8182
J. Phys. Chem. 1993,97, 8182-8192
Carbon Cluster Cations with up to 84 Atoms: Structures, Formation Mechanism, and Reactivity Gert von Helden, Ming-Teb Hsu, Nigel Gotts, and Michael T. Bowers' Department of Chemistry, University of California, Santa Barbara, California 93106 Received: March 30, 1993; I n Final Form: May 25, 1993
Carbon clusters are generated by laser desorption. Mass-selected beams are then pulse injected into an ion chromatography (IC) device. This devicetemporally and spatially separates thebeam into its isomericcomponents. Arrival time distributions (ATDs) are then measured at the detector. From these distributions, accurate mobilities are obtained for each isomeric component, along with the fractional abundance of each isomer. Different isomer structures are calculated using quantum chemical methods. A Monte Carlo technique uses these structures to obtain accurate theoretical mobilities. Comparison of theory with experiment allows unambiguous structural assignment of the various families of isomers present in the cluster beam. The results indicate that, for carbon cluster cations, linear structures exist up to Clo+. Several families of planar ring systems begin with monocyclic rings (ring I), which first appear at C7+ and persist beyond Ca+. Bicyclic rings (ring 11) are first observed a t Czl+ and persist beyond C a + , followed by tricyclic rings (ring 111, initiated at C30+) and tetracyclic rings (ring IV, initiated at Ca+). A 3-dimensional family we label as 3-Drings begins at CZ9+,whose structure is not yet unambiguously assigned. This family never exceeds 5% of the ions at any cluster size. Finally, the first fullereneis observed at C30+,with this family dominating above C50+. The growth pattern of carbon, beginning with C atoms, is shown to be linear monocyclic rings polycyclic rings fullerenes. No graphitic or "cup" shaped isomers are observed, eliminating these species as building blocks for fullerenes. Our structural data, when coupled with recently published annealing studies, indicate that fullerenes are formed from isomerization of hot planar ring systems and that monocyclic rings and fullerenes are close in energy between C ~ Oand + C36+with fullerenes dominating above c36+. Reactions of C7+ to CIS+ with 0 2 and NO are reported and indicate that linear chains are generally much more reactive than rings. Finally, Cm and C70 are made with up to four positive charges but retain the fullerene cage structure.
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I. Introduction Even before the synthesis of macroscopic quantities of fullerenes,' carbonclusters were the subject of an intenseresearch effort. Thevast amount of research up to 1988 has been reviewed by Welter and van &e.* Early studies on small carbon cluster ions with up to about 30 atoms used high-frequency spark evaporation: laser evaporation followed by direct detection of positive or negative ions: thermal evaporation of carbon,5 and secondary ion mass spectrometry.6 All thesestudiesshowed strong intensity variations with carbon cluster size in mass spectra. For example, higher intensities were observed- for clusters with an odd number of atoms up to Cg+. For larger clusters, a periodicity in intensity for every four atoms was observed.- These periodicities were interpreted as consistent with carbon chains for n I 9 and monocyclic rings for larger A breakthrough in the field occurred with the design of pulsed laser vaporization sources coupled with a supersonic expansion using an inert carrier gas.* These sources are capable of generating intense cluster beams having up to several hundreds of atoms in a cluster.gJ0 Remarkable size distributions were observed for carbon cluster cation^.^ For example, essentially no clusters were observed from about 26 to about 32 at0ms;9 clusters with an odd number of atoms for n > 30 were either absent or very weak? and enhanced intensities were observed for "magic" clusters containing 50,60, and 70 at0ms.~J0 It was then proposed that Cm was composed of a closed quasi-spherical carbon network containing 12 pentagons and 20 hexagons, and the name buckminsterfullerenewas These authors argued that Cm and C70 were also closed-shell cagecompounds, and eventually it became common to describe all even carbon clusters with greater than 30 atoms as "fullerenes". Experimental determination of structures for any of these clusters remained elusive, however, until Cm was first isolated1 and its structure investigated by traditional means. 0022-3654/93/2097-8 182$04.00/0
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For clusters other than the few fullerenes that could be isolated in bulk, unambiguous structural evidence was lacking, with the exception of somevery small clusters where spectroscopicmethods were applied and at least some molecular parameters determined.2J1 Reactivity studies12suggested that C7+, CS+,and Cg+ exist in two different isomeric forms, a reactiveform (presumably linear) and a less reactive form (presumably cyclic). For the negativeions, interpretation of photoelectron spectral) suggested that clusters with up to nine atoms are linear, Clo- exists in both linear and cyclic forms, and above Clo- the ions and/or neutrals are monocyclic rings. Coulomb explosion methods" have shown the possible presence of different isomers for C4-, C r , and c6-. Structural information also has been deduced from metastable mass ~pectr0metry.l~ These studies indicatestructural transitions occurring near Cl0+and C30+. For clusters with n < 24, the main metastable neutral loss was found to be Cp, consistent with the possible existence of linear and ring like clusters. Above C,O+, only C2 loss was observed for clusters with an even number of atoms. Between CN+and C30+ primary neutral fragment losses included Clo and C14, presumably intact monocyclic rings. Numerous computationalstudies on carbon clusters have been undertaken.16 High-level ab initio calculations have mainly focused on clusters containing up to 11 atomslh,b*dJ.iand Cm.16j* Recently, however, calculations have been done on clusters of intermediate ~ i z e . l C . ~ . ~Results f J ~ indicate that, for clusters with up to 1 1 atoms, the cluster ground state is either monocyclic or linear with the possibility of both structures coexisting for some cluster sizes. Recent MP2 and LDA calculations on C20, C14, and other ~ l u s t e r s ~ ~ . ~indicate L J J ~ a cagelike fullerene structure may be lowest in energy followed by cup or graphitic like "open fullerene" structures and then monocyclic rings. One of these studies16fproposed the C20 "cup" as a possible precursor in Cm formation. This proposal is in contrast to experimentalresults17 that indicate monocyclic rings are the dominant clusters for both 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 31, 1993 8183
Carbon Cluster Cations with up to 84 Atoms Magnet
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Figure 1. Schematic of the overall instrument. Carbon cluster ions are generated by laser vaporization/supersonic expansion. Ions are mass selected by the magnetic and electrostatic analyser and injected at low energy into the chromatography cell. Ions exiting the cell pass a quadrupole mass filter and are detected by standard ion counting techniques. Arrival time distributions are obtained using the ion gate preceding the cell. Pulses of 1-10 fis of mass-selected ions are injected, and their time of arrival at the detector is measured.
positive and negative ions in this size range and "cup" or fullerenes are totally absent for these clusters. In a short communication,'* we recently applied the method of "ion chromatography" (IC) l9 to carbon cluster cations with up to 60 atoms. Subsequently, we have expanded these efforts to small carbon cluster anions.17.z'JJ Various families of structural isomers have been identified. In this paper, we present further and much more complete IC results on the structures and reactivities of carbon cluster cations. Extensive semiempirical calculationsand subsequentcomputer modeling of mobilities yield unambiguous structural information for many of the isomeric species observed. We then use these data and new annealing results22 to suggest a carbon cluster growth mechanism.
II. Experimental Section
(a) Mobility Experiment. The experiment has been described in previous publi~ations,l~-~~ and only a brief outline will be given here. A schematicof the instrument is shown in Figure I. Carbon cluster ions are generated in a Smalley type laser vaporization/ supersonic expansion source. An excimer laser (308 nm, 300 mJ) is used to vaporize graphite from a rotating and translating rod. He, admitted from a pulsed valve (General Valve), is used as the expansion gas. Carbon clusters and cluster ions expand, 3 mm downstream from the vaporization laser, into vacuum through a 30° conical nozzle. No further ionization is used. The cluster beam passes a skimmer, and positive ions are accelerated to 5000 eV. Carbon clusters are then mass selected by a doublefocusing, reverse geometry mass spectrometer. Mass spectra are obtained following the mass spectrometer at an off-axis detector. In the mobility experiment, an electronic shutter following the mass spectrometer selects a 5-8 ps wide packet of a specificmassselected carbon cluster. This packet is then decelerated to a few electronvolts(less than 20) and injected into a high-pressure drift cell. Using these low injection energies, no fragmentation is observed. The cell is 4cm long and has 0.5-mm entrance and exit orifices. Helium at 2-5 Torr is used as a buffer gas. In some experiments, 0.1-1 mTorr of reactant gas is mixed with the buffer gas. Injected ions are quickly thermalized by the helium bath gas and drift through the cell under the influence of a weak electric field. Field strengths are between 2 and 10 V/cm, depending on the helium pressure. Ions exiting the cell pass through a quadrupole mass
filter and are detected using standard ion counting techniques. To measure arrival time distributions (ATDs), the quadrupole mass filter is either set to the mass of the ion of interest or, for clusters with more than 50 atoms, used in the RF only ion pipe mode. The mobility24 of a given ion is defined in eq 1:
K = bd/E (1) where bd is the drift velocity and k the drift field. More common is the reduced mobility, eq 2: P213.1 6K KO = -
160T
where P is the pressure in Torr and T the temperature in kelvin. To a good approximati~n,~~ the mobility is related in eq 3 to the average collision cross section of the ion with the bath gas:
(3) whereq is the total number of elementary charges, e the elementary charge, NOthe standard number density, p the reduced mass, kb the Boltzmann constant, and Q(*J) the collision integral. In the hard-sphere limit, the collision integral reduces to the hard-sphere collision cross section. The time an ion spends in the cell is then inversely proportional to the mobility of the ion and directly proportional to the average cross section of the i0n.2~ Mobilities can be obtained by recording an arrival time distribution (ATD) at different drift voltages on a multichannel scalar (2-ps channel width). Ions of the same mass but with different structures may have significantly different mobilities. These isomeric structures will be spatially and temporally separated while drifting through the cell, producing separate peaks in the ATD spectrum. Structures with large average cross section have a lower mobility and exit the cell at later times than compact structures with small cross sections. Both the absolute amount of the isomeric structures and their mobilities can be determined. Mobilitiesare determinedby two differentapproaches. Plotting the mean arrival time for a particular isomer versus l/Vgives a linear plot where the slope is inversely proportional to the mobility and theintercept equals the sumofthe timespent in thequadrupole and before the cell. Statistical uncertainties in these mobilities are usually better than f2%, although in some cases (ATDs with many, only partially resolved, isomers) the uncertainty can be as high as f4%. Alternatively,if the time that the ion spends outside the cell is known, the mobility can be determined by fitting the ATD with a theoretical model. (b) Fitting of the AT&. In order to obtain mobilities, isomer abundances and, in some experiments, reaction rate constants the ATD can be fit with a theoretical model." For a cylindrical drift tube, the ATD of a single ion type is given by eq 4
where ud is the drift velocity, z is the length of the cell, ro is the size of the exit aperture, c is a scaling factor for the intensity, k is the reaction rate constant (when reactant gases are mixed with the buffer gas), and 4and Dt are the longitudinal and transversal diffusion coefficients. To a good approximation, 4and Dt can be estimated by the Wannier expre~sion.2~ Equation 4 is valid for a delta pulse of ions entering the cell. If the input pulse width is comparable to the width of the ATD, the above expression has to be convoluted with the width of the input pulse. For multiple ion types with different drift velocities (and therefore different diffusion coefficients), the resulting ATD is just the sum of the ATDs for the individual ions. We employed a MarquardLevenberg least-squares.fitting algorithm to obtain drift velocities (and from this mobilities) and isomer abundances from the
von Helden et al.
8184 The Journal of Physical Chemistry, Vol. 97, No. 31, 1993
experimental ATD. In the case of no reactions occurring, the only adjustable parameters in this fit are the individual drift velocities,the fractional abundances of the different isomers with the condition that they add up to 1, and a scaling factor for the total intensity. In order to obtain isomeric specific reaction rate coefficients, first an ATD with no reactant gas is obtained. Fitting this ATD gives thedrift velocitiesand relative isomer abundances. Reactant gas is then mixed to the buffer gas. Scanning the quadrupole mass filter gives the product ion distribution. From this, a total rate constant ktotcan be obtained:
where Z is the number of reactant ions at time t, ZOthe number of reactant ions at t = 0, n the number density of reaction gas, and t the residence time averaged over the different isomers. In the limit of low conversion, the total rate constant is connected to the individual isomeric specific rate constants, ki,
, I
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Figure 2. Typical mass spectrum obtained at the off-axis detector before the drift cell. No further ionization beyond the laser vaporization pulse is used. The shape of the mass spectrum depends to some extent on conditions in the laser vaporization source.
symmetry can use up to 40 CPU minutes on a IBM RS/6000 workstation until satisfactory convergence is achieved. withf, being the fractional abundance of isomer i. An ATD with reaction gas mixed to the buffer gas in the cell can now be fit using expressions 4 and 6. In the case of two different isomers present, only two adjustable parameters are needed: the reaction rate coefficient for one of the ions and a scaling factor for the total intensity. (c) Mobility Simulation. In order to obtainadditional structural information from the mobility experiment, the cluster cross section has to be simulated as a function of cluster structure. The mobility can then be calculated using eq 3. The cross section has to be angle averaged over all possible orientations of the cluster about its center of mass, relative to the line of centers of the collision. Analytical solutions exist only for a few, very simple structures like spheres and cylinders. We chose a numerical Monte Carlo approach to calculate the angleaveraged, hard-spherecross section. First, an input structure of the cluster (from ab initio or semiempirical calculations) is rotated to a random orientation around its center of mass by choosing three random Euler angles. The cluster is then projected onto the xy plane, and the cross section for this orientation is determined by Monte Carlo integration. In implementing the Monte Carlo procedure, a two-dimensional rectangular box is put around the projected molecule with the two sides of the box tangent to the x and y extrema of the molecule. Next, random points inside the box are selected. If a chosen point is closer than the sum of the carbon and helium van der Waals radii to any of the atomic centers in the cluster, the assumption is that a collision has occurred. After choosing several hundred points, the converged collision cross section for this orientation is given by the ratio of 'hits" to the total number of points and multiplied by the area of the box. Convergence of the cross section for a given orientation is monitored by standard statistical methods. The Monte Carlo integration is stopped if the cross section for an orientation has converged to 1%. Next, the cluster is oriented to a new, randomly chosen set of Euler angles, and a new cross section is calculated by the same scheme. The whole process is repeated for several hundred Euler angle sets, and the average cross section is converged to better than 1%. For clusters with only one kind of atom, this procedure has only one adjustable parameter: the sum of the carbon and helium van der Waals radii. This parameter is held constant at 2.7 A (1.15 A for helium and 1.55 A for carbon) for all clusters in all the calculations reported here. (A value of 2.6 A was used in an earlier publication.18) In the present implementation, this algorithm is quite computer intensive. Large structures with very little
III. Results (a) Mass Spectrum. Figure 2 shows a mass spectrumof carbon cluster cations taken at the off axis detector prior to the drift cell. Note that the spectra reflect ions formed by the laser in the vaporization source, and no further ionization was used. The spectra show relatively little structure, and in contrast to most other carbon cluster mass spectra reported in the literature,&1° peaks that have been attributed "magic" numbers are not enhanced. The only real featuresin the spectraarea large increase in intensity observed at C11+ and odd/even alternations starting around C34+. Large clusters with an odd number of atoms are observed at relatively high intensity, however. The peaks for C@+and C,O+ show very little enhancement compared to their neighboring peaks. Although these general featureswere observed in all spectra from the source, the overall shapeof the mass spectra is quite sensitive to experimental conditions. By adjusting the timing of the pulsed valve with respect to the vaporization laser, the spectra can be tuned to favor smaller or larger clusters. (b) Arrival Time Distributions (ATDs). When a short pulse of mass-selected carbon cluster cations is injected into the drift cell, an ATD is obtained. Figures 3 and 4 show typical ATDs for some of the clusters studied. Drift times are multiplied by P/ V as a first-order compensation for different pressures and drift voltages used in the various scans. Clearly, the ATDs are complex and different peaks can be readily seen. The presence of multiple peaks can only be attributed to the presence of different structural isomers with different mobilities since mass-selected clusters are injected, and the only species exiting the cell are those injected. Some of the peaks are only partially resolved, and the ATD has to be fit in order to obtain accurate isomeric mobilities and abundances. Figure 3 shows the ATDs for C6+ to C11+. From C3+ to C6+, only one peak is observed in the ATD. Starting at C7+, a peak at shorter times appears, indicating the presence of a different isomer with a different cross section and mobility. As will be shown later, the 'fast" component corresponds to the monocyclic ring isomer whereas the slow component is due to the linear form of the carbon cluster. As can be seen in the figure, these two isomers coexist from C7+ through Clo+. From C11+ to CZO+, the linear isomer is no longer present, and only the peak for the monocyclic ring is observed. Starting at C21+,a shoulder on the monocyclic peak at shorter times is observed. We will call this new feature 'ring 11". The fraction of ring I1 increasesas cluster size increases and becomes comparable in size to the monocyclic (ring I) isomer near Cz8+.
The Journal of Physical Chemistry, Vol. 97, No. 31, 1993 8185
Carbon Cluster Cations with up to 84 Atoms
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Drift Time * V/P [ p * VLl’orr} Figure 3. Arrival time distributions (ATDs) for C6+to C11+. Only one peak is observed for C6+and C11+whereas clearly two peaks can be seen for the other clusters. C6+can be assigned to be purely linear and C11+ to be purely monocyclic ring. For all other ions in this figure, the longer time linear peak is shaded to guide the eye. See text for justificationof assignments.
Figure 4 shows the ATDs for C28+ to C33+. For c28+, the two partially resolved peaks of almost equal intensity result from the “ring I” and “ring 11” isomers. A new isomer at substantially shorter times is observed starting at C29+. It’s relative intensity is very low. Another one at even shorter times appears at C30+. We will call these isomers “3-D ring” and “fullerene”. (Justification for these assignments will come shortly.) Note that the “fullerene” peak is completely absent at c28+ and C29+. Between C30+ and Ca+, the resolution is no longer sufficient to completelyresolve the different “ring” features. Consequently, the ATD must be computer fit in order to obtain accurate mobilitiesand isomer abundances. Up to C30+,two “ring” isomers are sufficient in order to obtain a good fit of the ATD. Starting at C30+, a third “ring” isomer at shorter times than ring I1 is needed. We will call this feature “ring 111”. From C ~ Oto+C39+, these three rings isomers are sufficient in order to obtain a good fit for the combined unresolved “ring” feature. Figure 5 shows the experimental data (lines) and a fitted ATD (points) for C36+. Clearly, a good fit can be obtained with ring I, 11,111,“3-D ring”, and “fullerene” being present. From C a + on, a fourth feature at the short time end of the combined ring peak is needed in order to obtain an acceptable fit. A fit of the C a + ATD with only three “ring” isomers is shown in Figure 6a. Clearly, the fit cannot reproduce the short time shoulder at the unresolved“ring”feature. Including a “ring IV” isomer yields an acceptable fit (Figure 6b). The presence of the four unresolved isomer peaks in the ring feature introduces some uncertainty in the fitting procedure. Consequently,we decided not to try to fit the various ring features above C a + at this time. Nonetheless, the overall width of the composite peak beyond C a + indicates at least four different isomers contribute to this feature. The relative abundance of the “fullerene”peak, first appearing at C30+, shows very strong odd-even alternations, with larger intensities occurring for clusters with an even number of atoms.
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Drift Time * V/P [ ps * VLl’orr I Figure 4. ATDs for C28+ to C33+. The peaks labeled A correspond to the fullerene isomer and begin at C30+. The peaks labeled B correspond to a 3-Dring isomer and begin at C29+. The peaks labeled C, D, and E correspondto tri-, bi-, and monocyclicplanar ring structures,respectively, and are denoted ring 111, ring 11, and ring I throughout the paper. See text for justification of assignments. I .
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Figure 5. Experiment (line) and fit (points) for C36+ATD. Five isomers are used for the fit. From short to long times, these are fullerene, 3-D ring, ring 111, ring 11, and ring I. Clearly, a good fit can be obtained. See text for assignment of structures.
The peak for this feature gains slowly in intensity and becomes the dominant peak by C50+. Figure 7 shows ATDs for C59+, Cm+, and Gal+. For Cm+, the fullerene portion of the ATD constitutes more than 98% of the total intensity. Note, however, that C59+ and C61+ still retain a large fraction of “ring” isomers (3040%). (c) Structure Assignment. For each of these peaks, the ionic mobility can be determined. Figure 8 shows the inverse mobility of each of the different isomers as a function of cluster size. In the hard-sphere limit, the inverse mobility is proportional to the average collision cross section. As can be seen in the figure, the different isomers neatly group into different familiesof structures.
von Helden et al.
8186 The Journal of Physical Chemistry, Vol. 97, No. 31, 1993 Experiment
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Figure 6. Shown in part a (top) is an experiment (line) and fit (pints) for C , + ATD. Five isomers were used in the fit, similar to the C3s+ systemin Figures. Thefitclearlycannot reproducetheshoulderoocurring at short times in the broad ring feature. In part b (bottom) the same experimental ATD is shown, but the fit ATD includes six isomers, the same isomers as in Figure 5, plus a ring IV isomer. Clearly, the fit is excellent in this case and confirms the presence of the new ring IV isomer.
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Drift Time * V/P [ p * VDorr I Figure 7. ATDs for Css+, Cm+, and The large pcak at short times
corresponds to the fullerene isomer whereas the broad feature at longer times corresponds to multiple, unresolved two-dimensionalring isomers. Note that while for Cm+ the ATD consists of almost pure fullerene, a large fraction (30-408) of two-dimensionalring structures are observed for Cs9+ and c6l+.
For structurally related clusters, the inverse mobility (and so the mobility) is expected to be a smoothly varying function of cluster size. Lines are drawn in order to guide the eye. Since the
resolution in the experiment is not sufficient to unambiguously resolve the various "ring" families above Cm+, dashed lines are drawn for these isomers above&+. These "ring" isomers continue to be present, but an accurate mobility assignment is not possible from our ATDs under the resolution present in our experiment. Note the different 'slopes" in inverse mobilities of the different families as the clustersize increases. "Ring 11" and "ring 111" clearly parallel "ring I" as cluster size increases. The "3-D ring" and "fullerene" families show a much smaller increase in cross section (inverse mobility) as cluster size increases, indicatingthat these structure have a higher dimensionality than the "ring" families. As a point of reference, the mobilities of the "fullerene" isomers C a + and C70+ generatedby laser vaporizationof graphite can be compared to the mobility of Cw+ and C70+ generated by electron impact of a mixture of Cw and C70 vapor (see later in the paper). The mobilities from these two sets of experiments are identical within experimental uncertainty, indicating that the "fullerene" family indeed consists of 3-dimensional cage like structures. Consequently the "ring" structures, which have a lower dimensionality than the fullerenes, must be 2-dimensional and planar, or very near so. Possible cluster structures can now be calculated, and their simulated mobility can then be compared with the experiment. Since "accurate" ab initio calculationson clusterscontaining more than a few atoms are very computer intensive, we chose the semiempiricalPM325method using the program GAMESSX to calculatecluster structures. Experience indicates that, for carbon clusters, the calculated structures are acceptable even though the relative energies might be unreliable.17 All cluster structures were calculated as neutrals since this simplified the calculations, and only small changes in structure are expected upon ionization in the size range of importance here. The spin state for all clusters was chosen to be singlet, except for linear clusters with an even number of atoms that are expected to have a triplet ground state.13 Structures and mobilities were calculated for linear clusters with 6-10 atoms, monocyclic clusters with 6-40 atoms, and Cm, C32, C36, CN, Cm, CW,c 7 0 , and fullerenes. The results are given in Figure 9, where the theoretical results are represented by the lines and experiment by points. The agreement between calculated
The Journal of Physical Chemistry, Vol. 97, No. 31, 1993 0107
Carbon Cluster Cations with up to 84 Atoms 0.4 I
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Figure 9. Experiment (points)and calculated (lines) mobilities for linear, monocyclic, and fullereneclusters. For monocyclic rings and fullerenes, excellent agreement between calculation and experiment is apparent, confirming these structures. The agreement is not as good for small linear clusters for reasons given in the text. See text for details of the model used in the calculations.
TABLE Ik Energies and Calculated Mobilities for Different Cm Structures structure
relative energy (eV).
monocyclic r i n g bicyclic r i n g tricyclic ring (Fig. 1Oc) tricyclic ring (Fig. 1Od) “open fullerene” (Fig. l l c ) planar graphite fullereneve
+10.2 +12.2 +12.0 +11.8 +6.1 +12.2 0.0
mobility percent calcd exptl deviation/ 2.60 2.70 3.7 2.98 2.92 2.0 3.37 3.23 4.0 3.12 3.23 3.4 4.92 4.19d 17.4 4.26 4.19 1.7 1.6 5.68 5.49
PM3 energies relative to the lowest-energy structure. Mobility in units of (cm2/V-s). C Structure not shown. Mobility of the nearest experimental isomer. e PM3 heat of formation for the D2 isomer: 817 kcal/mol (the D s , isomer ~ was found to be 0.4 eV higher in energy and with identical mobility). f Absolute value of (calculated mobilityexperimental mobility)/experimental mobility. +, ,+ a)
C)
TABLE I: Energies and Calculated Mobilities for Different CX Structures structure
relative energy (eV).
monocyclic ring bicyclic ring tricyclic ring (Fig. loa) tricyclic ring (Fig. lob) “open fullerene” (Fig. 1lb) planar graphitec fullerenese
+4.7 +5.7 +7.3 +10.1 +3.6 +12.3 0.0
mobilitp calcd exptl 2.93 3.35 3.74 3.59 4.89 4.45 6.03
3.01 3.30 3.70 3.70 4.58d 4.58 5.93
percent deviation/ 2.6 1.6 ’ 1.1 3.0 6.8 2.8 1.7
PM3 energies relative to the lowest-energy structure. Mobility in units of (cm2/V*s).E Structure not shown. Mobility of the nearest experimental isomer. e PM3 heat of formation: 846 kcal/mol. f Absolute value of (calculated mobility - experimental mobility)/experimental mobility.
and experimental inverse mobilities for the monocyclic rings and fullerenes is very good, with typical deviations within 2%, which is the experimentaluncertainty. The agreement for linear clusters is comparatively poor; calculated mobilities are typically 10% too low. From the simulated mobilities it seems clear that, in our experiment, monocyclicrings are present from 7 to 40 atoms and above, fullerenes are present from 30 to above 84 atoms, and linear clustersexist with up to 10atoms. It also gives us confidence that, despite the approximations involved, mobilities of carbon clusters above Clo+can be simulated quite accurately, and these simulations can be used in order to test calculated structures for compatibility with experimentally observed mobilities. Possible “ring 11” structures for C24+ have been presented in a previous publication.17 Five nearly isoenergetic “bicyclic” C24 structures were proposed as possibly being responsible for the C24+ “ring 11” peak. These structures have two primary rings of sizes between 10 and 14 carbon atoms each. These structures generated mobilities in excellent agreementwith experiment. Good agreement between calculated and experimental mobilities was also obtained for bicyclic clusters of other sizes (Tables I and 11). Since it appears very likely that the “ring 11” family consists of two connectedrings, it seemsplausiblethat “ring 111” might consist of three connected rings. Figure 10 shows calculated (PM3) structures for c 3 6 and C a that may well contribute to the “ring 111” family of clusters. No symmetry has been assumed in these calculations. While the PM3 energies of these structures are larger than bicyclic or monocyclic rings of the same size, the
b)
Figure 10. PM3 optimized “tricyclic” structures for Csa+ and Ca+. No symmetry constraints were applied in the calculations. These structures give excellent agreement with experiment. See Tables I and I1 for relative energies and calculated mobilities.
calculated mobilitiesare in very good agreementwith experimental mobilities (see Tables I and 11). As cluster size increases, the possible number of permutations of atoms in two or three rings of different sizes for a given total number of atoms will increase, so that it is likely that each of the experimental “ring 11” or “ring 111” peaks consists of multiple, structurally closelyrelated isomers that have similar mobilities. An indication for this is the apparent loss of resolution for the “ring” families between C30+ and Cm+. Structural assignment for the “3-D ring” family is proving to be more difficult. The slope of the inverse mobility versus cluster size for this family is in between the slope of the presumably 2-dimensionalplanar ring families and the 3-dimensionalfullerene family, but closer to that of the fullerenes. We speculated in an earlier publication1*that this family might be due to unclosed, “open” fullerenes first proposed by Kroto and Smalley.lo Calculated structures for these so-called “open” fullerenes are shown in Figure 11 for C30, c36, and Cm. All the structures shown represent a portion of Cm BF. The C30 structure is just Cm BF sliced in half perpendicular to one of the C,symmetry axes while Cm “open”fullerene has the same symmetry as C30 open fullerene but has 10 more atoms around it’s outer perimeter. The C36 “open” fullerene has C3 symmetry and is also a Cm BF fragment. The PM3 energies and simulated mobilities of these structures are shown in Table 11. Their relative energies with respect to the monocyclic rings are quite low although the energies calculated at the PM3 level of theory are very uncertain. Simulated mobilities of all these “open” fullerene structures, however, fall almost exactly between the experimental mobilities for the fullerene and the 3-D ring families. There is no intensity in the ATDs at this location,and hence, no “open” fullerenesare present in our experiment. We did calculations on a number of other possible candidates for the 3-D ring family. Among them are
von Helden et al.
8188 The Journal of Physical Chemistry, Vol. 97, No. 31, 1993 0 )c o:
c)
b) C&
cto
C,+ clusters. n = even
side
side
side
Figure 11. PM3 optimized "open fullerene" cup structures for CW+,
C*+, and Ca+. No symmetryconstraintswere applied in thecalculations. Calculated mobilities of these structures indicate they are not observed in our experiments for clusters of any size.
10
30
50
70
0
Cluster Size loo
80
60
40
20
0 10
0
10
20
30
40
50
Cluster Size Figure 12. Relative abundances for all isomers,except the fullerenes,for clusters with up to 40 atoms. These relative abundances are insensitive tosourceconditions up to Clo+but depend somewhat on sourceconditions for larger species. The species plotted include linear ( 0 )and the series of planar ring systems: ring 1(0),ring 11(A),ring 111(A), ring Iv (m), and 3-Dring (+). Lines are drawn through the points simply to guide the eye. planar graphite sheets. For C36+and C a +the simulated mobilites for graphite sheets are in good agreement with experimental mobilities. Nonetheless, for reasons discussed later in the paper, we do not believe that these planar graphite structures give rise to the "3-D ring" family. A third possibility is "propeller" type molecules with planar ring systems whose planes are 120° apart, and each ring system is connected to a common pair of carbon atoms. These structures yield mobilities in reasonably good agreement with experiment and would explain why the 3-D ring family might start at C29+ (three rings of 11 atoms each). At this point, it is speculative to say what structures actually give rise to the "3-Dring" feature (although we can exclude a number of structures, among them cuplike "open" fullerenes), and we will address this issue in some more detail in a forthcoming pu blication.20 (e) Isomer Abundances. Isomer abundances can be obtained by fitting the ATD. Figure 12 shows the relative abundances of all the nonfullereneisomers up to C,+. Smoothed lines are drawn through the points toguide the eye. Clusters from 10to 40 atoms are dominated by planar ring systems. Within the ring families, ring I is dominating for clusters with up to about 25 atoms. The ring I1 isomer, first appearing at CzI+,gains rapidly in intensity
50
30
70
90
Cluster Size
Figure 13. Relative abundance of the sum of 2-dimensional (ring I to ring IV) and 3-dimensional (fullerene) isomers. In part a (top) even clusters are plotted and in part b (bottom), odd clusters. Note that fullerenes begin sooner and dominate more extensively (above C,) for
even clusters than for odd clusters.
and dominates for Clusters with more than 27 atoms, reaching up to 60% of the total signal for some clusters. It starts to fall off in relative contribution at around C35+ but still contributes to about 35%of the ion signal at C,+. Ring I11 first appears at C30+and reaches about 20% relative abundance at Ca+. Above C a , the different "ring" isomers are no longer resolved, and accurate fractional abundances could not be obtained. Nonetheless, thecentroid of the combined "ring" feature shiftsto shorter times as size increases, indicatingan increase in relativeabundance of the more compact multicyclic ring isomers. The feature we label "3-Drings" that startsoff at CB+continues to be present at a few percent abundance until the mid ~ O ' Sand , then it gradually decreases in intensity. Odd/even alternations are observed for this feature with the larger abundances being in the odd clusters. The relative abundance of this cluster never exceeds 5% in our experiment. The percentages of fullerene along with the sum of the 2-dimensional ring clusters (ring I to IV)are shown as a function of cluster size in Figure 13a for clusters with an even number of atoms and in Figure 13b for clusters with an odd number of atoms. Lines are drawn through the points to guide the eye. For clusters with an even number of atoms, the first fullerene is observed at C~O+, smoothly increases in fractional abundance, reaching 50%of the total ion intensity at about CM+,and finally becomes more than 98% abundant at CW+. Odd fullerenes, on
The Journal of Physical Chemistry, Vol. 97, No. 31. 1993 8189
Carbon Cluster Cations with up to 84 Atoms
TABLE IIk Reaction Rate Constants and Branching Ratios for Reactions of C,+ with 0 2 (All Numbers in Parentheses from Ref 12c)
n
44 5 6 7 8' 9 1Od
k, 10-10 cm3/sa structure of C,+ linear or cyclic
linear
branching ratios ionic product
c,o+
cyclic
2.6 (2.5)b
0.9 (1.9) 1.2 (1.3) 0.66 (1.3)
