Multi-Channel Gas-Phase Unimolecular Decomposition of Acetone

Subscriber access provided by UNIVERSITY OF TOLEDO LIBRARIES

A: Kinetics, Dynamics, Photochemistry, and Excited States

Multi-Channel Gas-Phase Unimolecular Decomposition of Acetone: Theoretical Kinetic Studies Vahid Saheb, and Meymanat Zokaie J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b02423 • Publication Date (Web): 13 Jun 2018 Downloaded from http://pubs.acs.org on June 14, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Multi-Channel Gas-Phase Unimolecular Decomposition of Acetone: Theoretical Kinetic Studies Vahid Saheb* , Meymanat Zokaie Department of Chemistry, Shahid Bahonar University of Kerman, Kerman 76169-14111, Iran Abstract The multi-channel thermal decomposition of acetone is studied theoretically. The isomerization of acetone molecule to its enol form, 1-propene-2-ol, is of especial interest in this research. Steady-state approximation is applied to the thermally-activated species CH3COCH3* and CH2C(CH3)OH*, and by performing some statistical mechanical manipulations, integral expressions for the rate constants for the formation of different products are derived. The geometries of the reactant, intermediate, transition states and products of the reaction are optimized at the MP2(full)/6-311++G(2d,2p) level of theory. More accurate energies are evaluated by single point energy calculations at the CBS-Q, G4 and CCSD(T,full)/augh-cc-pVTZ+2df levels of theory. In order to account correctly for vibrational anharmonicities and tunneling effects, microcanonical rate constants for various channels are computed by using semi-classical transition state theory. It is found that the isomerization of CH3COCH3 to the enol-form CH2C(CH3)OH plays an important role in the unimolecular decomposition reaction of CH3COCH3. The possible products originating from unimolecular decomposition of CH3COCH3 and CH2C(CH3)OH are investigated. It is revealed from present computed rate coefficients that the dominant product channel is the formation of CH2C(CH3)OH at low temperatures and high pressures due to the low barrier height for the isomerization process CH3COCH3 → CH2C(CH3)OH. However, at high temperatures and low pressures, the product channel CH3 + CH3CO becomes dominant. Also, the roaming product channels CH2CO + CH4

and C2H6 + CO could be important at high temperatures. 1. Introduction *

Corresponding author. Tel.: +98 34 33257433; fax: +98 34 33257433. E-mail address: [email protected]

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The thermal unimolecular reaction of acetone has been the subject of many experimental and theoretical studies due to its importance from both practical and theoretical standpoints.19

Many studies on the decomposition reaction of acetone are on the basis of the mechanism

proposed by Rice and Herzfeld in which the initiation reaction is C-C bond dissociation to CH3CO + CH3.2-9 During last few years, many theoretical studies have been performed on “roaming mechanism” as a new pathway in unimolecular decomposition reactions. In “roaming mechanism”, a dissociation fragment roams around other fragment for some time to make an abstraction reaction. Experimental evidences for the significance of the roaming pathways in the decomposition of CH3COCH3 forming CH4 + CH2CO and C2H6 + CO have been obtained from the photodissociation dynamics of acetone.10-11 The similar unimolecular decomposition reaction of acetaldehyde has also been the subject of many discussions and controversies. Although early theoretical and experimental kinetic studies have proposed the C-C bond dissociation of CH3CHO to CH3 + CHO as the kinetically significant initiation channel, but recent experimental measurements by sensitive apparatus and more sophisticated theoretical studies on the potential energy surface (PES) of CH3CHO12-18 have shown that other reaction paths may be important. Observation of considerable amount of the molecular product CH4 + CO in recent photodissociation and high-temperature shock-tube studies of CH3CHO have led to the proposal of the possibility of an active “roaming” mechanism.12-16 Nonetheless, by using a microtubular reactor equipped with sensitive detectors, Vasiliou and coworkers did not detect CH4 in the pyrolysis of CH3CHO and its deuterated isotopologues .16-17 Their observations raised doubts about the validity of the “roaming” pathway for CH4 formation. Instead, they detected CH3, CO, H, H2, CH2CHOH (vinyl alcohol), CH2CO (ketene), C2H2 and H2O. On the basis of their observations, they suggested that vinyl alcohol is an important reaction intermediate and


Page 2 of 36

Page 3 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


CH2CO, CH2CHOH, H2O and C2H2 are formed from the unimolecular decomposition of vinyl alcohol. Sivaramakrishnan et al. have attempted to answer to some paradoxes in the mechanism of the thermal unimolecular decomposition of CH3CHO by exploring the PES of the unimolecular reaction of CH3CHO and the subsequent reactions of CH3CHO and CH2CHOH with H atom.18 By modeling the overall reaction, they concluded that keto-enol tautomerization of CH3CHO to CH2CHOH could be an important process at high temperature. A recent theoretical study on the multi-channel thermal decomposition of acetaldehyde by our research group has revealed that CH3CHO ⇄ CH2CHOH process is indeed an important process.19 To date, all experimental and theoretical studies on the elementary unimolecular decomposition of acetone are concentrated on its dissociation to CH3CO + CH3. As mentioned above, recent experimental studies on the CH3COCH3 and the similar molecule, CH3CHO, reveal that other reaction paths could be of importance in the kinetics of the unimolecular reaction of acetone. In this research, the multi-channel elementary unimolecular decomposition reaction of acetone is studied theoretically. Here, it is attempted to consider all important reaction paths in statistical rate calculations. The CH3COCH3 ⇄ CH2C(CH3)OH isomerization process, the roaming CH4 + CH2CO and C2H6 + CO reaction paths have been of especial interest. After calculating the geometrical parameters and energies by ab initio methods, the thermal rate coefficients for various product channels are computed by using statistical rate theories. It is noteworthy to mention here that quasi-classical trajectory calculations are mostly used to investigate the kinetics of roaming pathways. Nonetheless, Klippenstein et al. have shown that statistical rate theories could be employed to compute the rate coefficients for roaming if accurate state counting procedures for the low frequency motions are used.20 3 ACS Paragon Plus Environment


Computational details Electronic-Structure Calculations: In this research, the geometries of all stationary points, i. e., minimum energy structures and saddle points are fully optimized by using second-order Møller-Plesset perturbation theory (MP2)21 method with the standard 6-311++G(2d,2p) basis set. Harmonic vibrational frequencies and xij vibrational anharmonicity coefficients of the optimized geometries, necessary for kinetic calculations, are calculated at the same level of theory. Higher levels of theory are employed to carry out more accurate energies. On the MP2/6-311++G(2d,2p) optimized geometries, single-point energy calculations at the CBSQ,22 G423 and uCCSD(T)/augh-cc-pVTZ+2df levels of theory are performed. UCCSD(T) stands for unrestricted coupled cluster method with single, double, and noniterative triple excitations.24 In Augh-cc-pVTZ+2df basis set25, presented by Martin and de Oliveira, d- and f-type basis functions with high exponents are added to aug-cc-pVTZ26 basis set so that innershell correlation effects are more properly described. In MP2 and CCSD(T) calculations, all electrons are included in the correlation calculations. The Gaussian 09 package of programs27 is employed to carry out all of the ab initio electronic-structure calculations. Kinetics calculations:

According to the Lindemann-Christiansen mechanism, a

unimolecular reaction occurs via a thermally activated intermediate and the following equation could be used to compute the first-order rate coefficient.28,29 exp− ∗ ⁄ ∗ ‡ = 1 ℎ 1 + ∗ ⁄! ∞

"

where E* is the total energy of a given reactant in its active modes. W(E+) is the sum of quantum states of transition state, k(E*) is the rate constant for decomposition of energized


Page 4 of 36

Page 5 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


molecule to product. ω is the rate constant for de-energization of the thermally activated intermediate and defined as ! = #$ % [']

(2)

In the above equation, βc is the collision efficiency coefficient for deactivation process, Z is collision frequency, and [M] is bath gas concentration. The following expression is derived by Troe30 for βc: #$ = 〈∆〉,-. ⁄〈∆〉,-. /0

(3)

where 〈∆〉,-. is the average energy transferred downward from thermally-activated reactant molecules to bath gas and FE is the energy dependence of the density of states. Here, by comparison with similar systems, a value of 130 cm-1 is taken from literature.31 As it is explained in the next section, the thermal unimolecular reaction of acetone proceeds through the formation of two activated intermediates (acetone and its enol isomer), each of which leads to different products. By a similar statistical mechanical manipulations for deriving equation 1, rate constant expressions for the formation different products are obtained. The derived expressions are explained in detail in the next section. k(E) in equation 1 could be calculated by RRKM statistical rate theory.28,29 According to RRKM theory, the energy-specific rate coefficient for the unimolecular decomposition reaction of a molecule having a total non-fixed energy E is given by =

12 4

ℎ 3

where L is the statistical factor, h is Plank’s constant, W(E+vr) is the sum of active vibrational and internal rotational states for the transition state, ρ(E) is the density of quantum states for reactant, Q1 and Q1+ are the partition functions for the adiabatic rotations in reactant and 5 ACS Paragon Plus Environment


transition state, respectively. Although RRKM theory has been employed successfully for calculating the rate coefficients of many elementary unimolecular reactions, but tunneling effects and vibrational anharmonicities are not properly treated in many conventional use of this theory. Both latter drawbacks of RRKM theory are properly treated in SCTST approach.32-35 In SCTST, developed by Miller and colleagues,32-35 W(E+vr) is replaced by G(E+vr), the cumulative reaction probability (CRP). The CRP is given by the following equation: 51‡ 1 = 6 6 … 6 6 8 1 5 < =

:;= :;
?@[2BC, ]

θ(n,T) is the barrier penetration integral which is related to harmonic vibrational frequencies and xij vibrational anharmonicity coefficients of the transition states according to following equations: BC, =

F∆ ΩG

1 + H1 +

2

4?GG ∆ ⁄ΩG

7

GQ

GQ GQ

LR

LR ORL

1 1 1 ∆ = ∆J" + K" − + 6 !L MCL + N + 6 6 ?LO MCL + N MCO + N 8 2 2 2 GQ

1 ΩG = ! SG − 6 ?̅LG MCL + N 9 2 LR

! SG = −V!G and

?̅LG = −V?LG 10

In eqs 5-7, F is the number of vibrational modes of the transition state and ωk is the 6 ACS Paragon Plus Environment

Page 6 of 36

Page 7 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


corresponding harmonic vibrational frequencies, ωF is the imaginary frequency of the saddlepoint, xkl’s are the matrix elements of vibrational anharmonicity constants for the vibrational modes orthogonal to the reaction coordinate, xkF’s are the anharmonicity constant matrix elements corresponding to the coupling between the reaction coordinate and the orthogonal degrees of freedom, xFF is the anharmonicity constant for the reaction coordinate. ∆E is the difference between the total energy and the vibrational energy at the transition state, and ∆V0 is the classical barrier height. The term ε0 is included due to thermochemical considerations. Miller’s formalism of SCTST has been computationally demanding and only applicable for small systems. Barker and co-workers36-39 have employed the Basire et al. algorithm40 for computing the density of states and CRPs. Basire and coworkers have considered the vibrations as a fully coupled anharmonic system and used a perturbation theory expansion to calculate quantum density of states. The Basire et al. have in turn employed the Wang and Landau’s Monte Carlo algorithm41,42 using a random walk in energy space to obtain an accurate number of states for classical statistical models. Barker’s modified SCTST algorithm is applicable to transition states with more than ten atoms. SCTST is a powerful method because the coupling between the vibrations in the saddle-point including reaction coordinate and multidimensional quantum mechanical tunneling are properly treated. In this research work, the useful codes of ADENSUM, SCTST and KTOOLS included in the MULTIWELL program package43, created by Barker and colleagues, are used for calculating the rate coefficients. ADENSUM is used to compute the rate densities of states for CH3COCH3 and 1-propene-2-ol. The CRPs for transition states are computed by employing SCTST code. As it is discussed in next section, some reaction channels proceed via roaming transition states. It is found that the PES is relatively flat around these transition states. Therefore, 20 points along the minimum energy path around these saddle-point geometries 7 ACS Paragon Plus Environment


are selected and the structure with the minimum sum of states (critical configuration)28 is explored by implementing KTOOLS program in MULTIWELL. All low frequency vibrations corresponding to hindered internal rotations are treated by a ro-vibrational G matrix-based algorithm

44-45

. The computed effective reduced masses and energies along the

hindered internal rotations are fitted by Fourier series and their corresponding sums of states are included in total sum of states.19 The above-mentioned theory is just applicable for estimating the sum of states of a tight transition state. As it will be shown in the next sections, two distinct channels of bond breaking is considered in the acetone decomposition leading to the products sets of CH3 + CH3CO and H + CH3COCH2. Such reactions proceeding through loose transition states can be treated by special theories. In the present work, VRC-TST46-51 is employed to calculate microcanonical rate coefficients for C-C and C-H bond breaking channels. According to this theory, the vibrational degrees of freedom can be divided into two sets of modes: transitional and conserved. The essence of transitional modes changes through the dissociation, while that of the conserved ones will be nearly unchanged. Having divided the coordinates into two sets, , X 12 the sum of active vibrational and rotational states for the transition state at a

determined J, is written as 0`

X 12 = Y" Z[ \ − ]ΩX ]d ] 11

In above equation, Z[ \ − ] is the number of quantum states for the conserved modes having an energy equal to or less than \ − ] where ′ is the accessible energy; i.e., minus the zero point corrected potential energy minimum at a specific value of reaction coordinate. ΩX ] d] is the number of states corresponding to the transitional modes at the given b and lies in ], ] + d]. Z[ and ΩX are respectively computed by the direct-count method and


Page 8 of 36

Page 9 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Mont Carlo procedures. A proper potential model, which describes the interactions of separating moieties, is required to evaluate X 12 . The sum of a bonding potential for the

bond scission and a nonbonded term for the inter-fragment potential would be a suitable potential model. J = Jd + Jed 12 The interactions between the nonbonded atoms are considered as van der Waals interactions and a sum of 6-12 Lennard-Jones potentials are employed for the nonbonded potential.50 Jed = ∑\,g 4]g h

ijk 2jk

−

ijk l m 13 2jk

Here, i and j are the labels for the atoms of the CH3 and COCH3 fragments, respectively. The εij and σij are the corresponding Lennard-Jones parameters. The prime shows that the atoms of C-C bond are not included in the summation. A Varshni equation is used to approximate the bonding potential describing the C-C and C-H breaking bonds. An orientation factor is also included in the potential to account the angular dependence of bonding potential energy according to the following equations. Jd = J1 opq r B − Bs opq B − Bs 14 2

J1 = t1 − u v w exp[−# x − xs ] − t 15 2

where J1 refers to the Varshni potential, B and B denote the bonding angles between a reference axes in the separating fragments and the bonding axis, and Bs and Bs are the equilibrium values; m and n are adjustable values. In eq 15, t and xs are bond dissociation energy and equilibrium bond distance, respectively, and # is an adjustable parameter. To carry out the VRC-TST calculations, the Variflex code has been used.51 9 ACS Paragon Plus Environment


Results and discussion On the basis of the optimized geometries and computed energies in the present electronicstructure calculations, the multi-channel unimolecular reaction of acetone could be presented by the following Lindeman-Christiansen type mechanism:


Page 10 of 36

Page 11 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ka

CH3COCH3 + M CH3COCH3* CH3COCH3* CH3COCH3* CH3COCH3* CH3COCH3* CH3COCH3*

k1 k2 k3A k3B k4 ki

OH

CH2CCH3

k6

CH3COCH3* + M CH3CO + CH3

(P1)

CH3COCH2 + H

(P2)

CH4 + CH2CO

(P3A)

CH4 + CH2CO

(P3B)

CO + C2H6

(P4)

CH2CCH3*

k-i

CH2CCH3* + M *

kd

OH

k5

(P5)

CH2CCH3 + M OH

CH2CCH2 + H2O

(P6)

CH3CCH + H2O

(P7)

CH2CO + CH4

(P8)

CH2COCH2 + H2

(P9)

OH

CH2CCH3*

k7

OH

CH2CCH3*

k8

OH

CH2CCH3*

k9

OH

The unimolecular decomposition of CH3COCH3 may occur via C-C and C-H bond dissociation reactions to give CH3CO + CH3 (P1) and CH3COCH2 + H (P2), respectively. Both latter reactions are barrierless processes and the C-C and C-H bond dissociation energies are computed to be 351.1 kJ mol-1 and 402.8 kJ mol-1, respectively. CH3COCH3 could decompose to yield CH4 + CH2CO (P3A) by passing through a tight saddle-point structure called TS3A. In this process, the H atom of one methyl functional group shifts to the C atom of the other CH3 group, and C-C bond dissociates simultaneously. The barrier height



for this process is 366.7 kJ mol-1 and the energy of the products (CH4 + CH2CO) is 92.1 kJ mol-1 higher than the reactant. CH4 + CH2CO may also be formed via a relatively loose transition state named TS3B. In the transition state TS3B, the C-C bond is extensively stretched and virtually broken. The unloosed CH3 group makes a roaming motion for some time to abstract the H-atom from the separating CH3CO group and form CH4 + CH2CO (P3B). Here, the barrier height for the latter reaction is computed to be 355.1 kJ mol-1. Another roaming reaction path is also studied in which the unloosed CH3 group attacks to the methyl group of CH3CO backward to form C2H6 + CO (P4). The barrier height of this SN2like reaction channel is 383.2 kJ mol-1 and the energy of the products relative to reactant is +25.7 kJ mol-1. CH3COCH3 could also isomerize to 1-propene-2-ol, syn-Enol, via TSi. The barrier height for this reaction channel is computed to be 273.6 kJ mol-1 and the energy of CH2C(CH3)OH is 48.3 kJ mol-1 higher than CH3COCH3. The chemically-activated intermediate CH2C(CH3)OH could in turn undergo some unimolecular decomposition reactions. It may isomerize back to CH3COCH3 (with the barrier height of 225.3 kJ mol-1) or undergo two H2O-elimination reactions to give CH2CCH2 + H2O (P6) and CH3CCH + H2O (P7). The reaction paths leading to P6 and P7 pass through saddle-point structures TS6 and TS7, respectively, with energies of 336.5 and 333.7 kJ mol-1 higher than syn-Enol. The energy of the products P6 and P7 are 116.1 and 114.1 kJ mol-1 higher than syn-Enol. The chemicallyactivated intermediate syn-Enol is converted to its conformational isomer, anti-Enol, by rotation of OH group about C-O bond. The barrier height for this conversion (relative to the syn-Enol) is found to be 17.9 kJ mol-1. Therefore, it is concluded that syn-Enol is easily converted to anti-Enol. The energy of anti-Enol is obtained to be equal with the reactant, CH3COCH3. Next, anti-Enol decomposes to yield CH4 + CH2CO (P8) through TS8 with an


Page 12 of 36

Page 13 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


energy of 393.8 kJ mol-1 higher than anti-Enol. It should be mentioned that the products of the reaction paths P3A, P3B and P8 are the same. The structures of reactant, intermediates and transition states are demonstrated in Figure 1. Figure 1 shows the singlet potential energy profile of the unimolecular decomposition of acetone, calculated at the CCSD(T)/Augh-cc-pVTZ+2df level. As aforementioned, all of the energies are also computed at the CBS-Q and G4 levels of theory for the purpose of comparison. The calculated energies by different electronic-structure calculation methods are provided in Table 1. It is seen that the computed energies at the CBS-Q and G4 levels of theory are in accordance with those computed at the CCSD(T)/Augh-cc-pVTZ+2df level. T1 diagnostic52 values for the reactant, intermediate and transition states are also reported in Table 1. The low values of T1 diagnostics indicates a single-reference electron correlation method is enough for the present calculations. It is noteworthy that Zhou and coworkers53 have studied the unimolecular decomposition of propene-2-ol by RRKM theory. The PES of unimolecular reaction of propene-2-ol is essentially the same as that for acetone. Zhou et al. have explored the PES at the CCSD(T)/6-311+G(3df,2p) //B3LYP/6-311G(d, p) level of theory. The relative energies of species involved in the present research are re-produced on the basis of the latter calculations and are given in Table 1 for the purpose of comparison. As can be seen, the energies computed in the present research, at the CCSD(T)/Augh-ccpVTZ+2df//MP2(full)/6-311++G(2d,2p) level of theory, are in good agreement with the data computed by Zhou et al. By applying the steady-state approximation to the thermally-activated species [CH3COCH3*] and [CH2C(CH3)OH *], and statistical thermodynamic treatment of the internal active modes, the following equations are derived for the first-order rate coefficients of different products:19



~

y

‡ exp −1 ⁄d 1 ! 5,1 ‡ = 16 ! + + + + z{ + zd + | − Q } ℎ

y

‡ exp −1 ⁄d 1 ! 5,1 ‡ = 17 ! + + + + z{ + zd + | − Q } ℎ

"

~

"

~

yz{

‡ exp −1 ⁄d 1 ! 5z{,1 ‡ = 18 ! + + + + z{ + zd + | − Q } ℎ

yzd

‡ exp −1 ⁄d 1 ! 5zd,1 ‡ = 19 ! + + + + z{ + zd + | − Q } ℎ

"

~

"

~

y|

‡ exp −1 ⁄d 1 ! 5|,1 ‡ = 20 ! + + + + z{ + zd + | − Q } ℎ

y

‡ exp −1 ⁄d 1 ! } 5,1 ‡ = 21 ! + + + + z{ + zd + | − Q } ℎ

yl

‡ exp −1 ⁄d 1 ! l } 5,1 ‡ = 22 ! + + + + z{ + zd + | − Q } ℎ

y

‡ exp −1 ⁄d 1 ! } 5,1 ‡ = 23 ! + + + + z{ + zd + | − Q } ℎ

y

‡ exp −1 ⁄d 1 ! } 5,1 ‡ = 24 ! + + + + z{ + zd + | − Q } ℎ

"

~

"

~

"

~

"

~

"

‡ ’ In equations 16 to 24, ki’s are microcanonical rate constants, 5,1 s are CRPs for the transition

states of the unimolecular reactions. S1 and S2 are given by the following relations: } = } 25 14 ACS Paragon Plus Environment

Page 14 of 36

Page 15 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


} = Q + ! + l + + Q 26 The derivation of the formula 16 to 24 and computed anharmonicity constant matrices for CH3COCH3, CH2C(CH3)OH and saddle-point geometries are provided in Supporting Information. In the present theoretical research work, it is attempted to have correct estimations of the sums of quantum states for transition states TS1 and TS2 (C-C and C-H bond dissociation channels), TS3B and TS4. For transition states TS3B and TS4 (roaming pathways), by using KTOOLS program in MULTIWELL, the structure with the minimum sum of states (critical configuration)28 is determined among 20 points along the minimum energy path around saddle-point geometry. Low frequency vibrations in these transition states are considered as hindered internal rotations and the effective reduced masses (and the corresponding sum of states) are computed by the ro-vibrational G matrix-based algorithm.4748

The sum of states for the C-C and C-H bond dissociation processes are computed by

employing equations (11) to (15). The parameters of Varshni equation, i. e., D, re and β for the reaction channel P1 are found to be 29332 cm-1, 1.50 Å and 0.32 Å-2, respectively. The corresponding values for the reaction channels P2 are 33651 cm-1, 1.09 Å and 0.46 Å-2, respectively. The computed rate coefficients for different products as a function of pressure at 500, 800, 1500 K and 2000 K are demonstrated in Figure 3. It is revealed from the present calculations that the products CH3CO + CH3 (P1) or CH2C(CH3)OH (P5) are the dominant product channels at all temperatures and pressures. Figure 3 shows that 1-propene-2-ol is the dominant product at lower temperatures. However, the rate coefficient for the product CH3CO + CH3 increases with a higher acceleration as temperature rises so that the reaction channel CH3CO + CH3 becomes dominant at elevated temperatures. The reaction channel P3B, CH4 + CH2CO, have a small contribution to overall rate constant at high temperature. The branching ratio for the latter reaction channel changes from 5 × 10-5 at 500 K to 0.01 at 15 ACS Paragon Plus Environment


2000 K. As aforementioned, CH4 + CH2CO is produced via three different reaction channels (P3A, P3B and P8). The rate constants for all these reaction channels along with the overall rate constant for the product CH4 + CH2CO are plotted in Figure 3. The product channel C2H6 + CO (P4) have a minor contribution at high temperature (the branching ratio of 0.001 at 2000 K). The product CH2CCH2 + H2O (P6) and CH3CCH + H2O (P7) are produced negligibly over all pressure and temperature ranges. The computed rate constants as a function of temperature for pressures 10, 500 and 2000 Torr are illustrated in Figure 4. These plots clearly show that at temperatures below about 1000 K, the dominant product is CH2C(CH3)OH formed from the isomerization of CH3COCH3. At high temperatures, CH3CO + CH3 (P1) is the dominant product channel. This result is reasonable because the barrier height for the isomerization process CH3COCH3 → CH2C(CH3)OH is relatively lower than other product channels arising from CH3COCH3. As a consequence, the barrier for the process CH3COCH3 → CH2C(CH3)OH could be more easily surmounted by the thermally-activated molecules CH3COCH3*, especially at lower molecular energies (lower temperatures). As aforementioned, the dissociation reaction channel CH3CO + CH3 occurs via a loose transition state. It is predicted that the latter dissociation process becomes dominant at higher temperatures due to its higher entropy of activation. Such processes shows high pre-exponential factors in their Arrhenius expressions. Recently, a similar conclusion has been reached on the unimolecular thermal reaction of acetaldehyde.17 To date, all experimental data are reported on the rate coefficient for the formation of CH3CO + CH3. The thermal rate constants for the formation of CH3CO + CH3 from unimolecular decomposition of acetone computed over temperature between 500 to 2000 K (P=500 Torr) are demonstrated in Figure 5. The available experimental data are also given for the purpose of comparison. As can be seen, the present computed rate constants are in good agreement with the most of the available experimental data. The present calculated rate 16 ACS Paragon Plus Environment

Page 16 of 36

Page 17 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


constants are underestimated at high temperatures in comparison with the value reported by Ernst et al.6 The present predicted rate coefficients reveals some new fact on the unimolecular dissociation of acetone. Here, it is shown that 1-propene-2-ol is indeed an important intermediate in the decomposition of acetone. In fact, that is the dominant product at lower temperature. Also, the products CH2CCH2 + H2O and CH3CCH + H2O originating from 1propene-2-ol could be observed at high temperatures. This fact is in accordance with the recent experimental observations of Vasiliou et al.16-17 and our previous theoretical investigation on the thermal decomposition of acetaldehyde.19 The computed rate coefficients show that the roaming pathways CH4 + CH2CO and C2H6 + CO are important channels especially at higher temperatures. The numerical values of the computed rate constants for the formation of various products for some selected temperatures at the pressures 10, 500 and 2000 Torr are given in the Supporting Information. It is attempted to present extended Arrhenius expressions for the computed rate coefficients of several product channels. The extended Arrhenius parameters for the rate coefficients of different products, at pressure 500 Torr, are provided in Table 2. The parameters of extended Arrhenius parameters for the pressures 10 and 2000 Torr are also given as Supporting Information. The branching ratios at 500 Torr for the product CH4 + CH2CO, relative to the product channel CH3CO + CH3, change from 5×10-5 at 500 K to 1.3×10-2 at 2000 K. The corresponding values for the product C2H6 + CO are found to be 6.2 ×10-8 and 1.7×10-3, respectively. These values of branching ratios show that the roaming product channels CH3CO + CH3 and C2H6 + CO could be important at high temperatures. The products CH2CCH2 + H2O and CH3CCH + H2O, originating from 1-propene-2-ol, has a minor contribution to the overall rate constant.



Conclusion In this theoretical research work, the multichannel unimolecular reaction of acetone is studied by statistical rate theories. The energies of molecular species and parameters necessary for kinetics calculations are computed by quantum-chemical calculations. In order to account suitably for vibrational anharmonicities and tunneling effect for reaction channels proceeding via tight transition states, SCTST is employed for calculating the microcanonical unimolecular rate coefficients. The rate constants for the dissociation channels CH3CO + CH3 and CH3COCH2 + H are computed by using VRC-TST. It is shown that due to the low barrier for the isomerization process CH3COCH3 → CH2C(CH3)OH in comparison with other possible unimolecular reaction channels, this process plays an important role in the kinetics of the unimolecular decomposition of CH3COCH3. The present calculations reveal that the enol-form of acetone, CH2C(CH3)OH, is the dominant product at low temperatures. At high temperatures, the rate of dissociation CH3COCH3 to CH3CO + CH3 becomes dominant. The formation of other products, especially CH4 + CH2CO and C2H6 + CO, become important at high temperatures. This theoretical study encourages further experimental studies on the unimolecular decomposition of acetone.

Acknowledgments We are grateful to Shahid Bahonar University of Kerman Research Council for the financial support of this research.


Page 18 of 36

Page 19 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Supporting Information The geometries, vibrational frequencies and moments of inertia for all species, numerical values of the computed rate coefficients, and the Arrhenius parameters and anharmonicity matrixes. This material is available free of charge via the Internet at http://pubs.acs.org.



References (1) Kohse-Hoinghaus, K.; Oswald, P.; Cool, T. A.; Kasper, T.; Hansen, N.; Qi, F.; Westbrook, C. K.; Westmoreland, P. R. Biofuel Combustion Chemistry: From Ethanol to Biodiesel. Angew. Chem. Int. Ed. 2010, 49, 3572−3597. (2) Rice, F. O.; Herzfeld, K. F. The Thermal Decomposition of Organic Compounds from the Standpoint of Free Radicals. VI. The Mechanism of Some Chain Reactions. J. Am. Chem. Soc. 1934, 56, 284−289. (3) Szwarc, M.; Taylor, J. W. Pyrolysis of Acetone and the Heat of Formation of Acetyl Radicals. J. Chem. Phys. 1955, 23, 2310-2314. (4) Clark, D.; Pritchard, H. O. Arrhenius Parameters of Some Reactions Involving Multiplicity Changes. J. Chem. Soc. London 1956, 2136-2140. (5) Ernst, J.; Spindler, K. Untersuchungen zum Thermischen Zerfall von Acetaldehyd und Aceton. Ber. Bunsenges. Phys. Chem. 1975, 79, 1163−1168. (6) Ernst, J.; Spindler, K.; Wagner, H. Gg. Untersuchungen zum Thermischen Zerfall von Acetaldehyd und Aceton. Ber. Bunsenges. Phys. Chem. 1976, 80, 645-650. (7) Mousavipour, S. H.; Pacey, P. D. Initiation and Abstraction Reactions in the Pyrolysis of Acetone. J. Phys. Chem. 1996, 100, 3573-3579. (8) Sato, K.; Hidaka, Y. Shock-Tube and Modeling Study of Acetone Pyrolysis and Oxidation. Combust. Flame 2000, 122, 291-311.


Page 20 of 36

Page 21 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(9) Wang, S.; Sun, K.; Davidson, D. F.; Jeffries, J. B.; Hanson, R. K. Shock-Tube Measurement of Acetone Dissociation Using Cavity-Enhanced Absorption Spectroscopy of CO. J. Phys. Chem. A 2015, 119, 7257-7262. (10) Goncharov, V.; Herath, N.; Suits, A. G. Roaming Dynamics in Acetone Dissociation. J. Phys. Chem. A 2008, 112, 9423–9428. (11) Lee, K. L. K.; Nauta, K.; Kable; S. H. Photodissociation of Acetone from 266 to 312 nm: Dynamics of CH3 + CH3CO Channels on the S0 and T1 States. J. Chem. Phys. 2017, 146, 044304, 1-12. (12) Houston, P. L.; Kable, S. H. Photodissociation of Acetaldehyde as a Second Example of the Roaming Mechanism. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 16079−16082. (13) Sivaramakrishnan, R.; Michael, J. V.; Klippenstein, S. J. Direct Observation of Roaming Radicals in the Thermal Decomposition of Acetaldehyde. J. Phys. Chem. A 2010, 114, 755−764. (14) Harding, L. B.; Georgievskii, Y.; Klippenstein, S. J. Roaming Radical Kinetics in the Decomposition of Acetaldehyde. J. Phys. Chem. A 2010, 114, 765−777. (15) Shepler, B. C.; Braams, B. J.; Bowman, J. M. “Roaming” Dynamics in CH3CHO Photodissociation Revealed on a Global Potential Energy Surface. J. Phys. Chem. A 2008, 112, 9344−9351. (16) Vasiliou, A.; Piech, K. M.; Zhang, X.; Nimlos, M. R.; Ahmed, M.; Golan, A.; Kostko, O.; Osborn, D. L.; Daily, J. W.; Stanton, J. F.; Ellison, G. B. The Products of the Thermal Decomposition of CH3CHO. J. Chem. Phys. 2011, 135, 014306.



(17) Vasiliou, A.; Piech, K. M.; Reed, B.; Zhang, X.; Nimlos, M. R.; Ahmed, M.; Golan, A.; Kostko, O.; Osborn, D. L.; David, D. E.; et al. Thermal Decomposition of CH3CHO Studied by Matrix Infrared Spectroscopy and Photoionization Mass Spectroscopy. J. Chem. Phys. 2012, 137, 164308. (18) Sivaramakrishnan, R.; Michael, J. V.; Harding, L. B.; Klippenstein, S. J. Resolving Some Paradoxes in the Thermal Decomposition Mechanism of Acetaldehyde. J. Phys. Chem. A 2015, 119, 7724−7733. (19) Saheb, V.; Hashemi, S. R.; Hosseini, S. M. A. Theoretical Studies on the Kinetics of Multi-Channel Gas-Phase Unimolecular Decomposition of Acetaldehyde. J. Phys. Chem. A 2017, 121, 6887–6895. (20) Klippenstein, S. J.; Georgievskii, Y.; Harding, L. B. Statistical Theory for the Kinetics and Dynamics of Roaming Reactions. J. Phys. Chem. A. 2011, 115, 14370−14381. (21) Møller, C.; Plesset, M. S. Note on an Approximation Treatment for Many-Electron Systems. Phys. Rev. 1934, 46, 618-622. (22) Montgomery, Jr., J. A.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VI. Use of Density Functional Geometries and Frequencies. J. Chem. Phys. 1999, 110, 2822-2827. (23) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-4 Theory. J. Chem. Phys. 2007, 126, 084108:1-12. (24) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. A Fifth-Order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157, 479483.


Page 22 of 36

Page 23 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(25) Martin, J. M. L.; de Oliveira, G. Towards Standard Methods for Benchmark Quality Ab Initio Thermochemistry-W1 and W2 Theory. J. Chem. Phys. 1999, 111, 1843-1856. (26) Kendall, R. A.; Dunning, T. H.; Harrison, R. J. Electron Affinities of the First‐Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96, 67966806. (27) Frisch, M. J.; Trucks, G.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. (28) Holbrook, K.; Pilling, M.; Robertson, S. Unimolecular Reactions; John Wiley & Sons, Inc.: Chichester, U. K., 1996. (29) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell Scientific: Oxford, U. K., 1990. (30) Troe, J. Theory of Thermal Unimolecular Reactions at Low Pressures. I. Solutions of the Master Equation. J. Chem. Phys. 1977, 66, 4745−4757. (31) Seakins, P. W.; Robertson, S. H.; Pilling, M. J.; Slagle, I. R.; Gmurczyk, G. W.; Bencsura, A.; Gutman, D.; Tsang, W. Kinetics of the Unimolecular Decomposition of Isopropyl: Weak Collision Effects in Helium, Argon, and Nitrogen. J. Phys. Chem. 1993, 97, 4450-4458. (32) Miller, W. H. Semiclassical Limit of Quantum Mechanical Transition State Theory for Nonseparable Systems. J. Chem. Phys. 1975, 62, 1899-1906. (33) Miller, W. -H. Semi-Classical Theory for Non-Separable Systems: Construction of “Good” Action-Angle Variables for Reaction Rate Constants. Faraday Discuss. Chem. Soc. 1977, 62, 40-46. 23 ACS Paragon Plus Environment


(34) Miller, W. H.; Hernandez, R.; Handy, N. C.; Jayatilaka D.; Willets, A. Ab Initio Calculation of Anharmonic Constants for a Transition State, with Application to Semiclassical Transition State Tunneling Probabilities. Chem. Phys. Lett. 1990, 172, 62-68. (35) Hernandez, R.; Miller, W. H. Semiclassical Transition State Theory. A New Perspective. Chem. Phys. Lett. 1993, 214, 129-136. (36) Nguyen, T. L.; Stanton, J. F.; Barker, J. R. Ab Initio Reaction Rate Constants Computed Using Semiclassical Transition-State Theory: HO + H2 → H2O + H and Isotopologues. J. Phys. Chem. A 2011, 115, 5118−5126. (37) Barker, J. R.; Nguyen, T. L.; Stanton, J. F. Kinetic Isotope Effects for Cl + CH4 ⇌ HCl + CH3 Calculated Using ab Initio Semiclassical Transition State Theory. J. Phys. Chem. A 2012, 116, 6408−6419. (38) Nguyen, T. L.; Barker, J. R. Sums and Densities of Fully Coupled Anharmonic Vibrational States: A Comparison of Three Practical Methods. J. Phys. Chem. A. 2010, 114, 3718-3730. (39) Nguyen, T. L.; Stanton J. F.; Barker, J. R. A Practical Implementation of Semi-Classical Transition State Theory for Polyatomics. Chem. Phys. Lett. 2010, 499, 9-15. (40) Basire, M.; Parneix P.; Calvo, F. J. Quantum Anharmonic Densities of States Using the Wang–Landau Method. J. Chem. Phys. 2008, 129, 081101. (41) Wang, F.; Landau, D. P. Efficient, Multiple-Range RandomWalk Algorithm to Calculate the Density of States. Phys. Rev. Lett. 2001, 86, 2050-2053. (42) Wang, F.; Landau, D. P. Determining the Density of States for Classical Statistical Models:


Page 24 of 36

Page 25 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


A Random Walk Algorithm to Produce a Flat Histogram. Phys. Rev. E 2001, 64, 56101. (43) Barker, J. R.; Ortiz, N. F.; Preses, J. M.; Lohr, L. L.; Maranzana, A.; Stimac, P. J.; Nguyen, T. L.; Kumar, T. J. D. MultiWell-2011.3 Software; Barker, J. R., Ed.; University of Michigan: Ann Arbor, Michigan, U.S.A., 2011; http://aoss.engin.umich.edu/multiwell/. (44) Harthcock, M. A.; Laane, J. Calculation of Kinetic Energy Terms for the Vibrational Hamiltonian: Application to Large-Amplitude Vibrations Using One-, Two-, and ThreeDimensional Models. J. Mol. Spectros. 1982, 91, 300-324. (45) Harthcock, M. A.; Laane, J. Calculation of Two-Dimensional Vibrational Potential Energy Surfaces Utilizing Prediagonalized Basis Sets and Van Vleck Perturbation Methods. J. Phys. Chem. 1985, 89, 4231-4240. (46) Klippenstein, S. J. Implementation of RRKM Theory for Highly Flexible Transition States with a Bond Length as the Reaction Coordinate. Chem. Phys. Lett. 1990, 170, 71-77. (47) Klippenstein, S. J. An Efficient Procedure for Evaluating the Number of Available States within a Variably Defined Reaction Coordinate Framework, J. Phys. Chem. 1994, 98, 1145911464. (48) Wardlaw, D. M.; Marcus, R. A. Unimolecular Reaction Rate Theory for Transition States of any Looseness. 3. Application to Methyl Radical Recombination. J. Phys. Chem. 1986, 90, 5383-5393. (49) Wardlaw, D. M.; Marcus, R. A. RRKM Reaction Rate Theory for Transition States of Any Looseness. Chem. Phys. Lett. 1984, 110, 230-234. (50) Klippenstein, S. J.; Khundkar, L. R.; Zewail, A. H.; Marcus, R. A. Application of Unimolecular Reaction Rate Theory for Highly Flexible Transition States to the Dissociation of NCNO into NC and NO. J. Chem. Phys. 1988, 89, 4761-4770.



(51) Klippenstein, S. J.; Wagner, A. F.; Dunbar, R. C.; Wardlaw, D. M.; Robertson, S. H. VARIFLEX: VERSION 1.00, 1999. (52) Lee, T. J.; Taylor, P. R. A Diagnostic for Determining the Quality of Single-Reference Electron Correlation Methods. Int. J. Quantum Chem., Quant. Chem. Symp. 1989, S23, 199207. (53) Zhou, C. W.; Li, Z. R.; Liu, C. X.; Li, X. Y. An ab initio/Rice–Ramsperger–Kassel– Marcus prediction of rate constant and product branching ratios for unimolecular decomposition of propen-2-ol and related H + CH2COHCH2 reaction. J. Chem. Phys. 2008, 129, 234301-9.


Page 26 of 36

Page 27 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure captions Figure 1. The geometries of reactant, enol intermediate and transition states calculated at the MP2(full)/6-311+G(2d,2p) level of theory. Figure 2. Relative energies of the stationary points located on the singlet ground-state potential energy surface of the unimolecular reaction of acetone. The energy values are given in kJ mol-1 and are calculated at the CCSD(T)/Augh-cc-pVTZ+2df//MP2(full)/6311+G(2d,2p) level. Figure 3. Dependence of the unimolecular rate constants for different reaction paths of the unimolecular decomposition of acetone on pressure at different temperatures. The reaction paths P3A and P3B are shown with different colors. Figure 4. The thermal rate coefficients for the unimolecular decomposition reaction of acetone computed at temperatures in the range of 500-2000 K at different pressures. The reaction paths P3A and P3B are shown with different colors. Figure 5. The thermal rate coefficients for the unimolecular decomposition of acetone to CH3CO + CH3 computed over temperature range of 500-2000 K. Experimental data are given for the purpose of comparison.



Table captions Table 1. The relative energies of the stationary points to their reactants, computed at various levels of theory in kJ mol-1. All values are corrected for zero point energies. Table 2. The Extended Arrhenius parameters, k = A. Tn .exp (-E/RT), for different products of the decomposition reaction acetone at the pressure 500 Torr.


Page 28 of 36

1. 37

1.22

8

3

116.9o

3 1.

1. 5 1

1.84

1 .3

1.49 12 5. 4 o

o

8.6 10

1.42

CH2COHCH3

CH3COCH3

o

o

48

96 3. 2 1

TS3B

TS4

1.14

1.60

1.33

1.55

1.6 7 5

1.136

1.702

2. 13

2.147

2.38

1.67 9 1.1

1. 08

1.48

TS3A

1 .4 7

1.484o

152.6o

TS6

TS7 1.60 0.84 1.69

1.84

1 .3

4

141.1 o

1 1. 3

0 1. 3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.39

Page 29 of 36

o

2 8.8 10

TSr

108.0o

TS8

TS9

Figure 1. The geometries of reactant, enol intermediate and transition states calculated at the MP2(full)/6-311+G(2d,2p) level of theory.



500

400

Relative Energy (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 36

TS3Broam

300

TS8

P2

TS4roam

TS6 TS3A

TS7

P1

TSi

200 P6

P3

100

P7

P8 TSr

P4

0

EnolA EnolB

Acetone

Figure 2. Relative energies of the stationary points located on the singlet ground-state potential energy surface of the unimolecular reaction of acetone. The energy values are given in kJ mol-1 and are calculated at the CCSD(T)/Augh-cc-pVTZ+2df//MP2(full)/6311+G(2d,2p) level.


Page 31 of 36

-10

-30

P2 P1

500 K P5

-15

-40

P1 -50

-20

P3B

-25

P4 P3A

-30

P7 P6

-35

P8 P2

-40

P9

-1

ln k / s

ln k / s-1

P3B P3A P4 P7 P6 P8 P2

-60

-70

P9 -80

-45

800 K

-50

-90 0

100

200

300

400

500

600

0

700

100

200

300

400

500

600

15

10

P1 P5

5

P1 P5

10

P3B

P3B

5

0

P4

P4 P3A P7 P6

-5

-10

P8

-15

P9 P2

ln k / s-1

-1

700

P (Torr)

P (Torr)

ln k / s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


P8

-5

P9 -10

1500 K

-20

P3A P7 P6

0

P2

2000 K

-15

-25

-20 0

100

200

300

400

500

600

700

0

100

P (Torr)

200

300

400

500

600

700

P (Torr)

Figure 3. Dependence of the unimolecular rate constants for different reaction paths of the unimolecular decomposition of acetone on pressure at different temperatures. The reaction paths P3A and P3B are shown with different colors.



20

10 Torr

ln k / s-1

0

-20

P5

-40

P1 P3B P3A P4 P7 P6 P8 P2 P9

-60

-80 0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

1000 / (T/K)

500 Torr 0

ln k / s-1

-20

P5

-40

P1 P3B P3A P4P7 P6 P8 P2 P9

-60

-80 0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

1000 / (T/K)

2000 Torr

0

-20

ln k / s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

P5

-40

P1 P3B P3A P4 P7 P6 P8 P2 P9

-60

-80 0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

1000 / (T/K)

Figure 4. The thermal rate coefficients for the unimolecular decomposition reaction of acetone computed at temperatures in the range of 500-2000 K at different pressures. The reaction paths P3A and P3B are shown with different colors.


Page 32 of 36

Page 33 of 36

20 Szwarc et al.1955 10

Clark et al. 1956 Ernst et al.1976 Mousavipour et al.1996 Sato et al. 2000 Wang et al. 2015 computed, 500 Torr

0

-1

ln (k/s )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-10

-20

-30

-40

-50 0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

1000/(T/K) Figure 5. The thermal rate coefficients for the unimolecular decomposition of acetone to CH3CO + CH3 computed over temperature range of 500-2000 K. Experimental data are given for the purpose of comparison.



Table 1. The relative energies of the stationary points to their reactants, computed at various

CCSD(T)† G4‡ CBS-Q‡ CCSD(T)§ T1 diagnostics TSi 274 275 277 0.015 TS3A 367 367 367 0.014 TS3B 355 341 346 0.023 TS4 388 371 374 0.019 TS6 385 386 389 0.013 TS7 382 382 385 0.015 TS8 406 407 407 0.014 TS9 0.010 430 430 428 428 syn-Enol 0.010 48 49 50 54 anti-Enol 54 55 56 72 CH3CO+CH3 (P1) 351 342 350 339 CH3COCH2+H (P2) 403 399 404 CH4+CH2CO (P3/8) 92 86 87 89 C2H6+CO (P4) 26 15 18 H2O+CH2CCH2 (P6) 164 157 160 169 H2O+CH3CCH (P7) 162 154 157 165 CH2COCH2+H2 (P9) 232 227 225 229 CH2COHCH2+H 427 428 427 422 CH2COH+CH3 (P11) 490 480 489 480 CH2CCH3+OH (P12) 511 502 512 501 CHCOHCH3+H 521 522 525 521 levels of theory in kJ mol-1. All values are corrected for zero point energies.

†

The basis set Augh-cc-pVTZ+2df is used for single-point energy calculations and all electrons are

included in correlation calculations. The geometries are optimized at the MP2(full)/6-311+G(2d,2p). ‡

The calculations are performed on the geometries optimized at the MP2(full)/6-311+G(2d,2p) level

of theory. §

Adopted from Ref. 52, computed at the CCSD(T)/6-311+G(3df,2p)//B3LYP/6-311G(d,p) level.


Page 34 of 36

Page 35 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. The Extended Arrhenius parameters, k = A. Tn .exp (-E/RT), for different products of the decomposition reaction acetone at the pressure 500 Torr.

Path P1 P2 P3A P3B P4 P5 P6 P7 P8 P9

A 6.0×1064 5.1×1066 6.6×1052 2.1×1058 2.1×1055 1.1×1038 3.7×1053 6.3×1051 6.5×1047 4.2×1042

n -14.94 -17.78 -12.52 -13.53 -12.79 -7.85 -12.87 -12.26 -11.60 -10.27


E (kJ/mol) 413.43 483.99 426.45 429.48 447.82 315.36 449.73 446.4 454.15 464.96


TOC:

ka CH3COCH3 + M CH3COCH3*

20

CH3COCH3* CH3COCH3* CH3COCH3*

0

k1

k3 k4 ki

CH3COCH3*

-20

500 Torr

kd

k2

CH2C(OH)CH 3*

k6

CH2C(OH)CH 3*

k7

CH3COCH3* + M CH3CO + CH3

(P1)

CH3COCH2 + H

(P2)

CH4 + CH2CO

(P3)

CO + C 2H6

(P4)

CH2C(OH)CH 3*

k-i

CH2C(OH)CH 3*+ M

ln k / s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 36

k5

CH2C(OH)CH3 + M CH2CCH2 + H2O (P6) CH3CCH + H2O (P7)

P5

-40

P1 P3B P3A P4P7 P6 P8 P2 P9

-60

-80 0.4

0.6

0.8

1.0

1.2

1.4

1.6

1000 / (T/K)


1.8

2.0

2.2

Multi-Channel Gas-Phase Unimolecular Decomposition of Acetone

Recommend Documents