Res Chem Intermed (2012) 38:2175–2190 DOI 10.1007/s11164-012-0535-8
An accurate theoretical study of energy barriers of alkaline hydrolysis of carboxylic esters Huajing Wang
Received: 29 September 2011 / Accepted: 9 March 2012 / Published online: 30 March 2012 Ó Springer Science+Business Media B.V. 2012
Abstract Hydrolysis of esters is one of the most important and frequently used reactions in both organic synthesis and biochemistry. While the reaction mechanism in solution is reasonably well understood, many questions still remain to be answered. In the present study, the combination method, MPW1B95/6-311?? G(3df,2p)//B3LYP/6-31?G(d)//HF//CPCM/UA0, was found to be reliably predict the energy barriers of alkaline hydrolysis of various esters. The MAD and RMSE were equal to 1.03 and 1.06 kcal/mol, respectively. With this authorized theoretical protocol in hand, we systematically studied the mechanisms of alkaline hydrolysis of ethyl benzoate. The acyl-oxygen cleavage BAC2 route is preferred over the alkyl-oxygen cleavage BAL2 route. Then, the total activation energy barriers of BAC2 and BAL2 routes of over 40 esters have been calculated. And this large body of data allows us to systematically study the various effects controlling the alkaline ester hydrolysis, including the polar effect, the steric effect, and the remote substituent effect. Also, the solvent effect has been extensively studied in this work. Furthermore, the differences between BAC2 and BAL2 routes of these effects are also discussed. The results enable us to predict the energy barrier of the hydrolysis of cyhalofop-butyl in aquatic solution. Keywords
Density functional theory Mechanisms Alkaline ester hydrolysis
Introduction Hydrolysis of esters has been studied more often than any other chemical reaction. The history of this work is a history of our growing understanding of reactions in H. Wang (&) Tianjin Economic Technological Development Area Polytechinc, Tianjin 300457, People’s Republic of China e-mail:
[email protected]
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solution [1–3], for the reaction has been a traditional proving ground for theories of chemical actions. As is well known, hydrolysis of esters can react in various media, ranging from alkaline solution to very strong acid, involving cleavage of either the acyl-oxygen or alkyl-oxygen bond [4–14]. Among these media, the hydrolysis reaction of carboxylic esters in basic solutions stands out as one of the most studied reactions in chemistry because of its common occurrence in many organic and biochemical processes [15–19]. It is known that some base catalysts can catalyze the ester hydrolysis by assisting the attack of a water molecule on the carbonyl group, but in basic solution, the hydrolysis reaction is mainly catalyzed by the hydroxide ion which act as a nucleophilic catalyst by direct attacking the ester carbonyl group [20, 21]. Therefore, in the present study, we will focus on the mechanisms of hydroxide ion-catalyzed ester hydrolysis. Over the years, many important and elucidative experimental studies have contributed to the understanding of the mechanistic features of ester hydrolysis [22, 23]. Some of the classical mechanistic studies with labeled 18O as tracer have further strengthened the evidence for acyl-oxygen cleavage in alkaline hydrolysis. The most important result of these investigations was proving the existence of a tetrahedral addition compound being an intermediate [24–28]. This hydrolysis model has been designated as BAC2 (basecatalyzed, acyl-oxygen cleavage, bimolecular) and is believed to occur through a two-step scheme [19]. This widely accepted mechanism consists of formation of tetrahedral intermediate as the first step, and decomposition or tetrahedral intermediate to products as the second step. The first step is usually the ratedetermining step. The kinetically important steps of hydrolysis reaction can be summarized by the simplified equations as shown in Scheme 1.
O
O R1COR2
+ OH
R1COR2
k-1
R1COR2
OH
RE
≠
O
k1
OH
O
TS1a
HBRa
R1COR2 OH
k2 ≠ O R1COH
+ R2O
O
O
R1COH
R1COH
OR2 PRa
HBPa
Scheme 1 Simplified equations of hydrolysis reaction
123
OR2 TS2a
INTa
An accurate theoretical study of energy barriers
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Although the BAC2 mechanism predominates in most alkaline ester hydrolysis, on some occasions a less common mode of ester hydrolysis, BAl2 (Scheme 2) [29] (base-catalyzed, alkyl-oxygen cleavage, bimolecular), would compete with the BAC2 mechanism. The BAl2 category, which leads to the same products as does the BAC2 category is essentially an SN2 substitution with a carboxylate leaving group. Although the mechanisms of ester basic hydrolysis have been experimentally studied for decades, the use of high-quality computational methods in the mechanistic studies of ester basic hydrolysis has only recently been reported. For example, Ornstein et al. [13] have reported a study on the basic hydrolysis of some carboxylic acid ester in gas phase, and after that they also reported a theoretical study of the basic hydrolysis of methyl acetate and methyl formate in solution [30]. Haeffner et al. [31] have studied the methyl acetate alkaline hydrolysis at the MP2 level including the calculations of solvent effects by the PCM model. Tantillo and Houk [32] reported a theoretical study of the phenyl acetate at the MP2 level with the solvent effects calculated through the PCM and SCI-PCM methods. Although all these studies further deepened our understanding of ester hydrolysis, only the BAC2 mechanism has been explored up to now. Furthermore, the use of the MP2 method to study the mechanisms is not only time-consuming but also suffers from relatively large errors in predicting the energy barriers and rate constant. Therefore, an alternative theoretical method should be considered in order to accurately and economically predict energy barriers and rate constants of hydrolysis of various esters. For this purpose, in this work, we have developed an ab initio method that can reliably predict the rate constants of hydrolysis of various carboxylic esters. Our work took advantage of the recent development of various solvation models and new DFT methods, which can be used to describe the solvation effects and gas energy with increasing precision and efficiency. By comparing the theoretical energy barriers with the experimental values, the optimal method was found to be capable of achieving a precision of RMSE = 1.06 and MAD = 1.03. With this authorized theoretical protocol in hand, we studied the detailed mechanisms of alkaline hydrolysis of carboxylic esters, including both the BAC2 and the BAl2 pathways. Finally, we conducted a systematic analysis of various factors that may affect the ester hydrolysis. These factors include polar effects, steric effects, remote substituent effects, and the effect of solvent.
O
O R1COR2
+ OH
RE
k3
≠
O
R1COR2
R1COR2
OH
OH
HBRb
TS1b
O R1CO + R2OH
PRb
Scheme 2 The BAl2 reaction
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Method development Theoretical methods In this section, various DFT methods were utilized to test their performance in reproducing the experimental energy barriers and rate constants. MP2 calculations were also conducted for comparison. The reason for choosing DFT methods is that they can always achieve a good compromise between the accuracy and the efficiency. As to the selection of DFT methods, we decide to compare the performances of commonly used B3LYP with the newly developed DFT functionals such as MPW1B95, MPW1 K, TPSSKCIS, and TPSSLYP1 W. Among these methods, the B3LYP functional was usually used for calculation of energy barriers [33, 34]. MPW1B95 [35] was based on the modified Perdew and Wang 1991 exchange functional (mPW or MPW) and Becke’s 1995 meta correlation functional (B95), where meta means that it depends on kinetic energy density as well as the density and the gradient of the density. MPW1 K [36] is an HDFT model with excellent performance for kinetic calculations. It has been optimized against a database of 20 forward barrier heights, 20 reverse barrier heights, and 20 energies of reaction. TPSSKCIS [37] is a multi-coefficient extrapolated density functional theory for thermochemistry and thermochemical kinetics. All the above-mentioned DFT methods are used in conjunction with the 6-311??G(2df,2p) basis set for single point energy calculation. And for the solution phase calculation, according to our previous studies [38], the IEF-PCM (Integral Equation Formalism of Polarizable Continuum Model), CPCM (Conductor-like Polarizable Continuum Model), and COSMO (Conductor-like Screening Model) were chosen to estimate the solvent effect. Also, the performances of five types of atomic radii, namely, UA0, BONDI, UAHF, UAKS, and PAULING, were compared for the construction of a solvent-inaccessible cavity in which the solute molecule resides [39–42]. For all systems studied, vibrational frequency calculations were carried out to confirm all the first-order saddle points and local minima on the potential energy surfaces. Intrinsic reaction coordinate (IRC) [43, 44] calculations were performed to verify the expected connections of the first-order saddle points with local minima on the potential energy surfaces. All calculations were done with the Gaussian 03 suite of programs [45]. Calculation method Having selected a number of theoretical methods, we next proceeded to derive the equations to calculate the free energy barrier and rate constant. Alkaline hydrolysis of substituted ethyl benzoates was chosen for testing the performances of different theoretical methods because of the availability of the kinetic data of this reaction. According to the kinetically important steps of ester hydrolysis summarized in Scheme 1, by using the steady-state assumption for the tetrahedral intermediate, the rate coefficient for the overall reaction can be readily shown as:
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An accurate theoretical study of energy barriers
k¼
2179
k1 k2 : k1 + k2
ð1Þ
For the circumstances of k2 k-1, k becomes equal to k1 and the addition step alone is rate-determining. The free energy barriers of this reaction can be equal to the free energy change of Eq. 2. R - C6 H4 COOEt þ OH ! TSla6¼ :
ð2Þ
If the free energy change of the above reaction in the ethanol solution is defined as DG=, then the rate constant can be readily calculated by Eq. 3. kT DG6¼ DG6¼ ¼ 12:79 : ð3Þ h 2:303 RT 2:303 RT Table 1 shows experimental rate constants of eight substituted ethyl benzoates and their energy barriers calculated by Eq. 3. We first set out to optimize the DFT methods for single point energy calculations. Geometries were fully optimized by B3LYP/6-31?G(d), and solvation-free energies were calculated by the default PCM/UA0 model. The results of these tests lg k ¼ lg
Table 1 Eight representative esters experimental values [46] tested for the method development No.
k (mol-1 L s-1)
lgk
DG= (kcal/mol)
Solvent
0.00
6.21 9 10-4
-3.21
21.82[19]
85 % ethanol
-0.17
2.80 9 10-4
-3.55
22.41[19]
85 % ethanol
-0.27
1.30 9 10-4
-3.89
22.76[19]
85 % ethanol
-0.66
1.43 9 10-5
-4.85
24.14[15]
85 % ethanol
0.78
7.20 9 10-2
-1.14
19.08[15]
85 % ethanol
0.66
3.12 9 10-2
-1.51
19.50[15]
85 % ethanol
0.06
8.97 9 10-4
-3.05
21.60[19]
85 % ethanol
0.23
2.67 9 10-3
-2.57
21.02[17]
85 % ethanol
p[47]
Compound
a
COOEt b
H3C
COOEt
c
H3 CO
COOEt
d
H2 N
COOEt
e
O2N
COOEt
NC
COOEt
f
g
F
COOEt
h
Cl
COOEt
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are shown in Table 2. B3LYP and MP2 provide noticeably worse results. For B3LYP, there is a large systematic deviation from the experimental values, which can be reflected by its large RMS error (RMSE = 2.29) and the high linear correlation coefficient (R = 0.99). The MP2 method has a relatively poor linear correlation with experimental values (R = 0.95). The best results were obtained by MPW1B95 with a RMSE of 1.23 kcal/mol, MAD of 1.21 kcal/mol and R of 0.99. After choosing a good DFT method for the single point calculation, we move to find an optimal solvation model for accurately estimating the solvent effects in our specific system [48–51]. For the calculation of solvation-free energies, the family of polarizable continuum model (PCM) algorithms has become a standard method due to its accuracy and flexibility. In PCM, the solute, possibly supplemented by some explicit solvent molecules belonging to the first solvation shells [52–55], is placed in a cavity formed by interlocking spheres, centered on solute atoms or atomic groups. Another very successful solvation model is the conductor-like PCM (CPCM), which has also been applied to the computation of the alkaline hydrolysis of methyl acetate in aqueous solution. The conductor-like screening COSMO method is based on the screening in conductors. The solute is placed in a cavity of a continuum medium with dielectric e equal to infinity to model a perfect conductor. The shape of the cavity is defined by the contour of the solvent accessible surface based on the conformation of the molecule and the van der Waals radii of the atoms [52–55]. Combining the restoring free energy with the free energy required to create a cavity, and the dispersion free energy that is proportional to the exposed surface area of the different atom types, COSMO [56, 57] theory can be used to predict vapor pressures and enthalpies of vaporization. Or, with the free energy difference between a molecule in a liquid mixture and in its pure liquid, vapor–liquid equilibrium can be predicted. Table 3 shows the performances of different solvent models in conjunction with MPW1B95 single point energies in predicting the experimental rate constants. By default, the UA0 model is chose to build the cavity. From Table 3, it can be seen that the performance of CPCM is slightly better than PCM (RMSE is 1.03 vs. 1.21 kcal/mol). COSMO model with a RMSE of 4.86 kcal/mol is not as good as CPCM and PCM. The deviation may come from the essential approximation made in COSMO theory that the structure of the solute is unchanged going from the gas phase to the perfect conductor phase, and to the real solution [56].
Table 2 Performances of DFT functionals for lgk calculations of hydrolysis of esters. (energies in kcal/ mol) Methods
R
SD
RMS error
MAD
Maximum error
Solvent model
B3LYP
0.99
0.29
2.29
2.27
2.86
PCM/UA0
MP2
0.95
0.62
1.37
1.24
1.91
PCM/UA0
MPW1 K
0.99
0.28
1.83
1.81
2.36
PCM/UA0
MPW1B95
0.99
0.23
1.23
1.21
1.76
PCM/UA0
TPSSKCIS
0.99
0.24
1.22
1.19
1.76
PCM/UA0
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Table 3 Performances of solvent models for the lgk calculations of hydrolysis of eight representative esters. (energies in kcal/mol) Methods
R
SD
RMS error
MAD
Maximum error
Solvent model
MPW1B95
0.99
0.23
1.23
1.21
1.76
PCM/UA0
MPW1B95
0.99
0.26
1.06
1.03
1.56
CPCM/UA0
MPW1B95
0.96
0.38
4.86
4.84
5.36
COSMO/UA0
Table 4 Performances of different radii for the lgk calculations of hydrolysis of eight representative esters. (energies in kcal/mol) Methods
R
SD
RMS error
MAD
Maximum error
Solvent model
MPW1B95
0.96
0.38
5.90
5.89
6.38
CPCM/Bondi
MPW1B95
0.99
0.26
1.06
1.03
1.56
CPCM/UA0
MPW1B95
0.94
0.55
7.86
7.84
8.65
CPCM/Pauling
MPW1B95
0.86
0.64
12.79
12.78
13.86
CPCM/UAHF
MPW1B95
0.78
0.78
4.36
4.30
5.01
CPCM/UAKS
MPW1B95
0.99
0.38
1.15
1.09
1.42
CPCM/1.10
MPW1B95
0.99
0.49
3.02
2.98
3.56
CPCM/1.20
In CPCM and PCM models, choosing a cavity is important because the accuracy of computed energies and properties depends on the size of the cavity. In the current study, the UA0, UAHF, UAKS, PAULING, and BONDI cavities were tested [52– 55]. The results are shown in Table 4. It is obvious that among these cavities the UA0 gives the best results, with a MAD of 1.03 kcal/mol and RMSE of 1.06 kcal/ mol. For the UA0 model [56, 57], we also modified the 1.10 or 1.20 times atom topological model applied on atomic radii of universal force field. But, unfortunately, they have not shown better performances than UA0 model. On all accounts, the optimal combination of theoretical method should be MPW1B95/6-311??G(3df,2p)//B3LYP/6-31?G(d)//HF//CPCM/UA0. The RMS error of this method is 1.06 kcal/mol, the MAD is 1.03 kcal/mol, and the corresponding maximum error is 1.56 kcal/mol.
Detailed pathways for alkaline hydrolysis of ethyl benzoate Here, using the optimal theoretical protocol developed above, we conducted a detailed mechanistic study of alkaline hydrolysis of ethyl benzoates in ethanol. It is well established that the usual pathway for the hydroxide ion reaction with carboxylic esters in ethanol solution takes place through the BAC2 mechanism. However, on some occasions, another less common mode of alkaline ester hydrolysis, BAl2, may compete with the BAC2 mode. It can lead to the same products as the BAC2 pathway, but is essentially an SN2 substitution with a carboxylate leaving group [13, 14].
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The BAC2 route Figure 1 shows the reaction steps for the alkaline hydrolysis of ethyl benzoate in ethanol for the BAC2 mechanism. Each step is numbered and the corresponding transition states are identified as TS1a and TS2a. In Fig. 1, the values in the brackets refer to free Gibbs energy changes in gas phase from the separated reactants (ethyl benzoate and hydroxide ion) and the values out of the parentheses refer to the corresponding energy changes in solution. By performing the IRC procedure [13, 14], it is found that on the potential energy surface this first-order saddle point connects two local minima, one associated with a tetrahedral intermediate INTa and the other associated with a stable hydrogenbond complex HBRa. The HBRa is more stable than the separated reactants in gas phase. But in ethanol solution, the HBRa energy is 16.70 kcal/mol larger than the separated reactants (ethyl benzoate and hydroxide ion). This phenomenon is mainly attributed to the strong electrostatic interactions between the separated ion and the solvent. The energy change from separated reactants PhCOOEt?OH- to the solvated first transition state TS1a is 22.64 kcal/mol, which is larger than the energy change from separated reactants to the solvated second transition state TS2a (DG=(TS2a) = 15.02 kcal/mol). Thus, the decomposition of the tetrahedral intermediate INTa should be much faster than its formation. And the formation of the tetrahedral intermediate should be the ratedetermining of BAC2 process in ethanol solvent. This result agrees very well with experiments. The experimental free energy barrier of the alkaline hydrolysis of PhCOOEt is 21.86 kcal/mol, while the theoretical value calculated by our mode amounts to 22.64 kcal/mol. For the proton exchange pathway (Fig. 2) that competes with the direct decomposition of the tetrahedral intermediate INTa, the calculated barrier of the proton exchange step (formation of TS3a) is 27.70, 12.68 kcal/mol higher than the energy barrier of direct decomposition of the tetrahedral intermediate INTa, or DG=(TS2a) (15.02 kcal/mol), therefore the proton exchange should be negligible in the BAC2 route of the hydrolysis reaction in ethanol solvent. The BAl2 route Figure 3 shows the corresponding free energy profile of BAl2 route of ester hydrolysis. It can be observed from Fig. 3 that the gas phase energy barrier predicted for this mode of hydrolysis of PhCOOEt is 9.32 kcal/mol, only 2.76 kcal/ mol higher than that of BAC2 route. However, the energy barrier predicted for the BAl2 process in ethanol solution is 28.37, 5.73 kcal/mol higher than that of BAC2 route ethanol solution (22.64 kcal/mol). These results indicate that for the hydrolysis of PhCOOEt, BAl2 route is negligible compared to the corresponding BAC2 route in ethanol solution, but the two routes are competitive in gas phase.
Hydrolysis of other esters In order to find whether the analysis for hydrolysis of ethyl benzoates also validate for other alkyl esters and to explore the substituent effects on the energy barriers, we
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2183
1.3629Å
kcal/mol 1.3346Å
2.6461Å 3.8922Å HBRa
1.4121Å TS2a
16.70 (-12.12)
15.02 (-15.67) INTa 6.14 (-21.14) 1.5242Å
RE+OH 0.00 (0.00)
2.0392Å
TS1a 22.64 (-5.56)
1.2603Å 1.3522Å 1.4803Å 1.2598Å PR -16.16 (-36.03)
reaction corrdinate Fig. 1 The potential energy surface for BAC2 model obtained from MPW1B95 calculations
kcal/mol Proton Exchange TS3a 27.70 (-2.20) 1.5242Å
Direct Decomposition TS2a 15.02 (-15.67)
1.4803Å
INTa
2.0392Å
6.14 (-21.14)
RE+OH 0.00 (0.00)
1.3522Å
1.4121Å
Reaction corrdinate Fig. 2 The potential energy surface for BAC2 model with proton exchange obtained from MPW1B95 calculations
have calculated the energy barriers of the BAC2 route for other 29 representative carboxylic esters (Table 5). It is found that the calculated energy barriers of BAC2 route agree very well with the experimental values for most carboxylic esters, which further demonstrates the reliability of the newly developed theoretical method in predicting the energy barriers of alkaline ester hydrolysis. But for three esters, that is
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kcal/mol
2 .25 58Å
1.804 0Å
1.4 920Å
3.0 643Å
T S1b 28.37 (-1.10)
HBR b 10.56 (-10.42)
RE 0.00 (0.00) 1.35 22Å
1.2599Å 1.2598Å
PR -31.81 (-51.69)
reaction corrdinate Fig. 3 The potential energy surface for BAl2 model obtained from MPW1B95 calculations
(CH3)3CCOOEt, CF3COOEt, and CCl3COOEt, the calculated energy barriers deviates from the experimental values by over 2 kcal/mol, indicating that the hydrolysis may not proceed through the BAC2 route. And a further calculation reveals that the calculated energy barriers of BAl2 route of these three esters are closer to the experimental energy barriers. Therefore, it may be concluded that three special esters possibly react through the BAl2 mechanism, or at least competition between BAl2 and BAC2 mechanisms.
Factors controlling alkaline ester hydrolysis Inductive effect From the data shown in Table 5, it is feasible to establish polar effects of substituents on the alkaline hydrolysis. Evaluating first the substituent at a-carbon of esters, it is found that the introduction of an electron-withdrawing group at a-carbon will decrease the energy barrier. This should be understandable, since the energy barriers of the hydrolysis are largely determined by the rate of nucleophilic hydroxide ion attacking the ester carbonyl group, and therefore any substituent that withdraws electrons from the carbonyl group will facilitate the nucleophilic attack at the carbonyl group and decrease the energy barrier. Taking the hydrolysis of CH3COOEt, ClCH2COOEt, and Cl2CHCOOEt, for example, as the amount of substituted chlorine increases, the electron withdrawing effect on the carbonyl group increases, and the substituted chlorine can decrease the electron density of the entire molecular system, and, therefore, increase the ability of the affinity, so their energy
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2185
Table 5 Energy barriers calculated at MPW1B95/6-311??G(2df,2p)//B3lyp/6-31?G* level for BAC2 process (exclude the proton exchange process) or BAl2 process (in parentheses) k (mol-1 L s-1)
DG (kcal/mol)
BAC2 (kcal/mol)
Errors (kcal/mol)
4.65 9 10-2
19.26 [58]
18.29
-0.97
70 % acetone
2.20 9 10-2
19.70 [58]
19.43
-0.27
n-C3H7CCOOEt
70 % acetone
8.81 9 10-3
20.24 [58]
19.86
-0.38
(CH3)3CCOOEt
70 % acetone
2.23 9 10-4
22.42 [58]
25.96 (20.54)
-2.17
CH3COOCH3
70 % acetone
0.108
18.76 [59]
17.19
-1.57
CH3COOCH2CH2CH3
70 % acetone
2.70 9 10-2
19.58 [59]
18.20
-1.37
CH3COOCH(CH3)2
70 % acetone
7.06 9 10-3
20.37 [59]
18.32
-2.05
CH3COOC(CH3)3
70 % acetone
2.65 9 10-4
22.32 [59]
19.94
-2.38
CH3COOCH2C6H5
60 % acetone
6.96 9 10-2
18.97 [60]
18.59
-0.38
CH3COOCH2C6H4CH3-p
60 % acetone
4.82 9 10-2
19.20 [60]
19.07
-0.13
CH3COOCH2C6H4NO2-p
60 % acetone
0.269
18.20 [60]
19.52
1.32
CH3COOC6H5
60 % acetone
0.537
17.75 [61]
15.81
-1.94 -2.17
Compound
Solvent
CH3COOEt
70 % acetone
CH3CH2COOEt
CH3COOC6H4CH3-p
60 % acetone
0.319
18.08 [61]
15.91
(C2H5)2CHCOOEt
70 % acetone
8.3 9 10-5
23.00 [58]
21.09
-1.91
CH3COOC6H4NO2-p
60 % acetone
8.05
16.09 [60]
14.68
-1.41
EtOOCCH2NH2
Water
0.723
17.45 [62]
18.14
0.69
MeOOCCH(NH2)CH2C6H5
Water
0.55
18.44 [63]
15.56
-2.88
MeOOCCH(NH2)CH2OH
Water
1.0
17.44 [64]
15.37
-2.07
MeCOOCH=CH2
Water
3.28
16.58 [65]
15.43
-1.15
ClCH2COOMe
Water
61.6
15.01 [66]
15.16
0.15
ClCH2COOEt
Water
33.2
15.37 [66]
15.56
0.19
Cl2CHCOOEt
Water
677
13.58 [66]
13.90
0.32
CF3COOEt
Water
15 9 105
8.72 [66]
12.74 (12.16)
3.44
CCl3COOEt
Water
2570
12.79 [66]
14.79 (12.12)
0.67
CH3SCH2COOEt
Water
0.92
17.49 [67]
18.97
1.48
CH2=CHCOOEt
85 % ethanol
4.67 9 10-3
20.70 [68]
20.03
-0.67
CH2=CHCH2COOEt
85 % ethanol
3.63 9 10-3
20.75 [68]
20.25
-0.50
trans-CH3CH=CHCOOEt
85 % ethanol
6.25 9 10-4
21.80 [68]
22.34
0.54
cis-CH3CH=C(CH3)COOEt
85 % ethanol
1.76 9 10-4
22.67 [68]
21.62
-1.05
RMS
–
–
–
–
1.50
MAD
–
–
–
–
1.15
barriers decrease gradually. Then, it becomes the substituent at the oxygen of the ester group. It is found that the polar effect of the substituent at this site is considerably smaller than those at a-carbon of esters. For example, for three esters, C6H5CH2COOCH3, p-CH3C6H4CH2COOCH3 and p-NO2C6H4CH2COOCH3, the change of energy barriers only covers a range less than 1 kcal/mol, although the electron withdrawing ability of the substituent at the carbon attached to the oxygen of ester group changes dramatically.
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Steric effect To study the steric effect, we systematically calculated the energy barriers of esters with the substituents of various sizes at the a-carbon of ester and the carbon attached to the oxygen of ester group. It is found that, for the substituent attached to the oxygen of ester group, the energy barrier increases as the size of the substituent increases. For instance, for CH3COOR, when R varies from CH3 to CH(CH3)2 to C(CH3)3, the corresponding energy barriers are 17.19, 18.32, and 19.94 kcal/mol, respectively. This is because, with the larger steric effect, the invasion of the OH- is more and more difficult. Remote substituent effect The remote substituent effect can provide further insight to the mechanisms of the ester hydrolysis. In the present study, the remote substituent effects on energy barriers of two systems, p-substituted ethyl benzoate and p-substituted phenyl acetate are studied (see below and Figs. 4 and 5). O G O G OEt O p-substituted ethyl benzoate p-substituted phenyl acetate Solvent effect The alkaline hydrolysis of esters normally involves the rate-determining addition of an anion upon a neutral molecule. Therefore, it is not expected to find that the energy barriers of ester hydrolysis are very sensitive to changes of solvents. This
-2
lgk
-3
lgk=-4.22+2.82σp R=0.99 N=8 sol=EtOH
-4
-5
-6
-7 -0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
σp Fig. 4 Linear-free energy correlation of alkaline hydrolysis for substituted ethyl benzoates in ethanol
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2187
-2
lgk=-4.14+2.61σp R=0.98 N=8 Sol= H2O
lgk
-3
-4
-5
-6
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
σp
Fig. 5 Linear-free energy correlation of alkaline hydrolysis for substituted ethyl benzoates in water
may because the alkaline hydrolysis of esters do not affect by the polarity of the solvent. The results are shown in Table 6.
Prediction In view of our results, we predict the energy barriers of cyhalofop-butyl hydrolysis in aquatic solution, and the method we selected is MPW1B95/6-311 ??G(2df,2p)// B3LYP/6-31?G(d), the energy barrier we calculated was 17.50 kcal/mol, and the experimental value is 17.92 kcal/mol, this result giving us more confidence to predict further hydrolysis processes of natural products.
Conclusion A series of ab initio molecular orbital and density functional theory calculations have been performed to examine the reaction pathways and corresponding energy barriers of the alkaline hydrolysis of carboxylic esters. The most accurate model for predicting the energy barriers and rate constants is a combination of MPW1B95/6311??G(2df,2p)//B3LYP/6-31?G(d) for gas energies calculation and the CPCM// UA0 model at B3LYP/6-311?G(d,p) level for solvation energies. Calculations using this accurate method provide much new information about the hydrolysis of esters. First, reaction coordinate calculations indicate that, while most carboxylic esters react through the BAC2 route, some esters react with the BAl2 route. For hydrolysis of ethyl benzoate, the energy barrier of the BAl2 route is 5.76 kcal/mol above that of the BAC2 route. Significantly, using detailed energy analysis, we found that the
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Table 6 Energy barriers of hydrolysis of ethyl benzoates in different solvents Entry
Compound
a
Ethanol (kcal/mol)
Water (kcal/mol)
Acetone (kcal/mol)
22.64
22.40
22.40
23.86
23.66
23.69
24.11
23.94
23.88
26.20
25.97
26.03
20.42
20.53
20.09
20.79
20.94
20.46
22.81
22.75
22.56
22.37
22.34
22.09
COOEt b
H3C
COOEt
c
H3CO
COOEt
d
H2N
COOEt
O2N
COOEt
NC
COOEt
e
f
g
F
COOEt
Cl
COOEt
h
calculated energy barriers of alkaline hydrolysis of esters all agree well with the experimental results. Second, with the newly developed theoretical method in hand, we next investigated the structural effects of esters on the reactivity of their alkaline hydrolysis, and found that energy barriers decrease when the electron-withdrawing power of substituents of esters increase. Further, steric effects on the alkaline hydrolysis of esters were not found to be evident in this system. Also, energy barriers are not very sensitive to changes of solvents. Finally, we predict the energy barriers of cyhalofop-butyl hydrolysis in aquatic solution.
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