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Adsorption of Small Molecules with the Hydroxyl Group on Sodium Halide Cluster Ions† Mamoru Tsuruta,‡ Ari Furuya,‡ Koichi Ohno,‡ Masami Lintuluoto,§ and Fuminori Misaizu*,‡ Department of Chemistry, Graduate School of Science, Tohoku UniVersity, 6-3 Aramaki, Aoba-ku, Sendai 980-8578, Japan, and Department of EnVironmental Information, Kyoto Prefectural UniVersity, Shimogamo, Sakyo-ku, Kyoto 606-8522, Japan ReceiVed: July 29, 2009; ReVised Manuscript ReceiVed: December 8, 2009
We have investigated adsorption of molecules with hydroxyl group, ROH, on sodium halide cluster ions, NanXn-1+ (X ) F and I, n ) 10-17) by mass spectrometry and by theoretical calculations. From analysis of the cluster ion intensities, the adsorption of one water molecule (R ) H) is most efficient for Na13X12+, whose structure has a NaX defect from a 3 × 3 × 3 cubic structure of n ) 14. This result suggests that the defect has an important role in the adsorption reaction. However, it is also found that the reactivity diminishes with increasing bulk size of the R group from H to CH3, (CH3)2CH, and (CH3)3C. These results imply that the adsorption reactivity is dominated by steric hindrance; the smaller molecules are adsorbed inside the basket structures of Na13X12+. Reactivity dependence on the basket size is also discussed by comparing the results of NanFn-1+ and NanIn-1+. 1. Introduction Adsorption reaction of water molecules on alkali halide (AH) surfaces, which is an initial step in the dissolution and deliquescence processes of salt, has been studied extensively for many years. This is partly because of its importance in atmospheric aerosol formation,1 and also because of a technological interest in the salt separation by contact electricity.2 The adsorption structure and dynamics on AH surfaces were examined by using techniques of microscopy developed recently3,4 and were discussed in connection with the role of defects in the crystal. The size and environment of these defects are dependent on the kind of alkali and halogen atom constituents, and thus the adsorption reactivity is expected to be different for each AH species. Investigations of AH microclusters (nanocrystals) also help the microscopic understanding of this phenomena, although there were a limited number of AH-cluster studies with water adsorbates so far.5,6 As for the studies of other molecular adsorption on AH clusters, ammonia adsorption on NanFn-1+ cluster ions was most extensively studied by Whetten and co-workers.5,7-9 The adsorption reactivity was found to be relatively higher at n ) 13 and 22 than adjacent sizes, which indicates that the ammonia molecule adsorbs at defect sites of the cluster ions, because these clusters have defects due to one NaF-unit lacking from the stable cubic structures of n ) 14 (3 × 3 × 3) and 23 (3 × 3 × 5) clusters. According to the paper by Whetten and co-workers, the high reactivity at n ) 13 and 22 was attributed to the basket-like structures, as shown in Figure 1b. However, the role of other crystal structures with deficiency cannot be ruled out, although the basket structure was suggested to be the most stable isomer from a Monte Carlo simulation.9 In the present study we have actually obtained three types of optimized cluster structures both for Na13F12+ (Figure 1) and for Na13I12+ from quantum-chemical calculations based on †
Part of the “W. Carl Lineberger Festschrift”. * Author to whom correspondence should be addressed. Electronic mail:
[email protected]. ‡ Tohoku University. § Kyoto Prefectural University.
Figure 1. Optimized structures of Na13F12+ clusters (black, Na+; white, F-) and relative energies: (a) edge-defect; (b) basket; (c) surface-defect structures.
density functional theory (DFT). These are based on the 3 × 3 × 3 cubic structure of n ) 14, and one NaX is lacking from an edge (edge-defect structure, Figure 1a), from the inside (basket structure, Figure 1b), or from a surface [surface-defect structure, Figure 1c). Among these, the edge-defect isomers are found to be the most stable for both AH cluster ions, as noted in the later section. The basket structures are less stable than the edgedefect isomers for NaF and NaI, respectively. Therefore, the contribution of the basket structure for molecular adsorption is found to be not so straightforward: Is a molecule really adsorbed inside the basket structure of n ) 13? To elucidate this issue, we have systematically examined the relative adsorption reactivity of simple hydroxide molecules ROH on Na13X12+ (X ) F and I) ions, by changing the bulk size of R from H (water) to CH3 (methanol), (CH3)2CH (2propanol), and (CH3)3C (2-methyl-2-propanol). We first show experimental results of mass spectrometry, followed by comparison with the results of DFT calculations on the possibility of ROH inclusion in the basket structures. The adsorption site in the Na13X12+ ions was also investigated by ultraviolet photodissociation experiment for the NanIn-1+(methanol) clusters. 2. Experimental Section We used three-stage differentially evacuated chambers, consisting of a cluster source, Wiley-McLaren -type ion acceleration grids of a time-of-flight mass spectrometer (TOFMS),
10.1021/jp9072312 2010 American Chemical Society Published on Web 12/18/2009
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and a homemade reflectron TOFMS. Part of the experimental apparatus were already described elsewhere,10-12 so we mainly show here the ion source of the AH clusters with molecular adsorbates. Sodium halide cluster ions were produced by a laser vaporization method of Na rod and following reaction with organic halide molecules (methyl iodide for NaI and hexafluorobenzene for NaF) expanded from a pulse valve (General Valve, Series 9) with He gas as adopted by Whetten and coworkers.13 Here the sodium rod was prepared from a lump (Nacalai, >99%) under a nitrogen atmosphere in a vacuum drybox, and it was quickly set to the vaporization source in the vacuum chamber just before evacuation. Cluster ions produced in the source were then reacted with ROH molecules in a flow reactor attached to the nozzle exit of the cluster forming block. The ROH samples were introduced to the flow reactor from another pulse valve (General Valve, Series 9) with He buffer gas. Resultant ions were collimated with a conical skimmer, and they were accelerated by pulsed electric fields of the Wiley-McLaren source of the TOFMS. Finally, the ions were detected with a dual microchannel plate (Hamamatsu, F1552-21S), after traveling through the reflectron TOFMS. The output signals were stored and averaged by a digital storage oscilloscope (LeCroy 9344C), and the data were sent to a personal computer via GPIB intereface. In the photodissociation or photodesorption experiment, the mass-separated ions in a first drift region of the reflectron were irradiated with a photolysis laser beam before entering the ionreflection region. Then original ions and photofragment ions were detected separately because of the TOF difference in the reflection region and the second drift region. For photodesorption experiment of the ions with a methanol molecule, the deuterated species CD3OD was used as an adsorbate to make the mass separation of both the parent and fragment ions more apparent. A pulsed Nd:YAG laser-pumped dye laser (Spectra Physics, GCR150/PDL-2) with a frequency doubling system (Inrad, Autotracker III) was used to generate a photolysis laser with wavelengths of 210-260 nm. 3. Calculation DFT calculations with 6-311G(d) basis set and B3LYP functional14 were performed to obtain stable geometrical structures of bare Na13X12+ ions and those of molecule-adsorbed Na13X12+ ions for the three defect structures from the 3 × 3 × 3 cubic structure of n ) 14 noted above. Harmonic vibrational frequencies of the ions were obtained at the same level of theory for zero-point energy correction. Single point energies were also calculated for various positions of the ROH adsorbates along adsorption (or desorption) coordinates with the geometries of ROH and Na13X12+ fixed at the optimized ones. All calculations were carried out by using the GAUSSIAN 03 package.15
NanXn-1+(ROH) + ROH a NanXn-1+(ROH)2
equilibrium constant K(n) 2
(2)
NanXn-1+(ROH)i-1 + ROH a NanXn-1+(ROH)i
equilibrium constant Ki(n)
(3)
These equilibrium constants were determined using concentrations of the cluster ions and ROH as
Ki(n)
)
[NanXn-1+(ROH)i] [NanXn-1+(ROH)i-1][ROH]
(4)
Because [ROH] is independent of the cluster size, we can define the following relative equilibrium constants, R(n) i :
Ri(n) )
[NanXn-1+(ROH)i] [NanXn-1+(ROH)i-1]
(5)
Then we can obtain R(n) i values from the relative intensities of cluster ions observed in mass spectra. In this treatment, it should be examined that the above successive reactions really satisfy equilibrium conditions. We confirmed these conditions by as a function of plotting the experimentally determined R(n) i (n) [ROH], because R(n) i ) Ki [ROH] should be proportional to the ROH concentration under the above assumptions. Although it is difficult to determine absolute values of [ROH], we monitored the background pressure of the vacuum chamber as a scaled ROH concentration. We measured mass spectra at various main chamber (Wiley-McLaren ion source chamber) pressures, by changing the gas pressure from the second pulse valve. Finally, we confirmed that R(n) i is proportional to the chamber pressure, that is, [ROH] at some pressure range, as shown in Figure 3. In this figure we obtained proportionalities of R1(5), R2(5), and R3(5) with the chamber pressure less than 3.2 × 10-4 Pa for CH3OH adsorption on Na5I4+. Also we obtained the intersecting points -4 of the lines with the R(5) i ) 0 axes (x axes) as (1.6-1.8) × 10 Pa, which correspond to the base pressures without introducing ROH/He gas from the second pulse valve. B. Substituent Dependence of ROH Adsorption Reactivity on NanXn-1+. As noted in the Introduction, we examined adsorption reaction of one ROH molecule on NanXn-1+ ions. In the mass spectrometric measurement for this study, the ROH sample gas concentration was lowered enough to ignore the adsorption of two or more molecules. Under this condition, the relative equilibrium constant for single molecule adsorption,
4. Results and Discussion A. Mass Spectrometric Measurements of ROH Adsorption Reactions on NanXn-1+ Ions. The adsorption reaction was examined by collision of the NanXn-1+ ion beam with ROH molecules in a flow reactor, followed by mass spectrometric measurements.11 Figure 2 shows a typical mass spectrum obtained for NanIn-1+ with methanol molecules for n ) 11-21. Here we first assume the following successive adsorption equilibrium reactions;
NanXn-1+ + ROH a NanXn-1+(ROH)
equilibrium constant K(n) 1
(1)
Figure 2. Typical time-of-flight mass spectrum of NanIn-1+ cluster ions with methanol adsorbates for n ) 11- 21.
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R(n) 1
)
[NanXn-1+(ROH)] [NanXn-1+]
Tsuruta et al.
(6)
should reflect the adsorption reactivity for each cluster ions. By using R1(n), we can discuss size dependence of the reactivity for a given ROH molecule. However, to compare the reactivities of different ROH molecules on some NanXn-1+ ions, it is necessary to scale the R1(n) values for different ROH adsorbates. It is difficult to obtain a reliable normalization factor for each R1(n); we tentatively used the scaled values to keep the averaged R1(n) values of n ) 10-12 constant for four different ROH adsorbates. This normalization analysis is based on the assumption that the adsorption reactivities at these sizes are not sensitively dependent on the substituent R. This hypothesis is further rationalized by the results of calculation that the interaction potentials between a molecule and the edge- and the surface-defect structure are comparable for all ROH adsorbates as noted below. Figure 4 shows scaled R1(n), that is, scaled relative intensities of NanXn-1+ (ROH) ions with respect to unreacted NanXn-1+ for n ) 10-17, obtained from the mass spectra. In water adsorption (the top panels of Figure 4), this relative intensity has a minimum at a cubic cluster of n ) 14 for both systems of X ) F and I. In contrast, the cluster with one NaX unit less than the cube, n ) 13, is the most reactive for both sodium halide systems, whereas another maximum was observed at 16 for NaF and at 15 for NaI. The propensity observed at n ) 13 and 14 is qualitatively the same as that for the NH3 adsorption reported by Whetten and co-workers,5,7-9 indicating that the molecules are preferentially adsorbed on the defect sites of the nanocrystals. Furthermore, this size dependency was most clearly appeared in the water adsorption, whereas it was commonly observed to some extent for the four different ROH molecules examined; the reactivity of Na13F12+ toward H2O is
Figure 3. Relative equilibrium constants Ri(5) of adsorption reactions of the ith methanol molecule on Na5I4+ ions for i ) 1, 2, and 3, as a function of main chamber pressure.
Figure 4. Scaled ratios of the ion intensities NanFn-1+(ROH)/NanFn-1+, and NanIn-1+(ROH)/NanIn-1+ as a function of n (10 e n e 17) for R ) H, CH3, (CH3)2CH, and (CH3)3. Ratios of each species are normalized at the averaged values for n ) 10-12.
about 1 order of magnitude higher than that of Na12F11+, whereas the ratio Na13F12+/Na12F11+ toward CH3OH was no more than 5.5. Although this ratio further decreases from CH3OH adsorption to (CH3)2CHOH and (CH3)3COH adsorption, the largest difference was observed between H2O and CH3OH adsorption. On the other hand, in the adsorption on NaI clusters, high reactivity at Na13I12+ is almost diminished for (CH3)2CHOH and (CH3)3COH adsorption, whereas it is still observed for CH3OH. The anomalous adsorption reactivity at n ) 13 has been further examined by photodissociation experiment for the NanIn-1+ ions with a methanol adsorbate. To detect the parent and fragment ions separately in mass spectra, we used deuterated methanol CD3OD instead of CH3OH in the photodissociation experiment. The NanIn-1+(CD3OD) ions were first excited with a UV laser to charge-transfer states localized on the bare NanIn-1+ ions. Then the neutralized NaI unit (or I + Na) was dissociated promptly from the cluster ions, followed by additional thermal desorption and fragmentation reactions, as discussed in our previous paper.11 Fragment-ion mass spectra
were obtained from NanIn-1+(CD3OD) for n ) 13-15 by irradiation with a laser at 220 nm (Figure 5). In this figure, intensity distributions of the fragment ions are strongly dependent on the cluster size. For example, the Na14I13+ ion was predominantly formed by fragmentation of one NaI unit and a methanol from Na15I14+(CD3OD) (Figure 5c), whereas the intensity of the Na13I12+(CD3OD) fragment was much higher than that of Na13I12+ from Na14I13+(CD3OD) (Figure 3b). These
Adsorption of Molecules with ROH on NaH
Figure 5. Typical mass spectra of photofragment ions from NanIn-1+(CD3OD) for n ) (a) 13, (b) 14, and (c) 15 at a photolysis laser energy of 5.64 eV (wavelength of 220 nm).
results imply that the stable ions show high intensities in the fragment-ion mass spectra, and therefore, the Na13I12+(CD3OD) ion is expected to be extraordinary stable as well as Na14I13+. Thus the fragment-ion intensities observed in Figure 5 were consistent with the result of adsorption reactivities shown in Figure 4. C. Stabilities of Na13X12+ Nanocrystals with ROH Adsorbates. Our main interest is whether the ROH adsorption predominantly proceeds for the Na13X12+ basket structure or not, as noted in the Introduction. For this purpose we first obtained the geometry and relative energies of the three Na13X12+ structures for X ) F and I by DFT calculation. As noted already, the edge-defect isomers (Figure 1a for Na13F12+) are the most stable for both Na13F12+ and Na13I12+ ions. The basket structures (Figure 1b for Na13F12+) are 0.03 and 0.17 eV less stable than the edge-defect isomers for NaF and NaI, respectively. The surface-defect isomer (Figure 1c for Na13F12+) is the least stable among the three isomers, with 0.24 (NaF) and 0.17 eV (NaI) less stable than the most stable structures. If the clusters are fully equilibrated at a room temperature of 300 K, the population of the basket isomer is estimated to be 8.3% and less than 0.1% of the edge-defect structure for Na13F12+ and Na13I12+, respectively, also considering degeneracy (the number of equivalent defect sites) of each structure. To obtain further information on the adsorption reactivity, we next calculated optimized structures of Na13F12+(ROH), in which the molecules are adsorbed at the defect site, for the three Na13F12+ isomers in Figure 1. We also examined other isomers in which the molecules are adsorbed at nondefect sites, and found that the binding energies for such isomers are smaller than those of the structures adsorbed at the defect sites. Although it was found that 2-propanol and 2-methyl-2-propanol are too large to fit inside the basket structure, all of the other combinations of the nanocrystal isomers and adsorbate molecules were found to have equilibrium structures similar to the examples for water adsorbate shown in the right of Figure 6. The following features were commonly observed for these structures with four different adsorbates: molecular adsorption does not significantly perturb the crystal structures as in the
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Figure 6. Potential energy curves along molecular desorption from three types of optimized structures of Na13F12+(ROH) (examples of water adsorbate shown on the right) calculated by B3LYP/6-311G [ROH ) H2O (O), CH3OH (b), (CH3)2CHOH (0), (CH3)3COH (9)]. These curves were obtained by shifting the molecule along the r axis (shown by the arrows in the cluster models) from the optimum position (∆r ) 0), with fixed geometry of ROH and Na13F12+. For the basket structure, only the results on H2O and CH3OH adsorption are shown.
case of NH3 adsorption,16 and the F- vacancy position is occupied by the oxygen atom or its lone pair of the adsorbate, as discussed in our previous paper11 and also reported by Homer et al. for NH3 adsorption.9 In water adsorption, the adsorption energies, which are defined as the energy differences between the molecule-adsorbed cluster and the free pair of bare AH cluster and the molecule, were calculated to be comparable for three isomers, in spite of the large difference in the circumstances of the adsorption sites: 1.38 eV for the edge-defect isomer and 1.24 and 1.23 eV for the basket and surface-defect structures, respectively. We have also calculated water-adsorption energies at the nondefect sites by optimization from various initial geometries. As a result, the adsorption energies at the corner and at the surface of the Na13F12+ basket isomer amount to 0.81 and 0.66 eV, respectively, which are far lower than the energies at the defect sites. Therefore, the ROH molecules are concluded to be predominantly adsorbed at defect sites of the nanocrystals, in agreement with the results that the Na13X12+ ions with defect sites are much more reactive with adsorbate molecules than cubic Na14X13+ ions observed in mass spectrometry and photodissociation experiments. From the calculated adsorption energies for four ROH adsorbates, it is also found that the adsorption reactivities are comparable for different adsorbates unless they sensitively depend upon the R substituent size, as in the basket structure. We can thus justify the normalization process of R1(n) in Figure 4. Next we calculated the energies successively by moving the ROH position away from the cluster ion, under the condition that the geometry of ROH and the AH nanocrystal was fixed. The left side of Figure 6 shows potential curves thus obtained along the molecular desorption coordinates, r, which are the axes indicated by arrows in the right structures for possible three Na13F12+(ROH) isomers. In this figure, interaction potentials are almost identical for the four ROH molecules with the edgedefect and surface-defect structures. On the other hand, for the basket structure, the potential curves are found to be sensitively dependent on the adsorbate molecule. The potential curve of Na13F12+(H2O) for the basket structure has a potential barrier of 0.7 eV, indicating that the repulsive interaction between H2O
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Figure 7. Schematic views from the opening surface of Na13F12+/ Na13I12+ basket structures and adsorbate molecules located at the surface. The Na+ (black), F- (white), and I- (white) radii correspond to their ion radii, 1.02, 1.33, and 2.20 Å, respectively.17 Atoms in the adsorbate species have radii proportional to their van der Waals radii [H, 1.20; C, 1.70; O, 1.40 Å].18
and the crystal ions has a maximum at the exit of the basket. For methanol adsorbate, the binding energy turns out to be negative (-0.2 eV), and the potential barrier is nearly 1.5 eV. Thus methanol cannot be adsorbed inside the basket, and neither can the larger adsorbates, 2-propanol and 2-methyl-2-propanol. This theoretical prediction that the Na13F12+ basket structure can accommodate a water molecule but not a methanol or larger alcohols agrees with the observed results shown above. It should also be noted that similar interactions are dominant in the adsorption of the four ROH molecules on Na13F12+, except for the steric hindrance of the R substituent. To discuss the ROHbinding potential surface in more detail, it is necessary to fulfill more rigorous calculation such as full optimization for the geometries of ROH and AH clusters. Consideration of the inside basket space based on ionic17 and van der Waals radii18 also supports this conclusion, as depicted in Figure 7, in which the uppermost layer atoms of the basket Na13X12+ ions and the adsorbate molecules are shown. Although these radii are not so rigorous, and although the crystal structure may change with the molecular approach, as suggested in the theoretical calculation for NH3 adsorption,16 only the water molecule can easily go through the opening of the Na13F12+ basket by changing its orientation from that in the optimized structure. In the same manner, we can conclude that the Na13I12+ basket isomer accommodates a methanol as well as a water molecule. This discussion also supports the experimental results for Na13I12+(ROH) shown above: the basket inner space of Na13I12+ can fit an ROH molecule with a size up to methanol. In both AH clusters, therefore, we can also expect that the remaining anomalous adsorption reactivity of (CH3)2CHOH and (CH3)3COH on Na13X12+ is due to other crystal structures with defect, predominantly due to the edge-defect structure considering from the relative stability of the isomers noted above. Figure 4 also indicates that the fraction of the moleculeadsorbed basket isomer may be higher than that for the free Na13X12+ basket structure, 0.1% to several percent at room temperature, as estimated above. Although the temperature of ions formed by laser vaporization in the present experiment may be rather higher than the room temperature, this result may be due to the fact that the basket structure is favorable to afford the adsorbate molecule. 5. Conclusion We have examined adsorption reactions of ROH molecules on NanFn-1+ and NanIn-1+ cluster ions by mass spectrometry
Tsuruta et al. and by theoretical calculations based on DFT. From the systematic study changing the bulk size of the substituent R in the ROH adsorbate molecules, new evidence was obtained that small molecules are adsorbed at the inner sites of basket-like Na13I12+ ions. We compared the observed size dependence of the adsorption reactivities for the four ROH molecules, H2O (water), CH3OH (methanol), (CH3)2CHOH (2-propanol), and (CH3)3COH (2-methyl-2-propanol). As a result, it was found that only small molecules like water and methanol can efficiently adsorb on Na13F12+ and Na13I12+. To explain this experimental result, we also obtained optimized geometries and energies for the Na13F12+(ROH) ions by DFT calculations for three isomers of the AH cluster ions, that is, edge-defect, basket, and surfacedefect structures. The stability of the Na13F12+ basket isomer with an ROH adsorbate is highly dependent on the size of the substituent R; only the Na13F12+(H2O) ion has a positive binding energy. In contrast, almost identical interaction potentials were obtained for all ROH molecules with the edge-defect and surface-defect Na13F12+ structures. Therefore, it is concluded that the observed anomalous adsorption reactivity for Na13F12+ are due to the efficient inclusion reaction of the small ROH molecule in basket isomer structures. In the present calculation, the adsorption structures at the defect sites have adsorption energies larger than those at nondefect sites, and thus the former structures may play an important role in the deliquescence process of salt. It is expected that the process is elucidated by future study for the systems with increased adsorbate molecules. Acknowledgment. This work was supported by The Salt Science Research Foundation, Nos. 0508, 0616, and 0710, and also in part by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS). The computations were partly performed at the Research Center for Computational Science, Okazaki, Japan. References and Notes (1) Finlayson-Pitts, B. J.; Pitts, J. N., Jr. Chemistry of the Upper and Lower Atmosphere; Academic Press: San Diego, 2000. (2) Singewald, A.; Ernst, L. Z. Phys. Chem. Neue Forge 1981, 124, 223. (3) Shindo, H.; Ohashi, M.; Tateishi, O.; Seo, A. J. Chem. Soc., Faraday Trans. 1997, 93, 1169. (4) Luna, M.; Rieutord, F.; Melman, N. A.; Dai, Q.; Salmeron, M. J. Phys. Chem. A 1998, 102, 6793. (5) Homer, M. L.; Livingston, F. E.; Whetten, R. L. Z. Phys. D 1993, 26, 201. (6) Fatemi, D. J.; Bloomfield, L. A. Phys. ReV. A 2002, 66, 013202. (7) Whetten, R. L. Acc. Chem. Res. 1993, 26, 49. (8) Homer, M. L.; Livingston, F. E.; Whetten, R. L. J. Am. Chem. Soc. 1992, 114, 6558. (9) Homer, M. L.; Livingston, F. E.; Whetten, R. L. J. Phys. Chem. 1995, 99, 7604. (10) Ohshimo, K.; Misaizu, F.; Ohno, K. J. Chem. Phys. 2002, 117, 5209. (11) Misaizu, F.; Tsuruta, M.; Tsunoyama, H.; Furuya, A.; Ohno, K.; Lintuluoto, M. J. Chem. Phys. 2005, 123, 161101. (12) Furuya, A.; Misaizu, F.; Ohno, K. J. Chem. Phys. 2006, 125, 094309. (13) Honea, E. C.; Homer, M. L.; Whetten, R. L. Int. J. Mass Spectrom. Ion Processes 1990, 102, 213. (14) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (15) Frisch, M. J.; et al. GAUSSIAN 03, revision B.04; Gaussian, Inc.: Pittsburgh PA, 2003. (16) Lintuluoto, M. J. Phys. Chem. A 2000, 104, 6817. (17) Shannon, R. D. Acta Crystallogr., Sect. A 1976, 32, 751. (18) Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Cornell University Press: Ithaca, NY, 1960.
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