Infrared spectroscopy of the molecular hydrogen solvated carbonium ions, CH+5(H2)n (n=1–6)

The infrared spectra for the molecular hydrogen‐solvated carbonium ions, CH+5(H2)n (n=1–6) in the frequency range of 2700–4200 cm−1 are presented. Spectroscopic evidence was found in support of the scrambling of CH+5 through the large amplitude motions such as the CH3 internal rotation and the in‐plane wagging motion of three‐center two‐electron bond. More importantly, the scrambling motions of CH+5 cores were slowed down considerably by attaching the solvent H2 molecules to the core ion. The complete freezing of the scrambling motions was found when the first three H2 molecules were bound to the CH+5 core. A good agreement between the experimental and the theoretical predictions was found in the dynamics of CH+5.


I. INTRODUCTION
Protonated alkanes are highly reactive intermediates in the acid-catalyzed transformations of hydrocarbons. 1 These nonclassical carbonium ions are known to form a threecenter two-electron (3c2e) bond having pentacoordinated carbon atoms and bridged hydrogens. 2 CH 5 ϩ is the simplest carbonium ion.
The existence of CH 5 ϩ was first reported by Tal'roze and Lyubinova in mass spectrometric studies on the protonation of alkenes and alkanes in 1952. 3 Olah and co-workers later reported that CH 5 ϩ played an important role as a reactive intermediate in super acid solution reactions. 4 CH 5 ϩ is now used as a common reagent for protonation of gas phase molecules in the chemical ionization mass spectrometry. 5 It is also of astrophysical interest in that it may play as an intermediate for generation of methane and formaldehyde in the cold galactic molecular clouds. 6 A number of the early theoretical calculations on the structures of CH 5 ϩ consistently suggested that the eclipsed C s (e-C s ) symmetry structure was the global minimum energy structure. 7-10 However, recent ab initio calculations at the most sophisticated level, performed by Schleyer and coworkers, found that the energy differences between the e-C s structure and other structures such as staggered C s (s-C s ) or C 2v were very small and became negligible when corrected for zero point energies ͑see Fig. 1 for the CH 5 ϩ structures͒. 11,12 The C 4v and D 3h structures were predicted to be higher in energy than the e-C s structure by 1 kcal/mol and 9 kcal/mol, respectively. As pointed out by Schleyer, Schaefer, and later, by Scuceria, 13 the early prediction that CH 5 ϩ is regarded as a complex between CH 3 ϩ and H 2 with a localized 3c2e bond is not valid, but CH 5 ϩ is likely to scramble constantly through the low lying s-C s and C 2v transition states, without possessing a definite equilibrium structure.
In contrast to the numerous theoretical works on CH 5 ϩ , only a few experiments have been performed previously to characterize indirectly the structure of CH 5 ϩ using mass spectrometry. 14 - 18 Hiraoka and co-workers measured ⌬H nϪ1,n 0 and ⌬S nϪ1,n 0 for the clustering reactions CH 5 ϩ ͑CH 4 ͒ nϪ1 ϩCH 4 ϭCH 5 ϩ ͑CH 4 ͒ n for nϭ1 -9 using a pulsed electron beam mass spectrometry. 14 They showed an irregular decrease in the values of Ϫ⌬H nϪ1,n 0 and Ϫ⌬S nϪ1,n 0 between nϭ2 and 3, suggesting a C s symmetry structure for CH 5 ϩ which contains a 3c2e bond, since the two acidic H atoms of the 3c2e bond would give the most favorable sites for the first two CH 4 ligands. However, this result only suggests the C s structure for the core ion CH 5 ϩ of CH 5 ϩ ͑CH 4 ͒ n , not for free CH 5 ϩ , because strong interaction between CH 5 ϩ and CH 4 could deform the structure of free CH 5 ϩ ͑⌬H 0,1 0 ϭ6.87 kcal/mol͒. In order to get more reliable information on the structure of CH 5 ϩ , they also measured ⌬H nϪ1,n 0 and ⌬S nϪ1,n 0 for the cluster ions CH 5 ϩ ͑H 2 ͒ n (nϭ1 -4), which were expected to have much weaker interactions between the core ion CH 5 ϩ and H 2 molecules. 15 Unlike the case for CH 5 ϩ ͑CH 4 ͒ n , a gradual decrease of ⌬H nϪ1,n 0 with n was observed for CH 5 ϩ ͑H 2 ͒ n , though a large gap in the van't Hoff plots was still seen between nϭ2 and 3. Based upon these observations, they proposed that CH 5 ϩ still has C s structure but the positive charge is more delocalized in CH 5 ϩ when it is complexed by H 2 .
Experiments using a Fourier transform ion cyclotron resonance ͑FTICR͒ mass spectrometry have been performed on the collisionally induced intramolecular randomization of hydrogen and deuterium atoms in CH 4 D ϩ and CD 4 H ϩ by the groups of Sefcik's, 16 Smith's, 17 and Heck's. 18 In these works, the product ion branching ratio ͓BH ϩ ͔/͓BD ϩ ͔ associated with the proton/deuteron transfer reaction from CH 4 D ϩ and CD 4 H ϩ to the base B was measured as a function of the average number (͗n͘) of primary ion/molecule collisions ͑CH 4 ϩ• /CD 4 or CD 4 ϩ• /CH 4 ͒. The idea of these studies was that if significant potential barriers exist for the scrambling motions of CH 5 ϩ , the D atom in CH 4 D ϩ and the H atom in CD 4 H ϩ would be located at one of the two H atoms forming a 3c2e bond in the C s structure, and the branching ratio will be 1:1 for both CH 4 D ϩ and CD 4 H ϩ cases ͑C s model͒. If small or no barriers exist for the scrambling motions, the branching ratio will be 4:1 and 1:4 for CH 4 D ϩ and CD 4 H ϩ cases, respectively ͑randomized model͒. However, the results were inconsistent in that Sefcik's 16 and Heck's results 18 supported the C s model with a localized 3c2e bond whereas Smith's results 17 suggested the randomized model.
Because of the difficulties in the indirect characterization of the structure of CH 5 ϩ , much effort has been given to obtain high resolution infrared ͑IR͒ spectra for CH 5 ϩ , but has achieved little success. One of the difficulties in the high resolution IR study is that CH 5 ϩ scrambles even at low temperatures, as predicted by the ab initio calculations, causing significant spectral congestion. The spectral congestion would be more extensive for the CH 5 ϩ ions produced in the conventional ion sources since the ions tend to possess considerable internal energy.
In an attempt to overcome the difficulties of performing IR spectroscopy on CH 5 ϩ , we have studied the molecular hydrogen solvated carbonium ions, CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6) where the H 2 molecules are weakly bound to the core ion. The motivation was the notion that the interactions between the core CH 5 ϩ ions and the H 2 molecules are weak enough to cause only a minor perturbation to CH 5 ϩ , yet strong enough to slow down the scrambling motions. According to Hiraoka and co-workers, the binding energies (⌬H nϪ1,n ) of the H 2 molecules to the CH 5 ϩ core were measured to be less than 2 kcal/mol. 15 Schaefer and co-workers also calculated the dissociation energy (D 0 ) of CH 5 ϩ ͑H 2 ͒ to be 1.46 kcal/mol at TZ2Pϩd CCSD͑T͒. 19 The experimental and theoretical dissociation energies and enthalpies for CH 5 ϩ ͑H 2 ͒ n (nϭ1 -4) are listed in Table I. Experimentally, the weakly bound clusters CH 5 ϩ ͑H 2 ͒ n have advantages over CH 5 ϩ in that the cooling of the cluster ions by supersonic expansion is more efficient than the cooling of the CH 5 ϩ ions, since the low frequency modes involving the core-ligand bonds would play an important role in the vibrational energy transfer from initially hot ions to the cold partners. As a preliminary result, the IR spectra for CH 5 ϩ ͑H 2 ͒ have been reported previously. 20 Very recently, we also reported a study on the dynamics of the molecular hydrogen solvated carbonium ions, CH 5 ϩ ͑H 2 ͒ n (nϭ1,2,3) by measuring the IR spectra for the C-H stretching modes of CH 5 ϩ ͑H 2 ͒ n (nϭ1,2,3), and performing ab initio molecular dynamics ͑MD͒ simulations on CH 5 ϩ ͑H 2 ͒ n (nϭ0 -3). 21 The results provided considerable insight into the scrambling motion of CH 5 ϩ , and revealed the slowdown of the scrambling of the CH 5 ϩ core by the solvent H 2 molecules in CH 5 ϩ ͑H 2 ͒ n (nϭ1,2,3). In this paper, we present the complete IR spectra of the molecular hydrogen solvated carbonium ions, CH 5 ϩ ͑H 2 ͒ n (n ϭ1 -6) including the IR spectra for the H-H stretching modes of the solvent H 2 molecules, obtained in the frequency range of 2700-4200 cm Ϫ1 . It will be shown that correlation of the spectral features for the C-H stretching modes of the core CH 5 ϩ with the number of solvent H 2 molecules in CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6) can provide information on the structure and dynamics of CH 5 ϩ . It will also be shown that the vibration-rotation transitions of the H-H stretching modes in CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6) can give additional information on the structure and dynamics of CH 5 ϩ as well as information about the interactions between the CH 5 ϩ core and the solvent H 2 molecules.

II. EXPERIMENTAL DETAILS
The experimental apparatus used in this work has been described previously. [22][23][24][25][26] A schematic of the machine is given in Fig. 2. Briefly, the molecular hydrogen solvated carbonium ions CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6) were produced from a high pressure corona discharge source and subsequent supersonic expansion through a 75 m nozzle. A schematic of the corona discharge ion source is shown in Fig. 3. The corona discharge was maintained in 50-150 Torr of gas with ultrahigh purity ͑UHP͒ H 2 and UHP CH 4 in a 3 000 000:1 ratio, flowing past a 1.0 kV potential from the discharge tip of the needle to the source body maintained at approximately 350 V above ground. The discharge current under these conditions was 10-40 A. The source was maintained at the optimum temperature for each kind of cluster ion in order to maximize the ion intensity, by heating up the source body cooled by contact with a liquid nitrogen reservoir. Typical source temperatures for the molecular hydrogen solvated carbonium  ions were between Ϫ20 and Ϫ70°C. Pressures in the source chamber were between 1ϫ10 Ϫ5 and 1ϫ10 Ϫ4 Torr during the experiment. To prevent the acceleration of ions in the higher pressure region, which causes internal excitation and dissociation of the ion clusters via collisions with the background gas, the potential of the skimmer was maintained within 1 V of that of the source body.
After the skimmer, the ion beam entered a second differential pumping region containing collimating and focusing lenses. The pressure in this region was typically an order of magnitude lower than that of the source region. The beam was directed into a 60°sector magnet mass analyzer through a third differentially pumped region maintained at 10 Ϫ8 Torr.
The mass-selected beam was then bent 90°in a dc quadrupole field, decelerated to less than 0.5 eV, and focused into a rf octapole ion trap through an entrance aperture lens. The ions were usually trapped here for ϳ2 ms before IR irradia-tion. Usually, 100-500 ions were trapped per cycle, depending upon the stabilities of the cluster ions. These numbers are too small to allow direct measurement of photon absorption.
The trapped, mass-selected clusters were then vibrationally excited by a pulsed, tunable infrared laser. A Quanta-Ray IR WEX was used as a tunable IR light source. The IR wavelength was produced in a LiNbO 3 crystal that generates the difference frequency between a Lambda Physics pulsed dye laser ͑Model FL3002E͒ and the 1.06 m fundamental of a Continuum Nd-YAG laser. The IR bandwidth was 0.2 cm Ϫ1 . The pulse duration was 6 ns with a 20 Hz repetition rate, and the laser power was 1-3 mJ/pulse in the 2700-4200 cm Ϫ1 frequency region scanned in this work.
If the ions absorb one IR photon in the tuning range of 2700-4200 cm Ϫ1 , the CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6) ions vibrationally predissociate into CH 5 ϩ ͑H 2 ͒ x ϩyH 2 (xϩyϭn). Large cluster ions are so weakly bound that the vibrational predissociation of these ions can produce two or more daughter ions which differ by the mass of H 2 . Roughly 0.5 ms after the laser pulse, the potential on the exit aperture was lowered to extract ions of all masses from the trap. These ions were filtered by a quadrupole mass spectrometer tuned to pass only the daughter ions CH 5 ϩ ͑H 2 ͒ x . The observation of the CH 5 ϩ ͑H 2 ͒ x signal as a function of laser frequency was a measure of the IR absorption of CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6). Daughter ions were counted with a Daly ion detector 27 for each laser shot. Background daughter ions resulting from the decay of metastable parent ions in the rf ion trap were monitored in a separate cycle with the laser off at each wavelength and subtracted from the laser on signal. The laser power was monitored at each data point, and spectra were normalized for the power of the tunable IR laser assuming a simple linear power dependence. For a typical experiment, signals were averaged for about 500 laser shots for CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6) at each wavelength in the 2700-3200 cm Ϫ1 and 4000-4150 cm Ϫ1 frequency regions, where the IR absorptions were found for CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6). In this experiment, the composition of ions in the beam was strongly dependent on the H 2 /CH 4 mixing ratios, source temperatures and source pressures. The experimental conditions used in this work were a H 2 :CH 4 ratio of 3 000 000:1, a source temperature of Ϫ30°C and a source pressure of 60-150 Torr. Figure 4 shows the mass spectrum for CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6) obtained under these conditions. The mass spectrum shows a Gaussian distribution of the CH 5 ϩ ͑H 2 ͒ n ions with the cluster size ranging from nϭ1 to nϭ6. For the cluster ions with nу6, the mass peaks were overlapped with the intense peaks due to C 2 H 5 ϩ (m/eϭ29), C 2 H 7 ϩ (m/eϭ31), and CH 5 ϩ ͑CH 4 ͒ (m/eϭ33). In this experiment, the maximum in the distribution of mass peaks was able to be easily shifted between nϭ1 and nϭ6 by changing the source pressures and source temperatures. The maximum ion intensities for large cluster ions were obtained when high source pressures and low source temperatures were used in the discharge.
As reported previously, 20 the CH 5 ϩ ͑H 2 ͒ ions were also produced using a H 2 :CH 4 ratio of 2000:1, a Ϫ40°C source temperature and 150 Torr source pressure. But, the IR spectra obtained with these two different conditions were similar to each other. The IR spectra of CH 5 ϩ ͑H 2 ͒ obtained with the latter conditions is presented in this paper, simply because of the superior signal-to-noise ratio.

A. Internally cold CH 5 ؉ (H 2 ) n ions
Since CH 5 ϩ is expected to scramble extensively even at the moderate temperatures, it is crucial to produce the ions in internally cold forms in order to obtain information about the structure and dynamics of the CH 5 ϩ cores in the molecular hydrogen solvated carbonium ions, CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6). Therefore, it seems appropriate to discuss the conditions of the carbonium ions ͓CH 5 ϩ and CH 5 ϩ ͑H 2 ͒ n ͔ produced in this experiment. As described in detail in the previous section, the carbonium ions were produced in a high pressure and low current corona discharge source and subsequent supersonic expansion. The ionization conditions were kept as soft as possible at the sacrifice of the ion intensity. Nevertheless, the carbonium ions were likely to be vibrationally excited by the discharge process, and were expected to cool down via collisions with cold neutral species in a small high pressure drift region and during supersonic expansion. It is well known that the collisional cooling strongly depends upon the efficiency of energy transfer from internally hot ions to the cold partners. If the cold partners ͑e.g., CH 4 ͒ possess similar vibrational frequencies as the internally hot ions, the ions would be cooled much more efficiently by the mechanism of resonant energy transfer. However, this mechanism may not be significant in the cooling process of the ions produced in this work, since the concentration of methane in the gas mixture was kept low in order to avoid the formation of larger hydrocarbon ions. Large hydrocarbon ions such as C 2 H 3 ϩ , C 2 H 5 ϩ , C 3 H 7 ϩ , and C 4 H 9 ϩ , instead of the carbonium ions, were found to be dominant in the mass spectrum when the concentration of methane was high ͑see Ref. 26 for the de-tails͒. Therefore, the primary mechanism for the cooling of the carbonium ions in this work would be nonresonant energy transfer, efficient only when the molecules possess low frequency vibrational modes.
According to the ab initio calculations on CH 5 ϩ and CH 5 ϩ ͑H 2 ͒, 11,19 the lowest vibrational frequency for e-C s CH 5 ϩ was predicted to be quite high ͑856 cm Ϫ1 ͒ since the CH 3 -H 2 torsional mode ͑145 cm Ϫ1 ͒ would be a free internal rotation. On the other hand, the molecular hydrogen solvated carbonium ions, CH 5 ϩ ͑H 2 ͒ n were predicted to possess several low frequency modes involving the core-ligand bonds. As a result, the CH 5 ϩ ions were expected to possess significant internal energy due to the inefficient cooling whereas the CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6) ions were expected to be internally cold. Besides, if CH 5 ϩ ͑H 2 ͒ n ions contain more internal energy than the solvation energy, it will dissociate and produce cooler ions.
Internally cold small clusters of CH 5 ϩ ͑H 2 ͒ n could also be formed during the flight before the mass selection in the magnetic sector, by releasing some H 2 molecules from the large clusters of CH 5 ϩ ͑H 2 ͒ n . The CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6) ions were further cooled down by storing them in an ion trap for ϳ2 ms, during which some radiative cooling took place. Metastable ions, if they exist, would dissociate during the trapping time, and their contributions to the observed IR spectra were eliminated by doing a background substraction with the experimental scheme of laser on and off. In this experiment, the background level with laser off was found to be less than 0.1% of the parent ions, indicating the cold nature of the molecular hydrogen solvated carbonium ions, CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6). Figure 5 shows the IR spectra for the molecular hydrogen solvated carbonium ions, CH 5 ϩ ͑H 2 ͒ n (nϭ1 -5) obtained in the frequency range of 2700-3200 cm Ϫ1 . The spectral features in this frequency region are due to the C-H stretching modes of the CH 5 ϩ cores in CH 5 ϩ ͑H 2 ͒ n (nϭ1 -5). Three C-H stretching bands were predicted by ab initio calculations in this frequency range, and the solid lines in Fig. 5 are the result of a least squares fit with three Gaussian peaks shown as dashed lines. But, one should note that each of the three fitted Gaussian peaks for CH 5 ϩ ͑H 2 ͒ and CH 5 ϩ ͑H 2 ͒ 2 ͓Figs. 5͑A͒-5͑C͔͒ does not necessarily represent a single vibrational mode of one CH 5 ϩ isomer, due to the expected scrambling of the CH 5 ϩ cores. The positions of the fitted Gaussian peaks are listed in Table III. Figure 6 shows the IR spectra for the molecular hydrogen solvated carbonium ions CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6) obtained in the frequency range of 4050-4150 cm Ϫ1 . The observed features are due to the H-H stretching modes of the solvent H 2 molecules in CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6). In this work, the signal to noise ratios of the IR spectra for the large clusters were found to be considerably lower than those for the small clusters, since the absolute number densities of the large clusters were found to be lower than the small clusters due to the weaker binding of the large clusters, and several vibrational predissociation channels available for FIG. 4. Mass spectrum showing the carbonium ion CH 5 ϩ and the molecular hydrogen solvated carbonium ions CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6). The mixing ratio of CH 4 :H 2 was 1:3 000 000, and the source temperature and the discharge current were Ϫ30°C and 20 A, respectively. the large clusters would compete each other, resulting in the smaller number of daughter ions at each channel.

(H 2 )
The IR spectra for the C-H stretching modes of CH 5 ϩ ͑H 2 ͒, shown in Figs. 5͑A͒ and 5͑B͒, were obtained by monitoring the CH 5 ϩ signal (m/eϭ17). As reported previously, 20,21 the two IR spectra ͓Figs. 5͑A͒ and 5͑B͔͒ were obtained with hot ion conditions and cold ion conditions, respectively ͑see Ref. 20 for the details of the source condi-tions͒. One broad feature with shoulders, centered at 2964 cm Ϫ1 , was observed in the IR spectrum with cold ion conditions ͓Fig. 5͑B͔͒, indicating the floppy nature of CH 5 ϩ . The shoulder features observed in the cold ion spectrum almost disappeared in the hot ion spectrum ͓Fig. 5͑A͔͒, revealing increased scrambling of the core CH 5 ϩ . The lowest frequency peak among three Gaussian peaks fitted into the observed IR spectrum with cold ion conditions was quite broad, extending from 2700 to 3100 cm Ϫ1 , centered at 2907 cm Ϫ1 ͓see Fig. 5͑B͒ and Table III͔. According to the recent ab initio calculation on CH 5 ϩ ͑H 2 ͒, 19 three C-H stretching frequencies for e-C s CH 5 ϩ core, the global minimum energy structure, were predicted to be 2898, 2998, and 3081 cm Ϫ1 , corresponding to the symmetric CH 3 breathing, symmetric CH 3 degenerate stretching, and asymmetric CH 3 stretching modes, as shown in Table II. These vibrational modes were also predicted to have more or less similar IR intensities. The C-H stretching frequencies for the low lying transition state structures such as s-C s and C 2v CH 5 ϩ were predicted to be 2914, 2968, and 3085 cm Ϫ1 for the former, and 2732, 2987, and 3094 cm Ϫ1 for the latter ͑Table II͒. 11 The two structures were regarded as the transition states along the CH 3 internal rotation, and along the in-plane wagging of the H2 between H1 and H3 in the CH 5 ϩ core, respectively ͑see Fig. 1͒. The latter motion will be referred to subsequently as the in-plane wagging motion. It is interesting to notice that the vibrational assignments for the two high C-H stretching frequencies of s-C s CH 5 ϩ core ͑2968 and 3085 cm Ϫ1 ͒ were the asymmetric CH 3 stretching and symmetric CH 3 degenerate stretching modes, respectively, which were switched in order, compared to the case for e-C s CH 5 ϩ . This could be the result of the substantial geometrical changes in the CH 3 group during the internal rotation, as expected from the differences in the optimized C-H bond lengths and angles 11,12 between e-C s CH 5 ϩ and s-C s CH 5 ϩ . This suggests that the vibrational modes involving the three C-H bonds could be strongly coupled to each other via the CH 3 internal rotation.
On the other hand, the C 2v CH 5 ϩ transition state consisted of two strong C-H bonds and three weak C-H bonds forming a four-center three-electron (4c3e) bond. Correspondingly, the three C-H stretching frequencies ͑2732, 2987, and 3094 cm Ϫ1 ͒ were assigned to the asymmetric C-H stretching mode involving two weak C-H bonds, symmetric and asymmetric C-H stretching modes involving two strong C-H bonds, respectively ͑Table II͒. 11 The 2732 cm Ϫ1 mode, strongly red-shifted from the other two C-H stretching FIG modes of the C 2v structure, were distinct from the C-H stretching modes of the C s ͑e-C s and s-C s ͒ structures, and could serve as an indicator of the scrambling of CH 5 ϩ via the in-plane wagging motion involving the C 2v transition state.
Based on the trend in the ab initio CH 3 stretching frequencies for different CH 5 ϩ structures, it can be predicted that if the CH 3 internal rotation ͑via s-C s transition state͒ and the in-plane wagging motion ͑via C 2v transition state͒ are unhindered, the observed spectrum for the CH 3 stretching vibrations will broaden considerably due to contributions from all the possible CH 5 ϩ structures along the two internal coordinates, which are expected to have different CH 3 stretching frequencies. Furthermore, the lowest CH 3 stretching vibration of e-C s CH 5 ϩ structure will be strongly coupled to the vibrational modes of the 3c2e bond by the in-plane wagging motion, and could have frequencies ranging from 2898 cm Ϫ1 ͑e-C s CH 5 ϩ core͒ to 2732 cm Ϫ1 ͑C 2v CH 5 ϩ core͒ if the inplane wagging motion is unhindered. Therefore, only appropriate statistical averages of the CH 3 stretching frequencies over the coordinates of the two scrambling motions will describe the observed spectral features properly.
The observation of one broad feature with shoulders in the IR spectrum ͓Fig. 5͑B͔͒ and the result of the broad Gaussian peak fitted into the low frequency shoulder, instead of three distinct CH 3 stretching bands as predicted by the ab initio calculation on e-C s CH 5 ϩ , clearly suggested that the CH 5 ϩ core in CH 5 ϩ ͑H 2 ͒ scrambles considerably via large am-plitude motions such as the CH 3 internal rotation involving the s-C s transition state, and the in-plane wagging motion involving the C 2v transition state. Nonetheless, the center of the observed feature at 2965 cm Ϫ1 was only 27 cm Ϫ1 redshifted from the average C-H stretching frequency of CH 4 ͑2992 cm Ϫ1 ͒, 28 reflecting the fact that when a hydrogen atom in CH 5 ϩ does not participate in the scrambling motions, its corresponding C-H bond is similar to the C-H bond in CH 4 . Figure 6͑A͒ shows the IR spectrum for the H-H stretching mode of the H 2 in CH 5 ϩ ͑H 2 ͒, obtained by monitoring the CH 5 ϩ signal (m/eϭ17) with 0.2 cm Ϫ1 laser resolution. The vibration-rotational spectrum shows clear P, Q, and R branches, indicating the A-type transition of a near symmetric top. The band origin was 4077.4 cm Ϫ1 , 82.6 cm Ϫ1 redshifted from free H 2 ͑4160 cm Ϫ1 ͒, which suggests that the interaction between the CH 5 ϩ core and the H 2 molecule in CH 5 ϩ ͑H 2 ͒ is dominated by the electrostatic charge-induced dipole interaction. The dipole moment of H 2 induced by the ion core allowed the H-H stretching mode to be IR active. The spacing of adjacent rotational lines ranged from 1.4 cm Ϫ1 to 1.6 cm Ϫ1 . The rotational lines were found to possess some fine structures, as shown in Fig. 6͑A͒. Two anomalously intense peaks were observed in the R-branch side, as indicated by asterisks in Fig. 6͑A͒, and they could be assigned to the Q branches of two hot band transitions. The rotational progressions of the hot band transitions may contribute to the wide spread of rotational lines with a high The numbers in parentheses are the frequencies scaled by the ratio of 2977 cm Ϫ1 , one of the observed peaks for CH 5 ϩ ͑H 2 ͒ 3 , and the corresponding ab initio C-H stretching frequency for the eclipsed C s CH 5 ϩ core at the level of theory. For example, the ratio was 2977/2993ϭ0. 995  background, observed in the R-branch side ͓see Fig. 6͑A͔͒. The full analysis of the vibration-rotational spectrum will be reported elsewhere.

CH 5
؉ (H 2 ) 2 Figure 5͑C͒ shows the IR spectrum for the C-H stretching modes of CH 5 ϩ ͑H 2 ͒ 2 , obtained by monitoring the CH 5 ϩ signal (m/eϭ17). Two spectral features, centered at 2957 cm Ϫ1 and 3078 cm Ϫ1 , were observed in the frequency range of 2700-3200 cm Ϫ1 . The broad and intense feature at 2957 cm Ϫ1 was fitted with two equal Gaussian peaks centered at 2930 and 2983 cm Ϫ1 , respectively, as shown in Fig. 5͑C͒ and Table III, and the narrow feature at 3078 cm Ϫ1 was fitted with one Gaussian peak. The ab initio C-H stretching frequencies for e-C s CH 5 ϩ in CH 5 ϩ ͑H 2 ͒ 2 , shown in Table II, were more or less similar to those for e-C s CH 5 ϩ in CH 5 ϩ ͑H 2 ͒ after appropriate scaling. The ab initio C-H stretching frequencies for s-C s and C 2v CH 5 ϩ cores in CH 5 ϩ ͑H 2 ͒ 2 were also expected to be similar to the corresponding frequencies for CH 5 ϩ ͑H 2 ͒. The low frequency shoulder feature observed in the IR spectrum for CH 5 ϩ ͑H 2 ͒ was not present in the spectrum for CH 5 ϩ ͑H 2 ͒ 2 . This suggested that the scrambling motion through the in-plane wagging motion ͑via C 2v transition state͒ may be frozen out by the two H 2 molecules in CH 5 ϩ ͑H 2 ͒ 2 , unlike the case for CH 5 ϩ ͑H 2 ͒. However, the scrambling of the CH 5 ϩ core through the CH 3 internal rotation was still extensive, indicated by the broad feature at 2957 cm Ϫ1 , and strong anharmonic couplings for the vibrational modes involving these three C-H bonds were also expected. Figure 6͑B͒ shows the IR spectrum of the H-H stretching modes for the two H 2 molecules in CH 5 ϩ ͑H 2 ͒ 2 , obtained by monitoring the CH 5 ϩ signal in the frequency range of 4050-4150 cm Ϫ1 . The IR spectrum was taken with 0.2 cm Ϫ1 laser resolution and 1 cm Ϫ1 scan step. In spite of the large scan step, the observed spectrum showed clear P, Q, and R branches, indicating the A-type transition of a near symmetric top. The presence of a single rotational progression sug-gested that the two H 2 molecules were bound to the two H atoms forming a 3c2e bond, with almost equal strength. In this case, the in-phase H-H stretching vibration of the two H 2 molecules would be responsible for the observed feature since the change of dipole moment due to the in-phase vibration would be along the A-axis of CH 5 ϩ ͑H 2 ͒ 2 . The band origin was ϳ4088 cm Ϫ1 , 72 cm Ϫ1 red-shifted from free H 2 , but 10 cm Ϫ1 blue-shifted from CH 5 ϩ ͑H 2 ͒. This indicated that the interactions between CH 5 ϩ core and two H 2 molecules in CH 5 ϩ ͑H 2 ͒ 2 were also the charge-induced dipole interactions, and the interactions were weaker for CH 5 ϩ ͑H 2 ͒ 2 since the positive charge of the core CH 5 ϩ was more delocalized in CH 5 ϩ ͑H 2 ͒ 2 .

CH 5
؉ (H 2 ) 3 Figure 5͑D͒ shows the IR spectrum for the C-H stretching modes of CH 5 ϩ ͑H 2 ͒ 3 , obtained by monitoring the CH 5 ϩ signal in the frequency range of 2800-3100 cm Ϫ1 . Three partially resolved peaks, centered at 2892, 2977, and 3062 cm Ϫ1 , were found in the IR spectrum. The presence of the three well-separated peaks suggested that the scrambling motions of the CH 5 ϩ core were almost frozen out by the three H 2 molecules in CH 5 ϩ ͑H 2 ͒ 3 , and the CH 5 ϩ core could be considered as semirigid. It is interesting to notice that the observed frequencies ͑2892, 2977, 3062 cm Ϫ1 ͒ match well with the three ab initio CH 3 stretching frequencies for e-C s CH 5 ϩ ͑2891, 2993, 3079 cm Ϫ1 ͒ and e-C s CH 5 ϩ ͑H 2 ͒ ͑2898, 2998, 3081 cm Ϫ1 ͒, calculated at TZ2P (ϩ f ) CCSD level, 19 as shown in Table II. The ab initio CH 3 stretching frequencies of e-C s CH 5 ϩ ͑H 2 ͒ 3 , calculated at MP2/6-311G(D, P) level, 29 also match well with the observed frequencies after appropriate scaling ͑see Table II͒. It suggests that the CH 5 ϩ core in CH 5 ϩ ͑H 2 ͒ 3 possesses an e-C s structure. Since the adiabatic approximations made in the normal mode analysis on the C-H stretching frequencies are expected to be valid due to the semirigidity of the CH 5 ϩ core, the three observed features could be assigned to the symmetric CH 3 breathing, symmetric CH 3 degenerate stretching, and asymmetric CH 3 stretching modes, according to the ab initio normal mode analysis. 19 Furthermore, the new scaling factors for the anharmonic corrections were calculated by the ratio of 2977 cm Ϫ1 , one of the observed frequencies, to the corresponding ab initio frequency for the e-C s CH 5 ϩ core at the level of theory. The rescaled frequencies are listed in the parentheses of Table II. Figure 6͑C͒ shows the IR spectrum for the H-H stretching modes of the three H 2 molecules in CH 5 ϩ ͑H 2 ͒ 3 , obtained by monitoring the CH 5 ϩ signal in the frequency range of 4050-4140 cm Ϫ1 . Unlike the cases for CH 5 ϩ ͑H 2 ͒ and CH 5 ϩ ͑H 2 ͒ 2 , one broad feature was observed in the spectrum. One of the reasons for the spectral congestion was that the third H 2 molecule in CH 5 ϩ ͑H 2 ͒ 3 was bound to the CH 5 ϩ core in a different environment from the first two H 2 molecules, indicating the presence of a 3c2e bond in the CH 5 ϩ core in CH 5 ϩ ͑H 2 ͒ 3 . The center of the broad feature was located at ϳ4099 cm Ϫ1 , 61 cm Ϫ1 red-shifted from free H 2 , but 11 cm Ϫ1 blue-shifted from that of CH 5 ϩ ͑H 2 ͒ 2 . This also suggested that the interactions of the CH 5 ϩ core with the H 2 molecules be- These frequencies in parentheses for nϭ1 and nϭ2 were obtained by fitting with three Gaussian peaks and two equal Gaussian peaks, respectively, even though they were not resolved in the observed spectra ͓see Figs. 5͑B͒ and 5͑C͔͒. c These frequencies were measured at the maximum of the Q branches. came weaker due to the increased charge delocalization in CH 5 ϩ ͑H 2 ͒ 3 .

CH 5
؉ (H 2 ) 4 Figure 5͑E͒ shows the IR spectrum for the C-H stretching modes of CH 5 ϩ ͑H 2 ͒ 4 , obtained by monitoring the CH 5 ϩ signal. Three peaks, centered at 2878, 2977, and 3067 cm Ϫ1 , were found in the IR spectrum. These three frequencies were similar to those for CH 5 ϩ ͑H 2 ͒ 3 ͑2892, 2977, and 3062 cm Ϫ1 ͒, which were assigned to the symmetric CH 3 breathing, symmetric CH 3 degenerate stretching, and asymmetric CH 3 stretching modes, respectively. This result indicated an e-C s structure for the CH 5 ϩ core in CH 5 ϩ ͑H 2 ͒ 4 , but also no significant solvation effect by the fourth H 2 molecule. Figure 6͑D͒ shows the IR spectrum for the H-H stretching modes of the H 2 molecules in CH 5 ϩ ͑H 2 ͒ 4 . The spectrum was also obtained by monitoring the CH 5 ϩ signal in the frequency range of 4050-4140 cm Ϫ1 . One broad feature was again found, centered at ϳ4106 cm Ϫ1 , 54 cm Ϫ1 red-shifted from free H 2 , but 7 cm Ϫ1 blue-shifted from CH 5 ϩ ͑H 2 ͒ 3 , indicating the weaker interaction due to the increased charge delocalization in CH 5 ϩ ͑H 2 ͒ 4 . In addition, the slight decrease in the frequency shift from the adjacent smaller cluster ͑7 cm Ϫ1 vs 11 cm Ϫ1 ͒ suggested that the solvent effect on the charge-induced dipole interaction between the hydrogen molecules and the CH 5 ϩ core started to decrease at nϭ4, which was consistent with the trend in the C-H stretching bands described above.

CH 5
؉ (H 2 ) n (n‫)6,5؍‬ Figure 5͑F͒ shows the IR spectrum for the C-H stretching modes of CH 5 ϩ ͑H 2 ͒ 5 . The IR spectrum was obtained by monitoring the CH 5 ϩ ͑H 2 ͒ signal (m/eϭ19) instead of the CH 5 ϩ signal, since the CH 5 ϩ ͑H 2 ͒ channel was found to be the major channel for the vibrational predissociation of CH 5 ϩ ͑H 2 ͒ 5 in the frequency range of 2700-3200 cm Ϫ1 . Three features, centered at 2879, 2972, and 3043 cm Ϫ1 , were found in the spectrum, in spite of the low signal to noise ratio. These three frequencies are similar to those for CH 5 ϩ ͑H 2 ͒ 3 and CH 5 ϩ ͑H 2 ͒ 4 , which were assigned to the symmetric CH 3 breathing, symmetric CH 3 degenerate stretching, and asymmetric CH 3 stretching modes of the e-C s CH 5 ϩ core, respectively. This suggested that the structure of the CH 5 ϩ core in CH 5 ϩ ͑H 2 ͒ 5 was not changed by the fifth H 2 molecule, but was still an e-C s structure. Figures 6͑E͒ and 6͑F͒ show the IR spectra for the H-H stretching modes of CH 5 ϩ ͑H 2 ͒ 5 and CH 5 ϩ ͑H 2 ͒ 6 , respectively. These IR spectra were obtained by monitoring the CH 5 ϩ signal, the major channel in this frequency region, which was different from the case for the C-H stretching bands. The additional photon energy in this frequency range was responsible for the complete dissociation. In both spectra, one broad feature was found, centered at 4109 and 4111 cm Ϫ1 , 51 and 49 cm Ϫ1 red-shifted from free H 2 , respectively. These features were only 3 and 2 cm Ϫ1 blue-shifted from the adjacent smaller clusters, respectively. This result suggested that the charge-induced dipole interactions between the H 2 molecules and the CH 5 ϩ core were almost in saturation for CH 5 ϩ ͑H 2 ͒ 5 and CH 5 ϩ ͑H 2 ͒ 6 .

A. Dynamics of CH 5 ؉ in CH 5 ؉ (H 2 ) n (n‫0؍‬ -6)
Since the IR spectra for CH 5 ϩ ͑H 2 ͒ n (nϭ1 -5) provided information about the scrambling motions of CH 5 ϩ cores, it seems appropriate to discuss the details of the dynamics of CH 5 ϩ by combining the results of this work and the previous theoretical works. Two crucial theoretical works have been performed previously by Schleyer and co-workers, and by us in collaboration with Liu and Tse. The first was the high level ab initio calculation at TZ2Pϩf CCSD level, and the second was the ab initio molecular dynamics ͑MD͒ simulation. The two theoretical methods seem to be complementary to each other such that the first provides very accurate electronic energies and harmonic frequencies of CH 5 ϩ , but only for a few optimized nuclear configurations, while the second can simulate all of the classical trajectories of CH 5 ϩ , allowed at the finite temperatures on the ground electronic potential surface, calculated by the density functional method which may not be as accurate as the first.
Both methods predicted the complete scrambling of CH 5 ϩ . According to the high level ab initio calculation, 11,12 the scrambling was predicted to occur through s-C s and C 2v structures, which were regarded as the transition states for the CH 3 internal rotation and the in-plane wagging motion. The two internal motions were expected to be strongly coupled to each other such that the CH 3 internal rotation would be free only when the 3c2e bond involved in the in-plane wagging motion is localized, like in the C s CH 5 ϩ structure. The same high level ab initio calculation on CH 5 ϩ ͑H 2 ͒ predicted almost the same results for the CH 5 ϩ core in CH 5 ϩ ͑H 2 ͒. At present, no high level ab initio calculation has yet been reported on CH 5 ϩ ͑H 2 ͒ n (nу2). Ab initio MD simulations have been performed on CH 5 ϩ ͑H 2 ͒ n (nϭ0 -3) as reported previously. 21 During the simulation of ϳ3 ps at a temperature of ϳ100 K, the 3c2e bond representing a C s structure for CH 5 ϩ could be formed among any pair of H atoms in CH 5 ϩ . For CH 5 ϩ ͑H 2 ͒, the 3c2e bond was more or less localized around the H atom of the CH 5 ϩ core which was complexed by the H 2 molecule. Scrambling through the two internal motions ͑via s-C s and C 2v transition states͒ were still expected to be significant. For CH 5 ϩ ͑H 2 ͒ 2 , the 3c2e bond was localized to the two H atoms which were bound by the two H 2 molecules. It was explained by the electron deficiency in the 3c2e bond which attracts the two H 2 molecules. Preference for the localized 3c2e bond was also predicted in the ab initio calculation at MP2/6-31G**, from the decrease in the angle of the 3c2e bond ͑ՄH1CH2͒ from 48.4°for CH 5 ϩ ͑H 2 ͒ to 47.7°for CH 5 ϩ ͑H 2 ͒ 2 ͓see Figs. 9͑A͒ and 9͑B͔͒. 15 But, the scrambling through the CH 3 internal rotation was still extensive. For CH 5 ϩ ͑H 2 ͒ 3 , the CH 5 ϩ core was semirigid with the CH 3 internal rotation considerably hindered, but the in-plane wagging motion unhindered.
In the IR spectrum for the C-H stretching modes of CH 5 ϩ ͑H 2 ͒ ͓Fig. 5͑B͔͒, as mentioned previously, the center of the observed feature ͑2965 cm Ϫ1 ͒ was only 23 and 27 cm Ϫ1 red-shifted from the average ͑2988 cm Ϫ1 ͒ of the three highest ab initio C-H stretching frequencies of a C s CH 5 ϩ ͑e-C s and s-C s ͒, as shown in Table II, and the average C-H stretching frequency ͑2992 cm Ϫ1 ͒ of CH 4 , respectively. This result suggested that most of the structures possessed by the CH 5 ϩ core during the scrambling still contain a CH 3 unit with strong C-H bonds like those in the optimized C s CH 5 ϩ structures or the C-H bonds in CH 4 . The overall broad feature and the broad low frequency shoulder observed in the IR spectrum were suggestive of the scrambling through the CH 3 internal rotation ͑via s-C s transition state͒ and the in-plane wagging motion ͑via C 2v transition state͒. Therefore, the CH 5 ϩ core in CH 5 ϩ ͑H 2 ͒ continues to scramble through the CH 3 internal rotation and the in-plane wagging motion, but the C-H bonds which are not directly involved in the nonclassical bond ͑3c2e or 4c3e bond͒, are expected to be strong like the C-H's in CH 4 . The A-type vibration-rotational transitions observed in the IR spectrum for the H-H stretching mode ͓Fig. 6͑A͔͒, suggested the structure of CH 5 ϩ ͑H 2 ͒ with the H 2 molecule weakly bound to one of the two H atoms forming the 3c2e bond, in good agreement with the theoretical predictions. 19 The anomalously intense peaks and the rotational fine features observed in the spectrum could be due to the scrambling motions involving the CH 3 internal rotation and in-plane wagging motion.
For CH 5 ϩ ͑H 2 ͒ 2 , one broad and intense peak at 2957 cm Ϫ1 and one narrow peak at 3078 cm Ϫ1 , were observed while the broad low frequency shoulder observed for CH 5 ϩ ͑H 2 ͒ was no longer present in the IR spectrum ͓Fig. 5͑C͔͒. This result was consistent with the theoretical prediction that the CH 5 ϩ core has a C s structure with the 3c2e bond localized. The scrambling through the in-plane wagging motion was expected to be considerably hindered. The broad feature at 2957 cm Ϫ1 suggested that the scrambling through the CH 3 internal rotation was still significant. Strong anharmonic couplings for the vibrational modes involving the CH 3 group were also expected. The broad and intense peak at 2957 cm Ϫ1 could be assigned to the two strongly coupled C-H stretching modes, while the narrow feature at 3078 cm Ϫ1 could be due to the other less coupled C-H stretching mode. The A-type vibration-rotational transitions observed in the IR spectrum for the H-H stretching modes ͓Fig. 6͑B͔͒, were suggestive of the CH 5 ϩ ͑H 2 ͒ 2 structure with the two H 2 molecules bound to the two H atoms forming the 3c2e bond in the CH 5 ϩ core. The in-phase vibration of the two H-H stretching modes would be exactly along the A axis of the ion when the CH 3 internal rotation is free.
For CH 5 ϩ ͑H 2 ͒ 3 , three partially resolved features, centered at 2892, 2977, 3062 cm Ϫ1 were observed in the IR spectrum ͓Fig. 5͑D͔͒, indicating the semirigid nature of the CH 5 ϩ core. Only scrambling would occur through quantum tunneling, causing the broad bandwidths. It is interesting to notice that the observed frequencies ͑2892, 2977, 3062 cm Ϫ1 ͒ match well with the three ab initio CH 3 stretching frequencies, for e-C s CH 5 ϩ ͑2891, 2993, 3079 cm Ϫ1 ͒ ͑Ref. 11͒ and e-C s CH 5 ϩ ͑H 2 ͒ ͑2898, 2998, 3081 cm Ϫ1 ͒. 19 It suggests that the CH 5 ϩ core in CH 5 ϩ ͑H 2 ͒ 3 possesses an e-C s structure. Correspondingly, the three C-H stretching frequencies could be assigned to the symmetric CH 3 breathing, symmetric CH 3 degenerate stretching, and asymmetric CH 3 stretching modes of e-C s CH 5 ϩ core in CH 5 ϩ ͑H 2 ͒ 3 . The ab initio MD simulation also predicted the semirigid nature of the CH 5 ϩ core, but predicted the scrambling through the in-plane wagging motion, different from the experimental result. The difference was attributed to the underestimation of the potential barrier for the in-plane wagging motion. 21 In addition, other isomers of CH 5 ϩ ͑H 2 ͒ 3 such as the structure with the third H 2 located out of plane to the 3c2e bond, may contribute to the observed IR spectrum.
For CH 5 ϩ ͑H 2 ͒ 4 , three resolved features, centered at 2878, 2979, and 3067 cm Ϫ1 , were observed in the IR spectrum ͓Fig. 5͑E͔͒, similar to the spectral features observed for CH 5 ϩ ͑H 2 ͒ 3 ͓Fig. 5͑D͔͒. This result suggested that the scrambling of CH 5 ϩ core was more or less frozen out by the first three H 2 molecules, and the addition of the fourth H 2 molecule resulted in only a minor change in the structure of the CH 5 ϩ core. It was consistent with the results of Hiraoka and co-workers' measurements 15 on ⌬H T 0 's of the clustering reactions, CH 5 ϩ ͑H 2 ͒ nϪ1 ϩH 2 ϭCH 5 ϩ ͑H 2 ͒ n ͑see Table I͒, in that the stabilization of the cluster ions by the fourth H 2 molecule was small, compared to the stabilization by the third H 2 ͑0.17 vs 0.04 kcal/mol͒. In the IR spectrum for the H-H stretching modes of CH 5 ϩ ͑H 2 ͒ 4 ͓Fig. 6͑D͔͒, the frequency shift of the observed feature from the adjacent smaller cluster decreased from that for CH 5 ϩ ͑H 2 ͒ 3 , which was consistent with the trend for the C-H stretching modes as described above.
For CH 5 ϩ ͑H 2 ͒ n (nϭ5,6), the trend of the spectral features observed in the IR spectrum ͓Figs. 5͑F͒, 6͑E͒, 6͑F͔͒, were similar to the case for CH 5 ϩ ͑H 2 ͒ 4 . The structures of the CH 5 ϩ cores were expected to be unchanged by the fifth and sixth H 2 molecules.

B. Stabilities and structures of CH 5 ؉ (H 2 ) n (n‫1؍‬ -6)
In this section, the stabilities of the solvated complexes, CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6) are discussed from the correlation between the H-H stretching frequencies and the strength of the interactions. Possible solvation structures are also presented.
As described previously, the interactions between CH 5 ϩ core and the H 2 molecules are dominated by the electrostatic charge-induced dipole interactions, where the strengths are proportional to the charge densities at the H atoms of CH 5 ϩ core, the binding sites for the H 2 molecules in CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6). The effect of the electrostatic interaction on the vibrational frequency of the solvent H 2 molecules has been addressed previously in the calculation of the Stark shifts of the H-H stretching modes as a function of the distance from the charge to H 2 molecule by Hunt and Poll. 30 The frequency shifts of the H-H stretching modes from free H 2 could be a measure of the strength of the electrostatic interactions. Figure 7 shows a plot of the peak positions of the H-H stretching modes as a function of the size of the clusters. The frequency shifts from free H 2 ͑4160 cm Ϫ1 ͒ decreased as the number of H 2 molecules increased, and reached a limit at nϭ4. This result clearly indicated that the positive charge of the CH 5 ϩ core was gradually delocalized as the size of the clusters increased. Figure 8 shows a plot of the correlation between the H-H stretching frequencies and the Ϫ⌬H T 0 's of the clustering reactions, CH 5 ϩ ͑H 2 ͒ nϪ1 ϩH 2 ϭCH 5 ϩ ͑H 2 ͒ n (nϭ1 -4), measured by Hiraoka and co-workers ͑see Table I͒. 15 The correlation followed the idea of the previous work by Hunt and Poll as described above. A good correlation was found between the H-H stretching frequencies and the Ϫ⌬H T 0 's of the clustering reactions, as shown in Fig. 8. From the correlation, the Ϫ⌬H T 0 's for the formation of CH 5 ϩ ͑H 2 ͒ 5 and CH 5 ϩ ͑H 2 ͒ 6 , which were not measured in the previous work by Hiraoka and co-workers, were calculated to be 1.52 and 1.49 kcal/mol, respectively. Furthermore, one could correlate the H-H stretching frequencies with the theoretical binding energies to test the consistency of the calculations.
Finally, it is appropriate to address the possible structures of the solvated complexes, CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6) by combining the results of this work and the results of the theoretical work. Figure 9 shows the possible structures of CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6). Both experimental and theoretical results 15,19 consistently suggested the structures shown in Figs. 9͑A͒ and 9͑B͒ for CH 5 ϩ ͑H 2 ͒ and CH 5 ϩ ͑H 2 ͒ 2 , where the H 2 molecules were bound to the H atoms forming the 3c2e bond in the CH 5 ϩ core. For CH 5 ϩ ͑H 2 ͒ 3 , the most stable structure was predicted to be the structure shown in Fig. 9͑C͒, but other structures such as the structure shown in Fig. 9͑D͒, where the third H 2 was located out of plane to the 3c2e bond, could be formed in internally hot ions. Due to the weak interactions between the CH 5 ϩ core and the H 2 molecules in CH 5 ϩ ͑H 2 ͒ n (nу4), the structures of the ions are better described as the mixture of several structures undergoing rapid isomerizations on the very shallow potential energy surfaces. But, it is still instructive to consider the local minimum energy structures for CH 5 ϩ ͑H 2 ͒ n (nу4). For CH 5 ϩ ͑H 2 ͒ 4 , the fourth H 2 could bind to either the H4 ͑or H5͒ of the CH 5 ϩ core ͓Fig. 9͑E͔͒ or the 3c2e bond in the out-ofplane fashion ͓Fig. 9͑F͔͒. For CH 5 ϩ ͑H 2 ͒ 5 , the fifth H 2 molecule could bind to the H5 ͑or H4͒ of the CH 5 ϩ core, completing the first solvation shell around the CH 5 ϩ core ͓Fig. 9͑G͔͒. In addition, the CH 5 ϩ ͑H 2 ͒ 5 ions could form the structures with one or two H 2 molecules binding to the 3c2e bond in the out-of-plane fashion ͓Fig. 9͑H͔͒. For CH 5 ϩ ͑H 2 ͒ 6 , the sixth H 2 molecule can bind to the 3c2e bond of the CH 5 ϩ core in the out-of-plane fashion ͓Fig. 9͑I͔͒ after the first solvation shell is complete at nϭ5. Other structures involving the isomers of CH 5 ϩ ͑H 2 ͒ 4 and CH 5 ϩ ͑H 2 ͒ 5 are also possible for CH 5 ϩ ͑H 2 ͒ 6 .

V. SUMMARY
The infrared spectra for the molecular hydrogen-solvated carbonium ions, CH 5 ϩ ͑H 2 ͒ n (nϭ1 -6) have been presented. Spectroscopic evidence has been presented in support of the scrambling of CH 5 ϩ through the large amplitude motions such as the CH 3 internal rotation and the in-plane wagging motion. More importantly, the scrambling motions of CH 5 ϩ cores were slowed down by attaching the solvent H 2 molecules to the core ion. The complete freezing of the scram-  bling motions was found when the first three H 2 molecules were bound to the CH 5 ϩ core. A good agreement between the experimental results and the theoretical predictions was found in the dynamics of CH 5 ϩ . A clear extension of this work would be to improve the resolution of the IR spectra for the H-H stretching modes of CH 5 ϩ ͑H 2 ͒ and CH 5 ϩ ͑H 2 ͒ 2 , which would provide additional information on the structures and the rotational and tunneling dynamics of both the CH 5 ϩ cores and the entire clusters. High order overtone transitions of free CH 5 ϩ can be measured by improving the schemes for vibrational excitation and probe with the use of high power IR and CO 2 lasers. In addition, significant efforts for the generation of internally cold CH 5 ϩ ions should be made, so that the IR spectra are not smeared out due to spectral congestion by the scrambling of CH 5 ϩ .

ACKNOWLEDGMENTS
We would like to thank Dr. John S. Tse at National Research Council ͑NRC͒ of Canada, for providing us with the results of his calculation prior to publication. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098.