Concerted Proton-Transfer Mechanism and Solvation Effects in the

Sep 25, 2007 - A Theoretical Study of the Formation of the Aminoacetonitrile Precursor of Glycine on Icy Grain Mantles in the Interstellar Medium. Den...
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J. Phys. Chem. C 2007, 111, 15026-15033

Concerted Proton-Transfer Mechanism and Solvation Effects in the HNC/HCN Isomerization on the Surface of Icy Grain Mantles in the Interstellar Medium Denise M. Koch,† Ce´ line Toubin,‡,§ Sichuan Xu,†,‡ Gilles H. Peslherbe,*,‡ and James T. Hynes*,†,| De´ partement de Chimie, UMR 8640 Pasteur, Ecole Normale Supe´ rieure, 24 rue Lhomond, Paris, F-75005 France, Centre for Research in Molecular Modeling and Department of Chemistry & Biochemistry, Concordia UniVersity, 7141 Sherbrooke Street West, Montreal, Quebec, Canada H4B 1R6, Laboratoire de Physique des Lasers, des Atomes et des Mole´ cules, UniVersite´ de Lille I, Cite´ Scientifique, 59655 VilleneuVe d’Ascq Cedex, France, and Department of Chemistry and Biochemistry, UniVersity of Colorado, Boulder, Colorado 80309-0215 ReceiVed: August 3, 2007

In order to better understand the isomerization between HNC and HCN on icy grain (or comet nuclei) surfaces in the interstellar medium in connection with a Strecker synthesis route to glycine, B3LYP/6-31+G(d,p) calculations have been carried out on the mechanisms of direct proton transfer (PT), where water molecules play a purely solvating role, and indirect PT, where water molecules participate in a proton relay mechanism. In the direct PT mechanism, a rather high-energy barrier exists for isomerization of HNC to HCN. In the much more important indirect mechanism, a concerted PT process is possible for isomerization in the presence of several water molecules. The calculations show that three water molecules bound to HNC and HCN give rise to a ring reaction significantly favoring the isomerization, a mechanism previously found for this reaction by Gardebien and Sevin (J. Phys. Chem. A 2003, 107, 3925). Further quite important solvation effects are included in the present work by addition of explicit solvating water molecules, and by a comparison with Polarizable Continuum Model (PCM) solvation. The final calculated free-energy barrier at 50 K is 3.4 kcal/ mol for the isomerization of HNC to HCN with three water molecules in a ring acting as a bridge for concerted PT and seven explicit solvating water molecules; PCM solvation of this entire system leads to a further free-energy barrier reduction of 0.8 kcal/mol. The back isomerization of HCN to HNC, however, is unlikely, with an estimated free-energy barrier of 9.5 kcal/mol at 50 K. These results imply that, on icy surfaces in the interstellar medium, the isomerization of HNC to HCN occurs relatively easily, and the implications for the Strecker synthesis of glycine are discussed.

1. Introduction The HCN f HNC system has been regarded as a model for unimolecular reactions1 and has therefore received wide attention.1-9 This system is also of considerable interest in the interstellar medium (ISM).9 Cometary hydrogen cyanide (HCN) was first observed by Huebner et al. in comet Kohoutek.6 Irvine et al. observed hydrogen isocyanide (HNC) in comet Hyakutake and determined the HNC/HCN ratio to be between 0.06 and 0.15.7 In cold interstellar clouds, HNC has an abundance which can approach or even exceed that of HCN;7,8 in contrast, the abundance is very small in hot molecular clouds.10 A number of gas-phase mechanisms have been proposed to account for the observed abundance ratios of HCN and HNC, depending on the temperature of the molecular clouds.3,5,8,11 HCN and HNC are associated with the formation of amino acid precursors through a possible Strecker synthesis route in the ISM.3,9,12-14 In a separate theoretical study, we have provided evidence for a favorable reaction pathway leading to aminoacetonitrile (H2NCH2CN) formation from the reaction of * Author to whom correspondence should be addressed. † Ecole Normale Supe ´ rieure. ‡ Concordia University. § Universite ´ de Lille I. | University of Colorado.

CH2NH with HNC, and not with HCN, at the icy surface of a cold interstellar grain or comet nuclei.14 This is the penultimate step for a Strecker synthesis route to glycine, the simplest amino acid. It was also argued that the aminoacetonitrile formation from HNC will be favored over the isomerization of HNC to the unfavorable HCN reactant, provided that the CH2NH and HNC molecules are nearest neighbors at the surface.14 When they are not nearest neighbors at the icy interstellar grain surface, however, it is possible that HNC converts relatively easily and effectively irreversibly to HCN. In the limiting case, a successful reaction of HNC with CH2NH would require arrival of a HNC molecule from the gas phase in the immediate vicinity of a CH2NH molecule, since any HNC initially at some distance from a CH2NH would likely isomerize to HCN before reaching the CH2NH via diffusion. Gardebien and Sevin have previously reported the reaction pathway of HNC isomerizing to HCN in contact with one to four water molecules modeling the surface of an interstellar grain.4 These authors found a one-step path involving a proton relay through a water chain, a mechanism analogous to that found for heterogeneous reactions on stratospheric ice15,16 as well as for the penultimate step of the Strecker synthesis route for glycine.14 However, the energy barrier for the HNC to HCN conversion was found to be rather high in the low-temperature ISM conditions (∼50 K), e.g. ∼8 kcal/mol in the presence of

10.1021/jp076220h CCC: $37.00 © 2007 American Chemical Society Published on Web 09/25/2007

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Figure 1. Optimized geometries of the stationary points for HNC/HCN isomerization via direct proton transfer with 0, 1, 2 water molecules using B3LYP/6-31+G(d,p). Interatomic distances in Å. The color scheme for the atoms is blue for N, green for C, red for O, and white for H.

TABLE 1: Thermodynamic Properties of the Stationary Points along HNC/HCN Isomerization via Direct Proton-Transfer Mechanisma

HNC TS‚HNC HCN HNC‚H2O TS‚H2O HCN‚H2O HNC‚2H2O TS‚2H2O HCN‚2H2O

∆E (ZPE)

∆G50K

∆G50K + ∆Gsolv (PCM)b

0.0 31.4 -13.4 0.0 31.6 -10.9 0.0 32.1 -10.4

0.0 30.6 -13.2 0.0 31.3 -10.9 0.0 32.1 -10.5

0.0 (-12.1) 36.2 (-6.5) -9.3 (-8.2) 0.0 (-17.2) 32.5 (-16.0) -9.3 (-15.6) 0.0 (-23.6) 34.4 (-21.3) -8.7 (-21.8)

a Relative properties with respect to HNC, including ZPE, in kcal/ mol. All calculations were performed with B3LYP/6-31+G(d,p). Refer to Figure 1 for molecular structures. b ∆Gsolv (PCM), PCM solvation free energy in parenthesis.

four water molecules.4 A detailed study of the isomerization of HNC to HCN including further important solvation effects is undertaken here to more fully characterize the isomerization, especially in connection with the issues of the HNC-CH2NH reaction discussed above. The outline of the remainder of this article is as follows. After a discussion of computational issues in section 2, a direct protontransfer route for the HNC isomerization is discussed in section 3, in which additional water molecules play a purely solvating, rather than a chemical role. Section 4 addresses an indirect proton transfer, or proton relay mechanism, where water molecules form a bridge connecting both ends of the HNC, providing a proton-transfer ring to catalytically effect the isomerization. The proton relay ring system is further solvated with explicit water molecules in section 5, and further solvation of this entire system via an implicit solvation model is examined in section 6. Section 7 concludes with a discussion of the implication of the results for the Strecker synthesis route to glycine. 2. Computational Details All calculations were performed with Becke’s three-parameter hybrid functional17 and the exchange functional of Lee, Yang,

and Parr (B3LYP),18 combined with the 6-31+G(d,p) basis set.19 All computations were performed with the GAMESS program package.20 The stationary point geometries were fully optimized and characterized as minima (no imaginary frequencies) or transition states by a frequency calculation and normal-mode analysis. Intrinsic reaction coordinate (IRC) calculations were performed with the standard step size of 10 (in units of 0.01 amu1/2‚Bohr). Zero point energies (ZPEs) were computed from the calculated harmonic frequencies, and thermodynamic data were evaluated within the rigid rotor-harmonic oscillator approximation. In the present work, several explicit water molecules have been included in a ring, which serve as a bridge for proton transfer, as was done by Gardebien and Sevin,4 as well as in our work on the HNC-CH2NH reaction14 and in earlier work on heterogeneous stratospheric reactions.15,16 The water ring and HNC constitute what is referred to as the “core reaction system” (CRS). Explicit “external” water molecules were then added around the CRS; these are not directly involved in the proton transfer but rather play a solvation role. This combined system is meant to model small icy grain particles as potential catalysts for the HNC isomerization.13 In determining the position of the solvating waters around the reaction core, the position of the atoms in the CRS was frozen, and four external solvating water molecules were fully optimized for the reactant, transition state, and product separately. The positions of these four external solvating waters were found to shift significantly (between 1 Å and 4 Å) along the reaction pathway, a phenomenon which would not be expected for water molecules frozen in the amorphous ice lattice of an icy grain mantle. In order to eliminate this unphysical behavior, the structures of the reaction species with the optimized positions of the four solvating water molecules were superimposed, with the carbon atom serving as a reference to superimpose the solvated structures (cf. Figure 5). This procedure resulted in 3 superimposed structures and therefore 12 water molecules around the superimposed core reaction systems. However, this procedure generated a number of solvating water molecules in these superimposed structures which had very similar positions, that is waters that were on top of each other with less than 0.5 Å difference in their oxygen

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Figure 2. Optimized geometries of the stationary points for HNC/HCN isomerization with 1 and 2 water molecules using B3LYP/6-31+G(d,p) via proton relay. Interatomic distances and bond angles in Å and degrees, respectively. The color scheme for the atoms is blue for N, green for C, red for O, and white for H.

TABLE 2: Mulliken Charge Distributions for Stationary Points along HNC/HCN Isomerization via Direct Proton Transfera H C N a

HNC

TS

HCN

HNC‚H2O

TS‚H2O

HCN‚H2O

HNC‚2H2O

TS‚2H2O

HCN‚2H2O

0.31 -0.06 -0.25

0.24 -0.11 -0.13

0.23 0.11 -0.34

0.41 -0.09 -0.32

0.29 -0.17 -0.19

0.31 0.14 -0.45

0.39 -0.03 -0.36

0.36 -0.15 -0.21

0.31 0.13 -0.44

Calculated with B3LYP/6-31+G(d,p). Refer to Figure 1 for molecular structures.

atom locations, an obvious physical impossibility due to repulsive forces. Accordingly, all but one of these waters were removed, such that 7 external solvating water molecules were retained for each reaction species. None of these 7 remaining waters move more than 0.1 Å in the reaction pathway, thus providing the desired mimic of the icy grain mantle surface environment. Since the external solvating waters did not move significantly during optimization, static single-point energy calculations for each reaction core species with the 7 external solvating water molecules were performed. The thermodynamic correction to the 0 K relative energies for the solvated CRS was considered to be the same as that of the CRS without explicit external solvation, since the position of the solvating water molecules is kept fixed in the calculations. Finally, external solvation has also been considered via calculations using the Polarizable Continuum Model (PCM).20 3. Direct Proton-Transfer Mechanism for HNC/HCN Isomerization Figure 1 shows the optimized geometries of the minimumenergy structures and transition states for the isomerization reaction of HNC to HCN (via a direct proton-transfer route, defined more precisely below) with zero, one, and two water molecules. In the three transition states shown, the H originally associated with HNC or HCN is situated approximately halfway toward complete transfer, slightly farther from N than from C. Because the proton in HNC is directly transferred to the C of the CN moiety to produce HCN without first being transferred to a water molecule, we term such a mechanism direct proton transfer, following ref 11. Conversely, isomerization pathways involving proton transfer to a water molecule will be termed a proton relay mechanism or indirect proton-transfer mechanism, again following the terminology of ref 11. In the former, direct, mechanism, water molecules play a solvation role, while in the latter, one or more waters serve as proton acceptors and donors.

A summary of the calculated thermodynamic data and Mulliken charges for the direct mechanism is presented in Tables 1 and 2. The HNC f HCN isomerization barrier ∆Eq (∼31 kcal/mol), which corresponds to the energy of the transition state TS‚nH2O (n ) 0, 1, 2) with respect to HNC‚nH2O, does not vary significantly when increasing the number of water molecules. The free-energy barrier at 50 K, ∆Gq50K, exhibits variations similar to that of ∆Eq. The results of additional water solvation via the dielectric continuum PCM model20 [∆G + ∆Gsolv(PCM)] at 50 K are listed in the last column of Table 1, while the Mulliken charges carried by the H, C, N atoms in the various intermediates are listed in Table 2. Inspection of the tables indicate that, as expected, the solvation free energy [∆Gsolv(PCM)] is directly related to the atomic charges; more precisely, the larger the charge polarization in the HNC/HCN subsystem, the larger is ∆Gsolv(PCM). The free-energy barriers at 50 K with PCM solvation for the three (n ) 0, 1, 2) direct proton-transfer pathways for HNC/HCN isomerization are about 34 ( 2 kcal/ mol. These results indicate that HNC/HCN isomerization via the direct proton-transfer mechanism is kinetically unfavorable because of the high free-energy barriers, even when considering solvation with a dielectric continuum PCM model. 4. Concerted Proton Relay Mechanism for HNC/HCN Isomerization Another possible mechanism for HNC/HCN isomerization is through proton relay.4,15,16 In this mechanism, with a single water molecule, the proton from HNC will not transfer directly to HCN, but will instead transfer to the water molecule that will in turn transfer it back to the CN moiety. With several water molecules, a full proton relay mechanism becomes possible, in which water molecules act not only as both proton acceptors and donors but as a bridge through which the proton transfers from one molecule to the other, possibly in a concerted way.

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Figure 3. Optimized geometries of the stationary points for HNC/HCN isomerization via proton relay with 3 and 4 water molecules, calculated with B3LYP/6-31+G(d,p). The color scheme for the atoms is blue for N, green for C, red for O, and white for H.

TABLE 3: Thermodynamic Properties of the Stationary Points along HNC/HCN Isomerization via Proton Relaya HNC‚H2O TS‚H2O HCN‚H2O HNC‚2H2O TS‚2H2O HCN‚2H2O HNC‚3H2O TS‚3H2O HCN‚3H2O HNC‚4H2O TS‚4H2O HCN‚4H2O

∆E (ZPE)

∆G50K

0.0 40.0 -10.9 0.0 17.7 -10.1 0.0 10.5 -9.9 0.0 9.9 -9.0

0.0 40.0 -10.9 0.0 17.8 -10.1 0.0 10.6 -9.9 0.0 9.9 -9.1

a Relative properties with respect to HNC‚nH O, including ZPE, in 2 kcal/mol. All calculations were performed with B3LYP/6-31+G(d,p). Refer to Figures 2 and 3 for molecular structures.

The optimized geometries of the stationary points along the HNC/HCN isomerization pathway for a one-water and twowater proton relay mechanism are shown in Figure 2, while those involving three and four waters are shown in Figure 3. Since Gardebien and Sevin4 have already reported results for HCN/HNC isomerization with up to four water molecules in a ring, we will only briefly report our results for these cases, whose energetics and thermodynamics are collected in Table

Figure 4. Changes of the reaction energy barrier (∆E) for HNC‚nH2O/ HCN‚nH2O isomerization via proton relay as a function of the number of water molecules n involved in the ring, calculated with B3LYP/631+G(d,p).

3. Figure 4 depicts the energy difference between the transition state and HNC‚nH2O, n being the number of water molecules involved in the ring; the HNC/HCN isomerization barriers decrease significantly until n ) 3 (∆Eq ∼ 10 kcal/mol) and exhibit no significant variation from n ) 3 to n ) 4.

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Koch et al. TABLE 5: Thermodynamic Properties of the Stationary Points along HNC/HCN Isomerization via Proton Relay with Explicit Solvent ∆E ∆G50K q (ZPE) δ∆E b ∆G50K δ ∆Gq50Kc + ∆Gsolv(PCM) HNC‚3H2O TS‚3H2O HCN‚3H2O HNC‚3H2O‚(H2O)7 TS‚3H2O‚(H2O)7 HCN‚3H2O‚(H2O)7

0.0 10.5 -9.9 0.0 3.3 -9.9

0.0 -7.2

0.0 10.6 -9.9 0.0 3.4 -9.9

0.0 -7.2

0.0 7.5 -8.2 0.0 2.6 -6.9

a Relative properties with respect to HNC‚3H2Oand HNC‚3H2O‚(H2O)7, including ZPE, in kcal/mol. All calculations were performed with B3LYP/6-31+g(d,p). b δ∆Eq ) ∆E(TS‚3H2O‚(H2O)7) - ∆E(TS‚3H2O). c δ∆Gq50K ) ∆G(TS‚3H2O‚(H2O)7) - ∆G(TS‚3H2O).

except for the ring with four waters, where the two methods agree to within 0.2 kcal/mol. This level of agreement is encouraging and suggests that the model chemistry used herein describes the HNC/HCN isomerization reaction reasonably well. We will next turn to consideration of solvation by additional water molecules of the reaction proton relay ring system, focusing on the case of a core reaction system (CRS) with three water molecules. Similar results are obtained for a CRS ring containing four water molecules. 5. Explicit External Solvation Effects in the Proton Relay Mechanism for HNC/HCN Isomerization

Figure 5. Optimized geometries of the stationary points for HNC/ HCN isomerization with three H2O in the proton relay ring and seven H2O as external solvent. The color scheme for the atoms is blue for N, green for C, red for O, and white for H. The hydrogen bonds between the core reaction system and the external solvating waters (shaded molecules) are shown as dotted lines.

TABLE 4: Comparison of Relative Energies Calculated by Gardebien and Sevin4 and the Present Calculationsa HCN‚2H2O TS‚2H2O HNC‚2H2O HCN‚3H2O TS‚3H2O HNC‚3H2O HCN‚4H2O TS‚4H2O HNC‚4H2O

ref 4b

present workc

0.0 29.7 (1.29 eV) 12.7 (0.55 eV) 0.0 23.0 (1.0 eV) 11.7 (0.51 eV) 0.0 19.1 (0.83 eV) 11.0 (0.48 eV)

0.0 27.7 (1.20 eV) 10.1 (0.44 eV) 0.0 20.4 (0.89 eV) 9.9 (0.43 eV) 0.0 18.9 (0.82 eV) 9.0 (0.39 eV)

a Relative properties with respect to HCN‚nH O, including ZPE, in 2 kcal/mol. b Calculated with CCSD(T)/6-311+G**//MP2/6-311+G**. c Calculated with B3LYP/6-31+G(d,p).

We compare our results, in Table 4, to those of Gardebien and Sevin4 for HCN to HNC isomerization with two, three and four waters in the ring, obtained with Coupled-Cluster theory including Single, Double, and Triple excitations21 for geometries that were optimized with second order Mo¨ller-Plesset perturbation theory22 and a 6-311+G** basis set23 (CCSD(T)/6311+G**//MP2/6-311+G**). These higher-level but more timeconsuming calculations yield energy barriers ∼2 kcal/mol higher than those of the present B3LYP/6-31+G(d,p) calculations,

External solvation effects for the HNC/HCN isomerization CRS can be modeled in two different ways: Via explicit water molecules and Via an implicit solvent description using the Polarizable Continuum Model (PCM). Because interstellar icy grain mantles are very different media from the solution environment modeled by PCM, we will focus in this section on the solvation effects due to explicit water molecules and differ a discussion of PCM solvation to the next section. Figure 5 shows the geometries of the minimum-energy structures and transition state with seven water molecules solvating the core reaction system. Solvating water molecules were placed around the N of the CN moiety, as well as around the dangling Hs of the water molecules within the core reaction system of the reactant, transition state, and product. Since the relative position of the water molecules within the CRS changes as one proceeds from the reactant to the transition state, and then to the product, which would be inconsistent with a cold, amorphous ice lattice, the positions of the external solvating water molecules were chosen such that the CRS is optimally solvated by fixed water molecules for the reactant, transition state, and product (see section 2). Table 5 lists the relative thermodynamic properties of the minimum-energy structures and transition state involved in the HNC/HCN isomerization reaction with three waters in the proton relay ring and external solvation. The addition of seven external water molecules [HNC‚3H2O‚(H2O)7] reduces the isomerization energy barrier and free-energy barrier at 50 K by 7.2 kcal/mol. Consequently, for isomerization of HNC‚3H2O‚ (H2O)7, the 50 K free-energy barrier is only 3.4 kcal/mol, compared to 10.6 kcal/mol for HNC‚3H2O without external solvation. 6. Solvation Models: Explicit Solvation vs PCM The Polarizable Continuum Model implemented in GAMESS is a popular and useful model for describing chemical systems in solution. In the ISM, however, the temperature is very low, in the range of 10-100 K, and it is unclear whether the PCM

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Figure 6. Relative reaction free energy at 50 K, in kcal/mol, for the HNC/HCN isomerization via proton relay, with three H2O in the ring and the same core reaction system with 7 external solvent molecules.

continuum perspective is appropriate. In this section, this issue is briefly examined via a comparison of the results of the continuum model and solvation from explicit water molecules. PCM is also used to estimate further solvation effects on the HNC‚3H2O‚(H2O)7 system. Table 5 lists the PCM solvation contributions for the core reaction system HNC‚3H2O and for the explicitly solvated HNC‚ 3H2O‚(H2O)7 system at a temperature of 50 K. PCM solvation predicts an isomerization free-energy barrier reduction at 50 K from 10.6 to 7.5 kcal/mol, i.e., a net PCM barrier change of -3.1 kcal/mol for the core reaction system HNC‚3H2O. This is to be compared with explicit solvation by seven waters of the core ring system, where the 50 K free-energy barrier drops from 10.6 to 3.4 kcal/mol, i.e., a net barrier change of -7.2 kcal/mol, which is clearly a much more significant solvation effect than predicted with PCM. As for PCM solvation of the larger HNC‚3H2O‚(H2O)7 system, it results in a reduction of the isomerization free-energy barrier from 3.4 kcal/mol to 2.6 kcal/mol, i.e., a rather small change of -0.8 kcal/mol. These results suggest that, for the isomerization of HNC‚3H2O, solvation has been largely accomplished via explicit external solvation of the core reaction system, and certainly more completely than by an exclusive use of PCM. Figure 6 summarizes our results by displaying the energy and free-energy changes along the HNC/HCN isomerization pathways in the gas phase, with three waters in the proton relay ring (HNC‚3H2O) and finally with the latter system surrounded by seven external solvating water molecules [HNC‚3H2O‚ (H2O)7]. The concerted proton-transfer mechanism induced by the ring water molecules reduces the isomerization energy and free-energy barriers at 50 K by 20.9 kcal/mol and 20.0 kcal/ mol, respectively. Further solvation by explicit water molecules reduces the energy and free-energy barrier at 50 K by an additional 7.2 kcal/mol. As a result, the HNC‚3H2O‚(H2O)7 isomerization free-energy barrier at 50 K is thus 3.4 kcal/mol (cf. Table 5), which is reduced to 2.6 kcal/mol with further PCM solvation. The HNC/HCN isomerization is exothermic by 13.4

kcal/mol in the gas phase and by 9.9 kcal/mol on a model ice surface (cf. Table 5). The low free-energy barrier of only 3.4 kcal/mol for HNC/ HCN isomerization with ten waters (three in the ring and seven external) indicates that the isomerization is feasible on very cold, amorphous ice surfaces. It should be effectively irreversible, since the reverse isomerization from HCN to HNC with ten waters is endothermic by 9.9 kcal/mol, with an isomerization barrier of around 13 kcal/mol; adding PCM solvation for HNC‚ 3H2O‚(H2O)7 does not paint a much different picture, as the reaction is still endothermic by 6.9 kcal/mol, with an isomerization barrier of 2.6 kcal/mol at 50 K (cf. Table 5). Since this PCM barrier reduction is very likely to be significantly overestimated due both to the limitations of PCM under ISM conditions and to an inappropriate solvation arising from above the surface, we consider it no further. 7. Reaction Rate It is of interest to compare the HNC f HCN isomerization reaction rate to the diffusion rate of HNC on ice surfaces at the low temperatures typical of the ISM. As discussed in the Introduction, we have found14 that when HNC and CH2NH are nearest neighbors, HNC will react with CH2NH to produce aminoacetonitrile more rapidly than it would isomerize to the nonreactive HCN form. If an HNC molecule located on the ice surface can diffuse to a CH2NH molecule before it isomerizes to HCN, then successful reaction is also possible. If an HNC cannot diffuse rapidly enough, then only those HNC molecules which land on the surface next to a CH2NH would produce aminoacetonitrile. As will now be seen, we cannot definitively say which of these scenarios applies, but we can at least give the question some perspective, which suggests that HNC diffusion is likely to be so slow that HNC is required to be a nearest neighbor of CH2NH for successful reaction to occur. Based on Transition State Theory,24 the reaction rate constant k can be evaluated as k ) (kbT/h)exp(-∆Gq50K/RT), where kb is the Boltzmann constant, T is the temperature, h is the Plank

15032 J. Phys. Chem. C, Vol. 111, No. 41, 2007 constant, and R is the molar gas constant. The 50 K rate constant for the HNC/HCN isomerization reaction at the ice surface is evaluated as 1.4 × 10-3 s-1 for ∆Gq50K ) 3.4 kcal/mol, the activation free energy of the surface reaction (without PCM solvation). This corresponds to a reaction lifetime of 714 s. To the best of our knowledge, the surface diffusion coefficients for HNC (or even HCN) in ice have not been reported.25 Devlin and Buch have classified ice adsorbates into three categories (weak, intermediate, and strong) according to the extent that the adsorbate will disrupt the surface, subsurface, and bulk ice.26 HCN (and thus probably HNC) is assigned26 to the intermediate class of adsorbates, which cause some restructuring of the surface of ice, but do not form hydrates and penetrate rapidly within the bulk of ice, as is the case for strong adsorbates such as HCl. No information on the surface diffusion of HCN (or HNC) is provided in ref 24, but sulfur dioxide (SO2) is also a member of the intermediate adsorbate class and its diffusion behavior may provide a guide for that of HNC. Livingston et al., while not being able to measure the surface diffusion coefficient of SO2, have provided an upper limit for this coefficient Ds as 4 × 10-11 cm2/s at ∼130 K.27 Based on this Ds value (assumed to apply to HNC), the mean distance traveled by the molecule is ∼1260 Å in 1 s. Unfortunately, the temperature dependence of Ds is unknown, so the appropriate reduction of this distance at ∼50 K is unknown. However, even with an Arrhenius activation energy factor for Ds taken as low as 2 kcal/mol, an HNC molecule would only diffuse ∼0.14 Å in the HNC lifetime of 714 s. This strongly suggests that an HNC molecule must initially be, or be close to being, a near neighbor of an CH2NH for successful production of aminoacetonitrile to occur. 8. Concluding Remarks In this article, B3LYP/6-31+G(d,p) electronic structure calculations were performed of various aspects of HNC/HCN isomerization in the presence of water molecules, especially in connection with the reaction on icy grain surfaces in the interstellar medium (ISM). In agreement with earlier work by Gardebien and Sevin4 with CCSD(T)/6-311+G**//MP2/6311+G**, it is found that the isomerization can proceed with considerable barrier lowering compared to the gas phase via a concerted proton transfer, from the nitrogen of the CN moiety to the carbon, through a bridge of several water molecules. Such a proton relay cycle has also been found in our separate study14 of the penultimate step of the Strecker synthesis route to glycine in the ISM and in earlier work on heterogeneous reactions on stratospheric ice.15,16 Further solvation of the HNC‚3H2O core reaction system by seven waters was shown to lead to further considerable reduction in the isomerization barrier: the freeenergy barrier at 50 K is 3.4 kcal/mol, with a slight further decrease to 2.6 kcal/mol with additional inclusion of implicit solvation with the Polarizable Continuum Model.20 The conclusion of the present work is that isomerization of HNC to HCN is feasible, though not rapid, on an ice surface at 50 K.28 (It is conceivable that the reaction is further accelerated by quantum proton tunneling, but this requires further investigation).29 However, even with an estimated 50 K HNC reactive lifetime of 714 s, very approximate estimates of the surface diffusion constant of HNC on ice suggest that the reaction of HNC and CH2NH in the penultimate step of the Strecker synthesis route to glycine discussed in the Introduction will probably only occur at the surface of icy grain mantles (or comet nuclei) if the two reaction partners are, or are close to being, initially nearest neighbors.

Koch et al. Acknowledgment. This work was supported by grants from the K.C. Wong Education Foundation (Hong Kong) at Ecole Normale Supe´rieure (ENS), the French CNRS-INSU Programme PCMI (J.T.H.), the U.S. National Science Foundation (CHE0417570, J.T.H.) and the Natural Sciences and Engineering Research Council (NSERC) of Canada (G.H.P.). The calculations were performed at ENS, the Re´seau Que´becois de Calcul Haute Performance (RQCHP), and at the Centre for Research in Molecular Modeling (CERMM), which was established with the financial support of the Concordia University Faculty of Arts & Science, the Ministe`re de l’EÄ ducation du Que´bec (MEQ), and the Canada Foundation for Innovation (CFI). G.H.P. holds a Concordia University Research Chair. D.M.K. holds a Chateaubriand postdoctoral fellowship from EGIDE (France) and an NSERC postdoctoral fellowship. References and Notes (1) Defrees, D. J.; Loew, G. H.; McLean, A. D. Astrophys. J. 1982, 257, 376. Pearson, P. K., III; Schaefer, H. F., III; Wahlgren, U. J. Chem. Phys. 1975, 65, 350. (2) Allen, T. L.; Goddard, J. D., III; Schaefer, H. F., III. J. Chem. Phys. 1980, 73, 3255. Aoki, W.; Tsuji, T.; Ohnaka, K. Astron. Astrophys. 1998, 340, 222; Bentley, J. A.; Bowman, J. M.; Gazdy, B.; Lee, T. J.; Dateo, C. E. Chem. Phys. Lett. 1992, 198, 563. Bieging, J. H. Astrophys. J. 2001, 549, L125. Bieging, J. H.; Shaked, S.; Gensheimer, P. D. Astrophys. J. 2000, 543, 897. Bowman, J. M.; Gazdy, B. J. Phys. Chem. A 1997, 101, 6384. Bowman, J. M.; Gazdy, B.; Bentley, J. A.; Lee, T. J.; Dateo, C. E. J. Chem. Phys. 1993, 99, 308. Gardebien, F.; Sevin, A. J. Phys. Chem. A 2003, 107, 3935. Gazdy, B.; Musaev, D. G.; Bowman, J. M.; Morokuma, K. Chem. Phys. Lett. 1995, 237, 27. Harris, G. J.; Polyansky, O. L.; Tennyson, J. Spectrochim. Acta A 2002, 58, 673. Hatchell, J.; Millar, T. J.; Rodgers, S. D. Astron. Astrophys. 1998, 332, 695. Hidayat, T.; Marten, A.; Bezard, B.; Gautier, D.; Owen, T.; Matthews, H. E.; Paubert, G. Icarus 1997, 126, 170. Ishida, K.; Morokuma, K.; Komornicki, A. J. Chem. Phys. 1977, 66, 2153. Kumeda, Y.; Minami, Y.; Takano, K.; Taketsugu, T.; Tsuneo, H. J. Mol. Struct. (THEOCHEM) 1999, 458, 285. Lee, T. J.; Rendell, A. P. Chem. Phys. Lett. 1991, 177, 491. Peric, M.; Mladenovic, M.; Peyerimhoff, S. D.; Buenker, R. J. Chem. Phys. 1984, 86, 85. Rao, V. S.; Vigjau, A.; Chandra, A. K. Can. J. Chem. 1996, 74, 1072. Redmon, L. T.; G. D. P., III; Bartlett, R. J. J. Chem. Phys. 1980, 72, 986. Rivelino, R.; Canuto, S. J. Phys. Chem. A 2001, 105, 11260. Rodgers, S. D.; Charnley, S. B. Astrophys. J. 1998, 501, L227. Shiba, Y.; Hirano, T.; Nagashima, U.; Ishii, K. J. Chem. Phys. 1998, 108, 698. Walch, S. P.; Bakes, E. L. O. Chem. Phys. Lett. 2001, 346, 267. Wooten, A.; N. J. E., II; Snell, R.; Bout, P. V. Astrophys. J. 1978, 225, L143. (3) Ehrenfreund, P.; Charnley, S. B. From Astrochemistry to Astrobiology; ESA-SP-496: Frascati, 2001. (4) Gardebien, F.; Sevin, A. J. Phys. Chem. A 2003, 107, 3925. (5) Hirota, T.; Yamamoto, S.; Mikami, H.; Ohishi, M. Astrophys. J. 1998, 503, 717; Pichierri, F. Chem. Phys. Lett. 2002, 353, 383. Tachikawa, H.; Iyama, T.; Fukuzumi, T. Astron. Astrophys. 2003, 391, 1. Talbi, D.; Ellinger, Y. Chem. Phys. Lett. 1996, 263, 385. Talbi, D.; Ellinger, Y. Astron. Astrophys. 1996, 314, 688. Talbi, D.; Ellinger, Y. Chem. Phys. Lett. 1998, 288, 155. (6) Huebner, W. F.; Snyder, L. E.; Buhl, D. Icarus 1974, 23, 580. (7) Irvine, W. M.; Bergin, E. A.; Dickens, J. E.; Jewitt, D.; Lovell, A. J.; Matthews, H. E.; Schloerb, F. P.; Senay, M. Nature 1998, 393, 547. Irvine, W. M.; Bockelee-Morvan, D.; Lis, D. C.; Matthews, H. E.; Biver, N.; Crovisier, J.; Davies, J. K.; Dent, W. R. F.; Gautier, D.; Godfrey, P. D.; Keene, J.; Lovell, A. J.; Owen, T. C.; Phillips, T. G.; Rauer, H.; Schloerb, F. P.; Senay, M.; Young, K. Nature 1996, 383, 418. (8) Irvine, W. M.; Schloerb, F. P. Astrophys. J. 1984, 282. Schilke, P.; Walmsley, C. M.; Forets, G. P. d.; Roueff, E.; Flower, D. R.; Guilloteau, S. Astron. Astrophys. 1992, 256, 595. (9) Woon, D. E. Icarus 2001, 149, 277. (10) Goldsmith, P. F.; D., L. W.; J., E.; Irvine, W. M.; Kollberg, E. Astrophys. J. 1981, 249, 524. (11) Charnley, S. B.; Ehrenfreund, P.; Kuan, Y.-J. Spectrochim. Acta A 2001, 57, 685-704. Winnewisser, G.; Herbst, E. Rep. Prog. Phys. 1993, 56, 1209. (12) Allamandola, L. J.; Bernstein, M. P.; Sandford, S. A.; Walker, R. L. Space Sci. ReV. 1999, 90, 219. d’Hendecourt, L.; Dartois, E. Spectrochim. Acta A 2001, 57, 669. Ehrenfreund, P.; Charnley, S. B. Ann. ReV. Astron. Astrophys. 2000, 38, 427. Ehrenfreund, P.; Dartois, E.; Demyk, K.; D’Hendecourt, L. Astron. Astrophys. 1998, 339, L17. Ehrenfreund, P.; Fraser, H. J. Solid State Astrochemistry; Kluwer Academic Press: Dordrecht, The Netherlands, 2002; Van Dishoeck, E. F. Faraday Discuss. 1998, 109, 31.

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