Ab initio kinetics for isomerization reaction of normal-chain hexadiene isomers

Chemical Physics Letters 663 (2016) 66–73

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Research paper

Ab initio kinetics for isomerization reaction of normal-chain hexadiene isomers Feiyu Yang, Fuquan Deng, Youshun Pan, Zemin Tian, Yingjia Zhang ⇑, Zuohua Huang ⇑ State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 10 May 2016 In final form 13 September 2016 Available online 19 September 2016 Keywords: Hexadienes Isomerization Transition state PES Rate constant

a b s t r a c t The ground-state potential energy surface (PES) of isomerization philosophy of ten normal-chain hexadiene isomers is computed by density functional methods using the geometries optimized at B3LYP/6-311++G (d, p) level of theory. These detailed reaction pathways are used to calculate the rate constants for the unimolecular isomerization reactions by transition state theory (TST) in the temperature range of 500–2500 K. Difference of rate constant between each hexadiene isomer is interpreted through the PES and Ḣ atom transfer, and only 2,4-hexadiene readily fulfills cis-cis to trans-trans conformation conversion. All the conversions are kinetically interpreted from the PES and ST geometry. Ó 2016 Elsevier B.V. All rights reserved.

1. Introduction Hexadienes are importantly conventional substances of organic synthesis for biopolymers and terpolymers [1], and also play a pivotal role as reaction intermediates in pyrolysis and oxidation of hexane, which is one of key unsaturated hydrocarbons in commercial fuel. Thus, they have received a great deal of attention recently. McEnally et al. [2] reported the decomposition and hydrocarbon growth processes for hexadiene-doped nonpremixed methane flames. They found that other than C3 + C3 and C4 + C2 pathways, highly unsaturated C6 can cyclize directly to aromatics. Moreover, Sharma et al. [3] proposed a sub-mechanism to describe the effect of hexadiene on methane oxidation. Along with GRI-Mech 2.11 [4], the model of Sharma et al. first provided numerical technique to calculate the mole fractions of various species in the doped flame. Besides these comparative researches, investigations on 1,5-hexadiene[5–10] and 2,4-hexadiene[11], as well as less sTable 1,2-hexadiene[12] and 2,3-hexadiene[13] have been performed individually. These studies mainly focus on decomposition and polymerization. As we well know that isomerization of fuel and intermediate species is an important conversion process for pyrolysis and oxidation at low and intermediate temperatures. However, to our knowledge, only limited information has been reported isomerization reactions of normal-chain hexadiene isomers[14]. ⇑ Corresponding authors. E-mail addresses: [email protected] (Y. Zhang), [email protected]. edu.cn (Z. Huang). http://dx.doi.org/10.1016/j.cplett.2016.09.038 0009-2614/Ó 2016 Elsevier B.V. All rights reserved.

In this work, we focus the investigation on ground-state PES of isomerization reactions of normal-chain hexadiene isomers including trans-1,3-hexadiene (E-1,3-C6H10), cis-1,3-hexadiene (Z-1, 3-C6H10), cis-1,4-hexadiene (Z-1,4-C6H10), trans-1,4-hexadiene (E-1,4-C6H10), 1,5-hexadiene (1,5-C6H10), cis,cis-2,4-hexadiene (Z,Z-2,4-C6H10), trans,trans-2,4-hexadiene (E,E-2,4-C6H10), trans, cis-2,4-hexadiene (E,Z-2,4-C6H10), 1,2-hexadiene (1,2-C6H10) and 2,3-hexadiene (2,3-C6H10). The theoretically computational methods are briefly described in the next section. The computational results are discussed in the third section. 2. Computational details 2.1. Ab initio calculations Without distinguishing cis and trans isomers, there will be 6 categories of hexadienes, namely 1,3-hexadinene (1,3-C6H10), 1,4hexadiene (1,4-C6H10), 1,5-hexadiene (1,5-C6H10), 2,4-hexadiene (2,4-C6H10), 1,2-hexadiene (1,2-C6H10) and 2,3-hexadiene (2,3C6H10). Nevertheless, the cis and trans structures have different impacts on olefin reactivity in certain circumstances. Transdiethylstilbestrol, for instance, has been widely used in pharmacological aspect as it is more considerately active than its cis isomer in terms of biology [15]. These distinguishing structures are thus worthy consideration, as listed Table 1. Geometries of the reactants, products and transition states on the ground-state PES of the hexadiene isomers were optimized by the B3LYP hybrid density functional [16–18] with the 6-311++G (d, p) basis. The single-point energy were further computed by a

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F. Yang et al. / Chemical Physics Letters 663 (2016) 66–73 Table 1 The names, structures and carbon atom number of hexadiene isomers. Name in this work

Species

Formula

Structure

R1 R2 R3 R4 R5 R6 R7 R8 R9 R10

trans-1,3-Hexadiene cis-1,3-Hexadiene cis-1,4-Hexadiene trans-1,4-Hexadiene 1,5-Hexadiene cis,cis-2,4-Hexadiene trans,trans-2,4-Hexadiene trans,cis-2,4-Hexadiene 1,2-Hexadiene 2,3-Hexadiene

E-1,3-C6H10 Z-1,3-C6H10 Z-1,4-C6H10 E-1,4-C6H10 1,5-C6H10 Z,Z-2,4-C6H10 E,E-2,4-C6H10 E,Z-2,4-C6H10 1,2-C6H10 2,3-C6H10

quadratic configuration interaction with singles, doubles and perturbative inclusion of triples (QCISD (T)), with the correlationconsistent, polarized-valence, double-f (cc-pVDZ) and triple-f (cc-pVTZ) basis set of Dunning [19]. To obtain more accurate evaluation of the energetic parameters, higher level single-point energy calculations were performed by the following equation to extrapolate the QCISD (T) energy to complete basis set limit (CBS) [20]:

 pffiffiffiffi ðXÞ ð1Þ ESCF ¼ ESCF þ A exp a X ; where

ðXÞ ESCF

ð1Þ

is the SCF (self-consistent field) energy calculated with ð1Þ

the basis set with cardinal number X and ESCF is the complete basis set limit energy and A and a are constants. When two-point extrapolation are conducted with X = 2 and 3, a = 4.42 and the value of A is ð1Þ

not necessary because it will be canceled during deriving ESCF . The ð1Þ

ESCF can be thus yield via ð1Þ

ESCF ¼

pffiffi pffiffi ð3Þ ð2Þ ea 3 ESCF  ea 2 ESCF pffiffi pffiffi a 3 a 2 e e

partition functions were calculated with the methodology of Pizter and Gwinn [22]. This treatment is recommended by Huynh et al. [23] and its reasonability has been proved in their work. Furthermore, T1 diagnostics were carried out to evaluate spin contamination effects. The average value of T1 diagnostics [24,25] is 0.01, suggesting that the spin contaminations are trivial. The intrinsic reaction coordinate (IRC) [26] computations were performed to validate the connection between the TSs and the corresponding reactants and products. All the ab initio calculations were performed with the Gaussian 09 [27] software and all the geometries, vibrational frequencies and inertia moments are available in Supplementary material. 2.2. Thermochemical properties Enthalpies of formation [28] at 0 K are derived via,

DHof ðC x Hy ; 0 KÞ ¼ xDHof ðC; 0 KÞ þ yDHof ðH; 0 KÞ  DHof ðC x Hy ; 0

X

D0

ð3Þ

P

in which KÞ and D0 denote the standard enthalpy of formation at 0 K and atomization energy of CxHy, respectively. Moreover, the atomization energy are defined as,

X

D0 ¼ xEðCÞ þ yEðHÞ  EðC x Hy Þ  ZPE;

ð4Þ

where E is the single-point energy and ZPE is the zero-point energy. In this work, the enthalpy formation of the elements C and H were taken from NIST JANAF database [29] (DHof ðC; 0 KÞ ¼ 0:2709 Hartree and DHof ðH; 0 KÞ ¼ 0:0823 Hartree) and the single-point energies of C and H were adopted from NIST Computational Chemistry Comparison and Benchmark Database [21] (EðCÞ ¼ 37:3800 Hartree and EðHÞ ¼ 0:4998 Hartree).

ð2Þ 2.3. Rate constant calculations

The vibrational frequencies, zero-point energies and inertia moments were obtained at B3LYP/6-311++G(d, p) level of theory (frequency scale factor of 0.967 recommended by Computational Chemistry Comparison and Benchmark Database [21] for B3LYP/6311G(d, p) level was approximately used here due to the negligible diffusion effect). We treated low frequencies vibrations with large torsional component as hindered rotors. The hindered rotation analysis was carried out at B3LYP/6-311++G(d, p) level, and new

The rate constant were calculated using the geometry, vibration, rotation and collision information of reactants and TSs using the ChemRate program [30] with the RRKM/Master Equation method. The isomerization reactions were conducted at high pressure limit in the temperature range of 500 to 2500 K, and they were fit to an empirical three-parameter form of the Arrhenius equation (Eq. (5)) to obtain the elementary rate parameters A, n

Table 2 The isomerization between hexadienes isomers and the reaction characteristics.

1,3-C6H10.

1,4-C6H10

1,5-C6H10

2,4-C6H10

1,2-C6H10

2,3-C6H10

R1

R2

R3

R4

R5

R6

R7

R8

R9

R10

R10

4MR

4MR

2H

2H

3H

4MR

4MR

4MR

2H

R9

4MR

4MR

2H

2H

2H

4MR

4MR

4MR

R8

6MR

6MR

4MR

4MR

2H

c-t iso.

c-t iso.

R7

6MR

6MR

4MR

4MR

2H

c-t iso.

R6

6MR

6MR

4MR

4MR

2H

R5

2H

2H

4MR

4MR

R4

4MR

4MR

c-t iso.

R3

4MR

4MR

R2

c-t iso.

R1 a. 4MR, 6MR, 2H, 3H and c-t iso represent 4-membered ring, 6-membered ring, double H transfer, triple H transfer and cis-trans isomerization, respectively. b. Blue and red denote the reactions can and cannot happen.

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F. Yang et al. / Chemical Physics Letters 663 (2016) 66–73

R1,R2 1,3-C6H10 do

H

tra

ns fer

4-m

em

re be

dr

ing

TS

em

TS

le

4-m be red S gT r in

6-m em be red rin g

ub

double H transfer

4-membered ring TS

R5 1,5-C6H10

trip

le

Ht

r sfe ran

r sfe

S

do

ub

gT rin

le

red be em 4-m

fer

do

S

ub

le

gT r in

H

tra n

ns

red be

tra

ns

H

em

le

tra

ub

H

do

fer

double H transfer

4-m

R6,R7,R8 2,4-C6H10

R3,R4 1,4-C6H10

4-membered ring TS

R10 2,3-C6H10

double H transfer

R9 1,2-C6H10

Fig. 1. The isomerization among 6 categories of hexadienes. The solid blue lines, dash blue lines and solid red lines denote that these reactions can completely, partially and not happen, respectively.

H2C

CH2 CH

and Ea. One-dimensional quantum mechanical tunneling treatments through Wigner [31] correction are accounted.

CH CH2

CH2

k ¼ AT n expðEa =RTÞ

ð5Þ

R5 H3C

C

3. Results and discussion

CH2

CH

CH3

CH

As mentioned above, all the hexadiene isomers can be classified into 6 categories: 1,3-hexadinene, 1,4-hexadiene, 1,5-hexadiene, 2,4-hexadiene, 1,2-hexadiene and 2,3-hexadiene. We assume that every species can be interconverted reciprocally, there will be thus

R10 Fig. 2. Comparison between the geometries of R5 and R10.

C 210 ¼ 45 probable reactions in terms of the combination equation. TS110(122.6)

TS29(125.5) T

TS810(124.1)

TS13(87.7)

TS16(72.1) TS18(72.0)

TS23(91. 9) 35(87.3) TS3

TS45(84.5) TS67(75.5)

TS26(72.8) TS38(70.5) TS24(71.0)

TS37(70.5) TS36(70.1)

TS14(71.0)

TS48(70.5) TS47(6 9.7) TS46(6 9.6)

R10(51.4) R9(53.1)

R3(7.9)

R5(9 .2)

R4(6.6)

R6(2.5)

R2(4.3) R1(2.9)

R7(0.0)

R8(1.2) Fig. 3. Potential energy surface (kcal/mol) of the isomerization of hexadiene isomers computed at the QCISD (T)/CBS level of theory. Green: 1:3 () 2:4 conversion; blue: 1:4 () 1:5 conversion; red: 1:4 () 1:3 conversion; purple: 1:4 () 2:4 conversion; black: conversions involving R9 and R10; brown: interconversion.

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F. Yang et al. / Chemical Physics Letters 663 (2016) 66–73

Fig. 4. Geometries of TS16, TS18 and TS26 optimized at B3LYP/6-311++G (d, p) level of theory.

Table 2 provides a summary of feasible isomerization of hexadienes isomers, and the corresponding reaction characteristics. However, only 19 TSs are obtained in this study due to some prohibited reaction pathways. Fig. 1 depicts the isomerization processes between the 6 hexadiene isomers and their TSs including 4membered ring, 6-membered ring, double H transfer, and triple H transfer and cis-trans isomerization. It can be therefore concluded from Table 2 and Fig. 1: (a) reactions undergoing through double and triple H transfer TSs are infeasible; (b) only conversions via 4- or 6-membered ring TSs are favorable, however partially for some conversions. This section will focus on interpreting the reaction feasibility and rate constants with different TS types.

0

log(k)

It is clearly seen from Fig. 1, reactions via double or triple H transfer are hard to take place as these conversions are beyond the scope of elementary reactions. Alternatively, these conversions are implemented indirectly through at least one intermediate. For instance, 1,3-hexadiene fails to be directly isomerized to 1,5hexadiene, but it can be converted to 1,4-hexadiene first and then from 1,5-hexadiene. Note that the geometries of R5 and R10 are in an apparent discrepancy and only C2 owns identical amount of H atoms, Fig. 2. Therefore, the conversion between R5 and R10 requires 3 H atom migrations simultaneously, which makes at least two intermediates are required to achieve indirect isomerization between these two species. 3.2. Six membered ring reactions

5

-5

-10

-15

Rxn16 Rxn18 Rxn26

-20 455

3.1. Double and triple H transfers

500

556

625

714

833 1000 1250 1667 2500 5000

Temperature (K) Fig. 5. Rate constants of the isomerization reactions between 1,3-hexadiene and 2,4-hexadiene.

117.3

113.2

H2C

CH

81.2

CH2

(2)

Six-membered ring TS only occurs during the conversion of 1, 3-hexadiene and 2,4-hexadiene (1:3 () 2:4, same for other conversions below), Table 2. Among the 6 reactions involving 6membered ring TS, named Rxn16 (indicates the isomerization from R1 to R6, same for below), Rxn17, Rxn18, Rxn26, Rxn27 and Rxn28 respectively, only Rxn16, Rxn18 and Rxn26 are favorable. As shown in Table 1, R6 can provide two cis C@C bonds leading to shorter distance between C1 and C5 sites (or C2 and C6 sites), meaning that the R6 is readily isomerized to R1 and R2. In contrast, R7 provides two trans C@C bonds leading to longer distance between C1 and C5 sites (or C2 and C6 sites), indicating H atom hardly transfers to the target carbon site. As a result, Rxn17 and Rxn27 are unfavorable to happen. Only the isomerization of R8 and R1 is favorable as the R8 is geometrically asymmetric, leading the different H atom transfer process between from C6 to C2 position and from C5 to C1 position. While Rxn18 only undergoes the former transfer because this H-shift provides a 6-membered ring TS with lower ring strain.

116.2

78.8

H2C

CH2

111.7

CH

CH

CH

CH3

CH

CH

CH3

112.6

112.3

106.7

112.2

112.6

90.5

1,3-C6H10

1,4-C6H10

(1)

(3)

107.8

112.9

112.4

115.7

87.8

H3C

CH

CH

H2C

CH2

CH

CH

CH3

112.4

112.9

107.8

2,4-C6H10

CH 111.7

111.7

CH CH2 87.8

CH2 115.7

1,5-C6H10

Fig. 6. The CAH bond dissociation energies (kcal/mol) of the hexadiene isomers and hydrogen atom transfer of 4-membered ring reactions involving 1,4-hexadiene.

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F. Yang et al. / Chemical Physics Letters 663 (2016) 66–73

5

5

0

0

-5

log(k)

log(k)

-5 -10

-10

-15

Rxn13 Rxn14 Rxn23 Rxn24

-20 -25 -30 455

500

556

625

714

833 1000 1250 1667 2500 5000

Temperature (K) Fig. 7. Rate constants of the isomerization reactions between 1,3-hexadiene and 1,4- hexadiene.

-15

-20

-25 455

Rxn35 Rxn45 500

556

625

714

833 1000 1250 1667 2500 5000

Temperature (K) Fig. 9. Rate constants of the isomerization reactions between 1,3-hexadiene and 1,4- hexadiene. Solid lines: consider low frequency vibrations as hindered rotors. Dash lines: consider low frequency vibrations as harmonic oscillators.

3.3. Four membered ring reactions Except 6-membered ring TS, some reactions can also undergo through 4-membered ring TS, Fig. 1, these reactions can be readily classified into 2 categories: (a) reactions associated with 1,4hexadiene (R3 and R4), and (b) reactions associated with 1,2hexadiene (R9) and 2,3-hexadiene (R10). Obviously, the former category can happen completely while the later one can only partially take place.

Fig. 8. The geometries of TS13, TS14, TS23 and TS24 optimized at B3LYP/6-311++G (d, p) level of theory.

In order to access an in-depth understanding of the isomerization from energy perspective, the PES is calculated at the QCISD (T)/CBS level of theory, Fig. 3. These energies are the adiabatic ground state electronic energy obtained from Eq. (2) at QCISD (T)/CBS level plus the scaled zero point of energy obtained at B3LYP/6-311++G (d, p) level. In addition, the calculated rate constants of the three feasible reactions and their corresponding TS geometries are illustrated in Figs. 4 and 5 respectively. It can be seen form Fig. 3, that all the three favorable TSs have the energy around 70 kcal/mol. It is noteworthy that TS18 (TS of Rxn18, same for below) and TS26 have similar compact 6-membered ring structure, while TS16 has a relatively looser and larger ring with a thorn structure at C5, Fig. 4. The similar geometries and close energies of TS18 and TS26 give rise to almost identical rate constants of Rxn18 and Rxn26, as presented in Fig. 5.

3.3.1. Reactions involving R3 or R4 Both the Table 2 and Fig. 1 show that, all the 4-membered reactions involving 1,4-hexadiene (R3 and R4) can readily happen. The 1,4-hexadiene can convert to 1,3-, 1,5-, and 2,4-hexadienes, because it shares a mutual C@C bond position with these three hexadienes and the other C@C bonds locate at the adjacent positions. 1,4- to 2,4-hexadiene isomerization, for example, they share the C@C bond at C4 position, and the left C@C bond at C1 position on the 1,4-hexadiene is adjacent to that at C2 position on the 2,4hexadiene. It means that 1:4 () 2:4 conversion only undergoes H transfer from C3 to C1 position via 4-menbered ring TS with other C@C bond unchanged. Under the impact of C@C bond, the allyl CAH bond is readily broken due to lower bond dissociation energy (BDE), Fig. 6. Free H atom adds subsequently to the neighboring C@C bond via 4-membered ring TS. The discussions on 1,4hexadiene converting to 1,3-, 1,5-, and 2,4-hexadienes will be presented as below. For 1:4 () 1:3 conversion, the potential barriers of Rxn14 and Rxn24 are predicted to be 71.0 kcal/mol, Fig. 3. However, the energy barriers of Rxn13 and Rxn23 are 87.7 and 91.9 kcal/mol, which are around 20 kcal/mol higher than the former ones. While the energy of R4 is around 6.6 kcal/mol lower than that of R3.

Fig. 10. Geometries of TS35 and TS45 optimized at B3LYP/6-311++G (d, p) level of theory.

71

5

0

0

-10

log(k)

log(k)

F. Yang et al. / Chemical Physics Letters 663 (2016) 66–73

-5

-30

-10

Rxn36 Rxn37 Rxn38

-15 455

-20

500

556

625

714

Rxn46 Rxn47 Rxn48

833 1000 1250 1667 2500 5000

Temperature (K) Fig. 11. Rate constants of the isomerization reactions between 2,4-hexadiene and 1,4- hexadiene.

Compared to Rxn13 and Rxn23, the Rxn14 and Rxn24 are both kinetically and thermodynamically preferred. In keeping with the PES, the rate constants of Rxn14 and Rxn24 are larger than those of Rxn13 and Rxn23 due to lower TS energy barrier, Fig. 7. Also, as can be seen from perspective of TS geometries shown in Fig. 8, TS13 has a similar geometry structure as the TS23, and same happens to TS14 and TS24. Obviously, the similar TS structures and the barrier heights contribute to the similar rate constants in Fig 7. Fig. 9 shows the comparison of the rate constants of 1:4 () 1:5. The rate constants of Rxn 35 and Rxn 45 share very similar activation energies due to the close barrier height (79.4 kcal/mol for Rxn 35 and 77.9 kcal/mol for Rxn 45. Moreover, the Rxn35 and Rxn45 show slightly different TS structures, Fig. 10. The 4-membered ring of TS35 approximately stays in a plane. For TS45, however, the nomadic H atom is out of the plane determined by the other 3 carbon atoms. As can be concluded, the discrepancy of the rate constants are majorly contributed to the different geometry between TS35 and TS45. Fig. 11 shows the rate constants of 1:4 () 2:4 reactions. The activation energy and the intercept are approximately determined by the partition function of reactants and transition state (together with the transmission coefficient). The close barriers in Fig. 3 contribute to the close slopes and the similar geometries, Fig. 12,

Rxn29 Rxn110 Rxn810

-40 455

500

556

625

714

833 1000 1250 1667 2500 5000

Temperature (K) Fig. 13. Rate constants of the isomerization reactions Rxn29, Rxn110 and Rxn810.

indicating that all the TSs will exhibit similar vibrational and rotational behaviors, resulting in they possess similar partition functions. All these reactions therefore share close rate constants. 3.3.2. Reactions involving R9 or R10 1,2- and 2,3-hexadiene (R9 and R10) are different from the hexadienes discussed above because they offer two adjacent C@C bonds. Note that the 2,3-hexadiene may intuitively have both cis and trans conformers, however the optimized geometry of R10 shows that the two adjacent C@C bonds stay at perpendicular positions. Consequently, only one conformer of R10 are available. As shown in Fig. 3, the adjacent C@C bonds structure is much unstable with potential energies over 50 kcal/mol. The potential energies of TS29, TS110 and TS810 are as high as 125.5, 122.6 and 124.1 kcal/mol, respectively. Moreover, these three TSs are in geometric similarity, Fig. 14. As a result, these two factors cause the close and low rate constants of the three reactions. (See Fig. 13) 3.4. Cis-trans interconversions Besides the reactions discussed above, there is a distinct type of reaction–cis-trans isomerization. In theory, there are 5 cis-trans isomerization reactions, namely Rxn12, Rxn34, Rxn67, Rxn68 and

Fig. 12. Geometries of TS36, TS37, TS38, TS46, TS47 and TS48 optimized at B3LYP/6-311++G (d, p) level of theory.

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F. Yang et al. / Chemical Physics Letters 663 (2016) 66–73

Fig. 14. Geometries of TS29, TS110 and TS810 optimized at B3LYP/6-311++G (d, p) level of theory.

5 0 -5

log(k)

-10 -15

Rxn13 Rxn16 Rxn23 Rxn26 Rxn36 Rxn38 Rxn46 Rxn48 Rxn29 Rxn810

-20 -25 -30 -35 -40 500

556

625

714

833

1000

1250

Rxn14 Rxn18 Rxn24 Rxn35 Rxn37 Rxn45 Rxn47 Rxn67 Rxn110 1667

2500

Temperature (K) Fig. 15. Rate constants of the interconversion reactions Rxn67 and the geometry of TS67.

Fig. 16. Rate constants for the isomerization reactions between hexadiene isomers.

Table 3 Elementary rate constants for hexadiene isomerization reactions with Arrhenius forma at high pressure limit.

a

Rxn

logA

Ea

n

Rxn

logA

Ea

n

Rxn13 Rxn14 Rxn16 Rxn18 Rxn23 Rxn24 Rxn26 Rxn35 Rxn36 Rxn37

62.8687 63.7310 61.9998 58.1596 62.8911 63.7283 58.0342 61.8448 63.7578 62.5692

38114.8 32235.3 32547.4 31960.8 39181.3 31753.3 31738.7 36085.7 30245.3 30185.7

14.9094 14.7889 14.3969 13.79 15.0001 14.8056 13.7877 14.6746 15.0657 14.7295

Rxn38 Rxn45 Rxn46 Rxn47 Rxn48 Rxn67 Rxn29 Rxn110 Rxn810

62.5701 63.9831 61.3354 61.1543 62.3080 62.0205 53.1826 54.1645 53.5865

30187.2 35866.1 30110.9 30261.7 30540.2 33 845 47585.1 47157.1 47566.5

14.7297 14.9667 14.2534 14.2056 14.5000 14.5533 12.2784 12.4722 12.392

k ¼ AT n expðEa =RTÞ; units: s1, Ea: cal mol1, T: K.

Rxn78, but only Rxn67 are passible. It is well known that C@C bond cannot rotate and the four atoms connecting with C@C bond have to stay in the same plane, leading to hardly happen Rxn12, Rxn34, Rxn68 and Rxn78. Unlike these four reactions, two C@C bonds connected by a single bond rotate simultaneously to achieve the transfer from R6 to R7. Fig. 15 illustrates the rate constant of Rxn67 and the geometry of TS67, and it is found that the conjugated alkene structure allow two C@C bonds to rotate at the same time.

Moreover, Rxn13 and Rxn23 with the highest barriers of 84.8 and 87.6 kcal/mol show smaller rate constants and lower reactivity. The reactions associated with R3 and R4 are most active, while 6-membered ring reactions and interconversion exhibit moderate reactivity. There is no doubt that, this ground-state PES is dominated by 4-membered ring reactions.

4. Conclusions 3.5. Comparison of rate constants To obtain an overall insight of all these conversions, the rate constants computed are fitted to empirical Arrhenius equations (Eq. (5)) and presented in Table 3 as well as in Fig. 16. Considering unstable structures and high energies, the reactions involving adjacent C=C bonds (Rxn29, Rxn110 and Rxn810) are less competitive.

In this work, the hexadiene isomers are optimized at B3LYP/6311++G (d, p) level and the energies are estimated at QCISD (T)/ cc-pV1Z level. Rate constants of the isomerization reactions between ten normal-chain hexadienes are obtained, and 19 feasible isomerization processes are seriously considered. The reaction feasibility analysis shows that the conversions involving two or more H atoms migration simultaneously are beyond the scope of

F. Yang et al. / Chemical Physics Letters 663 (2016) 66–73

elementary reaction and thus are inhibitory. There are 6 reactions involving 6-menbered ring TS but only Rxn16, Rxn18 and Rxn26 are favorable. In addition, with relatively higher ring strain, sixmembered ring reactions are less competitive than those involving 4-membered ring TSs. Fifteen of the 19 reactions undergo via the 4membered ring structure. All the 4-membered ring reactions involving R3 and R4 can readily proceed and exhibit the highest reactivity. In contrary, 4-memberd reactions involving R9 and R10, which consist of adjacent C=C bonds, exhibit the highest potential energy level and the lowest reactivity. For the 5 interconversion processes, since C@C bond cannot rotate and the four atoms connecting with C@C bond have to stay in the same plane, Rxn12, Rxn34, Rxn68 and Rxn78 can hardly happen. Only Rxn67 is promising because there are two C@C bonds connected by a single bond rotate simultaneously. Acknowledgments The authors acknowledge the financial support of the National Natural Science Foundation of China under Grant Nos. 91441203 and 91541115, and the National Basic Research Program under Grant No. 2013CB228406. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2016.09. 038. References [1] Z. Yu, M. Marques, M.D. Rausch, J.C.W. Chien, J. Polym. Sci., Part A: Polym. Chem. 33 (1995) 979. [2] C.S. McEnally, L.D. Pfefferle, Combust. Flame 152 (2008) 469. [3] S. Sharma, M.R. Harper, W.H. Green, Combust. Flame 157 (2010) 1331. [4] C. Bowman, R. Hanson, D. Davidson, W. Gardiner Jr, V. Lissianski, G. Smith, D. Golden, M. Frenklach, M. Goldenberg, 1995. . [5] H.S. Makowski, B.K.C. Shim, Z.W. Wilchinsky, J. Polym. Sci. Part A: Gen. Papers 2 (1964) 1549. [6] M.J. Goldstein, M.S. Benzon, J. Am. Chem. Soc. 94 (1972) 7147.

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[7] M.J.S. Dewar, E.F. Healy, Chem. Phys. Lett. 141 (1987) 521. [8] M.J. McGuire, P. Piecuch, J. Am. Chem. Soc. 127 (2005) 2608. [9] A. Fridlyand, P.T. Lynch, R.S. Tranter, K. Brezinsky, J. Phys. Chem. A 117 (2013) 4762. [10] P.T. Lynch, C.J. Annesley, C.J. Aul, X. Yang, R.S. Tranter, J. Phys. Chem. A 117 (2013) 4750. [11] J. Saltiel, O. Dmitrenko, W. Reischl, R.D. Bach, J. Phys. Chem. A 105 (2001) 3934. [12] G.F. Hennion, J.J. Sheehan, J. Am. Chem. Soc. 71 (1949) 1964. [13] K.B. Wiberg, Y.-G. Wang, S.M. Wilson, P.H. Vaccaro, W.L. Jorgensen, T.D. Crawford, M.L. Abrams, J.R. Cheeseman, M. Luderer, J. Phys. Chem. A 112 (2008) 2415. [14] F. Battin-Leclerc, A. Rodriguez, B. Husson, O. Herbinet, P.A. Glaude, Z. Wang, Z. Cheng, F. Qi, J. Phys. Chem. A 118 (2014) 673. [15] V.W. Winkler, M.A. Nyman, R.S. Egan, Steroids 17 (1971) 197. [16] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [17] A.D. Becke, J. Chem. Phys. 96 (1992) 2155. [18] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [19] A.W. Jasper, S.J. Klippenstein, L.B. Harding, B. Ruscic, J. Phys. Chem. A 111 (2007) 3932. [20] J.M.L. Martin, O. Uzan, Chem. Phys. Lett. 282 (1998) 16. [21] h.c.n.g. NIST Computational Chemistry Comparison and Benchmark DataBase, 2015. [22] B.A. Ellingson, V.A. Lynch, S.L. Mielke, D.G. Truhlar, J. Chem. Phys. 125 (2006) 084305. [23] L.K. Huynh, M. Tirtowidjojo, T.N. Truong, Chem. Phys. Lett. 469 (2009) 81. [24] T.J. Lee, P.R. Taylor, Int. J. Quantum Chem. 36 (1989) 199. [25] T.J. Lee, A.P. Rendell, P.R. Taylor, J. Phys. Chem. 94 (1990) 5463. [26] K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, Chem. Phys. Lett. 157 (1989) 479. [27] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J.A. Montgomery, Jr., J.E. Peralta, F. Ogliaro, M. Bearpark, J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam, M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels, Ö. Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, D.J. Fox, R.E. Gaussian 09, Gaussian Inc, Wallingford CT, 2009. [28] L.A. Curtiss, K. Raghavachari, P.C. Redfern, J.A. Pople, J. Chem. Phys. 106 (1997) 1063. [29] h.k.n.g.j. NIST JANAF Database. [30] V.B. Mokrushin, V. Tsang, W. Zachariah, M.R. Knyazev, V.D. ChemRate, Version 1.5.8 ed., National Institute of Standards and Testing: Gaithersburg, MD, 2009. [31] E.P. Wigner, in: A.S. Wightman (Ed.), Part I: Physical Chemistry. Part II: Solid State Physics, Springer, Berlin Heidelberg, Berlin, Heidelberg, 1997, p. 96.