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\begin{document}

\title{Kinetics and Degradation Mechanism of Atmospheric Isoprene (2-methyl-1,
3-butadiene (C5H8)) with Chlorine Radical and Its Derivatives -- A DFT
Study}



\author[1]{Mohanapriya Subramani}%
\author[1]{Akilan Rajamani}%
\author[1]{Ramasamy Shankar}%
\affil[1]{Bharathiar University}%


\vspace{-1em}



  
  \date{May 17, 2024}


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\selectlanguage{english}
\begin{abstract}
Isoprene (2-methyl-1, 3-butadiene (C5H8)) is one of the most prominent
and abundant non-methane hydrocarbon existing in the lower level of the
troposphere. In this work, possible reaction mechanism of chlorine (Cl)
radical initiated isoprene and its subsequent reactions are investigated
using quantum chemical methods. The calculated thermodynamic result
shows that the reaction of isoprene with the Cl radical at the terminal
C=C bond position plays an important role to predict the end products.
The calculated rate coefficient for the reaction between isoprene and Cl
radicals (Cl addition at C1, C3, C4 and C5 positions) is found to be
4.89?10-11, 6.91?10-10, 1.63?10-10 and 8.12?10-10 cm3/molecule/sec at
298K. The branching ratio and atmospheric lifetime have been calculated
from the reaction rate coefficient values of isoprene+Cl. The reaction
force analysis predicts Cl radical addition at the terminal C=C bond
position plays a dominant role by structural rearrangement. The kinetic
and thermodynamic results reveal that the electrophilic addition of Cl
radical to the terminal carbon atom plays the dominant role in the
marine boundary. Further, the subsequent reaction of Cl-isoprene adduct
radical helps for the development of ozone layer during daytime.%
\end{abstract}%



\sloppy


\textbf{Introduction}

The reactions of non-methane hydrocarbons (NMHCs) with atmospheric
oxidizing species (such as hydroxyl (OH) radical, nitrate
(NO\textsubscript{3}) radical, ozone (O\textsubscript{3}) molecule and
chlorine radical (Cl.\selectlanguage{english})) are most important in the earth's troposphere
and these contribute to the formation of secondary organic aerosols
(SOAs)\textsuperscript{{[}1--4{]}}. Among such non-methane hydrocarbons,
isoprene (2-methyl-1, 3-butadiene
(C\textsubscript{5}H\textsubscript{8})) is one of the most prominent and
abundant non-methane hydrocarbon existing in the lower level of the
troposphere which is released into the atmosphere through various
biogenic and anthropogenic processes \textsuperscript{{[}5,6{]}}. Like
methane, the excretion of isoprene in the world is around 500-600 Tgc
year\textsuperscript{-1} due to the unfinished combustion of diesel
fuels, gasoline, automobile exhausts, petroleum refining, plastic, or
rubber industries and other biogenic volatile organic compounds
(BVOCs)\textsuperscript{{[}7--9{]}}. Due to this excessive emission,
isoprene plays a central role in the tropospheric chemistry related to
air quality and climate change. The abundant isoprene in the atmosphere
undergoes several chemical processes, which is leading to their
potential removal from the atmosphere and transformation processes in
the atmosphere. Especially, oxidation processes can reduce the
atmospheric lifetime of biogenic isoprene in the daytime and it
contributes to the formation of secondary organic aerosols
(SOAs)\textsuperscript{{[}10{]}}.

For the last few decades, there are several experimental and theoretical
studies have been reported on the kinetics of reactions of isoprene with
atmospheric oxidants. M.L. Ragains and B.J. Finloyson Pitts have
experimentally studied the kinetics and mechanism of the reaction of Cl
atom with isoprene at 760 Torr and 298K using relative rate
techniques\textsuperscript{{[}11{]}}. Another important experimental
study on isoprene was done byYuri Bedjanian et al., where they studied
the kinetics of the reaction of isoprene+Cl and obtained the overall
rate coefficient over the temperature range of 233-320 K at 1
Torr\textsuperscript{{[}12{]}}. Inseon Suh and Renyi Zhang have
investigated the degradation mechanism of Cl initiated isoprene and
measured the rate constant between Cl atom and isoprene is (4.0\selectlanguage{ngerman}±0.3)
\selectlanguage{english}?10\textsuperscript{-10}
cm\textsuperscript{3}molecule\textsuperscript{-1} S\textsuperscript{-1}
at 5 to 10 Torr and 298K \textsuperscript{{[}13{]}}. Subsequently,
Inseon Suh et al. both experimental and theoretically study the reaction
of isoprene+NO\textsubscript{3} and they measured the rate coefficient
in the pressure range of 5-7 Torr at 298+-2K using chemical ionization
mass spectrometry (CIMS) detection \textsuperscript{{[}14{]}}. Recently,
Victoria P. Barber et al reported the formation of four carbon criegee
intermediate from ozonolysis of isoprene \textsuperscript{{[}15{]}}.
Earlier this year, a theoretical investigation on isoprene was done by
Xirui Guo et al., where they studied the reaction of isoprene with Cl
radical and the reaction rate constants for tight and loose transition
states were calculated by RRKM theory and canonical variational
transition state theory (CVT) respectively \textsuperscript{{[}16{]}}.
From the earlier literature, the OH radicals and O atoms are well known
most important oxidants in the troposphere, which are responsible for
the removal of VOCs in the atmosphere. Meanwhile, Cl radicals are also
highly reactive in the coastal and marine boundaries. This highly
reactive Cl radical is produced in the marine boundary as a consequence
of both direct emission and chemical processes. Generally, particle
bound chlorine released into the gas phase through heterogeneous
processes on particulate surfaces or sea salt aerosols. Recently, Luo et
al reported that the emission of Cl radicals from seawater is estimated
to be 1792.6 Tg Cl yr\textsuperscript{-1} \textsuperscript{{[}17{]}} and
it is comparably higher than that of other sources (such as dust 15 Tg
Cl yr\textsuperscript{-1} and volcanic eruptions 2 Tg Cl
yr\textsuperscript{-1}). Therefore, in the present study aimed to
investigate the degradation of isoprene with Cl radical along with their
intermediates, transition states and product radicals in the presence of
O\textsubscript{2}, NO and H\textsubscript{2}O molecules. The earlier
investigation mainly focused on primary reaction of isoprene with Cl
radical which hinders the understanding of secondary reactions from Cl
radical initiated isoprene and formation of SOAs from Cl radical
initiated isoprene. A detailed theoretical study on the kinetics of Cl
initiated isoprene and the secondary reaction is yet to be known.
Therefore, in this work, a quantum chemical study is used to understand
the initial and subsequent reaction of isoprene+Cl. The canonical
variational transition (CVT) state theory
\textsuperscript{{[}18{]}}including small curvature tunneling
(SCT)\textsuperscript{{[}19{]}} is used to calculate the relative rate
coefficient for the reaction of isoprene+Cl. The obtained rate
coefficients are used to determine the lifetime of isoprene for the
removal of Cl radicals. In addition to that, the reaction force analysis
is also calculated to find out the structural fate of the reaction and
their results are correlated with the relative energy profile in the
present work.

\textbf{Computational details}

The geometric parameters of all the reactants, transition states,
intermediates, and products involved in the proposed reaction mechanism
are optimized using M06-2X functional and 6-311+G* basis set. The
above-mentioned hybrid meta-generalized gradient-approximations (hybrid
meta-GGAs) M06-2X is recommended for studying thermochemistry, kinetics,
noncovalent interactions \textsuperscript{{[}20--23{]}}. The
corresponding harmonic vibrational frequency calculations are performed
to identify the nature of stationary points on the potential energy
surface using the same level of theory \textsuperscript{{[}24{]}}. The
local minima are confirmed with the real frequency in all reactants,
intermediates and product structures, whereas the corresponding
transition structure has only one imaginary frequency. Further, the
reaction path is calculated through intrinsic reaction coordinates
(IRCs) \textsuperscript{{[}25{]}} to find the right transition states
which connect the two equilibrium structures \textsuperscript{{[}26{]}}.
To obtain more accurate relative energies, the single point energy is
carried out using CCSD (T) \textsuperscript{{[}27{]}} functional and
6-311+G* level of theory. Thermodynamic properties enthalpy (\selectlanguage{greek}Δ\selectlanguage{english}H),
entropy (\selectlanguage{greek}Δ\selectlanguage{english}S) and Gibbs free energy (\selectlanguage{greek}Δ\selectlanguage{english}G) are calculated by including a
thermodynamic correction to the potential energy surface at 298.15 K and
1 atmospheric pressure. All the electronic structure calculations are
performed using Gaussian 09 program package \textsuperscript{{[}28{]}}.
In this study, the kinetic rate constants are calculated by the
canonical variational transition (CVT) state
theory\textsuperscript{{[}18{]}} including small curvature tunneling
(SCT)\textsuperscript{{[}19{]}} over the temperature range of 278-350 K
which are performed at M06-2X/6-311+G* level of theory.

\textbf{Fukui functional analysis}

The Fukui function is one of the most important concepts in Density
Functional Theory (DFT). It is widely used to predict active sites and
provides information about local site reactivity within the molecule.
The Fukui function can be defined as,

\(f=\left(\frac{\partial\rho(r)}{\partial N}\right)_{v}\) (1)

Where N is the number of atoms within the molecule, \selectlanguage{greek}ρ\selectlanguage{english}(r) is electron
density in the partial derivatives, v represents the external potential.
Due to discontinuity, this equation cannot be evaluated
directly\textsuperscript{{[}29,30{]}}. Hence, the following modified
equation is used for calculating Fukui
function\textsuperscript{{[}31{]}}

\(\text{\ f}_{k}^{+}=\left[q\left(n+1\right)-q\left(N\right)\right]\)For nucleophilic attack (2)

\(\text{\ f}_{k}^{-}=\left[q\left(N\right)-q\left(n-1\right)\right]\)For electrophilic attack (3)

\(\text{\ f}_{k}^{0}=\frac{1}{2}\left[q\left(n+1\right)-q\left(n-1\right)\right]\)For radical attack (4)

Where +, -, and 0 signs denote the nucleophilic, electrophilic and
radical attack.

\textbf{Reaction force analysis}

A chemical reaction is mainly expressed in terms of geometrical changes
of structural parameters and rearranging of the electron densities
involved in the chemical process. But, the relative energy profile does
not give us complete information about the chemical reaction. Hence, the
reaction force concept is applied for finding structural and electronic
changes existing along the complete chemical reaction
process\textsuperscript{{[}32--35{]}}. The reaction force
F(\selectlanguage{greek}ξ\selectlanguage{english})\textsuperscript{{[}36{]}} is defined as

\(F\left(\xi\right)=-\selectlanguage{greek}\frac{\text{dE}}{\text{dξ}}\selectlanguage{english}\) (5)

On the other hand, the reaction force profile provides an energy
partition of the activation and reaction energies \selectlanguage{greek}Δ\selectlanguage{english}\(E^{\neq}\)
and \selectlanguage{greek}Δ\selectlanguage{english}\(E\) respectively. Therefore (\selectlanguage{greek}Δ\selectlanguage{english}E\selectlanguage{ngerman}\textsuperscript{°})
and (\selectlanguage{greek}Δ\selectlanguage{english}\(E^{\neq}\)) takes the following form
\textsuperscript{{[}37--39{]}}

\(\left(\selectlanguage{greek}\text{ΔE}\selectlanguage{english}\right)=W_{1}+W_{2}+W_{3}+W_{4}\) (6)

\(\left(\Delta E^{\neq}\right)=W_{1}+W_{2}\) (7)

From equation (6) and (7), W\textsubscript{1}, W\textsubscript{2},
W\textsubscript{3}, and W\textsubscript{4} are the reaction works
involved in the mechanism.

\begin{equation}
W_{1}=-\int_{\xi_{R}}^{\xi_{1}}{F\left(\xi\right)d\xi>0}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }W_{2}=-\int_{\xi_{1}}^{\xi_{\text{TS}}}{F\left(\xi\right)d\xi>0}\nonumber \\
 \end{equation}\begin{equation}
W_{3}=-\int_{\xi_{\text{TS}}}^{\xi_{2}}{F\left(\xi\right)d\xi<0}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }W_{4}=-\int_{\xi_{2}}^{\xi_{p}}{F\left(\xi\right)d\xi<0}\nonumber \\
 \end{equation}

\textbf{Results and discussion}

The reaction mechanism of chlorine radical initiated isoprene is
analyzed through four different pathways and its subsequent reactions
shown in \textbf{Scheme 1} . The geometry of the reactant, transition
states, intermediates and products for the above mentioned reaction
mechanism are calculated at M06-2X/6-311+G* level of theory. The
corresponding harmonic vibrational frequency calculations are achieved
by the same level of theory and all transition states are confirmed by
using IRC calculation. In addition to that, a single point energy
calculation for the involved reaction mechanism is carried out by CCSD
(T)/6-311+G* level of theory. The calculated condensed Fukui function
values are used to find the most favorable active site in the reactant
by the nucleophilic\({(f}_{k}^{+})\), electrophilic\({(f}_{k}^{-}\))
and radical\({(f}_{k}^{-}\)) attack and their corresponding values are
listed in supplementary \textbf{(Table S1-S4).}

\textbf{Formation of Cl-isoprene adduct radicals}

Isoprene can react with Cl radical at the C=C double bond positions such
as C1, C3, C4, and C5 which lead to the formation of Cl isoprene adduct
radical (C\textsubscript{5}H\textsubscript{8}Cl) intermediates (I1a,
I1b, I1c, and I1d) and their optimized structures are shown
in\textbf{Figure 1} The intermediates I1a, I1b, I1c, and I1d are formed
along with the activation energy values of 7.63, 13.57, 12.14 and 13.14
kcal/mol respectively and their corresponding relative energy profile is
shown in \textbf{Figure 2} . In isoprene, the condensed Fukui function
value of C3, C1, C4, and C5 atoms are found to be 0.051, 0.038, -0.016,
and -0.025 respectively. In the Cl radical, the condensed fukui function
value is found to be 0.043. During the formation of Cl isoprene adduct
radical intermediates (I1a, I1b, I1c and I1d), the obtained condensed
Fukui function value shows that the nucleophilic carbon C3, C1, C4 and
C5 atoms tend to interact with the electron deficient electrophilic Cl
radical. During this Cl radical addition, the \selectlanguage{greek}π \selectlanguage{english}bond is cleaved
homolyticly in between the (C=C) atoms and it leads to form the covalent
bond between (C---Cl) atoms. In the case of bond formation, the Cl
radical able to accommodate the electron as a lone pair which can
stabilize the structures by resonance delocalization. As shown
in\textbf{Figure 1} , the intermediates I1a, I1b, I1c, and I1d are
formed through the transition states TS1a, TS1b, TS1c, and TS1d, where
the obtained single imaginary frequency values are -318.896
cm\textsuperscript{-1}, -241.151 cm\textsuperscript{-1}, -829.152
cm\textsuperscript{-1}, and -241.115 cm\textsuperscript{-1}respectively,
confirms the transition state on PES by IRC calculations. During the
addition of Cl radical at C1 position, the bond length of (C1---C2),
(C1---C3) and (C1=C4) atoms are found to be 1.502 \selectlanguage{ngerman}Å, 1.461 Å and 1.343 Å
respectively. Whereas in the formation of intermediate I1a, the bond
length of (C1---C2), (C1---C3) and (C1=C4) atoms elongated around 0.01
Å, 0.04 Å and 0.1 Å respectively. After that addition of Cl radical at
C3 position, the bond length of (C3=C5), and (C3---C1) atoms are found
to be 1.338 Å and 1.461 Å respectively. The previously reported bond
length of C=C and C---C atoms are 1.33Å and 1.54Å respectively and these
results are in good agreement with the obtained results
\textsuperscript{{[}40{]}}. During the formation of intermediate I1b,
the bond length gets elongated around 0.128 Å and 0.042 Å. During Cl
radical addition at C4 position, the bond length between C4 and C1 atoms
are found to be 1.339 Å, while in the formation of intermediate I1c, the
bond length is extended around 0.14 Å. In the formation of intermediate
I1d, the bond length between C5 and C3 atom elongated around 0.15Å, The
Cl---C bond distances in intermediates I1c and I1d are 1.83Å and 1.83Å
respectively where the bond length of Cl---C atoms is very similar in
both intermediates. Another two adduct radical intermediates I1a and I1b
with Cl radical addition to the internal positions C1 and C3 atoms
contain well localized double bonds and the Cl---C bond distances in
intermediates I1a and I1b are 1.90Å and 1.88Å respectively, which is a
little higher than those of the intermediates I1c and I1d with the
terminal Cl radical addition. In the present work, the obtained bond
length of C---Cl atoms is well correlated with the previously available
experimental investigation\textsuperscript{{[}41{]}}. As given in
(\textbf{Table 1} ), the formation of Cl isoprene adduct radical
intermediates I1a, I1b, I1c, and I1d are found to be exothermic with the
enthalpy (\selectlanguage{greek}Δ\selectlanguage{english}H) values of -13.230, -13.852, -26.326, and -26.111 kcal/mol
and these intermediates are also found to be exoergic with the Gibbs
free energy (\selectlanguage{greek}Δ\selectlanguage{english}G) values of -11.647, -13.100, -26.421, -25.231 kcal/mol
respectively. The calculated thermodynamical values are well correlated
with previous results\textsuperscript{{[}42{]}} and the results are
compared in (\textbf{Table 1)} . The \selectlanguage{greek}Δ\selectlanguage{english}H\textless{}0 and \selectlanguage{greek}Δ\selectlanguage{english}G\textless{}0
reveals that the reactions are spontaneous and more feasible. The
thermodynamic results reveal that the terminal addition of Cl radical
with the isoprene is thermodynamically more favorable than the Cl
addition of the internal positions (C1 and C3). Wenfang Lei and Renyi
Zhang also reported that the Cl radical addition at terminal positions
(C4 and C5) has lower enthalpy (\selectlanguage{greek}Δ\selectlanguage{english}H) values than the Cl radical addition
at the internal positions (C1 and C3) \textsuperscript{{[}43{]}}. Hence,
the Cl radical addition reaction reveals that the addition of Cl radical
at the terminal position is thermodynamically more favourable in the
marine boundary.

\textbf{Formation of chloroalkenyl peroxy radical criegee intermediates}

The Cl isoprene adduct radical intermediates I1a, I1b, I1c, and I1d lead
to form a chloroalkenyl peroxy radical criegee intermediates I2a, I2b,
I2c, and I2d by the addition of O\textsubscript{2} molecule and their
optimized structures are shown in (\textbf{Figure 3)} . The criegee
intermediates I2a and I2d are formed with the activation energy values
of 2.245, 2.594 kcal/mol respectively, I2b and I2c formed in a
barrierless reaction and their relative energy profile are shown
in\textbf{Figure 4.} These criegee intermediates are formed through the
transition states TS2a, TS2b, TS2c, and TS2d with the single imaginary
frequency values of -278.725, -108.025, -178.434, and -341.418
cm\textsuperscript{-1} respectively. In Cl isoprene adduct radical
intermediates (I1a, I1b, I1c, \& I1d), the active sites are found to be
at carbon (C4, C5, C1, and C3) positions and their obtained
corresponding condensed fukui function values are -0.439, -0 45, -0.267,
and -0.265. These active sites tend to interact with the electron-rich
nucleophilic oxygen O15 atom with the condensed fukui function value of
-0.046. During the O\textsubscript{2} addition at the C4 position, the
bond length of (C4---O15), (C4---Cl) and (O15---O16) atoms are found to
be 2.897 \selectlanguage{ngerman}Å, 1.472 Å, and 1.189 Å respectively, While in the formation of
intermediate I2a, the bond length is elongated around 0.11Å, 1.46Å, and
0.06Å respectively. In O\textsubscript{2} addition at the C5 position,
the bond length between C5---C3 atom is found to be 1.467 Å, while in
the formation of intermediate I2b the bond length elongated around
0.05Å. During the addition of O\textsubscript{2} molecule at chiral
carbon atom C1, the bond length of (C1---C3), (C1---C4), and (C1---C2)
atoms are found to be 1.402Å, 1.479Å, and 1.496Å whereas in the
formation of intermediate I2c the bond length lengthened around 0.1Å,
0.06Å, and 0.01Å respectively due to an increased \selectlanguage{greek}σ \selectlanguage{english}nature of (C---C)
bond. Simultaneously, the \selectlanguage{greek}π \selectlanguage{english}bond is being transferred to the newly
formed C---O\textsubscript{2} bond. At the time of
O\textsubscript{2}addition at the C3 position, the bond length of
(C3---C1), (C3---C5), and (C3---H9) atoms are found to be 1.399\selectlanguage{ngerman}Å,
1.476Å, and 1.085Å respectively and in the formation of criegee
intermediate I2d, the bond length become elongated around 0.1Å, 0.04Å,
and 0.01Å respectively. During the formation of criegee intermediates,
the bond angle decreases with increasing bond length due to the high
electronegativity of Cl isoprene adduct radical intermediates I1a, I1b,
I1c, and I1d. Thus, the formation of chloroalkenyl peroxy radical
criegee intermediate I2a, I2b, I2c, and I2d are found to be exothermic
with the enthalpy values of -30.523, -30.067, -17.498 and -17.430
kcal/mol and also found to be exoergic with the Gibbs free energy values
of -26.308, -24.315, -12.544, and -13.9 kcal/mol respectively. The
thermodynamically calculated enthalpy (\selectlanguage{greek}Δ\selectlanguage{english}H) and Gibbs free energy (\selectlanguage{greek}Δ\selectlanguage{english}G)
values are compared with the previously available literature
\textsuperscript{{[}44{]}}, listed in (\textbf{Table 2)} . The negative
values of enthalpy reveal that the reactions are spontaneous and more
feasible. The spontaneity of the crieege intermediates in the atmosphere
further leads to a subsequent reaction with NO or OH radical.

After that, the intermediates I2a, I2b, I2c, and I2d, the reactions
occur with two different steps. As shown in \textbf{Scheme. 1,} one step
is the formation of intermediates I3a, I3b, I3c, and I3d by the addition
of NO radical and another step is the formation of intermediates I6,
I6c, and I6d by decomposition.

\textbf{Formation of chloroalkenylalkoxy radical intermediates}

Under the atmospheric condition, chloroalkenyl peroxy radical criegee
intermediates I2a, I2b, I2c, and I2d react with the presence of nitrogen
monoxide (NO) radical possesses chloroalkenylalkoxy radical
intermediates I3a, I3b, I3c, and I3d respectively and their optimized
structure are shown in \textbf{Figure. 5.} As shown in \textbf{Figure.
6,} the intermediates I3a, I3b, I3c, and I3d are formed with the
activation energy values of 24.786, 29.171, 30.775, and 29.493 kcal/mol
respectively. During this reaction, the condensed fukui function
analysis is used to find the active site of the chloroalkenyl peroxy
radical criegee intermediates I2a, I2b, I2c, and I2d, where the active
sites are found to be at terminal oxygen atom for each criegee
intermediates. The condensed fukui function values are found to be
-0.297, -0.187, -0.194 and -0.199 at the O16 position of each
intermediates I3a, I3b, I3c, and I3d respectively, which tends to
attract the electron-deficient electrophilic atom N17 with the condensed
Fukui function value of -0.162. The NO radical addition reaction is
observed through the transition states TS3a, TS3b, TS3c, and TS3d with
the single imaginary frequency value of -110.945, -182.017, 88.346, and
210.912 cm\textsuperscript{-1} respectively. The TSs are confirmed by
IRC calculation through PES. During the NO radical addition reaction
with the criegee intermediate I2a, the bond length of (O18---N17) and
(O16---O15) atoms are found to be 1.1 \selectlanguage{ngerman}Å and 1.4Å, whereas in the
formation of intermediate I3a bond length extended around 0.01Å and 0.05
Å respectively. During the addition of NO radical with the intermediate
I2b, the bond length of O15---O16 and N17---O18 atoms are found to be
1.4Å and 1.1Å and in the formation of intermediate I3b, the bond length
elongated around 0.02Å and 0.08Å respectively. Similarly, the formation
of intermediate I3c, the bond length of (N17---O18) and (O16---O15)
atoms lengthened around 0.2Å and 0.02Å respectively. As shown in
(\textbf{Tabe 3)} the formation of intermediate I3a, I3b, I3c, and I3d
is endothermic with the enthalpy (\selectlanguage{greek}Δ\selectlanguage{english}H) values of 23.741, 28.643, 30.495,
and 30.599 kcal/mol and that they are endoergic with the Gibbs free
energy (\selectlanguage{greek}Δ\selectlanguage{english}G) value of 26.908, 30.893, 32.901, and 33.117 kcal/mol
respectively which reveals that the reactions are less feasible and
non-spontaneous. Further, the covalent bond between O15 and O16 atoms in
an intermediates I3a, I3b, I3c, and I3d gets completely cleaved to form
an intermediate I4a, I4b, I4c, and I4d respectively. As shown in
(\textbf{Table 4),} the intermediates I4a, I4b, I4c, and I4d are formed
in a barrier less reaction. During the formation of intermediate I4a,
I4b, I4c, and I4d, the nitrogen dioxide (NO\textsubscript{2}) eliminated
into the atmosphere due to cleavage of the covalent bond between O15 and
O16. In these steps, NO\textsubscript{2} elimination from respective
intermediates are observed through the transition states TS4a, TS4b,
TS4c, and TS4d. The reaction enthalpy for the elimination of
NO\textsubscript{2} from an intermediates I3a, I3b, I3c, and I3d are
found to be exothermic with their corresponding values are -43.304,
-37.914, -34.574, and -36.904 kcal/mol, and also the Gibbs free energies
are found to be exoergic with the values of -41.848, -37.133, -34.118,
and -36.941 kcal/mol respectively. By the negative values of the
thermodynamic parameters of NO\textsubscript{2} elimination, the
reactions are more feasible and spontaneous. Thus, the eliminated
NO\textsubscript{2} helps to increase the level of ozone under
atmospheric photo-oxidation.

As shown in \textbf{Figure 7,} intermediates I4a, I4b, I4c, and I4d
undergoes decomposition to form four different product P1, P2, P3, and
P4 as a SOAs through transition states TS5a, TS5b, TS5c, and TS5d which
is confirmed by the IRC calculation. The product P1, P2, P3, and P4 are
formed with the activation energy values of 7.635, 13.572, 6.231, and
13.143 kcal/mol respectively and it is shown in relative energy
profile\textbf{Figure 8} . Both P1 and P2 are the products obtained from
the addition of chlorine atom to C1 and C3 position respectively and
they are formed by the homolytic bond fission between respective C---C
atoms. Other end products of the isoprene reactions are P3 (methyl vinyl
ketone (MVK)) and P4 (methacrolein (MACR)) and they are the potential
end products obtained from the addition of chlorine atom to the terminal
carbon C4 and C5 atoms. The addition of Cl atom at terminal position C4
and C5 also generates the CH\textsubscript{2}Cl and it subsequently
reacts to produce formyl chloride. As given in (\textbf{Table 4)} , the
thermodynamic parameters for the formation of end products P1, P2, P3,
and P4 are found to be exothermic with the enthalpy values of -6.334,
-0.539, -0.129, and -1.157 kcal/mol respectively. Moreover, they are
found to be exoergic with the Gibbs free energy values of -10.353,
-3.778, -5.479, and -2.189 kcal/mol respectively. From the thermodynamic
results, the negative values reveal that the formation of product P1,
P2, P3, and P4 are more feasible and spontaneous. During the formation
of products, obtained entropy values 13.483, 10.858, 17.942, and 8.871
mol\textsuperscript{-1} K\textsuperscript{-1} are also indicated that
the reactions are spontaneous and irreversible. The potential end
products P1, P2, P3, and P4 are reactive in its own right and can
contribute to O\textsubscript{3} production as well as provide a source
of free radicals through their photolysis.

\textbf{Reaction of criegee intermediates with H\textsubscript{2}O}

By the decomposition, the criegee intermediates I2a, I2b, I2c, and I2d
are leads to produce CH\textsubscript{2}Cl, CH\textsubscript{2}OO
radical, and chlorine containing hydrocarbons. The stabilized criegee
intermediates CH\textsubscript{2}OO, and two I6 intermediates are formed
such as I6c and I6d, derived from chloroalkenylperoxy radical
intermediates I2c and I2d respectively. Under the humid condition,
CH\textsubscript{2}OO reacts with H\textsubscript{2}O leads to the
formation of hydroxymethyl hydroperoxide (HMHP) intermediate I7a along
with the activation energy values of 7.612 kcal/mol and it is shown in
the relative energy profile \textbf{Figure 10)} . This reaction is
energetically more favorable and it is compared with previously
available literature reported with the activation energy value of 8.1
kcal/mol \textsuperscript{{[}45{]}}. The reaction between
CH\textsubscript{2}OO and H\textsubscript{2}O starts with the formation
of hydrogen-bond (COO[?]H\textsubscript{2}O) and it is shown
in\textbf{Figure 9} . The existence of hydrogen bond has been recently
pointed out by Aplincourt et al and Ramon Crehuet et
al\textsuperscript{{[}45,46{]}}. During the addition of
H\textsubscript{2}O, the bond length of (O4---O5) and (C1---O4) atoms
are found to be 1.3\selectlanguage{ngerman}Å and 1.2Å respectively and these found bond lengths
are agreed well with the previously reported value of 1.3 and 1.2Å with
other methods \textsuperscript{{[}47{]}}. While in the formation of
hydroxymethyl hydroperoxide (HMHP) intermediates I7a, the bond lengths
increased around 0.05Å and 0.17Å respectively. Before the formation of
HMHP, the reaction of CH\textsubscript{2}OO with H\textsubscript{2}O
goes on through the TS7 and it is confirmed by the IRC calculation. As
shown in \textbf{(Table 5)} the thermodynamic calculation for the
formation of intermediate HMHP is found to be exothermic and exoergic
with the enthalpy (\selectlanguage{greek}Δ\selectlanguage{english}H) value of -41.501 kcal/mol and Gibbs free energy
value of -0.063 kcal/mol respectively. From the thermodynamic
parameters, negative values indicate that the reaction is feasible and
more spontaneous. Thermodynamically obtained enthalpy and Gibbs free
energy values are compared with the previously reported values of -40.7
kcal/mol and -41.3 kcal/mol respectively \textsuperscript{{[}45{]}}.
Finally, HMHP undergoes unimolecular decomposition to produce
H\textsubscript{2}CO+H\textsubscript{2}O\textsubscript{2} with the
activation energy value of 55.17 kcal/mol and it is compared with the
previously available literature 48.1 kcal/mol\textsuperscript{{[}45{]}}.
As shown in \textbf{Figure 9,} the bond length of (O5---O4) and
(C1---O7) atoms are found to be 1.417\selectlanguage{ngerman}Å and 1.396Å respectively in HMHP
and the bond length between (O5---O4) atoms elongated around 0.006Å due
to the addition of hydrogen atom. Thermodynamic parameters for the
formation of H\textsubscript{2}CO+H\textsubscript{2}O\textsubscript{2}
are found to be endoergic and endothermic with the enthalpy (\selectlanguage{greek}Δ\selectlanguage{english}H) value
of 13.63 kcal/mol and the Gibbs free energy value of 10.63 kcal/mol
respectively. The positive values of the formation of
H\textsubscript{2}CO+H\textsubscript{2}O\textsubscript{2} reveal that
the reaction is less feasible and nonspontaneous. These results agree
with the experimental observation \textsuperscript{{[}48{]}} that
indicates only the formation of formic acid in the decomposition of
HMHP. The obtained final by product in the present work is in good
agreement with the previous experimental work\textsuperscript{{[}48{]}}.

On the other hand in the presence of H\textsubscript{2}O the formed
intermediates I6b and I6c from chloroalkenylperoxy radical intermediates
(I2c\&I2d) lead to the formation of hydroxy hydroperoxide intermediates
I7b and I7c with the activation energy values of 9.840 and -26.469
kcal/mol respectively. The reaction between intermediates (I7b \& I7c)
and H\textsubscript{2}O starts with the formation of a hydrogen bond
(COO[?]H\textsubscript{2}O) and it is shown in \textbf{Figure. 9.} During
the addition of H\textsubscript{2}O with intermediate I6b, the bond
length of (C2---C1), (C3---C1), (C1---O11), and (O11---O12) atoms are
found to be 1.475\selectlanguage{ngerman}Å, 1.457Å, 1.261Å, and 1.377Å respectively, whereas, in
the formation of intermediate I7b, the bond length become elongated
around 0.04Å, 0.05Å, 0.16Å, and 0.04Å respectively. In the formation of
I7b, the bond angle decreased around 13.8°, 10.50°, 8.49°, and 8.64°
respectively. Further, the intermediate I7b decomposed to yield the
product P6 (MVK) as a SOAs and H\textsubscript{2}O\textsubscript{2} as
shown in \textbf{Figure 9} . As shown in \textbf{Figure 11} , the
product P6 is formed with the activation energy value of 47.877
kcal/mol. The product P6 is obtained through the transition state TS8b
with a single imaginary frequency value of -1799.744
cm\textsuperscript{-1} and it is confirmed by IRC calculation. J.Fan et
al \textsuperscript{{[}49{]}} and D. Huang et al
\textsuperscript{{[}50{]}} also indicated the yield of MVK
experimentally through decomposition and this result is in good
agreement with the present work. During the formation of product P6, the
calculated enthalpy (\selectlanguage{greek}Δ\selectlanguage{english}H) and Gibbs free (\selectlanguage{greek}Δ\selectlanguage{english}G) energy values are 6.219 and
2.369 kcal/mol which shows that the reaction is endothermic and
endoergic. Based on thermodynamic parameters, the formation of MVK
through the addition of H\textsubscript{2}O is found to be less feasible
and non-spontaneous compare to the formation of MVK in product P3.

During the addition of H\textsubscript{2}O with intermediate I6c, the
bond length of (C4---C1), (C3---C1), (C2---C1), and (O11---O12) atoms
are found to be 1.3\selectlanguage{ngerman}Å, 1.4Å, 1.5Å, and 1.3Å respectively whereas, during
the formation of I7c, the bond length become elongated around 0.1Å,
0.06Å, 0.004Å, and 0.03Å respectively. Beyond this, the formed
intermediate I7c decomposed to produce product P7 (MACR) as a SOAs and
H\textsubscript{2}O\textsubscript{2}. As shown in \textbf{Figure 11,}the
product P7 is formed with the activation energy value of 48.427 kcal/mol
and it is formed through the transition state TS8c with the single
imaginary frequency value of -1805.916 cm\textsuperscript{-1}which is
verified by the IRC calculation. As given in \textbf{(Table 5),} the
formation of MACR is found to be endothermic with the enthalpy (\selectlanguage{greek}Δ\selectlanguage{english}H)
value of 7.794 kcal/mol and endoergic with the Gibbs free energy (\selectlanguage{greek}Δ\selectlanguage{english}G)
value of 3.615 kcal/mol. The calculated thermodynamic values revealed
that the formation of end product P7 via intermediate I7c is less
feasible and non-spontaneous when compared with the formation of end
product P4 through Cl addition in the present work. Hence, the
non-spontaneity of this reaction reveals that the water molecule could
affect the properties of potential end products P6 (MVK) and P7 (MACR).

\textbf{Kinetic analysis}

According to the above discussed PESs, the formation of isoprene adduct
radical leads to the formation of SOAs through subsequent reactions. The
rate constants for the reaction between isoprene and Cl radicals are
carried out over the temperature range of 278K-348K with an interval of
10K at 1 atm pressure. The CVT/SCT is used to calculate the rate
constant for the formation of Cl isoprene adduct radicals
(K\textsubscript{1a}, K\textsubscript{1b}, K\textsubscript{1c}, \&
K\textsubscript{1d)} at M06-2X/6-311+G* level of theory. The rate
constant for the reaction of isoprene with Cl radical to C1, C3, C4, and
C5 positions is found to be 4.89?10\textsuperscript{-11},
6.91?10\textsuperscript{-10}, 1.63?10\textsuperscript{-10} and
8.12?10\textsuperscript{-10} cm\textsuperscript{3}/molecule/sec
respectively at 278K. At high-temperature 350K, the rate constant for
the reaction of isoprene with Cl radical to C1, C3, C4, and C5 positions
is found to be 6.38?10\textsuperscript{-11},
8.12?10\textsuperscript{-10}, 7.52?10\textsuperscript{-10} and
8.83?10\textsuperscript{-10}cm\textsuperscript{3}/molecule/sec. These
obtained rate constants K\textsubscript{1a}, K\textsubscript{1b},
K\textsubscript{1c}, and K\textsubscript{1d} are listed in\textbf{(Table
6)} and the obtained reaction rate constants are increased with
increasing temperature which is displayed in\textbf{Figure 12} . In this
study, the calculated rate constants for the primary Cl-isoprene adduct
radical is feasible with the experimentally reported values of
5.55?10\textsuperscript{-10}\textsubscript{,}4.48?10\textsuperscript{-10}cm\textsuperscript{3}molecule\textsuperscript{-1}s\textsuperscript{-1{[}42,51{]}}.
This result reveals that the reaction between Cl radical and isoprene is
kinetically and thermodynamically more favorable in the marine boundary.

The branching ratios are calculated for K\textsubscript{1a},
K\textsubscript{1b}, K\textsubscript{1c}, and K\textsubscript{1d} at the
temperature range of 278K to 348K and its calculated values are listed
in \textbf{(Table 7).} The branching ratio plot for rate constant
associated with the formation of I1a, I1b, I1c and I1d are shown
in\textbf{Figure 13} . Hence, the calculated total kinetic rate constant
is used to calculate the atmospheric lifetime. The atmospheric lifetime
of Cl-isoprene adduct radical can be calculated using the following
given expression

\begin{equation}
\tau=\frac{1}{K\left[\text{Cl}\right]}\nonumber \\
 \end{equation}

Where K is the total rate constant obtained from the above kinetic
studies and Cl is the atmospheric concentration of the Cl atom. Under
the atmospheric condition, the Cl concentration is
1?10\textsuperscript{5} molecules per cm\textsuperscript{3{[}52{]}}. The
troposphere lifetime (\(\tau\)) of isoprene is estimated from
the total rate coefficient value of primary Cl-isoprene adduct radical
reaction at the temperature range of 298K. The lifetime of Cl-isoprene
adduct radical is estimated to be 6.49 hours at the temperature of 298K
using the average atmospheric concentration of Cl atom. The lifetime
reported in this study is in good agreement with the Gaia Fantechi et al
estimated values of 5 hours\textsuperscript{{[}53{]}}.

\textbf{Energy and reaction force profiles}

In Figure 14 \& 15, the energy and reaction force profiles along with
the partition of the reaction coordinates are shown. As stated by the
transition state theory (TST), an energy profile of the all reaction
path are characterized in three critical points such as two minimum
points, one reactant (\(\xi_{R})\) and another product
(\(\xi_{p})\), and one maximum point for the transition structure
(\(\xi_{\text{TS}})\). In the reaction force profile, the critical points
are divided into three separate reaction regions that are
reactants\(\ \xi_{R}\rightarrow\xi_{1}\),\(\xi_{1}\rightarrow\xi_{2}\) and
\(\xi_{2}\rightarrow\)product\({(\ \xi}_{p})\). The first region is the
preparation region associated with the reactants
(\(\xi_{R}\),\(\xi_{1}\)), where the structural distortion
takes place mainly by the bond stretching, angle bending, etc. In this
region, when the negative (retarding) reaction force reaches its
greatest strength at the point\(\xi_{1}\), the reaction force
\(F\left(\xi\right)\) becomes minimum. The second region is a transition
state region which is located from \(\xi_{1}\) to its maximum
point at \(\xi_{2}\) and where the structural rearrangements
take place by the bond breaking and bond forming. All of these extensive
changes produce a positive reaction force which starts at
\(\xi_{1}\)that gradually overcomes the retarding one. At the
point\(\ \xi_{\text{TS}}\), the positive deriving force is dominant and
continues to increase until it reaches its maximum reaction force
at\(\xi_{2}\) where the system has been changed as the states of
the products. Finally, the third region is the product region which is
located from the F (\selectlanguage{greek}ξ\selectlanguage{english}) maximum at \(\xi_{2}\) to its minimum
point at\(\xi_{p}\). In this region, the system involves
structural relaxation to reach its final state after the maximum point
at \(\xi_{2}\) and the reaction force F (\selectlanguage{greek}ξ\selectlanguage{english}) declines to zero to
reach the equilibrium geometry of the products.

On the other hand, reaction force calculation has been performed to
estimate the amount of work done in each elementary step of the chemical
reaction. The calculated work is done for the formation of Cl isoprene
adduct radical intermediates I1a, I1b, I1c, and I1d are listed in
supplementary \textbf{(Table S5)} . From the \textbf{(Table S5),} the
formation of Cl-isoprene adduct radical intermediates (I1a, I1b, I1c,
and I1d), 70\%, 77.5\%, 74.1\%, and 77.6\% of activation energy is due
to the geometrical rearrangement and the remaining 30\%, 22.5\%, 25.9\%,
and 22.4\% of activation energy is due to electronic reordering
respectively. In this mechanism, the potential end products P3 (MVK with
CH\textsubscript{2}O) and P4 (MACR with CH\textsubscript{2}O) is formed
through the addition of Cl, O\textsubscript{2} and NO radical pathway.
During the formation P3, 71\% \& 29\% of activation energies are mainly
due to the geometrical rearrangement and electronic reordering
respectively. Similarly, the formation of P4, 72\% \& 28\% of activation
energies were due to geometrical rearrangement and electronic reordering
respectively. On the other hand, the potential end products P6 (MVK with
H\textsubscript{2}O\textsubscript{2}) and P7 (MACR with
H\textsubscript{2}O\textsubscript{2}) is formed through the addition of
Cl, O\textsubscript{2}, and H\textsubscript{2}O pathway. In the
formation of P6 and P7, 75\% \& 76\% of activation energies are due to
geometrical rearrangement, the remaining 25\% \& 24\% of activation
energies are due to electronic reordering respectively listed
in\textbf{(Table S6).} This analysis shows that the potential product P3
and P4 are formed with less activation energy than the potential product
of P6 and P7, which confirms that the formation of MVK and MACR through
Cl, O\textsubscript{2}, and NO radical addition pathway is more
favorable than the formation of MVK and MACR through Cl,
O\textsubscript{2}, and H\textsubscript{2}O addition pathway. The
kinetic study also reveals that the formation of MVK and MACR via Cl,
O\textsubscript{2}, and NO radical addition pathway is more favorable.
The relative energy profile also shows that the formation of MVK through
Cl, O\textsubscript{2}, and NO radical addition pathway has less
activation energy than the formation of MVK through Cl,
O\textsubscript{2}, and H\textsubscript{2}O addition pathway. Similarly,
the formation of MACR through Cl, O\textsubscript{2}, and NO radical
addition pathway has less activation energy than the formation of MACR
via Cl, O\textsubscript{2}, and H\textsubscript{2}O addition pathway.
Thus the result shows that the H\textsubscript{2}O molecule can affect
the formation of SOAs such as MVK and MACR. All previous results are in
good agreement with this reaction force analysis.

\textbf{CONCLUSION}

In this present work, the atmospheric reaction of isoprene initiated by
chlorine atom at various channels and subsequent reactions by the
addition of O\textsubscript{2} molecule, NO radical, and
H\textsubscript{2}O were investigated by using quantum chemical methods.
The kinetics of the primary and subsequent reactions of isoprene were
carried out by CVT/SCT. The electronic structure of reactant, transition
state, intermediate complexes, intermediates, and products were
optimized with M06-2X/6-311+G* level of theory and their corresponding
single point energy was carried out by using CCSD (T)/6-311+G* level of
theory. All reactants, intermediates, and products possess zero
imaginary frequency and transition states possess a single imaginary
frequency. All Transition States were confirmed through Intrinsic
Reaction Coordinates (IRC) to identify the preferred reactants,
intermediates and products. The conclusions of the brief explorations
are summarized below,

\begin{enumerate}
\tightlist
\item
  The initial reaction of isoprene was studied by Cl radical addition at
  the various position with the C---C bond breaking which leads to the
  formation of secondary reaction and its bond length and bond angles
  were calculated from the optimized structure.
\item
  All the reaction paths are found to be exothermic and spontaneous with
  a maximum energy barrier. Whereas the potential end product (MVK,
  MACR) through Cl, O\textsubscript{2}, and NO radical addition pathway
  is found to be more spontaneous and feasible compared to the formation
  of the end product (MVK, MACR) through Cl, O\textsubscript{2}, and
  H\textsubscript{2}O addition pathway. The calculated \selectlanguage{greek}Δ\selectlanguage{english}H = -0.129
  kcal/mol (MVK through Cl, O\textsubscript{2}, and NO) \textgreater{}
  \selectlanguage{greek}Δ\selectlanguage{english}H= 6.219 kcal/mol (MVK through Cl, O\textsubscript{2}, and
  H\textsubscript{2}O) and \selectlanguage{greek}Δ\selectlanguage{english}G= -5.479 kcal/mol (MACR through Cl,
  O\textsubscript{2}, and NO) \textgreater{} \selectlanguage{greek}Δ\selectlanguage{english}G= 2.369 kcal/mol (MACR
  through Cl, O\textsubscript{2}, and H\textsubscript{2}O).
\item
  The most favorable active site of isoprene is found to be at terminal
  C4 and C5 position with its corresponding value is 0.289 and 0.099 by
  using Condensed Fukui Function analysis and also it elucidates the
  concept of bond breaking and bond forming.
\item
  The calculated rate constants for the reaction between isoprene and Cl
  radical is found to be 4.89?10\textsuperscript{-11},
  6.91?10\textsuperscript{-10}, 1.63?10\textsuperscript{-10} and
  8.12?10\textsuperscript{-10} cm\textsuperscript{3}/molecule/sec
  respectively at 278K and it is compared with the experimental rate
  coefficient of 4.6?10\textsuperscript{-10} at 298K. The lifetime of
  Cl-isoprene adduct radical is estimated to be 6.49 hours at the
  temperature of 298K using the average atmospheric concentration of Cl
  atom
\item
  The reaction force analysis reveals that the geometrical rearrangement
  of each structure plays a major part than electronic reordering. The
  formation of Cl-isoprene adduct radical intermediates (I1a, I1b, I1c,
  and I1d), 70\%, 77.5\%, 74.1\%, and 77.6\% of activation energy is due
  to the geometrical rearrangement and the remaining 30\%, 22.5\%,
  25.9\%, and 22.4\% of activation energy is due to electronic
  reordering respectively.
\item
  Conclusively, the kinetic and thermodynamic results reveal that the
  electrophilic addition of Cl radical to the terminal carbon atom plays
  the dominant role in the marine boundary and H\textsubscript{2}O
  molecule can affect the formation of SOAs such as MVK and MACR. The
  calculated lifetime in this work reveals that the isoprene degrade
  quickly in the atmosphere.
\end{enumerate}

\textbf{Conflicts of interest}

No conflicts to declare

\textbf{ACKNOWLEDGEMENTS}

One of the authors is thankful to the Rashtriya Uchchatar Shiksha
Abhiyan (RUSA) Official Memorandum no. IQAC/RUSA2.0/PF/2020/1, Dated:
03.02.2020 for funding to establish High Performance Computational
facilities in Bharathiar University.

****************************************

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