific site within a molecule and the corresponding results are presented in the Supplementary Table S2.1 and S2.2. ... Formation of primary ozonide by O initiated primary reaction: (Pathway-) The first step of the degradation pathway of allyl alcohol with O3 reaction profile proceeds with the cycloaddition of oxygen atoms to the carbon bonds (C1 = C2 ) of unsaturated allyl alcohol, which tends to form an intermediate of primary ozonide (1,2,3-trioxolane) P1. A new fivemembered ring (primary ozonide) is formed through the earlier transition state (TS1) with the relative energy barrier of 1.31 kcal/mol at M06-2X/6-311++G(d,p) level of theory and this relative energy barrier is comparable with the CCSD(T) method, respectively. Moreover, the single imaginary frequency also confirms the transition state on the potential energy surface and also the corresponding energy barrier is quite comparable with the previous literature [56–58]. In the reactant, the C1 and C2 carbon atoms are found to be highly nucleophilic and the corresponding condensed Fukui function values are

MOLECULAR PHYSICS

5

Table . Energy barrier E (in kcal/mol) enthalpy H (in kcal/mol) and Gibbs free energy G (in kcal/mol) for the proposed scheme of allyl alcohol with O calculated at M-X/-++G(d,p) level of theory and E (in kcal/mol) calculated at CCSD/cc-pVDZ level of theory. M-X/-++G(d,p) E

H

G

E

. . (.)a − . . (.)a . . . − . . . . . − . . − . . . − . . . − . . . ()c − . . . (.)d − . . . − . . − . . − .

. . − . (−)b (−.)a . . . . − . . − . . . − . . − . . . − . . . − . . . − . . . − . . . . . − . . − .

. . − . (−.)a . . . − . − . . − .

. . − . . − . . . − . . . . . − . . − . . . . . . − . . . − . . . − . . . − . . − . . − .

Stationary Points React+O TS P TS CI +Gly SCI +Formic TS P SCI + HCHO TS(i) I TS P TS P SCI +Gly TS P SCI +SO TS P SCI +CH TS P SCI +CH OO TS P Uni(a) UTS Uni UTS Uni UTS Uni a b c d

CCSD (T)/cc-pVDZ



− . − . . − . . . − . . . − . . . − . . . − . . . . . − . − . − .

Y. Sun et al., . Ref [] Z.J. Buras et al., . Ref [] R. Crehuet et al., . Ref [] Y.T.Su et al., . Ref []

found to be 0.163 and 0.117 and also oxygen atoms O2 and O3 in the ozone molecule are found to be highly electrophilic and the corresponding nucleophile values are found to be 0.359 and 0.148, respectively. Hence, in the reactant the C1 and C2 atoms are found to be highly nucleophilic which leads to form a covalent bond with the highly electrophilic of O2 and O3 oxygen atoms which leads to form a primary ozonide P1 with the considerable energy barriers. Moreover, the bond length of carbon ˚ in the reactant, atoms (C1 –C2 ) is found to be 1.334 A whereas in the formation of the TS1 it gets elongated ˚ and also in the intermediate it is further around 0.190 A ˚ respectively. In weakened and elongated around 0.213 A, the intermediate (P1), the bond length of oxygen atoms of (O2 –O3 ) and (O3 –O4 ) is also found to be weakened and ˚ respectively it gets elongated around 0.181 and 0.171 A, at the above level of theory. The bond angle between oxygen atoms θ(O2 –O3 –O4 ) is found to be 117.162º in the reactant, whereas in the formation of the transition state

(TS1) and intermediate (P1) it is found to be decreased around 3.518º and 15.484º, respectively. Further, the results obtained from NOFF, the values for both the bonding and antibonding orbitals of f + nbo and f − nbo in the reactant BD(O2 –O3 ) and BD* (O2 –O3 ) are found to be electrophilic (ability to donate electrons) quite favour the formation of the primary ozonide (P1). The vibrational frequency of C1 –H2 bond in the reactant is found to be 3084.88 cm−1 and in the intermediate (P1) it is found to be 3004.19 cm−1 therefore, the corresponding decrease in the frequency is red-shifted around 80 cm−1 . The thermodynamic parameters obtained for the formation of intermediate (P1) at M06-2X/6-311++G(d,p) level of theory are found to be exothermic with the value H of −68.33 kcal/mol and Gibbs free energy G is found to be exergonic, i.e. spontaneous reaction has occurred with the value of −56.62 kcal/mol. The enthalpy H and Gibbs free energy G are comparable with the results of the previously available literature

6

C. ELAKIYA ET AL.

Table . Energy barrier E (in kcal/mol) enthalpy H (in kcal/mol) and Gibbs free energy G (in kcal/mol) for the proposed scheme of allyl alcohol with O calculated at M-X/-++G(d,p) level of theory and E (in kcal/mol) calculated at CCSD/cc-pVDZ level of theory. M-X/-++G(d,p) Stationary Points P TS CI +HCHO SCI +HCHO TS P SCI +HCOOH TS P SCI +Gly TS P SCI +SO TS P Uni(b) UTS Uni a

CCSD/cc-pVDZ

E

H

G

E

− . . (.)a − . . . − . . . − . . . − . . . − . . . .

− . . − . . . − . . . − . . . − . . . − . . . − .

− . . − . . . − . . . − . . . − . . − . − . . . − .

− . . − . . . − . . . − . . . − . . . − . . . .

Y. Sun et al., . Ref []

[56–58]. This analysis suggests that the formation of ozonide in the primary reaction (P1) is thermodynamically most favourable reaction path and the energy barriers profile of the primary reaction pathway is shown in Figure 1. ... Formation of criegee intermediate (CI ): (Pathway-) The primary ozonide (P1) decomposes to form two possible carbonyl molecule (glycolaldehyde and

Figure . Relative energy profile corresponding to the reactions of allyl alcohol with O calculated at M-X/-++G(d,p) level of theory.

formaldehyde) and criegee intermediate (CI), i.e. criegee intermediate (CI1 ) + Gly and criegee intermediate (CI2 ) + HCHO. For the first case of decomposition reaction, the homolytic cleavage has occurred between O3 –O4 and C1 –C2 bonds which leads to form a glycolaldehyde and biradical intermediate (CH2 OO) with the considerable energy barriers. The biradical intermediate is reached through the transition state TS2 with the relative energy of 19.17 kcal/mol at the M06-2X/6-311++G(d,p) level of theory and is quite comparable with the decomposition reaction of ethyl acrylate with ozone molecule of 13.73 kcal/mol at CCSD(T)/6-31G(d)+CF level of theory [59]. The earlier TS2 conforms a true transition state with a single imaginary frequency of −483.05 cm−1 at

Table .. The selected optimized geometrical parameters of bond length r (A˚ ), bond angle θ ( ) calculated using M-X/++G(d,p) and CCSD/cc-pVDZ level of theories. M-X/-++G(d,p)

CCSD/cc-pVDZ

Geometrical Parameters

R+O

TS

P

R+O

TS

P

r(C -C ) r(O -O ) r(O -O ) θ (O -O -O )

. . . . P1 . . . . Uni(a) . Uni(a) . Uni(a) . . Uni(b) . .

. . . . TS2 . . . . UTS1 . UTS2 . UTS3 . . UTS4 . .

. . . . CI1 +Gly . . . . Uni1 . Uni2 . Uni3 . . Uni4 . .

. . . . P1 . . . . Uni(a) . Uni(a) . Uni(a) . . Uni(b) . .

. . . . TS2 . . . . UTS1 . UTS2 . UTS3 . . UTS4 . .

. . . . CI1 +Gly . . . . Uni1 . Uni2 . Uni3 . . Uni4 . .

r(C -C ) r(O -O ) r(O -O ) θ (C -O -O ) r(C -O ) r(H -H ) r(O -H ) r(C -O ) r(O -O ) r(C -O )

MOLECULAR PHYSICS

7

Table .. The selected optimized geometrical parameters of bond length r (A˚ ), bond angle θ ( ) calculated using M-X/++G(d,p) and CCSD/cc-pVDZ level of theories. M-X/-++G(d,p)

CCSD/cc-pVDZ

Geometrical Parameters

SCI +HCOOH

TS

P

SCI +HCOOH

TS

P

(O -H ) (C -O ) (C = O )

. . . I3 . . . I3 . . . SCI1 +Gly . . . SCI1 +SO2 . . . . SCI1 +C2H4 . . . . . SCI1 +CH2 OO . .

. . . TS5 . . . TS6 . . . TS7 . . . TS8 . . . . TS9 . (.)a . (.)a . . . TS14 . .

. . . P3 . . . P4 . . . P5 . . . P6 . . . . P7 . . . . . P12 .(.)b .(.)b

. . . I3 . . . I3 . . . SCI1 +Gly . . . SCI1 +SO2 . . . . SCI1 +C2H4 . . . . . SCI1 +CH2 OO . .

. . . TS5 . . . TS6 . . . TS7 . . . TS8 . . . . TS9 . . . . . TS14 . .

. . . P3 . . . P4 . . . P5 . . . P6 . . . . P7 . . . . . P12 . .

r(O -O ) r(C -O ) r(H -O ) C -O C -O O -O r(C -O ) r(C -O ) θ (H -C -H ) r(O -O ) r(S = O ) r(C -O ) θ (O -C -H ) r(C -O ) r(C -C ) r(O -O ) r(C -C ) θ (O -O -C ) r(C -O ) r(C -O ) a b

R. Crehuet et al.,  Ref [] Y.T. Su et al., . Ref []

the above level of theory. From the primary ozonide (P1), the condensed Fukui function values of carbon and oxygen atoms (C1 , C2 , O3 and O4 ) are found to be highly nucleophilic and the corresponding values are found to be 0.040, 1.102, 0.186 and 0.212, respectively as shown in Supplementary Table S1.2. Due to that, homolytic cleavage has occurred in-between carbon atoms C1 –C2 and also oxygen atoms O3 –O4 which tend to form CI1 + Gly. Moreover, the bond length between O3 –O4 atoms in the CI1 + Gly is also found to be weakened and gets ˚ in TS2 and also in elongated around 0.64 and 3.462 A the intermediate (CI1 +Gly), respectively. The bond angle between θ(C1 –O2 –O3 ) atoms is found to be 102.644◦ in the P1, whereas in the transition state and also in the intermediate (CI1 + Gly) it gets increased around 8.949◦ and 16.09◦ , respectively at the above-mentioned level of theory. The bonding and antibonding orbitals of NOFF in the P1 of (C1 –O3 ) and (C2 –O4 ) bonds are electrophilic which have the ability to donate electrons and the corresponding values are summarised in Supplementary Table S2.1. The vibrational frequencies of C2 –H3 and C3 –H5 bonds in the primary ozonide P1 are found to be 3106.36 and 2978.08 cm−1 and also their corresponding vibrational frequencies for the CI1

+ Gly are found to be 2978.08 and 2998.87 cm−1 which are close to the alkanes. The intermediate CI1 + Gly is found to be endothermically less stable with the reaction enthalpy of 1.88 kcal/mol and stimulated reaction of endoergic with the free energy of 6.79 kcal/mol at M062X/6-311++G(d,p) level of theory. The positive value of the reaction enthalpy is found to be endothermic which is highly reactive and also less stable; it quite favours the homolytic cleavage of primary ozonide reaction. The low structural stability of the peroxy radicals CI1 is found to be highly reactive, which can easily dissociate as the secondary pollutant and recombine with atmospheric pollutants and to produce environment hazardous compounds such as carbon monoxide, carbon dioxide, methanol, etc. as the resultant product with considerable energy barriers. ... Unimolecular decomposition reaction: (Pathway-) In the reaction step, the simplest biradical intermediate (CI1 ) undergoes unimolecular dissociation to form CO + H2 O, CO2 + 2H, HCOOH which are more hazardous to the environment as the resultant product (Uni1, Uni2,Uni3) at M06-2X/6-311++G(d,p) level of

8

C. ELAKIYA ET AL.

Table .. The selected optimized geometrical parameters of bond length r (A˚ ), bond angle θ ( ) calculated using M-X/++G(d,p) and CCSD/cc-pVDZ level of theories. M-X/-++G(d,p) Geometrical Parameters r(O -O ) r(C = O ) r(C -C ) θ (C -O -O ) r(C -O ) r(C -O ) r(C -O ) r(C -O ) R(C -O ) r(C -O ) r(C -O ) r(C -C ) r(C -O ) r(S = O ) r(O -O ) C

CCSD/cc-pVDZ

P

TS

CI +HCHO

P

TS

CI +HCHO

. . . . SCI2 +HCHO . . . SCI2 +HCOOH . . . SCI2 +Gly . . . SCI2 +SO2 . .

. . . . TS10 . . (.)c . TS11 . . . TS12 . . . TS13 . .

. . . . P8 . . (.)c . P9 . . . P10 . . . P11 . .

. . . . SCI2 +HCHO . . . SCI2 +HCOOH . . . SCI2 +Gly . . . SCI2 +SO2 . .

. . . . TS10 . . . TS11 . . . TS12 . . . TS13 . .

. . . . P8 . . . P9 . . . P10 . . . P11 . .

W. Wei et al.,  Ref []

theory. The biradical intermediate (CI1 ) dissociate to form CO + H2 O through UTS1 with the energy barrier of 7.78 kcal/mol at M06-2X/6-311++G(d,p) level of theory. The formation of the product (Uni1) is found to be endoergic with the enthalpy value of 128.66 kcal/mol and endoergic with the stimulated reaction value of 91.85 kcal/mol at the above-mentioned level of theory. In the second decomposition pathway, the peroxy radical CH2 OO is transformed into the CO2 + 2H through UTS2 with the energy barrier of 7.84 kcal/mol. Further, in the CI1 , the homolytic cleavage has been occurred in bonds between C1 –H1 , C1 –H2 and O1 –O2 atoms, due to the cleavage a new covalent bond is formed in between ˚ and elimiH1 –H2 atoms with the bond length of 0.741 A nates as H2 molecule along with the carbon dioxide as the final product (Uni2). This reaction is highly exothermic by −124.24 kcal/mol and highly spontaneous reaction with exergonic of −133.81 kcal/mol, respectively. During the third decomposition path, the HCOOH (Uni3) is formed through the UTS3 of relative energy barrier of 22.46 kcal/mol at M06-2X/6-311++G(d,p) level of theory. This reaction is found to be exothermic with the value of −97.70 kcal/mol and the spontaneous reaction with the exergonic value of −82.91 kcal/mol, respectively. Comparing the energy barriers of these three unimolecular dissociation processes, it is confirmed that the formation of CO + H2 O is found to be minimal barrier height of 7.78 kcal/mol which is thermodynamically favourable for the unimolecular dissociation. The potential energy surface plot for the above decomposition pathways is shown in Figure 2(a,b).

Figure . Relative energy profile corresponding to the reactions of unimolecular decomposition with CI and CI calculated at MX/-++G(d,p) level of theory.

... Secondary reactions of CI with atmospheric radicals: (Pathway-) In the secondary reaction step, the stabilised criegee intermediate (SCI1 ) undergoes addition and recombination with atmospheric species such as formic acid, formaldehyde, glycolaldehyde, sulphur dioxide, ethylene and biradical (CH2 OO) to form HPMF (P2), formaldehyde + formic acid (P3), formaldehyde + carbon monoxide + water (P4), [1,2,4]trioxolane (P5), HCHO + sulphur trioxide (P6), 1,2 dioxolane (P7) and [1,2,4,5]tetroxane (P12) as end products of the secondary reaction profile.

MOLECULAR PHYSICS

Path 4.1: In the secondary reaction step of 4.1, the carbonyl oxide (CI1 ) reacts with HCOOH to form hydroperoxy methyl formate (HPMF) P2 through the late transition state (TS4) with the relative energy of 9.35 kcal/mol is calculated at M06-2X/6-311++G(d,p) level of theory which is in agreement with the value of 10.09 kcal/mol at CCSD(T) method. Due to the additional reaction, the condensed Fukui function values of O2 and H4 atoms are found to be highly nucleophilic and the values are found to be 0.024 and 0.116 and also C2 and O4 atoms are found to be highly electrophilic with the values of 0.508 and 0.641, respectively at above-mentioned level of theory. The O2 –H4 bond in the intermediate (CI1 ) gets cleaved and H4 atom tends to bind with the O4 atom ˚ and the corresponding bond length is found to be 0.965 A. The vibrational frequency for C2 –H2 in the reactant (SCI1 + Formic) is 3048.60 cm−1 and their corresponding vibrational frequency of the product (P2) is 3042.07 cm−1 has resulted in red shift and the red-shifted value is found to be 7 cm−1 . This result quite favours the elongation ˚ The vibrational frequency of C–H bond around 0.07 A. of H1 –C1 is red-shifted by 34 cm−1 . From the obtained results, this reaction path is exothermic and exergonic of spontaneous reaction in nature with the values of H = −44.239 kcal/mol and G = −22.963 kcal/mol, respectively at the above level of theory. Path 4.2: In the second path, stabilised CI1 reacts with formaldehyde to form intermediate I3 which leads to form secondary reaction profile such as two resultant products P3 (HCHO + HCOOH) and P4 (HCHO + CO + H2 O) are formed. These products P3 and P4 are identified through the earlier TS5 and TS6 with the relative energy barrier of 62.49 and 3.32 kcal/mol at M06-2X/6311++G(d,p) level of theory, both barriers are in good agreement with the CCSD(T) method. Due to the existence of high relative energy barrier, the product P3 is found to be not feasible and not considered in the present work. The product P4 (HCHO + CO + H2 O) is formed with considerable energy barriers which are hazardous to the troposphere than the parent compound (allyl alcohol). The bond length of O1 –O2 atoms gets elongated around 1.772 which tends to form the end cyclic product P4. The vibrational frequency of C1 –H1 for the reactant is found to be 3026.84 cm−1 and their corresponding vibrational frequency of the product is found to be 2936.21 cm−1 , the product is red-shifted around 90 cm−1 . This result quite favours the elongation of C–H bond around ˚ in the product P4. Both the reactions are found 0.007 A to be highly exothermic and the value of H is found to be −67.83 and −63.81 kcal/mol and highly spontaneous with exergonic value of G is found to be −121.41 and −144.33 kcal/mol at M06-2X/6-311++G(d,p) level of theory, respectively.

9

Path 4.3: The intermediate CI1 reacts with glycolaldehyde to form the product P5 with the elimination of the methyl group CH2 as the resultant product. The relative energy barrier for this reaction path is obtained through the earlier TS7 with the value of 16.75 kcal/mol. In the reactant (CI1 + Gly), the condensed Fukui function values of carbon atoms C1 and C2 are found to be highly electrophilic with the values of 0.326 and 0.259 and also oxygen atoms O3 and O4 are found to be highly nucleophilic with the values of 0.578 and 0.040, respectively at M062X/6-311++G(d,p) levels of theory. Hence, the covalent bond is formed C2 –O3 and C1 –O4 atoms through the oxidation process of the reaction profile and the bond length ˚ which tends to staare found to be 1.392 and 1.419 A bilise the product P5. The vibrational frequency of reactant for C2 –H3 is found to be 2927.70 cm−1 and their corresponding vibrational frequency of product is found to be 3153.11 cm−1 resulting in blue-shifted by −225 cm−1 at the above level of theory. The product P5 is found to be exothermic and exergonic of spontaneous reaction and the values are found to be −3.38 and −6.37 kcal/mol at M06-2X/6-311++G(d,p) level of theory. Path 4.4: In the path 4.4, the criegee intermediate reacts with SO2 through the oxidation process and tends to form stable secondary product P6 (HCHO + sulphur trioxide), which contributes atmospheric sulphuric acid production [32,58]. The product (P6) HCHO + SO3 is formed through the earlier TS8 with the relative energy of 19.07 kcal/mol at M06-2X/6-311++G(d,p) level of theory. The condensed Fukui function values of oxygen atoms O1 and O2 are found to be highly nucleophilic and the corresponding values are found to be 0.055 and 0.399; hence, the homolytic cleavage has been occurred between O1 – O2 atoms. Moreover, S1 atom in sulphur dioxide is highly electrophilic and the Fukui function value is found to be 0.068 which tends to bind with the electrophilic oxygen atom of O2 atom to form a S1 = O2 bond at the abovementioned level of theory. With the aid of that, a new double bond is formed between S1 = O2 atoms and the ˚ and corresponding bond length is found to be 1.086 A quite favours the formation of the product P6. The C1 –O1 bond length in reactant is found to be contracted around ˚ and accompanied by the blue shift of the frequen0.027 A cies of −157 cm−1 , respectively at the above level of theory. The C1 –H2 is red-shifted and leads to decrease in the vibrational frequencies that lead the bond length elon˚ The P6 reaction profile is found to gated around 0.002 A. be exothermic with the value of H = −66.07 kcal/mol and spontaneous of exergonic reaction with the value of G = −59.29 kcal/mol, respectively. Path 4.5: The next step in the reaction path is the formation of 1,2 dioxolane (P7) which are obtained through the earlier transition state of TS9 with the minimal

10

C. ELAKIYA ET AL.

relative energy of 1.88 kcal/mol at M06-2X/6311++G(d,p) level of theory and agree with the previous theoretical value of 2.0 kcal/mol [60]. The condensed Fukui function values of carbon atoms C1 and C2 are found to be highly nucleophilic and the values are found to be 0.039 and 0.474 and also O1 and C3 atoms are found to be having high nucleophile values of 0.597 and 0.026, respectively at the above-mentioned level of theory. Hence, the electron donating character of O1 and C3 atoms leads to form a covalent bond with the electron accepting carbon atoms of C1 and C2 tends to form the end product P7. The bond lengths of C2 –C3 atoms ˚ are quite agree with the previous found to be 2.379 A available literature [61]. The vibrational frequencies of H1 –C1 and C1 –C3 bonds are found to be 3167.50 and 1671.42 cm−1 , respectively and their corresponding stretching frequencies for the product P7 are found to be 3083.78 and 1490.68 cm−1 which are red-shifted. This red shift quite favours the bond length elongation ˚ respectively of (C–C) atoms around 0.010 and 0.210 A, at the M06-2X level of theory. This reaction is highly exothermic by −63.316 kcal/mol and highly spontaneous reaction with exergonic of −106.08 kcal/mol at M06-2X/6-311++G(d,p) level of theory, respectively. Path 4.6: In this step of the self-reaction profile, the biradical intermediate CH2 OO reacts with biradical CH2 OO to form the stable product P12 ([1,2,4,5]tetroxane) through the dimerisation reaction. The relative energy for the formation of the product is 7.59 kcal/mol through the earlier transition state TS14 at the M06-2X/6311++G(d,p) level of theory are comparable with the previous dimerisation reaction [27] . The condensed Fukui function values of carbon atoms C1 and C2 are found to be highly electrophilic and also oxygen atoms O2 and O4 are highly nucleophilic to form the resultant product P12. Moreover, the bond lengths of C1 –O2 and C2 –O4 atoms ˚ during the formation of are found to be 1.413 and 1.413 A product P12 quite agree with the previous theoretical literature of carboxyl bond of dimerisation reaction profile [27]. The thermodynamic properties of the reaction are found to be highly exothermic and exergonic and the values are found to be −83.58 and −111.99 kcal/mol, respectively. Therefore, the highly negative reaction energy values are found to be spontaneous in nature. Moreover, the stretching frequency of C2 –O1 atoms is red-shifted and the value is found to be 4 cm−1 . Hence, the bond ˚ respeclength is found to be elongated around 0.008 A, tively. Figure (3a,b) shows the corresponding energy profile for the above-mentioned reaction profile of pathway 4. Among the reaction path 4.1–4.6, the 4.5 reaction path is thermodynamically favourable for the formation of the P7 (1,2 dioxolane) because of the minimal energy barrier

Figure . (a,b) Relative energy profile corresponding to the reactions of SCI reacted with various species calculated at M-X/++G(d,p) level of theory.

at M06-2X/6-311++G(d,p) level of theory and in agreement with the previously available literature. The huge negative value of exothermic reaction confirms that the product P7 is found to be more stabilised end product of the reaction profile and also confirms less favour for reverse reaction profile. ... Formation of criegee intermediate (CI ): (Pathway-) In this reaction pathway, CI2 + HCOH is obtained through the earlier transition state (TS3) with the single imaginary frequency of −510.24 cm−1 and the corresponding relative energy is 27.79 kcal/mol at M06-2X/6311++G(d,p) level of theory and this is quite comparable with that of the previous literature of 15.37 kcal/mol [59]. From the primary ozonide P1, the obtained condensed Fukui function values of carbon atoms C1 and C2 and also oxygen atoms O2 and O3 are highly nucleophilic and the corresponding electrophile values are found to be

MOLECULAR PHYSICS

0.040, 1.102, 0.164 and 0.186, respectively at the abovementioned level of theory. Hence, the homolytic cleavage has occurred between C1 –C2 and O2 –O3 atoms to form CI2 + HCHO. During the dissociation reaction, bond length between O2 –O3 atoms gets elongated around 1.484 ˚ to form TS3 and CI2 + HCHO. The carboxyl and 2.047 A group in formaldehyde possess the double bond charac˚ Moreover, the bond ter with the bond length of 1.204 A. angle between θ(C2 –O4 –O3 ) atoms in the intermediate P1 is found to be 102.300◦ , whereas in the formation of the transition state and also in the CI2 + HCHO, the bond angle is found to be weakened and gets increased around 8.045◦ and 14.313◦ , respectively. Due to the dissociation process, the resultant bonding and antibonding orbitals of NOFF, BD(O3 –O4 ) and BD*(O3 –O4 ) in SCI2 + HCHO are electrophilic. The vibrational frequency of C3 –H5 bond in the primary ozonide is found to be 3057.72 cm−1 and their corresponding vibrational frequency of the CI2 + HCHO is found to be 3074.56 cm−1 . This result suggested that the bond is blue shift with the value of −17 cm−1 ; this result quite favours the contraction of C–H ˚ From the obtained thermodynamic bond around 0.003 A. properties, the reaction is found to be exothermic with the value of −6.96 kcal/mol and the spontaneous reaction with the exergonic value of −48.02 kcal/mol, respectively. The energy profile corresponding to the reaction is shown in Figure 1. ... Unimolecular decomposition reaction: (Pathway-) The biradical intermediate (CI2 ) undergoes unimolecular decomposition to form the product (Uni4) O2 + OH– CH = CH2 through TS (UTS4) with the energy barrier of 40.16 kcal/mol at M06-2X/6-311++G(d,p) level of theory. The product (Uni4) is obtained through the breaking of C2 –O2 bond and shares its charges and tends to form oxygen molecule as a by-product and also quite favours the formation of Uni4. Further, the bond length of O2 –O3 atoms in the reactant is found to be ˚ whereas the bond length gets contracted around 1.195 A ˚ ˚ and C2 –O2 atoms get elongated around 1.531 A 0.170 A to form the stable product (Uni4). This reaction profile is formed exothermically with the reaction enthalpy of −24.47 kcal/mol and exergonic with the spontaneous reaction of −1.99 kcal/mol at M06-2X/6-311++G(d,p) level of theory. The condensed form of Fukui function for the formation of Uni4 is listed in Supplementary Table S1.18. ... Secondary reactions SCI with atmospheric radicals: (Pathway-) As shown in Scheme 1, there are four possible reaction processes of secondary reactions with the stabilised

11

criegee intermediate (SCI2 ). The products P8, P9, P10 and P11 are formed when SCI2 reacts with secondary pollutant in the troposphere such as formaldehyde, formic acid, glycolaldehyde and sulphur dioxide to form a resultant product which are harmful to the surrounding. Path 7.1: The criegee intermediate (CI2 ) easily reacts with HCHO to form [1,2,4]trioxolan-3-yl-methonal (P8) through the earlier TS10 with the relative energy of 2.94 kcal/mol. In the reactant, the condensed Fukui function values of carbon atoms C1 and C2 are found to be highly electrophilic and the corresponding nucleophile values are found to be 0.005 and 0.273 and the oxygen atoms O1 and O2 are found to be highly nucleophilic and the corresponding electrophile values are found to be 0.535 and 0.087, respectively at the above-mentioned level of theory. Hence, due to this charge sharing a covalent bond is formed in-between C1 –O1 and C2 –O2 atoms ˚ and favours with the bond length of 1.407 and 1.410 A the formation of the resultant product P8. The vibrational frequency of C2 –C3 bonds in the reactant is found to be 1634.38 cm−1 and their corresponding frequency of the product (P8) is found to be 1409.42 cm−1 and the product is red-shifted by 225 cm−1 and the bond length elon˚ in between (C–C) atoms, respecgation around 0.031 A tively. The thermodynamic parameters obtained for this reaction are exothermic and spontaneous in nature with the obtained values of H = − 44.80 kcal/mol and G = −46.62 kcal/mol, respectively at the abovementioned level of theory. Path 7.2: In this path, the intermediate (CI2 ) reacts with formic acid (HCOOH) to form 2-hydroperoxy-2methoxy-ethanol through the earlier TS11 with the relative energy of 4.45 kcal/mol. From the obtained values of condensed Fukui function in the SCI2 + HCOOH, the C2 atom is found to be highly nucleophilic which leads to form a covalent bond with the electrophilic atom of O2 to form C2 –O2 as product P9. Further, the bond length of ˚ at the formation of the prodC2 –O2 is found to be 1.432 A uct P9, respectively. The stretching frequency of C1 –O1 is red-shifted and the red-shifted value is found to be 13 cm−1 . This frequency quite favours the elongation of C–O ˚ The formation of this path occurs bond around 0.005 A. in an exothermic and exergonic reaction with the values of H = −34.95 kcal/mol and G = −38.95 kcal/mol, respectively. Path 7.3: The next path in the secondary reaction profile is that the carbonyl oxide (CI2 ) reacts with glycolaldehyde (CH2 OHCH = O) through the transition state TS12 to form 5-Hydroxymethyl-[1,2,4]trioxolan-3yl-methanol as a resultant product (P10) with the relative energy of 7.78 kcal/mol at M06-2X/6-311++G (d,p) level of theory. The condensed Fukui function values of carbon atoms (C2 and C3 ) are found to be highly

12

C. ELAKIYA ET AL.

electrophilic and the corresponding nucleophile values are found to be 0.341 and 0.013 which leads to form a covalent bond with the highly nucleophilic atom of O3 and O5 with the corresponding values of 0.045 and 0.545 to form the product P10. Moreover, the bond length for the formation of bonds C3 –O5 and C2 –O3 are found to be ˚ respectively at the abovecontracted to 1.301 and 1.412 A, mentioned level of theory. As reported in Supplementary Table S5, the C1 –H1 , C2 –H3 and C3 –H4 bonds are found to increase in the frequency and the bond lengths are contracted which suggests that the bonds are blue shift and the blue-shifted values are found to be −11, −9 and −101 cm−1 , respectively at the above level of theory. The computed enthalpy and Gibbs free energy of the reaction reported in Table 2 show that the reaction is exothermic and spontaneous reaction with exergonic in nature. Path 7.4: The final step of the secondary reaction profile, the by-product P11 is formed through the electrophilic addition of CI2 by secondary pollution of SO2 in the atmosphere through the earlier transition state TS13 with the relative energy of 6.08 kcal/mol at M06-2X/6311++G (d,p) level of theory. The condensed Fukui function of the peroxy radicals of oxygen atoms O2 and O3 are highly nucleophilic with the values of 0.526 and 0.286 which cleaves and O3 atom tends to bind with the highly electrophilic atom of sulphur dioxide S1 with the value of 0.093, respectively. The bond length of S1 = O3 is found to ˚ and quite favours the formation of the prodbe 1.426 A uct P11 at M06-2X/6-311++G (d,p) level of theory. The vibrational frequencies of C2 –O2 and C1 –C2 bonds are found to be 1623.57 and 1398.74 cm−1 and their corresponding vibrational frequencies for the product are found to be 1774.95 and 1416.27 cm−1 which are blueshifted. The formation of the product P11 is found to be exothermic with the enthalpy value of −56.03 kcal/mol and exergonic with the spontaneous reaction value of −70.99 kcal/mol at the above-mentioned level of theory. The energy profile for the corresponding pathway 7 is shown in Figure 4(a,b). Compared to the other secondary pollution reacted with the CI2 in the reaction steps of pathway 7, the minimal energy barrier is obtained with the value of 2.94 kcal/mol during the formation of [1,2,4]trioxolan3-yl-methonal (P8). The spin density is the measure of the probability electron at a specific position which depends on the exchange–correlation functional. Spin density profiles were calculated from the single-point energy at the optimised structure of SCI1 and SCI2 intermediates at M06-2X level of theory. In the spin density calculation both the positive and negative values can be found, where the electron density associated with a spin aligned parallel to the applied field is taken as positive, and

Figure . (a,b) Relative energy profile corresponding to the reactions of SCI reacted with various species calculated at M-X/++G(d,p) level of theory.

that corresponding to antiparallel spin as negative [62,63]. In the present study, the criegee intermediate (SCI1 ) and the spin density of C1 and O3 radical atoms in the carboxyl group are found to be 0.981 and 0.951, respectively. Moreover, the spin density at the C1 position of carbon atom is found to be higher than the O3 atom of SCI1 intermediate. In the case of SCI2 , the distributions of spin density for C2 and O3 atoms are found to be 0.300 and 0.488, respectively. But the distribution of spin density of SCI2 intermediate is found to be maximum for O3 atom rather than the C2 in the carboxyl group. The SCI1 intermediate has the maximum spin density which is highly reactive than the SCI2 intermediate and the corresponding spin density values are tabulated in S7. From the obtained results, it is observed that the carboxyl carbon atom acts significantly to stabilise the intermediate in the above-mentioned reaction profile. Moreover, in both intermediates (SCI1 and SCI2 ), the spin density and branching ratio calculations quite favour the reaction profile. Comparatively, SCI1 is favourable to the reaction profile.

MOLECULAR PHYSICS

13

Table . Rate constant (cm /molecule/sec) for the most favourable reactions of the formation of primary ozonide (kP ), formation of HCHO + CO +H CO (kP ) and formation of , dioxolane (kP ) formation of -hydroperoxy--methoxyethanol (kP ). Temperature (K)       a b c

kP × −

kP × −

kP × −

kP × −

. . . (. × − )a (. × − )b . . .

. . .

. . . (. × − )c

. . .

. . .

. . .

. . .

Ref. []. Ref. []. Ref. [].

3.2. Kinetic analysis Rate constant is the key parameter in the kinetic studies of reaction that can be calculated using canonical variational transition state theory (CVT) with small curvature tunnelling corrections (SCT) over the temperature range from 258 to 358 K at 1 atm pressure with ZPE-corrected energy, gradients and hessians calculated at M06-2X/6-311++G (d,p) level of theory. The calculated rate coefficient for the favourable paths (the paths with the minimum energies) for the primary and secondary reactions (P1, P4, P7 and P9) represented as kP1, kP4, kP7 and kP9 are listed in Table 4. The tunnelling factor for the other reactions of rate constant is kinetically inaccessible due to the broad energy barrier and is listed in Supplementary Tables S3.1–S3.3. The rate constantfor the formation of primary ozonide kP1 calculated at 258 K, is found to be 0.964 × 10−15 cm3 /molecule/sec whereas at the higher temperature (298 K) the rate constant is found to be 1.190 × 10−15 cm3 /molecule/sec at the above level of theory. From the obtained results, it is suggested that at the higher temperature, the reaction of allyl alcohol with O3 molecule occurs rapidly and hence the reaction found to occur favourably in the lower layer of the troposphere. The calculated initial reaction rate constant is comparable to the experimental value determined for allyl alcohol with O3 ((1.8 ± 0.2)×10−17 cm3 /molecule/sec) by Le Person et al. [11]. In addition, Wang et al. [64] calculated the rate constant by DFT method indicates that the theoretical rate constant value is two order of magnitude higher than the experimental value. From Table 4, it is observed that the rate constant at 298 K for the formation of secondary pollutant HCHO + CO + HCO (kP4 ) is found to be 1.237 ×10−13 cm3 /molecule/sec. The calculated rate coefficient for the formation of kP7 (1,2dioxolane) is found to be 0.194×10−13 cm3 /molecule/sec at 298 K and the experimental work of Buras et al.

[61] suggested that the rate coefficient for the formation of 1,2-dioxolane was 3.8 × 10−14 cm3 /molecule/sec, nearly an order of smaller magnitude. Figure 5 shows the Arrhenius plot for the variation of the In KT versus the inverse of the temperature. From the observed results, the temperature changes at 20 K increments from 258 to 358 K including 298 K shows that the positive temperature has been occurred and found to be increased along with the temperature increases for the rate constant of kP1, kP4, kP7 and kP9 and the calculated values are listed in Table 4. Percentage contribution for the primary reaction paths (kP1, kCI1 + Gly and kCI2 + HCHO ) to the total rate coefficient for the reaction of ozone with CH2 = CHCH2 OH over the temperature range of 258−358 K are shown in Figure S9. Using the overall rate constant, the branching ratio analysis for the reaction channel of primary reaction kP1 has been carried out in the temperature range 258– 358 K shows that the contribution is 94% at 298 K to the atmospheric degradation of the unsaturated alcohol with ozone molecule as tabulated in Supplementary Table S4.1. Moreover, from the primary ozonide, the branching ratio for the formation of glycolaldehyde and formaldehyde are found to be 59% and 36%, respectively at 298 K which is in agreement with the experimental results [11]. The percentage contribution for the path kp9 is 0.98 at 298 K in the pathway 7 and other negligible branching ratios are tabulated in Supplementary Table S4.2. 3.3. Atmospheric effects Kinetic data are used to access the atmospheric lifetime and fate of unsaturated alcohols in the troposphere. The tropospheric lifetime (τ ) of allyl alcohol can be estimated by assuming that its removal from the troposphere [65] occurs through the reaction with O3 molecule. The rate constant data obtained contribute to a better definition of its tropospheric lifetime [66]. The pollutants in the atmosphere from both natural and anthropogenic

14

C. ELAKIYA ET AL.

Figure . Arrhenius plot for the rate coefficient data obtained for the formation of primary ozonide kP (a), formation of secondary reactions kP , kP and kP (b–d) over the temperature range – K calculated at M-X/-++G(d,p) level of theory.

sources can create some environmental harms such as photochemical smog, acid rain and degradation of the ozone layer [67]. Hence, it is important to know the time that such species remain in the atmosphere and their degradation mechanisms in the tropospheric lifetime of allyl alcohol with O3 molecule were calculated using the formula: τO3

1 = kO3 [O3 ]

where kO3 is the rate coefficient of the reaction of allyl alcohol with O3 molecule at 298K as 1.190 × 10−15 cm3 /molecule/sec. The lifetime of allyl alcohol at M062X/6-311++G(d,p) level of theory is estimated to be τO3 ≈ 10 hours, respectively at 298 K using the average atmospheric concentration of ozone 7 × 1011 molecules/cm3 . This short lifetime indicates that allyl alcohol will be oxidised near its emission sources [1,11]. 3.4. Global warming potentials Global warming potentials (GWPs) are the relative measure of how much heat a greenhouse gas traps in the

atmosphere. It is a measure of the time-integrated radiative forcing of the climatic system due to a pulse release of a particular gas, relative to carbon dioxide (usually taken as a reference molecule) [32,68]. Here, GWPs for allyl alcohol are estimated (relative to CO2 ) using the expression given by Balaganesh et al. [69] as GWP =

a ∫t0 e−t/τ dt AGWPCO2

where ‘a’ is the total instantaneous infrared radiative frequency (Wm−2 ppbv−1 ) and AGWP is the absolute GWP for CO2 for different horizons of time (t), with the calculated lifetime (τ ). The calculated GWPs for different horizons of time obtained by M06-2X/6-311++G (d,p) level of theory are reported in Table 5. Allyl alcohol is an important contributor to the greenhouse effect and the estimated GWP is found to be 28.21 for 10 years. This means allyl alcohol is approximately 28.21 times more heat-absorptive than carbon dioxide per unit of weight. The GWPs for the allyl alcohol in comparison with the carbon dioxide versus different horizons of time are shown in Figure 6. From the table, it is observed that

MOLECULAR PHYSICS

Table . Global warming potential (GWP) of allyl alcohol computed at different horizons of time using M-X/-++G(d,p) level of theory. Horizon of time (years)      a

GWP of allyl alcohol

r

. . (.)a . . .

Ref. [].

r

r

r

15

The potential energy diagram shows that the initial primary ozonide reaction is thermodynamically favourable with a barrier height of 1.31 kcal/mol at M06-2X/6-311++G(d,p) level of theory. The rate constant for the primary pollutant of ozonide formation kp1 is 1.190 × 10−15 cm3 /molecule/sec at 298 K and comparable with the experimental value of kO3 = (1.8 ± 0.2)× 10−17 cm3 /molecule/sec and for the formation of HCHO + CO + HCO (kP4 ) is the favourable secondary pollutant and the values is found to be 1.237 × 10−13 cm3 /molecule/sec. The branching ratio analysis for the reaction paths is tabulated and shows that the formation of glycolaldehyde and formaldehyde (59% and 36%) agrees with available experimental values. The atmospheric lifetime of primary ozonide removed rapidly through physical and chemical processes in the lower troposphere and have short atmospheric lifetime ≈10 hours which is not a major contributive to global climatic change. The GWPs compared with the CO2 show that the GWP gradually decreases over the horizons of time.

Acknowledgment Figure . GWPs of allyl alcohol compared with CO computed at different horizons of time using M-X/-++G(d,p) level of theory.

the GWP declines as the horizon of time increases. This decrease in GWP may be due to that, allyl alcohol is gradually removed from the atmosphere through natural removal mechanisms and its influence on the greenhouse effect declines.

4. Conclusion The theoretical results presented in this study provide useful information for the oxidation of allyl alcohol in the atmosphere. The following are the main conclusions obtained from the results.

r All the reactants and products possess real frequencies, whereas the transition state structure possesses only one imaginary frequency which is confirmed by the vibrational analysis. r Thermodynamic properties such as energy barrier E, enthalpy H and Gibbs free energy G in kcal/mol were calculated using DFT method and E is comparable with the CCSD(T) method.

One of the authors R. Shankar is thankful to the Department of Science and Technology (DST) India for awarding the research project (Sanction No. SR/FTP/PS-151/2011 dated 26/09/2012) under the Fast Track Scheme.

Disclosure statement No potential conflict of interest was reported by the authors.

Funding Department of Science and Technology (DST), Government of India, New Delhi. (Sanction No. SR/FTP/PS-151/2011 dated 26/09/2012)

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