Mechanism of Acid-Catalyzed Hydrolysis of Formamide from Cluster

Nov 17, 2010 - Jing Wang , Jiande Gu , Minh Tho Nguyen , Greg Springsteen , and Jerzy Leszczynski. The Journal of Physical Chemistry B 2013 117 (32), ...
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J. Phys. Chem. A 2010, 114, 12918–12927

Mechanism of Acid-Catalyzed Hydrolysis of Formamide from Cluster-Continuum Model Calculations: Concerted versus Stepwise Pathway Binju Wang and Zexing Cao* Department of Chemistry and State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen UniVersity, Xiamen 360015, China ReceiVed: July 15, 2010; ReVised Manuscript ReceiVed: October 14, 2010

The acid-catalyzed hydrolysis of formamide in aqueous solutions was investigated by ab initio calculations. Solvent effects on the hydrolysis reaction were reasonably considered by the cluster-continuum model with explicit water molecules in the first solvation shell, and the selection of hydration cluster plays an important role in reliable estimation of thermodynamic values for the hydrolysis reaction. Possible concerted and stepwise mechanisms of the O-protonated and N-protonated pathways were investigated by extensive calculations. On the basis of unbiased theoretical treatments on all plausible pathways, the O-protonated stepwise pathway was shown to be the favored mechanism, and the predicted activation free energies for the rate-determining step and the breaking of the C-N bond are 21.8 and 9.4 kcal/mol by B3LYP, respectively. The present results show good agreement with experiment and provide a complete description of the acid-catalyzed hydrolysis of formamide. Introduction

SCHEME 1: Acid-Assisted Hydrolysis of Formamide

Amide hydrolysis is an important class of reactions and has received considerable attention due to its relevance to various biochemicalprocesses,bothexperimentally1-3 andtheoretically.4-29 The hydrolysis of formamide can be viewed as a primary model for studying the cleavage of peptide bonds, and extensive theoretical calculations have been devoted to exploration of its possible mechanisms, including the acid-catalyzed4-11 and base-catalyzed4,12-20 pathways. In the acid-catalyzed hydrolysis of formamide, there are two possibilities for the protonation of amides as the initial step of the hydrolysis reaction, namely, O-protonation and N-protonation. Generally, the amide hydrolysis reaction may proceed by either an O-protonated or a N-protonated pathway. For normal amides, the carbonyl oxygen is the strongest donor of a lone pair, and the O-protonated formamide is more stable than the N-protonated species by 14 kcal/mol.4 Accordingly, the amide hydrolysis will basically follow an O-protonated pathway. Experimental studies on the mechanism of acid-catalyzed hydrolysis of amides proposed that the overall reaction is composed of four steps as shown in Scheme 1.30-32 Step i is the protonation of amide at the carbonyl oxygen, and this step was assumed to be a rapid and pre-equilibrium process. Step ii is an attack of an adjacent water molecule with the concerted proton abstraction by the second water, yielding a tetrahedral intermediate and H3O+, and this step is believed to be the ratedetermining step. Step iii is the protonation of the intermediate at the nitrogen atom by the excess proton from the outer water phase or the newly generated proton in reaction step ii. Step iv is the C-N bond breaking, accompanied by deprotonation of one hydroxyl group. The acid-catalyzed hydrolysis of amides has been experimentally well established,1,2,30-32 whereas the detailed mechanisms at the atomic scale level are farraginous and ill-defined theoretically.4-7 For the acid-catalyzed hydrolysis of amide, early * Corresponding author. Fax:+ 86-592-2183047. E-mail: zxcao@ xmu.edu.cn.

calculations generally lead to a concerted mechanism, consisting of the nucleophilic attack of one water on the carbonyl carbon with the concerted proton transfer to the nitrogen assisted by the second water, as described in Scheme 2 (the O-protonated concerted pathway). Although the previously predicted activation energies listed in Table 1 for such a reaction pathway are comparable with the experimental value of 22.8 kcal/mol,33 the detailed mechanism is clearly inconsistent with the stepwise mechanism proposed by experimental studies.1,2,30-32 Recent constrained molecular dynamics simulations by Zahn9 lend support to the experimental results. More recently, the baseand acid-catalyzed hydrolyses of amides were investigated by MP2 calculations.10 Although only one or two water molecules were explicitly considered in their computational modes, good agreement between theory and experiment was obtained. Despite the fact that the O-protonation is more favorable thermodynamically, the N-protonation pathway cannot be excluded completely. In an acid-catalyzed isomerization of tertiary amides, RCONR1R2, the N-protonation plays a crucial role as shown in Scheme 3.34-36 On the other hand, if the resonance among valence bond structures in amide is significantly impaired, such as in the β-lactam, the amide nitrogen may become more basic than the carbonyl oxygen, and thus,

10.1021/jp106560s  2010 American Chemical Society Published on Web 11/17/2010

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SCHEME 2

TABLE 1: Predicted Activation Barriers (kcal/mol) for the O-Protonated Concerted Mechanism of the Acid-Catalyzed Hydrolysis of Formamide in the Literature theory

activation barrier

ref

state

MP2/6-31G**//4-31G MP3/6-31G**//3-21G B3LYP/6-311++G** MP2// B3LYP/6-311++G**

∆Eq ) 24.0 ∆Gq ) 19.1 ∆Eq ) 24.5 ∆Eq ) 21.8 ∆Gq ) 29.1 ∆Eq ) 14.3

4 5 7 7 7 7

gas gas gas gas gas solution

SCHEME 3

the N-protonated pathway will be involved in the acid-catalyzed hydrolysis of amides.3 The specific-acid-catalyzed reaction is quite widespread and extremely important in organic chemistry, and it was extensively studied experimentally.3,30,36-41 In previous theoretical studies, except for a few ab initio molecular dynamics simulations, the hydronium ion (H3O+) was widely used to model the proton in solution.4,10,21,22 Presumably, the proton will be involved in a complex hydrogen bond network in the condensed phase, and such a simple model is unlikely to predict reasonable relative energies for related acid-catalyzed reactions, although the use of the dielectric continuum model may improve the description of the solvent effect to a certain extent. Theoretical calculations on the hydration free energy of the proton show that the first hydration shell of the proton requires at least four water molecules,42,43 and the predicted hydration free energy is about -263 kcal/mol, showing good agreement with the experimental results of 262.4 kcal/mol44 and 264.1 kcal/mol.45 This suggests that the proton in solution basically exists as the H9O4+ complex. The H3O+ model coupled with the dielectric continuum solvent

will underestimate the hydration free energy of the proton by about 16 kcal/mol. Such a large deviation may influence the description of thermodynamic and dynamic properties of the chemical reactions. Clearly, the suitable hydrated cluster models for the proton and reactive species in solution are very important for the reaction energetics and the proton-transfer mechanism. In the present work, we have performed extensive ab initio calculations on the acid-catalyzed hydrolysis of formamide, and various hybrid cluster-continuum models and mechanisms were evaluated and reexamined. A full picture of the acid-catalyzed C-N bond cleavage of formamide was presented. The detailed comparison of different reaction pathways, including the concerted and stepwise mechanisms for the O-protonated and N-protonated pathways, was made on the basis of our calculations. Computational Details Cluster-Continuum Model. The dielectric continuum model has been widely used to study chemical reactions in solution. However, due to the complete loss of the solvent structure, this model cannot account for the important solute-solvent interaction in the first solvation shell, and these interactions are especially important in the protic solvents or when a strong hydrogen bond network exists.20 To overcome this problem, we adopted the cluster-continuum model proposed by Pliego and Riveros,46 where the central compound is solvated explicitly by some solvent molecules and the resulting cluster is treated by a dielectric continuum model. The explicit solvent molecules can cover the most important solute-solvent interactions in the first solvation shell, while the continuum part accounts for longrange electrostatic interactions by the bulk solvent. This hybrid cluster-continuum model was verified to be practicable for the determination of the solvation free energy47 and pKa for some organic cations.48 Here the conductor-like polarizable continuum model (CPCM)49 with a UAKS cavity was used in our calculations, and its accuracy has been tested in the calculation

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TABLE 2: Calculated Hydration Free Energies (kcal/mol) of the Proton and the Proton Affinities (kcal/mol) of Formamide by B3LYP and CCSD(T) species

B3LYP/6-311+G(2df,2p) CCSD(T)/6-31+G(d,p)

+

H [H4O2] H+[H8O4] H+[formamide O] H+[formamide N]

-256.1 -262.4 -263.6 -251.2

-257.3 -263.5 -265.1 -255.3

of hydration free energies for a number of neutral and ionic organic molecules.50 Methodology. All calculations were performed with the Gaussian 03 package.51 The geometries of all transition states, reactants, and intermediates involved in the reaction were fully optimized in solution by Becke’s three-parameter hybrid exchange functional (B3LYP)52,53 with the 6-311+G(2df, 2p) basis set. Frequency calculations were carried out at the equilibrium geometries to confirm the first-order saddle points and local minima located on the potential energy surfaces. The dependence of the basis set on B3LYP calculations was examined. The correlation between stable structures and transition states was checked by analysis of the corresponding imaginary frequency mode and by the intrinsic reaction coordinate (IRC) calculations. For comparison, the single-point energy calculations at the CCSD(T)/6-31+G(d,p) level were performed for all optimized structures. Our test calculations indicate that CCSD(T) calculations with both the 6-31+G(d,p) and 6-311++G(d,p) basis sets predict quite similar results. In estimation of the free energy, the direct calculations in combination with the frequency analysis in solution were performed, although the theoretical treatment based on a thermodynamic cycle has been widely used for prediction of the free energy in solution. Our cluster-continuum model calculations indicate that the effect of zero-point energy is negligible for these systems here. The direct calculation of the free energy in solution was also used in recent calculations,54-56 and it was shown to be feasible. More importantly, most of the transition states, reactants, and intermediates cannot be located in calculation only with the gas-phase cluster model, since many charged compounds, especially for the proton or the hydronium ion, cannot be stabilized in the gas phase due to loss of the bulk solvent effect. As mentioned above, the calculated hydration free energy of the proton in solution by the clustercontinuum model is about -263 kcal/mol,42,43 showing good agreement with the experimental values of -262.4 kcal/mol44 and -264.1 kcal/mol.45 However, the gas-phase predicted hydration free energy of the proton is only -222 kcal/mol,42 suggesting a remarkable effect of the bulk solvent on the stabilization of the proton in solution. For comparison, the integral equation formalism polarizable continuum model (IEFPCM)58 implemented in Gaussian 0959 was utilized to model the bulk solvent effect. Cluster-continuum model calculations in combination with CPCM and IEFPCM for the bulk solvent effect predict comparable results as shown in Table 1S in the Supporting Information. Results and Discussion Protonation of Formamide. As a test of the computational approach and the calibration of the reference energy for the proton in solution, we first calculated the hydration free energy of the proton, according to reaction 1 and eq 4. As Table 2 shows, the predicted hydration energy of the proton in the form of H9O4+ is -263.5 kcal/mol at the CCSD(T) level and -262.4 kcal/mol at the B3LYP level, respectively, values which are in

Figure 1. Optimized geometries of the neutral and corresponding protonated clusters.

excellent agreement with the experimental values of -262.4 kcal/mol44 and -264.1 kcal/mol.45 When the solvated proton is modeled by H5O2+, the proton hydration free energy is -257.3 kcal/mol at the CCSD(T) level and -256.1 kcal/mol at the B3LYP level, respectively, and it was remarkably underestimated. These results indicate that the proton in solution mainly exists as the H9O4+ complex as shown in previous studies.42,43 There are two sites for the protonation of formamide, i.e., O-protonation at the carbonyl oxygen and N-protonation at the amide nitrogen atom, and the corresponding protonated complexes are denoted as H+[formamide O] and H+[formamide N], respectively. The proton attachment to oxygen or nitrogen of formamide in aqueous solution can be described by reactions 2 and 3. The optimized geometries of the neutral model clusters and protonated clusters involved in the protonation of formamide are displayed in Figure 1. The proton affinities57 of formamide for O-protonation and N-protonation can be defined by the free energy change in aqueous solution according to reactions 2 and 3 and are calculated by eqs 5 and 6, where the free energies of neutral and protonated clusters can be directly calculated by the SCRF method.60,61 Ggas(H+) is 6.3 kcal/mol by the wellestablished approaches.42 The predicted proton affinities for the O-protonation of formamide are -265.1 kcal/mol at the CCSD(T) level and -263.6 kcal/mol at the B3LYP level, respectively. Accordingly, the proton attachment to the carbonyl oxygen of formamide in solution is an energetically favored process with an energy release of 1.6 kcal/mol by CCSD(T) and 1.2 kcal/mol by B3LYP at room temperature. These results show that there is no notable thermodynamic effect for step i

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Figure 2. B3LYP-optimized structures of selected species involved in the O-protonated concerted mechanism for the formamide hydrolysis, TS1a, TS1b, and TS1c for the nonassisted process and TS1d, TS1e, and TS1f for the water-assisted reaction. 1f-R and 1f-P are the reactant and intermediate correlated by the transition state TS1f.

in the acid-catalyzed hydrolysis of formamide. From Table 2, we note that the O-protonation is energetically more favorable than the N-protonation by 9.8 kcal/mol by CCSD(T) and 12.4 kcal/mol by B3LYP, which is close to the previous value of 12.6 kcal/mol at the MP2-PCM level.7

H + (gas) + H2nOn(aq) f H+[H2nOn](aq) H+(gas) + formamide(aq) f H+[formamide O](aq) H+(gas) + formamide(aq) f H+[formamide N](aq)

(1)

(2)

(3)

∆Ghyd(H+) ) Gaq(H+[H8O4]) - Gaq(H8O4)Ggas(H+)

(4) ∆Ghyd(H+) ) Gaq(H+[formamide O]) Gaq(formamide) - Ggas(H+) (5) ∆Ghyd(H+) ) Gaq(H+[formamide N]) Gaq(formamide) - Ggas(H+) (6) O-Protonated Concerted Pathway. Six cluster models with different numbers of water molecules were examined. Figure 2

TABLE 3: Thermodynamic Values for the O-Protonated Concerted Mechanisma B3LYP/6-311+G(2df,2p) model ∆ZPE 1a 1b 1c 1d 1e 1f

-3.8 -1.2 -1.8 -2.1 -0.2 -0.6

q

∆E

q

36.9 38.8 39.1 19.0 22.3 25.3

∆H

q

36.1 36.8 36.1 20.6 20.6 23.9

∆G

CCSD(T)/6-31+G(d,p)

∆Gr

∆Gq

∆Gr

36.7 -1.5 38.8 4.0 38.9 2.8 23.4 -0.1 25.2 2.0 25.9 -0.4

37.4 38.0 37.6 20.9 22.3 25.1

-2.2 0.1 -1.7 -3.9 -2.7 -5.9

q

a Units of kilocalories per mole and T ) 298.15 K. ∆Eq ) activation energy, ∆Hq ) activation enthalpy, ∆Gq ) activation free energy, and ∆Gr ) free energy of reaction. Cluster-continuum models 1a, 1b, 1c, 1d, 1e, and 1f refer to Figure 2. Zero-point energies are included except for the activation energy (∆Eq).

presents the optimized structures of six corresponding transition states for the concerted nucleophilic attack of water on the O-protonated formamide in aqueous solution. The predicted activation energies and thermodynamic values are compiled in Table 3. The transition states TS1a, TS1b, and TS1c are responsible for the nonassisted pathways, while TS1d, TS1e, and TS1f correspond to the water-assisted reactions. For the nonassisted processes, three transition-state structures (TS1a, TS1b, and TS1c) lead to comparable activation barriers, and the explicit involvement of more water molecules does not change the activation free energies remarkably for the nonassisted concerted processes. For the water-assisted concerted mechanisms with the transition states TS1d, TS1e, and TS1f, the direct involvement of a

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Figure 3. B3LYP-optimized structures of selected species involved in the O-protonated stepwise mechanism. In TS2b, a chlorine anion (Cl-) was introduced as a counterion to neutralize the system. 2d-R and 2d-P are the reactant and intermediate correlated by TS2d.

single water molecule in the concerted addition of water to the O-protonated intermediate of formamide can significantly reduce the activation free energies. Similar to those of the nonassisted pathways, the activation free energies are less sensitive to the number of water molecules involved in hydrogen bond interactions with formamide. The predicted activation free energies finally converge to a value of about 26 kcal/mol by B3LYP or 25 kcal/mol by CCSD(T) as the first solvation shell of the O-protonated formamide is explicitly saturated by hydrogen bond interactions (TS1f). We also note that the activation free energy for TS1f is slightly larger than that for TS1d by 4.2 kcal/mol at the CCSD(T) level as shown in Table 3. This can be ascribed to the decrease of the positive charges at the carbonyl carbon due to the formation of more hydrogen bonds in TS1f in comparison with TS1d. Mulliken populations reveal that the positive charge of the carbonyl carbon atom in TS1f is reduced to 0.225 from 0.266 in TS1d, and such a decrease of positive charge on the carbonyl carbon makes its electrophilic ability become weak, resulting in a relatively high barrier. O-Protonated Stepwise Pathway. A stepwise mechanism for the acid-catalyzed hydrolysis of amides was proposed in experimental studies,1,2,30-32 where the nucleophilic attack of the adjacent water molecule on amides is activated by protonation of the carbonyl oxygen, and the following proton abstraction by the second water molecule yields the neutral tetrahedral intermediate and H3O+. This proposed mechanism has been explored by Car-Parrinello molecular dynamics (CPMD) simulations,9 and the predicted activation free energy is 19 kcal/ mol, compared to the experimental value of 22.8 kcal/mol.33 However, previous QM calculations basically lead to a concerted mechanism,4-7 although a recent theoretical study at the MP2 level on the stepwise pathway reasonably reproduces the experimental results.10 In the MP2 calculations, only one water molecule was involved in the concerted addition to formamide, leading to a substantially high free energy barrier of 45 kcal/ mol.10 The use of H3O+ as the proton in solution may predict biased relative energies in QM calculations on the hydrolysis

TABLE 4: Thermodynamic Values for the O-Protonated Stepwise Mechanisma B3LYP/6-311+G(2df,2p) model ∆ZPE 2a 2b 2c 2d

q

-0.54 -0.8 0.67 -0.6

∆E

q

∆H

q

9.4 8.6 10.3 8.3 17.9 17.3 18.2 15.9

∆G

CCSD(T)/6-31+G(d,p)

∆Gr

∆Gq

∆Gr

14.2 11.7 12.6 9.6 20.4 18.6 21.8 20.9

12.7 11.2 18.1 19.8

8.9 6.7 14.8 17.7

q

a Units of kilocalories per mole and T ) 298.15 K. ∆Eq ) activation energy, ∆Hq ) activation enthalpy, ∆Gq ) activation free energy, and ∆Gr ) free energy of reaction. Cluster-continuum models 2a, 2b, 2c, and 2d refer to Figure 3. Zero-point energies are included except for the activation energy (∆Eq).

reaction. Presumably, as the hydrated proton in solution is treated as H3O+, the hydration free energy of the proton will be remarkably underestimated, which artificially enhances the protonation tendency of formamide and its neutral tetrahedral intermediate involved in the hydrolysis reaction. As shown in previous studies,42,43 more water molecules should be explicitly involved in the reaction system to model the proton in solution and the hydrogen bond interactions. Two additional water molecules at least are required to saturate the strong hydrogen bond in the first solvation shell of H3O+, as shown in the transition structure TS2a in Figure 3. Optimized geometries of selected species involved in the reaction are depicted in Figure 3, and the corresponding thermodynamic values are collected in Table 4. To evaluate the effect of various cluster-continuum models on the reaction energetics, four classes of clusters were considered in the calculation. As Figure 3 shows, four water molecules participated in the hydrolysis reaction with the transition structure TS2a. A chlorine anion (Cl-) as a counterion was introduced into TS2a, yielding the transition-state structure TS2b, to neutralize the reaction system and investigate the effect of a counterion on the specific-acid-catalyzed reaction. In the transi-

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Figure 4. B3LYP-optimized structures of selected species involved in the N-protonated concerted mechanism. 3d-R and 3d-P are the reactant and intermediate correlated by the transition state TS3d.

tion-state structures TS2c and TS2d, one and three additional water molecules are involved in the hydrogen bond interactions with the O-protonated amide moiety, respectively. The predicted activation free energies for the attack of water on the O-protonated species with the concerted proton transfer to the second water with the transition state TS2a are 14.2 kcal/ mol by B3LYP and 12.7 kcal/mol by CCSD(T), respectively, much lower than the experimental value of 22.8 kcal/mol.33 The presence of Cl- leads to an activation free energy of 12.6 kcal/ mol by B3LYP or 11.2 kcal/mol by CCSD(T), and the corresponding thermodynamic properties of reaction are less changed, showing the independence of the specific-acidcatalyzed reactions on the counterion. On the contrary, as more water molecules are explicitly included in the cluster-continuum model, the activation free energies remarkably increase to 20.4 kcal/mol for TS2c and 21.8 kcal/mol for TS2d at the B3LYP level, values which are in good agreement with the experimental value of 22.8 kcal/mol.33 Accordingly, the explicit involvement of more water molecules in the cluster-continuum mode is important for the reliable description of the O-protonated stepwise pathway as shown in Table 4 and Figure 3. The hydrogen bond interactions from surrounding explicit water molecules, especially the strong hydrogen bond with the hydroxyl group as shown in TS2c, can effectively disperse the positive charge of the carbonyl carbon atom in the O-protonated species. Mulliken populations reveal that the positive charge on the carbonyl carbon is 0.210 in TS2d, compared to 0.254 in TS2a, and thus, the electrophilic ability of the carbon site becomes weak, leading to a relatively large barrier for TS2d. Clearly, the inspection of the results in Tables 3 and 4 reveals that for the O-protonated hydrolysis mechanism the stepwise pathway is more favorable dynamically than the concerted pathway by 5.3 kcal/mol at the CCSD(T) level as the first solvation shell is saturated by explicit water molecules (TS1f versus TS2d). This shows good agreement with the experimental finding.31 N-Protonated Concerted Pathway. In this section we present the reaction mechanism for the N-protonated concerted hydrolysis of formamide in solution. Optimized structures of selected species involved in the reaction pathways are depicted in Figure 4, and the predicted thermodynamic values are

TABLE 5: Thermodynamic Values for the N-Protonated Concerted Mechanisma B3LYP/6-311+G(2df,2p) model ∆ZPE 3a 3b 3c 3d

-2.1 -0.4 -1.0 -0.6

q

∆E

q

∆H

q

∆G

q

∆Gr

32.2 29.1 31.9 -11.6 14.7 12.2 18.1 -10.9 4.6 1.0 7.6 -13.7 11.2 8.5 13.6 -11.4

CCSD(T)/6-31+G(d,p) ∆Gq

∆Gr

32.4 20.3 10.4 14.1

-13.2 -12.2 -14.7 -14.4

a Units of kilocalories per mole and T ) 298.15 K. ∆Eq ) activation energy, ∆Hq ) activation enthalpy, ∆Gq ) activation free energy, and ∆Gr ) free energy of reaction. Cluster-continuum models 3a, 3b, 3c, and 3d refer to Figure 4. Zero-point energies are included except for the activation energy (∆Eq).

presented in Table 5. Transition states TS3a, TS3b, and TS3c correspond to the nonassisted, one-water-assisted, and twowater-assisted mechanisms, respectively. The transition-state structure TS3d contains three additional water molecules involved in the hydrogen bond interactions with the -(NH3)+ moiety, compared to TS3c. These transition states from various computational model clusters for the N-protonated concerted pathway correspond to the nucleophilic attack of water on the carbonyl carbon with concerted proton transfer from the water molecule to the carbonyl oxygen, leading to an ammonia-diol intermediate. As the optimized geometries of TS3d show, all these structural changes do not occur simultaneously, and the C-O bond coupling from the nucleophilic attack of water is prior to the proton transfer from water to the carbonyl oxygen. The predicted thermodynamic values in Table 5 show that the activation free energy decreases rapidly from 31.9 kcal/mol in TS3a to 7.6 kcal/mol in TS3c by B3LYP with the increase of water molecules directly involved in the attack of water on the N-protonated species from TS3a to TS3c. On the contrary, in consideration of the hydrogen bond interactions of the -(NH3)+ moiety with three water molecules, the activation energy increases to 13.6 kcal/mol by B3LYP and 14.1 kcal/ mol by CCSD(T) for TS3d. As discussed above, this can be ascribed to the effect of surrounding hydrogen bond interactions on the electrophilicity of the carbonyl carbon. Generally, the inclusion of explicit water molecules in the reaction process facilitates the H transfer along the water chain, resulting in a

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Figure 5. B3LYP-optimized structures of selected species involved in the N-protonated stepwise mechanism. 4b-R and 4b-P are the reactant and intermediate correlated by TS4b.

TABLE 6: Thermodynamic Values for the N-Protonated Stepwise Mechanisma B3LYP/6-311+G(2df,2p) model ∆ZPEq ∆Eq ∆Hq ∆Gq 4a 4b

-1.0 -0.9

1.3 8.1

-2.1 6.1

4.3 8.5

CCSD(T)/6-31+G(d,p)

∆Gr

∆Gq

∆Gr

-13.6 -7.8

7.1 9.1

-14.5 -10.8

a Units of kilocalories per mole and T ) 298.15 K. ∆Eq ) activation energy, ∆Hq ) activation enthalpy, ∆Gq ) activation free energy, and ∆Gr ) free energy of reaction. Cluster-continuum models 4a and 4b refer to Figure 5. Zero-point energies are included except for the activation energy (∆Eq).

substantial reduction of the free energy barrier, and a relatively large cluster, explicitly composed of more solvent molecules, may provide a reasonable description of the solvent effect in the hybrid cluster-continuum model calculation. N-Protonated Stepwise Pathway. Analogous to the Oprotonated stepwise pathway, the attack of water on the carbonyl carbon of the N-protonated species can follow a stepwise mechanism. Optimized structures of selected species involved in the reaction are depicted in Figure 5, and the corresponding thermodynamic values are collected in Table 6. In the transition structure TS4b compared to TS4a, three additional water molecules are added to saturate the hydrogen bond interactions with the -(NH3)+ moiety. All attempts to locate the intermediate H3O+ from the attack of the first water molecule coupled with the proton transfer to the second water molecule fail in calculation, since the intermediate is less stable, and the reaction directly evolves into an ammonia-diol intermediate like the N-protonated concerted mechanism in all fullgeometry optimizations of the intermediate starting from TS4a and TS4b. Such instability of the intermediate H3O+ can be ascribed to the presence of a strong proton acceptor, · · · (H)(HO)C-O-, from the attack of the first water to · · · HCdO and the proton abstraction by the second water, and the C-O- group as a strong base can easily acquire a proton through the hydrogen bond chain · · · C-O- · · · · · · H2O · · · · · · H3O+ · · · . The reaction path analysis62,63 in Figure 6 shows the character of a stepwise-continuous pathway, in which the first proton transfer to the adjacent H2O yields H3O+, along with the C-O bond coupling, and the following hydrogen

transfer from H3O+ to the carbonyl oxygen through one water molecule leads to the more stable ammonia-diol intermediate. The predicted activation free energies for TS4b are 8.5 kcal/mol by B3LYP and 9.1 kcal/mol by CCSD(T). We note that the N-protonated stepwise hydrolysis pathway is more favorable dynamically than the N-protonated concerted pathway by 5.0 kcal/mol as the first solvation shell is saturated with explicit water molecules at the CCSD(T) level (TS4b versus TS3d). Generally, the N-protonated mechanism is much more facile than the O-protonated mechanism for both concerted and stepwise pathways. The N-protonation will destroy the intramolecular conjugation interactions and weaken the C-N bond strikingly. However, in consideration of the fact that the O-protonated formamide is more stable than the N-protonated formamide by 11.7 kcal/mol at the CCSD(T) level and the damage of conjugation interactions may result in a barrier for the N-protonation, the N-protonated intermediate is less accessible, and the acid-catalyzed hydrolysis of formamide essentially follows the O-protoned mechanism as observed experimentally. Cleavage of the C-N Bond. Experimentally, it was assumed that the cleavage of the C-N bond is assisted by the protonation of the nitrogen atom in the tetrahedral intermediate from the attack of the first water with the concerted proton abstraction by the second water. Followed by the proton transfer from the hydroxyl group of the diol intermediate to the water phase, the final products of formic acid and ammonia are formed. Although this process is clear experimentally30-32 and was investigated by CPMD simulations,9 the detailed molecular mechanism for the breaking of the C-N bond from QM calculations is not available in previous QM calculations. Optimized geometrical parameters of selected species involved in the C-N bond dissociation are depicted in Figure 7, and the corresponding thermodynamic values are presented in Table 7. The transition states TS5a and TS5b correspond to the protonation at the N-site of the tetrahedral intermediate, while TS6a and TS6b are transition states for the C-N bond dissociation. As Table 7 shows, the protonation step experiences very a small activation energy of 2.4 kcal/mol (TS5a) or 1.0 kcal/mol (TS5b) at the B3LYP level, and the corresponding free energy of reaction, ∆Gr, is -9.3 kcal/ mol (TS5a) or -10.8 kcal/mol (TS5b). The energy release at the protonation step may facilitate the following C-N bond dissociation. The B3LYP-predicted activation free energy for the C-N bond dissociation is 10.6 kcal/mol (TS6a) or 9.4 kcal/mol (TS6b), which is comparable with 9 kcal/mol by CPMD simulations.9 As Table 7 shows, CCSD(T) calculations with a relatively small basis set predict larger activation free energies than B3LYP calculations. Relative Free Energy Profiles for the Acid-Catalyzed Hydrolysis. The relative free energy profiles for the low-energy O-protonated and N-protonated stepwise pathways are presented in Figure 8. As shown in Figure 8, the N-protonated hydrolysis is much more favorable dynamically than the O-protonated pathway, and once the N-protonated initial state is formed, the N-protonated mechanism will dominate the amide hydrolysis. However, due to the inaccessibility of the N-protonated precursor as compared with the O-protonated species, the N-protonated mechanism is unlikely responsible for the acid-catalyzed hydrolysis of formamide. Actually, the ratio of O- to N-protonated species was calculated to exceed 106 for simple amides such as dimethylacetamide (DMA).64 As can be seen from Figure 8, the O-protonated stepwise reaction is composed of four steps as suggested in the

Acid-Catalyzed Hydrolysis of Formamide

J. Phys. Chem. A, Vol. 114, No. 49, 2010 12925

Figure 6. Evolution of the transition-state structure TS4b toward the diol intermediate in the N-protonated concerted mechanism.

Figure 7. B3LYP-optimized structures of selected species in the N-protonated stepwise mechanism. TS5a and TS5b are the transition states for the protonation of the tetrahedral intermediate, and TS6a and TS6b are the transition states for the breaking of the C-N bond. 5b-R, 6b-R and 5b-P, 6b-P are the intermediates and products correlated by the transition states TS5a and TS5b, respectively.

experiment. The initial step is the protonation of the carbonyl oxygen atom of amide. The proton attachment to formamide

in solution is exothermic by 1.2 kcal/mol by B3LYP. The second step, the nucleophilic attack of the adjacent water

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Wang and Cao

TABLE 7: Thermodynamic Values for the N-Protonated Concerted Mechanisma B3LYP/6-311+G(2df,2p) model

∆ZPE

5a 5b 6a 6b

-2.3 -2.2 -3.3 -2.5

q

∆E

q

2.4 1.0 11.6 9.7

∆H

q

0.0 -1.3 7.9 6.9

CCSD(T)/6-31+G(d,p) ∆G

q

0.4 -1.9 10.0 9.4

∆Gr

∆Gq

∆Gr

-9.3 -10.8 4.5 7.2

1.1 -1.6 16.2 15.5

-11.0 -12.6 10.6 13.7

a Units of kilocalories per mole and T ) 298.15 K. ∆Eq ) activation energy, ∆Hq ) activation enthalpy, ∆Gq ) activation free energy, and ∆Gr ) free energy of reaction. Cluster-continuum models 5a, 5b, 6a, and 6b refer to Figure 7. Zero-point energies are included except for the activation energy (∆Eq).

Figure 8. Relative free energy profiles (kcal/mol) along the O-protonated and N-protonated stepwise mechanisms by B3LYP.

molecule on the carbonyl carbon atom coupled with the proton abstraction by the second water, is the rate-determining step with an activation free energy of 21.8 kcal/mol by B3LYP, and the predicted barrier shows good agreement with the experimental value of 22.8 kcal/mol.33 The third step is the protonation of the tetrahedral intermediate at the nitrogen site, and the activation free energy is almost negligible at room temperature. The last step is the breaking of the C-N bond, along with the proton transfer from one of the hydroxyl groups to the outer water phase, and the predicted activation free energy is 9.4 kcal/mol by B3LYP. The free energy of reaction, ∆Gr, is 10.7 kcal/mol for the overall acid-catalyzed hydrolysis of formamide. Conclusions Various cluster-continuum models for the acid-catalyzed hydrolysis of formamide have been evaluated by B3LYP and CCSD(T) calculations. The calculations show that the explicit inclusion of more water molecules in the cluster-continuum model is very important for a reasonable description of the proton in solution and hydrogen bond interactions involved in the amide hydrolysis. On the basis of extensive calculations, both concerted and stepwise mechanisms of the N-protonated and O-protonated pathways have been explored, and a complete picture for the acid-catalyzed hydrolysis of formamide was presented. The present results lead to an O-protonated stepwise mechanism for the low-energy acid-catalyzed hydrolysis of formamide as proposed by experiment and provide a basis to reconcile discrepancies in assessing the favored mechanism from previous QM calculations. Predicted thermodynamic values show good agreement with experiment and available CPMD simulations. Acknowledgment. This work was supported by the National Science Foundation of China (Grants 20733002 and 20873105) andtheMinistryofScienceandTechnology(Grant2011CB808504). Supporting Information Available: Comparison of G03/ CPCM and G09/IEFPCM calculations, optimized Cartesian coordinates, and energies of various species involved in the

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