Cooperative Effect of Solvent in the Neutral Hydration of Ketenimine

Dec 11, 2009 - Sadhana Kumbhar , Saibal Jana , Anakuthil Anoop , Mark P. Waller ... Sun , Xiao-Peng Wu , Song Geng , Yi Ren , Ning-Bew Wong , Wai-Kee ...
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J. Phys. Chem. A 2010, 114, 595–602

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Cooperative Effect of Solvent in the Neutral Hydration of Ketenimine: An ab Initio Study Using the Hybrid Cluster/Continuum Model Xiao-Ming Sun,† Xi-Guang Wei,† Xiao-Peng Wu,† Yi Ren,*,†,‡ Ning-Bew Wong,*,‡ and Wai-Kee Li§ College of Chemistry, Key Laboratory of Green Chemistry and Technology, Ministry of Education, and Key State Laboratory of Biotherapy, Sichuan UniVersity, Chengdu 610064, People’s Republic of China, Department of Biology and Chemistry, City UniVersity of Hong Kong, Kowloon, Hong Kong, and Department of Chemistry, The Chinese UniVersity of Hong Kong, Shatin, N.T., Hong Kong ReceiVed: August 17, 2009; ReVised Manuscript ReceiVed: NoVember 17, 2009

The detailed reaction pathways for the hydration of ketenimine by water and water clusters containing up to five explicit water molecules (CH2dCdNH + (n + 1)H2O f CH3CONH2 + nH2O, n ) 0-4) in the gas phase have been investigated by the MP2 method in conjunction with the 6-31+G* and 6-311++G** basis sets, and the effects of bulk solvent are taken into account according to the conductor-like polarizable continuum model (COSMO). In the hybrid cluster/continuum model, apart from one directly attacking water molecule, four explicit water molecules participating in the water-assisted hydrolysis of ketenimine are divided into two groups, one involving in the proton relay and the other near the nonreactive nitrogen or carbon atom. Two possible reaction channels, water addition across the CdC bond or across the CdN bond of ketenimine, are discussed. Our results indicate that the kinetically favorable mechanism involves an eight-membered ring transition state structure formed by a proton transfer chain of three water molecules. Meanwhile, two additional cooperative water molecules near the nonreactive region assist the hydration by engaging in hydrogen bonding to the substrate; such an interaction is found to be important in the hydration of ketenimine and other cumulenes. The lowest rate-determining activation barriers of CdC and CdN addition are 98.9 and 95.1 kJ/mol, respectively, suggesting that the two channels are competitive when more water molecules take part in the hydration. COSMO solution models do not modify the calculated energy barriers in a significant way. 1. Introduction 1

Ketenimines were first prepared by Staudinger et al. in the 1920s, and they have attracted considerable interest as substrates for the synthesis of heterocycles, largely through processes involving cycloaddition reactions.2-5 Ketenimines are isoelectronic with allenes and ketenes, and they can be represented by resonance structures 1a, 1b, and 1c, resulting in electron deficiency on CR and electron sufficiency on Cβ and N.

oxygen of a water molecule undergoing in-plane attack on the electron-deficient CR of ketenimine, in addition to having either the protonation of Cβ or reversible protonation of N, with acetamide being finally formed though tautomerization. The two pathways are shown as follows Path A

CH2dCdNH + H2O f CH3C(OH)dNH f CH3CONH2 (1) Path B

CH2dCdNH + H2O f CH2dC(OH)NH2 f CH3CONH2 (2)

Depending on the ketenimine structure, the mechanism of the water addition to ketenimine is believed to involve the * Corresponding authors: Y. Ren, fax +86-28-85412907, e-mail [email protected]; N. B. Wong, fax +852-27887406; e-mail [email protected]. † Sichuan University. ‡ City University of Hong Kong. § The Chinese University of Hong Kong.

In the early kinetics studies of the acid-catalyzed and uncatalyzed hydration of ketenimines, Hegarty et al.6 examined the rate of hydration of a series of ketenimines, including Ph(R1)dCdNR2 (R1 ) H or Me; R2 ) iso-Pr, Ph, C6H11, or sec-Bu) and Me2CdCdNsPh. Later on, Hegarty et al.7 reported the experimental results on the hydration of the sterically hindered N-isopropyldimesitylketenimine and N-isopropylbis(pentamethylphenyl)ketenimine at pH ) 2. Their results show that in aqueous solution the reactions of ketenimines are dominated by rate-determining proton transfer to either Cβ or N depending on the substituents. Usually, the C-protonation of ketenimines is more thermodynamically facile; however, hemiaminals will be formed by N-protonation of ketenimines (etheneimines) if Cβ is sterically hindered. Studies of the stability of ketenimines were also carried out,8-10 and comparison between C-protonation and N-protonation indicates that the

10.1021/jp907957k  2010 American Chemical Society Published on Web 12/11/2009

596 J. Phys. Chem. A, Vol. 114, No. 1, 2010 protonated form, the nitrilium ion (CH3sCtNH+), is much more stable than keteniminium ions (CH2dCdNH2+) due to the considerable CtN triple bond character, as supported by X-ray data in the former case. In the early theoretical studies by Nguyen et al. on the hydration of the parent ketenimine,11,12 only the possibility of the addition across the CdC bond was considered and it was proposed that the reaction of water dimer with the ketenimine was favored, compared to the reaction with a single water molecule. Later on, they studied two possible hydration pathways, at CdC and CdN bonds, with up to three water molecule(s), at the level of CCSD(T)/6-31G**//MP2/6-31G** + ZPE (HF/6-31G**).13 They suggested that the addition of water across the CdN bond is favored in the hydrations of one or two water molecules, whereas a reverse situation will occur when a chain of three water molecules was used to model the process. In a similar nucleophilic addition, the amination of ketenimine, it was confirmed that the initial addition of amine proceeded along the CdN bond rather than the CdC bond.14-16 Accordingly, in neutral or basic condition, the favorable mechanism of hydration of parent ketenimine is uncertain. In the hydration of heterocumulene, the surrounding water molecules can play the catalytic role by being located mainly in the reactive region and acting as a hydrogen bridge through donating or accepting protons to promote the proton transfer in numerous studies.11-13,17-25 Furthermore, water molecules can, in addition to taking part in the proton transfer, also interact with each other in the nonreactive region.26 This explains the catalytic effect of the solvent on the hydration of heterocumulene, such as NHdCdNH,27-29 CO2,30,31 COS,32 CS233 and PhNSO.34 It was reported that the interaction among the water molecules and the reactant can influence the structures of the stationary points as well as the activation barriers of these reactions. For example, in the hydration of COS, due to two other water molecules near the nonreactive oxygen atom, the activation barrier of the rate-determining step can be considerably reduced, from 137.4 kJ/mol in the three-water hydration to 107.9 kJ/mol for the five-water hydration. Similar results are also observed in the hydration processes of HCONMe2,35 SO2,36 as well as heterocyclic formamidine.37 But up to now no theoretical work has been reported on the cooperative effect of water molecule(s) located in the nonreactive region in the hydrolysis of CH2dCdNH. In the present paper, we aim to obtain insight into the hydration mechanism of parent ketenimine in the neutral aqueous solution and explore the cooperative effect of water, using a combined supermolecular/continuum model. The number of participating water molecules is large enough to give convergent activation energies. The objective of our study is 3-fold: (1) to settle the question of whether water molecules attack across the CdC bond or the CdN bond and to find the most favorable reaction pathway for the hydration of ketenimine; (2) to analyze and compare the cooperative effective in the hydration of ketenimine with directly catalyzing hydration by proton transfer; (3) to make a comparison between the hydration of ketenimine with carbodiimide. These studies would help us to better understand the reaction process and the cooperative effect in the hydration of the parent heterocumulenes. 2. Details of Calculations All calculations were performed using the Gaussian 03 package.38 The geometries of all reactants, precomplexes, intermediates, transition structures (TSs), and products were fully optimized and confirmed by vibrational frequency analysis at

Sun et al. the level of MP2/6-31+G* and then further optimized at MP2/ 6-311++G**. The relative energies among the species include the MP2/6-31+G* zero-point vibrational energies (ZPE) correction, with a scaling factor of 0.98.39 Thermal and entropy corrections were computed by standard statistical methods. Charge distributions were obtained from the wave functions calculated at the MP2/6-311++G** level, employing natural population analysis (NPA).40 The catalytic effect of water molecule(s) described in this paper is explained by the geometric changes and NPA analysis among the species involved in the rate-determining step. The effect of a polar environment on the reaction path has been taken into account by calculating single-point energies in water (ε ) 78.41) at the gas phase MP2/6-311++G** geometries employing the conductor-like polarizable continuum model (COSMO).41 Throughout the present study, all atomic distances are in angstroms (Å), and all angles are in degrees (deg). All relative energies (in kJ/mol) are computed by the Gibbs free energy changes at 298 K, denoted as ∆G without COSMO correction and ∆G(sol) with COSMO treatment. All of the absolute Gibbs free energies (Table S1 in Supporting Information), MP2/6311++G** optimized structures, and charge distribution (Table S2 in Supporting Information) of all the species are presented in the Supporting Information. 3. Results and Discussion In order to distinguish the two possible reaction channels, path A or path B, described in the introduction section, italic prefixes a and b are used to differentiate the species involved in the concerted nucleophilic addition of water molecule taking place across the CdC bond or CdN bond of CH2dCdNH. We will discuss these pathways separately. The species involved in the reactions are M, TS, In, or P, representing precomplex, transition state, intermediate, and product, respectively. These species names have subscripts i and j (i, j ) 0, 1, or 2), connected by a hyphen, which refer to the number of water molecules participating in the proton transfer (number i) or taking part in hydrogen bonding with the substrate (number j) to catalyze the hydration of CH2dCdNH. The following discussions will consist of three main parts. First, we present the influence of the number of explicit solvent molecules on the potential energy surface (PES) of the hydration of ketenimine in the presence of up to three water molecules participating in the proton relay without explicit cooperative solvent molecule(s), that is i ) 0-2; j ) 0. Then we will add one or two other water molecule(s) (j ) 1-2) near the nonreactive nitrogen or carbon atom in order to discern the cooperative effect of water molecule(s) on the PES of hydration. Finally, we will compare the catalytic effect caused by two groups of explicit solvent molecules. We also made a comparison between the hydration carbodiimide and ketenimine and focus on the bulk solvent effects. 3.1. Hydration of Ketenimine without Cooperative Water Molecule (j ) 0). The reaction pathways of CH2dCdNH + (n + 1)H2O f CH3CONH2 + nH2O (n ) i + j; i ) 0-2, j ) 0) have been studied by different methods in previous papers,11-13 but they only cover the first step of the hydration reaction. To better understand the full hydrolysis process of ketenimine, here, we did these reactions again at the MP2/6-311++G** level. The hydration of ketenimine starts with the initial nucleophilic addition of one water molecule across the CdC or CdN bond. The final product, acetamide or hydrated acetamide, is formed by tautomerization. Considering the similarity of one-, two-,

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Figure 1. MP2/6-311++G** optimized structures of the stationary points along the two-water hydration of ketenimine across the CdC bond (path A1-0) and the CdN bond (path B1-0). All bond lengths are in angstroms (Å) and bond angles are in degrees. The relative energies (in kJ/mol) reported above the arrows are ∆G values without COSMO correction (boldface) and below the arrows are the corresponding ∆Gsol values with COSMO correction (italic). For each TS, the number in parentheses corresponds to the sole imaginary vibrational frequency.

and three-water hydrolysis, in the present work, we only comment on the mechanism of the two-water hydration of ketenimine. Figure 1 illustrates the optimized geometries of all the stationary points located along the potential energy profile and summarizes the main geometric features for the two-water hydration of ketenimine, and the corresponding relative Gibbs free energies, with or without the COSMO treatment, are also presented. Figures S1 and S2 in Supporting Information show the hydration mechanism of one- and three-water hydration of ketenimine. An examination on all the precoordination structures between ketenimine and the two-water chain shows that there are two possible minima: a-M1-0 and b-M1-0, corresponding to two different pathways (path A1-0 and path B1-0). For these two pathways, addition of the water molecule leads to two sixmembered ring TSs, a-TS1-0 and b-TS1-0, in which proton transfers from water to the terminal atom (Cβ or N) of ketenimine through a water bridge. The structures that naturally follow from a-TS1-0 and b-TS1-0 are a-In1-0 and b-In1-0, respectively, which are less stable than the isomeric a-In′1-0 and b-In′1-0. Next, we have the formation of the water-assisted tautomerization TSs, a-TS′1-0 and b-TS′1-0. The final product, monohydrated ketenimine (a-P1-0 or b-P1-0), is formed through tautomerization. It is observed from Figure 1 and Figures S1 and S2 in Supporting Information that, for pathways Ai-0 (i ) 0-2), the reaction barriers in the first step are 236.4 (i ) 0), 165.8 (i )

1), and 145.5 kJ/mol (i ) 2). The tautomeric barriers of the second step are 128.5 (i ) 0), 39.3 (i ) 1), and 36.4 kJ/mol (i ) 2), respectively, significantly lower than those in the first step by more than 100 kJ/mol. These trends are also observed in the pathways Bi-0 (i ) 0-2), where the barrier for addition across the CdN bond are 202.9 (i ) 0), 148.3 (i ) 1), and 135.6 kJ/mol (i ) 2), and the tautomeric barriers are 164.7 (i ) 0), 76.8 (i ) 1), and 65.6 kJ/mol (i ) 2). These results indicate that (1) the first step for the hydrolysis of ketenimine is always rate-determining; (2) for the three cases at hand, the activation barriers (∆G) of the first step across the CdN bond are found to be lower than the corresponding ones across the CdC bond by 33.5, 17.5, and 9.9 kJ/mol, suggesting that the addition across the CdN bond is always favored over that across the CdC bond; (3) with the incorporation of explicit water molecule(s), the ratedetermining activation barriers are reduced dramatically by 70.6 kJ/mol (A0-0 f A1-0) and by 90.9 kJ/mol (A0-0 f A2-0) for the additions across the CdC bond or by 54.6 kJ/mol (B0-0 f B1-0) and by 67.3 kJ/mol (B0-0 f B2-0) for the additions across the CdN bond. This trend can be attributed to the fact that the formation of a four-center TS is symmetry forbidden in a-TS0-0 or b-TS0-0, and additional H2O molecule(s) are needed to make the reaction concerted,42 and another factor may be the ring strain associated with the four-membered cyclic TS. The participation of an additional water molecule makes the hydrolysis more efficient than the one-water process, due to the stability gained from a six-membered ring TS structure. Even

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Figure 2. . MP2/6-311++G** optimized structures and relative energy values (in kJ/mol) of the stationary points along the three-water hydration of ketenimine across the CdC bond (path A1-1) and the CdN bond (path B1-1) in the presence of one explicit cooperative water molecule.

so, the two reacting centers are not bridged in this TS. The addition of the third water molecule can bridge the gap and carry out the proton transfer in a comfortable and facile way. Compared with two-water hydration, inclusion of a third water molecule in the supermolecule substantially decreases the energy barrier of the CdC addition by 20.3 kJ/mol and that of the CdN addition by 12.7 kJ/mol with respect to the two-water hydration. This gives an overall preference of 9.9 kJ/mol in favor of the CdN addition over the CdC addition, which is not in agreement with the previous published calculations by Nguyen et al.,13 where the addition across the CdC bond is more favorable in the three-water hydration, with the barriers being calculated relative to the separated reactants (CH2dCdNH + 3H2O). To account for the discrepancies between ours results and those of Nguyen et al., we reoptimized the geometries of a-TS2-0 and b-TS2-0 at the MP2/6-31G** level, the same as that used by Nguyen et al., and compared the two sets of absolute energies. It is found that two possible TS structures, denoted as b-TS12-0 and b-TS1′2-0, are located for the addition across the CdN bond, in which b-TS1′2-0 is higher in energy than b-TS12-0 by 10.8 kJ/mol. Meanwhile, a-TS12-0 is found to be more stable than b-TS1′2-0 by 3.6 kJ/mol but less stable than b-TS12-0 by 7.2 kJ/mol. These results imply that the addition across the CdN bond is always more favorable once the more reasonable TSs are located.

3.2. Hydration of Ketenimine in the Presence of Explicit Cooperative Water Molecule(s). From the foregoing calculations, it is clear that single-water hydration is an unfavorable pathway. Therefore this process is not considered in this section, and only the rate-determining step of hydration will be discussed in the following. 3.2.1. With One CooperatiWe Water Molecule (j ) 1). To study the cooperative effect in the hydration of ketenimine: first, one water molecule is located near the nonreactive terminal atom, involving a six-membered ring hydrogen-bonding structure. We will explore three- and four-water hydrations with one cooperative water molecule. The optimized geometries and relative energies are presented in Figure 2 (i ) j ) 1) and Figure 3 (i ) 2 and j ) 1) As shown in Figure 2, for the three-water hydration in the presence of one cooperative water, the precomplex M1-1 can lead to two possible TSs: one is across the CdC bond (a-TS1-1), and the other is across the CdN bond (b-TS1-1), while the third water molecule is placed either near the nonreactive nitrogen atom (path A1-1) or near the nonreactive carbon atom (B1-1). In the rate-determining step of path A1-1, the PT process takes place via a six-membered ring TS, with a ∆Gq of 125.5 kJ/ mol, lower than that in path A1-0 by 40.3 kJ/mol. In path B1-1, the third water molecule is hydrogen-bonded with the nonreactive terminal carbon, and its ∆Gq of 113.1 kJ/mol is 35.2 kJ/

Hydration of Ketenimine

Figure 3. MP2/6-311++G** optimized structures and relative energy values (in kJ/mol) of the stationary points for the first step of fourwater hydration of ketenimine across the CdC bond (path A2-1) and the CdN bond (path B2-1) in the presence of one explicit cooperative water molecule.

mol lower than the corresponding value in path B1-0, indicating that the third water molecule can also catalyze the hydration of ketenimine by cooperative effect instead of by proton shuttle. The variation of activation barriers could be interpreted by the different rate-determining TSs. Upon comparing path A1-0 and A1-1, or B1-0 and B1-1, it is seen that the bond formation between CR and O1 has progressed further with the inclusion of one water molecule near the nonreactive nitrogen (or carbon atom), and the CR-O1 distance is reduced by 0.051 Å from a-TS1-0 to a-TS1-1, and 0.119 Å from b-TS1-0 to b-TS1-1, accompanying the decrease of the Cβ-CR-N angle from 142.4° (a-TS1-0) to 137.2° (a-TS1-1), or from 144.3° (b-TS1-0) to 137.9° (b-TS1-0). In addition, for the CdC bond addition, the H3-Cβ distance in a-TS1-1 is shorter than that in a-TS1-0 by 0.061 Å, and similar result is also observed in the CdN bond addition, where the H4-N distance is decreased by 0.146 Å from b-TS1-0 to b-TS1-1. Obviously, these geometrical changes can stabilize the TS structures. Putting one explicit water molecule near the nonreactive nitrogen atom in the a-TS2-0 or near the nonreactive carbon atom in the b-TS2-0 can lead to two four-water hydration TSs, called a-TS2-1 or b-TS2-1. The aforementioned results and explanation can also be applied when we compare a-TS2-1 with a-TS2-0, or b-TS2-1 with b-TS2-0. The rate-determining barriers are reduced from 145.5 (a-TS2-0) to 109.9 kJ/mol (a-TS2-1), and from 135.6 (b-TS2-0) to 99.5 kJ/mol (b-TS2-1), accompanying the decrease of the CR-O1 distance from 1.487 Å in a-TS2-0 to 1.444 Å in a-TS2-1, and from 1.546 Å in b-TS2-0 to 1.456 Å in b-TS2-1. All these results show that one explicit water molecule can catalyze the hydration through hydrogen bonding with ketenimine, instead of directly participating in the proton relay. Inspection of the energy activation barriers in Figures 2 and 3 shows that all rate-determining barriers for the addition across the CdN bond are lower than those across the CdC bond by more than 10 kJ/mol, indicating that the CdN addition is energetically favored. 3.2.2. With Two CooperatiWe Water Molecules (j ) 2). The above discussions show that the energy activation barriers of the rate-determining step are greatly reduced when one water molecule takes part in cooperation near the nonreactive atom.

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Figure 4. MP2/6-311++G** optimized structures and relative energy values (in kJ/mol) of the stationary points for the first step of fourwater hydration of ketenimine across the CdC bond (path A1-2) and the CdN bond (path B1-2) with two explicit cooperative water molecules.

Figure 5. MP2/6-311++G** optimized structures and relative energy values (in kJ/mol) of the stationary points for the first step of fivewater hydration of ketenimine across the CdC bond (path A2-2) and the CdN bond (path B2-2) with two explicit cooperative water molecules.

It is interesting to check what happens when the cooperative water chain is further lengthened by one additional water molecule. As reported previously, the hydrogen bonding in an eightmembered ring is stronger than that in a six-membered ring, which will reduce the barrier when two explicit water molecules are involved in the hydrogen bonding with substrate through an eight-membered ring TS. Figures 4 and 5 show the optimized geometries and activation barriers of the first step for the fourand five-water hydration in the presence of two cooperative water molecules. In the four-water hydration of ketenimine including two cooperative water molecules (j ) 2), the precomplexes, b-M2-1 or a-M2-1, located in pathways A2-1 and B2-1, can be viewed as the starting structure for the addition across the CdC bond or across the CdN bond, corresponding to the rate-determining TS a-TS1-2 or b-TS1-2, in which there is an eight-membered hydrogen-bonding structure and proton is transferred through a six-membered ring relay.

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TABLE 1: Energy Activation Barriers (in kJ/mol) for the First Step in the Hydration of Ketenimine in the Gas Phase, ∆Gq, and in Aqueous Solvent, ∆Gqsol CdC addition pathway CH2dCdNH + H2O CH2dCdNH + 2H2O CH2dCdNH + 3H2O CH2dCdNH + 4H2O CH2dCdNH + 5H2O a

A0-0 A1-0 A1-1 A2-0 A1-2 A2-1 A2-2

∆Gq a

236.4 165.8b 125.5b 145.5c 107.6b 109.9c 98.9c

CdN addition ∆Gqsol

pathway

∆Gq

∆Gqsol

235.6 156.1 138.7 130.5 118.1 112.0 99.8

B0-0 B1-0 B1-1 B2-0 B1-2 B2-1 B2-2

202.9 148.3 113.1 135.6 102.2 99.5 95.1

204.3 146.2 123.2 126.4 109.7 103.0 95.7

Four-memebered ring TS. b Six-membered ring TS. c Eight-memebered ring TS.

As shown in Figure 4, the two explicit water molecules are located near the nonreactive nitrogen in the a-TS1-2 or carbon atom in the b-TS1-2, where three stronger hydrogen bonds are formed with angles of (159.5-173.2°) for the CdC addition and (159.4-173.8°) for the CdN addition, obviously more efficient than those in a-TS1-1 and b-TS1-1, where the corresponding angles are 141.4° and 161.7° for the CdC addition and 134.0° and 157.5° for the CdN addition. Moreover, due to the presence of one additional cooperative water molecule, a quite advanced nucleophilic attack on the CR atom is observed in the two TSs, where the CR-O1 distance is reduced from 1.467 Å in a-TS1-1 to 1.446 Å in a-TS1-2 or from 1.486 Å in b-TS1-1 to 1.461 Å in b-TS1-2. Meanwhile, the activation barriers of 107.6 kJ/mol (a-TS1-2, CdC addition) and 102.2 kJ/mol (bTS1-2, CdN addition) are lower than a-TS1-1 by 17.9 kJ/mol or b-TS1-1 by 10.9 kJ/mol, respectively, indicating that the cooperative effect induced by eight-membered ring hydrogen bonding is stronger than by the six-membered ring hydrogenbonding structure . According to our previous studies, in the five-water hydration of ketenimine, the most favorable mechanism seems to be involving a rate-determining eight-membered ring TS (a-TS2-2 or b-TS2-2 in Figure 7), where nearly perfectly oriented hydrogen bonds (with angles around 164-177°) exist in the proton transfer TSs. Meanwhile, another eight-membered ring hydrogen-bonded structures induces these two TSs tighter than other TSs in the present study, as seen from the shorter distance of CR-O1 (1.430 Å in a-TS2-2 and 1.436 Å in b-TS2-2). Rehybridization at CR has also progressed further than other TSs, and the Cβ-CR-N angles of 133.8° for a-TS2-2 and 133.7° for b-TS2-2 are also smaller than those found in other TSs. The activation barriers are 98.9 kJ/mol for a-TS2-2 and 95.1 kJ/mol for b-TS2-2, lower than the other corresponding barriers, once again showing the addition across the CdN bond is more favorable, same as previous discussions. The energy activation barriers of the rate-determining step with up to five water molecules are summarized in Table 1. 3.3. Further Comparison of Geometries, Natural Charge Distributions, and Activation Barriers among the Hydration Pathways of Ketenimine. The results in Figures 1-5 indicate that the activation energy barrier of the rate-determining step decreases as the number of the participating water molecules increases. Comparison between five-water hydrolysis of CH2dCdNH and other cases (one- to four-water hydrolysis) shows that the rate-determining activation barrier in the hydrolysis of CH2dCdNH depends on the number of explicit water molecules directly participating in the proton transfer and the cooperative water molecule(s) on the nonreactive region. Taking the eight-membered ring TSs across the CdN bond as examples, the activation barrier, ∆Gq(sol), decreases with the number of nonreactive water molecules in the

following order: 126.4 (b-TS2-0, j ) 0) < 103.0 (b-TS2-1, j ) 1) < 95.7 kJ/mol (b-TS2-2, j ) 2), suggesting that there are enhanced cooperative effects with two water molecules involved than with one water molecule near the nonreactive region. If we fix one water molecule on the nonreactive atom, i.e., j ) 1, and concentrate on only the TSs across the CdN bond, it is found that the barriers decrease from ∆Gq(sol) ) 123.2 kJ/mol (six-membered ring b-TS1-1) to 103.0 kJ/mol (eight-membered ring b-TS2-1), showing that the hydrolysis of CH2dCdNH via an eight-membered ring TS is most favorable, due to the better catalytic effect of the two-water chain. These interesting results can be rationalized by the geometrical features of TSs, especially by comparing the hydrogen bonds in the supermolecular model and the CR-O1 distance in the TS structures. Although it is difficult to detect the geometry of a hydrogen bond, a statistical analysis of X-ray crystallographic data has shown that most effective hydrogen bonds in crystals deviate from linearity by 10-15°. The angles of hydrogen bonds in b-TS2-1 are about 164-177°, obviously more optimal than those in the b-TS1-1 (about 154°); this is made possible by the stronger repulsion among three highly electronegative atoms, destabilizing b-TS1-1 in the process. Thus the barrier in the three-water hydrolysis process of CH2dCdNH is higher than that in the four-water hydrolysis TS across the CdN bond by 20.1 kJ/mol. Previous discussions have shown that the rate-determining barrier for the CdC bond addition is always higher than the corresponding one for the CdN bond addition, suggesting that the addition across the CdN bond is more favorable than across the CdC bond. This result can be explained by electrostatic potential (ESP) analysis of the parent CH2dCdNH, where the ESP value in the region around nitrogen atom is more negative, implying the nitrogen atom bearing one lone pair is electron-rich and, hence, it is the preferred target for electrophilic attack. At the same time, the terminal nitrogen atom is also less sterically hindered; thus it facilitates the proton transfer from a water molecule to the nitrogen atom. It is worth noticing that the ketenimine would prefer to undergo N-protonation to the Cβ-protonation, and the formation of (+)CH3-CtNH is more exothermic than the formation of CH2dCdNH2(+) by 88.1 kJ/mol (see eq 3), implying that the addition across the CdC bond of ketenimine is thermodynamically controlled, whereas the addition across the CdN bond of ketenimine is kinetically controlled. But the barrier difference between the CdN and CdC addition decreases with the increment of cooperative water molecule(s), which can be expressed by the ∆∆Gi-jq, defined as ∆Gq(a-TSi-j) - ∆Gq(b-TSi-j). Inspection of the rate-determining barriers in Figures 2, 4, and 6 reveals the following decreasing order: 17.5 (∆∆Gq1-0) > 12.4 (∆∆Gq1-1)

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Figure 6. MP2/6-311++G** optimized structures of the stationary points for the first step of five-water hydration of carbodiimide (path C2-2). The relative energies (in kJ/mol) reported above the arrows are ∆G values without COSMO correction.

TABLE 2: Selected NPA Charge Changes of H2CCNH Moiety from Precomplexes to the Rate-Determining TSs, ∆q(CH2CNH), the Corresponding Activation Gibbs Free Energies (kJ/mol), ∆Gq, and the Cr-O1 Distance (Å), r(Cr-O1), in the Rate-Determining TSs pathway Bi-j i i i i i i

) ) ) ) ) ) a

1, 2, 1, 1, 2, 2,

j j j j j j

) ) ) ) ) )

0 0 1 2 1 2

precom f TS

∆q(CH2CNH)

∆Gq

r(CR-O1)

b-M1-0 f b-TS1-0 b-M2-0 f b-TS2-0 M1-1 f b-TS1-1 a-M2-1 f b-TS1-2 b-M2-1 f b-TS2-1 M2-2 f b-TS2-2 c-M2-2 f c-TS2-2a

-0.334 -0.366 -0.382 -0.395 -0.414 -0.420 -0.425a

148.3 135.6 113.1 102.2 99.5 95.1 89.7a

1.605 1.546 1.486 1.461 1.456 1.436 1.421a

For the five-water hydration of carbodiimide (see Figure 6).

> 5.4 kJ/mol (∆∆Gq1-2). Such an order can be also attributed to the stronger hydrogen bonding in a-TS1-2. -877.3 kJ/mol

CH2dCdNH2+ 79 CH2dCdNH + -789.2 kJ/mol

H+ 98 CH3sCtNH+

(3)

The variation of activation barriers could also be explained by the electrical relaxation associated with the formation of ratedetermining TS. Here, we only discuss the addition across the CdN bond. With the attacking of water molecule toward the central carbon atom (CR) of ketenimine, the electrons will transfer from the water molecule cluster to the H2CCNH moiety for the process b-Mi-j f b-TS i-j. The lower activation barrier will be induced by the more negative ∆q values, defined as q(CH2CNH in TS) - q(CH2CNH in precomplex), with the increase of the number of explicit water molecule(s). This prediction was confirmed by NPA in Table 2, showing that the ∆q values become more negative steadily as we proceed from two-water hydration to five-water hydration, accompanying the decrease of CR-O1 bond and the rate-determining activation Gibbs free energies. A closer inspection of the activation barriers in Figures 1-5 and Figures S1 and S2 in Supporting Information unveils that the hydration of CH2dCdNH can be catalyzed in two ways, one through reducing the strain of proton transfer ring, the other through the hydrogen bonding formed by water molecules and terminal atom(s). It will be interesting to compare these two effects: Which is more important, or are they comparable? The rate-determining barrier difference between b-TS1-1 and b-TS2-1 is 13.6 kJ/mol, which is slightly larger than that between b-TS1-1 and b-TS1-2 by 2.7 kJ/mol, implying that these two effects are comparable and neither one can be neglected. 3.4. Comparison between the Hydration of Ketenimine with Carbodiimide. A study on the cooperative effect of solvent in the neutral hydration of carbodiimide was previously

Figure 7. MP2/6-311++G** optimized structures of the main stationary points in the solvent with PCM model for the one-water hydration of ketenimine across the CdC bond (path A′0-0) and the CdN bond (path B′0-0). The relative energies (in kJ/mol) reported above the arrows are Gibbs energies with PCM model and below the arrows are the corresponding ∆Gsol values with COSMO correction.

reported,27-29 where the third explicit water molecules prefer to be located in the nonreactive region, involving a ratedetermining six-membered ring instead of an eight-membered ring TS structure, similar to pathway A1-1 or B1-1 in the present study. In order to stress the importance of cooperative effect of solvent for the hydration of other heterocumulenes, here we calculate the five-water hydration of carbodiimide, where the precomplex and TS are denoted as c-M2-2 and c-TS2-2, respectively (see Figure 6), and compare with the corresponding hydration pathway of ketenimine at the same level to check the influence of cooperative effect on the hydration of carbodiimide. The optimized structures of c-M2-2 and c-TS2-2 and the gas-phase ∆Gq values are presented in Figure 6, which shows that the activation Gibbs free energy is 89.7 kJ/mol, lower than the previously reported barrier (109.6 kJ/mol) in the three-water hydration of carbodiimide at the MP2(full)/6-31G* level, and also lower than the corresponding one in the hydration of ketenimine (path B2-2) by 5.4 kJ/mol. Meanwhile a shorter CR-O1 distance (1.421 Å) is observed in c-TS2-2 with a more negative ∆q value [q(HNCNH in c-TS2-2) - q(HNCNH in c-M2-2)]. These results indicate that (1) five-water hydration is more favorable than the three-water hydration of carbodiimide when there exists a rate-determining TS structure involving an eight-membered proton transfer ring, and other two water molecules located in the nonreactive region playing the cooperative effect and (2) there is an enhanced cooperative effect of solvent in the hydration of carbodiimide due to the stronger hydrogen bonding between water dimer and the more electronegative nonreactive nitrogen atom in the HNCNH moiety. 3.5. Effects of Water Bulk Solvent on the Hydration of Ketenimine. In order to check if the obvious barrier differences exist between the single point calculation and optimization in solution, we reoptimized the structures M0-0, a-TS0-0, and b-TS0-0 in solution with PCM model, then single-point energies with COSMO treatment is calculated as shown in Figure 7. It is found that the optimization in solution only slightly modify the activation barrier in solution, and barrier difference is within 1 kJ/mol, suggesting that the single-point calculation for describing the performance of hydration of ketenimine in solution is reliable. When the bulk solvent effect with COSMO treatment is taken into account, the ∆Gqsol values are not significantly modified when more than three explicit water molecules are involved in the hydration. Indeed, it is found from Table 1 that the activation

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Gibbs free energies in the gas phase and in solution are almost the same, with ∆Gq ) 98.9 kJ/mol and ∆Gqsol ) 99.8 kJ/mol for path A2-2, and ∆Gq ) 95.1 kJ/mol and ∆Gqsol ) 95.7 kJ/ mol for path B2-2. This is likely due to the fact that the main solvent contribution has already been taken into account by the explicit water molecules. In addition, the differences of the activation barrier between the CdC bond and the CdN bond addition decrease from one-water to five-water hydration, with only 4.1 kJ/mol for the five-water hydration, implying that these two kinds of additions, across the CdC and CdN bonds, are competitive when more explicit water molecules are involved in the hydration. Still, the latter is slightly preferred 4. Conclusion A comprehensive study on the hydration mechanism of ketenimine with up to five water molecules has been carried out by ab initio methods. In addition, the effects of water bulk solvent are taken into account. The main conclusions from the present paper can be summarized as follows: (1) In all the hydration pathways of ketenimine in the presence one to five water molecules, the first step involving nucleophilic addition of water is always rate-determining. Specifically, the addition across the CdN bond is more favorable than addition across the CdC bond, and they become competitive processes with more water molecules involved in the hydration, which may result from the fact that the terminal nitrogen atom is a better hydrogen acceptor. (2) The hydration of CH2dCdNH can be assisted by proton relay or cooperative effect, and these two effects is comparable and neither one can be ignored. Our results suggest that Lewis and Glaser’s model is a better fit for the ketenimine case in the existing mechanisms for hydration of cumulenes; that is, it is necessary to consider the cooperative role of the solvent molecule(s) in the nonreactive region. The catalytic effect of the water molecule(s) in the hydration can be explained by the structural and electronic features of rate-determining TSs. (3) In the gas-phase, the five-water hydration of CH2dCdNH with the lowest MP2/6-311++G** rate-determining energy barrier, 98.9 kJ/mol for the addition of the CdC bond and 95.1 kJ/mol for the addition of the CdN bond, involves dual eightmembered ring TSs, where two explicit water molecules are involved in the eight-membered ring TS across the CdC or CdN bond, with two other water molecules near the nonreactive forming a hydrogen-bonded eight-membered ring. (4) There is an enhanced cooperative effect for the hydration of carbodiimide due to the stronger hydrogen bonding between water molecule(s) and nonreactive nitrogen atom in HNCNH moiety in the rate-determining TS. (5) Compared with the gas-phase results, the barrier differences are smaller for the hydration of CH2dCdNH with COSMO treatment, indicating that the bulk solvent does not modify the reaction barriers in a significant way. Acknowledgment. This work is supported by a Strategic Grant (Project No. 7002334) awarded to N.B.W. from the City University of Hong Kong. Supporting Information Available: MP2/6-311++G** optimized structures of all species reported in this paper and the absolute Gibbs free energies (kJ/mol) with and without COSMO correction. This material is available free of charge via Internet at http://pubs.acs.org. References and Notes (1) Staudinger, H.; Hauser, E. HelV. Chim. Acta 1921, 4, 887.

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