Theoretical prediction of the mechanistic pathways ...

Molecular Physics An International Journal at the Interface Between Chemistry and Physics

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Theoretical prediction of the mechanistic pathways and kinetics of methylcyclohexane initiated by OH radicals Saheen Shehnaz Begum, Ramesh Chandra Deka & Nand Kishor Gour To cite this article: Saheen Shehnaz Begum, Ramesh Chandra Deka & Nand Kishor Gour (2018): Theoretical prediction of the mechanistic pathways and kinetics of methylcyclohexane initiated by OH radicals, Molecular Physics To link to this article: https://doi.org/10.1080/00268976.2018.1436202

Published online: 06 Mar 2018.

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MOLECULAR PHYSICS,  https://doi.org/./..

RESEARCH ARTICLE

Theoretical prediction of the mechanistic pathways and kinetics of methylcyclohexane initiated by OH radicals Saheen Shehnaz Begum, Ramesh Chandra Deka and Nand Kishor Gour Department of Chemical Sciences, Tezpur University, Tezpur, India

ABSTRACT

ARTICLE HISTORY

In this manuscript, we have systematically depicted the theoretical prediction of H-absorption from methylcyclohexane initiated by OH radical. For this we have performed dual-level of quantum chemical calculations on the gas-phase reactions between methylcyclohexane (MCH) and OH radical. Geometry optimisation and vibrational frequency calculations have been performed at BHandHLYP/6-311G(d,p) level of theory along with energetic calculations at coupled cluster CCSD(T) method using the same basis set. All the stationary points of titled reaction have been located on the potential energy surface. It has also been found that the H-abstraction takes place from –CH site of MCH, which is the minimum energy pathway than others. The rate constant was calculated using canonical transition state theory for MCH with OH radical and is found to be 3.27 × 10−12 cm3 molecule−1 s−1 , which is in sound agreement with reported experimental data. The atmospheric lifetime of MCH and branching ratios of the reaction channels are also reported in the manuscript.

Received  December  Accepted  January 

1. Introduction The number of volatile organic compounds (VOCs) that are released into the troposphere is gigantic, and in fact scary for the future of life on earth. It is well known that the main sources of its emission are both biogenic and anthropogenic [1,2]. Among the different classes of VOCs emitted into the atmosphere the significant ones are alkanes, alkenes, aromatic hydrocarbons and oxygenated compounds. Methylcyclohexane (MCH), a volatile organic compound, is one of the important class of hydrocarbon compounds that belongs to cycloalkane category which is widely used in diesel, gasoline, jet airways and others, and is also found in vehicle exhaust emission gases [3–6]. It can be removed either by dry deposition or photolytic degradation with oxidants such as OH radicals and Cl atoms present in the atmosphere. CONTACT Nand Kishor Gour

nkgour@tezu.ernet.in

©  Informa UK Limited, trading as Taylor & Francis Group

KEYWORDS

MCH; MEP; PES; CCSD(T); rate constant

From the reported values of rate coefficients of OH− and Cl− , the global tropospheric lifetime is estimated and it has been affirmed that it is the OH radical which is mainly responsible for the removal pathways of the methylcyclohexanes [7,8]. In sea-water environments, however, the most prominent reactions in tropospheric degradation after sunrise can be attributed to the Cl reactions. Atkinson [9] was the first to study the reaction of MCH with OH radical and the rate constant was reported to be 0.96 × 10−12 cm3 molecule−1 s−1 at 298 K. Recently, Ballesteros et al. [10] determined the rate constant for MCH + OH reaction experimentally utilising conventional relative kinetic measurements at 298 K and 720 Torr of air by FTIR and found it to be (11.8 ± 0.12) × 10−12 cm3 molecule−1 s−1 .

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The occurrence of reaction such as MCH with OH and other analogous reactions are vital for the environment, as these lead to removal of an important class of VOCs. Although sound experimental techniques are available to study such reactions, these are not sufficient. The observations made experimentally provide merely the overall rate constant. Thus, it is challenging to envision the mechanism by which the reaction occurs. Thermochemical study and determination of degree of contribution of individual reaction channel towards overall rate constant is also difficult to anticipate experimentally. Computational calculations lift several such limitations that experimentalists come across when dealing with these reactions and obtain quantitative values. Quantum chemical methods are a boon for provision of detailed insight into the mechanistic pathways, thermo-chemistry and kinetics of any reaction. Considering all such aspects, we have opted for the theoretical study to describe the reaction mechanism and kinetics of MCH with OH radicals. From the best of the literature survey we carried out, the detailed theoretical study of MCH with OH radical is a pioneer work in this regard. For investigation of the reaction mentioned above, dual-level of quantum chemical methods has been employed and all the different probabilities of Habstraction have been considered to make the work wholesome. The abstraction of H atom from MCH may occur from –CH3 group or –CH or –CH2 giving rise to five different possibilities as presented in the following reaction channels (R1–R5):

As already stated, we have employed duel-level of theory for this work. Geometry optimisation and calculation of frequency of the species involved in the various reaction channels are carried out at a low level of theory. In addition, a higher level of theory is employed for calculations at single point, for all the species. Potential energy diagram is constructed using the described duallevel of method. The rate constant of individual reaction paths and the rate constant determined in overall, all are determined using canonical transition state theory (CTST) [11]. The branching ratio of each reaction channel and atmospheric life time of MCH is determined. Having a definitive thermo-chemical data on a firm theoretical basis is the only intent of the present investigation. Eventually, a corroboration narrative is done relating the rate constants retrieved from theoretical methods as well as experimental procedures.

2. Computational methodology The geometries of reactants (MCH and OH), reaction complexes (RC2, RC3 and RC5), transition states (TS1– TS5) and products (P1, P2, P3, P4, P5 and H2 O) in the reaction channels (R1–R5) are optimised by application of hybrid density functional (BHandHLYP) [12] with 6311G(d,p) basis set in density functional theory. Employing the same theory level at which geometry optimisation is performed, calculations for vibrational frequencies are done so as to affirm the attributes of stationary points on potential energy surface (PES). For characterisation of stationary points, the frequencies that are computed are found to be real and positive which in turn correspond to stable minima on the PES. The transition states in reaction path R1–R5 are procured utilising synchronous transition-guided quasi-Newton method [13]. Presence of a single imaginary frequency (NIMAG = 1) suggests that the first-order saddle point has been determined. Calculations for intrinsic reaction coordinate (IRC) are performed additionally, to ascertain smooth transition of reactants via the transition states to corresponding products. Intrinsic reaction coordinate calculation based on Gonzales–Schelgel steepest-descent mechanism is performed with gradient 0.05 (amu)1/2 -bohr [14] in massweighed Cartesian to generate the minimum energy path or minimum energy pathway (MEP). Reaction energy barriers are highly susceptible to change in theoretical level used, thus, attainment of reaction energies that are theoretically consistent, necessitates the requirement of higher order relative energies that are correlation corrected as well as energies obtained by density functional theory. Coupled-cluster theory of triple excitation [CCSD(T)] [15] is a higher level method and this is used for computation of single point energies by employing

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Table . Reaction enthalpy and Gibb’s free energy values (in kcal mol− ) for the H-abstraction reaction channels (R–R) calculated at BHandHLYP/G(d,p) and CCSD(T)//BHandHLYP/-G(d,p) levels of theory.

Reaction channels R R R R R

BHandHLYP/-G(d,p)

CCSD(T)//BHandHLYP/-G(d,p)

r H 

r G 

r H 

r G 

–. –. –. –. –.

–. –. –. –. –.

–. –. –. –. –.

–. –. –. –. –.

6-311G(d,p) basis set. For the reaction initiated by OH radical, the diffuse functions in the basis set has not been included as several studies [16,17] have established that the inclusion of diffuse or polarisation functions to the 6311G(d,p) basis set is inconsequential. Literature surveys indicate several studies of H-abstraction reactions with credible results for energy and kinetics studies [18–25] obtained by CCSD(T)//BHandHLYP dual-level method. GAUSSIAN 09 [26] is a versatile package for carrying out electronic calculations and for the study reported in this paper, the same has been used owing to its credibility.

3. Results and discussion All calculations for the reaction of MCH with OH radical are performed at theory level BHandHLYP/6-311G(d,p) along with CCSD(T)//BHandHLYP/6-311G(d,p). The reaction enthalpies (r H°) and free-energy of reactions (r G°) are tabulated in Table 1. With reference to Table 1, the values of free energy depict that the reaction paths from R1 to R5 are exergonic (r G°< 0), the enthalpy of reaction (r H°) values for H abstraction pathways from R1 to R5 also portray the exothermic nature of each channel, thus making each thermodynamically facile (r G°< 0). The enthalpy of reaction and Gibb’s free energy values of reaction for reaction channel R2 are more negative, suggesting that product of reaction channel of all the reaction paths, R2 is thermodynamically more feasible, consequently making the hydrogen abstraction for reaction channel R2 thermodynamically more viable. The rate constant of reaction channel R2 is also expected to be higher and the reaction faster than the other reaction channels (R1, R3, R4, R5). The potential sites for hydrogen abstraction in MCH are four, i.e. the – CH3 (R1), –CH (R2) and –CH2 group (R3–R5); thereby generating five corresponding transition states (TSs) for each H- abstraction reaction of MCH with OH radical. The optimised geometries of all species along with reaction complexes (RC2, RC3 and RC5) and transition states (TS1–TS5) have been obtained at level BHandHLYP/6311G(d,p) are shown in Figure 1. It should be noted

that, for radicals, the value of spin contamination has very little significance for RCs, OH radical and TSs. The value of is 0.752 for RCs and OH radical, and for TSs, the value of is 0.764, before annihilation, which is only slightly larger than the expected value of = 0.750 for doublets. The parameters for structure of reactants (MCH and OH), reaction complexes (RC2, RC3 and RC5), transition states (TS1, TS2, TS3, TS4 and TS5) and products (P1, P2, P3, P4, P5 and H2 O) that are involved in the reactions (R1–R5) are also presented in Figure 1. From the optimised structure of transition states (TS1–TS5), for reaction channels (R1–R5), the percentage elongation of the C–H bond which is disintegrating is observed to be 12.9%, 9.2%, 10.8%, 11.1% and 10.9% from that of the equilibrium length in MCH, while the O–H bond which is forming in TS1–TS5 is found to be longer by 34.6%, 42.6%, 39.5%, 37.7% and 39.4%, respectively with respect to equilibrium bond length of O–H bond in H2 O. It clearly reflects that, the elongation of bond which is forming (O–H) in TSs is greater than that of the bond (C–H) which is disintegrating. This suggests that the transition states in the reactions (R1–R5) reside near the corresponding reactant. This fact befits with the Hammond’s postulate [27] which states that such a reaction is exothermic. The frequency calculation values for each species undergoing reactions from R1 through R5 are given in Table 2. On the PES, the stable minima of reactants and products are characterised by the presence of real positive vibrational frequencies. The transition states have only one imaginary frequency that are affirmed by analysis of normal mode, the values of which are 1664i (TS1), 988i (TS2), 1330i (TS3), 1417i (TS4) and 1338i (TS5), respectively. The versatile program ChemCraft [28] has been available for visualisation of all vibrations corresponding to the calculated imaginary frequencies. The visualisation portrays that reactants and corresponding products are smoothly connected by a distinct transition state geometry during that transformation. To further corroborate the observation that respective transition state is readily connected to each reactant that transforms into product,

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Figure . Optimised geometries of all species including RCs and TSs of MCH + OH at BHandHLYP/-G(d,P) level of theory.

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Table . Unscaled vibrational frequencies of reactants, products and transition states at BHandHLYP/-G(d,p) level of theory. Species MCH RC RC RC TS TS TS TS TS P P P P P H O OH

Vibrational frequencies (cm− ) , , , , , , , , , , , , , ,, , , , , , , ,  , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,  , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,  , , , , , , , , , , , , , , , , , , , , , , , , , , ,, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,  , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,  i, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,, , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,  i, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,  i, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,  i, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,, , , , , , , , , , , , , , , , , , , , , , ,  i, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,  , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,  , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,  , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,  , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,  , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,  , ,  

IRC, i.e. intrinsic reaction coordinate calculations have also been carried out. The level of theory for IRC calculation has been kept the same as that of optimisation and frequency calculations so as to maintain an uniformity in computation. Single point energy calculations were further refined for the species in the H-abstraction reaction path, by employing couple cluster CCSD(T)/6-311G(d,p) level of theory at BHandHLYP/6-311G(d,p) optimised geometries. It is Table 3 which columnates the relative energies, including zero-point energy for the species involved in the reaction. The PES for the reaction MCH + OH is schematically represented as in diagram in Figure 2. For the convenience of moulding of the energy diagram, reactants’ ground state energies have been arbitrarily taken to be zero. The CCSD(T) method has been used to calculate the barrier heights for hydrogen abstraction from R1, R2, R3, R4 and R5. The relative energy profile has been created by utilising the indirect mechanism in which reaction complex (RC) is required to be determined when the relative energy height of the transition states generated in less than 1 kcal mol−1 . Thus, as shown in Figure 2,

Table . Total energy (including zero-point correction) values (in hartree) at BHandHLYP/-G(d,p) and CCSD(T)//BHandHLYP/-G(d,p) level of theories for all species along with relative energies (with respect to reactants) values (in kcal mol− ). Species

Total energy

R.E.

Total energy

R.E.

MCH + OH RC RC RC TS TS TS TS TS P + H O P + H O P + H O P + H O P + H O

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

. –. –. –. . . . . . –. –. –. –. –.

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

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

TS1 and TS4, generated by reaction channel R1 and R4 have a high barrier height of 3.18 and 1.92 kcal mol−1 , respectively. However, TS2, TS3 and TS5 corresponding to reaction channel R2, R3 and R5 have a comparatively

6

S. S. BEGUM ET AL.

Figure . Schematic potential energy diagram for the MCH + OH reactions at  K. Relative energies (in kcal mol− ) are calculated at the CCSD(T)//BHandHLYP/ G(d,p) level of theory.

lower barrier height of −0.01, 0.82 and 0.95 kcal mol−1 , respectively. Since, relative energy barrier height obtained for TS2, TS3 and TS5 is lower than 1 kcal mol−1 , thus, reaction complex has been determined for these three as shown in Figure 2. The transition state barrier height shows that hydrogen abstraction is most facile for the

tertiary carbon of the cyclohexane ring having methyl substitution (reaction channel R2) than the rest of the reaction channels. For better corroboration of the values obtained by theoretical study with experimental data, literature survey was carried out. But experimental information of

MOLECULAR PHYSICS

H-abstraction reaction of MCH by OH radical and data such as energy barrier for MCH + OH reaction is not available. The information obtained so far, be it enthalpy change or free energy values or the barrier height of proton abstraction, all these aid in the manifold understanding of not only the mechanism but also the kinetics and thermochemical properties of such reactions. This in turn can be of utmost importance in atmospheric modelling. 3.1. Rate constant and branching ratios For determination of rate constant of the titled reaction, we have used CTST, which accounts for one-dimensional semi classical multiplicative tunnelling correction factor. It is given by the expression: k = σr (T )

kB T Q‡T S −E # exp h QR RT

(1)

In Equation (1), σ r represents symmetry number, which numerically varies based on the hydrogen atom that is abstracted and is related to the degeneracy of reaction path. At temperature T, (T) represents the factor for tunnelling correction. The total partition functions for reactants as well as transition states are QR and Q‡ TS , respectively. The barrier height is represented by E# , kB is the Boltzmann constant, h is the Plank’s constant and R represents the universal gas constant. Observations lead us to believe that a two-step mechanism is followed for proton abstraction by OH in case of R2, R3 and R5 reaction channels. The initial step is the formation of pre-reactive complexes (RCs) which has been assigned a pre-equilibrium rate constant (Keq ). The initial step is followed by generation of water and corresponding radicals in the second step. The rate constant can be obtained for this step also, say (k†2 ) . The expression of rate constant for these two processes is given by Keq =

QRC e(ER −ERC )/RT QA × QB

(2)

and k†2 is obtained from TST from the expression: k†2 = σ  (T )

kB T QT S −(ET S −ERC )/RT e h QRC

(3)

The rate constants for H-abstraction reactions for R3– R5 are obtained by the following expression: k = Keq × k2 = σr (T )

kB T Q‡T S −(ET S −ER )/RT e h QR

(4)

7

In Equation (4), QA , QB , QTS and QRC are the total partition functions (per unit volume) of the reactants, transition states and reaction complexes, respectively. ETS , ERC and ER represent the ZPE corrected total energies of transition state, reaction complexes and reactants, respectively. The CTST expression (Equation (1) turns out to be the final expression required for barrier height and rate constant determination regardless of pre-reactive reactant complex energies. However, the shape of the PES is modified by tunnelling factor which is affected by the generation of pre- and post-reaction complexes. The excited state of radical OH is accounted for in the calculation of electronic partition function for the reactant, with a 139.7 cm−1 splitting due to spin–orbit coupling [29]. For tunnelling correction factor estimation (T), Eckart’s unsymmetrical barrier method [30] has been used. These values for TS1, TS2, TS3, TS4 and TS5 have been found to be 1.87, 11.80, 3.75, 4.42 and 3.82, respectively at 298 K and 1 atm pressure. The computation of vibrational frequencies at BHandHLYP/6-311G(d,p) level at 298 K gives the partition functions for each transition state and reactant. The per unit volume evaluation of translational partition function has been done. The total partition function is the product of individual partition functions such as the translational, rotational, vibrational, electronic, etc. Most of the vibrational modes were treated as quantummechanical harmonic oscillators. Chuang and Truhlar [31] developed the hindered-rotor approximation that has been employed to determine the partition function of belonging to lower vibration modes corresponding to hinder rotor. The branching ratios of each H abstraction pathway give the individual input towards the overall reaction rate. It is determined applying the following expression: 1/2 =

k1/2 × 100 ktotal

(5)

Reactions might occur concurrently and in certain scenarios even generate same products, thus, experimental determination of partial rate coefficients can be ruled out, leading to availability of experimental data only for overall reactions. Theoretical methods, which have been proved to be reliable, are no less than a boon for the complete understanding of chemical systems. The only convenient criterion for such purpose, in most cases, is the coronation of experimental and computed overall data. The rate constants (in cm3 molecule−1 s−1 ) for H abstraction corresponding to reactions (R1–R5) are found to be 6.60 × 10−14 , 1.25 × 10−12 , 9.24 × 10−13 , 3.54 × 10−13 and 6.80 × 10−13 cm3 molecule−1 s−1 , respectively at 298 K and 1 atm. Mixing or crossover between

8

S. S. BEGUM ET AL.

different pathways would alter the results dramatically, hence, it is assumed that each path is independent of the other. Consequently, the addition of the rate coefficients of each reaction pathway generates the overall rate constant corresponding to the reaction represented by MCH + OH. The rate constant for the overall reaction is calculated (3.27 × 10−12 cm3 molecule−1 s−1 ) at 298 K and 1 atm and it is in fine accord with the experimental value of 9.6 × 10−12 cm3 molecule−1 s−1 as reported by Atkinson [9] and 11.8 × 10−12 cm3 molecule−1 s−1 reported more recently by Ballesteros et al. [10]. The favourable concurrence between the experimental data and computed overall results procured in this attempt supports the attributes of kinetic data that has been obtained. The utilisation of the partial rate constants, obtained from independent reaction path, is also validated by the concurrence of the results. The branching ratios calculated at 298 K for reactions (R1–R5) are 2%, 38%, 28%, 11% and 21%, respectively indicate precisely that H-abstraction from R2 has the most significant contribution to overall rate constant in comparison to the rest of the reaction channels.

branching ratio calculations suggest R2 channel is kinetically more contending than all others. The atmospheric life time of MCH is further computed to be 1.77 days. Data such as the rate constants, branching ratios, atmospheric life-time, is extremely beneficial for thorough thermo-kinetic design of various other atmospheric reactions involving such species.

Acknowledgments Saheen Shehnaz Begum is grateful for the DST-INSPIRE fellowship provided by DST (No: DST/INSPIRE Fellowship/[IF160624]). NKG acknowledges University Grant Commission (UGC), New Delhi for furnishing Dr D. S. Kothari Post-Doctoral Fellowship (Award letter no: F.42/2006(BSR)/CH/14-15/0217). All the authors are thankful to Tezpur University for providing the research facilities.

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

Funding 3.2. Atmospheric implication Estimation of atmospheric lifetime (τeff ) of MCH can be determined by speculating that its eradication from the atmosphere occurs mainly by its reaction with OH radicals. It can be written as [32] eff ≈ τOH

(6)

where = (kOH × [OH])−1 . The global average atmospheric OH radical concentration is taken to be 2.0 × 106 molecules cm−3 [33] and the value calculated for kOH to be 3.27 × 10−12 cm3 molecule−1 s−1 , the lifetime of MCH in the atmosphere is evaluated to be 1.77 days.

4. Conclusions For abstraction of H atom from MCH by OH radicals, investigation has been carried out at CCSD(T)//BHandHLYP/6-311G(d,p) level of theory, to determine the reaction kinetics of the reaction as well as the PES. It has been found that for each reaction channels, R1–R5, the barrier height calculated at CCSD(T) is 3.18, −0.01, 0.82, 1.92 and 0.95 kcal mol−1 , respectively. The thermal rate constant for this reaction at 298 K and 1 atm is computed to be 3.27 × 10−12 cm3 molecule−1 s−1 which is in sound consonance with experimental data available. Based on the results generated during this study, the observation that reaction channel R2, i.e. abstraction of H occurs from –CH site of MCH is the predominant pathway, can be said affirmatively. The

DST-INSPIRE fellowship provided by DST [grant number DST/INSPIRE Fellowship/[IF160624]]; University Grant Commission (UGC), New Delhi [award letter number F.42/2006(BSR)/CH/14-15/0217].

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