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Photoionization and density functional study of clusters of alkali metal atoms solvated with acetonitrile molecules, M(CH3CN)n (M=Li and Na)
26 February 1999
Chemical Physics Letters 301 Ž1999. 356–364
Photoionization and density functional study of clusters of alkali metal atoms solvated with acetonitrile molecules, M žCH 3 CN /n žM s Li and Na / Keijiro Ohshimo, Hironori Tsunoyama, Yoshihiro Yamakita, Fuminori Misaizu ) , Koichi Ohno Department of Chemistry, Graduate School of Science, Tohoku UniÕersity, Aramaki, Aoba-ku, Sendai 980-8578, Japan Received 22 October 1998; in final form 25 December 1998
Abstract Photoionization mass spectroscopy of clusters of alkali metal atoms solvated with acetonitrile molecules, MŽCH 3 CN. n ŽM s Li and Na., has shown that their ionization potentials decrease from n s 1 to 3, while they increase for n 0 4. Calculations based on density functional theory are also made for these clusters and their cations with n s 1–3. The nature of the anomalous n dependence of the ionization potential is discussed in relation to the stabilization of neutral clusters due to dipole–dipole interaction between acetonitrile molecules. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction The clusters of an alkali metal atom solvated with polar solvent molecules have been studied extensively by experiments and theoretical calculations in the past decade w1x. One of the interests in these studies is the mechanism of electron transfer from an alkali atom to solvent molecules, which causes formation of solvated electrons in polar solvents. Among these studies, water and ammonia have often been chosen as polar solvent molecules. The ionization potentials ŽIP. of the clusters of an alkali metal atom solvated with water, MŽH 2 O. n ŽM s Li w2x, Na w3–5x ) Corresponding author. Fax: q81 22 217 6580; e-mail: [email protected]
and Cs w6x., and with ammonia, MŽNH 3 . n ŽM s Li w2,7x, Na w5,8x, Cs w6x., have been investigated by photoionization mass spectroscopy. These studies have revealed that the n dependence of the IPs does not change with alkali atoms but with solvent molecules; the IPs of MŽH 2 O. n clusters show a plateau behavior, while those of MŽNH 3 . n clusters decrease monotonically with increasing n. At large-n limit, these IPs reach values comparable with the Ž3.3 vertical detachment energy ŽVDE. of ŽH 2 O.y n Ž . eV. and ŽNH 3 .y 1.45 eV extrapolated to n ™ ` n w9,10x. Therefore, these clusters form an ion-pair structure w11x containing a metal cation and a solvated electron at large n. These electron transfer from alkali atom to solvent molecules in these clusters have been investigated by theoretical calcula-
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 0 4 4 - 5
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tions w11–15x. Barnett and Landman mentioned that a plateau behavior of IPs similar to that found in MŽH 2 O. n clusters may be present in other polar solvent molecules having a large enough dipole moment to stabilize the transferred electron w12x. Acetonitrile has a large dipole moment Ž3.92 D., much larger than those of water Ž1.85 D. and ammonia Ž1.47 D.. It was recently found that this large dipole moment stabilizes cluster anions ŽCH 3 CN.y n Ždipole-bound state. w16–18x. The IPs of the clusters of Cs atom solvated with acetonitrile, CsŽCH 3 CN. n , were also measured w6x. In contrast to water- and ammonia-solvated clusters, their IPs show an anomalous dependence on n; the IPs for n s 2 and 3 are lower than those for 4 ( n ( 6, and a plateau behavior appears for n 0 12. It was also suggested that this anomalous dependence is related to the large dipole moment of acetonitrile w6x. In order to get further insight into the role of the dipole moment in the stability of the clusters of an alkali atom solvated with molecules, experiments on clusters of other alkali atoms solvated with molecules and theoretical calculations for neutral and ionic clusters are necessary. In the present study, we measured the IPs of clusters of Li and Na atoms solvated with acetonitrile molecules, MŽCH 3 CN. n Ž n s 1–8., as photoionization thresholds in the gas phase. The structures of the neutral and ionic clusters were optimized on the basis of density functional theory ŽDFT.. The results are used for discussion on the n dependence of their IPs.
2. Experimental We used two-stage differentially evacuated chambers consisting of a cluster source and a Wiley–McLaren-type time-of-flight ŽTOF. mass spectrometer w19x. Clusters of MŽCH 3 CN. n ŽM s Li and Na. were generated by a pickup source w3,4x by a combination of laser vaporization w20x and pulsed supersonic expansion. A mixture gas of helium and acetonitrile Žtypical mixing ratio is 95:5. was expanded from a pulsed valve ŽGeneral Valve series 9, orifice diameter 0.8 mm. with a stagnation pressure of 4–9 atm. The second harmonic of a Nd:YAG laser ŽLumonics
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HY-400, 532 nm. was focused onto a metal rod, which was rotated and translated for stabilizing the vaporizing conditions, placed at about 10 mm downstream from the nozzle. The timings of valve opening and laser vaporization were optimized by a digital delayrpulse generator ŽStanford Research DG535. so that solvated clusters were produced at the highest efficiency. The prepared cluster beam was collimated by a conical skimmer Žthroat diameter of 1 mm. positioned about 30 mm downstream from the nozzle. The clusters were ionized by irradiation with a laser beam at 200 mm downstream from the skimmer. The ionization laser system consisted of a dye laser ŽLumonics HD-300. pumped by a Nd:YAG laser ŽSpectra-Physics GCR-150-10. and frequency doubling crystals ŽBBO, KDP. installed in an autotracker ŽLumonics HT-1000.. Photon energies from 3.26 to 5.58 eV Ž380-222 nm. were accessible by this system. The intensity of the ionization laser was monitored by a photodiode ŽHamamatsu S1772-02. or by a joulemeter ŽGentec ED-100A.. In order to avoid multiphoton ionization processes, the power of the ionization laser was kept under 4 mJrcm2 during the measurement. The cluster ions formed by photoionization were accelerated to about 3 keV at right angles to the directions of the cluster beam and the ionization laser. Field ionization could not be avoided because of this continuous acceleration field. The width of the Stark shift caused by field ionization was estimated to be about 0.02 eV in this field. The accelerated ions were introduced to a field-free flight tube of 550 mm length, and mass-separated ions were detected by a dual microchannel plate ŽHamamatsu F1552-21S.. The output signals were stored and averaged by a digital storage oscilloscope ŽLeCroy 9361., and the data were sent to a personal computer ŽNEC PC-9801DA. via a GPIB computer interface. Photoionization mass spectra were measured by scanning the photon energy in order to determine the IPs of these clusters. The sample rod of lithium ŽWako, ) 99%. was made from a lump under argon atmosphere in order to avoid formation of lithium nitride. The sodium ŽNacalai, ) 99%. sample rod was produced in the same way under nitrogen atmosphere. The acetonitrile sample ŽNacalai, ) 99%. was placed in a
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reservoir, where helium gas was bubbled at room temperature.
3. Calculation The molecular structures of neutral clusters of MŽCH 3 CN. n ŽM s Li and Na; n s 1–3. and their cations were optimized by a DFT program of GAUSSIAN 94 w21x. The 6-311 q q G ) ) basis set was used for calculations for n s 1 and 2, and the 3-21 q G ) basis set was used for n s 3. The B3LYP functional w22x was utilized in the present calculations. The dipole moment of acetonitrile molecule obtained by the present calculations Ž4.06 D by B3LYPr6-311q q G ) ) , 4.13 D by B3LYPr3-21 q G ) . is slightly larger than the experimental value Ž3.92 D.. In contrast, the dipole moment calculated using the MP2r6-311q G ) level is recently reported to be 3.95 D w23x, which is consistent with the experimental value. Therefore, the calculations based on DFT may overestimate the dipole moment of acetonitrile. However, in a recent study of AlŽNH 3 . cluster w24x the IP calculated with DFT ŽB3LYPr631 q G ) . agrees well with the experimental ionization threshold. Therefore, it is expected that DFT works well for estimation of the interaction energy between a metal atom and a solvent molecule. The results of optimization of all the geometrical parameters in MŽCH 3 CN. and MqŽ CH 3 CN. show that the geometrical distortion of acetonitrile molecule is small. These results are consistent with those of ab initio SCF calculations for MqŽ CH 3 CN. with the 4-31G basis set w25x. Therefore, the geometrical parameters of acetonitrile molecule were fixed to the values determined by microwave spectroscopy w26x in the calculations for n s 2 and 3. Moreover, we made a natural population analysis w27x of the optimized structures in order to obtain the extent of electron transfer between the alkali atom and the molecules. It is well known that Mulliken populations are very sensitive to the basis set, particularly as the basis set is enlarged. Especially, Mulliken populations were found to be unreliable for various organic and inorganic lithium compounds w28x. However, the atomic charges in lithium compounds are well described using a natural population analysis
w27x. Therefore, we used the natural charge instead of the Mulliken charge to estimate the charge distributions within clusters.
4. Results and discussion 4.1. Photoionization mass spectra and ionization potentials of M(CH3 CN)n (M s Li and Na) clusters Fig. 1 shows the TOF mass spectra of LiŽCH 3 CN. n and NaŽCH 3 CN. n clusters. These spec-
Fig. 1. Typical photoionization TOF mass spectra of clusters of Li and Na atoms solvated with the acetonitrile molecules. The laser wavelength for ionization was 222 nm Ž5.58 eV.. Ža. Liq ŽCH 3 CN. n . Liq ŽCH 3 CN. nŽH 2 O. Ž`. and Liq ŽCH 3 CN. nŽCN. Ž). are also assignable. Žb. Naq ŽCH 3 CN. n . Naq ŽCH 3 CN. nŽH 2 O. Ž`. and Naq ŽCH 3 CN. nŽCN. Ž). are also assignable.
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tra are obtained by one-photon ionization by irradiation with a laser beam of 222 nm Ž5.58 eV.. Cluster ions, LiqŽ CH 3 CN. n and NaqŽ CH 3 CN. n , are observed up to n s 19 and 23, respectively. Strong peaks are found at n s 4 for LiqŽ CH 3 CN. n and at n s 8 for NaqŽ CH 3 CN. n . These features, which are independent of the wavelength of the ionization laser, suggest that the first solvation shells of these cluster ions are filled at these cluster sizes. This magic number, n s 4 for LiqŽ CH 3 CN. n clusters, is consistent with the number of solvent molecules in the first shell for Liq ion in acetonitrile solution Ž4.7., as determined by IR absorption spectroscopy w29x. We also obtained the TOF mass spectra of NaqŽ CH 3 CN. n ions directly produced by laser vaporization and found a magic number at n s 8 w30x. The number of the molecules in the first shell for Naq obtained in this study Ž n s 8. is consistent with ˚ . and Liq Ž0.60 A˚ . the ionic radii of Naq Ž0.95 A w31x. Although a strong peak at n s 4 is also found for NaqŽ CH 3 CN. n in Fig. 1b, this behavior cannot be directly related to the stability of ions, because this feature is found to depend on the conditions of cluster formation. Along with the series of MqŽ CH 3 CN. n , weak signals assignable to Mq ŽCH 3 CN. nŽH 2 O. Ž`, Fig. 1. and MqŽ CH 3 CN. nŽCN. Ž), Fig. 1. are also observed. The former ions arise from the presence of water impurity in the acetonitrile sample, and the latter is formed by photodissociation of acetonitrile molecules. The ionization potentials IPŽ n. determined for n s 1–8 of MŽCH 3 CN. n ŽM s Li and Na. are plotted in Fig. 2 along with the IPs of Li and Na atoms w32x. For both clusters, IPŽ n. is found to decrease monotonically with n for n s 1–3, whereas it increases for n 0 4. The results of a photoionization study of CsŽCH 3 CN. n also show a similar behavior for the n dependence of IPŽ n. w6x. In CsŽCH 3 CN. n , IPŽ n. decreases with n up to 3, but those for n s 4–6 are higher than those for n s 2 and 3. Therefore, this anomalous dependence of IPŽ n. is likely to be characteristic of alkali metal–acetonitrile clusters. The IPŽ n. values of the clusters of alkali metal solvated with other molecules such as water or ammonia do not show such a dependence w2,5–7x. In these cases the IPŽ n. values show a relatively smooth dependence on the number of solvent molecules and never increase with n.
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Fig. 2. IPŽ n. values of Ža. LiŽCH 3 CN. n and Žb. NaŽCH 3 CN. n for ns1–8.
4.2. Calculated structures and ionization potentials for n s 1 and 2 Optimized structures of neutral and ionic clusters, MŽCH 3 CN. n and MqŽ CH 3 CN. n ŽM s Li and Na; n s 1–3. are calculated in order to understand the interaction between a metal atom with acetonitrile molecules. The optimized structures of LiŽCH 3 CN. n and NaŽCH 3 CN. n clusters Ž n s 1 and 2. are shown in Figs. 3 and 4. Table 1 lists the total binding energies D En and their differences, D Eny1, n Žs D En y D Eny1 .. The total binding energies are evaluated by yD En s E M Ž CH 3 CN . n y E w M x y nE w CH 3 CN x
Ž M s Li, Liq, Na and Naq . ,
Ž 1.
where EwMŽCH 3 CN. n x is the total energy of the cluster MŽCH 3 CN. n , EwMx and EwCH 3 CNx are the total energies of an alkali metal atom Žion. and an acetonitrile molecule, respectively. We also calcu-
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Fig. 3. Optimized structures of neutral LiŽCH 3 CN. n Ž n s 1 and 2. and their ions calculated with B3LYPr6-311q q G ) ) . Bond lengths ˚ and degrees. The structure of acetonitrile determined by microwave spectroscopy is also shown. Values in and angles are shown in A parentheses are the natural charges.
late the adiabatic IPs ŽAIP. of neutral clusters MŽCH 3 CN. n ŽM s Li and Na; n s 1 and 2. from the D En of neutral and ionic clusters and the IPs of alkali metal atoms w32x ŽTable 1.. These AIP values are estimated under the assumption that the zero-point energy of the neutral clusters is equal to that of the ionic clusters. For n s 1 and 2, acetonitrile molecules coordinate with metal atom Žion. at the N atom of the CN group in the optimized structures of the neutral and ionic clusters. In these structures, the total binding energies, D En , are largely due to the interaction between
the metal atom and acetonitrile molecules. As shown in Figs. 3 and 4, the bond length between the Naq ion and the N atomŽs. of CH 3 CN is longer than that ˚ This between Liq and the N atomŽs. by about 0.4 A. is consistent with the difference in the maximum number of acetonitrile molecules in the first solvation shell as noted above; the number of molecules necessary to screen the surface of the ion is larger for Naq than for Liq. For n s 1, the calculated AIPs ŽLiŽCH 3 CN., 3.85 eV and NaŽCH 3 CN., 3.86 eV. are nearly the same as the experimental values ŽLiŽCH 3 CN., 3.93 eV and NaŽCH 3 CN., 3.92 eV.
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Fig. 4. Optimized structures of neutral NaŽCH 3 CN. n Ž n s 1 and 2. and their ions calculated with the B3LYPr6-311q q G ) ) . Bond ˚ and degrees. Values in parentheses are the natural charges. lengths and angles are shown in A
Table 1 Binding energies and ionization potentials for MŽCH 3 CN. n ŽM s Li and Na; ns1 and 2. M
n
D En Žkcalrmol. a,b
D Eny1, n Žkcalrmol. b,c
AIPcalc ŽeV. d
IPobs ŽeV. e
Li
1 2 1 2 1 2 1 2
11.1 22.6 4.24 7.67 46.6 80.7 33.7 61.3
11.1 11.5 4.24 3.44 46.6 34.1 33.7 27.7
3.85 2.78 3.86 2.82
3.93 3.20 3.92 3.32
Na Liq Naq a
Total binding energy. Calculated with B3LYPr6-311qqG ) ) level. c Increment of binding energy. d Adiabatic ionization potential calculated with B3LYPr6-311qq G ) ) level. e Ionization potential observed in the present study. b
within experimental error. For n s 2, however, the calculated values are smaller than the experimental values by f 0.5 eV. This discrepancy may have the following two reasons. First, the structures of acetonitrile molecules are fixed in the optimization for n s 2. Second, the structures of the ionic clusters differ significantly from those of neutrals. Accurate potential surfaces of neutral clusters and ions are necessary to discuss this discrepancy more quantitatively. 4.3. Anomalous size dependence of ionization potentials As shown in Fig. 2, IPŽ n. decreases with n for n ( 3 and gradually increases from n s 4. This behavior suggests that the differences in the total binding energies, D Eny 1, n , of the cluster ions are higher
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than those of the neutral clusters for n ( 4 and that those of the cluster ions are lower than those of the neutral clusters for n 0 5. For n s 1, the D E0,1 values of the ions are calculated to be 35.5 Žfor Li. and 27.4 kcalrmol Žfor Na. higher than that of the neutrals ŽTable 1. because charge–dipole interaction becomes important in the ions, whereas dipole-induced dipole interaction dominates in the neutrals. This tendency is considered to be valid also for n s 2–4. In contrast, the D Eny 1, n values of neutrals exceed those of ions for n 0 5. One possible explanation for this behavior is that the large dipole moment of acetonitrile molecule plays an important role to fix it in a stable mutual orientation in neutral clusters. Recent theoretical calculations show that dipole–dipole interaction is an important factor to stabilize acetonitrile clusters w23x. We will discuss this point in the case of MŽCH 3 CN. n clusters in some detail. For n s 3, two optimized structures of NaŽCH 3 CN. 3 are found as shown in Fig. 5. In the most stable isomer A, three acetonitrile molecules coordinate with a Na atom at the N atom of the CN group ŽN-side. for n s 1 and 2. In contrast, another
isomer B has a structure in which one acetonitrile molecule coordinates with a Na atom from the methyl side while two acetonitrile molecules coordinate from the N-side. Isomer B is found to be less stable than isomer A by 12.8 kcalrmol Ž0.555 eV. at B3LYPr3-21q G ) . The calculated AIPs of two isomers are 2.51 eV Žisomer A. and 1.96 eV Žisomer B., while the experimental value is 2.80 eV for NaŽCH 3 CN. 3 . These calculated IPs suggest that isomer A dominates in NaŽCH 3 CN. 3 . The stability of isomer B is partly due to the large dipole moment of acetonitrile molecule. In order to estimate how much interaction energy between the solvent molecules contributes to the stabilization of these isomers, we have also calculated the solvent–solvent interaction energy, D Es defined by Hashimoto and Morokuma w13x. The D Es values are estimated to be y8.69 kcalrmol Žy0.377 eV. for isomer A and 1.96 kcalrmol Ž0.085 eV. for isomer B. In isomer A, the negative D Es value indicates that the interaction between acetonitrile molecules is repulsive. In isomer B, a pair of acetonitrile molecules with nearly opposite directions is stabilized by the dipole–dipole interactions between them. In other words, dipole–
Fig. 5. Optimized structures of NaŽCH 3 CN. 3 calculated by B3LYPr3-21q G ) level. Top Ža1., side Ža2.: views of isomer A. Top Žb1., ˚ and degrees. Values in parentheses are the natural charges. side Žb2.: views of isomer B. Bond lengths and angles are shown in A
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dipole interaction contributes to the D E2,3 value of isomer B. These dipole–dipole interactions are expected to increase with n, and the structure such as isomer B may become more stable than isomer A for neutrals. It is also expected that the total energies of neutrals are stabilized with increasing n by these dipole–dipole interactions and the values of D Eny 1, n decrease slowly as n increases. For isomer B with n 0 4, the second solvation shell may be formed because of the repulsion between the methyl group of acetonitrile molecules. However, the situation in the ions is different from those in the neutrals. The NaqŽ CH 3 CN. 3 ion has a planar stable structure, in which three acetonitrile molecules coordinate with a Naq ion from the N-side. If an acetonitrile molecule coordinates with a metal ion from the methyl side, the Coulomb repulsion between the positive charges of H atoms of the methyl group and an alkali ion will be very large. Therefore, the structure such as isomer B of neutral NaŽCH 3 CN. 3 should not be stable for the NaqŽ CH 3 CN. 3 ion. As n increases, the repulsion between acetonitrile molecules will increase because all acetonitrile molecules coordinate with the Naq ion from the N-side. Recent results of ab initio SCF calculations of KqŽ CH 3 CN. n Ž n s 1–6. reveal that all acetonitrile molecules coordinate with the Kq ion from the N-side in the most stable structure, and the values of D Eny 1, n decrease rapidly for n 0 5 because of the repulsion between acetonitrile molecules w33x. For LiŽCH 3 CN. 3 , we cannot find a stable structure such as isomer B of NaŽCH 3 CN. 3 . This fact can be explained straightforwardly as follows. As shown in Table 1, the D E0,1 value of LiŽCH 3 CN. is larger than that of NaŽCH 3 CN. by 6.9 kcalrmol Ž0.30 eV.. In other words, the binding between the Li atom and the acetonitrile molecule is much stronger than that between Na and acetonitrile. This is because the orbital interaction between the 2s orbital of Li and the sCN orbital of acetonitrile is stronger than that between the 3s orbital of Na and the sCN orbital. Because of this large binding energy, the dipole–dipole interaction between acetonitrile molecules does not dominate in LiŽCH 3 CN. 3 , in contrast to the case of NaŽCH 3 CN. 3 . However, the interaction between the Li atom and one acetonitrile molecule for n 0 4 is expected to be smaller than that for n ( 3. Thus,
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the structure in which certain acetonitrile molecules coordinate with the Li atom from the methyl side may be stabilized in LiŽCH 3 CN. n Ž n 0 4. as discussed for NaŽCH 3 CN. n , though no calculation is yet available for clusters with n 0 4. In addition to the interaction in the neutrals, the size dependence of IPs can be explained by the structures of the ions. As for LiqŽ CH 3 CN. n cluster ions, the observed maximum number of acetonitrile in the first solvation shell is n s 4 ŽFig. 1a.. Hence, for n 0 5 in LiqŽ CH 3 CN. n ions the acetonitrile molecules cannot coordinate with the Liq ion directly and the D Eny 1, n values should be very small for n 0 5. Therefore, the D Eny 1, n values of ions are expected to be smaller than those of neutrals for n 0 5. The observation that the D Eny 1, n values of neutral MŽCH 3 CN. n clusters are larger than those of ions for n 0 5 may also originate from electron transfer from the alkali metal atom to the acetonitrile molecules, as discussed for MŽH 2 O. n and MŽNH 3 . n clusters. This stabilization by electron–dipole interaction is probable because of the resemblance of the geometrical structures of Na ŽCH 3 CN . n and NaŽNH 3 . n for n s 1–3 w14x. However, this stabilization is estimated to be much smaller for n ( 3 from the natural population analysis of the neutral clusters; for n s 2 and 3, the natural charges shown in Figs. 3–5 reveal that the valence electron of the metal atom transfers only slightly to the acetonitrile molecules. This mechanism, which is characteristic of the neutral MŽCH 3 CN. n clusters, can be related to the formation of dipole-bound anions in which the excess electron is stabilized by the dipole moment. Although this electron transfer has only a small effect on the D Eny 1, n values for the n range in this study, this effect on the n dependence of the IPs may become more important at larger n values.
Acknowledgements The authors thank the Computer Center of the Institute for Molecular Science for provision of the NEC HSP and HPC computer. FM acknowledges the financial support from the Sumitomo Foundation. This work has also been supported in part by a Grant-in-Aid for Scientific Research from the
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Japanese Ministry of Education, Science, and Culture.
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Chemical Physics Letters 301 Ž1999. 356–364
Photoionization and density functional study of clusters of alkali metal atoms solvated with acetonitrile molecules, M žCH 3 CN /n žM s Li and Na / Keijiro Ohshimo, Hironori Tsunoyama, Yoshihiro Yamakita, Fuminori Misaizu ) , Koichi Ohno Department of Chemistry, Graduate School of Science, Tohoku UniÕersity, Aramaki, Aoba-ku, Sendai 980-8578, Japan Received 22 October 1998; in final form 25 December 1998
Abstract Photoionization mass spectroscopy of clusters of alkali metal atoms solvated with acetonitrile molecules, MŽCH 3 CN. n ŽM s Li and Na., has shown that their ionization potentials decrease from n s 1 to 3, while they increase for n 0 4. Calculations based on density functional theory are also made for these clusters and their cations with n s 1–3. The nature of the anomalous n dependence of the ionization potential is discussed in relation to the stabilization of neutral clusters due to dipole–dipole interaction between acetonitrile molecules. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction The clusters of an alkali metal atom solvated with polar solvent molecules have been studied extensively by experiments and theoretical calculations in the past decade w1x. One of the interests in these studies is the mechanism of electron transfer from an alkali atom to solvent molecules, which causes formation of solvated electrons in polar solvents. Among these studies, water and ammonia have often been chosen as polar solvent molecules. The ionization potentials ŽIP. of the clusters of an alkali metal atom solvated with water, MŽH 2 O. n ŽM s Li w2x, Na w3–5x ) Corresponding author. Fax: q81 22 217 6580; e-mail: [email protected]
and Cs w6x., and with ammonia, MŽNH 3 . n ŽM s Li w2,7x, Na w5,8x, Cs w6x., have been investigated by photoionization mass spectroscopy. These studies have revealed that the n dependence of the IPs does not change with alkali atoms but with solvent molecules; the IPs of MŽH 2 O. n clusters show a plateau behavior, while those of MŽNH 3 . n clusters decrease monotonically with increasing n. At large-n limit, these IPs reach values comparable with the Ž3.3 vertical detachment energy ŽVDE. of ŽH 2 O.y n Ž . eV. and ŽNH 3 .y 1.45 eV extrapolated to n ™ ` n w9,10x. Therefore, these clusters form an ion-pair structure w11x containing a metal cation and a solvated electron at large n. These electron transfer from alkali atom to solvent molecules in these clusters have been investigated by theoretical calcula-
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 0 4 4 - 5
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tions w11–15x. Barnett and Landman mentioned that a plateau behavior of IPs similar to that found in MŽH 2 O. n clusters may be present in other polar solvent molecules having a large enough dipole moment to stabilize the transferred electron w12x. Acetonitrile has a large dipole moment Ž3.92 D., much larger than those of water Ž1.85 D. and ammonia Ž1.47 D.. It was recently found that this large dipole moment stabilizes cluster anions ŽCH 3 CN.y n Ždipole-bound state. w16–18x. The IPs of the clusters of Cs atom solvated with acetonitrile, CsŽCH 3 CN. n , were also measured w6x. In contrast to water- and ammonia-solvated clusters, their IPs show an anomalous dependence on n; the IPs for n s 2 and 3 are lower than those for 4 ( n ( 6, and a plateau behavior appears for n 0 12. It was also suggested that this anomalous dependence is related to the large dipole moment of acetonitrile w6x. In order to get further insight into the role of the dipole moment in the stability of the clusters of an alkali atom solvated with molecules, experiments on clusters of other alkali atoms solvated with molecules and theoretical calculations for neutral and ionic clusters are necessary. In the present study, we measured the IPs of clusters of Li and Na atoms solvated with acetonitrile molecules, MŽCH 3 CN. n Ž n s 1–8., as photoionization thresholds in the gas phase. The structures of the neutral and ionic clusters were optimized on the basis of density functional theory ŽDFT.. The results are used for discussion on the n dependence of their IPs.
2. Experimental We used two-stage differentially evacuated chambers consisting of a cluster source and a Wiley–McLaren-type time-of-flight ŽTOF. mass spectrometer w19x. Clusters of MŽCH 3 CN. n ŽM s Li and Na. were generated by a pickup source w3,4x by a combination of laser vaporization w20x and pulsed supersonic expansion. A mixture gas of helium and acetonitrile Žtypical mixing ratio is 95:5. was expanded from a pulsed valve ŽGeneral Valve series 9, orifice diameter 0.8 mm. with a stagnation pressure of 4–9 atm. The second harmonic of a Nd:YAG laser ŽLumonics
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HY-400, 532 nm. was focused onto a metal rod, which was rotated and translated for stabilizing the vaporizing conditions, placed at about 10 mm downstream from the nozzle. The timings of valve opening and laser vaporization were optimized by a digital delayrpulse generator ŽStanford Research DG535. so that solvated clusters were produced at the highest efficiency. The prepared cluster beam was collimated by a conical skimmer Žthroat diameter of 1 mm. positioned about 30 mm downstream from the nozzle. The clusters were ionized by irradiation with a laser beam at 200 mm downstream from the skimmer. The ionization laser system consisted of a dye laser ŽLumonics HD-300. pumped by a Nd:YAG laser ŽSpectra-Physics GCR-150-10. and frequency doubling crystals ŽBBO, KDP. installed in an autotracker ŽLumonics HT-1000.. Photon energies from 3.26 to 5.58 eV Ž380-222 nm. were accessible by this system. The intensity of the ionization laser was monitored by a photodiode ŽHamamatsu S1772-02. or by a joulemeter ŽGentec ED-100A.. In order to avoid multiphoton ionization processes, the power of the ionization laser was kept under 4 mJrcm2 during the measurement. The cluster ions formed by photoionization were accelerated to about 3 keV at right angles to the directions of the cluster beam and the ionization laser. Field ionization could not be avoided because of this continuous acceleration field. The width of the Stark shift caused by field ionization was estimated to be about 0.02 eV in this field. The accelerated ions were introduced to a field-free flight tube of 550 mm length, and mass-separated ions were detected by a dual microchannel plate ŽHamamatsu F1552-21S.. The output signals were stored and averaged by a digital storage oscilloscope ŽLeCroy 9361., and the data were sent to a personal computer ŽNEC PC-9801DA. via a GPIB computer interface. Photoionization mass spectra were measured by scanning the photon energy in order to determine the IPs of these clusters. The sample rod of lithium ŽWako, ) 99%. was made from a lump under argon atmosphere in order to avoid formation of lithium nitride. The sodium ŽNacalai, ) 99%. sample rod was produced in the same way under nitrogen atmosphere. The acetonitrile sample ŽNacalai, ) 99%. was placed in a
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reservoir, where helium gas was bubbled at room temperature.
3. Calculation The molecular structures of neutral clusters of MŽCH 3 CN. n ŽM s Li and Na; n s 1–3. and their cations were optimized by a DFT program of GAUSSIAN 94 w21x. The 6-311 q q G ) ) basis set was used for calculations for n s 1 and 2, and the 3-21 q G ) basis set was used for n s 3. The B3LYP functional w22x was utilized in the present calculations. The dipole moment of acetonitrile molecule obtained by the present calculations Ž4.06 D by B3LYPr6-311q q G ) ) , 4.13 D by B3LYPr3-21 q G ) . is slightly larger than the experimental value Ž3.92 D.. In contrast, the dipole moment calculated using the MP2r6-311q G ) level is recently reported to be 3.95 D w23x, which is consistent with the experimental value. Therefore, the calculations based on DFT may overestimate the dipole moment of acetonitrile. However, in a recent study of AlŽNH 3 . cluster w24x the IP calculated with DFT ŽB3LYPr631 q G ) . agrees well with the experimental ionization threshold. Therefore, it is expected that DFT works well for estimation of the interaction energy between a metal atom and a solvent molecule. The results of optimization of all the geometrical parameters in MŽCH 3 CN. and MqŽ CH 3 CN. show that the geometrical distortion of acetonitrile molecule is small. These results are consistent with those of ab initio SCF calculations for MqŽ CH 3 CN. with the 4-31G basis set w25x. Therefore, the geometrical parameters of acetonitrile molecule were fixed to the values determined by microwave spectroscopy w26x in the calculations for n s 2 and 3. Moreover, we made a natural population analysis w27x of the optimized structures in order to obtain the extent of electron transfer between the alkali atom and the molecules. It is well known that Mulliken populations are very sensitive to the basis set, particularly as the basis set is enlarged. Especially, Mulliken populations were found to be unreliable for various organic and inorganic lithium compounds w28x. However, the atomic charges in lithium compounds are well described using a natural population analysis
w27x. Therefore, we used the natural charge instead of the Mulliken charge to estimate the charge distributions within clusters.
4. Results and discussion 4.1. Photoionization mass spectra and ionization potentials of M(CH3 CN)n (M s Li and Na) clusters Fig. 1 shows the TOF mass spectra of LiŽCH 3 CN. n and NaŽCH 3 CN. n clusters. These spec-
Fig. 1. Typical photoionization TOF mass spectra of clusters of Li and Na atoms solvated with the acetonitrile molecules. The laser wavelength for ionization was 222 nm Ž5.58 eV.. Ža. Liq ŽCH 3 CN. n . Liq ŽCH 3 CN. nŽH 2 O. Ž`. and Liq ŽCH 3 CN. nŽCN. Ž). are also assignable. Žb. Naq ŽCH 3 CN. n . Naq ŽCH 3 CN. nŽH 2 O. Ž`. and Naq ŽCH 3 CN. nŽCN. Ž). are also assignable.
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tra are obtained by one-photon ionization by irradiation with a laser beam of 222 nm Ž5.58 eV.. Cluster ions, LiqŽ CH 3 CN. n and NaqŽ CH 3 CN. n , are observed up to n s 19 and 23, respectively. Strong peaks are found at n s 4 for LiqŽ CH 3 CN. n and at n s 8 for NaqŽ CH 3 CN. n . These features, which are independent of the wavelength of the ionization laser, suggest that the first solvation shells of these cluster ions are filled at these cluster sizes. This magic number, n s 4 for LiqŽ CH 3 CN. n clusters, is consistent with the number of solvent molecules in the first shell for Liq ion in acetonitrile solution Ž4.7., as determined by IR absorption spectroscopy w29x. We also obtained the TOF mass spectra of NaqŽ CH 3 CN. n ions directly produced by laser vaporization and found a magic number at n s 8 w30x. The number of the molecules in the first shell for Naq obtained in this study Ž n s 8. is consistent with ˚ . and Liq Ž0.60 A˚ . the ionic radii of Naq Ž0.95 A w31x. Although a strong peak at n s 4 is also found for NaqŽ CH 3 CN. n in Fig. 1b, this behavior cannot be directly related to the stability of ions, because this feature is found to depend on the conditions of cluster formation. Along with the series of MqŽ CH 3 CN. n , weak signals assignable to Mq ŽCH 3 CN. nŽH 2 O. Ž`, Fig. 1. and MqŽ CH 3 CN. nŽCN. Ž), Fig. 1. are also observed. The former ions arise from the presence of water impurity in the acetonitrile sample, and the latter is formed by photodissociation of acetonitrile molecules. The ionization potentials IPŽ n. determined for n s 1–8 of MŽCH 3 CN. n ŽM s Li and Na. are plotted in Fig. 2 along with the IPs of Li and Na atoms w32x. For both clusters, IPŽ n. is found to decrease monotonically with n for n s 1–3, whereas it increases for n 0 4. The results of a photoionization study of CsŽCH 3 CN. n also show a similar behavior for the n dependence of IPŽ n. w6x. In CsŽCH 3 CN. n , IPŽ n. decreases with n up to 3, but those for n s 4–6 are higher than those for n s 2 and 3. Therefore, this anomalous dependence of IPŽ n. is likely to be characteristic of alkali metal–acetonitrile clusters. The IPŽ n. values of the clusters of alkali metal solvated with other molecules such as water or ammonia do not show such a dependence w2,5–7x. In these cases the IPŽ n. values show a relatively smooth dependence on the number of solvent molecules and never increase with n.
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Fig. 2. IPŽ n. values of Ža. LiŽCH 3 CN. n and Žb. NaŽCH 3 CN. n for ns1–8.
4.2. Calculated structures and ionization potentials for n s 1 and 2 Optimized structures of neutral and ionic clusters, MŽCH 3 CN. n and MqŽ CH 3 CN. n ŽM s Li and Na; n s 1–3. are calculated in order to understand the interaction between a metal atom with acetonitrile molecules. The optimized structures of LiŽCH 3 CN. n and NaŽCH 3 CN. n clusters Ž n s 1 and 2. are shown in Figs. 3 and 4. Table 1 lists the total binding energies D En and their differences, D Eny1, n Žs D En y D Eny1 .. The total binding energies are evaluated by yD En s E M Ž CH 3 CN . n y E w M x y nE w CH 3 CN x
Ž M s Li, Liq, Na and Naq . ,
Ž 1.
where EwMŽCH 3 CN. n x is the total energy of the cluster MŽCH 3 CN. n , EwMx and EwCH 3 CNx are the total energies of an alkali metal atom Žion. and an acetonitrile molecule, respectively. We also calcu-
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Fig. 3. Optimized structures of neutral LiŽCH 3 CN. n Ž n s 1 and 2. and their ions calculated with B3LYPr6-311q q G ) ) . Bond lengths ˚ and degrees. The structure of acetonitrile determined by microwave spectroscopy is also shown. Values in and angles are shown in A parentheses are the natural charges.
late the adiabatic IPs ŽAIP. of neutral clusters MŽCH 3 CN. n ŽM s Li and Na; n s 1 and 2. from the D En of neutral and ionic clusters and the IPs of alkali metal atoms w32x ŽTable 1.. These AIP values are estimated under the assumption that the zero-point energy of the neutral clusters is equal to that of the ionic clusters. For n s 1 and 2, acetonitrile molecules coordinate with metal atom Žion. at the N atom of the CN group in the optimized structures of the neutral and ionic clusters. In these structures, the total binding energies, D En , are largely due to the interaction between
the metal atom and acetonitrile molecules. As shown in Figs. 3 and 4, the bond length between the Naq ion and the N atomŽs. of CH 3 CN is longer than that ˚ This between Liq and the N atomŽs. by about 0.4 A. is consistent with the difference in the maximum number of acetonitrile molecules in the first solvation shell as noted above; the number of molecules necessary to screen the surface of the ion is larger for Naq than for Liq. For n s 1, the calculated AIPs ŽLiŽCH 3 CN., 3.85 eV and NaŽCH 3 CN., 3.86 eV. are nearly the same as the experimental values ŽLiŽCH 3 CN., 3.93 eV and NaŽCH 3 CN., 3.92 eV.
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Fig. 4. Optimized structures of neutral NaŽCH 3 CN. n Ž n s 1 and 2. and their ions calculated with the B3LYPr6-311q q G ) ) . Bond ˚ and degrees. Values in parentheses are the natural charges. lengths and angles are shown in A
Table 1 Binding energies and ionization potentials for MŽCH 3 CN. n ŽM s Li and Na; ns1 and 2. M
n
D En Žkcalrmol. a,b
D Eny1, n Žkcalrmol. b,c
AIPcalc ŽeV. d
IPobs ŽeV. e
Li
1 2 1 2 1 2 1 2
11.1 22.6 4.24 7.67 46.6 80.7 33.7 61.3
11.1 11.5 4.24 3.44 46.6 34.1 33.7 27.7
3.85 2.78 3.86 2.82
3.93 3.20 3.92 3.32
Na Liq Naq a
Total binding energy. Calculated with B3LYPr6-311qqG ) ) level. c Increment of binding energy. d Adiabatic ionization potential calculated with B3LYPr6-311qq G ) ) level. e Ionization potential observed in the present study. b
within experimental error. For n s 2, however, the calculated values are smaller than the experimental values by f 0.5 eV. This discrepancy may have the following two reasons. First, the structures of acetonitrile molecules are fixed in the optimization for n s 2. Second, the structures of the ionic clusters differ significantly from those of neutrals. Accurate potential surfaces of neutral clusters and ions are necessary to discuss this discrepancy more quantitatively. 4.3. Anomalous size dependence of ionization potentials As shown in Fig. 2, IPŽ n. decreases with n for n ( 3 and gradually increases from n s 4. This behavior suggests that the differences in the total binding energies, D Eny 1, n , of the cluster ions are higher
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than those of the neutral clusters for n ( 4 and that those of the cluster ions are lower than those of the neutral clusters for n 0 5. For n s 1, the D E0,1 values of the ions are calculated to be 35.5 Žfor Li. and 27.4 kcalrmol Žfor Na. higher than that of the neutrals ŽTable 1. because charge–dipole interaction becomes important in the ions, whereas dipole-induced dipole interaction dominates in the neutrals. This tendency is considered to be valid also for n s 2–4. In contrast, the D Eny 1, n values of neutrals exceed those of ions for n 0 5. One possible explanation for this behavior is that the large dipole moment of acetonitrile molecule plays an important role to fix it in a stable mutual orientation in neutral clusters. Recent theoretical calculations show that dipole–dipole interaction is an important factor to stabilize acetonitrile clusters w23x. We will discuss this point in the case of MŽCH 3 CN. n clusters in some detail. For n s 3, two optimized structures of NaŽCH 3 CN. 3 are found as shown in Fig. 5. In the most stable isomer A, three acetonitrile molecules coordinate with a Na atom at the N atom of the CN group ŽN-side. for n s 1 and 2. In contrast, another
isomer B has a structure in which one acetonitrile molecule coordinates with a Na atom from the methyl side while two acetonitrile molecules coordinate from the N-side. Isomer B is found to be less stable than isomer A by 12.8 kcalrmol Ž0.555 eV. at B3LYPr3-21q G ) . The calculated AIPs of two isomers are 2.51 eV Žisomer A. and 1.96 eV Žisomer B., while the experimental value is 2.80 eV for NaŽCH 3 CN. 3 . These calculated IPs suggest that isomer A dominates in NaŽCH 3 CN. 3 . The stability of isomer B is partly due to the large dipole moment of acetonitrile molecule. In order to estimate how much interaction energy between the solvent molecules contributes to the stabilization of these isomers, we have also calculated the solvent–solvent interaction energy, D Es defined by Hashimoto and Morokuma w13x. The D Es values are estimated to be y8.69 kcalrmol Žy0.377 eV. for isomer A and 1.96 kcalrmol Ž0.085 eV. for isomer B. In isomer A, the negative D Es value indicates that the interaction between acetonitrile molecules is repulsive. In isomer B, a pair of acetonitrile molecules with nearly opposite directions is stabilized by the dipole–dipole interactions between them. In other words, dipole–
Fig. 5. Optimized structures of NaŽCH 3 CN. 3 calculated by B3LYPr3-21q G ) level. Top Ža1., side Ža2.: views of isomer A. Top Žb1., ˚ and degrees. Values in parentheses are the natural charges. side Žb2.: views of isomer B. Bond lengths and angles are shown in A
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dipole interaction contributes to the D E2,3 value of isomer B. These dipole–dipole interactions are expected to increase with n, and the structure such as isomer B may become more stable than isomer A for neutrals. It is also expected that the total energies of neutrals are stabilized with increasing n by these dipole–dipole interactions and the values of D Eny 1, n decrease slowly as n increases. For isomer B with n 0 4, the second solvation shell may be formed because of the repulsion between the methyl group of acetonitrile molecules. However, the situation in the ions is different from those in the neutrals. The NaqŽ CH 3 CN. 3 ion has a planar stable structure, in which three acetonitrile molecules coordinate with a Naq ion from the N-side. If an acetonitrile molecule coordinates with a metal ion from the methyl side, the Coulomb repulsion between the positive charges of H atoms of the methyl group and an alkali ion will be very large. Therefore, the structure such as isomer B of neutral NaŽCH 3 CN. 3 should not be stable for the NaqŽ CH 3 CN. 3 ion. As n increases, the repulsion between acetonitrile molecules will increase because all acetonitrile molecules coordinate with the Naq ion from the N-side. Recent results of ab initio SCF calculations of KqŽ CH 3 CN. n Ž n s 1–6. reveal that all acetonitrile molecules coordinate with the Kq ion from the N-side in the most stable structure, and the values of D Eny 1, n decrease rapidly for n 0 5 because of the repulsion between acetonitrile molecules w33x. For LiŽCH 3 CN. 3 , we cannot find a stable structure such as isomer B of NaŽCH 3 CN. 3 . This fact can be explained straightforwardly as follows. As shown in Table 1, the D E0,1 value of LiŽCH 3 CN. is larger than that of NaŽCH 3 CN. by 6.9 kcalrmol Ž0.30 eV.. In other words, the binding between the Li atom and the acetonitrile molecule is much stronger than that between Na and acetonitrile. This is because the orbital interaction between the 2s orbital of Li and the sCN orbital of acetonitrile is stronger than that between the 3s orbital of Na and the sCN orbital. Because of this large binding energy, the dipole–dipole interaction between acetonitrile molecules does not dominate in LiŽCH 3 CN. 3 , in contrast to the case of NaŽCH 3 CN. 3 . However, the interaction between the Li atom and one acetonitrile molecule for n 0 4 is expected to be smaller than that for n ( 3. Thus,
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the structure in which certain acetonitrile molecules coordinate with the Li atom from the methyl side may be stabilized in LiŽCH 3 CN. n Ž n 0 4. as discussed for NaŽCH 3 CN. n , though no calculation is yet available for clusters with n 0 4. In addition to the interaction in the neutrals, the size dependence of IPs can be explained by the structures of the ions. As for LiqŽ CH 3 CN. n cluster ions, the observed maximum number of acetonitrile in the first solvation shell is n s 4 ŽFig. 1a.. Hence, for n 0 5 in LiqŽ CH 3 CN. n ions the acetonitrile molecules cannot coordinate with the Liq ion directly and the D Eny 1, n values should be very small for n 0 5. Therefore, the D Eny 1, n values of ions are expected to be smaller than those of neutrals for n 0 5. The observation that the D Eny 1, n values of neutral MŽCH 3 CN. n clusters are larger than those of ions for n 0 5 may also originate from electron transfer from the alkali metal atom to the acetonitrile molecules, as discussed for MŽH 2 O. n and MŽNH 3 . n clusters. This stabilization by electron–dipole interaction is probable because of the resemblance of the geometrical structures of Na ŽCH 3 CN . n and NaŽNH 3 . n for n s 1–3 w14x. However, this stabilization is estimated to be much smaller for n ( 3 from the natural population analysis of the neutral clusters; for n s 2 and 3, the natural charges shown in Figs. 3–5 reveal that the valence electron of the metal atom transfers only slightly to the acetonitrile molecules. This mechanism, which is characteristic of the neutral MŽCH 3 CN. n clusters, can be related to the formation of dipole-bound anions in which the excess electron is stabilized by the dipole moment. Although this electron transfer has only a small effect on the D Eny 1, n values for the n range in this study, this effect on the n dependence of the IPs may become more important at larger n values.
Acknowledgements The authors thank the Computer Center of the Institute for Molecular Science for provision of the NEC HSP and HPC computer. FM acknowledges the financial support from the Sumitomo Foundation. This work has also been supported in part by a Grant-in-Aid for Scientific Research from the
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Japanese Ministry of Education, Science, and Culture.
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