Chemical Physics Letters 256, 101 (1996)

Charge-Exchange and Cluster Formation in an rf Paul Trap: Interaction of Alkali Atoms with C60+
Stuart Pollack, Douglas Cameron, Mordechai Rokni1, Winfield Hill and J. H. Parks
Rowland Institute for Science, Cambridge, Massachusetts 02142-1297

1 Permanent address: Physics Department, Hebrew University, Jerusalem, Israel


A Paul ion trap was used to study the formation of clusters under controlled temperature and pressure conditions. Exposure of cold C60+ ions to Li flux leads to the formation of LinC60+ clusters (n=1-18) occurring by the sequential association of Li atoms. Cluster formation dependence on He pressure displayed a competition between vibrational relaxation and unimolecular dissociation. Collisions with Na, K, Rb and Cs atoms, resulted in dissociative charge-exchange. Decay rates of C60+ ions resulting from these low energy charge-exchange collisions were consistent with Langevin capture rates.

1. Introduction

dougla-R2-E019.jpg (135274 bytes)
C60 in toluene. A solution used in the initial purification of C60 before extracting the solid and vaporizing it in an oven for these experiments.

Paul ion traps provide an opportunity to study the formation of charged clusters stored in an environment which can control the energy of both translational and vibrational degrees of freedom. The dynamics occurring within the trapped ion cloud can be controlled by varying the temperature and pressure of a background neutral He gas under conditions in which binary collisions are the dominant ion-neutral interaction. As a consequence, the rates of dynamic processes involved in cluster formation can be reduced to the order of 1-10 s-1 compared to 105-106 s-1 occurring in laser vaporization and gas aggregation sources. In these cluster sources, dynamic processes must proceed at fast rates to optimize formation, and in such an environment it is exceedingly difficult to isolate and measure specific processes of interest. However, rf trap measurements can afford to be performed at much slower rates as a result of long trapped ion lifetimes. At these longer timescales, experiments can obtain quantitative measurements of the competing dynamics in the growth of charged clusters including associative collisions, vibrational relaxation and unimolecular dissociation.

The alkali-C60+ system presents a relatively well defined collision process in which the isotropic interaction potential and absence of initial vibrational energy provide an opportunity to develop a better understanding of cluster formation processes. Furthermore, the study of alkali-C60+ collisions may offer insights for the formation of unique cluster species in which the C60 microsurface plays a role in determining cluster structure and composition. Previous work by Martin [1,2] demonstrated the formation of (alkali)nC60 clusters with n up to 500 atoms in a gas aggregation source. Although details of the cluster formation processes could not be analyzed in such a complex source environment, the increased stability of certain n values was correlated with specific electronic and atomic shell structures. In other experiments, the formation of smaller KnC60+ clusters with n=2-4 was observed [3] to be produced in a laser vaporization source. In this case, conditions in the source were also relatively uncertain and the analysis primarily considered the energetic constraints on cluster formation.

2. Experimental

The C60+ ions were stored within an rf Paul trap in which they were relaxed by collisions with a cold He background gas and exposed to alkali flux. The rf trap and associated electronics have been described in detail elsewhere [4] and only changes specific to these experiments will be discussed here. The trap was positioned within a UHV chamber evacuated to a base pressure of <2x1010 Torr and cooled to ~90 K by mounting to the copper baseplate of a liquid nitrogen Dewar. Low temperature, high purity (<1 ppm) He gas was controlled by a UHV leak valve and admitted into the trap directly through an aperture in the ring electrode.

C60 molecules were emitted from an effusive oven operating at ~450 C and entered the trap through an aperture in the ring electrode. Ions were formed within the trap by an electron beam pulse of ~1 ma/cm2 entering an aperture in the endcap electrode. The trapped ions were detected by resonant ejection [5,6] of the cold ion cloud into the external dynode of an electron multiplier. Comparison of the electron multiplier signals with in-situ electronic detection [4] provided the basis for absolute ion-number measurements with a detection sensitivity of ~5 ions. The number of trapped C60+ ions was ~103 for typical e-beam pulselengths of 200 ms. Detection signals derived from ejected ions depended linearly on stored ion number under these conditions. In the absence of alkali flux, the number of C60+ ions was essentially constant as trapped C60+ lifetimes were measured to be 10 min.

An effusive beam of alkali atoms emitted from a Knudsen oven entered the trap through an aperture of 1.0 mm diameter in the ring electrode and exited through an opposing aperture. Cs, Rb, K, Na, and Li atoms were incident on the ~0.2 mm diameter ion cloud with a flux of ~1013 cm2 s1. A shutter controlled the time interval (0.1-10 s) during which C60+ ions were exposed to the alkali flux. The relative collision energies in these experiments covered the range ~60 to 120 meV. The decay of C60+ ions resulting from alkali collisions was measured as a function of He pressure to account for attenuation by He scattering. The accuracy with which the alkali flux could be determined was the principle systematic uncertainty in these rate measurements. At the alkali flux levels used in these experiments, we found that directly measuring the flux by thin film deposition or ion current following ionization by a Re hot wire, did not provide a quantitative, reproducible calibration. Using well-known reaction rates to calibrate the flux was considered; however, we could not identify such rate measurements involving alkali charge-exchange at thermal collision energies. As a result, the flux levels were calculated from alkali vapor pressures [7] and temperature variations within the oven limited determination of the absolute rates to within a factor of ~2-3.

In these experiments, the trap was sequenced through a set of stable operating points at which (a) C60+ ions were formed and trapped, (b) lighter mass fragments C602n+ formed during ionization were eliminated, (c) the ion kinetic and vibrational energy were relaxed, (d) the alkali flux was admitted for a period of time and (e) the ions were resonantly ejected for detection. Experimental sequences were performed by varying the amplitude of the rf drive voltage at frequency /2=1 MHz in order to change the ion trajectory parameter qz=2eVrf/M(z0)2. This parameter depends on the ion mass, M, rf drive amplitude, Vrf, and separation of the trap endcap electrodes given by 2z0=0.6 cm. The C60+ ions were produced and stored at qz=0.47 for a period of 20 s to relax the ion cloud. At the He densities used in these measurements, a C60+ ion performed ~104 to 106 collisions during this interval. For the vibrational relaxation rate obtained from measurements discussed in Section 3.2, these He densities are estimated to thermalize both the translational and vibrational degrees of freedom.

3. Results and Discussion

3.1 Dissociative charge-exchange

Collisions of Cs, Rb, K and Na with C60+ ions resulted in dissociative charge-exchange. Charge-exchange rates were obtained by measuring the decay of C60+ ions during exposure to alkali flux. Rb and Cs ions produced in these collisions were trapped simultaneously with the remaining C60+ ions. This provided an opportunity to measure the growth of trapped Rb+ and Cs+ ions for comparison with the corresponding C60+ decay. Figure 1 displays an example of the decay of C60+ and growth of 85Rb+/87Rb+ ions as the Rb flux exposure time was increased. The error bars in figure 1 indicate the measurement uncertainty due to statistical fluctuations of ion numbers and the variation of oven temperature during the experimental run.

Figure 1. The decay of C60+ ion number (open circles) and growth of Rb+ ions (closed circles) resulting from charge-exchange are plotted versus Rb flux exposure times. Mass spectra traces of both C60+ and 85Rb+/ 87Rb+ ions at 0.2 sec (left) and 2.0 sec (right) are shown superimposed on the plots. Solid lines show exponential fits.

The data displayed in figure 1 was analyzed by assuming an exponential time dependence for both the decay of C60+ ions and the growth of Rb+ ions. The rate for C60+ decay was measured to be identical to the rate of Rb+ growth within experimental uncertainty for all He pressures between 1.6x104 and 1.3x103 Torr and extrapolated to a rate of kexp=3.060.70 s1 in the zero pressure limit. This indicates that charge-exchange was the only process responsible for the measured time dependence in these experiments. Observations for Cs collisions were similar to those for Rb. The lighter mass alkali ions, Na and K, could not be trapped simultaneously with C60+ ions. However, an exponential decay of C60+ ions was observed for collisions with all alkali atoms including Li.

Figure 2. The charge-exchange rate constants, <vrsexp>=kexp[<vr>/<FA>], derived from the decay of C60+ is plotted for each alkali polarizability, aA, and reduced mass, m. The rate constants calculated for Langevin, <vrsL>, and modified Langevin, <vrsL*>, trajectories are shown for comparison. Solid lines show linear fits.

Measurements of the charge-exchange rates were observed to be reproducible over a wide range of experimental conditions. Figure 2 shows the scaling of the charge-exchange rate constants, <vrsexp>kexp[<vr>/<FA>], with alkali polarizability aA and reduced mass . Here <FA> is the velocity averaged alkali flux, <vr> is the average relative velocity and kexp is the experimental rate extrapolated to zero He pressure. Also shown in figure 2 are velocity averaged rate constants calculated for Langevin [8,9] capture trajectories, <vrsL>, and for modified capture trajectories, <vrsL*>. This modification of the Langevin model accounted for the finite size of the C60+ ion. It was assumed that in the presence of the charge-induced dipole interaction, the positive charge on the C60 ion was delocalized over a small region of the C60 surface area. Furthermore, the charge was considered to be sufficiently mobile to maintain a minimum distance from the neutral atom during the collision trajectory. A model [10,11] based on similar considerations has been applied to describe charge transfer from multiply charged C60 ions. In figure 2, the absolute rate constants for all alkalis are observed to be higher than Langevin rates by a constant factor of ~3.2, and higher than modified Langevin rates by a factor of ~1.7. The error bars in figure 2 include (a) random scatter in the data due to fluctuations in the temperature of ~1K about the oven setpoint, and fluctuations in the initial ion number; and (b) a systematic error in the temperature used to calculate the alkali flux resulting from a nonuniform oven temperature. A temperature variation of 3-6% higher than the setpoint was measured within the oven using 0.4 mm diameter thermocouples at several oven positions. The data for a given oven temperature setpoint were reproducible to within the random scatter (23%) and the corresponding rates were consistently higher than the calculated rates. The experimental rates were consistent with the Langevin and modified Langevin rates when higher oven temperatures were taken into account.

The linear relationship displayed by all rate constants in figure 2 is consistent with the physics of low energy ion-neutral collisions. In the absence of a permanent dipole moment, the ion-neutral interaction predicts a maximum rate [9] constant based on the Langevin capture cross section <vrsL>(aA/)1/2. The results displayed in figure 2 strongly suggest that the experimental rates were determined by Langevin capture collisions, kexpkL. However, these results do not distinguish between the two Langevin models. The first study of dissociative charge-exchange involving mass selected clusters was performed [12] by Brchnigac, who investigated collisions of Cs with Nan+ clusters occurring at high energies (1 keV). At these energies, charge-exchange cross sections were determined not by capture impact parameters but by curve crossing radii. Charge-exchange at thermal collision energies involving smaller molecules [13] has clearly indicated that an upper limit to the cross section can result from Langevin processes.

Alkali-C60+ collisions occurring at impact parameters larger than Langevin or modified Langevin would not result in capture trajectories but could contribute to the charge-exchange rate. The extent to which these non-capture trajectories contribute is uncertain for Na, K, Rb and Cs, since they involved dissociative charge-exchange. In the case of Li, capture trajectories were clearly important since LinC60+ cluster formation was observed. Dissociative charge-exchange observed in collisions involving the other alkalis could be the result of capture followed by rapid dissociation of the alkali ion. To consider this possibility, RRKM dissociation rates were calculated [14-16] for each alkali-C60+ complex assuming an internal energy given by the sum of the difference in ionization potentials and a binding energy estimated by the charge-induced dipole interaction. In this calculation the sum and density of vibrational states were evaluated by direct count using vibrational frequencies for neutral C60 [17]. The internal energy was assumed to be given by the difference in the alkali and C60 ionization potentials. The binding energy of the alkali ion-C60 charge transfer product, was estimated by evaluating the charge-induced dipole interaction energy, e2a/2rsep4, using the C60 calculated polarizability [18] (a~80 3) and a separation distance, rsep, given by the sum of the alkali ionic radius and the C60 radius (3.5 ). Although these approximations underestimate the dissociation rate, the relative rates are more important in the following comparison. The dissociation lifetime of ~10 s calculated for LiC60+ would be sufficient to stabilize the complex by He collisions. However, an estimated dissociation lifetime of only ~25 ms for NaC60+ is consistent with the observed absence of Na complexes. Dissociation lifetimes of less than 1 ms were obtained for all other alkali-C60+ complexes. Consequently, the observation of dissociative charge-exchange does not exclude the presence of capture trajectories.

3.2 LinC60+ Cluster formation

The formation kinetics for LiC60+ (n=1) and for n>1 were studied as a function of He pressure in separate experiments. Analysis for the n=1 formation yielded values for the Li-C60+ binding energy and the vibrational relaxation rate of LiC60+ by He. Although the formation of LiC60+ competed with unimolecular dissociation, the formation of LinC60+ for n>1 proceeded without significant dissociative loss.

Figure 3. Mass spectra of LinC60+ clusters are displayed for several Li flux exposure times. The number of remaining C60+ ions are indicated on the left. The arbitrary scale on the vertical axis is related to electron multiplier current and the mass axis (amu) common to all spectra is shown on bottom trace. Top trace: 2 sec, cluster mass peaks for n=1-4 are indicated. Middle trace: 4 sec, cluster number for n=3 is indicated. Bottom trace: 8 sec, cluster number for n=7 is indicated and positions of n=1 and C60+ masses are shown by vertical lines.

Figure 3 shows the mass spectra of resonantly ejected LinC60+ clusters which resulted from exposing C60+ ions to Li flux for different time intervals. These spectra were averaged over 5 experimental sequences and were taken at 1.5x103 Torr He pressure and ~90 K trap temperature. This cluster formation was not observed for trap temperatures 170 K; however, the C60+ decay rate was constant within experimental uncertainty over the range 90-300 K. As shown in figure 3 for increasing flux exposure times, the C60+ ion peak decreases and the cluster spectrum broadens and moves to higher masses. The spectra in figure 3 exhibit clusters up to n=14 after an initial number of ~2000 C60+ ions were exposed to Li flux for 8 s, and clusters with up to 18 Li atoms were observed. The cluster yield, defined as the total number of LinC60+ clusters appearing in a mass spectrum divided by the number of C60+ ions lost, was observed to vary from 5-80% over the range of parameters used in these measurements.

It is interesting to note that the mass distributions shown in figures 3 and 4, which are derived from formation kinetics, do not exhibit exceptionally high peaks at either Li7C60+ or Li12C60+. Martin [1] observed such peaks for laser heated clusters which presumably resulted [19,20] from the enhanced cluster stability of specific electronic and shell structures. Cluster stability distributions might also be observed for trapped LinC60+ clusters by inducing vibrational excitation through resonantly excited collisions [21] with He so that the resulting mass spectrum was characterized by dissociation processes.

Anderson and co-workers have performed ion beam measurements [22] of Li+, Na+, and K+ collisions with neutral C60 vapor which were carried out primarily to study the mechanisms of alkali ion insertion within the C60 shell over an energy range from 0 to 150 eV. In addition to the formation of endohedral complexes, collisions resulted in fragmentation and thermionic emission. The appearance energies of ~6 eV for Li@C60+ and ~18 eV for Na@C60+ and ~40 eV for K@C60+ preclude the observation of such endohedral complexes in our trap experiments performed at thermal collision energies. These beam experiments were carried out using a C60 vapor temperature of ~615 K, corresponding to an initial C60 internal energy of ~2.4 eV. Even at low ion beam energies, alkali ion-C60 complexes resulting from charge-induced dipole interactions, would not remain stable during the ~1 msec time of flight to the detector with this internal energy. The dependence of the formation of stable LiC60+ complexes on the internal energy will be discussed further below.

LiC60+ formation

The number of LiC60+ ions formed as a function of He pressure was measured to obtain information about the formation kinetics. The dominant processes were described by


where kL, kL(2), kvib and kRRKM are respectively the rates for Langevin capture collisions for n=1, capture rate for n=2, vibrational relaxation, and dissociation of LiC60+. The bracketed terms [LiC60+]* and [Li2C60+]* indicate vibrationally excited complexes formed in the respective collisions.

The formation kinetics for LiC60+ displayed in Eq. (1) can be expressed by a rate equation which accounts for dissociation and relaxation processes only during the interval after a charge-exchange collision. A time dependent RRKM dissociation rate, Krrkm(E0,Eint), was calculated for an internal energy Eint determined by . The internal energy immediately after a charge-exchange collision is given by Eint(0)=DE+E0, where DE is the difference in the ionization potentials ofC60 (7.6 eV) [23] and Li (5.39 eV) and E0 is the Li binding energy. In this derivation, no assumption was made regarding the relative size of the various rates involved. The rate equation solution for M1(t), the number of LiC60+ clusters, is given by


where N0 is the initial number of C60+ ions. The parameters kvib and E0 are determined by fitting this solution to the number of LiC60+ clusters detected in the mass spectra as a function of He pressure.

The experimental rate kexpkL was obtained at each pressure by measuring the decay of C60+ ions as previously described. The LiC60+ decay rate, kL(2), was measured by first isolating the LiC60+ ion mass and then exposing these cluster ions to Li flux for varying shutter intervals as displayed in figure 4 for an interval of 4.5 s. Figure 4 shows the detection of mass selected LinC60+ ions for n=1,3 and 4 and the resulting mass spectra.

Figure 4. Mass spectra of isolated LinC60+ clusters for n=1,3 and 4 are displayed on the left side indicating the initial cluster number for each n. The mass spectra resulting from exposure of LinC60+ to Li flux for the times indicated are shown to the right side of each cluster trace. The number of remaining cluster ions and the peak number of new clusters are indicated in each mass spectrum. All mass spectra were obtained at He pressure of 2.3x103 Torr. The mass axes (amu) common to all spectra are shown on the bottom traces.

A fit of the number of LiC60+ clusters formed as a function of He pressure to Eq. (2) was obtained by minimizing c2 for 11 He pressures over the range 1.4x104 to 8.0x103 Torr. Formation of LiC60+ was not observed for He pressures <3.5x105 Torr. The best fit to all data sets yields a value of <E0>=1.50.1 eV. This binding energy can be compared with Hartree-Fock calculations [24,25] of Na+C60 and Li+C60 interactions which yield an estimate for the LiC60+ binding energy of 1.3 eV. Variation of the best fit value for <E0> using different sets of C60 vibrational frequencies in the calculation of kRRKM was within the indicated uncertainty.

Although the parameter kvib could not be determined independently, the fit does yield a value of kvib at each He pressure given the binding energy <E0>=1.5 eV. A plot of kvib versus He density yields an upper bound of the rate constant for vibrational relaxation, kHe<1x1014 s1 cm3. This analysis provides a qualitative description of the relaxation process for low energy He-LiC60+ collisions. In these collisions only the lowest LiC60+ vibrational modes, comparable to the low frequency collective modes of C60 having hn200-500 cm1, exchange energy effectively. Such collisions will involve a large portion of the cluster mass M so that on average only a fraction of the mode energy ~(m/M)hn1 cm1 can be transferred per collision. This is comparable to the energy transferred per collision as estimated [26] by the upper bound of kHe, DEvib<kHeEint(0)/Z1 cm1 where Z= <vrel>~2.8x1010 s1 cm3 with s, the He-LiC60+ hard sphere cross section, and vrel, the relative collision velocity. This energy transfer per collision by He is only a fraction (1/50) of that measured previously for smaller polyatomic molecules [27,28] which may be a consequence of the absence of low frequency bending modes in the C60 molecule.

The upper bound of the rate constant for vibrational relaxation, kHe, is consistent with the assumption that the He densities used in these measurements have thermalized the trapped C60+ ions during the 20-40 s storage interval prior to alkali flux exposure. C60 neutrals were ionized by electrons having an average energy of ~100 eV as a consequence of propagation through the rf trap fields. Electron energy transfer to the vibrations during ionization is rapidly dissipated by the evaporative loss of C2 molecules, requiring a dissociation energy [29] of 7.1 eV, and also by infrared radiative decay [30]. The decrease in internal energy was indicated by the absence of continuing dissociation on the 1-10 s timescale. A dissociation time of tD1 s corresponds to an internal energy of ~30 eV considering only C2 evaporation and to ~20 eV if infrared decay contributes significantly [22]. At the upper bound of kHe, the vibrational cooling rate by He is on the order of ~1 s1 for the He pressures used in these measurements, and collisions will relax an internal energy of ~30 eV to ~0.01 eV, corresponding to a vibrational temperature of ~100 K, within the 20-40 s ion storage interval. Similar estimates indicate that these vibrational relaxation rates were sufficient to stabilize the LiC60+ complex.

LinC60+ formation (n>1)

The formation kinetics of LinC60+ clusters for n>1 was studied by first isolating a LinC60+ ion mass for a specific n and then exposing the ions to Li flux as displayed in figure 4. The dominant formation kinetics of LinC60+ n>1 was described by


where kL(n) is the Langevin capture rate for n>1. In this kinetics model, the formation of a cluster with n+1 proceeds via the capture of a Li atom without significant dissociation. This was observed in each mass spectrum originating from a cluster with n>1 which displayed a constant number of ions independent of the Li exposure time. The vibrational relaxation rates which were competing with dissociation in the formation of LiC60+ clusters, appear to rapidly dominate dissociation in the formation of clusters with a higher number of Li atoms. This can be explained by assuming lower ionization potentials for LinC60 compared to C60, which resulted in less energy transferred to the vibrational modes. This has been shown to be the case for ionization potentials calculated [3] for KnC60 clusters.

These kinetics can be expressed by a set of rate equations having solutions for the cluster number Mn(t) for each n given by


where M1(0) is the initial number of LiC60+ clusters. This solution satisfies the condition that as observed in the mass spectra. The Langevin capture rates kL(n) for n=1-5 were determined by the decays of the corresponding Lin1C60+ clusters. It was found that the rates kL(n) were independent of n and identical to the n=1 Langevin capture rate within experimental uncertainty. The resulting mass spectra associated with the decay of each Lin1C60+ cluster could be calculated quantitatively from Eq. (4) using the measured value for kexp =kL as previously determined by C60+ decay in the zero He pressure limit.

It is important to point out that the kL(n) rates of the formation of clusters for n>1 were dominated by collisions involving capture trajectories since formation of these clusters proceeded without significant ion loss. The result that the measured rate for C60+ decay, kexp, was equal to these formation rates kL(n) strongly supports the implication that Li-C60+ collisions predominantly involve capture trajectories. This result probably applies to the other alkali atoms as well but has not been demonstrated as conclusively.


One of us (JHP) would like to thank Abraham Szke, David Tomanek and Mark Pederson for relevant discussions during the progress of this work. This research was fully supported by The Rowland Institute for Science.


[1] U. Zimmermann, A. Burkhardt, N. Malinowski, U. Nher and T. P. Martin J. Chem. Phys. 101 (1994) 2244.

[2] T. P. Martin, N. Malinowski, U. Zimmermann, U. Nher and H. Schaber, J. Chem. Phys. 99, 4210, (1993).

[3] P. Weis, R. D. Beck, G. Bruchle and M. M. Kappes, J. Chem. Phys. 100 (1994) 5684.

[4] J. H. Parks, S. Pollack and W. Hill, J. Chem. Phys. 101 (1994) 6666.

[5] M. A. Armitage, J. E. Fulford, N.-H. Duong, R. J. Hughes and R. E. March, Can. J. Chem. 57 (1979) 2108.

[6] J. E. Fulford, D.-N. Hoa, R. J. Hughes, R. E. March, R. F. Bonner and G. J. Wong, J. Vac. Sci. Technol. Phys. 17 (1980) 829.

[7] Selected Values of the Thermodynamic Properties of the Elements, American Society for Metals, 1973.

[8] P. Langevin, Ann. Chim. Phys. 5, 245 (1905) and an English translation which appears in E. W. McDaniel, Collision Phenomena in Ionized Gases (Wiley, New York, 1964), p. 701.

[9] G. Gioumousis and D. P. Stevenson, J. Chem. Phys. 29 (1958) 294.

[10] S. Petrie, J. Wang and D. K. Bohme, Chem. Phys. Letters 204 (1993) 473.

[11] S. Petrie, G. Javahery, J. Wang and D. K. Bohme, J. Phys. Chem. 96 (1992) 6121.

[12] C. Brchnigac, Ph. Cahuzac, J. Leygnier, R. Pflaum and J. Weiner, Phys. Rev. Letters 61 (1988) 314.

[13] K. M. Ervin and P. B. Armentrout, J. Chem. Phys. 83 (1985) 166.

[14] P. J. Robinson and K. A. Holbrook, Unimolecular Reactions; (Wiley, London, 1972).

[15] F. A. Khan, D. E. Clemmer, R. H. Schultz and P. B. Armentrout, J. Phys. Chem. 97 (1993) 7978.

[16] M. F. Jarrold in Clusters of Atoms and Molecules, ed. H. Haberland (Springer-Verlag, Berlin, 1994) p. 163.

[17] R. E. Stanton and M. D. Newton, J. Phys. Chem. 92, 2141 (1988).

[18] M. R. Pederson and A. A. Quong, Phys. Rev. B46, 13584 (1992).

[19] J. Kohanoff, W. Andreoni and M. Parrinello, Chem. Phys. Letters 198 (1992) 472.

[20] M. Braga, S. Larsson, A. Rosn and A. Volosov, Astron. Astrophys. 245 (1991) 232.

[21] K. L. Morand, S. H. Hoke II, M. N. Eberlin, G. Payne and R. Graham Cooks, Org. Mass Spectrom. Ion Process. 27 (1992) 284.

[22] Z. Wan, J. F. Christian, Y. Basir and S. L. Anderson, J. Chem. Phys. 99, 5858 (1993).

[23] J. de Vries, H. Steger, B. Kamke, C. Manzel, B. Weisser, W. Kamke and I. V. Hertel, Chem. Phys. Letters 188 (1992) 159.

[24] A. S. Hira and A. K. Ray, Phys. Rev. A52 (1995) 141.

[25] A. S. Hira, private communication.

[26] J. R. Barker, J. Phys. Chem. 88 (1984) 11.

[27] B. M. Toselli and J. R. Barker, J. Chem. Phys. 97 (1992) 1809.

[28] J. Shi and J. R. Barker, J. Chem. Phys. 88 (1988) 6219.

[29] M. Foltin, M. Lezius, P. Scheier and T. D. Mrk, J. Chem. Phys. 98, 9624 (1993).

[30] R. C. Dunbar, Int. J. Spectrom. Ion Proc. 100, 423 (1990).