theoretical study on the kinetics and mechanism of the reaction of

December 20, 2008 20:0 WSPC/178-JTCC

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Journal of Theoretical and Computational Chemistry Vol. 7, No. 6 (2008) 1227–1250 c World Scientific Publishing Company

THEORETICAL STUDY ON THE KINETICS AND MECHANISM OF THE REACTION OF CYCLOHEXYL ISOCYANIDE AND 1,1,1,5,5,5-HEXAFLUROPENTANE-2,4-DIONE USING DFT METHOD

MEHDI D. DAVARI, AMENEH TAGHIZADEH, HOMAYOON BAHRAMI, MANSOUR ZAHEDI∗ and AHMAD SHAABANI Department of Chemistry, Faculty of Sciences Shahid Beheshti University P. O. Box 19395-4716, Evin Tehran 19839-6313, Iran ∗[email protected]

Received 2 January 2008 Accepted 4 April 2008 Kinetics and mechanism of the reaction between cyclohexyl isocyanide and 1,1,1,5,5,5hexafluropentane-2,4-dione has been investigated by utilizing transition state theory and using B3LYP/6-31G∗ method. Based on previous experimental studies, two paths namely direct attack and conjugate addition have been proposed. Energy changes vs intrinsic reaction coordinate (IRC) along these paths have been studied both in the gas phase and considering nonspecific solvent effect under Onsager’s model while all intermediate and possible transition states’ geometries obtained and optimized. Small differences have been observed between gas phase and solution phase results. Taking advantage of the thermodynamic and kinetic calculated parameters, observed reaction rate constants and activation energies have been acquired. Computational results suggest that the conjugate addition path is totally unacceptable, while a new path has been proposed, which is both energetically and kinetically preferred to direct attack path. This new path undergoes the Michael addition along with a Cope–Claisen-type rearrangement. In this path, a new intermediate has been encountered for the first time, which contains a five-membered ring of four carbon atoms and one oxygen atom. NBO analysis has revealed that in such intermediate, oxygen lone pair has resonance with C–C π bond inside and C–N π bond outside of the ring leading to this species special stability. Molecular orbital calculations satisfy NBO findings. Keywords: Kinetics; mechanism; cyclohexyl isocyanide; 1,1,1,5,5,5-hexafluropentane-2,4dione; B3LYP method; NBO analysis.

∗ Corresponding

author.

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1. Introduction Unique cycloaddition character of isocyanides causes these compounds to undergo reactions as both nucleophile and electrophile. These reactions include a dipolar intermediate species. The electrophilic end of the dipolar moiety can bond to the isocyanide electron pair (carbon electron pair), whereas at the same time the latter carbon becomes electrophile in character and thereby forms ring with the electron rich end of the dipole intermediate. If the dipole contains two atoms (such as carbonyl group), a three-membered ring is formed. In making larger rings, either one of the precursors, isocyanide or dipolar species involves in the cycloaddition reaction to a larger extent or the dipole includes more than two atoms.1−3 Two valuable reviews on the isocyanides’ properties, experimental identification, reactions, syntheses, and their applications been appeared recently,4,5 Experimentally, it has been shown that cyclohexyl isocyanide undergoes a complex reaction with 1,1,1,5,5,5-hexafluropentane-2,4-dione (HFPD) to afford 1-cylohexyl-3,5-bis(trifluoromethyl)-5-hydroxy-1H-pyrrole-2(5H)-ones as the sole product and in a fairly high yields. Reaction of cyclohexyl isocyanide with HFPD via a conjugate (or direct) attack gives imino-oxirane. The latter then undergoes a fast Cope–Claisen-type rearrangement to form a γ-lactam. Although the spectroscopic characteristics such as 1 H NMR, 13 C NMR, IR, and Mass spectra of both imino-oxirane and γ-lactam are similar; however, X-ray crystallography has confirmed the latter as the actual product.6 The overall reaction can be illustrated as CF3 OH

O

+ F3 C

CF3

N

C

F3C HO

N

O

.

(1)

In the proposed mechanisms of Ref. 6 for above reaction (Fig. 1), two paths have been suggested. Path 1 includes direct addition of cyclohexyl isocyanide to the carbonyl carbon atom to yield imino-oxirane as intermediate 1. The latter species then undergoes a fast Cope–Claisen-type rearrangement to give product. In path 2, however, intermediate 2 is generated by conjugate addition of cyclohexyl isocyanide to hetero-diene β-carbon. Intermediate 3 is formed from intermediate 2, which leads to product via intermediate 1 formation. The extent of reliability and precision of the above proposed mechanisms for this and other cycloaddition reactions is not well determined and is a matter of debate. In the above proposed mechanisms, isocyanide’s carbon atom acts as a nucleophile and distinction between these two mechanisms lies under the tendency of ring formation via either direct attack or conjugate addition in the generated intermediates. Since experimental works have been unable to come up with a preference


00443

Theoretical Study on the Kinetics and Mechanism of the Reaction of Cyclohexyl Isocyanide

1229 CF3

OH OH

CF3

CF3

O

CF3

R

+

N

direct

C

F3C

C

CH

Cope-Claisen

O

rearrangement

addition R = cyclohexyl

Path 1

N

F3 C HO

N

O

R

R

Int-1

conjugate addition

Path 2

CF3

CF3 R

+

N

C

C

CH

OH

C O-

Int-2

CF3

R

+

N

C

C O-

CH

C

CF3

OH

Int-3

Fig. 1. Proposed paths for the reaction of cyclohexyl isocyanide and HFPD in Ref. 6.

for one mechanism vs the other, it is hoped that theoretical calculations may shed more light on these and other possible mechanisms. To achieve this goal, kinetics and mechanism of the aforementioned reaction have been fully investigated using B3LYP method. As will be discussed in the forthcoming sections, we have been able to reject one of the two above paths, while an alternative new mechanism has been proposed. Since dichloromethane with a low dielectric constant has been the reaction medium in experimental work and it turns out that it does not have any specific interaction with involved species in reaction, it seems sufficient to investigate the solvent effects using the Onsager model. In order to determine the relative stabilities as well as to study intramolecular donor–acceptor interactions of the species involved in the cycloaddition reactions, natural bond orbital (NBO) analysis has been employed. Molecular orbital (MO) evaluations based on quantum mechanical calculations have been carried out and confirmed the NBO results.

2. Computational Scheme The Gaussian 98 program Revision A.97 has been used as a basic program and HyperChem version 7 as a graphical medium. All calculations have been performed on IBM-PC (Pentium IV). Based on conclusions drawn from our previous work8 and due to the desired structures being of medium size, we have used B3LYP method.9 Basis set optimization performed led us to choose 6-31G(d)10 basis functions in this investigation. Full optimizations without any symmetry constraint have been performed with FOPT keyword and a Z-matrix with C1 point group. Basis set superposition error has been calculated using MASSAGE keyword. Molecular volumes have been evaluated using VOLUME keyword, while SCRF and DIPOLE keywords have been employed for nonspecific solvent calculation under Onsager’s


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model.11 QST2 and QST3 keywords have been utilized for finding probable transition states on reaction pathways. Wherever necessary, OPT = Z-MATRIX has been used for potential energy search along the reaction coordinate. Vibrational frequency calculations on all species studied both in gas phase and in solution confirmed the minimum geometries and transition states on their corresponding potential surfaces by having zero and one imaginary frequency, respectively. Thermodynamics parameters have been obtained based on frequency calculation results. The NBO analysis has been used to obtain the lone pair hybridization and second2 12 ). order interaction energies (∆Eij 3. Result and Discussions Various routes along the reaction coordinate have been inspected using B3LYP method. All moieties on the reaction paths have been fully optimized in order to either confirm or reject the possible existence of the previously proposed species. By determining the molecules involved in the reaction, total electronic energy and kinetic parameters have been obtained for each one in order to be able to evaluate each path with respect to energy advantage. NBO analysis has been carried out to find out about the stability of species with respect to the way electrons are located in their hybrid orbital and determining the possible donor–acceptor interactions between them. MO evaluations based on quantum mechanical calculations have been carried out to complement the NBO results. The implementations of above tasks are explained in the following sections.

3.1. Determining the computation level In order to choose an appropriate basis set, a series of optimization calculations using various Pople-type basis sets with B3LYP method were performed on the product. The structural parameters (bond distances and angles) for each level were compared with the corresponding X-ray crystallography data. At the B3LYP/631G(d) level, acceptable differences for bond distances of less than 0.01 ˚ A led us to suffice to this level. Differences for bond angle values and with all levels remained less than 1◦ , meaning that no distinction among various levels can be judged based on bond angles.

3.2. Structural optimization and calculation of energy All structures including precursors, intermediates, and transition states were determined along all proposed reaction paths. Full geometry optimization at B3LYP/631G∗ level was performed on all species once for the gas phase and another time assuming condense phase utilizing the Onsager nonspecific solvent model. Energy values obtained were used to judge about the relative stabilities of the species on each path and also to decide about the most favorable path energetically.


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3.2.1. Geometry optimization of proposed intermediates Figure 1 presents the two paths that have been suggested by Yavari et al.6 To explore the reliability of such proposal, all intermediates were designed and fully optimized. Intermediate 1 along path 1 was confirmed as a minimum structure with no imaginary frequency observed by vibrational analysis. Intermediates 2 and 3 along path 2, however, were both unstable, namely achieving a minimum structure of these species was fruitless and resulted in new structures after optimization. By forming a bond between carbon and oxygen atoms and generating a five-membered ring, compound 2 converts to a new intermediate 1 as shown in Fig. 2. Performing vibrational analysis and observing no imaginary frequency for the latter species confirmed it as an intermediate on path 2. Optimization of compound 3 led to C–C bond rupture and regeneration of the original precursors. Therefore, intermediates 2 and 3 (Fig. 1) were determined as unstable moieties whose existence as possible intermediates along path 2 is rejected, which means that conjugate addition (path 2, Fig. 1) mechanism is totally unacceptable. Regarding the above findings, we have proposed a new path 2 on Fig. 2 as well as the original path 1 and have presented corresponding mechanisms for each path. In path 1, reactants are converted to intermediate 1, which undergoes a Cope–Claisen rearrangement to yield product. In the second proposed mechanism, reactants experience new intermediate 1 before proceeding to intermediate 1, which then converts to product via a rearrangement as in path 1. 3.2.2. Gas phase search for transition state 1 structure between precursors and intermediate 1 in path 1 Figure 3 illustrates all structures accompanied with the numbering system used in the text along path 1 for reaction. All efforts to find a transition state between Int-1 OH O CF3

Path 1

CF3

+

R N C R= cyclohexyl

CF3

O R N C

CF3

F3C

CH

HO

C C CF3

Path 2 [1+4] cycloaddition reaction

O R N

C

C

N R

O

OH

CF3

C CH F3C OH

Int-1′ Fig. 2. Proposed paths for the reaction of cyclohexyl isocyanide and HFPD after optimization of intermediates.


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3

OH

O +

R

-

N

C

1

2

6

5

2

4

N

C

C

9

CH

CF3 C

H11

Cyclohexyl isocyanide

CF3

O

10

O

CF3

2

4

C

C

1

10

C 2

R

4

1

5

5 CH

C6 CF3

CF3

C

N

CH

9

OH

Transition state-1 3

3

6 7

9

1,1,1,5,5,5-Hexafluropentane-2,4-dione

N

CF3

1

5

4

10

F3C

R

10

O

7 8

3

9

C6

F3C

7

OH

7

OH

Intermediate-1


F3C

4

5

C

CH

3

O

7 6

2

OH

C

C 1

N

9

CF3

C

Product Fig. 3. The numbering system used for all species in path 1 for the reaction of cyclohexyl isocyanide and HFPD.

precursors and intermediate 1 via QST2 method were fruitless. In order to come up with an appropriate initial guess of the possible transition state, C2–O3 bond of intermediate 1 was scanned by 0.2 ˚ A increments in five steps, while this bond length was constrained and all other parameters were relaxed to be fully optimized. Comparison of energies at these five points revealed a structure at the maximum value of energy with the above bond broken while C2–C4 bond distance increased. The latter structure was chosen as a tentative guess and utilized for a QST3 calculation routine. Optimization and frequency analysis on this moiety validated it as the appropriate transition state 1 (Fig. 3). Closer inspection reveals that transition


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state 1 is actually identical to intermediate 3 of Fig. 1. Namely, the experimentally proposed intermediate 3 of this figure represents a transition state and is not a minimum on the potential energy surface. 3.2.3. Gas phase search for transition state 2 structure between intermediate 1 and product in path 1 A comparison between intermediate 1 and product (Fig. 3) shows that the desired transition state 2 can be approached by lengthening N1–C6 bond in the product molecule. Thus for a suitable estimate of transition state 2, N1–C6 bond was increased by 0.3 ˚ A increments in five steps, while this parameter was constrained and all others were relaxed to be fully optimized. The structure with maximum energy among five above candidates with the N1–C6 bond broken was used as an entry for QST3 calculation procedure. The final optimized structure was corroborated as transition state 2 (Fig. 3) by vibrational frequency analysis. 3.2.4. Potential energy changes along path 1 Having all key points on the potential energy surface of path 1 determined and optimized, a basis set superposition error was performed, which revealed that the reactants energies must be corrected for this error by 7.02 kcal mol−1 . Figure 4 depicts the energy changes along path 1 in gas phase. As it is evident, activation energy (Ea1 ) to reach transition state 1 from reactants is 44.74 kcal mol−1 while that for transition state 2 from intermediate 1 (Ea2 ) amounts to 15.65 kcal mol−1 . Since the reaction of cyclohexyl isocyanide and HFDP has been performed in an aprotic dichloromethane as solvent, to examine the solvent effect we have applied Onsager’s nonspecific solvent effect model with dielectric constant of 8.93. In a similar course to gas phase calculations described in sections above, all species along path 1 were optimized in condensed medium. Basis set superposition error for this case was 6.65 kcal mol−1 . Same trend as in gas phase was observed with Ea1 equal to 43.94 kcal mol−1 and Ea2 amounting 14.43 kcal mol−1 . A comparison

Energy (kcal. mol-1)

80.00

TS-1 TS-2

60.00

Ea1

40.00 20.00

Int-1

Ea2

∆ E1 Reactants Product

0.00

Reaction Coordinate Fig. 4. Energy diagram for path 1 in gas phase.


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M. D. Davari et al.

between gas phase and solution results reveals that applying solution effect has minor influence and the overall trend remains unchanged as expected.

3.2.5. Search for transition state 1 structure between precursors and intermediate 1 in path 2 Figure 5 includes all structures together with the corresponding numbering systems used in the text for path 2. In order to obtain an initial guess of the possible transition 7 8

3 +

N

C

1

2

10

CF3

OH

O

-

4 4

10

6

5

F3C

C

3

9

O

CF3

5

CH

H11

R

Cyclohexyl isocyanide 1,1,1,5,5,5-Hexafluropentane-2,4-dione

1

2

6

N

C

C

7

OH

9

F3C


CF3 C

R

2

R

C

5

N

1 N

C

9

OH

F3C

9 F 3C

3

10 CF3

10

O

R

N

CF3

2

4

C

C

1

5

CH

C 7

3

C4

2

CH

6

1

O

4

3O

C

6

5 CH

C6 9

CF3

7

OH

7 OH

Intermediate-1´ Transition state-2

Intermediate-1 10

3

F3C

O 10

C 2

R

4

CF3

C

N 1

5 CH

4

5

C

CH

O

7 6

2 3

OH

C

C 1

N

9

CF3

C 9

C6

F3C 7

OH

Transition state-3

Product

Fig. 5. The numbering system used for all species in path 2 for the reaction of cyclohexyl isocyanide and HFPD.


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state 1, C2–C6 bond of intermediate 1 was scanned by 0.3 ˚ A increments in four steps, while this bond length was fixed at each step and all other parameters were relaxed to be fully optimized. Comparison of energies for above four points revealed a structure at the maximum value of energy with the above bond partially broken. The latter trial structure was utilized for a QST3 calculation routine. Optimization and frequency analysis on this moiety confirmed it as the appropriate transition state 1 (Fig. 5). Closer inspection reveals that transition state 1 is actually identical to intermediate 2 of Fig. 1. Namely, the experimentally proposed intermediate 2 of this figure represents a transition state and is not a minimum on the potential energy surface. 3.2.6. Finding transition state 2 structure between intermediate 1 and intermediate 1 in path 2 Applying a normal QST2 routine resulted in a structure, which was verified as transition state 2 after vibrational frequency analysis. 3.2.7. Potential energy variations along path 2 By attaining and optimizing all key points on the potential energy surface of path 2, the reactant’s energies were corrected for basis set superposition error, which was already calculated and amounted to 7.02 kcal mol−1 . Figure 6 illustrates the energy variations along path 2 in gas phase. As it is evident, activation energy (Ea1 ) to reach transition state 1 from reactants is 34.15 kcal mol−1 while that for transition state 2 from intermediate 1 (Ea2 ) and transition state 3 from intermediate 1 amount to 45.38 and 15.65 kcal mol−1 , respectively. In a similar course to gas phase calculations described in sections above, all species along path 2 were optimized in condensed medium using the Onsager model. Taking into account basis set superposition error (6.65 kcal mol−1 ), same trend as in gas phase was observed with Ea1 , Ea2 , and Ea3 being equal to 31.68, 42.51, and TS-3

TS-2

TS-1

Int-1

-1

Energy(kcal.mol)

60.00

Ea3

40.00

Ea1 20.00

Reactants

Ea2

∆E2

∆E1 Int-1' Product

0.00

Reaction Coordinate Fig. 6. Energy diagram for path 2 in gas phase.


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14.44 kcal mol−1 , respectively. A comparison between gas phase and solution results again reveals that applying solvent has minor effects and the overall trend remains unchanged as expected. 3.3. Kinetics consideration of reaction paths using transition state theory It is important to note that since the precursors and products of the reaction along both paths of Fig. 2 are identical, no distinction can be made between them based on thermodynamical grounds. Thus, kinetic consideration of these paths seems necessary. With regard to the two possible routes mentioned above and having all energies calculated for precursors, intermediates, transition states, and products along with the thermodynamic quantities obtained from vibrational frequency analyses, kinetics of each of the presented mechanisms have been investigated and corresponding activation energies have been acquired. Based on such task, the kinetically preferred path for the reaction progression has been determined. 3.3.1. Introduction of preliminary mechanisms and corresponding rate equations for paths 1 and 2 Taking into accounting the results presented earlier, the following mechanism can be written for path 1 of the reaction: k1

A + B Int-1, k−1 k

2 Int-1 −→ P,

(2) (3)

where A and B stand for reactants, P for product, and Int-1 for intermediate 1. Rate equation corresponding to such mechanism can be given as d[P ] = k2 [Int-1]. dt With a straightforward algebra, we get Rate =

Rate = kobs [A][B], kobs =

k1 k2 , k−1 + k2

(4)

(5) (6)

where kobs represents the observed rate in path 1 of the reaction. Applying same logic for path 2, we have k1

A + B Int-1 , k−1 k2

Int-1 Int-1, k−2

k3

Int-1 P,

(7) (8) (9)


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where A and B represent precursors, Int-1 and Int-1 are intermediates, and P is reaction product, all for path 2. Same rate equation as (5) and considering various rate constants in this case leads to the following kobs expression: kobs =

k1 k2 k3 . k−2 k1 + k3 (k −1 + k2 )

(10)

Employing the Arrhenius equation and utilizing observed rate constants given above for two paths, the following two equations for activation energies of paths 1 and 2 will be resulted, respectively, k2 Ea1 + k−1 (Ea2 + ∆E1 ) , k−1 + k2

(11)

k−1 k−2 (∆E1 + ∆E2 + Ea3 ) + k−1 k3 (∆E1 + Ea2 ) + k2 k3 Ea1 , k−1 k−2 + k3 (k−1 + k2 )

(12)

Eaobs = Eaobs =

where Eai s are the activation energies shown in Figs. 4 and 6, and ∆Ei s denote energy changes accompanied for ith step of a mechanism. Applying the calculated rate constants, Eai ’s and ∆Ei ’s, desired kobs and Eaobs can be evaluated for two paths. 3.3.2. Evaluation of kobs for paths 1 and 2 of the reaction Having done frequency analyses for all species at several temperatures and at 1 atm pressure, desirable thermodynamical parameters were computed for both paths. Table 1 includes the activation Gibbs free energies at five different temperatures for two paths. Employing transition state theory and utilizing the relation13−15 : k=

RT − −∆G∓ e RT . NA h

(13)

Rate constant values have been obtained for every step of each path and the results have been presented in Table 1. Taking advantage of data compiled in the latter table and using Eqs. (6) and (10), kobs values have been calculated in the temperature range 25 to 45 ◦ C for both paths and the resulting data have been sorted in Table 1. Attempting to plot ln(kobs ) and ln(kobs /T ) vs 1/T revealed linear relations (not shown) with correlation coefficients (R2 ≈ 1), which indicated the obedience of kobs to both the Arrhenius16 and Eyring equations14 as well as confirming the accuracy of kinetic study. Taking into account the kobs values at various temperatures of Table 1, the overall kobs for two paths can be expressed as Path 1 : Path 2 :

kobs = 1.181 × 103 T e−22108.0/T dm3 molecule−1 s−1 . 3

kobs = 1.098 × 10 T

0.39 −18527.1/T

e

3

dm molecule

−1 −1

s

(14) .

(15)

3.3.3. Determination of kinetically favorable path As was stated earlier, Eqs. (11) and (12) can be used to obtain an estimate of Eaobs for paths 1 and 2 by taking advantage of data compiled in Table 1. Average Eaobs values so obtained are ∼ 46 and ∼ 38 kcal mol−1 for paths 1 and 2, respectively.


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M. D. Davari et al. Table 1. Activation Gibbs free energy (kcal mol−1 ), rate constant, thermal activation energy (kcal mol−1 ), and observed rate constant kobs (L mol−1 s−1 ) values at different temperatures for the paths 1 and 2 of the reaction. T (K)

Path 1 ∆G= 1

∆G= −1 ∆G= 2

298.15

303.15

308.15

313.15

318.15

53.61

53.85

53.99

54.13

54.27

21.00

21.00

20.98

20.95

20.93

16.26

16.22

16.25

16.28

16.30

k1

1.89 × 10−3

5.74 × 10−3

1.97 × 10−2

6.50 × 10−2

2.09 × 10−1

k−1

2.55 × 10−3

4.56 × 10−3

8.48 × 10−3

1.56 × 10−2

2.76 × 10−2

7.5

13.015

19.14

28.25

42.64

45.91

45.95

45.99

46.04

46.08

22.53

22.54

22.55

22.55

22.55

∆E1

23.38

23.41

23.45

23.49

23.53

Ea= 2

14.66

14.65

14.64

14.62

14.61

1.89 × 10−3

5.74 × 10−3

1.97 × 10−2

6.50 × 10−2

2.09 × 10−1

46.01

46.15

46.33

46.51

46.69

42.17

42.10

42.09

42.08

42.08

41.46

41.33

41.30

41.26

41.23

12.70

12.54

12.53

12.52

12.51

16.26

16.22

16.25

16.28

16.30

698.32

2034.76

5333.72

13605.20

33712.00

7.64 × 10−19

2.83 × 10−18

9.00 × 10−18

2.80 × 10−17

8.22 × 10−17

10−18

10−17

10−17

10−16

3.20 × 10−16

104

1.70 × 104

k2 Ea= 1 Ea= −1

kobs Path 2 ∆G# 1

∆G# −1 ∆G# 2 ∆G# −2 ∆G# 3 k1 k−1 k2 k−2 k3

2.52 ×

3.03 ×

103

1.01 ×

5.74 ×

103

3.30 ×

8.35 ×

103

1.04 ×

1.19 ×

7.52

13.01

19.40

28.25

42.64

35.77

35.80

35.84

35.88

35.92

42.54

42.54

42.55

42.56

42.56

∆E1

−6.77

−6.74

−6.71

−6.67

−6.64

Ea= 2

43.35

43.35

43.36

43.37

43.38

Ea= −2

13.20

13.20

13.21

13.21

13.21

∆E2

30.15

30.15

30.15

30.16

30.17

Ea= 3

14.66

14.65

14.64

14.62

14.61

kobs

5.65

21.10

44.95

118.63

325.18

Ea= 1 Ea= −1

Therefore, activation energy for path 2 is lower than that of path 1 by ∼ 8 kcal mol−1 . Calculated kobs of Table 1 reveal that path 2 rate constant is larger than that of path 1 by a factor ranging from 1556 to 3676. All in all, as far as kinetics of the reaction is concerned, proposed path 2 is more favorable than path 1.


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3.3.4. Proposed mechanisms for paths 1 and 2 of the reaction Evaluation of all stages involved and introduction of mechanisms for the two reaction paths become feasible by modification of the preliminary mechanisms already presented while taking into account the necessary parameters such as kobs and Eaobs , which have been calculated. 3.3.4.1. Introduction of a mechanism for path 1 of the reaction Looking back at Eq. (6) for kobs of path 1 and noting the results summarized in Table 1, it becomes clear that k−1 values can be ignored relative to those of k2 since they are much less than the latter values. Thus above equation can be simplified as kobs = k1 ,

(16)

such an expression is corroborated with an inspection of kobs and k1 values of Table 1. Same practice for Eaobs of Eq. (11) leads to the simplified expression: Eaobs = Ea1 .

(17)

Regarding Eqs. (16) and (17), it is revealed that for path 1 of the reaction, production of intermediate 1 is the rate determining step of the process. Thus, in view of this final conclusion the following mechanism can be proposed for path 1: k

1 Int-1 Slow, A + B ←−

k

2 P Int-1 ←−

Fast.

(18) (19)

3.3.4.2. Introduction of a mechanism for path 2 of the reaction Looking closely at the results summarized in Table 1 for path 2, it is evident that the denominator of second expression in Eq. (10) for kobs of path 2 can be ignored, which leads to the reduced form: kobs =

k1 k2 k3 = K1 K2 k3 , k−1 k−2

(20)

where K1 and K2 represent equilibrium constants for first and second step of the reaction, respectively. Similar approach for Eaobs expression of Eq. (12) (path 2) let us ignore second and third expressions, of the numerator and also second expression of the denominator of this equation, which leads to the simplified form: Eaobs = ∆E1 + ∆E2 + Ea3 .

(21)


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Taking into account Eqs. (20) and (21), the following mechanism can be presented for path 2 of the reaction, which suggests two initial equilibriums followed by the third product generation step: K1

A + B Int-1 , K2

Int-1 Int-1, K3

Int-1 P.

(22) (23) (24)

3.4. NBO analysis In order to have a chemical understanding with regard to the relative stabilities of species involved in each reaction path, an NBO analysis has been attempted. Employing such analysis in the following sections, localization of bonding electrons, lone pairs, and unpaired electrons in hybrid orbitals have been investigated. By considering donor–acceptor interactions among these orbitals, relative stabilities of all components involved in the reaction and for each path with respect to electrons resonances and configurations have been determined. 3.4.1. NBO analysis of reaction’s path 1 Tables 2 and 3 illustrate results involved for atoms hybridization in some of bonding and antibonding interactions for reactants, transition state, intermediate 1, and product. Table 4 summarizes some lone pair hybridization while NBO second-order

Table 2. Hybridization of some bonding and antibonding interactions for cyclohexyl isocyanide and HFPD. Interaction

Hybridization

Cyclohexyl isocyanide BD(1) N1–C2 0.5663(sp2.29 )c + 0.8242 (sp0.85 )N BD(2) N1–C2 0.5212 (p)c + 0.8534 (p)N BD(3) N1–C2 0.5207 (p)c + 0.8537 (p)N HFPD BD(1) C6–O7 BD(1) C6–C9 BD(1) O7–H8 BD*(1) O7–H8 BD(1) C6–C5 BD(2) C6–C5 BD*(2) C6–C5 BD(1) C4–O3 BD(2) C4–O3 BD*(2) C4–O3 BD(1) C4–C10 BD*(1) C4–C10

0.5790* (sp 2.67 )c+0.8153 (sp 1.92 )O 0.7172 (sp2.30 )c + 0.6969 (sp2.02 )c 0.8907 (sp3.00 )o + 0.4546 (s)H 0.4546 (sp3.00 )o − 0.8907 (s)H 0.7078 (sp1.35 )c + 0.7064 (sp1.86 )c 0.6402 (p)c + 0.7682 (p)c 0.7682 (p)c − 0.6402 (p)c 0.5875 (sp2.27 )c + 0.8092 (sp1.47 )O 0.5598 (p)c + 0.8286 (p)O 0.8286 (p)c − 0.5598 (p)o 0.7106 (sp2.27 )c + 0.7036 (sp2.03 )c 0.7036 (sp2.27 )c − 0.7106 (sp2.03 )c


00443


1241

Table 3. Hybridization of some bonding and antibonding interactions of all species in path 1 for the reaction of cyclohexyl isocyanide and HFPD. Interaction

Transition state 1 0.7927 + 0.6096 0.8449 (p)N + 0.5349 (p)C 0.7998 (p)N + 0.6003 (p)C

0.7640 (sp1.51 )N + 0.6452 (sp1.26 )c 0.7681 (p)N + 0.6404 (p)\c —

BD(1) C6–C2 BD(2) C6–C2

0.7100 (sp1.25 )c + 0.7042 (sp1.57)c 0.6913 (p)c + 0.7226(p)c

0.7075 (sp1.28 )c + 0.7067 (sp1.63 )c 0.6758 (p)c + 0.7371 (p)c

BD(1) C6–C9 BD(1) C6–O7

0.7141 (sp2.30 )c + 0.7001 (sp1.91 )c 0.5764 (sp2.99 )c + 0.8172 (sp1.99 )o

0.7168 (sp2.28 )c + 0.6973 (sp1.97 )c 0.5762 (sp2.93 )c + 0.8173 (sp1.93 )o

BD(1) C2–C4 BD(1) C2–O3

0.7488 (sp0.78 )c + 0.6628 (sp4.68 )C —

0.6798 (sp2.13 )c + 0.7334 (sp2.65 )c 0.5613 (sp3.18 )c + 0.8276 (sp3.34 )o

BD(1) C4–O3 BD(1) C4–C10 BD(1) C5–C4

0.7853 (sp2.09 )O + 0.6191 (sp2.84 )c 0.7203 (sp2.79 )c + 0.6937 (sp1.95 )c 0.7030 (sp1.97 )c + 0.7112 (sp2.33 )c

0.8135 (sp6.69 )o + 0.5816 (sp8.76 )c 0.7247 (sp2.45 )c + 0.6891 (sp1.94 )c 0.6984 (sp2.01 )c + 0.7157 (sp1.99 )c

BD*(1) BD*(2) BD*(2) BD*(1) BD*(1)

— 0.5349 (p)N − 0.8449 (p)c 0.7226 (p)c − 0.6913 (p)c — 0.6628 (sp0.78 )c − 0.7488 (sp4.68 )c

0.6452 (sp1.51 )N − 0.7640 (sp1.26 )c 0.6404 (p)N − 0.7681 (p)c 0.7371 (p)c − 0.6758 (p)c — —

0.7030 (sp2.33 )c − 0.7112 (sp1.97 )c 0.6937 (sp2.79 )c − 0.7203 (sp1.95 )c

— —

BD*(1) C4–C5 BD*(1) C4–C10 Interaction

(sp1.33 )C

Intermediate 1

BD(1) N1–C2 BD(2) N1–C2 BD(3) N1–C2

N1–C2 N1–C2 C6–C5 C2–O3 C2–C4

(sp0.93 )N

Transition state 2

BD(1) N1–C6 BD(1) N1–C2

0.7738

BD(1) C6–C5

0.7107

— 0.6335 (sp1.97 )C

0.7764 0.7935

0.7035(sp1.97 )C

0.7147

(sp2.05 )N + (sp1.36 )c + (sp2.11 )c

Product (sp2.30 )N + (sp2.08 )N + (sp2.62 )c +

0.6302 (SP2.93 )c 0.6086 (SP2.14 )c 0.6994 (SP2.41 )c

BD(1) C6–C9 BD(1) C6–O7

+ 0.7151 0.5694 (sp2.95 )c +

0.6991(sp2.00 )C 0.8221 (sp1.78 )o

0.7153 + 0.6988 (sp1.91 )c 3.54 0.5832 (sp )c + 0.8124 (sp2.21 )o

BD(1) C2–C4

0.6758 (sp2.13 )c + 0.7371 (sp1.95 )c

0.6856 (sp1.89 )c + 0.7279 (sp2.32 )c

(sp1.95 )c

(sp3.00 )c

BD(1) C2–O3 BD(2) C2–O3

+ 0.8043 0.5943 0.5571 (p)c + 0.8305 (p)o

(sp1.45 )o

0.5917 (sp1.99 )c + 0.8062 (sp1.36 )o 0.5621 (p)c + 0.8271 (p)o

BD(1) C5–C4 BD(2) C5–C4 BD(1) C4–C10

0.7077 (sp1.75 )c + 0.7065 (sp1.71 )c 0.7558 (p)c + 0.6548 (p)c 0.7216 (sp2.44 )c + 0.6923 (sp1.90 )c

0.7005 (sp1.69 )c + 0.7137 (sp1.64 )c 0.6901 (p)c + 0.7237 (p)c 0.7266 (sp2.12 )c + 0.6871 (sp1.88 )c

BD*(1) N1–C2

0.6335 (sp2.05 )N + 0.7738 (sp1.97 )c

0.6086 (sp2.08 )N − 0.7935 (sp2.14 )c

(sp1.95 )c

(sp1.45 )o

BD*(1) C2–O3 BD*(2) C2–O3

0.8043 − 0.5943 0.8305 (p)c − 0.5571 (p)o

BD*(1) C2–C4 BD*(2) C5–C4

0.7371 (sp2.13 )c − 0.6758 (sp1.95 )c 0.6548 (p)c − 0.7558 (p)c

— 0.8271 (p)c − 0.5621 (p)o 0.7279* (sp1.89 ) − 0.6856 (sp 0.7237 (p)c − 0.6901 (p)c

2.32 )c

2 interaction energies (∆Eij ) for a few donor–acceptor interactions are mentioned 2 in Table 5. ∆Eij represents noncovalent delocalization effects, which are associated with interactions between filled (donor) and unfilled (acceptor) orbitals. Such interactions are naturally described as being of “donor–acceptor”, “charge transfer”, or generalized “Lewis base–Lewis acid” type.


1242

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M. D. Davari et al. Table 4. Hybridization of some lone pairs of all species in path 1 for the reaction of cyclohexyl isocyanide and HFPD. Cyclohexyl isocyanide Lone pair

hyba

occb

LP(1) C2

sp0.42

1.97

HFPD

TS-1

hyb

occ

hyb

occ

LP(1) O3 LP(2) O3 LP(3) O3

sp0.80 sp23.35

1.97 1.85

sp0.50 p p

1.98 1.87 1.62

LP(1) O7 LP(2) O7

sp1.45 p

1.97 1.74

sp1.19 p

1.98 1.86

Int-1 Lone pair

hyb

LP(1) N1 LP(2) N1

sp2.34

LP(1) O3 LP(2) O3

sp0.56 p

LP(1) O7 LP(2) O7

sp1.22 p

TS-2 occ

hyb

1.86

sp1.80

Product occ

hyb

occ 1.72

p

1.93 1.11

sp24.78

1.98 1.81

sp0.70 p

1.97 1.85

sp0.73 p

1.97 1.85

1.98 1.85

sp1.38 p

1.97 1.77

sp1.07 p

1.97 1.94

p

0.88

LP*(1) C6 a hyb

stands for hybridization. b occ stands for occupancy.

2 (kcal mol−1 )) Table 5. NBO second-order interaction energies (∆Eij for some donor–acceptor interactions in path 1 for the reaction of cyclohexyl isocyanide and HFPD.

Donor LP(3) LP(3) LP(2) LP(2) LP(2)

O3 O3 O3 O3 O3

Acceptor

TS-1

BD*(1) BD*(2) BD*(1) BD*(1) BD*(2)

16.41 13.07 17.19 14.06 16.41

C2–C4 N1–C2 C4–C10 C4–C5 N1–C2

LP(1) N1 LP(2) N1

BD*(1) C2–O3 BD*(2) C2–O3

LP(2) O7 BD(2) C5–C4

LP*(1) C6 LP*(1) C6

Int-1

TS-2

35.4 29.37 66.62 71.53 78.4

By taking a closer look at Tables 4 and 5 for transition state 1, it is evident that charge transfer from O3 p-orbital causes strength of π and σ bonds to decrease between N1 and C2 atoms and between C2 and C4 atoms, respectively. This fact 2 values of 13.07 and 16.41 kcal mol−1 for charge transitions is obvious from ∆Eij from LP(3)O(3) to BD*(2)N1–C2 and to BD*(1)C2–C4, respectively. Same tables suggest that charge transfer from O3 p-orbital brings about weakening of σ bonds between C4 and C10, as well as C4 and C5 atoms. This aspect becomes clear


00443


1243

by taking into account the charge transitions from LP(3)O(3) to BD*(2)C4–C10 2 values amount to 17.19 and 14.06, respectively. and to BD*(1)C4–C5 whose ∆Eij Therefore in the transition state 1, presence of nonbonding electrons in two oxygen’s orbitals is associated with lowering of bond orders in C2-N1, C2–C4, C4–C10, and C4–C5 bonds. Therefore, the main factor in destabilization of this transition state moiety can be attributed to the weakening of σ-bonds between atoms C2–C4, C4– C5, and C4–C10. The aforementioned interaction (especially charge transfer from LP(3)O3 to BD*(1)C2–C4 and BD*(2)N1–C2) can be regarded as confirmation of the transition state 1 formation. Note that the results of Tables 4 and 5 indicate that π bond of C2 and N1 atoms has been weakened due to O3 p-orbital charge transfer in intermediate 1. Such fact can be recognized by charge transfer from LP(2)O3 to BD*(2)N1–C2 in intermediate 1 whose second-order interaction energy is 35.4 kcal mol−1 . Tables 4 and 5 also reveal interaction of N1 hybrid orbital to σ bond between O3 and C2 atoms in intermediate 1. This observation is associated 2 value equal with the charge transfer from LP(1)N1 to BD*(1)C2–O3 with a ∆Eij −1 to 29.37 kcal mol . Such interaction is an indication of a tendency for σ bond dissociation between C2 and O3 bond in above species, which is in accord to the change expected along the reaction coordinate for path 1 mechanism as indicated for the position of intermediate 1 in Fig. 4. With regard to Table 4, it becomes clear that each of N1 and C6 atoms of transition state 2 contains a single electron in its corresponding p-orbitals. Thus, this compound can be regarded as a di-radical species. Paying closer attention to Tables 4 and 5 results, it is evident that charge transfer from C4–C5 π bond to C6 nonbonding p-orbital in the above transition state has occurred. Such fact is clear from the interaction of BD(2)C4–C5 as donor to LP*(1)C6 as acceptor with a second-order interaction energy of 78.4 kcal mol−1 . In addition, by looking at above tables, charge transfer from N1 p-orbital to C2–O3 π bond greatly reduces the latter bond’s strength. Such claim is supported by taking into account the donor LP(2)N1– 2 value amounting to 66.62 kcal mol−1 . acceptor BD*(2)C2O3 interaction with a ∆Eij However, in the above resonance species, transfer of an electron pair between C6 and C7 atoms accompanies with a π bond formation between them, which adds stability to this compound. Above observations are validated by considering charge transfer from LP(2)O7 to LP*(1)C6 with its second-order interaction energy of 71.53 kcal mo−1 . Therefore, even though transition state 2 species as a di-radical becomes less stable relative to transition state 1 due to charge transfer from donor BD(2)C4–C5 to acceptor LP*(1)C6 as well as from LP(2)N1 to BD*(2)C2–O3, but electron pair resonance between O7 and C6 atoms counteracts above effect thereby reducing its energy level with respect to that of transition state 1. From point of view of hybridization changes and with regard to results presented in Tables 2 and 3, it is informative to point out change of C2 atom’s of cyanide hybridization from sp to sp3 and that of C6 atom of HFPD from sp2 to sp3 along path 1 of reaction.


1244

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M. D. Davari et al.

3.4.2. NBO analysis of reaction’s path 2 Table 6 summarizes results obtained for atoms hybridization in some of bonding and antibonding interactions for all species involved in path 2 of reaction. Table 7 includes some lone pair hybridization while NBO second-order interaction energies 2 ) for a few donor–acceptor interactions are given in Table 8 for same path. (∆Eij Considering results of Tables 7 and 8, it becomes clear that in transition state 1, intense charge transfer from O3 p-orbital has weakened C4–C5 π bond.

Table 6. Hybridization of some bonding and antibonding interactions for all species in path 2 for the reaction of cyclohexyl isocyanide and HFPD. Interaction

Intermediate 1

Transition state 1

BD(1) N1–C2 BD(2) N1–C2 BD(3) N1–C2

0.7954 (sp0.94 )N + 0.6061 (sp1.26 )c 0.5878 (p)c + 0.8090 (p)N 0.5927 (p)c + 0.8054 (p)N

0.7714 (sp1.39 )N + 0.6364 (sp1.57 )c 0.7595 (p)N + 0.6505 (p)c —

BD(1) C2–C6

0.7314 (sp0.80 )c + 0.6819 (sp3.72 )c

0.6978 (sp1.92 )c + 0.7162 (sp2.92 )c

(sp1.44 )c

1.72 )c

0.7122 (sp1.33 )c + 0.7020 (sp1.84 )c 0.7026 (p)c + 0.7116 (p)c

BD(1) C4–C5 BD(2) C4–C5

+ 0.7116 (sp 0.7025 0.5962 (p)c + 0.8028 (p)c

BD(1) C4–O3 BD(1) C2–O3

0.5971 (sp2.34 )c + 0.8022 (sp1.59 )o —

0.5678 (sp3.15 )c + 0.8232 (sp2.30 )o 0.5558 (sp2.74 )c + 0.8313 (sp2.40 )o

BD(1) C6–O7 BD(1) C6–C9 BD(1) C5–C6

0.5911 (sp3.83 )c + 0.8066 (sp2.31 )o 0.7253 (sp2.93 )c + 0.6884 (sp1.98 )c 0.6675 (sp2.35 )c + 0.7446 (sp2.06 )c

0.5912 (sp3.60 )c + 0.8065 (sp2.29 )o 0.7213 (sp2.96 )c + 0.6927 (sp1.91 )c 0.6962 (sp2.33 )c + 0.7179 (sp2.64 )c

BD(1) C4–C10

0.7039 (sp 2.44)c + 0.7103 (sp 1.83)c

0.7213 (sp

BD*(2) C4–C5 BD*(1) C4–C10

0.8028 (p)c − 0.5962 (p)c 0.7103 (sp 2.44)c − 0.7039 (sp 1.83)c

0.7116 (p)c − 0.7026 (p)c —

BD*(1) O3–C2 BD*(2) C2–N1 Interaction

+ 0.6926 (sp1.94 )c

0.5558 (sp2.40 )o − 0.8313 (sp2.74 )c 0.7595 (p)c − 0.6505 (p)N

— — Transition state 2

Intermediate 1

BD(1) N1–C2 BD(2) N1–C2 BD(3) N1–C2

(sp1.33 )c

0.8043 0.5943 0.8140 (p)N + 0.5808 (p)C 0.8094 (p)N + 0.5872 (p)C

0.7640 (sp1.51 )N + 0.6452 (sp1.26 )c 0.7681 (p)N + 0.6404 (p)c —

BD(1) C5–C4 BD(1) C4–C10

0.7143 (sp1.79 )C + 0.6999 (sp1.46 )C 0.7012 (sp2.50 )C + 0.7130 (sp1.86 )C

0.6984 (sp2.01 )c + 0.7157 (sp1.99 )c 0.7247 (sp2.45 )c + 0.6891 (sp1.94 )c

BD(1) C4–O3 BD(2) C4–O3

0.5955 (sp2.25 )C + 0.8034 (sp1.50 )O 0.5518 (p)C + 0.8340 (p)O

0.8135 (sp6.69 )o + 0.5816 (sp8.76 )c

BD(1) C6–C2 BD(1) C6–O7 BD(1) C6–C9

0.6331 (sp5.75 )C + 0.7741 (sp0.77 )C 0.5852 (sp3.50 )C + 0.8109 (sp2.03 )O 0.7225 (sp2.81 )C + 0.6914 (sp1.96 )C

— 0.5762(sp2.93 )c + 0.8173 (sp1.93 )o 0.7168(sp2.28 )c + 0.6973 (sp1.97 )c

BD(1) C6–C5 BD(2) C6–C5

0.7309 (sp1.72 )C + 0.6825 (sp2.04 )C —

0.7075 (sp1.28 )c + 0.7067 (sp1.63 )c 0.6758 (p)c + 0.7371 (p)c

BD(1) C2–C4 BD(1) C2–O3 BD*(1) C2–C6 BD*(2) C4–O3 BD*(1) C4–C10

(sp0.92 )N +

2.04 )c

— —

0.6798 (sp2.13 )c + 0.7334 (sp2.65 )c 0.5613 (sp3.18 )c + 0.8276 (sp3.34 )o

0.6331(sp0.77 )C − 0.7741 (sp5.74 )C 0.8340 (p)C − 0.5518 (p)O 0.7130* (sp 2.50)C − 0.7012 (sp 1.86)C

— — —


00443


1245

Table 6. (Continued ) Interaction

Transition state 3

Product

BD(1) N1–C6 BD(1) N1–C2

— 0.7738 (sp2.05 )N + 0.6335 (sp1.97 )C

0.7764 0.7935

BD(1) C6–C5

0.7107 (sp1.36 )c + 0.7035 (sp1.97 )C

0.7147

(sp2.11 )c

(sp2.30 )N + (sp2.08 )N + (sp2.62 )c +

0.6302 (SP2.93 )c 0.6086 (SP2.14 )c 0.6994 (SP2.41 )c

BD(1) C6–C9 BD(1) C6–O7

+ 0.6991 0.7151 0.5694 (sp2.95 )c + 0.8221

(sp2.00 )C (sp1.78 )o

0.7153 + 0.6988 (sp1.91 )c 0.5832 (sp3.54 )c + 0.8124 (sp2.21 )o

BD(1) C2–C4

0.6758 (sp2.13 )c + 0.7371 (sp1.95 )c

0.6856 (sp1.89 )c + 0.7279 (sp2.32 )c

(sp1.95 )c

(sp3.00 )c

BD(1) C2–O3 BD(2) C2–O3

+ 0.8043 0.5943 0.5571 (p)c + 0.8305 (p)o

(sp1.45 )o

0.5917 (sp1.99 )c + 0.8062 (sp1.36 )o 0.5621 (p)c + 0.8271 (p)o

BD(1) C5–C4 BD(2) C5–C4

0.7077 (sp1.75 )c + 0.7065 (sp1.71 )c 0.7558 (p)c + 0.6548 (p)c

0.7005 (sp1.69 )c + 0.7137 (sp1.64 )c 0.6901 (p)c + 0.7237 (p)c

BD(1) C4–C10

0.7216 (sp2.44 )c + 0.6923 (sp1.90 )c

0.7266 (sp2.12 )c + 0.6871 (sp1.88 )c

BD*(1) N1–C2

0.6335 (sp2.05 )N − 0.7738 (sp1.97 )c

0.6086 (sp2.08 )N − 0.7935 (sp2.14 )c

BD*(1) C2–O3 BD*(2) C2–O3

0.8043 (sp1.95 )c + 0.5943 (sp1.45 )o 0.8305 (p)c − 0.5571 (p)o

— 0.8271 (p)c − 0.5621 (p)o

BD*(1) C2–C4 BD*(2) C5–C4

0.7371 (sp2.13 )c − 0.6758 (sp1.95 )c 0.6548 (p)c − 0.7558 (p)c

0.7279* (sp1.89 ) − 0.6856 (sp2.32 )c 0.7237 (p)c − 0.6901 (p)c

Table 7. Hybridization of some lone pairs of all species in path 2 for the reaction of cyclohexyl isocyanide and HFPD. Cyclohexyl isocyanide Lone pair

hyba

occb

LP(1) C2

sp0.42

1.97

HFPD

Int-1

TS-1

hyb

occ

hyb

occ

hyb

occ

LP(1) O3 LP(2) O3 LP(3) O3

sp0.80 sp23.35

1.97 1.85

sp0.63 P P

1.97 1.85 1.59

sp1.48 p

1.97 1.79

LP(1) O7 LP(2) O7

sp1.45 P

1.97 1.74

sp1.08 P

1.98 1.93

sp1.03 p

1.98 1.94

sp2.75

1.87

LP(1) N1 TS-2 Lone pair

hyb

LP(1) O3 LP(2) O3

Sp0.67

LP(1) O7 LP(2) O7

Int-1 occ

hyb

P

1.98 1.88

sp0.56

sp1.20 p

1.97 1.90

LP(1) N 1 LP(2) N 1 LP(1) C5

p

occ

hyb

P

1.98 1.81

sp0.70

sp1.22 P sp2.34

Product occ

hyb

occ

p

1.97 1.85

sp0.73 p

1.97 1.85

1.98 1.85

sp1.38 p

1.974 1.77

sp1.07 p

1.97 1.94

1.86

sp1.80 p

1.93 1.11

sp24.78

1.72

p

0.88

1.26

LP*(1)C6 a hyb

TS-3

stands for hybridization. b occ stands for occupancy.


1246

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M. D. Davari et al. 2 (kcal mol−1 )) for some Table 8. NBO second-order interaction energies (∆Eij donor–acceptor interactions in path 2 for the reaction of cyclohexyl isocyanide and HFPD.

Donor

Acceptor

TS-1

LP(3) O3 LP(2) O3 LP(2) O3

BD*(2) C4–C5 BD*(2) C4–C5 BD*(2) N1–C2

95.65

LP(1) N1 LP(2) N1

BD*(1) C2–O3 BD*(2) C2–O3

LP(1) C5 LP(1) C5

BD*(1) C2–C6 BD*(2) C4–O3

LP(2) O7 BD(2) C4–C5

LP*(1) C6 LP*(1) C6

Int-1

TS-2

Int-1

26.66 29.85

35.4

25.99

29.37

TS-3

66.62 28.68 114.83 71.53 78.4

Such observation is justified by donor LP(3)O(3) acceptor BD*(2)C4–C5 interaction with a second-order interaction energy value of 95.65 kcal mol−1 . Thus, extensive reduction in C4–C5 π bond strength can be regarded as a factor in introduction of activation barrier in reaching from reactants to intermediate 1 via transition sate 1. From Tables 6–8, it is understood that in intermediate 1 , σ bond strength between O3 and C2 atoms drops due to charge transfer from N1 sp2 hybrid orbital, which is 2 associated with the interaction between LP(1)N1 and BD*(1)C2–O3 having a ∆Eij −1 value of 25.99 kcal mol . This fact is in accord to this intermediate’s position in Fig. 6 as far as the reaction coordinate and changes of molecular geometry from reactant to this species are concerned. Similarly, Tables 6–8 also reveal that charge transfer from O3 p-orbital causes a loss of C4–C5 and N1–C2 π bonds strength. This fact is evident if we note charge transfers of LP(2)O3 to BD*(2)C4–C5 and to BD*(2)N1–C2 whose second-order interaction energies are 26.66 and 29.85 kcal mol−1 , respectively. The aforementioned two interactions denote π resonance among C5, C4, and O3 as well as resonance among N1, C2, and O3 atoms, which assure intermediate 1 stability. Table 7 indicates the fact that a nonbonding electron pair can be attributed to C5 atom’s p-orbital of transition state 2. As it is suggested by results in Table 8, charge transfer from C5 p-orbital leads to loss of σ bond strength between C2 and C6 atoms. Such case is evident also from charge transfer of LP(1)C5 to BD*(1)C2–C6 2 value of 26.68 kcal mol−1 . Such interaction has destabilized transition with a ∆Eij state 2 such that its energy level has been raised relative to that of intermediate 1 with a considerable amount. Besides, regarding Table 8, weakening of C4–O3 π bond strength can be accounted for by charge transfer from C5 p-orbital. This observation is associated with interaction between LP(1)C5 and BD*(2)C4–O3 having a second-order interaction energy of 114.83 kcal mol−1 . The latter interaction signifies stabilizing resonance interaction among C5, C4, and O3 that can be held responsible for transition state 2 having almost same energy level as that of transition state 1. Comparison between interactions involved in intermediate 1 to those of intermediate 1 based on results given in Table 8 suggests that the effective


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C4-C10

p of O3

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p of O3 C2-C 4

C4-C5

(a)

(b)

Fig. 7. (a) HOMO and (b) HOMO-1 of transition structure 1 in path 1 of the reaction.

factor in making the former species more stable than the latter can be attributed to stabilizing resonance in this molecule. It can be emphasized that transition state 3 of path 2 is actually the same as transition state 2 of path 1 whose interactions had already been discussed in the preceding sections. Noting to these interactions, it is conclusively clear that stabilizing resonance existing between C6 and O7 atoms of above species can be held accountable of it having comparable energy level as that of transition state 2 in path 2, even though it is di-radical in nature. 3.5. MO analysis The molecular orbital calculations have been carried out for all components involved in the two reaction paths. Such analysis let us investigate bonding and antibonding electronic interactions for electrons existing in outermost occupied MOs. 3.5.1. MO analysis of path 1 The HOMO and HOMO-1 of transition state 1 as shown in Figs. 7(a) and 7(b) are selected for the following discussions and also confirmation of NBO analysis. In HOMO, O3 p-orbital shows antibonding interaction with phase combination of orbitals residing on C4 and C10 and those on C4 and C5 atoms, which leads to weakening of C4–C10 and C4–C5 σ bonds. In addition, HOMO-1 of same species reveals antibonding interaction of O3 p-orbital with phase combination of orbitals on C2 and C4 atoms causing reduction in electron cloud density of this bond, which results in weakening of C2–C4 σ bond. Figures 8(a) and 8(b) depict HOMO-1 and HOMO-2 of intermediate 1, respectively. In HOMO-1, O3 p-orbital antibonding interaction with the electronic cloud formed by N1 and C2 atoms can be mentioned, which results in weakening of N1–C2 π bond strength in this species. In HOMO2, however, nitrogen atom’s sp2 hybrid orbital involves antibonding interaction with phase combination of orbitals on C2 and O3 atoms. Such interaction leads to


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sp2 of N

C2-O3

N1-C2

p of O3

(a)

(b)

Fig. 8. (a) HOMO-1 and (b) HOMO-2 of intermediate 1 in path 1 of the reaction.

p of O3

N1-C2

p of O3

C4-C 10 C4-C5 C4-C 5

(a)

(b)

Fig. 9. (a) HOMO of transition structure 1, and (b) intermediate 1 in path 2 of the reaction.

weakening of C2–O3 σ bond. All above results completely corroborate with those presented in NBO analysis earlier. 3.5.2. MO analysis of path 2 Figure 9(a) illustrates HOMO molecular orbital of transition state 1 in path 2 of reaction. As it is apparent, O3 p-orbital in this HOMO shows antibonding interaction with the electronic cloud resulting from C4 and C5 overlap leading to weakening of C4–C5 π bond. In Fig. 9(b), HOMO MO of intermediate 1 in path 2 has been visualized. This HOMO refers to O3 p-orbital antibonding interaction with phase combination of orbitals residing on N1 and C2 as well as C4 and C5 atoms. Such interaction has resulted in weakening of N1–C2 and C4–C5 π bonds.


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Again all above observations are all in full accord to previously presented NBO analysis for path 2 of reaction. 4. Conclusions Kinetics and mechanism of the reaction between cyclohexyl isocyanide and HFPD has been investigated by utilizing transition state theory and using B3LYP method. 6-31G∗ basis set has been chosen based on a series of optimization calculation using various basis sets. Such task was carried out on product molecule since comparison between available X-ray structural parameters and calculated data was feasible for this species. Based on previous experimental studies, two paths namely direct attack and conjugate addition have been proposed for the desired reaction. Path 1 includes direct addition of cyclohexyl isocyanide to the carbonyl carbon atom of HFPD to yield imino-oxirane as an intermediate. The latter species then undergoes a fast Cope–Claisen-type rearrangement to give product. As has been presented elsewhere, we have proposed a new path 2 as well as the original path 1 and have presented corresponding mechanisms for each path. In the newly found path 2, reactants are encountered by a new intermediate having a five-membered ring including an oxygen atom as a ring member. Product formation occurs by conversion of above species to another intermediate, which is the same as that of path 1. Our kinetics analysis has revealed that for path 1 of the reaction, production of intermediate is the rate determining step of the process. Whereas, path 2 includes two initial equilibriums followed by a product formation step. NBO analysis of reaction path 1 indicates that in the first transition state, p-orbitals of the oxygen atom bearing minus charge weaken some of σ bonds in this species. While in the intermediate molecule, nitrogen atom’s lone pair weakens the bond existing between isocyanide’s carbon atom and HFPD’s oxygen atom. Moreover, the second transition state is a di-radical species, for which NBO analysis reveals unusual stability due to resonance between these unpaired electrons and π electron cloud of this species. For path 2 of the reaction, such analysis shows that for transition state 1 some positive charge can be assigned to nitrogen atom while some negative charge to one of oxygen atoms that tend to yield keto form by coming into resonance with its adjacent π bond. NBO also shows that in the first intermediate of path 2 oxygen lone pair in five-membered ring has resonance with π bonds inside and outside of the ring leading to this species stability. The same analysis for second transition state of path 2 reveals that even though carbon’s lone pair has resonance with π bond of C=O, but such lone pair weakens the main σ bond generated via isocyanide attack to alkane–dione of this transition state, which results in a less stable species compared with aforementioned intermediate. MO calculations satisfy some of NBO findings. Overall, computational results suggest that our newly proposed path 2 involving the Michael addition along with a Cope–Claisen-type rearrangement tends to be both the energetically and kinetically favorable route.


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Acknowledgments The authors are grateful to Professor Seik Weng Ng for making available his software (G98W) and hardware (machine time) facilities. The authors would also like to thank the Research and Graduate Study Councils of Shahid Beheshti University for financial support. References 1. Ugi I, Isonitrile Chemistry, Academic Press, New York, 1971. 2. Patai S, Rappoport Z, The Chemistry of the Functional Groups, Wiley, Chichester, UK, 1993. 3. Moderhack D, Synthesis 1083, 1985. 4. D¨ omling A, Ugi I, Angew Chem Int Ed Engl 39:3168, 2000. 5. Domling A, Chem Rev 106(1):17, 2006. 6. Yavari I, Shaabani A, Asghari S, Olmstead MM, Safari N, J Fluorine Chem 86:77, 1997. 7. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery, Jr, JA, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA, Gaussian 98, Revision A.9, Gaussian, Inc., Pittsburgh, PA, 1998. 8. Zahedi M, Bahrami H, Shahbazian Sh, Safari N, Ng SW, J Mol Struct Theochem 633:21, 2003. 9. Becke AD, J Chem Phys 98:5648, 1999. 10. Onsager GL, J Am Chem Soc 58:1486, 1936. 11. Wong MW, Frisch MJ, Wiberg KB, J Am Chem Soc 114:1645, 1992. 12. Reed AE, Curtiss LA, Wienhold F, Chem Rev 88:899, 1998. 13. Eyring H, J Chem Phys 3:107, 1935. 14. Wynne-Jones WF, Eyring H, J Chem Phys 3:492, 1935. 15. Eyring H, Chem Rev 3:107, 1935. 16. Arrhenius S, Z Phys Chem (Leipzig) 4:226, 1889.

theoretical study on the kinetics and mechanism of the reaction of

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