Comutational and Theoretical Chemistry 974 (2011

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Computational and Theoretical Chemistry 974 (2011) 133–142

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Analyzing the efficiency in intramolecular amide hydrolysis of Kirby’s N-alkylmaleamic acids – A computational approach Rafik Karaman ⇑ Faculty of Pharmacy, Al-Quds University, P.O. Box 20002, Jerusalem, Palestine

a r t i c l e

i n f o

Article history: Received 9 June 2011 Received in revised form 18 July 2011 Accepted 19 July 2011 Available online 10 August 2011 Keywords: Enzyme catalysis Intramolecular proton transfer DFT calculations Strain effects Maleamic acid amide derivatives Amide hydrolysis

a b s t r a c t A mechanistic study using DFT calculation methods at B3LYP/6-31G (d,p), B3LYP/311+G (d,p) levels and hybrid GGA (MPW1k) on an intramolecular acid catalyzed hydrolysis of maleamic (4-amino-4-oxo-2butenoic) acids (Kirby’s N-alkylmaleamic acids) 1–7 confirmed that the reaction proceeds in three steps: (1) proton transfer from the carboxylic group to the adjacent amino carbonyl carbon, (2) nucleophilic attack of the carboxylate anion onto the protonated carbonyl carbon; and (3) dissociation of the tetrahedral intermediate to provide products. Furthermore, the calculation results indicate that the rate-limiting step is dependent on the reaction medium. When the calculations were run in the gas phase the rate-limiting step was the nucleophilic attack of the carboxylate anion to form the tetrahedral intermediate, whereas when the calculations were conducted in the presence of a cluster of water the dissociation of the tetrahedral intermediate was the rate-limiting step. When the leaving group (CH3NH2) in 1–7 was replaced with a group having a low pKa value (such in 10) the rate-limiting step of the hydrolysis in water was the formation of the tetrahedral intermediate. In addition, the calculations demonstrate that the efficiency of the intramolecular acid-catalyzed hydrolysis by the carboxy group is remarkably sensitive to the pattern of substitution on the carbon–carbon double bond. The rate of hydrolysis was found to be linearly correlated with the strain energy of the tetrahedral intermediate or the product. Systems having strained tetrahedral intermediates or products experience low rates and vice versa. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction The extraordinary high efficiency of enzymes in catalysis of biochemical reactions depends on a combination of few factors that most of them have been recognized but none of them was fully understood. Despite the growing research being devoted to the chemistry of enzyme catalysis a number of incredibly important factors remain to be investigated. The high rates of intramolecular reactions are fascinating for chemists because they are reminiscent of the efficiency of enzyme catalysis and it is widely believed that a common source is, at least for a significant part, responsible both effects [1]. The similarity between intramolecularity and enzymes has stimulated a number of chemists and biochemists to design chemical models based on intramolecular reactions consisting of two reactive centers in order to understand the mode and the mechanism by which enzymes exert their high catalytic activities [1]. Over the past 50 years suggestions have been arose from attempts to interpret changes in reactivity versus structural variations in intramolecular systems. Among theses are: (1) Koshland ‘‘orbital steering’’ which proposes that rapid intramolecularity ⇑ Tel.: +972 2 2790413; fax: +972 2 2790413. E-mail address: [email protected] 2210-271X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.comptc.2011.07.025

arises from a severe angular dependence of organic reactions as in the case of the lactonization of hydroxy acids [2]; (2) ‘‘proximity’’ in intramolecular reactions (near attack conformation) model as proposed by Bruice and demonstrated in the lactonization of half-esters of di-carboxylic acids [3]; (3) ‘‘stereopopulation control’’ based on the concept of freezing a molecule into a productive rotamer as suggested by Cohen [4], and (4) Menger’s ‘‘spatiotemporal hypothesis’’ postulates that the rate of reaction between two reactive centers is proportional to the time that the two centers reside within a critical distance [5]. Studies on intramolecularity have played a fundamental role in elucidating the chemistry of the groups involved in enzyme catalysis as well as in unraveling the mechanisms available for particular processes. Thus, it is quite safe to assume that these studies have the capability to provide a sufficient understanding of how efficiency depends on structure in intramolecular catalysis which in turns could shed some light on related problems in enzyme catalysis [6,7]. Recently I have been engaged in studying the mechanistic pathways for a number of intramolecular processes that have been used as enzyme models as well as prodrug linkers [8]. Using DFT and ab initio molecular orbital methods at different levels, I have investigated: (a) acid-catalyzed lactonization of hydroxy-acids as


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R. Karaman / Computational and Theoretical Chemistry 974 (2011) 133–142

O H

H

Me

NHMe

NHMe

OH

H

OH

Me

O

O

O

Me

NHMe

NHMe

OH

OH

O

O

O

O

1

2

3

4

O

O NHMe OH

H

O NHMe OH

Et

H

O NHMe

O

O

5

6

7

OH

Pr

H

N N

N

O

OH

OH

H

O NH2

O N

O

O

O

10

9

CH3

8

O N

H

HO

Me

O

O

NHMe

OH

Pr

O H

H

Et

Scheme 1. Chemical structures for maleamic acid derivatives 1–10.

researched by Cohen [4,8b] and Menger [5,8a], (b) SN2-based-cyclization reactions of di-carboxylic semi-esters to yield anhydrides as studied by Bruice [3,8c], (c) intramolecular SN2-based ring-closing reactions as explored by Brown’s group [9,8f] and Mandolini’s group [10,8m], (d) proton transfer between two oxygens in Kirby’s acetals [7,8g–8l], and proton transfer between nitrogen and oxygen in Kirby’s enzyme models [7,8k], (e) proton transfer between two oxygens in rigid systems as investigated by Menger, [5,8e,8o] and (f) proton transfer from oxygen to carbon in some of Kirby’s enol ethers [11,8n]. The salient points emerged from these studies are: (1) the driving force for accelerations in rate of intramolecular processes are both entropy and enthalpy effects [8c]. This is contrarily to what was proposed by Bruice [3] that enthalpic effects are the only source for such accelerations. In the cases by which enthalpic effects were predominant such as in ring-closing reactions [9,10], steric effects was the driving force for the accelerations [8c,8f,8m], whereas in the cases of proton transfer reactions [7] proximity orientation (stabilization of the transition state by hydrogen bonding) was the dominant factor to affect the reaction rate [8e–8o]. This is in accordance with the findings by Kirby and coworkers [7]. (2) The type of the reaction being intermolecular or intramolecular is determined on the distance between the two reactive centers. In the situations by which the distance between the two reactive centers exceeds 3 Å an intermolecular reaction is preferred whereas, distances below this value permit an intramolecular engagement [8a]. This is in an agreement with the experimental results reported by Menger’s group [3]. (3) The efficiency of proton transfer between two oxygens [7] and between nitrogen and oxygen in Kirby’s acetal systems [7] is due to a strong hydrogen bonding developed in the products and the corresponding transition states leading to them [8a,8e–8o]. This result

confirms the conclusions emerged from experimental findings by Kirby’s group [7]. In this Letter, I report a computational study which revealed the mechanism and the factors affecting the reaction rate for intramolecular acid catalyzed hydrolysis of maleamic (4-amino4-oxo-2-butenoic) acids (Kirby’s N-alkylmaleamic acids) 1–7.

2. Calculations methods The DFT calculations at B3LYP/6-31G (d,p) and B3LYP/311+G (d,p) levels and the density functional from Truhlar group (hybrid GGA: MPW1k) [12] were carried out using the quantum chemical package Gaussian-98 [13]. The starting geometries of all the molecules presented in this study were obtained using the Argus Lab program [14] and were initially optimized in the presence of one molecule of water at the AM1 level of theory, followed by an optimization at the HF/6-31G level [13]. The calculations were carried out based on the restricted Hartree–Fock (RHF) method with full optimization of all geometrical variables. An energy minimum (a stable compound or a reactive intermediate) has no negative vibrational force constant. A transition state is a saddle point which has only one negative vibrational force constant [15]. The ‘‘reaction coordinate method’’ [16] was used to calculate the activation energy in systems 1–10. In this method, one bond length is constrained for the appropriate degree of freedom while all other variables are freely optimized. The activation energy values for the approach processes were calculated from the difference in energies of the global minimum structures (GM) and the derived transition states (TS2 in Scheme 2). Similarly, the activation energies of the dissociation processes were calculated from the


135


NHMe R1

O

PT

H O

R2

R1

O

R1

O

H

H H

R1 H N

H

Me

B

O

O

Neutral pH

R2

R2

O

R1

O

R1

O

O

O

INT3

TS3

B

H H

H-

R2 O

O

H

NHMe OH

H

N

O

R2

P

Me

Me

N

R1

O

O

TS2

INT1

TS1

O

R2

O

O

GM

O

O

R2

OH

R1

F

OH

H

O

R2

NHMe

NHMe

NHMe

N

ut Ne

H

ra

H lp

INT2

Me O

R1

H

O R2 H

OH R1 H

H N

R1

O NHMe OH

O Me

R2

O

H

TS5

OH

R1

B

O

Acidic pH

R2 O

NHMe

R2

O

O

INT4

TS4

Scheme 2. Proposed mechanistic pathway for the acid-catalyzed hydrolysis of 1–7. R1 and R2 are alkyl groups. PT, F and B refer to proton transfer, tetrahedral intermediate formation and tetrahedral intermediate breakdown, respectively. GM, INT, TS and P refer to global minimum, intermediates, transition states and products, respectively.

difference in energies of the global minimum structures (GM) and the corresponding transition states (TS4 in Scheme 2). Verification of the desired reactants and products was accomplished using the ‘‘intrinsic coordinate method’’ [16]. The transition state structures were verified by their only one negative frequency. Full optimization of the transition states was accomplished after removing any constrains imposed while executing the energy profile. The activation energies obtained from DFT at B3LYP/6-31G (d,p) level of theory for 1–10 were calculated with and without the inclusion of solvent (water and ether). The calculations with the incorporation of a solvent were performed using the integral equation formalism model of the Polarizable Continuum Model (PCM) [17]. In this model the cavity is created via a series of overlapping spheres. The radii type employed was the United Atom Topological Model on radii optimized for the PBE0/6-31G (d) level of theory. 3. Results and discussion Kirby and coworkers have studied the hydrolysis reactions of 1– 7 to the corresponding maleamic acids under acidic conditions. Their study revealed that the cleavage of the amide linkage is due to intramolecular nucleophilic catalysis by the adjacent

2 H rGM ε O3 O 1 rAP φ

8O

7 6

Me 9

N

4

α

R1

β

R2

Syn O

H

H

5

HN

Me

O

O

R1

Anti

R2

GM Chart 1. Representation of an acid-catalyzed hydrolysis in Kirby’s acid amides 1–7. GM is the global minimum structure. rGM and rAP are the hydrogen bond distance and the approach distance, respectively. a, b, e and h are bond angles.


136


Fig. 1a. DFT optimized structures for the global minimum (GM) in processes 1–8.

Fig. 1b. DFT optimized structures for the intermediates (INT2) in the processes 1–8.

carboxylic acid group. Based on the fact that the tetrahedral intermediate isomaleimide was converted quantitatively into N-methylmaleamic acid, they suggested that the rate-limiting step is the dissociation of the tetrahedral intermediate [18]. Later on, in 1990, Katagi has studied the reaction mechanism of the hydrolysis reaction using AM1 semiempirical method. Katagi has concluded that the rate-limiting step is the one by which the tetrahedral intermediate is formed [19]. Since Katagi’s calculations were conducted in the gas phase with only two molecules of water we sought to theoretically study this reaction using DFT methods, which are superior to semiempirical methods, and to run the calculations in the gas phase, in presence of one and two molecules of water and as well as in the presence of water as a solvent due to the importance of the solvent in stabilizing or destabilizing the entities involved in the hydrolysis reaction.

The objects of this work were to: (a) investigate whether the rate-limiting step in 1–7 is the formation or the dissociation of the tetrahedral intermediate, and to unravel the nature of the driving force(s) for the extraordinary high rates observed for the intramolecular acid catalyzed hydrolysis of 2 and 5, (b) identify those structural factors associated with high reactivity in intramolecular reactions, in the expectation that similar factor will be operative in enzyme catalysis and some important prodrugs systems also. Computational efforts were directed toward elucidation of the transition and ground state structures (global minimum, intermediates and products) for the acid catalyzed hydrolysis of 1–7 in the presence of one and two molecules of water, in presence of a water as a solvent (PCM model, see Supplementary data) and in the gas phase. It is expected that the stability of the ground states and their derived intermediates, transition states, and products will behave



137

Fig. 1c. DFT optimized structures for transition state TS4 structures in processes 1–8.

Fig. 2. (a) Energy profile for the acid catalyzed hydrolysis of 1 and 2 in the gas phase (GP) and water (H2O). (b) Energy profile for the acid catalyzed hydrolysis of 3 and 4 in the gas phase (GP) and water (H2O). (c) Energy profile for the acid catalyzed hydrolysis of 5 and 6 in the gas phase (GP) and water (H2O). (d) Energy profile for the acid catalyzed hydrolysis of 7 in the gas phase (GP) and water (H2O). GM, TS2, INT2, TS4 and P are global minimum, transition state 2, intermediate 2, transition state 4 and product structures, respectively (for chemical structures see Scheme 2).

differently in the gas phase (or solvent having low dielectric constant) and in water.

3.1. General consideration Because the energy of a carboxylic acid amide molecule is strongly dependent on its conformation and the latter determines its ability to be engaged in intramolecular hydrogen bonding, we were concerned with the identification of the most stable conformation (global minimum) for each of Kirby’s acid amides 1–7 calculated in this study. This was accomplished by 360° rotation of the carboxylic group about the bond C6AC7 (i.e. variation of the dihedral angle O1C7C6C5, Chart 1), and 360° rotation of the carbonyl amide group about the bond C4AC5 (i.e. variation of the dihedral angle O3C4C5C6) in increments of 10° and calculation of the conformational energies (see Chart 1).

In the DFT calculations for 1–7, two types of conformations in particular were considered: one in which the amide carbonyl is syn to the carboxyl group and another in which it is anti. It was found that the global minimum structures for 1–7 all reside in the syn conformation (see Fig. 1a). Using the quantum chemical package Gaussian-98 [13] I have calculated the DFT B3LYP/6-31G (d,p) kinetic and thermodynamic parameters for the proposed pathways for the reactions of 1–7 [18,19]. The proposed paths for the ring-closing reactions of 1–7 are illustrated in Scheme 2. The enthalpic and entropic energies in the gas phase and in the presence of a cluster of water for the global minimum structure (GM), the five different transition states, TS1, TS2, TS3, TS4 and TS5, the four different intermediates INT1, INT2, INT3 and INT4 and the products (P) for the pathways in 1–7 were calculated (Scheme 2). Table S1 (Supplementary data) summarizes the energy values for 1GM–7GM, 1INT2–7INT2, 1TS2–7TS2 and 1TS4–7TS4.


138


Table 1 DFT (B3LYP) calculated kinetic and thermodynamic properties for the acid catalyzed hydrolysis of 1–8. System

log krel 7

log EM17 (Exp)

log EM (Calc)

Es (INT2) (kcal/mol)

Es (P) (kcal/ mol)

Es (GM) (kcal/ mol)

DGzBEth (kcal/ mol)

DGzFEth (kcal/ mol)

DGzBGP (kcal/mol) In high pH

Exp DGà12 (kcal/mol)

1 2 3 4 5 6 7 8

0 4.371 1.494 -4.377 2.732 1.516 1.648 –

7.724 15.86 7.742 1.255 15.190 6.962 8.568 –

8.52 18.08 11.93 4.81 15.82 12.76 12.57 –

20.55 16.16 17.32 27.89 19.25 17.59 18.55 13.64

25.08 18.93 21.70 32.75 23.13 22.95 24.00 12.10

10.16 10.82 9.40 12.30 9.18 5.12 6.20 –

34.27 16.32 29.53 40.23 18.51 29.53 28.35 –

31.35 21.29 28.23 39.27 22.34 27.50 27.76 –

45.55 33.59 44.68 53.5 34.52 45.72 43.53 –

23.70 17.30 21.14 30.70 19.75 – – –

1

B3LYP refers to values calculated by B3LYP/6-31G (d, p) method. DGà is the calculated activation free energy (kcal/mol). Es refers to strain energy calculated by Allinger’s MM2 z z method [19]. INT2 and P refer to intermediate 2 and product, respectively. EM refers to effective molarity; EM ¼ eðDGinter DGintra Þ=RT . BEth and FEth refer to tetrahedral intermediate breakdown and tetrahedral intermediate formation calculated in ether, respectively. BGP refers to tetrahedral intermediate calculated in the gas phase. Exp Refers to experimental value. Calc refers to DFT calculated values. Krel refers to relative rate.

Table 2 DFT (B3LYP) calculated energy profiles for the acid catalyzed hydrolysis of 1–7. Entity

1 DGà/ GP

1 DGà/ H2O

2 DGà/ GP

2 DGà/ H2O

3 DGà/ GP

3 DGà/ H2O

4 DGà/ GP

4 DGà/ H2O

5 DGà/ GP

5 DGà/ H2O

6 DGà/ GP

6 DGà/ H2O

7 DGà/ GP

7 DGà/ H2O

GM TS2 INT2 TS4 P1

0 33.53 14.10 28.08 15.18

0 26.10 4.62 33.06 25.24

0 27.08 12.07 16.42 1.57

0 17.90 11.93 20.05 11.02

0 32.54 18.66 24.90 12.02

0 24.80 19.68 27.93 21.69

0 45.37 30.22 34.42 21.11

0 32.16 32.43 35.76 30.28

0 26.87 11.46 17.41 3.51

0 17.89 14.71 23.12 8.29

0 32.12 17.69 23.83 10.96

0 23.87 18.19 27.19 20.38

0 32.30 5.84 24.86 11.46

0 24.4 18.86 27.38 20.83

B3LYP refers to values calculated by B3LYP/6-31G (d, p) method. DGà is the calculated activation free energy (kcal/mol). GM, TS2, INT2, TS4 and P1 refer to global minimum, transition state 2, intermediate 2, transition state 4 and product 1, respectively. GP and H2O refer to calculated in the gas phase and water, respectively.

Fig. 3. A representation of an energy profile for acid-catalyzed hydrolysis of 2 as calculated in the gas phase (GP) and in water (W). GM. TS2, TS4, INT2 and P1 refer to global minimum, transition state 2, transition state 4, intermediate 2 and product structures, respectively. DGzFGP and DGzFW are the calculated activation free energy (kcal/mol) for the tetrahedral tetrahedral intermediate formation in the gas phase and water, respectively. DGzBGP and DGzBW are the calculated activation free energy (kcal/mol) for the tetrahedral tetrahedral intermediate breakdown in the gas phase and water, respectively.


139


(b) Calculated ΔG# vs Experimental ΔG#

(a) MM2 Es vs log krel 35 y = -1.5145x + 25.675

40

2

R = 0.9376

30

Calculated Δ G #

y = 1.3613x - 2.1015

MM2 Es

25

y = -1.3407x + 21.03

20

2

R = 0.9126 30

y = 1.5777x - 10.81 2

2

R = 0.8835

R = 0.9384

20 15

-6

-4

10

-2

0

2

4

10

6

10

15

20

25

30

35

Experimental ΔG#

log krel

(c) ΔGF# vs ΔGB#

(d) Calculated log EM vs Experimental log EM

50

20

y = 0.8768x + 11.224 2

R = 0.946

16

Calculated log EM

ΔG F#

40

30

8

y = 0.8094x + 4.7508 2

R = 0.8617

y = 0.7981x + 1.3463

20

2

R = 0.938

10

12

15

20

25

30

35

4

40

ΔGB#

0

0

4

8

12

16

20

Experimental log EM

Fig. 4. (a) Plot of MM2 Es vs. log krel in 1–7, where the blue points for the Es values of the intermediates and the pink points for that of the products. krel is the relative rate. (b) Plot of the DFT calculated DGà vs. the DFT experimental DGà in 1–7, where the blue points for the values calculated in the gas phase and the pink points for that calculated in the presence of water. (c) Plot of the DFT calculated DGzF vs. the DFT calculated DGzB in 1–7, where the blue points for the values calculated in the gas phase and the pink points for that calculated in the presence of water. DGzF is the activation energy for the tetrahedral intermediate formation and DGzB is the activation energy for the tetrahedral intermediate collapse.(d) Plot of the calculated log EM vs. the experimental log EM in 1–7. EM is the effective molarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Figs. 1a–1c illustrate the gas phase DFT optimized calculated structures for GM 1H2O, INT2 1H2O and TS4 1H2O in 1–7. It is worthy to note, that the geometries of the entities involved in the hydrolysis reaction (GM, INT, TS and P) were slightly affected by the presence of 1H2O molecule. In fact, the calculated bond

distances and bond angles in the gas phase and in presence of one molecule of water were found to differ in less than 0.05 Å and 1°, respectively whereas the difference in the energies did not exceed 2 kcal/mol. For example, the H2AO3 distance for 2GM in the gas phase was 1.53 Å whereas that with a molecule of water


140


was 1.57 Å. The calculated values for angles a and b for 2GM in the gas phase were 127.8° and 124.8° whereas that calculated in the presence of a water molecule were 128.1° and 124.7°, respectively. Using the calculated enthalpies and entropies for the GM and the different transition states in 1–7, I have calculated the enthalpic activation energies (DHà), entropic activation energies (TDSà), and the free activation energies in the gas phase and in water (DGà) for the different paths (Scheme 2). The calculated values are summarized in Tables S2 and illustrated graphically in Fig. 2. Careful examination of the calculated DFT energy values in the gas phase listed in Table S2 (Supplementary data) and illustrated in Fig. 2 indicates that the rate-limiting step for the acid-catalyzed hydrolysis of 1–7 is the step by which the carboxyl group approaches the amide carbonyl carbon (formation of the tetrahedral intermediate, step F in Scheme 2). The free activation energy range for the proton transfer process (step PT in Scheme 2), tetrahedral intermediate formation (F) and tetrahedral intermediate breakdown (step B in Scheme 2) are 17.77–19.33 kcal/mol, 26.87– 45.37 kcal/mol and 16.42–36.77 kcal/mol, respectively. Further, the free activation energy for the rate-limiting step (F) is about 6–9 kcal higher than that for the breakdown process and about 6–22 kcal/mol above that of the proton transfer step. In contrast, the DFT energy calculations in the presence of water as a solvent, dielectric constant of 78.39 (Table S2) confirmed that the rate-limiting step in the acid-catalyzed hydrolysis of 1–7 is the step by which the tetrahedral intermediate is collapsed (breakdown, step B in Scheme 2). The difference in the activation energies of the two steps, the intermediate collapse and intermediate formation, is about 3–7 kcal/mol. In addition, when the calculations were run in the presence of ether the rate-limiting step in processes 2 and 5 was the formation of the tetrahedral intermediate whereas for the other processes the dissociation of the tetrahedral intermediate was the rate-determining step (Table 1). For examining the effect of water on the activation energies (barriers) for the tetrahedral intermediate approach and dissociation processes, DFT calculations of the entities involved in process 2 were done in the gas phase and in the presence of one and two water molecules. The calculation results shown in Table 2 indicate clearly that the difference between the activation energy for the approach and the collapse of the tetrahedral intermediate is not largely affected by the presence or the absence of a molecule of water. The combined results depicted in Table S2 and Fig. 2 suggest that water has a profound effect on the stabilization of the tetrahedral intermediate (INT2) formed along the reaction pathway which consequently results in increasing the energy barrier needed for the collapse of the tetrahedral intermediate. It is worthy to note that Katagi in his semiempirical study has concluded that the rate-limiting step in this kind of reactions is the formation of the tetrahedral intermediate. The discrepancy between our DFT and Katagi’s AM1 results is attributed to the fact that Katagi has included two molecule of water in his calculations but without considering the effect of water as a solvent. In fact, our results in the presence of one and two molecules of water and in the gas phase (absence of water) are in accordance with the results obtained by

Katagi’s AM1 calculations [19]. Furthermore, the calculations in the presence of ether (dielectric constant 4.5) indicate that 2 and 5 are the most solvent sensitive processes among 1–7. This might be due to the small difference in the barriers for the tetrahedral intermediate formation and breakdown (Tables 1 and S2). In order to investigate the role of the leaving group (CH3NH2) on the mode and the nature of the mechanism, calculations for the hydrolysis of maleamic acid amides having a leaving group with a higher pKa (process 9, prodrug of the antihypertensive atenolol) and lower pKa (process 10, prodrug of sildenafil for the treatment of erectile dysfunction) were done. The results revealed that the rate-limiting step in 9 is similar to that in 1–7 (DGzB ¼ 39:12 kcal vs. (DGzF ¼ 35:72 kcal=mol) whereas that in 10 is the formation of the tetrahedral intermediate ((DGzB ¼ 13:55 kcal vs. (DGzF ¼ 40:74 kcal=mol), where DGzB and DGzF are the activation energy for the tetrahedral intermediate breakdown and formation, respectively. The discrepancy in the mechanisms between the two processes might be related to a lower nucleophilicity of the leaving group in 10 compared to that in 9. A representation of the energy profiles for process 2 as calculated in the gas phase and in the presence of water as a solvent is illustrated in Fig. 3. On the other hand, the DFT calculation results in the gas phase and in water revealed that the rate-limiting step for the hydrolysis of 1–7 in a neutral pH (non-acidic conditions) is the breakdown of the tetrahedral intermediate (B in neutral pH in Scheme 2 and Table 1). This result is in a good agreement with Kirby’s experimental findings which indicate that 1–7 undergo a fast hydrolysis when they were exposed to acidic pH (acidic) while their rates at a higher pH’s were very slow [18]. It should be noted that the route by which TS5 is formed is about 1.40 kcal/mol more stable than that by which TS3 is afforded. In order to shed some light on the factors responsible for the unusual accelerations in rate of the acid-catalyzed hydrolysis of 2 and 5, and to examine whether the discrepancy in rates for processes 1–7 stems from steric effects (strain energy) or other effects I have calculated, using Allinger’s MM2 method [20], the strain energy values for the reactants (GM), intermediates (INT) and products (P) in 1–7. The MM2 strain energies (Es) for these entities are listed in Table 1. The MM2 calculated Es values were examined for correlation with the experimental relative rate values, log krel (Table 1). Strong correlations were obtained with a correlation coefficient R2 = 0.88 for the correlation with the intermediates values and R2 = 0.94 for that of the products (Fig. 4a). On the other hand, attempt to correlate the Es values for the GM structures with the experimental log krel resulted in a random correlation with R2 = 0.14. The results shown in Fig. 4a indicate that the rate of the reaction for systems having less-strained intermediates or products such as 2 and 5 are higher than that having more strained intermediates or products such as 1 and 4. This might be attributed to the fact that the transition state structures in 1–7 resemble that of the corresponding intermediates or products (Figs. 1b and 1c). In order to draw credibility to the DFT calculations the calculated DFT free activation energies in the gas phase ðDGzBGP Þ and in water ðDGzBW Þ were correlated with the corresponding experimen-

Table 3 Comparison between calculated energies for 1–3 using B3LYP/6-31G (d,p), MPW1 K and B3LYP/6-311+G (d,p) methods. System

B3L DHà/F

B3L DGà/F

MPW1 Hà/F

MPW1 DGà/F

B3311 DHà/F

B3311 DGà/F

B3L DHà/ B

B3L DGà/ B

MPW1 DHà/B

MPW1 DGà/B

B3311 DHà/B

B3311 DGà/B

1 2 3

32.46 25.67 30.68

33.53 27.08 32.57

29.78 26.85 28.03

29.67 27.78 29.21

31.32 23.68 28.98

33.20 24.04 32.77

27.31 13.93 24.41

28.08 16.42 24.9

25.07 16.94 22.61

25.79 19.01 23.40

27.42 15.00 23.85

29.16 16.31 26.44

B3L, MPW1 and B3311 refer to B3LYP/6-31G (d,p), MPW1 and B3LYP/6-311+G (d,p) methods, respectively. DHà and DGà is the calculated enthalpic and activation free energy (kcal/mol), respectively. B and F refer to breakdown and formation, respectively (see Scheme 2). All values were calculated with a molecule of water in the gas phase.



tal free activation energies (Exp DGà) [18]. Strong correlations were found with R2 value of 0.94 for the correlation with the calculated values in the gas phase and an R2 = 0.91 for those calculated in the presence of a cluster of water (Fig. 4b). For testing whether the factors affecting the barrier magnitude for the formation of the tetrahedral intermediate (step F in Scheme 2) are the same as that influence the collapse process barrier (B in Scheme 2), the calculated activation energies in the gas phase and in water for the formation of the tetrahedral intermediate ðDGzF Þ were correlated with the energies needed for its collapse ðDGzB Þ. Fig. 4c illustrates the correlation between the two parameters where the correlation coefficients (R2) for both the calculated values in the gas phase and in the presence of water were 0.95. This result indicates that the driving force for the formation and collapse of the tetrahedral intermediate is the same and the rate of the hydrolysis reaction is dependent on the intermediate strain energy. High rates were achieved when the tetrahedral intermediate is relatively unstrained while the rates in systems having strained intermediates were found to be decreased. In order to confirm that the DFT calculations at B3LYP/6-31G (d,p) are not dependent on the specific theoretical method used processes 1–3 were calculated at B3LYP/311+G (d,p) level and with hybrid GGA (MPW1 k) functional as well. The comparisons between the activation energy values calculated by the three methods are listed in Table 3. Linear correlations were found between the values calculated with a strong correlation coefficient (R2 about 0.98). The effective molarity (EM) parameter is commonly used for predicting the efficiency of intramolecular reactions when bringing two functional groups in a close proximity. Intramolecularity is usually measured by the effective molarity parameter. EM is defined as the rate ratio (kintra/kinter) for corresponding intramolecular and intermolecular processes driven by identical mechanisms. Ring size, solvent and reaction type are the main factors affecting the EM value. Cyclization reactions via intramolecular nucleophilic addition are much more efficient than intramolecular proton transfer reactions. EM values in the order of 109–1013 M were measured for intramolecular processes occurring through nucleophilic addition. Whereas for proton transfer processes values of less than 10 M were obtained except for those reactions involve strong hydrogen bonding in their transition states [6]. The intermolecular process 8 (Scheme 1) was calculated to be utilized in the calculation of the effective molarities (EM) for the corresponding intramolecular processes 1–7. Using Eqs. (1)–(4), we derived Eq. (5) which describes the EM parameter as a function of the difference in the activation energies of the intra- and the corresponding intermolecular processes. The values calculated using equation 5 for processes 1–7 are shown in Table 1.

EM ¼ kintra =kinter

ð1Þ

DGzinter ¼ RT ln kinter

ð2Þ

DGzintra ¼ RT ln kintra

ð3Þ

DGzintra DGzinter ¼ RT ln kintra =kinter

ð4Þ

ln EM ¼ ðDGzintra DGzinter Þ=RT

ð5Þ

where T is the temperature in Kelvin and R is the gas constant. The calculated log EM values for 1–7 were examined for correlation with the log EM experimental values [18]. The correlation results along with the correlation coefficients are illustrated in Fig. 4d. Inspection of the log EM values listed in Table 1 and Fig. 4d revealed that 2 and 5 were the most efficient processes

141

among 1–7, whereas process 4 was the least. The discrepancy in rates between 2 and 5 on one hand and 4 on the other hand is attributed to strain effects. Although the calculated and experimental EM values are comparable there is a discrepancy in their absolute values. This is due to the fact that the experimental measurement of the EM values in 1–7 was conducted in the presence of aqueous acid whereas the DFT calculations were done in plain water. The dielectric constant value for a mixture of acid/water is expected to be different from that of water (78.39) and hence the discrepancy in the calculated and experimental EM values [21]. 4. Summary and conclusions In summary, the DFT calculation results confirmed that the mechanism of an intramolecular acid-catalyzed hydrolysis of Kirby’s acid amides 1–7 involves three steps: (1) proton transfer from the carboxylic group to the adjacent amino carbonyl carbon, (2) nucleophilic attack of the carboxylate anion thus formed onto the protonated carbonyl carbon; and (3) dissociation of the tetrahedral intermediate to furnish products. In addition, the calculations demonstrate that the nature of the mechanism dependent on the reaction solvent (medium). In aqueous medium the reaction rate-limiting step is the collapse of the tetrahedral intermediate whereas in the gas phase the tetrahedral intermediate formation is the rate-limiting step. Furthermore, the calculations establish that the acid-catalyzed hydrolysis efficiency is largely sensitive to the pattern of substitution on the carbon–carbon double bond. The rate of hydrolysis was found to be linearly correlated with the strain energy of the tetrahedral intermediate or the product. Systems having strained tetrahedral intermediates or products experience low rates and vice versa. Further, a linear correlation between the calculated DFT EM values and the experimental EM values demonstrates the credibility of using DFT methods in predicting energies as well as rates for reactions of the type described herein. Acknowledgments The Karaman Co. and the German-Palestinian-Israeli fund agency are thanked for support of our computational facilities. Special thanks are given to Angi Karaman, Donia Karaman, Rowan Karaman and Nardene Karaman for technical assistance. Appendix A. Supplementary material B3LYP/6-31G (d,p) and B3LYP/311+G (d,p) xyz Cartesian coordinates and absolute energies for the global minimum (GM), intermediate (TS2) and transition state (TS4) structures for processes 1–8. Table S1: DFT calculated properties for the acid-catalyzed hydrolysis of 1–7. Table S2: DFT (B3LYP) calculated kinetic and thermodynamic properties in the gas phase for the acid catalyzed hydrolysis of 1–8. Supplementary data associated with this article can be found, in the online version, at doi:10.1016/ j.comptc.2011.07.025. References [1] (a) K.R. Hanson, E.A. Havir, in: P.D. Boyer (Ed.), The Enzymes, third ed., vol. 7, Academic Press, New York, 1972, p. 75; (b) V.R. Williams, J.M. Hiroms, Biochem. Biophys. Acta 139 (1967) 214; (c) C.B. Klee, K.L. Kirk, L.A. Cohen, P. McPhie, J. Biol. Chem. 250 (1975) 5033; (d) K.R. Hanson, E.A. Havir, Biochemistry 7 (1968) 1904; (e) For a review in this topic, see A.W. Czarink, in: J.F. Liebman, A. Greenberg (Eds.), Mechanistic Principles of Enzyme Activity, VCH Publishers, New York, NY, 1988.; (f) T.C. Bruice, S.J. Benkovic, Bioorganic Mechanisms, vols. I and II, Benjamin, Reading, MA, 1966.;


142

[2]

[3]

[4]

[5]

[6] [7]

R. Karaman / Computational and Theoretical Chemistry 974 (2011) 133–142 (g) W.P. Jencks, Catalysis in Chemistry and Enzymology, McGraw, New York, 1969; (h) M.L. Bender, Mechanism of Homogeneous Catalysis from Protons to Proteins, Wiley Interscience, New York, 1971; (i) D.L. Nelson, M.M. Cox, Lehninger Principles of Biochemistry, Worth Publishers, New York, 2003; (j) A. Fersht, Structure and Mechanism in Protein Science: A guide to Enzyme Catalysis and Protein Folding, W.H. Freeman and Company, New York, 1999; (k) R. Pascal, Eur. J. Org. Chem (2003) 1813; (l) R. Pascal, Bioorg. Chem. 31 (2003) 485; (m) G.F. Sweigers, Mechanical Catalysis, John Wiley & Sons, Hoboken, NJ, 2008; (n) C. Walsh, Enzymatic Reaction Mechanism, San Francisco, Freeman, 1979; R.B. Silverman, The Organic Chemistry of Enzyme-Catalyzed Reactions, San Diego, Academic, 2002; (o) D.A. Kraut, K.S. Carroll, D. Herschlag, Annu. Rev. Biochem. 72 (2003) 517; (p) A. Radzicka, R. Wolfenden, J. Am. Chem. Soc. 118 (1996) 6105; (q) M.J. Snider, R. Wolfenden, J. Am. Chem. Soc. 122 (2000) 11507; (r) A.T. Kallarakal, B. Mitra, J.W. Kozarich, J.A. Gerlt, J.G. Clifton, G.A. Petsko, G. Kenyon, Biochemistry 34 (1995) 2788; (s) Z.R. Wu, S. Ebrahimian, M.E. Zawrotny, L.D. Thornburg, G.C. Perez-Alvarado, P. Brothers, R.M. Pollack, M.F. Summers, Science 276 (1997) 415; (t) M. Karplus, J.D. Evanseck, D. Joseph, P.A. Bash, M.J. Field, Faraday Discuss. 93 (1992) 239. (a) A. Dafforn, D.E. Koshland Jr., Proc. Natl. Acad. Sci. USA 68 (1971) 2463; (b) A. Dafforn, D.E. Koshland Jr., Bioorg. Chem. 1 (1971) 129; (c) A. Dafforn, D.E. Koshland Jr., Biochem. Biophys. Res. Commun. 52 (1973) 779; (d) D.R. Storm, D.E. Koshland Jr., Proc. Natl. Acad. Sci. USA 66 (1970) 445; (e) D.R. Storm, D.E. Koshland Jr., J. Am. Chem. Soc. 94 (1972) 5805; (f) D.R. Storm, D.E. Koshland Jr., J. Am. Chem. Soc. 94 (1972) 5815. (a) T.C. Bruice, F.L. Lightstone, Acc. Chem. Res. 32 (1999) 127; (b) F.L. Lightstone, T.C. Bruice, J. Am. Chem. Soc. 119 (1997) 9103; (c) F.L. Lightstone, T.C. Bruice, J. Am. Chem. Soc. 118 (1996) 2595; (d) F.L. Lightstone, T.C. Bruice, J. Am. Chem. Soc. 116 (1994) 10789; (e) T.C. Bruice, W.C. Bradbury, J. Am. Chem. Soc. 90 (1968) 3803; (f) T.C. Bruice, W.C. Bradbury, J. Am. Chem. Soc. 87 (1965) 4846; (g) T.C. Bruice, U.K. Pandit, J. Am. Chem. Soc. 82 (1960) 5858; (h) T.C. Bruice, U.K. Pandit, Proc. Natl. Acad. Sci. USA 46 (1960) 402. (a) S. Milstein, L.A. Cohen, J. Am.Chem. Soc. 92 (1970) 4377; (b) S. Milstein, L.A. Cohen, Proc. Natl. Acad. Sci. USA 67 (1970) 1143; (c) S. Milstein, L.A. Cohen, J. Am. Chem. Soc. 94 (1972) 9158; (d) R.T. Borchardt, L.A. Cohen, J. Am. Chem. Soc. 94 (1972) 9166; (e) R.T. Borchardt, L.A. Cohen, J. Am. Chem. Soc. 94 (1972) 9175; (f) R.T. Borchardt, L.A. Cohen, J. Am. Chem. Soc. 95 (1973) 8308; (g) R.T. Borchardt, L.A. Cohen, J. Am. Chem. Soc. 94 (1972) 8313; (h) M.M. King, L.A. Cohen, J. Am. Chem. Soc. 105 (1983) 2752; (i) P.S. Hillery, L.A. Cohen, J. Org. Chem. 48 (1983) 3465. (a) F.M. Menger, M. Ladika, J. Org. Chem. 35 (1990) 3006; (b) F.M. Menger, M. Ladika, J. Am Chem. Soc. 110 (1988) 6794; (c) F.M. Menger, Acc. Chem. Res. 18 (1985) 128; (d) F.M. Menger, J.F. Chow, H. Kaiserman, P.C. Vasquez, J. Am. Chem. Soc. 105 (1983) 4996; (e) F.M. Menger, Tetrahedron 39 (1983) 1013; (f) F.M. Menger, J. Grosssman, D.C. Liotta, J. Org.Chem. 48 (1983) 905; (g) F.M. Menger, A.L. Galloway, D.G. Musaev, Chem. Commun. (2003) 2370; (h) F.M. Menger, Pure Appl. Chem. 77 (2005) 1873. and references therein. A.J. Kirby, Adv. Phys. Org. Chem. 17 (1980) 183. and references therein. (a) A.J. Kirby, Acc. Chem. Res. 30 (1997) 290; (b) A.J. Kirby, A. Parkinson, J. Chem. Soc., Chem. Commun. (1994) 707;

[8]

[9] [10] [11] [12]

[13] [14]

[15] [16] [17]

[18]

[19] [20] [21]

(c) C.J. Brown, A.J. Kirby, J. Chem. Soc., Perkin Trans. 2 (1997) 1081; (d) G.-A. Craze, A.J. Kirby, J. Chem. Soc., Perkin Trans. 2 (1978) 354; (e) G.-A. Craze, A.J. Kirby, R. Osborne, J. Chem. Soc., Perkin Trans. 2 (1978) 357; (f) G.-A. Craze, A.J. Kirby, J. Chem. Soc., Perkin Trans. 2 (1974) 61; (g) S.E. Barber, K.E.S. Dean, A.J. Kirby, Can. J. Chem. (1999) 792; (h) A.J. Kirby, M.F. de Silva, D. Lima, C.D. Roussev, F. Nome, J. Am. Chem. Soc. 128 (2006) 16944; (i) N. Asaad, J.E. Davies, D.R.W. Hodgson, A.J. Kirby, J. Phys. Org. Chem. 18 (2005) 101; (j) A.J. Kirby, M.F. Lima, D. de Silva, C.D. Roussev, F. Nome, J. Am. Chem. Soc. 128 (2006) 16944; (k) E. Hartwell, D.R.W. Hodgson, A.J. Kirby, J. Am. Chem. Soc. 122 (2000) 9326. (a) R. Karaman, Tetrahedron Lett. 49 (2008) 5998; (b) R. Karaman, Bioorg. Chem. 37 (2009) 11; (c) R. Karaman, Tetrahedron Lett. 50 (2009) 452; (d) R. Karaman, Bioorg. Chem. 37 (2009) 106; (e) R. Karaman, J. Mol. Struct. (Theochem) 910 (2009) 27; (f) R. Karaman, Tetrahedron Lett. 50 (2009) 6083; (g) R. Karaman, Tetrahedron Lett. 50 (2009) 7304; (h) R. Karaman, J. Mol. Struct. (Theochem) 940 (2010) 70; (i) R. Karaman, J. Mol. Struct. (Theochem) 939 (2010) 69; (j) R. Karaman, Tetrahedron Lett. 51 (2010) 2130; (k) R. Karaman, H. Hallak, Chem. Biol. Drug Des. 76 (2010) 35; (l) R. Karaman, Tetrahedron Lett. 51 (2010) 5185; (m) R. Karaman, S. Alfalah, Int. Rev. Biophys. Chem. 1 (2010) 14; (n) R. Karaman, Tetrahedron Lett. 52 (2011) 699; (o) R. Karaman, Comput. Theor. Chem. 963 (2011) 427. R.F. Brown, N.M. Van Gulick, J. Org. Chem. 21 (1956) 1046. C. Galli, L. Mandolini, Eur. J. Org. Chem. (2000) 3117. (a) A.J. Kirby, N.H. Williams, J. Chem. Soc., Perkin Trans. 2 (1994) 643; (b) A.J. Kirby, N.H. Williams, J. Chem. Soc., Chem. Commun. (1991) 1643. (a) Y. Zhao, D.G. Truhlar, Acc. Chem. Res. 41 (2008) 157; (b) Y. Zhao, D.G. Truhlar, J. Chem. Theory Comput. 4 (2008) 1849; (c) J. Zheng, Y. Zhao, D.G. Truhlar, J. Chem. Theory Comput. 5 (2009) 808. Gaussian 98, Revision A.7, Gaussian, Inc., Pittsburgh, PA, 1998. (a) C.J. Casewit, K.S. Colwell, A.K. Rappe’, J. Am. Chem. Soc. 114 (1992) 10024; (b) C.J. Casewit, K.S. Colwell, A.K. Rappe’, J. Am. Chem. Soc. 114 (1992) 10035; (c) C.J. Casewit, K.S. Colwell, A.K. Rappe’, J. Am. Chem. Soc. 114 (1992) 10046; (d) A.K. Rappe’, W.A. Goddard, J. Phys. Chem. 95 (1991) 3358; (e) A.K. Rappe’, K.S. Colwell, C.J. Casewit, Inorg. Chem. 32 (1993) 3438. J.N. Murrell, K.J. Laidler, Trans Faraday Soc. 64 (1968) 371. (a) K. Muller, Angew. Chem. Int. Ed. Engl. 19 (1980) 1; (b) M.J.S. Dewar, S. Kirschner, J. Am. Chem. Soc. 93 (1971) 4290. (a) M.T. Cancès, B. Mennucci, J. Tomasi, J. Chem. Phys. 107 (1997) 3032; (b) B. Mennucci, J. Tomasi, J. Chem. Phys. 106 (1997) 5151; (c) B. Mennucci, M.T. Cancès, J. Tomasi, J. Phys. Chem. B 101 (1997) 10506; (d) J. Tomasi, B. Mennucci, M.T. Cancès, J. Mol. Struct. (Theochem) 464 (1997) 211. (a) A.J. Kirby, P.W. Lancaster, J. Chem. Soc. Perkin Trans. II (1972) 1206; (b) M.F. Aldersley, A.J. Kirby, P.W. Lancaster, R.S. McDonald, C.R. Smith, J. Chem. Soc. Perkin Trans. II (1974) 1487; (c) A.J. Kirby, R.S. McDonald, C.R. Smith, J. Chem. Soc. Perkin Trans. II (1974) 1495. T. Katagi, J. Comput. Chem. 11 (1990) 1094. U. Burker, N.L. Allinger, Molecular Mechanics, American Chemical Society, Washington, DC, 1982. It should be noted that DFT calculations in the presence of a mixture of acid and water are not feasible.