Stepwise Association of Hydrogen Cyanide and ... - ACS Publications

Jun 6, 2012 - Isaac K. Attah , Ahmed M. Hamid , Michael Meot-Ner (Mautner) , and M. S. El-Shall , Saadullah G. Aziz and Abdulrahman O. Alyoubi...
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Stepwise Association of Hydrogen Cyanide and Acetonitrile with the Benzene Radical Cation: Structures and Binding Energies of (C6H6•+) (HCN)n, n = 1−6, and (C6H6•+)(CH3CN)n, n = 1−4, Clusters Ahmed M. Hamid, Abdel-Rahman Soliman, and M. Samy El-Shall* Department of Chemistry, Virginia Commonwealth University, Richmond, Virginia 23284, United States ABSTRACT: Equilibrium thermochemical measurements using the ion mobility drift cell technique have been utilized to investigate the binding energies and entropy changes associated with the stepwise association of HCN and CH3CN molecules with the benzene radical cation in the C6H6•+(HCN)n and C6H6•+(CH3CN)n clusters with n = 1− 6 and 1−4, respectively. The binding energy of CH3CN to the benzene cation (14 kcal/mol) is stronger than that of HCN (9 kcal/mol) mostly due to a stronger ion−dipole interaction because of the large dipole moment of acetonitrile (3.9 D). However, HCN can form hydrogen bonds with the hydrogen atoms of the benzene cation (CHδ+···NCH) and linear hydrogen bonding chains involving HCN···HCN interaction. HCN molecules tend to form externally solvated structures with the benzene cation where the ion is hydrogen bonded to the exterior of HCN chains. For the C6H6•+(CH3CN)n clusters, internally solvated structures are formed where the acetonitrile molecules are directly interacting with the benzene cation through ion−dipole and hydrogen bonding interactions. The lack of formation of higher clusters with n > 4, in contrast to HCN, suggests the formation of a solvent shell at n = 4, which is attributed to steric interactions among the acetonitrile molecules attached to the benzene cation and to the presence of the blocking CH3 groups, both effects make the addition of more than four acetonitrile molecules less favorable.

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Dissociative proton transfer is observed in the C6H6•+(H2O)n clusters with n ≥ 4 resulting in the generation of H3O+(H2O)3 and the phenyl radical.10 Phenyl acetylene (C8H6•+) forms two kinds of CHδ+···O hydrogen bonds with comparable energies through the interaction of water molecules with the hydrogen atoms of the phenyl and acetylene groups.11 Hydration of the acetylene radical cation (C2H2•+) results in the formation of the covalent ions C2H3O+ and C2H4O•+ produced with an overall rate coefficient that increases with decreasing temperature.12 The reactivity, combined with energetics, suggest that the C2H4O•+ adduct is vinyl alcohol (H2CCHOH•+), while the protonated ketene CH2COH+ is the most likely observed C2H3O+ ion.12 The measured hydration energy can confirm the covalent nature of the ions as in the case of the acetylene trimer ion (C2H2)3•+ where its sequential hydration energies with 1−6 water molecules are found to be identical to those of the benzene ion, thus confirming the formation of benzene cations in ionized acetylene clusters.13,17 Similarly, the measured hydration energy combined with structural calculations of the acetylene dimer ion (C4H4•+) confirms the formation of cyclobutadiene•+ as the major isomer of the C4H4•+ ions formed in ionized acetylene clusters.14 Interestingly, the

INTRODUCTION Hydrogen bonding interactions involving ionized aromatics are important in radiation chemistry, electrochemistry, polymerization in aqueous solvents, and in astrochemical environments.1−5 Organic ions can form hydrogen bonds with solvents in nature, for example, in icy grains doped with polycyclic aromatic hydrocarbons that are subjected to ionizing radiation in interstellar dust grains.6−8 These interactions and processes are not well characterized at the molecular level since little work has been focused on the reactions of ionized aromatics with polar solvent molecules, and much of our understanding is based on chemical intuition and approximate theoretical descriptions.2−5 Insight into the basic molecular interactions can be obtained from the energies and structures of the key species involved in the stepwise association of organic cations. In recent papers, we examined such interactions in the hydration of the organic ions: benzene (C6H6•+), cyclic C3H3+, acetylene (C2H2•+), acetylene dimer (C2H2)2•+, acetylene trimer (C2H2)3•+, phenyl acetylene (C8H6•+), pyridine•+, 2-flouropyridine•+, and protonated pyridine using a combination of equilibrium thermochemical measurements and ab initio calculations.9−16 The hydration energies of these organic ions vary over an unexpected wide range from 8 to 16 kcal/mol depending on the nature of the hydrogen bonding interaction.9−16 The benzene•+ interacts with water molecules by relatively weak CHδ+···O hydrogen bonds resulting in stepwise hydration energies, ΔH°n−1,n, that are nearly constant at 8.5 ± 1 kcal/mol from n = 1−6.9,10 © 2012 American Chemical Society

Special Issue: Peter B. Armentrout Festschrift Received: April 24, 2012 Revised: June 1, 2012 Published: June 6, 2012 1069

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Figure 1. Schematic diagram of the mass-selected ion mobility system at VCU.

hydration energy of the cyclic C3H3+ ion (11.7 kcal/mol) is stronger than those of the C6H6•+ and C8H6•+ ions because of the higher charge density on the C3H3+ ion as compared to the larger radical cations C6H6•+ and C8H6•+.15 The hydration energy can also identify the nature of the charge on the ion and distinguish between a conventional radical cation and a distonic ion. For example, the measured hydration energies of the pyridine and 2-F pyridine radical cations (15−16 kcal/mol) are consistent with distonic structures of these ions (•C5H4NH+ and •C5H3FNH+, respectively) where the protonated nitrogen sites form stronger NH+···OH2 hydrogen bonds similar to protonated pyridines.16 The stepwise hydration of different organic ions can thus provide prototypical models for understanding structural and energy changes associated with hydration, which could lead to a molecular level understanding of complicated phenomena in the condensed phase such as hydrophobic hydration and clathrate formation.2,4 In addition to water, other polar molecules containing a lone pair of electrons such as hydrogen cyanide (HCN), acetonitrile (CH3CN), and ammonia (NH3) can participate in hydrogen bonding interactions with the ring hydrogen atoms (CHδ+) of ionized aromatics. HCN is an important atmospheric compound known to be produced by biomass burning.18 HCN is also one of the main interstellar/nebula molecules, and CH3CN is common and relatively stable in these environments.19 In fact, over 100 organic molecules, including benzene, polycyclic aromatic hydrocarbons (PAHs), and polycyclic aromatic nitrogen heterocyclics (PANs), are present in interstellar clouds and in solar nebulae.18−25 Since molecules in outer space are subjected to ionizing radiation from stars, radioactive decay, and cosmic rays, small cyclic ions such as benzene may act as nucleation centers for the condensation of astrochemical molecules such as hydrogen cyanide and acetonitrile to form clusters where the ionic cores can catalyze intracluster reactions leading to complex organics.27−29 Therefore, HCN and CH3CN could play important roles in the formation of larger nitrogen-containing species and PANs. Energy barriers may prevent reactions at low temperatures in interstellar medium, but these reactions may be permitted at high temperatures or under intense UV radiation in the solar nebulae.22−25 Ion−molecule processes, particularly those that lead to the formation of larger species either through chemical addition or association reactions, are of particular interest for the formation of complex organics, clustering, and polymerization in astrochemical environments.26−28 In this article, we report the first study of the association of HCN and CH3CN molecules with an organic ion, the benzene radical cation, as model systems for hydrogen bonding interactions between the ring hydrogen atoms (CHδ+) and the lone pair of electrons on the nitrogen atom. The benzene cation provides multiple CHδ+ sites that could be saturated by hydrogen bonding interactions with multiple HCN or CH3CN molecules. However, unlike CH3CN, HCN molecules could

form a hydrogen bonding chain extended out of the benzene cation through the CHδ+···N hydrogen bonding link. If the hydrogen bonding interaction between HCN molecules (HCN···HCN) is comparable to the interaction with the benzene cation CH+···NCH, then no blocked structures are expected to form, and no significant drop in the binding energy should be observed if the next HCN molecule adds to another CHδ+ site of the ring or the HCN molecule already connected to the ring. For the CH3CN molecules, one expects a significant drop in the binding energy once the maximum number of CH3CN molecules is attached to the ring since additional molecules may join only through very weak CH3···NCCH3 interaction.

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EXPERIMENTAL SECTION The gas phase ion association experiments were performed using the VCU mass-selected ion mobility spectrometer. The details of the instrument can be found in several publications and only a brief description of the experimental procedure is given here.10,11,14 Figure 1 illustrates the essential components of the ion mobility system. In the experiments, the molecular ions of benzene (C6H6•+) are formed by electron impact ionization using electron energy of 60−70 eV following the supersonic expansion of 40 psi (2.8 bar) of ultra high pure helium seeded with about 1−4% of benzene vapor through pulsed supersonic nozzle (500 μm) to the vacuum source chamber with 10−7 mbar pressure. C6H6•+ ions are massselected by the first quadrupole mass-filter and injected in 30− 50 μs pulses into the drift cell, which contains neutral HCN gas or CH3CN vapor (Sigma-Aldrich, 99.9%) in a mixture with helium buffer gas. Flow controllers (MKS # 1479A) are used to maintain a constant pressure inside the drift cell within ±1 mTorr. The temperature of the drift cell can be controlled to better than ±1 K using four temperature controllers. Liquid nitrogen flowing through solenoid valves is used to cool down the drift cell. The reaction products can be identified by scanning a second quadrupole mass filter located coaxially after the drift cell. The arrival time distributions (ATDs) are collected by monitoring the intensity of each ion as a function of time. The reaction time can be varied by varying the drift voltage. The injection energies used in the experiments (8−14 eV, laboratory frame) are slightly above the minimum energies required to introduce the ions into the cell against the HCN/ He or CH3CN/He outflow from the entrance orifice. Most of the ion thermalization occurs outside the cell entrance by collisions with the HCN or CH3CN vapor escaping from the cell entrance orifice. At a cell pressure of 0.2 Torr, the number of collisions that the C6H6•+ encounters with the neutral molecules within the 1.5 ms residence time inside the cell is about 104 collisions, which is sufficient to ensure efficient thermalization of the C6H6•+ ions. HCN is prepared by adding 8 g of sodium cyanide (NaCN) (Sigma-Aldrich, 97%) into a 500 mL stainless steel bubbler, 1070

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which is then placed in liquid nitrogen and evacuated followed by the addition of 4 mL of pure sulfuric acid (H2SO4) (Aldrich, 99.999%) through a stainless steel tube extension of the inlet valve of the bubbler. Following the reaction of sulfuric acid with the sodium cyanide salt inside the bubbler, HCN gas evolves, and the bubbler is allowed to warm up to room temperature. The pressure in the HCN line is monitored by a Baratron pressure gauge (MKS-626A13TBD). The equilibrium reactions are represented by eq 1. [C6H6•+(RCN)n − 1] + RCN ⇄ [C6H6•+(RCN)n ]

Table 2. Measured Thermochemistry (−ΔH°n−1,n and −ΔS°n−1,n) of the Formation of C6H6•+(CH3CN)n Clusters; with n = 1−3 and the Corresponding Calculated Binding Energies benzene•+ (CH3CN)n

(1)

(2)

1 2 3 4 5 6

−ΔH° 9.2 8.0 7.5 7.3 6.6b 6.4b

−ΔS° 19.1 17.8 19.4 21.7 21.7 21.7

−ΔG°d 3.5 2.7 1.7 0.8 0.1 −0.1

ΔEe,f 9.4 8.2 7.5 7.3

(9.2) (7.8) (7.3) (7.1)

g

−ΔH°g

−ΔG°g

8.7 8.2 7.3 7.1

2.3 1.9 −0.1 −0.5

−ΔG°g

1 2 3 4

14.0 10.7 9.2 7.4(b)b

19.9 18.4 21.8 21.8

8.1 5.2 2.7 0.9

13.0 (12.7) 10.5 (10.6) 9.2 (9.7)

12.2 10.0 8.8

5.7 3.3 1.0

RESULTS AND DISCUSSION Association of HCN with the Benzene Radical Cation. Figure 2a displays the mass spectrum obtained following the injection of the mass-selected C6H6•+ ion into the drift cell containing 0.9 Torr He at 298 K. It is clear that no dissociation products are observed consistent with the low injection energy used (13.8 eV, lab). In the presence of 0.1 Torr HCN vapor in the drift cell at 298 K, the first two association products C6H6•+(HCN)n with n = 1 and 2 are observed as shown in Figure 2b. As the temperature decreases, the ion intensity of C6H6•+ significantly decreases and eventually disappears as the equilibrium shifts to higher C6H6•+(HCN)n clusters. At 178 K (the lowest achievable temperature before the condensation of HCN), the cluster population is dominated by the C6H6•+(HCN)n series from n = 2 to 6 with n = 3 and 4 being the major ions observed. A good test of equilibrium comes from the identical ATDs of the ions coupled by equilibrium. If the C6H6•+(HCN)n−1 and C6H6•+(HCN)n ions are in equilibrium, their ATDs must be identical. This is evident from the ATDs shown in Figure 3 for the C6H6+(HCN)n ions with n = 0−4. The equilibrium constants for the stepwise association of HCN with C6H6•+ (reaction 1) measured at different temperatures yield the van’t Hoff plots shown in Figure 4. The resulting ΔH° and ΔS°

benzene•+(HCN)n n

−ΔH°g

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Table 1. Measured Thermochemistry (−ΔH°n−1,n, −ΔS°n−1,n, and −ΔG°n−1,n) of the Formation of C6H6•+(HCN)n Clusters; with n = 1−6 and the Calculated Binding Energies, Enthalpies, and Free Energies

c

ΔEef

THEORETICAL SECTION DFT calculations of the structure of the benzene•+(RCN)n clusters were carried out at the B3LYP/6-311++G(d,p) and M06-2X/6-311++G(d,p) levels using the Gaussian03 and Gaussian09 suites of programs, respectively.30,31 Frequency calculations have been performed for all the optimized geometries at the same level of theory to obtain the zero point vibrational energy (ZPVE) and to verify the absence of any imaginary frequencies. The calculated binding energies (with respect to benzene•+(RCN)n−1 + RCN) were corrected for BSSE using the scheme of Boys and Bernardi as described in the Gaussian programs.30,31 ΔH° and ΔG° values for the stepwise formation of the benzene•+(RCN)n with n = 1−4 were also calculated for the lowest energy structures according to thermochemical calculations outlined in the Gaussian03 program.30

Where I[C6H6+(RCN)n−1], I[C6H6+(RCN)n] are the integrated intensities of the ATDs of the reactant and product ions, respectively, and PRCN is the pressure of HCN or CH3CN in atmosphere inside the drift cell. The equilibrium constant, Keq, is measured at different temperatures, and from a van’t Hoff plot, ΔH° and ΔS° values are obtained from the slope and intercept, respectively. The measured values are duplicated at least three times, and the average values are reported in Tables 1 and 2 with the corresponding uncertainties.

a

−ΔG°d

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[C6H6 (RCN)n ] [C6H6+(RCN)n − 1][RCN] I[C6H6+(RCN)n ] I[C6H6+(RCN )n − 1]PRCN

−ΔS°c

ΔH°n−1,n units are kcal/mol. bObtained from the measured ΔG°3,4 at 226 K assuming ΔS° of 22 cal/mol·K. cΔS°n−1,n units are cal/mol·K; estimated errors, ΔH° ± 1 and ΔS° ± 2.0. dΔG°n−1,n at 298 K, units are kcal/mol. eΔE (kcal/mol) calculated by B3LYP/6-311++G(d,p). f Values between brackets calculated with ZPE and BSSE counterpoise corrections included. gΔH° calculated from the sum of the electronic and thermal enthalpies; ΔG° (298 K) calculated from the sum of the electronic and thermal free energies of the lowest energy structures obtained from the B3LYP/6-311++G(d,p) method (units are kcal/ mol).

+

=

−ΔH°a

a

where R = H or CH3 for HCN or CH3CN, respectively. The establishment of equilibrium is verified when (1) a constant ratio of the integrated intensity of the product to the reactant ions is maintained over the residence time of the ions at constant pressure and temperature, and (2) the ATDs of the reactant and product ions are identical indicating equal residence times. When the equilibrium conditions are wellestablished, the equilibrium constant, Keq, can be measured using eq 2. Keq =

n

ΔH°n−1,n units are kcal/mol. bObtained from the measured ΔG°4,5 and ΔG°5,6 at 178 K assuming ΔS° of 22 cal/mol·K. cΔS°n−1,n units are cal/mol·K; estimated errors, ΔH° ± 1 and ΔS° ± 2.0. dΔG°n−1,n at 298 K, units are kcal/mol. eΔE (kcal/mol) calculated by B3LYP/6311++G(d,p). fValues between brackets calculated with ZPE and BSSE counterpoise corrections included. gΔH° calculated from the sum of the electronic and thermal enthalpies; ΔG° (298 K) calculated from the sum of the electronic and thermal free energies of the lowest energy structures obtained from the B3LYP/6-311++G(d,p) method (units are kcal/mol). a

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Figure 4. Van’t Hoff plots for the equilibria C6H6•+(HCN)n−1 + HCN ⇔ C6H6•+(HCN)n for n = 1−4.

to be attached to the C6H6+ ion. This interaction could involve C−Hδ+···N hydrogen bonding where the benzene cation acts as the proton donor to the lone pair of electron on the nitrogen atom of the HCN molecule. The C−Hδ+···N interaction may be comparable to the weak hydrogen bonding interaction among HCN molecules where linear chains are expected to be formed without interruption. Association of CH3CN with the Benzene Radical Cation. Figure 5 displays the mass spectra obtained upon the injection of the C6H6•+ ion into the drift cell in pure He and in the presence of 0.2 Torr CH3CN vapor at different temperatures. At 303 K, most of the benzene ions are incorporated into the C6H6•+(CH3CN)n clusters with n = 1 and 2 as shown in Figure 5c. The comparison with HCN under similar conditions (Figure 2b) clearly indicates that the binding of CH3CN to the benzene cation is significantly stronger than that

Figure 2. Mass spectra obtained following the injection of the massselected C6H6•+ (B) into the drift cell containing He and HCN vapor at different pressures and temperatures as indicated.

values for the formation of the C6H6•+(HCN)n clusters are listed in Table 1. The measured thermochemical values shown in Table 1 indicate that the binding energies of C6H6•+(HCN)n do not follow the regular decrease with n typically observed in a stepwise ion solvation.32 This suggests the presence of multiple binding sites with comparable energies for the HCN molecules

Figure 3. ATDs of the benzene•+(HCN)n ions with n = 0−2 obtained following the injection of the benzene ions into 0.1 Torr of HCN vapor at 263 K (left) and at 210 K for n = 2−4 (right). 1072

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Figure 6. Van’t Hoff plots for the equilbria C6H6•+(CH3CN)n−1 + CH3CN ⇔ C6H6•+(CH3CN)n for n = 1−3.

could be used to obtain an estimate of ΔH°3,4 assuming a ΔS° of 22 cal/mol·K (similar to the measured ΔS°2,3). This estimate results in ΔH°3,4 = 7.4 kcal/mol, which is lower than that of ΔH°2,3 of 9.2 kcal/mol due to the decrease in the effective charge remaining on the benzene cation and hence the decrease in the ion−dipole interaction with the fourth acetonitrile molecule. However, the absence of a sharp drop in the binding energy suggests that four acetonitrile molecules can still interact directly with the benzene cation and perhaps constitute a solvent shell where the cation is internally solvated within the solvent shell. This is supported by the failure to observe more than four acetonitrile molecules associated with the benzene cation even at the lowest possible temperature (226 K) before the condensation of the acetonitrile vapor. The calculated structures of the C6H6•+(CH3CN)4 clusters shown below confirm the formation of a solvent shell consisting of four acetonitrile molecules directly attached to the benzene ring, and therefore, the fifth molecule is not able to directly interact with the benzene cation. Despite the strong bonding of CH3CN, this methyl-blocked ligand cannot form a hydrogen bonding network or chain as the HCN ligand, and therefore, a solvent shell characteristic feature is observed in the stepwise solvation of the benzene cation with acetonitrile molecules. Structures of the HCN Hydrogen Bonding Chains Attached to the Benzene Ion. To gain insight into the roles of the benzene cation−HCN and HCN−HCN interactions in determining the structures and energetics of the C6H6•+(HCN)n clusters, we calculated the lowest energy structures of the C6H6•+(HCN)n clusters and their binding energies (with respect to C6H6•+(HCN)n−1 + HCN) using DFT at the B3LYP/6-311++G(d,p) level. To test the accuracy of the B3LYP function, we also carried out the calculations for C6H6•+(HCN) using the M06-2X functional, which is known to be accurate for van der Waals (vdW) and weak ion− molecule interactions.33,34 The three lowest energy structures of the C6H6•+(HCN) cluster calculated using the B3LYP and M06-2X functions at the 6-311++G(d,p) level are shown in Table 3. Both the B3LYP and M06-2X functions predict the lowest energy isomer of C6H6•+(HCN) to be a bifurcated structure with HCN binding to two CH hydrogen atoms by 2.5 Å and

Figure 5. Mass spectra obtained following the injection of the massselected C6H6•+ (B) into the drift cell containing He and CH3CN vapor at different pressures and temperatures as indicated. H3O+A3 is the stable cluster ion H3O+(CH3CN)3 formed with the water trace impurity in the drift cell at low temperatures.

of HCN. This is also confirmed by the observation of the C6H6•+(CH3CN) at a temperature as high as 419 K as shown in Figure 5b (BA cluster). Interestingly, at the lowest temperature used (226 K), the most prominent ion observed is the C6H6•+(CH3CN)3 and only a very minor intensity is observed for the C6H6•+(CH3CN)4 cluster. This is quite different from the association of HCN with the benzene cation where C6H6•+(HCN)n clusters with n > 5 could be observed without obvious restrictions. The van’t Hoff plots of the first three CH3CN additions onto the benzene cation are shown in Figure 6, and the resulting ΔH° and ΔS° are listed in Table 2. The sequential binding energies shown in Table 2 follow the trend of decreasing ΔH°n−1,n with increasing n, which can be expected for association reactions dominated by ion−dipole interactions.32 Furthermore, the sequential entropy loss values are consistent with ion−dipole interactions where internal rotation and low frequency vibrations are retained.32 Comparison of the thermochemical data shown in Tables 1 and 2 confirms that CH3CN binds more strongly to the benzene cation than HCN and explains the observation of C6H6•+(CH3CN) at a significantly higher temperature (419 K) for typical ionic hydrogen bonded clusters. Also, a significant drop in the binding energy (24%) is observed upon the addition of the second acetonitrile molecule to the C6H6•+(CH3CN) cluster in contrast to the small change observed upon the addition of the second HCN molecule to the C6H6•+(HCN) cluster (13%). Although the van’t Hoff plot for the formation of C6H6•+(CH3CN)4 could not be obtained due to the small intensity of the C6H6•+(CH3CN)4 ion at temperatures higher than 226 K, the measured ΔG°3,4 at 226 K 1073

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Table 3. Lowest Energy Structures of the C6H6•+(HCN) Cluster Calculated Using the M06-2X and the B3LYP Functions at the 6-311++G(d,p) Levela

structures obtained using the M06-2X function are (1-b) in which the HCN molecule lies above the plane of the benzene ring with the nitrogen atom 3.2 Å away from the center of the ring, and (1-c), which consists of a linear C−Hδ+···NCH hydrogen bond of 2.2 Å. With both the M06-2X and B3LYP functions, the ion−dipole structure (1-b) is similar in energy to the lowest energy structure 1-a within 0.2−0.4 kcal/mol. However, with the B3LYP function structure, 1-b has the HCN molecule tilted by 76° above the plane of the benzene ring with a distance of 2.7 Å from the closest carbon atom in the ring. On the basis of the comparison between the B3LYP and M06-2X functions, it can be concluded that the two functions produce similar lowest energy structures of the C6H6•+(HCN)n clusters although the M06-2X appears to overestimate the binding energy. Therefore, the B3LYP function at the 6-311+ +G(d,p) level was used to predict the lowest energy structures of the C6H6•+(HCN)n clusters with n = 2−4. The calculated structures are shown in Figure 7, and the binding energies and thermochemical quantities (ΔH°n−1,n and ΔG°n−1,n) calculated for the lowest energy structure of each cluster are listed in Table 1. It is clear that the calculated ΔH°n−1,n values agree well with the experimental values as shown in Table 1. However, the calculated −ΔG°n−1,n are considerably lower than the measured quantities suggesting that the calculated entropy losses ΔS°n−1,n are significantly larger than the values obtained from van’t Hoff plots. Three isomers (2-a, 2-b, and 2-c) with essentailly the same relative energies and binding energies of 7.6−7.8 kcal/mol in excellent agreement with the experimental value of 8 kcal/mol are predicted for the C6H6•+(HCN)2 cluster as shown in Figure 7. The similar energies indicate that the second HCN molecule binds to the C−Hδ of the benzene cation or to the C−H of the first HCN molecule with hydrogen bonds of comparable energies. This is consistent with the similar length of the C− Hδ···NCH (2.2 Å) and the NCH···NCH bonds (2.1 Å), which are shorter than the C−Hδ···NCH distances in the bifurcated structure 1-a (2.5 and 2.6 Å).

RE is relative total energy, ΔE is binding energy, and the value in brackets includes ZPE and BSSE corrections. a

2.6 Å (B3LYP) or 2.4 Å and 2.5 Å (M06-2X) bonds as shown in Table 3 (structures 1-a). This geometry is similar to that previously predicted for the hydrated benzene cation C6H6•+(H2O).10 We note that the binding energy calculated by the B3LYP function (9.2 kcal/mol corrected for ZPE and BSSE) is in excellent agreement with the experimental value in contrast to the value calculated by the M06-2X function (10.6 kcal/mol corrected for ZPE and BSSE), which appears to overestimate the binding energy. The other two low energy

Figure 7. Low energy structures of the C6H6•+(HCN)n clusters with n = 2−4 calculated at the B3LYP/6-311++G(d,p) level. RE is relative total energy; ΔE is binding energy with the ZPE and BSSE corrections. Energies and distances are in kcal/mol and Angstroms, respectively. 1074

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Figure 8. Low energy structures of the C6H6•+(CH3CN)n clusters with n = 1−4 calculated at the B3LYP/6-311++G(d,p) level. RE is relative total energy; ΔE is binding energy with the ZPE and BSSE corrections. Energies and distances are in kcal/mol and Angstroms, respectively. (*) Structures 4-b and 4-c are calculated at the B3LYP/6-31+G(d,p) level.

The structures of the C6H6•+(HCN)n clusters with n = 3 and 4 show a small tendency for the solvation of the benzene cation where two hydrogen bonding sites with the ring hydrogen atoms are observed. Structure (3-b) shows an extended hydrogen bonding chain with three HCN molecules attached to the benzene cation through a bifurcated structure. Structure (4-a) represents an optimum configuration where two HCN···HCN hydrogen bonds are formed in addition to one C−Hδ···NCH bond and a bifurcated ion−dipole interaction with the benzene cation. Structure (4-b) is the only structure among the C6H6•+(HCN)3 and C6H6•+(HCN)4 clusters where HCN molecules interact with the benzene cation through three sites involving two hydrogen bonds and an ion−dipole interaction. The small energy differences between the different structures corresponding to the same cluster size imply that an ensemble of different configurations could exist at a given temperature and therefore, the measured binding energy represents an average value of the binding energies of these different structures. Structures of the Solvated Benzene Ion by CH3CN Molecules. Figure 8 displays the optimized structures of the lowest energy isomers of the C6H6•+(CH3CN)n clusters with n = 1−4, calculated at the B3LYP/6-311++G(d,p) level.

The lowest energy isomer of the C6H6•+(CH3CN) cluster (structure 1-a) has a bifurcated structure with the nitrogen atom of acetonitrile interacting with two CH hydrogen atoms of the benzene cation by 2.4 Å and 2.5 Å bonds as shown in Figure 8. The structure is similar to that of the C6H6•+(HCN) cluster shown in Table 3. Another isomer (1-b in Figure 8) with a nearly similar energy (0.3 kcal/mol higher than 1-a after the BSSE correction) shows the CH3CN molecule to be almost perpendicular to the benzene plane by 78.4° angle and a distance of 2.6 Å to the closest carbon atom of the ring. The third most stable isomer 1-c is 0.7 kcal/mol higher than 1-a and has a linear C−Hδ···NCCH3 hydrogen bond of 2.1 Å. The three structures 1-a, 1-b, and 1-c in Figure 8 have comparable binding energies (corrected for ZPE and BSSE) of 12.7, 12.4, and 12.0 kcal/mol, respectively, but are significantly lower than the experimental value of 14.0 kcal/mol. The three lowest energy isomers of the C6H6•+(CH3CN)2 cluster 2-a, 2-b, and 2-c have similar relative total energies within 1 kcal/mol and all show direct interactions with the benzene cation. The lowest energy structure 2-a has a binding energy of 10.6 kcal/mol similar to the experimental value of 10.7 kcal/mol. It represents an ion−dipole interaction through a bifurcated structure with distances of 2.4 Å and 2.6 Å from the 1075

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indicated by the lowest energy structures shown in Figure 9. It is clear that both water and HCN tend to form externally solvated structures with the benzene cation where the ion is hydrogen bonded to the exterior of a solvent cluster. This is motivated by the tendency of water and HCN to form hydrogen-bonded network and chains, respectively. Because of the strong ion−dipole interaction between the benzene cation and acetonitrile, internally solvated structures, where the inner solvent molecules are bonded directly to the ion, are formed. In fact, of all the calculated structures with up to four solvent molecules, the C6H6•+(CH3CN)4 cluster with low energy structures suggesting the formation of a solvent shell where all the hydrogen atoms of the benzene cation are directly involved in C−Hδ···N linear hydrogen bonds or ion−dipole bifurcated structures. The failure to observe the formation of the C6H6•+(CH3CN)5 cluster even at the lowest temperature before the condensation of the acetonitrile vapor is a manifestation of the solvent shell effect where the additional molecules outside the shell are weakly bound by dispersion interactions due to the presence of the CH3 blocking group, which may only provide a very weak CH3···N interaction similar to dispersion interaction. Applications in Astrochemistry. Hydrogen cyanide and acetonitrile are significant components of interstellar clouds and solar nebulae, and benzene itself was also identified recently in protoplanetary nebulae.6,7,23 These molecules are subject to ionizing radiation, producing stable molecular ions. In these low-temperature environments, HCN and acetonitrile can condense on the ions forming organic-doped ice grains. The present systems model these processes, in particular, because the astrochemical condensation also involves stepwise addition of gas phase molecules. The questions of external versus internal solvation and formation of a solvent shell are relevant. With internal solvation, the organic component will become isolated in ice. The inclusion of polar interstellar molecules such as acetonitriles that do not allow the formation of extended hydrogen bonding networks with the organic ions can facilitate the internal solvation of the aromatic ions. However, external solvation with molecules such as water and hydrogen cyanide allows the aromatics to remain on the grain surface and undergo reactions with other incoming organic molecules.

nitrogen atom to two hydrogen atoms of the benzene cation in addition to a hydrogen bonding interaction with a distance of 2.2 Å between the acetonitrile nitrogen atom and the β-ring hydrogen. The three lowest energy isomers of the C6H6•+(CH3CN)3 cluster 3-a, 3-b, and 3-c have similar relative total energies within less than 0.6 kcal/mol and result in binding energies similar to the experimental value of 9.2 kcal/mol. The three structures represent solvation of the benzene cation through three sites involving two bifurcated structures and a linear hydrogen bond involving three or four ring hydrogen atoms and the nitrogen atoms of the three acetonitrile molecules. The three lowest energy isomers of the C6H6•+(CH3CN)4 cluster 4a, 4-b, and 4-c show complete solvation of the benzene cation where all the C−Hδ hydrogens have been used in the formation of linear hydrogen bonding or bifurcated ion−dipole structures with the nitrogen atoms of the four acetonitrile molecules. Interestingly, the lowest energy isomer (4-a) shows the formation of two hydrogen bonding and two ion−dipole structures. The calculated structures of the C6H6•+(CH3CN)4 cluster strongly suggest the formation of a solvent shell consisting of four acetonitrile molecules surrounding the benzene cation. This is consistent with the lack of observation of the C6H6•+(CH3CN)5 cluster even at the lowest possible temperature of 226 K before the condensation of acetonitrile vapor. Comparison of the Solvent Interaction of Water, Hydrogen Cyanide, and Acetonitrile. It is of interest to compare the association behaviors of hydrogen cyanide and acetonitrile molecules toward the benzene cation with that of water. Table 4 compares the stepwise association enthalpies ΔH°n−1,n, and Figure 9 compares the lowest energy structures for n = 1−4 for the three solvent molecules. Table 4. Comparison of the Association Enthalpy of Benzene•+(Solvent)n Clusters for Water, Hydrogen Cyanide, and Acetonitrile with n = 1−4 −ΔH°n−1,n [benzene•+(solvent)n]

a

n

H2Oa

HCN

CH3CN

1 2 3 4

9.0 8.0 8.0 10.3

9.2 8.0 7.5 7.3

14.0 10.7 9.2 7.4

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SUMMARY AND CONCLUSIONS Equilibrium thermochemical measurements using an ion mobility drift cell technique have been utilized to investigate the binding energies and entropy changes associated with the stepwise association of HCN and CH3CN molecules with the benzene radical cation in the C 6 H 6 •+ (HCN) n and C6H6•+(CH3CN)n clusters with n = 1−6 and 1−4, respectively. The binding energy of CH3CN to the benzene cation (14 kcal/ mol) is much stronger than that of HCN (9 kcal/mol) mostly due to a stronger ion−dipole interaction attributed to the large dipole moment of acetonitrile (3.9 D). However, HCN can form hydrogen bonds with the hydrogen atoms of the benzene cation (CHδ+···NCH) and linear hydrogen bonding chains (HCN···HCN) extended out of the benzene ring. For the C6H6•+(CH3CN)n clusters, evidence is presented for the formation of a solvent shell consisting of four acetonitrile molecules directly interacting with the benzene cation through ion−dipole interactions. The formation of a solvent shell is attributed to the steric interactions among the acetonitrile molecules attached to the benzene cation and to the presence

Reference 10.

Table 4 and Figure 9 provide some interesting comparisons. The first observation is that the association enthalpies ΔH°n−1,n for water and HCN are very similar for the first three steps (n = 1−3), and smaller than the corresponding values for acetonitrile. This is mostly due to stronger ion dipole interaction within the C6H6•+(CH3CN)n clusters given that the dipole moment of acetonitrile, HCN and water are 3.92, 2.98, and 1.85 Debye, respectively.35 The enthalpy change for the addition of the fourth solvent molecules increases for water and remains constant for HCN and acetonitrile. This can be explained by the solvent−solvent interaction since, in both water and HCN, a direct solvent−solvent hydrogen bonding interaction is involved, which is stronger in H2O−H2O than in HCN−HCN. For acetonitrile, the fourth molecule is still interacting directly with the benzene cation through ion−dipole forces and no CH3CN−CH3CN interaction is involved as 1076

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Figure 9. Comparison of the minimum energy structures of C6H6•+(HCN)n, C6H6•+(H2O)n, and C6H6•+(CH3CN)n with n = 1−4 calculated at the B3LYP/6-311++G(d,p) level. (The structures of C6H6•+(H2O)n, calculated at the ROHF/6-31+G** level, are taken from ref 10.) (13) Momoh, P. O.; El-Shall, M. S. Chem. Phys. Lett. 2007, 436, 25− 29. (14) Momoh, P. O.; Hamid, A. M.; Abrash, S. A.; El-Shall, M. S. J. Chem. Phys. 2011, 134, 204315. (15) Mabrouki, R.; Ibrahim, Y.; Xie, E.; Meot-Ner, M.; El-Shall, M. S. J. Phys. Chem. A 2006, 110, 7334−7344. (16) Ibrahim, Y.; Mabrouki, R.; Meot-Ner, M.; El-Shall, M. S. J. Phys. Chem. A 2007, 111, 1006−1014. (17) Momoh, P. O.; Abrash, S. A.; Mabourki, R.; El-Shall, M. S. J. Am. Chem. Soc. 2006, 128, 12408−12409. (18) Li, Q. B.; Jacob, D. J.; Yantosca, R. M.; Heald, C. L.; Singh, H. B.; Koike, M.; Zho, Y. J.; Sachse, G. W.; Streets, D. G. J. Geophys. Atmos. 2003, 108, 8827. (19) Fraser, H. J.; McCoustra, R. S.; Williams, D. A. Geophys. R. Astron. Soc. 2002, 43, 210−218. (20) Brooke, T. Y.; Tokunaga, A. T.; Weaver, H. A.; Crovisier, J.; Bockelee-Morvan, D.; Crisp, D. Nature 1996, 383, 606−607. (21) McKay, C. P.; Borucki, W. J. Science 1997, 276, 390−392. (22) Fegley, B. Space Sci. Rev. 1999, 90, 239−252. (23) Gudipati, M. S.; Allamandola, L. J. Astrophys. J. 2003, 596, L195−L198. (24) Herbst, E. J. Phys. Chem. A 2005, 109, 4017−4029. (25) Sanford, S. A.; Aleon, J.; et al. Science 2006, 314, 1720−1724. (26) Rhee, Y. M.; Lee, T. J.; Gudipati, M. S.; Allamandola, L. J.; Head-Gordon, M. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 5274−5278. (27) Gudipati, R. S.; Allamandola, L. J. Astrophys. J. 2006, 638, 286− 292. (28) Gudipati, M. S.; Allamandola, L. J. Astrophys. J. 2004, 615, L177−L180. (29) Ascenzi, D.; Aysina, J.; Tosi, P.; Maranzana, A.; Tonachini, G. J. Chem. Phys. 2010, 133, 184308 (1−9). (30) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.;

of the blocking CH3 groups; both effects make the addition of further acetonitrile molecules less favorable.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Drs. Yehia M. Ibrahim (PNNL, USA) and Edreese H. Alshraeh (Alfaisal University, Saudi Arabia) for carrying out some of the thermochemical measurements on the C6H6•+(CH3CN)n clusters. We thank the National Science Foundation (CHE-0911146) and NASA (NNX07AU16G) for the support of this work.

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