Prediction of Kinetic Isotope Effects for Various Hydride Transfer

Article pubs.acs.org/JPCA

Prediction of Kinetic Isotope Effects for Various Hydride Transfer Reactions Using a New Kinetic Model Guang-Bin Shen,† Ke Xia,† Xiu-Tao Li,† Jun-Ling Li,† Yan-Hua Fu,† Lin Yuan,† and Xiao-Qing Zhu*,†,‡ †

Department of Chemistry, The State Key Laboratory of Elemento-Organic Chemistry and the ‡Collaborative Innovation Center of Chemical Science and Engineering, Nankai University, Tianjin 300071, China S Supporting Information *

ABSTRACT: In this work, kinetic isotope effect (KIEself) values of 68 hydride self-exchange reactions, XH(D) + X+ → X+ + XH(D), in acetonitrile at 298 K were determined using a new experimental method. KIE values of 4556 hydride cross transfer reactions, XH(D) + Y+ → X+ + YH(D), in acetonitrile were estimated from the 68 determined KIEself values of hydride self-exchange reactions using a new KIE relation formula derived from Zhu’s kinetic equation and the reliability of the estimations was verified using different experimental methods. A new KIE kinetic model to explain and predict KIE values was developed according to Zhu’s kinetic model using two different Morse free energy curves instead of one Morse free energy curve in the traditional KIE theories to describe the free energy changes of X−H bond and X−D bond dissociation in chemical reactions. The most significant contribution of this paper to KIE theory is to build a new KIE kinetic model, which can be used to not only uniformly explain the various (normal, enormous and inverse) KIE values but also safely prodict KIE values of various chemical reactions.

I. INTRODUCTION Kinetic isotope effect (KIE) is a ubiquitous kinetic phenomenon of chemical reactions,1−7 and has received a wide application in examining the mechanism of various chemical reactions.8−11 The primary KIE values are usually 2−9;12−15 some of the reactions show enormous KIE values (KIE > 9).16−20 Chemists used to use the two different theories to explain the difference of KIE values: one is the classical zero-point energy theory21−24 and the other is the quantum tunneling theory.25−28 Although these two different traditional KIE theories can be used to explain some experimental observations,29−31 but they can not explain all KIE values, and not to mention predicting KIE values of various chemical reactions, which means that the two traditional KIE theories all have fundamental problems. In this work, a new KIE kinetic model was developed according to Zhu’s kinetic model for hydride transfer reactions reported previously.32 The new KIE kinetic model not only can uniformly explain all the KIE values, but also can predict KIE values of various chemical reactions. As a first application example of the new KIE kinetic model, KIE values of 4556 hydride transfer reactions in acetonitrile at 298 K are estimated herein. The results are all reliable.

Table 1. Notations of Chemical Reactions, Rate Constants, Activation Free Energy, and Free Energy Change Used in This Work

II. PREDICTION METHOD OF KIE VALUES To make the following description more concise, some chemical concepts, such as chemical reactions, rate constants, activation free energy and free energy change in this work were expressed using some special notations (see Table 1).

(2)

© 2016 American Chemical Society

reactions

notations

rate constant

activation energy

free energy change

XH + Y → X + YH XD + Y → X + YD XD + X → X + XD YD + Y → Y + YD

XH/Y XD/Y XD/X YD/Y

kXH/Y kXD/Y kXD/X kYD/Y

ΔG‡XH/Y ΔG‡XD/Y ΔG‡XD/X ΔG‡YD/Y

ΔGoXH/Y ΔGoXD/Y ΔGoXD/X ΔGoYD/Y

According to the definition of KIE and the Eyring equation (eq 1), it is clear that the magnitude of KIE is only dependent on the difference of the activation energies between the two chemical reactions with the different isotopic atoms (H and D) (eq 2). Eyring equation: k = (kBT /h) exp( −ΔG‡/RT )

(1)

KIE: kXH/Y kXD/Y

=

⎧ ΔG⧧ XH/Y −ΔG⧧ XD/Y ⎫ ⎪ ⎪ ⎬ = exp⎨ − ⎪ ⎪ RT exp[−ΔG XD/Y /RT ] ⎩ ⎭

exp[−ΔG⧧ XH/Y /RT ] ⧧

Received: October 16, 2015 Revised: January 22, 2016 Published: March 3, 2016 1779

DOI: 10.1021/acs.jpca.5b10135 J. Phys. Chem. A 2016, 120, 1779−1799

Article

The Journal of Physical Chemistry A

Table 2. Point-to-Point Comparisons between eq 4 and Marcus Cross Relation Formula about the Origin, Nature, and Prerequisite

Zhu’s equation:37

From eq 2, it is clear that, as long as activation energies of hydrogen atom transfer reactions (XH/Y) and the corresponding deuterium atom transfer reactions (XD/Y) are available, KIE values (KIEXH/Y) of the chemical reactions can be obtained, which means that the key work to predict KIE values of chemical reactions is to estitimate activation energies of hydrogen atom transfer reactions and the corresponding deuterium atom transfer reactions. How do we estimate the activation energies of chemical reactions? If the Marcus equation (eq 3) is used to estimate the activation energies of hydrogen atom transfer reactions (ΔG‡XH/Y) and the deuterium atom transfer reactions (ΔG‡XD/Y) according to the corresponding thermodynamic driving forces (ΔGoXH/Y and ΔGoXD/Y), the results show that the activation energies of hydrogen atom transfer reactions are all equal or close to the activation energies of the corresponding deuterium atom transfer reactions (i.e., ΔG‡XH/Y ≅ ΔG‡XD/Y), because the free energy changes of hydrogen atom transfer reactions (ΔGoXH/Y) are all equal or quite close to the free energy changes of the corresponding deuterium atom transfer reactions (i.e., ΔGoXH/Y ≅ ΔGoXD/Y).33 That is, if Marcus equation (eq 3) is used to estimate KIE values of chemical reactions, the results show that KIE values of all chemical reactions are equal or close to 1 (i.e., KIEXH/Y ≅ 1), which evidently is not true. The main reason is that the Marcus theory violates the law of conservation of energy.34,35 This result proves that the Marcus theory is wrong once again. Marcus’ equation: ‡ ΔG XH/Y =

ΔG‡ XH/Y = 1/2(ΔG‡ XH/X + ΔG‡ YH/Y ) + 1/2ΔGo XH/Y (4)

ΔG‡ XD/Y = 1/2(ΔG‡ XD/X + ΔG‡ YD/Y ) + 1/2ΔGo XD/Y (5)

kXH/Y kXD/Y ⎧ ΔG⧧ XH/X − ΔG⧧ XD/X + ΔG⧧ YH/Y − ΔG⧧ YD/Y ⎫ ⎪ ⎪ ⎬ = exp⎨ − ⎪ ⎪ 2RT ⎩ ⎭ (6)

kXH/Y kXD/Y

kXH/X kXD/X

×

k YH/Y k YD/Y

(7)

In our previous paper,32 we developed a new kinetic equation (eq 4)36 according to Zhu’s kinetic model to replace the Marcus equation for the kinetic description of hydride transfer reactions, because Marcus theory was discovered to violate the law of conservation of energy.34,35 In order to make a distinction between eq 4 and the Marcus cross relation formula (see Table 2), eq 4 in this paper is called Zhu’s equation.37 When the eq 4 is used to describe the kinetics of isotopic atom of hydrogen (D) transfer reactions, eq 4 is replaced by eq 5. Since the free energy change of hydrogen atom (H) transfer reactions is equal or quite close to that of the isotopic atom (D) transfer reactions,33 eq 6 and eq 7 can be derived from eq 4 and

⎞ ° ΔG XH/Y λ⎛ ⎜1 + ⎟ λ 4⎝ ⎠

(λ is a constant)

=

(3) 1780


Article

The Journal of Physical Chemistry A Scheme 1. Structures and Marks of 68 Hydride Donors Examined in This Work

eq 5 through eq 3 using the assumption that ΔGoXD/Y is equal to ΔGoXH/Y. From eq 7, it is clear that the magnitude of KIE of a chemical reaction is equal to the square root of the product of the two KIEself values of the corresponding two self-exchange reactions (there in after, KIEself is used to represent the KIE of the self-exchange reactions for simplicity). Obviously, eq 7 can be used to estimate KIE values of various chemical reactions as long as the KIEself values of the corresponding two selfexchange reactions are available. In order to test the application of eq 7, the KIE values of 4556 hydride transfer reactions (XH/Y+) are examined using eq 7 according to the KIEself values of the corresponding 68 hydride selfexchange reactions (XH/X+). The structures and marks of the hydride donors examined in this work are shown in Scheme 1.

III. DETERMINATION OF KIESELF Although the KIEself values of hydride self-exchange reactions (XH + X+ → X+ + XH) cannot be directly determined using conventional experimental methods due to no change between the reactants system and the products system,32 eq 7 can induce us to develop an efficient method to determine the KIEself values of various hydride self-exchange reactions in solution from the KIE values of the related hydride cross transfer reactions, because the KIE values of hydride cross transfer reactions (i.e., XH + Y+ → X+ + YH, X ≠ Y) generally can be determined using conventional experimental techniques as long as the thermodynamic driving forces of the hydride cross transfer reactions are appropriate. In order to obtain the KIEself values of various hydride self-exchange reactions in acetonitrile and establish the data library, 1H, 2H, and 7(MeO)H in Scheme 1 as well as their corresponding salts [1+, 2+, and 7(MeO) +] are carefully chosen as the hydride donors and hydride acceptors to construct three different hydride cross transfer reactions (eqs 8−10) and the mechanisms of the three hydride transfer reactions are proved by products analysis and the stoichiometry (1:1 mol/mol) (see Figures 1 and 2), respectively.

According to eqs 8−10, three equations, eqs 11−13, can be derived from eq 7:

1781

(KIE1H/2+)2 = KIE1H/ 1+ × KIE2H/ 2+

(11)

(KIE2H/7(MeO)+)2 = KIE2H/2+ × KIE 7(MeO)H/ 7(MeO)+

(12)


Article


Figure 3. Profile of the UV−vis absorbance of 1+ at λ = 420 nm during the hydride transfer from 1H to 2+ (black line) and from 1D to 2+ (red line). Conditions: 0.07 mM 2+, 3.34 mM 1H, and 3.35 mM 1D in dry acetonitrile at 298 K.

Figure 1. Comparison of UV-absorption spectra of the reactants (1H and 2+) and the products (1+ and 2H) for the hydride transfer from 1H to 2+ in acetonitrile.

(KIE1H/ 7(MeO)+)2 = KIE1H/ 1+ × KIE 7(MeO)H/ 7(MeO)+

(13)

1H + 1+ → 1+ + 1H

(14)

2H + 2+ → 2+ + 2H

(15)

7(MeO)H + 7(MeO)+ → 7(MeO)+ + 7(MeO)H

(16)

Table 3. Second Rate Constants (k2) and KIE of the Three Hydride Cross Transfer Reactions (eq 8-10) in Acetonitrile at 298 K hydride transfer reactions +

1H(D)/2 2H(D)/7(MeO) 1H(D)/7(MeO)

In eqs 11−13, KIE1H/1+, KIE2H/2+ and KIE7(MeO)H/7(MeO)+ are the KIEself of the three hydride self-exchange reactions (eqs 14-16), respectively. KIE 1H/2 + , KIE 2H/7(MeO) + and KIE1H/7(MeO)+ are the KIE of the three hydride cross transfer reactions (eqs 8−10), respectively, which can be directly derived from the corresponding second rate constants in acetonitrile at 298 K. The latter are determined using the stopped-flow UV−vis method (see Figure 3). The second rate constants (k2) and KIE of the three hydride transfer reactions (eq 8−10) are listed in Table 3. Athough the KIE values of the three hydride cross transfer reactions can be determined, the KIEself values of the hydride self-exchange reactions (eqs 14−16) cannot be derived from eqs 11−13, respectively, because each equation contains two unknowns. However, if the three eqs 11−13 are treated together to get a simultaneous solution after substituting the known data in Table 2 into the equations, the KIEself values of the three hydride self-exchange reactions (eqs 14−16) in acetonitrile at 298 K can be obtained. The result is that KIEself = 3.70 for 1H/1+, KIEself = 6.92 for 2H/2+, and KIEself = 1.61 for 7(MeO)H/7(MeO)+ in acetonitrile at 298 K, respectively. Since 1H and 2H are often used as good hydride donors,39−41 2+ and 7(MeO)+ are often used as good hydride

k2(H)a

k2(D)b

1.74 × 10 1.41 × 102 1.43 × 106 2

+ +

KIEXH/Yc

3.44 × 10 4.24 × 101 5.87 × 105 1

5.06 3.33 2.44

a

k2(H) is the second rate constant of the hydride transfer from XH in acetonitrile at 298 K. The data of k2 (M−1 s−1) are derived from experimental measurements using stoped-flow UV−vis spectrometer and the uncertainty is smaller than 5%. bk2(D) (M−1 s−1) is the second rate constant of the hydride transfer from XD in acetonitrile at 298 K, which are also derived from experimental measurements using stopped-flow UV−vis spectrometer and the uncertainty is smaller than 5%. cKIE = k2(H)/k2(D).

acceptors,42,43 and the corresponding KIEself values of the three hydride self-exchange reactions in acetonitrile at 298 K have been determined, it is not difficult to get the KIEself values of any another hydride self-exchange reactions XH + X+ →X+ + XH in acetonitrile at 298 K as long as the KIE value of the related hydride cross transfer reaction that one reactant is one of 1H, 2H, 2+ and 7(MeO)+ (eqs 17−20) and their extension can be determined in acetonitrile at 298 K. In this work, the KIEself values of 68 hydride self-exchange reactions (XH/X+) in acetonitrile at 298 K (see Table 5) were obtained from the KIE values of the corresponding 68 hydride cross transfer reactions in acetonitrile at 298 K according to eq 7. All of the latter values can be determined using the stopped-flow UV−vis method in our laboratory, and the detailed results are listed in Table 4.

Figure 2. (a) Absorption spectral changes observed for an acetonitrile solution of 2+ (0.11 mM) at various 1H concentrations (see the arrow in the figure). (b) Plot of the absorbance at 420 nm vs the molar ratio [1H]/[2+]. 1782


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Table 4. Second-Order Rate Constants of 65 Hydride Cross Transfer Reactions from XH(D) to Y+ in Acetonitrile at 298 K together with the Corresponding KIEXH/Y+ Values XH(D)/Y+

no. 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

+

1H(D)/14 1H(D)/15(G)+ G = p-CH3O p-CH3 p-H p-F p-CN 1H(D)/16(G)+ G = p-CH3 p-H p-Br p-CF3 p-CN 1H(D)/17(G)+ G = p-CH3O p-CH3 p-H p-Cl p-CF3 1H(D)/18(G) + G = p-CH3 p-H p-Cl p-CF3 1H(D)/19(G) + G = p-CH3 p-H p-Cl p-CF3 2H(D)/6+ 2H(D)/7(G) + G = p-CH3 p-H p-Cl p-Br p-CF3 2H(D)/8+ 2H(D)/9(G)+ G = p-CH3O p-CH3 p-H p-Cl p-CF3 3H(D)/2+ 4(G)H(D)/2+ G = p-CH3O p-CH3 p-H p-Cl p-CN 5H(D)/2+ 10H(D)/7(MeO)+ 11H(D)/7(MeO)+ 12(G)H(D)/8+ G = p-CH3O p-CH3 p-H p-Cl p-CF3 m-CH3O

k2(H)a

k2(D)b

2.18 × 10

2

KIEXH/Y+ c

4.15 × 10

1

5.25

1.20 1.39 1.58 2.03 4.65

× × × × ×

102 102 102 102 102

2.58 2.92 3.35 4.45 1.03

× × × × ×

101 101 101 101 102

4.65 4.76 4.72 4.56 4.51

5.23 5.99 7.97 9.75 4.96

× × × × ×

102 102 102 102 102

1.12 1.25 1.63 2.05 1.04

× × × × ×

102 102 102 102 102

4.67 4.79 4.89 4.76 4.77

1.04 1.13 1.59 2.14 2.83

× × × × ×

101 101 101 101 101

2.01 2.20 2.99 4.00 5.34

2.82 5.47 1.34 4.23

× × × ×

10−2 10−2 10−1 10−1

5.05 9.95 2.48 8.05

× × × ×

10−3 10−3 10−2 10−2

5.58 5.50 5.40 5.25

8.30 1.90 4.50 1.62 1.65

× × × × ×

10−4 10−3 10−3 10−2 10−2

1.40 3.20 7.80 2.87 3.39

× × × × ×

10−4 10−4 10−4 10−3 10−3

5.93 5.94 5.70 5.60 4.87

2.93 4.14 6.31 5.72 9.82 4.06

× × × × × ×

102 102 102 102 102 104

8.51 1.21 1.81 1.73 3.03 8.28

× × × × × ×

10−1 102 102 102 102 103

3.44 3.42 3.49 3.31 3.24 4.90

2.43 3.39 3.62 5.34 7.06 7.83

× × × × × ×

102 102 102 102 102 10−1

6.65 9.19 9.70 1.43 1.90 1.91

× × × × × ×

10−1 10−1 10−1 102 102 10−1

3.65 3.69 3.73 3.73 3.72 4.10

3.35 3.11 1.77 1.22 2.58 9.24 9.92 2.98

× × × × × × × ×

102 102 102 102 10−1 10−1 10−1 102

1.19 1.07 4.84 3.32 5.61 2.25 3.34 7.86

× × × ×

102 102 10 10

× 10−1 × 10−1 × 10−1

2.82 2.91 3.66 3.67 4.60 4.11 2.97 3.79

2.56 2.31 1.73 9.11 2.86 1.33

× × × × × ×

103 103 103 102 102 103

8.93 7.13 5.35 2.90 8.70 4.17

× × × × × ×

2.87 3.24 3.23 3.14 3.29 3.19

1783

5.17 5.14 5.32 5.35 5.30

102 102 102 102 10−1 102


Article

The Journal of Physical Chemistry A Table 4. continued k2(H)a

XH(D)/Y+

no.

k2(D)b

KIEXH/Y+ c

+

52 53 54 55 56 57 58 59 60 61 62 63 64 65

3H(D)/13(G) G = R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = OCH3 R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = CH3, R8 = CH3 R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl

3.74 1.97 3.12 5.81 5.34 4.03 6.50 1.06 9.83 2.87 1.86 1.52 9.53 8.44

× × × × × × × × × × × × × ×

102 102 102 102 102 101 102 103 102 103 103 102 102 102

9.27 5.23 8.57 2.55 2.62 9.65 2.09 3.85 3.00 8.43 8.42 6.21 2.46 2.29

× × × × ×

10−1 10−1 10−1 102 102

× × × × × × × ×

102 102 102 102 102 101 102 102

4.03 3.77 3.64 2.28 2.04 4.18 3.11 2.75 3.28 3.40 2.21 2.45 3.87 3.69

a k2(H) is the second-order rate constant of the hydride transfer from XH in acetonitrile at 298 K. The data (M−1 s−1) are obtained from experimental measurements by the UV−vis method. The uncertainty is smaller than 5%. bk2(D) is the second-order rate constant of the hydride transfer from XD in acetonitrile at 298 K. The data (M−1 s−1) are obtained from experimental measurements by the UV−vis method. The uncertainty is smaller than 5%. cKIE = k2(H)/k2(D).

Table 5. KIEself Values of 68 Hydride Self-exchange Reactions (XH/X+) in Acetonitrile at 298 Ka no. 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

XH/X+ 1H/1+ 2H/2+ 3H/3+ 4(G)H/4(G)+ G = p-CH3O p-CH3 p-H p-Cl p-CN 5H/5+ 6H/6+ 7(G)H/7(G)+ G = p-CH3O p-CH3 p-H p-Cl p-Br p-CF3 8H/8+ 9(G)H/9(G)+ G = p-CH3O p-CH3 p-H p-Cl p-CF3 10H/10+ 11H/11+ 12(G)H/12(G)+ G = p-CH3O p-CH3 p-H p-Cl p-CF3 m-CH3O 13(G)H/13(G)+ G = R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H R7 = Cl, R8 = H

KIEself

no

3.70 6.92 2.47

35 36 37 38 39 40 41 42 43 44 45

1.15 1.22 1.94 1.95 3.06 2.44 3.43 1.61 1.71 1.69 1.76 1.58 1.52 3.47

46 47 48 49 50 51 52 53 54 55

1.93 1.97 2.01 2.01 2.00 5.48 8.92

56 57 58 59 60

2.37 3.03 3.01 2.84 3.12 2.93

61 62 63 64

6.58 5.75 5.36 2.10

65 66 67 68

XH/X+ G = R7 = F, R8 = H R7 = H, R8 = OCH3 R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = CH3, R8 = CH3 R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 14H/14+ 15(G)H/15(G)+ G = p-CH3O p-CH3 p-H p-F p-CN 16(G)H/16(G)+ G = p-CH3 p-H p-Br p-CF3 p-CN 17(G)H/17(G)+ G = p-CH3O p-CH3 p-H p-Cl p-CF3 18(G)H/18(G)+ G = p-CH3 p-H p-Cl p-CF3 19(G)H/19(G)+ G = p-CH3 p-H p-Cl p-CF3

KIEself 1.68 7.07 3.92 3.06 4.36 4.68 1.98 2.43 6.06 5.51 7.45 5.84 6.12 6.02 5.62 5.50 5.89 6.20 6.46 6.12 6.15 7.22 7.14 7.65 7.74 7.59 8.42 8.18 7.88 7.45 9.50 9.54 8.90 8.60

a

The KIEself values of XH/X+ are derived from an available KIEself value of YH/Y+, such as KIEself of 1H/1+ and the corresponding available KIE(XH/Y+) using eq 7. The latter are listed in Table 3. 1784


Article

The Journal of Physical Chemistry A 1H + Y + → 1+ + YH

(17)

2H + Y + → 2+ + YH

(18)

XH + 2+ → X + + 2H

(19)

XH + 7(MeO)+ → X + + 7(MeO)H

(20)

experimental errors. These results also support that eq 7 is reliable.44

IV. PREDICTION OF KIE VALUES OF HYDRIDE TRANSFER REACTIONS Since the KIEself values of 68 hydride self-exchange reactions have been obtained, the KIE values of 4556 hydride cross transfer reactions in acetonitrile at room temperature can be estimated from the 68 KIEself values according to the knowledge of mathematics (A268 = 4556). As the hydride transfer reaction of XH/Y+ is the reverse hydride transfer reaction of YH/X+, in fact, among the 4556 hydride cross transfer reactions, only 2278 chemical reactions are thermodynamically allowed. To save space, herein only 496 KIE values of hydride transfer reactions in acetonitrile at 298 K are given which are derived from the KIEself values of the corresponding 32 hydride self-exchange reactions that all the XH do not have the remote substituents (Table 6), since the remote substituents have Hamment linear correlation with the KIE (see section VI). As all of the chemical reactions in Table 6 are the common and fundamental organic chemical reactions, the KIE values in Table 6 should be very useful and valuable to study the reaction mechanisms and the structure of the transition state.

VI. FACTORS AFFECTING KIESELF 1. Effect of the Parent Structures of Hydride Donors on the KIEself. From Table 5, it is clear that the KIEself values of the 68 hydride self-exchange reactions in acetonitrile at 298 K range from 1.15 for 4(MeO)H/4(MeO)+ to 9.54 for 19(Me)H/19(Me)+. Such a large range of the KIEself values (1.15−9.54) indicates that the parent structure of the hydride donors (XH) should have great effect on the KIEself. In order to discover the main factor of the parent structures resulting in the large range of the KIEself values, the KIEself values of 32 hydride self-exchange reactions that all the structures of the hydride donors (XH) do not have the remote substituents are shown in Figure 5 as a showcase for visual examination. From Figure 5, it is clear that the effect of parent structure of the hydride donors on the KIEself values is quite great, but no main structural factors can be found, which means that the structural factors should be quite multifaceted and complex. 2. Effect of Reaction Rate (k2) on the KIEself. As is wellknown, for the same series of reactions with the change of ΔGo, a consensus is that KIE decreases as the reaction rate increases, or KIE increases as the reaction rate decreases; i.e., the relationship between KIE and reaction rate (k2) is more or less inversely proportional, which can be well rationalized using semiclassical transition state theory due to the ΔGo change of the reactions.21−24 However, for the hydride self-exchange reactions where ΔGo is 0, is it the same relationship between the KIEself and the reaction rate as for the same series of reactions where ΔGo is not zero? In order to elucidate the dependence of KIEself on the reaction rate, the plot of the natural logarithms of KIEself against the natural logarithms of the second-order rate constants was made (see Figure 6). From Figure 6, it is clear that the points are widely dispersed, which means that the effect of reaction rate on the KIEself values is obvious and quite complex. Since no a linear relationship between the natural logarithms

V. VERIFICATION OF THE PREDICTIONS OF KIE VALUES In order to verify the reliability of eq 7, the KIEself values in Table 5 need verification using the different and independnent experimental method, because all the KIEself values in Table 5 are derived from eq 7. Herein, the hydride self-exchange reaction of 2H with the corresponding cation (2+) (eq 21) was examined as an example. From eq 21, it is clear that the rate constant of eq 21 cannot be directly determined using a conventional experimental method, because no spectral signal change of the reaction can be used to monitor the reaction progress. However, the rate constant of the hydride transfer from 2(N−CH3)H to 2(N−CD3)+ in CD3CN at 298 K (eq 22) can be determined using the conventional 1H NMR technique, because the chemical shifts of N−CH 3 in 2(N−CH3)H (3.36 ppm) and in 2(N−CH3)+ (4.76 ppm) are different (Figure 4) and the kinetic isotope effect of deuterium in CD3 group on the hydride transfer reaction should be quite small (due to the secondary kinetic isotope effect). The result of KIEself is 6.89. The perfect agreement between the experimental result (6.89) and the theoretical value (6.92) indicates that eq 7 is reliable.44 To further verify the reliability of eq 7, the KIE values of the 18 hydride cross transfer reactions among the 496 hydride cross tranfer reactions in Table 6 were examined using experimental method in acetonitrile at 298 K, because they all were derived from eq 7, too. The results (derived from Table S2 in the Supporting Information) are listed in Table 7. From Table 7, it is clear that the experimental results all are quite close to the theoritic results, and the differences are all within the 1785


Article

The Journal of Physical Chemistry A Table 6. Prediction of KIE Values of 496 Hydride Transfer Reactions in Acetonitrile at 298 Ka 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

ΔGoXH/Y+

KIEXH/Y+

no.

−11.80 −12.80 −27.20 −31.20 −31.60 −7.40 −3.70

5.06 3.56 2.50 3.58 2.73 5.74 3.34

−16.40 −17.20 −16.00 −18.80 −16.70 −13.90 −16.70 −18.70 −19.70 −21.10 −21.50 −14.10 −18.60 −17.40 −10.50 −14.20 −13.00 −9.70 −1.00 −15.40 −19.40 −19.80

4.93 4.61 4.45 2.79 2.49 5.11 3.81 3.36 4.02 4.16 2.71 3.00 4.74 4.52 5.25 4.72 4.79 5.32 4.87 3.42 4.90 3.73

59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

H, R8 = H OCH3, R8 = H CH3, R8 = H Cl, R8 = H F, R8 = H H, R8 = OCH3 H, R8 = F H, R8 = Br H, R8 = Cl Cl, R8 = Cl Br, R8 = Br CH3, R8 = CH3 Br, R8 = CH3 CH3, R8 = Cl

−4.60 −5.40 −4.20 −7.00 −4.90 −2.10 −4.90 −6.90 −7.90 −9.30 −9.70 −2.30 −6.80 −5.60 −2.40 −1.20 −5.10 −16.90 −17.90 −32.30 −36.30 −36.70 −12.50 −8.80

6.75 6.31 6.09 3.81 3.41 6.99 5.21 4.60 5.49 5.69 3.70 4.10 6.48 6.17 6.45 6.55 3.02 4.13 2.91 2.04 2.93 2.23 4.69 2.73

83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112

H, R8 = H OCH3, R8 = H CH3, R8 = H Cl, R8 = H F, R8 = H

−21.50 −22.30 −21.10 −23.90 −21.80

4.03 3.77 3.64 2.28 2.0

113 114 115 116 117

XH/Y+

no. +

1H/2 1H/6+ 1H/7+ 1H/8+ 1H/9+ 1H/11+ 1H/12+ 1H/13(G)+ R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = 1H/14+ 1H/15+ 1H/16+ 1H/17+ 2H/6+ 2H/7+ 2H/8+ 2H/9+ 2H/13(G)+ R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = 2H/15+ 2H/16+ 3H/1+ 3H/2+ 3H/6+ 3H/7+ 3H/8+ 3H/9+ 3H/11+ 3H/12+ 3H/13(G)+ R7 = R7 = R7 = R7 = R7 =


1786

ΔGoXH/Y+

KIEXH/Y+

H, R8 = OCH3 H, R8 = F H, R8 = Br H, R8 = Cl Cl, R8 = Cl Br, R8 = Br CH3, R8 = CH3 Br, R8 = CH3 CH3, R8 = Cl

−19.00 −21.80 −23.80 −24.80 −26.20 −26.60 −19.20 −23.70 −22.50 −15.60 −19.30 −18.10 −14.80 −15.20 −27.00 −10.10 −3.50 −28.00 −42.40 −46.40 −46.80 −4.50 −22.60 −18.90

4.18 3.11 2.75 3.28 3.40 2.21 2.45 3.87 3.69 4.29 3.86 3.91 4.35 2.68 3.66 2.19 2.18 2.58 1.81 2.59 1.97 3.26 4.16 2.42


−31.60 −32.40 −31.2 −34.00 −31.90 −29.10 −31.90 −33.90 −34.90 −36.30 −36.70 −29.30 −33.80 −32.60 −25.70 −29.40 −28.20 −24.90 −6.90 −4.90 −11.70 −23.50 −6.60 −24.50 −38.90 −42.90 −43.30 −1.00 −19.10 −15.40

3.57 3.34 3.22 2.02 1.81 3.70 2.76 2.44 2.91 3.01 1.96 2.17 3.43 3.27 3.80 3.42 3.47 3.85 3.98 4.30 3.00 4.11 2.45 2.89 2.03 2.91 2.21 3.66 4.67 2.71

H, R8 = H OCH3, R8 = H CH3, R8 = H Cl, R8 = H F, R8 = H

−28.10 −28.90 −27.70 −30.50 −28.40

4.01 3.75 3.62 2.26 2.02

XH/Y+ R7 R7 R7 R7 R7 R7 R7 R7 R7

= = = = = = = = =

3H/14+ 3H/15+ 3H/16+ 3H/17+ 4H/1+ 4H/2+ 4H/3+ 4H/5+ 4H/6+ 4H/7+ 4H/8+ 4H/9+ 4H/10+ 4H/11+ 4H/12+ 4H/13(G)+ R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = R7 = 4H/14+ 4H/15+ 4H/16+ 4H/17+ 4H/18+ 4H/19+ 5H/1+ 5H/2+ 5H/3+ 5H/6+ 5H/7+ 5H/8+ 5H/9+ 5H/10+ 5H/11+ 5H/12+ 5H/13(G)+ R7 = R7 = R7 = R7 = R7 =


Article

The Journal of Physical Chemistry A Table 6. continued no. 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176

R7 R7 R7 R7 R7 R7 R7 R7 R7

= = = = = = = = =

XH/Y+

ΔGoXH/Y+

KIEXH/Y+

no.

H, R8 = OCH3 H, R8 = F H, R8 = Br H, R8 = Cl Cl, R8 = Cl Br, R8 = Br CH3, R8 = CH3 Br, R8 = CH3 CH3, R8 = Cl

−25.60 −28.40 −30.40 −31.40 −32.80 −33.20 −25.80 −30.30 −29.10 −22.20 −25.90 −24.70 −21.40 −3.40 −1.40 −14.40 −18.40 −18.80

4.15 3.09 2.73 3.26 3.38 2.20 2.43 3.85 3.67 4.26 3.83 3.89 4.32 4.47 4.82 2.41 3.45 2.63

177 178 179 180 181 182 183 184 185 186 187 188

−3.60 −4.40 −3.20 −6.00 −3.90 −1.10 −3.90 −5.90 −6.90 −8.30 −8.70 −1.30 −5.80 −4.60 −1.40 −0.20 −4.00 −4.400 −0.40 −10.70 −22.50 −5.60 −23.50 −37.90 −41.90 −42.30 −18.10 −14.40

4.75 4.44 4.29 2.68 2.40 4.92 3.67 3.24 3.87 4.01 2.61 2.89 4.56 4.35 4.54 4.61 2.42 1.84 2.64 4.50 6.16 3.68 4.34 3.04 4.36 3.32 6.99 4.06

−27.10 −27.90 −26.70 −29.50 −27.40 −24.60 −27.40 −29.40 −30.40 −31.80 −32.20 −24.80 −29.30

6.00 5.61 5.42 3.39 3.03 6.22 4.63 4.09 4.89 5.06 3.29 3.65 5.76

5H/14+ 5H/15+ 5H/16+ 5H/17+ 5H/18+ 5H/19+ 6H/7+ 6H/8+ 6H/9+ 6H/13(G)+ R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = OCH3 R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = CH3, R8 = CH3 R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 6H/15+ 6H/16+ 7H/8+ 7H/9+ 8H/9+ 10H/1+ 10H/2+ 10H/3+ 10H/6+ 10H/7+ 10H/8+ 10H/9+ 10H/11+ 10H/12+ 10H/13(G)+ R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = OCH3 R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = CH3, R8 = CH3 R7 = Br, R8 = CH3

1787

189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234

XH/Y+ R7 = CH3, R8 = Cl 10H/14+ 10H/15+ 10H/16+ 10H/17+ 10H/18+ 10H/19+ 11H/2+ 11H/6+ 11H/7+ 11H/8+ 11H/9+ 11H/13(G)+ R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = OCH3 R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = CH3, R8 = CH3 R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 11H/14+ 11H/15+ 11H/16+ 11H/17+ 12H/2+ 12H/6+ 12H/7+ 12H/8+ 12H/9+ 12H/11+ 12H/13(G)+ R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = OCH3 R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = CH3, R8 = CH3 R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 12H/14+ 12H/15+ 12H/16+ 12H/17+ 13(H,H)H/7+ 13(H,H)H/8+ 13(H,H)H/9+ 13(H,H)H/13(G)+ R7 = OCH3, R8 = H

ΔGoXH/Y+

KIEXH/Y+

−28.10 −21.20 −24.90 −23.70 −20.40 −2.40 −0.40 −4.40 −5.40 −19.80 −23.80 −24.20

5.49 6.39 5.74 5.83 6.47 6.70 7.23 7.86 5.53 3.88 5.56 4.23

−9.00 −9.80 −8.60 −11.40 −9.30 −6.50 −9.30 −11.30 −12.30 −13.70 −14.10 −6.70 −11.20 −10.00 −3.10 −6.80 −5.60 −2.30 −8.10 −9.10 −23.50 −27.50 −27.90 −3.70

7.66 7.16 6.91 4.33 3.87 7.94 5.91 5.22 6.24 6.46 4.20 4.66 7.35 7.01 8.15 7.33 7.44 8.26 4.56 3.21 2.26 3.23 2.46 5.18

−12.70 −13.50 −12.30 −15.10 −13.00 −10.20 −13.00 −15.00 −16.00 −17.40 −17.80 −10.40 −14.90 −13.70 −6.80 −10.50 −9.30 −6.00 −10.80 −14.80 −15.20

4.45 4.16 4.02 2.51 2.25 4.61 3.43 3.03 3.62 3.75 2.44 2.70 4.27 4.07 4.74 4.26 4.32 4.80 3.33 4.78 3.64

−0.80

6.15


Article

The Journal of Physical Chemistry A Table 6. continued no. 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290

XH/Y+ R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 13(CH3O,H)H/7+ 13(CH3O,H)H/8+ 13(CH3O,H)H/9+ 13(CH3O,H)H/13(G)+ R7 = Cl, R8 = H R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 13(CH3,H)H/7+ 13(CH3,H)H/8+ 13(CH3,H)H/9+ 13(CH3,H)H/13(G)+ R7 = H, R8 = H R7 = OCH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 13(Cl,H)H/7+ 13(Cl,H)H/8+ 13(Cl,H)H/9+ 13(Cl,H)H/13(G)+ R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br 13(F,H)H/7+ 13(F,H)H/8+ 13(F,H)H/9+ 13(F,H)H/13(G)+ R7 = OCH3, R8 = H R7 = Cl, R8 = H R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 13(H,CH3O)H/7+ 13(H,CH3O)H/8+ 13(H,CH3O)H/9+ 13(H,CH3O)H/13(G)+ R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H

ΔGoXH/Y+

KIEXH/Y+

no.

−2.40 −0.30 −0.30 −2.30 −3.30 −4.70 −5.10 −2.20 −1.00 −10.00 −14.00 −14.40

3.72 3.32 5.08 4.49 5.36 5.55 3.61 6.31 6.02 3.12 4.47 3.40

−1.60 −1.50 −2.50 −3.90 −4.30 −1.40 −0.20 −11.20 −15.20 −15.60

3.47 4.19 5.01 5.19 3.37 5.90 5.63 3.01 4.31 3.28

291 292 293 294 295 296 297 298 299 300 301 302 303 304

−0.40 −1.20 −2.80 −0.70 −0.70 −2.70 −3.70 −5.10 −5.50 −2.60 −1.40 −8.40 −12.40 −12.80

5.94 5.55 3.35 3.00 4.58 4.05 4.83 5.01 3.26 5.70 5.43 1.88 2.70 2.05

−0.90 −2.30 −2.70 −10.50 −14.50 −14.90

3.03 3.13 2.04 1.68 2.41 1.84

−0.50 −2.10 −2.00 −3.00 −4.40 −4.80 −1.90 −0.70 −13.30 −17.30 −17.70

3.11 1.88 2.27 2.71 2.80 1.82 3.19 3.04 3.46 4.95 3.77

−2.50 −3.30 −2.10

6.82 6.38 6.16 1788

305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346

XH/Y+ R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = CH3, R8 = CH3 R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 13(H,CH3O)H/15+ 13(H,F)H/7+ 13(H,F)H/8+ 13(H,F)H/9+ 13(H,F)H/13(G)+ R7 = OCH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 13(H,Br)H/7+ 13(H,Br)H/8+ 13(H,Br)H/9+ 13(H,Br)H/13(G)+ R7 = Cl, R8 = H R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br 13(H,Cl)H/7+ 13(H,Cl)H/8+ 13(H,Cl)H/9+ 13(H,Cl)H/13(G)+ R7 = Cl, R8 = Cl R7 = Br, R8 = Br 13(Cl,Cl)H/7+ 13(Cl,Cl)H/8+ 13(Cl,Cl)H/9+ 13(Cl,Cl)H/13(G)+ R7 = Br, R8 = Br 13(Br,Br)H/7+ 13(Br,Br)H/8+ 13(Br,Br)H/9+ 13(CH3,CH3)H/7+ 13(CH3,CH3)H/8+ 13(CH3,CH3)H/9+ 13(CH3,CH3)H/13(G)+ R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = Br, R8 = CH3

ΔGoXH/Y+

KIEXH/Y+

−4.90 −2.80 −2.80 −4.80 −5.80 −7.20 −7.60 −0.20 −4.70 −3.50 −0.30 −10.50 −14.50 −14.90

3.85 3.45 5.26 4.65 5.55 5.75 3.74 4.14 6.55 6.24 6.52 2.57 3.69 2.81

−0.50 −2.10 0.00 −2.00 −3.00 −4.40 −4.80 −1.90 −0.70 −8.50 −12.50 −12.90

4.75 2.87 2.57 3.46 4.13 4.28 2.79 4.87 4.65 2.27 3.26 2.48

−0.10 −1.00 −2.40 −2.80 −7.50 −11.50 −11.90

2.53 3.65 3.78 2.46 2.71 3.89 2.96

−1.40 −1.80 −6.10 −10.10 −10.50

4.52 2.94 2.81 4.03 3.07

−0.40 −5.70 −9.70 −10.10 −13.10 −17.10 −17.50

3.04 1.83 2.62 1.99 2.03 2.90 2.21

−2.30 −3.10 −1.90 −4.70 −2.60 −2.60 −4.60 −5.60 −7.00 −7.40 −4.50

4.00 3.74 3.61 2.26 2.02 3.09 2.73 3.25 3.37 2.19 3.84


Article

The Journal of Physical Chemistry A Table 6. continued XH/Y+

ΔGoXH/Y+

R7 = CH3, R8 = Cl 13(CH3,CH3)H/15+ 13(Br,CH3)H/7+ 13(Br,CH3)H/8+ 13(Br,CH3)H/9+ 13(Br,CH3)H/13(G)+ R7 = Cl, R8 = H R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br 13(CH3,Cl)H/7+ 13(CH3,Cl)H/8+ 13(CH3,Cl)H/9+ 13(CH3,Cl)H/13(G)+ R7 = Cl, R8 = H R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = Br, R8 = CH3 14H/2+ 14H/6+ 14H/7+ 14H/8+ 14H/9+ 14H/13(G)+ R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = OCH3 R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = CH3, R8 = CH3 R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 14H/15+ 14H/16+ 15H/7+ 15H/8+ 15H/9+ 15H/13(G)+ R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl

−3.30 −0.10 −8.60 −12.60 −13.00

3.66 3.82 3.20 4.59 3.49

−0.20 −0.10 −1.10 −2.50 −2.90 −9.80 −13.80 −14.20

3.57 4.31 5.14 5.33 3.46 3.05 4.37 3.33

−1.40 −1.30 −2.30 −3.70 −4.10 −1.20 −1.30 −2.30 −16.70 −20.70 −21.10

3.40 4.11 4.90 5.08 3.30 5.78 7.18 5.06 3.55 5.08 3.87

−5.90 −6.70 −5.50 −8.30 −6.20 −3.40 −6.20 −8.20 −9.20 −10.60 −11.00 −3.60 −8.10 −6.90 −3.70 −2.50 −13.00 −17.00 −17.40

7.00 6.55 6.32 3.96 3.54 7.26 5.40 4.77 5.70 5.90 3.84 4.25 6.72 6.41 6.70 6.80 3.19 4.57 3.48

−2.20 −3.00 −1.80 −4.60 −2.50 −2.50 −4.50 −5.50 −6.90 −7.30 −4.40 −3.20 −14.20 −18.20

6.29 5.88 5.68 3.56 3.18 4.86 4.29 5.12 5.31 3.45 6.04 5.76 3.24 4.64

no. 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403

16H/7+ 16H/8+

KIEXH/Y+

1789

XH/Y+

no. 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461

+

16H/9 16H/13(G)+ R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = OCH3 R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = CH3, R8 = CH3 R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 16H/15+ 17H/2+ 17H/6+ 17H/7+ 17H/8+ 17H/9+ 17H/13(G)+ R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = OCH3 R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = CH3, R8 = CH3 R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 17H/14+ 17H/15+ 17H/16+ 18H/1+ 18H/2+ 18H/3+ 18H/6+ 18H/7+ 18H/8+ 18H/9+ 18H/11+ 18H/12+ 18H/13(G)+ R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = OCH3 R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br

ΔGoXH/Y+

KIEXH/Y+

−18.60

3.53

−3.40 −4.20 −3.00 −5.80 −3.70 −0.90 −3.70 −5.70 −6.70 −8.10 −8.50 −1.10 −5.60 −4.40 −1.20 −2.10 −3.10 −17.50 −21.50 −21.90

6.39 5.97 5.76 3.61 3.23 6.62 4.93 4.36 5.20 5.39 3.50 3.88 6.13 5.84 6.11 7.28 5.12 3.60 5.15 3.92

−6.70 −7.50 −6.30 −9.10 −7.00 −4.20 −7.00 −9.00 −10.00 −11.40 −11.80 −4.40 −8.90 −7.70 −0.80 −4.50 −3.30 −8.30 −20.10 −3.20 −21.10 −35.50 −39.50 −39.90 −15.70 −12.00

7.09 6.63 6.40 4.01 3.58 7.35 5.48 4.84 5.78 5.98 3.89 4.31 6.81 6.49 7.55 6.79 6.89 5.50 7.52 4.49 5.30 3.72 5.33 4.05 8.54 4.96

−24.70 −25.50 −24.30 −27.10 −25.00 −22.20 −25.00 −27.00 −28.00 −29.40 −29.80

7.34 6.86 6.62 4.14 3.71 7.60 5.66 5.00 5.97 6.19 4.02


Article

The Journal of Physical Chemistry A Table 6. continued no. 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 a

XH/Y+ R7 = CH3, R8 = CH3 R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 18H/14+ 18H/15+ 18H/16+ 18H/17+ 19H/1+ 19H/2+ 19H/3+ 19H/6+ 19H/7+ 19H/8+ 19H/9+ 19H/11+ 19H/12+ 19H/13(G)+ R7 = H, R8 = H

ΔGoXH/Y+

KIEXH/Y+

no.

−22.40 −26.90 −25.70 −18.80 −22.50 −21.30 −18.00 −10.30 −22.10 −5.20 −23.10 −37.50 −41.50 −41.90 −17.70 −14.00

4.46 7.04 6.71 7.81 7.02 7.12 7.91 5.94 8.13 4.85 5.72 4.02 5.75 4.38 9.22 5.36

−26.70

7.92

479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496

XH/Y+ R7 R7 R7 R7 R7 R7 R7 R7 R7 R7 R7 R7 R7 19H/14+ 19H/15+ 19H/16+ 19H/17+ 19H/18+

= = = = = = = = = = = = =

OCH3, R8 = H CH3, R8 = H Cl, R8 = H F, R8 = H H, R8 = OCH3 H, R8 = F H, R8 = Br H, R8 = Cl Cl, R8 = Cl Br, R8 = Br CH3, R8 = CH3 Br, R8 = CH3 CH3, R8 = Cl

ΔGoXH/Y+

KIEXH/Y+

−27.50 −26.30 −29.10 −27.00 −24.20 −27.00 −29.00 −30.00 −31.40 −31.80 −24.40 −28.90 −27.70 −20.80 −24.50 −23.30 −20.00 −2.00

7.41 7.15 4.48 4.00 8.21 6.12 5.40 6.45 6.68 4.35 4.81 7.60 7.25 8.43 7.58 7.69 8.54 8.83

13(G1,G2)H = 13(R7 = G1, R8 = G2)H.

Figure 4. 1H NMR spectra changes of the mixture of 2(N−CH3)D (25.38 mmol L−1) and 2(N−CD3)+ (25.38 mmol L−1) in CD3CN at 298 K. From top to bottom, the reaction times are 20, 85, 148, 210, and 292 min, respectively.

values have a linear relationship with ΔGoH−D[4(G)H], and the larger the bond dissociation free energy is, the larger the KIEself is (see the insect in Figure 7). 4. Effect of the Remote Substituents on the KIEself. For the hydride cross transfer reactions that the hydride donors [X(G)H] have the remote substitients [X(G)H/Y+], such as 4(G)H/2+, etc., the remote substituents (G) have Hamment linear effects on the ln(KIEX(G)H/Y+), and normally the electrondonating groups in the hydride donors can make KIE become smaller, the electron-withdrawing groups can make KIE become larger. An acceptable explanation is that the electrondonating groups can make the position of the transition state move to the reactants due to the increase of the thermodynamic driving force (ΔGo).21−24,32,34 For the hydride selfexchange reactions, X(G)H/X(G)+, although the position of the transition state can not vary with the remote substituents, the remote substituents (G) also should have Hamment linear

of KIEself and the natural logarithms of the second-order rate constants can be found for all the points, the reaction rate is not the only factor to affect the KIEself. 3. Effect of the X−H Bond Dissociation Energy ΔGoH−D(XH) on the KIEself. While all the free energy changes of the hydride self-exchange reactions are zero, the bond dissociation energies of the hydride donors are different. Evidently, it is interesting to examine the effect of the X−H bond dissociation energy on the KIEself. Figure 7 gives the plot of the natural logarithms of KIEself values against the X−H bond dissociation free energies of the hydride donors. From Figure 7, it is clear that although the effect of ΔGoH−D(XH) on the KIEself values is obvious, no a linear relationship can be found for all the points, which means that ΔGoH−D(XH) is not the only factor to affect the KIEself. However, for the same series of hydride selfexchange reactions, such as 4(G)H/4(G)+, although ΔGo of the reactions are all equal to zero, the natural logarithms of KIEself 1790


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Table 7. Comparison of Theoretical KIE Values of 18 Hydride Transfer Reactions with the Corresponding Experimental Ones in Acetonitrile at 298 K no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 a

XH/Y+ +

4H/16(CH3) 4H/16(CN)+ 4(CH3O)H/16+ 4(Cl)H/16+ 4(CH3O)H/14+ 4(CN)H/14+ 4H/15(CH3O)+ 4H/15(CN)+ 10H/7(CH3)+ 10H/7(CF3)+ 10H/9(CH3O)+ 10H/9(CF3)+ 11H/9(CH3O)+ 11H/9(CF3)+ 11H/7(CH3)+ 11H/7(CF3)+ 17(CH3O)H/8+ 17(Cl)H/8+

KIEXH/X+a

KIEYH/Y+b

KIEXH/Y+(theor)c

KIEXH/Y+(exp)d

ΔKIEe

1.94 1.94 1.15 1.95 1.15 3.06 1.94 1.94 5.48 5.48 5.48 5.48 8.92 8.92 8.92 8.92 7.22 7.74

5.89 6.15 6.20 6.20 7.45 7.45 5.84 5.50 1.71 1.52 1.93 2.00 1.95 2.02 1.71 1.52 3.47 3.47

3.38 3.45 2.67 3.48 2.93 4.77 3.37 3.27 3.06 2.89 3.29 3.31 4.15 4.22 3.91 3.68 5.01 5.18

3.42 3.48 2.75 3.56 3.00 4.61 3.26 3.37 2.93 2.78 3.38 3.32 4.04 4.17 3.80 3.76 4.96 5.31

−0.04 −0.03 −0.08 −0.08 −0.07 0.16 0.11 −0.10 0.13 0.11 −0.09 −0.01 0.11 0.05 0.11 −0.08 0.05 −0.13

Derived from Table 4. bDerived from Table 4. cDerived from the corresponding KIEXH/X+ values and the corresponding KIEYH/Y+ according to eq 7. Derived from experimental measurements using UV−vis method. eΔKIE = KIEXH/Y+(theor) − KIEXH/Y+(exp).

d

Figure 5. Visual comparison of KIEself among the 32 well-known hydride donors (XH) in acetonitrile at 298 K.

it is clear that the line slope of ln(KIE4(G)H/4(G)+) against σ is 1.035, which is just 2 times of that of ln(KIE4(G)H/2+) against σ (0.516). The reason is that for the hydride cross transfer reaction 4(G)H/2+, only one reactant has remote substituents; but for the hydride self-exchange reaction 4(G)H/4(G)+, both of the two reactants have remote substituents. This result verifies eq 7 again.

effects on the ln(KIE[X(G)H/X(G)+]) according to eq 7, and the slope of the line of ln(KIEX(G)H/X(G)+) against σ should be 2 times larger than that of the corresponding line of ln(KIEX(G)H/Y+) against σ. In order to test and verify this prediction, the plots of ln(KIE4(G)H/4(G)+) and the corresponding ln(KIE[4(G)H/2+) against σ were made (Figure 8). From Figure 8, 1791


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values, one is the classical zero-point energy theory,21−24 and the other is the quantum tunneling theory.25−29 Although these two traditional KIE theories can all explain some experimental results, respectively, they cannot explain all the experimental results. Specifically, for the classical zero-point energy theory, it can explain the normal KIE values, but cannot explain the inverse and enormous KIE values. For the quantum tunneling theory, although it can explain the enormous KIE values, it cannot explain the inverse and normal KIE values. In fact, in chemical reactions, atom transfer should not have tunneling effect.48,49 This fact indicates these two traditional KIE theories (the classical zero-point energy theory and the quantum tunneling theory) all have fundamental problems. In order to develop a correct KIE kinetic model that can give a unified explanation of the various (normal, enormous and inverse) KIE values, the prerequisites of the two traditional KIE theories are examined (Figure 9). By examining the kinetic models of the two traditional KIE theories (Figure 9), it is found that the prerequisite of the two traditional KIE theories is that they all require that hydrogen atom transfer and deuterium atom transfer in chemical reactions all take place along the same potential energy surface, that is, the Morse potential curves of X−H bond dissociation and X−D bond dissociation in the chemical reactions must be the same (see Figure 10a). Since X−H bond is completely different from the corresponding X−D bond in bond energy, bond length and bond angle, it is clear that the prerequisite of the two traditional KIE theories that X−H bond and X−D bond are regarded as the same chemical bond is absolutely incorrect. In fact, it is this prerequisite (or assumption) that makes the two traditional KIE theories (classical zero-point energy theory and the quantum tunneling theory) all cannot explain all the experimental results. In view of the common error of the two traditional KIE theories, in this work a new KIE kinetic model (Figure 11) is developed using Zhu’s kinetic model32 according to the mechanism of hydrogen atom self-exchange reactions XH(D)/X (Scheme 2), in which two different Morse curves (Figure 10b) are used to describe the free energy change of X−H bond dissociation and X−D bond dissociation in the chemical reactions, respectively.32 In Figure 11, ΔG‡XH/X(XH) is the molar free energy change of XH releasing H for the reaction XH/X going from the initial state (IS) to the transition state (TS). ΔG‡XH/X(X) is the molar free enegy change of X capturing H for the reaction XH/X going from the initial state (IS) to the transition state (TS). ΔG‡XD/X(XD) is the molar free energy change of XD releasing D for the reaction XD/X going from the initial state (IS) to the transition state (TS). ΔG‡XD/X(X) is the molar free enegy change of X capturing D for the reaction XD/X going from the initial state (IS) to the transition state (TS). ΔGSE is the difference of the ground state energies between XH and XD in chemical reactions, which is equal to the difference of zeropoint energies between XH and XD (ΔZPE). ΔZPE of XH and XD can be estimated from the difference of stretching and bending vibration frequencies between the C−H bond and the C−D bond according to ΔZPE = 1/2hcL[(vC−H − vC‑D)str + 2(vC−H − vC‑D)bend].50 The result is that ΔZPE (ΔGSE) = 2.55 kcal/mol. The intersecting point of the Morse-type free energy curve of XH releasing H and the Morse-type free energy curve of X capturing H is defined as the point of the transition state for the hydride self-exchange reactions, because at this point, the bond energies of the left X···H bond of the hydrogen

Figure 6. Effect of the rate constants on the KIEself.

Figure 7. Effect of the X−H bond dissociation free energies of hydride donors on the KIEself.

Figure 8. Effects of the remote substituents (σ) on KIEself.

VII. A UNIFIED EXPLANATION OF THE VARIOUS KIE VALUES As is well-known, the range of KIE values for chemical reactions is quite large (0.47−50 for hydride transfer reactions). Conventionally, if the KIE value is between 1 and 9, the KIE is called normal KIE;12−15 if the KIE value is larger than 9, the KIE is called enormous KIE;4 if the KIE value is smaller than 1, the KIE is called inverse KIE.18,45−47 In the literature, chemists used two traditional theories to explain the difference of KIE 1792


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Figure 9. Kinetic models of the traditional two KIE theories (classical zero-point energy theory and quantum tunneling theory).

Figure 10. Dependence of the free energy changes of X−H bond and X−D bond dissociations in chemical reactions on the internuclear separation (Morse-type free energy curves).

the hydride self-exchange reaction ΔG‡XH/X should equal to the sum of the absorbed free energy of the hydride donor XH at the transition state for releasing H, ΔG‡XH/X(XH), and the released free energy of the hydride acceptor X at transition state for capturing H, ΔG‡XH/X(X) (see eqs 23 and 24). From eqs 23 and 24, eq 25 can be derived according to eq 6 and eq 4, and the detailed derivation of eq 25 is provided in the Supporting Information. According to eq 25, the following predictions can be made: (1) If the value of ΔG‡XD/X(XD) − ΔG‡XH/X(XH) is larger than 0.5ΔZPE (1.275 kcal/mol), but smaller than ΔZPE (2.55 kcal/mol), the KIE value is larger than 1, but smaller than 73.7 (see case 1 in Figure 12, normal KIE). (2) If the value of ΔG‡XD/X(XD) − ΔG‡XH/X(XH) is equal to ΔZPE (2.55 kcal/mol), the KIE value is 73.7 (see case 2 in Figure 12). (3) If the value of ΔG‡XD/X(XD) − ΔG‡XH/X(XH) is larger than ΔZPE (2.55 kcal/mol), the KIE value is larger than 73.7 (see case 3 in Figure 12, enormous KIE). (4) If the value of ΔG‡XD/X(XD) − ΔG‡XH/X(XH) is smaller than 0.5ΔZPE (1.275 kcal/mol), the KIE value is smaller than 1 (see case 4 in Figure 12, inverse KIE).24,44 Evidently, eq 25 not only can be used to explain various (normal, enormous and inverse) KIE but also can be used to estimate the KIE of various chemical reactions according to ΔG‡XH/X(XH) values and the corresponding ΔG‡XD/X(XD) values. The ΔG‡XH/X+(XH) values and the corresponding ΔG‡XD/X+(XD) values of 68 hydride

Figure 11. New KIE kinetic model developed in this work: the kinetic model of hydrogen atom transfer reactions (black line); the kinetic model of deuterium atom transfer reactions (red line).

atom and the right H···X bond of the hydrogen atom are equal. However, the free energy of G-axis at the intersecting point is not the activation energy of the reaction, because in this model, the Morse-type curve is not used to describe the energy change of the reactant system or the product system. Since the Morsetype curve of XH releasing H is to describe the state energy change of XH, the Morse-type curve of X capturing H is to describe the state energy change of X, the activation energy of

Scheme 2. Mechanism of the Hydrogen Atom Self-Exchange Reactions (XH/X)

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Figure 12. Dependence of KIEself of hydrogen atom self-exchange reactions XH(D)/X on the difference between ΔG‡XD/X(XD) and ΔG‡XH/X(XH).

self-exchange reactions XH(D)/X+ in acetonitrile at 298 K are summarized in Table 8. Since the difference of ΔG‡XH/Y+(XH) and ΔG‡XD/X+(XD) directly results from the difference of the corresponding two Morse curve curvatures of XH and XD and the Morse curve curvatures depend entirely on the reaction system XH(D)/X+ and the environment, the figures in Table 8 should serve as a benchmark for computational studies of the dependence of Morse curve curvatures on the reaction system and the environment. In order to make readers more easily understand the physical meaning of the new KIE kinetic model, a detailed comparison of the new KIE kinetic model and the traditional KIE kinetic model is made in Table 9. ΔG‡ XH/X = ΔG‡ XH/X (XH) + ΔG‡ XH/X (X)

(23)

ΔG‡ XD/X = ΔG‡ XD/X (XD) + ΔG‡ XD/X (X)

(24)

reaction side-products, reduce reaction rate, produce isotope reagents and so on. Athough the KIE of chemical reaction has received extensive investigations for a long time, the safe prediction of KIE still is a chemical conundrum. In this work, the following contributions and conclusions can be made: (1) An efficient experimental method to determine KIEself was developed, by which KIEself values of 68 hydride self-exchange reactions in acetonitrile at 298 K were measured. (2) Effects of the parent structure of hydride donors, reaction rate, X−H bond dissociation free energy, and remote substituent on KIEself are examined; the results show: (a) effect of the parent structure of hydride donor on the KIEself is obvious but complex, no main origin can be found; (b) Effect of reaction rate on KIEself is observed, but no simple tendency can be found; (c) Effect of X−H bond dissociation free energy of hydride donors on KIEself is quite complex, no linear relationship was found. (d) ln(KIEself) has a linear relatioship with the Hammett parameters of the remote substituents, and the line slope is 2 times larger than that of the corresponding hydride cross transfer reactions. (3) An efficient relation equation to predict KIE (eq 7) was developed according to Zhu’s equation, by which KIE values of 4556 hydride cross transfer reactions in acetonitrile were safely estimated using the determined 68 KIEself values.

KIE XH/X = {exp[ΔG‡ XD/X (XD) − ΔG‡ XH/X (XH) − 0.5ΔZPE]/RT }2 (25)

VIII. SUMMARY AND CONCLUSIONS The KIE value of chemical reactions is a characteristic and very important kinetic parameter of a chemical reaction, which has extensively been used to diagnose reaction mechanisms, control 1794


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Table 8. Activation Free Energies of XH(D)/X+ (ΔG‡XH/X+ and ΔG‡XD/X+), Activation Free Energies of X−H(D) bonds [ΔG‡XH/X+(XH) and ΔG‡XD/X+(XD)] of XH(D)/X+ in Acetonitrile at 298 K, and Molar Free Energy Changes of XH Releasing Hydride Anions in Acetonitrile [ΔGoH−D(XH)] XH(D)/X+

no. 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

+

1H/1 2H/2+ 3H/3+ 4(G)H/4(G)+ p-CH3O p-CH3 p-H p-Cl p-CN 5H/5+ 6H/6+ 7(G)H/7(G)+ p-CH3O p-CH3 p-H p-Cl p-Br p-CF3 8H/8+ 9(G)H/9(G)+ p-CH3O p-CH3 p-H p-Cl p-CF3 10H/10+ 11H/11+ 12(G)H/12(G)+ p-CH3O p-CH3 p-H p-Cl p-CF3 m-CH3O 13(G)H/13(G)+ R7 = H, R8 = H R7 = OCH3, R8 = H R7 = CH3, R8 = H R7 = Cl, R8 = H R7 = F, R8 = H R7 = H, R8 = OCH3 R7 = H, R8 = F R7 = H, R8 = Br R7 = H, R8 = Cl R7 = Cl, R8 = Cl R7 = Br, R8 = Br R7 = CH3, R8 = CH3 R7 = Br, R8 = CH3 R7 = CH3, R8 = Cl 14H/14+ 15(G)H/15(G)+ p-CH3O p-CH3 p-H p-F p-CN 16(G)H/16(G)+ p-CH3 p-H p-Br

ΔGoH−D(XH)a

ΔG‡XH/X+b

ΔG‡XD/X+c

ΔG‡XH/X+(XH)d

ΔG‡XD/X+(XD)e

ΔΔf

64.4 76.2 59.3

20.74 19.88 26.76

21.52 21.02 27.29

42.57 48.04 43.03

44.24 49.89 44.57

1.67 1.85 1.54

48.0 48.5 49.2 50.3 51.8 52.7 77.2

36.33 35.92 35.89 35.23 35.57 33.16 20.89

36.42 36.04 36.28 35.62 36.23 33.68 21.61

42.17 42.21 42.54 42.76 43.69 42.93 49.04

43.49 43.55 44.02 44.24 45.29 44.47 50.68

1.32 1.34 1.48 1.48 1.6 1.54 1.64

90.2 90.6 91.6 92.5 92.5 93.5 95.6

23.16 22.69 23.28 23.68 23.80 24.1 21.85

23.44 23.02 23.59 24.02 24.07 24.41 22.59

56.68 56.65 57.44 58.09 58.15 58.83 58.72

58.10 58.09 58.87 59.54 59.56 60.23 60.37

1.42 1.44 1.43 1.45 1.41 1.4 1.65

93.5 94.3 96.0 97.6 100.0 53.7 71.8

25.81 26.22 27.84 28.98 31.05 42.80 23.39

26.22 26.62 28.26 29.40 31.48 43.80 24.69

59.66 60.26 61.92 63.29 65.53 48.25 47.60

61.14 61.74 63.41 64.78 67.02 50.03 49.52

1.48 1.48 1.49 1.49 1.49 1.78 1.92

66.4 67.5 68.1 69.2 70.9 69.0

32.96 31.99 31.73 31.39 31.06 31.14

33.48 32.64 32.38 32.01 31.73 31.78

49.68 49.74 49.91 50.29 50.98 50.07

51.22 51.35 51.52 51.88 52.59 51.67

1.54 1.61 1.61 1.59 1.61 1.60

80.8 81.6 80.4 83.2 81.1 78.3 81.1 83.1 84.1 85.5 85.9 78.5 83.0 81.8 74.9

22.62 24.18 22.44 24.50 22.50 22.76 22.27 23.69 24.78 24.91 25.82 21.39 23.71 22.66 18.28

23.73 25.21 23.42 24.94 22.81 23.91 23.07 24.35 25.64 25.81 26.22 21.91 24.77 23.66 19.46

51.71 52.89 51.42 53.85 51.80 50.53 51.68 53.39 54.44 55.20 55.86 49.94 53.36 52.23 46.60

53.54 54.68 53.19 55.35 53.23 52.38 53.36 55.00 56.15 56.93 57.34 51.48 55.16 54.01 48.46

1.83 1.79 1.77 1.50 1.43 1.85 1.68 1.61 1.71 1.73 1.48 1.54 1.80 1.78 1.86

77.2 77.6 78.6 78.9 80.3

21.29 21.52 22.36 22.37 22.78

22.33 22.58 23.42 23.38 23.79

49.24 49.56 50.48 50.63 51.54

51.04 51.37 52.29 52.42 53.32

1.80 1.81 1.81 1.79 1.78

76.9 77.4 78.2

19.25 19.58 20.05

20.29 20.66 21.14

48.07 48.49 49.12

49.87 50.31 50.95

1.80 1.82 1.83

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The Journal of Physical Chemistry A Table 8. continued no. 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68

XH(D)/X+ p-CF3 p-CN 17(G)H/17(G)+ p-CH3O p-CH3 p-H p-Cl p-CF3 18(G)H/18(G)+ p-CH3 p-H p-Cl p-CF3 19(G)H/19(G)+ p-CH3 p-H p-Cl p-CF3

ΔGoH−D(XH)a

ΔG‡XH/X+b

ΔG‡XD/X+c

ΔG‡XH/X+(XH)d

ΔG‡XD/X+(XD)e

ΔΔf

79 77.1

20.61 19.51

21.67 20.58

49.80 48.30

51.61 50.12

1.81 1.82

71.7 72.8 74.1 75.8 78.4

18.69 19.69 20.58 21.93 24.20

19.85 20.84 21.78 23.13 25.39

45.19 46.24 47.34 48.87 51.30

47.05 48.10 49.22 50.74 53.17

1.86 1.86 1.88 1.87 1.87

55.7 56.1 56.7 57.7

9.69 9.31 8.84 8.48

10.94 10.54 10.06 9.66

32.70 32.70 32.77 33.09

34.60 34.60 34.66 34.96

1.90 1.90 1.89 1.87

53.5 54.1 54.5 55.4

11.67 11.29 10.66 10.05

12.99 12.61 11.96 11.31

32.58 32.69 32.58 32.72

34.52 34.63 34.51 34.63

1.94 1.94 1.93 1.91

ΔGoH−D(XH) is the molar free energy change of XH to release hydride anions in acetonitrile, the values of which are derived from literature;32 the unit is kcal/mol. bΔG‡XH/X+ is the activation free energy of the reaction XH/X+ in acetonitrile, the values of which are derived from literature;32 the unit is kcal/mol. cΔG‡XD/X+ is the activation free energy of the reaction XD/X+ in acetonitrile, the values of which are derived from ΔG‡XH/X+ values and KIEXH/X+ values according to the equation: ΔG‡XD/X+ = ΔG‡XH/X+ + RT ln(KIEXH/X+); the unit is kcal/mol. dΔG‡XH/X+(XH) is the molar free enegy change of the X−H bond for the reaction XH/X+ going from the initial state (IS) to the transition state (TS), the values of which are derived from ΔG‡XH/X+ values and ΔGoH−D(XH) values using the equation ΔG‡XH/X+(XH) = 0.5[ΔG‡XH/X+ + ΔGoH−D(XH)]; the unit is kcal/mol. e ΔG‡XD/X+(XD) is the molar free enegy change of the X−D bond for the reaction XD/X+ going from the initial state (IS) to the transition state (TS), the values of which are derived from ΔG‡XD/X+ values and ΔGoH−D(XH) values using the equation ΔG‡XD/X+(XD) = 0.5[ΔG‡XD/X+ + ΔGoH−D(XH) + ΔZPE], the unit is kcal/mol. fΔΔ = ΔG‡XD/X+(XD) − ΔG‡XH/X+(XH). a

Table 9. Point-to-Point Comparisons between the New KIE Kinetic Model (Zhu’s KIE Kinetic Model) and the Traditional KIE Kinetic Model about the Prerequisite, Model, and Origin of KIE

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(4) A new KIE kinetic model was developed using Zhu’s kinetic model to explain and predict KIE. The new KIE kinetic model not only can give a uniform explanation of the various (normal, enormous and inverse) KIEs but also can make a prediction of KIE value for various chemical reactions. (5) The origin of KIE is the difference of the X−H bond and the X−D bond in chemical reactions. KIE values are dependent on the difference of the two Morse free energy curves describing the dissociation of the X−H bond and the X−D bond in chemical reactions. (6) eq 7 has been verified to be successful for hydride transfer reactions. Since the development of eq 7 is only on the basis of the common chemical reactions (XH/Y), eq 7 should be also suitable for proton transfer reactions, hydrogen atom transfer reactions and many other atom or atom-group transfer reactions. The greatest contribution of this paper is to develop a new KIE kinetic model using two different Morse free energy curves instead of one Morse free energy curve in the traditional KIE theories to describe the free energy changes of the X−H bond and the X−D bond dissociation in chemical reactions. The new KIE kinetic model not only can give a uniform explanation of the various (normal, enormous and inverse) KIE values but also can make predictions of KIE values for various chemical reactions. Undoubtedly, the information provided in this paper should has very important scientific significance for theoretical chemists and experimental chemists to understand and further examine the nature of the kinetic isotope effect.

Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b10135. Evidence for the free energy changes, detailed derivations of eq 4 and eq 25, Table S2, the detailed synthetic routes or general preparation procedures of the 68 XH(D) and their salts, and copies of 1H MNR spectra of some typical hydride donors and their salts (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(X.-Q.Z.) E-mail: [email protected]. Telephone: (+86)022-23499184. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the National Natural Science Foundation of China (Grant Nos. 21472099, 21390400, and 21102074) and the 111 Project (B06005) is gratefully acknowledged.

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REFERENCES

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IX. EXPERIMENTAL SECTION Materials. All reagents were of commercial quality from freshly opened containers or were purified before use. Reagent grade acetonitrile was refluxed over KMnO4 and K2CO3 for several hours and was doubly distilled over P2O5 under argon before using.51 The 68 organic hydride compounds, XH(D), and their corresponding salts perchlorate (X+ClO4−) were synthesized according to conventional synthetic strategies.52−56 The typical synthetic routes of the 68 organic hydride compounds, XH(D), and their corresponding salts perchlorate (X+ClO4−) were provided in the Supporting Information. All the target products were identified by 1H NMR and MS. Kinetic Measurements. The kinetics of the hydride transfer reactions were conveniently monitored by an Applied Photophysics SX.18MV-R stopped-flow which were thermostated at 298 K under strict anaerobic conditions in dry acetonitrile.57 The method of the kinetic measurement was pseudo-first-order method. The concentration of the hydride donor was maintained at more than 20-fold excess of the hydride acceptor to attain pseudo-first-order conditions. The kinetic traces were recorded on an Acorn computer and analyzed by Pro-K Global analysis/ simulation software or translated to PC for further analysis. The well data fitting used the equation Abs = P1 × EXP(−P2*x) + P3, which was integrated in the Pro-K Global analysis/simulation software or Origin Software, and P2 was the pseudo-first-order rate constants k1. Thus, the second-order observed rate constants (kobs) were derived from plots of the pseudo-first-order rate constants versus the concentrations of the excessive reactants. In each case, it was confirmed that the rate constants derived from three to five independent measurements agreeing within an experimental error of ±5%. 1797


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Classical but New Kinetic Equation for Hydride Transfer Reactions. Org. Biomol. Chem. 2013, 11, 6071−6089. (33) Since the effect of compound structures on the difference of zero-point-energy between the X−H bond and the X−D bond is quite small, the assumption (ΔGoXH/Y ≅ ΔGoXD/Y) is reasonable. In order to further support the assumption, the free energy changes of the following three H− transfer reactions and the corresponding three D− transfer reactions in acetonitrile were determined using experimental method: (i) 1H(D) + 7(MeO)+ → 1+ + 7(MeO)H(D), (ii) 2H(D) + 7(MeO)+ → 2+ + 7(MeO)H(D), and (iii) 1H(D) + 2+ → 1+ + 2H(D). The results show that the three ΔGoXD/Y+ values are all equal or quite close to the corresponding ΔGoXH/Y+, and the derivations are all smaller than 0.1 kcal/mol. The detailed experimental results are provided in the Supporting Information. (34) Zhu, X.-Q.; Yang, J.-D. Direct Conflict of Marcus Theory with the Law of Conservation of Energy. J. Phys. Org. Chem. 2013, 26, 271− 273. (35) Zhu, X.-Q.; Yang, J.-D. The Fundamental Flaw of Marcus Theory. Chem. J. Chinese Univ. 2013, 34 (10), 2247−2253. (36) The detailed derivation of eq 4 is provided in the Supporting Information. (37) Equation 4, ΔG‡XH/Y = 1/2(ΔG‡XH/X + ΔG‡YH/Y) + 1/ 2ΔGoXH/Y), looks like the Marcus cross relation when the part with ΔGoXH/Y squared is removed [ΔG‡XH/Y = 1/2(0.25λXH/X + 0.25λYH/Y) + 1/2ΔGoXH/Y] in form, but the origin and the nature of eq 4 is thoroughly different from that of Marcus cross relation. Equation 4 is derived from Zhu’s kinetic model for hydride transfer reactions (see ref 32), ΔG‡XH/X and ΔG‡YH/Y in eq 4 are all variables when ΔGoXH/Y is changed. The Marcus cross relation is derived from the Marcus equation according to two assumptions: (i) λ = λXH/Y and (ii) λXH/Y = 1/2(λXH/X + λYH/Y). It is clear that λXH/X and λYH/Y in Marcus cross relation are all constants when ΔGoXH/Y is changed, because λ in the Marcus equation is a constant when ΔGoXH/Y is changed. From Marcus’ two original papers describing Marcus theory,58,59 it is clear that the essential prerequisite of the Marcus equation is that λ is a constant rather than a variable when ΔGoXH/Y is changed. If λ is a variable when ΔGoXH/Y is changed, the Marcus equation cannot be obtained. In other word, if λ is not a constant when ΔGoXH/Y is changed, the Marcus equation is wrong. That is, if λXH/X and λYH/Y are not constants when ΔGoXH/Y is changed, the present Marcus cross relation formula is wrong. However, until now in Marcus’ cycle there are many chemists who still incorrectly regard λ in the Marcus equation as a variable and extensively misuse it in many research fields; the main reason is that they lack a profound understanding of Marcus theory and ignore the essential prerequisite of the Marcus equation (see refs 34 and 35). Since eq 4 is directly derived from Zhu’s kinetic model describing the kinetics of hydride transfer reactions,32 and the origin and nature of the eq 4 is completely different from that of Marcus cross relation, eq 4 in this paper is called Zhu’s equation to make a distinction between eq 4 and the Marcus cross relation formula. The detailed comparison of the origin and nature between the eq 4 and the Marcus cross relation formula is provided in Table 2. (38) Mayer, J. M. Simple Marcus-Theory-Type Model for HydrogenAtom Transfer/Proton-Coupled Electron Transfer. J. Phys. Chem. Lett. 2011, 2, 1481−1489. (39) Zhu, X.-Q.; Zou, H.-L.; Yuan, P.-W.; Liu, Y.; Cao, L.; Cheng, J.P. A Detailed Investigation into the Oxidation Mechanism of Hantzsch 1, 4-Dihydropyridines by Ethyl α-Cyanocinnamates and Benzylidenemalononitriles. J. Chem. Soc., Perkin Trans. 2 2000, 1857−1861. (40) Zhu, X.-Q.; Li, H.-R.; Li, Q.; Ai, T.; Lu, J.-Y.; Yang, Y. Determination of the C4-H Bond Dissociation Energies of NADH Models and Their Radical Cations in Acetonitrile. Chem. - Eur. J. 2003, 9 (4), 871−880. (41) Perrin, C. L.; Zhao, C. Intramolecular Kinetic Isotope Effect in Hydride Transfer from Dihydroacridine to a Quinolinium Ion. Rejection of a Proposed Two-Step Mechanism with a Kinetically Significant Intermediate. Org. Biomol. Chem. 2008, 6, 3349−3353. (42) Zhu, X.-Q.; Mu, Y.-Y.; Li, X.-T. What are the Differences between Ascorbic Acid and NADH as Hydride and Electron Sources 1798


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The Journal of Physical Chemistry A in vivo on Thermodynamics, Kinetics, and Mechanism? J. Phys. Chem. B 2011, 115, 14794−14811. (43) Zhu, X.-Q.; Tan, Y.; Cao, C.-T. Thermodynamic Diagnosis of the Properties and Mechanism of Dihydropyridine-Type Compounds as Hydride Source in Acetonitrile with “Molecule ID Card. J. Phys. Chem. B 2010, 114, 2058−2075. (44) In the paper,38 Mayer used eq 7 to estimate the KIE of hydrogen atom transfer from RuIIIimH to TEMPO• in acetonitrile, and found that the result is different from the experimental measurement. The reason could be that the KIEself value of RuIIIimH/RuIIIim• in CD3CN is not reliable rather than that tunneling takes place in the reaction (see ref 48), because NMR is an unreliable technique to determine the KIEself of RuIIIimH/RuIIIim• by hydrogen atom transfer (a radical reaction) (see: Wu, A.; Mayer, J. M. Hydrogen atom transfer reactions of a ruthenium imidazole complex: hydrogen tunneling and the applicability of the Marcus cross relation. J. Am. Chem. Soc. 2008, 130, 14745−14754. ). (45) Cheng, T.-Y.; Bullock, R. M. Isotope Effects on Hydride Transfer Reactions from Transition Metal Hydrides to Trityl Cation. An Inverse Isotope Effect for a Hydride Transfer. J. Am. Chem. Soc. 1999, 121, 3150−3155. (46) Hewitt, J. T.; Concepcion, J. J.; Damrauer, D. H. Inverse Kinetic Isotope Effect in the Excited-State Relaxation of a Ru(II)-Aquo Complex: Revealing the Impact of Hydrogen-Bond Dynamics on Nonradiative Decay. J. Am. Chem. Soc. 2013, 135, 12500−12503. (47) Cheng, T.-Y.; Bullock, R. M. Hydride Transfer from (η5-C5Me5) (CO)2MH (M= Fe, Ru, Os) to Trityl Cation: Different Products from Different Metals and the Kinetics of Hydride Transfer. Organometallics 2002, 21, 2325−2331. (48) It is true that observations of tunneling effects in chemical reactions, especially in the enzyme catalytic reactions were extensively reported. However, the observations of tunneling effects in chemical reactions all are spurious. By examining the evidence of tunneling effects reported in the literature, it is found that the key evidence of the tunneling phenomenon is that the Arrhenius plots were found to be a curved line rather than a straight line within a certain temperature range, because the bent Arrhenius plot means that the activation energy of the chemical reactions is a variable rather than a constant when the reaction temperature is changed. Since classic transition state theory and collision theory all can not explain the activation energy change of chemical reactions when the reaction temperature is changed, some quantum chemists applied the volatility of particles (i.e., the tunneling of particles) to explain it. As a result, the bent Arrhenius plot is considered as the key evidence that the chemical reactions have tunneling effects. According to the Arrhenius equation, it is true that the activation energy of a chemical reaction is a constant when the reaction temperature alters. However, as is well-known, for the same chemical reaction in solution, if the reaction medium is changed, the activation energy of the chemical reaction is also changed, which means that activation energy of chemical reactions is not only dependent on the nature of the reactants but also dependent on the nature of the reaction media. Since the nature of reaction media can be changed by temperature, it is evident that the activation energy of chemical reactions, in general, should be a variable rather than a constant when the reaction temperature is changed. In fact, the bent Arrhenius plot of a chemical reaction within a certain temperature range is a precise indicator that the nature of the reaction media is changed when temperature alters within the temperature range, rather than an indicator that the tunneling takes place in the reactions. If the origin of tunneling theory describing the kinetics of atom transfer reactions is examined carefully, it is found that the tunneling of atom in chemical reactions is derived from the de Broglie wave of the atom. As is well-known, the de Broglie wave of atoms (i.e., the tunneling of atoms) in quantum mechanics only determines the probability density of finding the atom at a given point in molecule. Evidently, the tunneling of atoms in molecule has nothing to do with the rate of the atom transfer from one molecule (atom-donor) to another molecule (atom acceptor) in the atom transfer reactions. In fact, the nature of the de Broglie wave of a atom in molecules may be negligible,

otherwise, the crystal structure of molecules can not be determined. Lacking a profound understanding of the nature of the particle de Broglie wave (i.e., the tunneling of particles), some chemists, such as, Bell incorrectly used the tunneling of particles to explain the bent Arrhenius plot lines (see: Bell, R. P. The Tunnel Effect in Chemistry, Chapman and Hall, London, 1980). (49) In fact, if the enormous KIE values resulting from atomic tunneling effect were true,50 the fact that the electron transfer reactions have activation energies could not be explained, because the de Broglie wavelength of electrons (λ/pm: 2690)50 is much larger than that of hydrogen atoms (λ/pm: 63 and 45 for H and D, respectively).50 (50) Isaacs, N. S. Physical Organic Chemistry, 2nd ed., Longman Press: London, 1995; pp 293, 304. (51) Zhu, X.-Q.; Zhang, M.-T.; Yu, A.; Wang, C.-H.; Cheng, J.-P. Hydride, Hydrogen Atom, Proton, and Electron Transfer Driving Forces of Various Five-Membered Heterocyclic Organic Hydrides and Their Reaction Intermediates in Acetonitrile. J. Am. Chem. Soc. 2008, 130, 2501−2516. (52) Xia, K.; Shen, G.-B.; Zhu, X.-Q. Thermodynamics of Various F420 Coenzyme Models as Sources of Electrons, Hydride Ions, Hydrogen Atoms and Protons in Acetonitrile. Org. Biomol. Chem. 2015, 13, 6255−6268. (53) Kalla, R. V.; Elzein, E.; Perry, T.; Li, X.; Palle, V.; Varkhedkar, V.; Gimbel, A.; Maa, T.; Zeng, D.; Zablocki, J. Novel 1, 3-Disubstituted 8-(1-benzyl-1 H-pyrazol-4-yl) Xanthines: High Affinity and Selective A2B Adenosine Receptor Antagonists. J. Med. Chem. 2006, 49, 3682− 3692. (54) Taylor, E. C.; Sowinski, F.; Yee, T. T.; Yoneda, F. New Syntheses of Alloxazines. J. Am. Chem. Soc. 1967, 89, 3369−3370. (55) Legrand, Y.-M.; Gray, M.; Cooke, G.; Rotello, V. M. Model Systems for Flavoenzyme Activity: Relationships between Cofactor Structure, Binding and Redox Properties. J. Am. Chem. Soc. 2003, 125, 15789−15795. (56) Pintér, Á .; Sud, A.; Sureshkumar, D.; Klussmann, M. Autoxidative Carbon−Carbon Bond Formation from Carbon-Hydrogen Bonds. Angew. Chem., Int. Ed. 2010, 49, 5004−5007. (57) Zhu, X.-Q.; Zhang, J.-Y.; Cheng, J.-P. Negative Kinetic Temperature Effect on the Hydride Transfer from NADH Analogue BNAH to the Radical Cation of N-Benzylphenothiazine in Acetonitrile. J. Org. Chem. 2006, 71, 7007−7015. (58) Marcus, R. A. J. Chem. Phys. 1956, 24, 966−978. (59) Marcus, R. A. J. Chem. Phys. 1956, 24, 979−989.

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NOTE ADDED AFTER ASAP PUBLICATION This paper was published ASAP on March 15, 2016, with text errors in section VII. The corrected version was reposted on March 24, 2016.

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Prediction of Kinetic Isotope Effects for Various Hydride Transfer

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