J. Phys. Chem. 1995,99, 10736-10741
10736
Dissociation Energies for Small Carbon Cluster Ions (Cz-19') Measured by Collision-Induced Dissociation Marianne B. Sowa-Resat, Paul A. Hintz, and Scott L. Anderson* Department of Chemistry, State University of New York, Stony Brook, New York 11 794-3400 Received: May 8, 1995@
We report a collision-induced dissociation (CID) study of the stability and fragmentation behavior of carbon cluster ions, C,+ (n = 2-19). Measurements were made of the absolute CID cross sections, fragment appearance potentials, and fragment branching ratios. Dissociation threshold energies have been extracted for each cluster size by fitting the data. The threshold energies fluctuate strongly with cluster size. Small clusters show strong evedodd alternations in stability, and the results are in good agreement with theoretical dissociation energies. For larger clusters a periodicity of four atoms is observed, superimposed on an overall decrease in stability with increasing size. For most cluster sizes the dominant fragmentation channel is loss of C3. For CIS+, c16+, and Ctg+, loss of five atoms is a major channel, dominant in the case of cl6+and (219'.
I. Introduction An interesting aspect of carbon cluster chemistry and energetics is the well-documented change in geometric structure with cluster size. A number of theoretical investigations, starting in 1959 with Pitzer and Clementi,' have predicted that the most stable isomer should change from linear to monocyclic as the chain length grows long enough to offset the strain energy in forming a ring. For the linear isomers, the odd size clusters were predicted to be more stable than neighboring even sizes. More recent semiempirical and ab initio studies have refined this picture somewhat. Hoffman2 and Ray3 predicted linear structures for C I Oand lower, while Raghavachari and cow o r k e d 5 have found C3, c6, and Cg to be monocyclic rings. These discrepancies reflect the small energy differences between the linear and cyclic structures in the transitional size range. Though not studied as extensively, similar transitional behavior has been observed in ab initio studies on the cationic cluster^.^,^ In the range from C7+ to Cg+, von Heldon and co-workers6~' found that the monocyclic ring is about 1 eV lower in energy than the linear isomer. For nonzero temperatures, entropy tends to favor the linear isomer due to the larger number of lowfrequency vibrational modes. The predicted linear to cyclic transition has been observed experimentally as changes in cluster ion reactivity.8-' In general, C,+ with six or fewer atoms are found to be quite reactive, as expected for a linear isomer with unsaturated terminal atoms. Clo+ and larger have substantial activation barriers for many reactions, consistent with a monocyclic structure where all the carbon centers are coordinatively saturated. In the intermediate regime, C~+-CS+,reactivity is consistent with a linear combination of the two isomers. Recently, ion chromatography has provided more direct data on the size ranges where the structural transitions occur and the possibilities for interconversion.l2-l6 Despite this experimental and computational attention, the energetics for small carbon clusters are not well established. In the thermochemical literature, AHf values are available for small neutral C, ( n = 2-7),I7-I9 and for cations, heats of formation are available for clusters containing up to four atoms.20 Bach and Eyler2' have used charge transfer to bracket potentials for
* Corresponding author. Present address: Chemistry Department, University of Utah, Salt Lake City, UT 841 12. c z Abstract published in Advance ACS Abstracts, June 15, 1995. 0022-3654/95/2099-10736$09.00/0
c6-24+, and these IPS can be combined with the neutral energetics to yield approximate energetics for cations containing up to seven atoms. Guesic et al. reported a photodissociation study of C3-20+,**3~~ putting the dissociation energies at less than 2.53 eV for C5+ and larger. Considering that one might expect something approximating CC double bonding in the clusters, such low dissociation energies are surprising and in poor agreement with theory. Several years ago,24 we gave a brief report of a collisioninduced dissociatiodphotodissociation study of C,+ fragmentation, giving dissociation appearance energies and concluding that the photodissociation studies of Guesic et al. suffered from multiphoton absorption. In this paper we give a full account of the work, extend the cluster size range to C1gf, analyze the fragment appearance energies to extract quantitative dissociation thresholds, and propose a dissociation mechanism. Carbon dissociation has also been studied by metastable decay experiments. Radi et al.25reported studies on C5-11+ formed directly in a laser-generated plasma. The fragmentation patterns were dominated by the tendency to lose C3. C,l+ was an exception, dissociating predominantly by loss of a carbon atom Using similar experimental techniques, Lifshitz and co-workersZ6 measured kinetic energy release distributions for unimolecular decomposition of Cn+,(n = 10-13, 18). Clusters were formed from conjugated perchloro-hydrocarbon precursors by dissociative ionization. Loss of a carbon atom was found to be the dominant channel for CII+ and CIZ+,with other sizes preferentially losing C3. Upon collisional activation, the branching became complex and all possible daughter fragments were observed. Both experiments employed statistical phase space theory to extract energetics. Very recently, Shelimov et a1.I6 have reported drift tube experiments on C,+ ( n = 6-30). Using a model of their multicollision drift tube environment, they extracted dissociation thresholds, as well as activation energies for isomer interconversion.
11. Experimental Method The guided ion beam apparatus employed in these studies has been described in detail previo~sly,~' and only a brief description will be given here. Carbon cluster ions are produced by laser ablation of a pure carbon target (Aesar 99.999 at. %) inside a radio frequency (rf) trap. A pulsed jet of helium is directed across the target surface during the laser pulse. This 0 1995 American Chemical Society
Dissociation Energies for C2- 19’ Measured by CID 1.5
I
I
J. Phys. Chem., Vol. 99, No. 27, 1995 10737 I
1
Right Hand 0
/L
Experiment
= Best Fit N-
1.0
$4 v
A
0.1 x Rate
v
10 x Rate
Scale
1
I
! = I
.+ 4
Q) 0
wl v)
0.5 Left Hand
v)
k
b 0
u
0.0 2
7
6
3
4
5
0
6
7
8 9 13 1 1 17 13 14 15 16 i 7 18 19
Number of Atoms in Cluster
Collision Energy ( e V )
-
Figure 1. Typical CID cross section for C14+ C, I + (O),along with the best convoluted fit to the data (H).To show the relative insensitivity of the fits to the RRKM rates, we also plot fits obtained by increasing (A) and decreasing (v) the RRKM rates of the best fit by a factor of 10.
helps sweep the nascent clusters into the next section of the instrument and also begins to thermalize the hot clusters. To complete the thermalization process, the clusters are stored in a labyrinthine rf trap filled with Torr of N2, where the clusters are estimated to undergo > 5 x lo4 collisions. The clusters emerging from the trap are accelerated into a homemade Wien velocity filter, where primary mass selecton occurs. The mass-selected beam is then decelerated and injected into a set of rf octapole ion guides, where the collision energy is set and the ions are guided through a collision cell. The cell surrounds a section of the ion guide and is filled with the neutral target gas at a pressure low enough to maintain single-collision conditions. Preliminary studies were done using 0.20 mTorr of Ar, and the final cross sections ,were measured with 0.20 mTorr of Xe target gas, which has been found to be a more efficient CID target. (In the case of C2+, cross sections were only measured for the Ar target because of low primary ion beam intensity.) Fragment ions and residual parent ions are collected by the ion guide and accelerated into a quadrupole mass spectrometer where they are mass analyzed and then counted. Retarding potential analysis indicates that the lab frame translational energy spread of the beam is -0.2 eV (full width half-maximum). To check the efficiency of our storage- thermalization method, experiments were also performed using He and Ar in the cooling trap. Pressures were varied several orders of magnitude relative to our normal operating pressure and produced no significant change in the CID thresholds. The pressure of Ar and Xe used in the scattering cell was also varied, and multiple collision effects were found to be insignificant under our normal operating conditions. 111. Results and Fitting
Absolute cross sections were measured for collision energies from 0.1 to 10 eV for all fragment ions produced by CID of C ~ + - C I ~ +Typical . data are shown in Figure 1 for dissociation of C14+ to CII + , which is the only significant product ion. The results for all cluster sizes are summarized in Figure 2. The bars give the absolute cross sections for each fragment ion observed at a collision energy of 10 eV, well above the threshold range. For most of the parent cluster ions, the dominant
3:,c
men'-,
E!E!c,’*
[“ICn:,
Figure 2. Bar graph, left-hand scale: total cross sections and branching pattern for the dissociation of C2-19’ at 10 eV collision energy. Each segment represents the cross section for a particular product channel. Scatter plot, right-hand scale: stability (lowest EO)as a function of size.
fragmentation channel is production of Cn-3+, most likely in conjunction with C3 elimination. For C4+, the lower energy C+ C3 channel dominates, but at high energies about a quarter of the branching is to the higher energy20 C3+ C product channel. For C5+, the only significant channel is C3+ C2, which is somewhat surprising in that the C2+ C3 channel is nearly isoenergetic. For C7+, C9+, and Clo+, loss of C2 is also a minor channel. For Cis+, C I ~ +and , C I ~ +production , of Cn-5+ is a major fragmentation pathway, and the energy dependence suggests that this corresponds to C5 loss, rather than multiple fragmentation. The magnitudes of the total CID cross sections vary dramaticaly with size, with a factor of -20 difference between C1 I + and C17+. The complete set of cross sections as a function of energy for each size cluster can be found as Figure 3-4 in the thesis of Sowa-Resat.28 To extract quantitative energetics from the data, we must account for broadening in the energy dependence of the experimental cross sections from the distributions of primary beam and target gas translational e n e r g ~ ~ and ~ , ~of O cluster ion internal energy. For this we use the usual convolution and fit a p p r ~ a c h . ~A ” ~model ~ is assumed for the collision energy dependence of the “true” cross section, and then this is convoluted with the experimental broadening functions. The “true” cross section is adjusted until the convoluted result is in agreement with experiment. For our “true” cross section function, we have adopted the commonly used “modified line of centers’’ (LOC) form:
+
+
+
+
Lavail
where A is a normalization factor, EO is the dissociation threshold, and n is a parameter which varies the curvature of the function. For n = 1 this reduces to the canonical line of centers however, in practice n is just a fitting parameter and usually is greater than 1. Eavail is the total energy available to the reaction, including the collision energy, rotational energy, and vibrational energy of the cluster ions. The vibrational energy has been calculated assuming that the clusters are equilibrated at 350 K, using vibrational frequencies from ab initio calculations where they are available (see below).
10738 J. Phys. Chem., Vol. 99, No. 27, 1995
Sowa-Resat et al.
TABLE 1: Appearance Energies, Best Fit Dissociation Thresholds (EO),and Fit Parameters ( n ) for Dissociation of Cn-, with Several Sets of Literature Results Given for Comparison (See Text) dissociation appearance fit threshold fit thermochemical Eo from channel energy energy (Eo) parameter n Eo metastable decay
c*+- c+ c3+ C'
-c4+--- c,+ -- c,+ cS+ c9- -c14T-c11+ --- cIl+ c13cist C14' Clst CM+
5.4 6.4 1.4 4.4 5.4 5.6 4.6 6.0 8.0 5.0 5.6 6.2 6.2 7.6 6.8 5.2 5.8 5.8 6.2 5.8 6.6 5.6 5.8 6.0
c16'
5.8
C*+ C' Czf
CS'
c3-
C6+
C?+
c4+
C8-
Cio+ Cll+ Cl*f
4
cl3'
C6+ Clf a C7-
Ce+ C9'
ClO'
C I S + Cio+
c12+
Cisf-
c17+
C18-
5.4 6.7 7.5 4.1 5.7 6.0 5.2 6.3 8.2 5.3 5.7 6.2 5.9 7.3 6.5 4.9 5.5 5.6 5.6 5.0 5.1 4.7 4.8 5.1 4.9
2.85 1.85 1.78 1.58 1.77 2.45 1.97 2.50 2.50 2.24 2.50 1.01 2.10 1.40 1.70 2.15 1.10 1.07 1.13 2.10 3.03 1.73 2.35 1.53 1.27
5.47" 6.45" 7.55" 4.70" 5.53" 7.25" 6.256 9.376 8.766
7.7' 5.5' 5.2'
5.2' 5.3c 5.6' 7.2' 7.5d 7.2d 6.0d
8.2d
"Reference 20. Estimated from data in refs 18, 19, and 21. Reference 25. dReference 26. For the larger reactant clusters, there is an additional complication. As the number of intemal degrees of freedom of the cluster increases, an increasing amount of energy is required in excess of the dissociation limit, to drive fragmentation on the experimental time scale (100-200 ps). This results in a so-called "kinetic shift", a shift of the fragmentation appearance energy with respect to the hue dissociation threshold. To correct for the kinetic shift, we have taken the following approach. Rather than assuming a "true" cross section function, we assume a "true" energy transfer probability function:
where Elransf is the energy transferred from collision energy to internal energy and EcOl is the collision energy. The energy available to drive dissociation is then simply Eavall = Elransf Ewbration i- Ero,ation. To extract threshold energies (EO)we use a Monte Carlo program that accurately simulates the experiment. For each experimental collision energy, the simulation samples the velocity distributions of the ion beam and the thermal target gas to find Ecoland VCM(the velocity of the center-of-mass frame in the lab). The resulting P(Elran,,)distribution is then sampled to find Elransf.This is combined with ErOtatlOn and Evlbratlon obtained by sampling the respective distributions, to give Eavall. Eavall is fed into an RRKM model (see below) to calculate the dissociation rate, which finally is compared to the detection time (calculated from VCM)in order to decide whether that sample would result in observable dissociation or not. This process is repeated for 5-10 000 samples at each experimental energy, thereby building up a simulated o d ) s j ( E ) for comparison with experiment. The functional form for P(Elran,f) was chosen to allow diect comparison with threshold parameters extracted from the modified LOC cross section approach described above. The n parameter in the P(Elransf) function has an effect equivalent to
+
that of the n parameter in the modified LOC cross section. The threshold energy (EO)does not appear directly in the P(E,,,,f) approach, but comes into play indirectly as the threshold energy used in calculating RRKM dissociation rates, k(Eava,1).Nonetheless, the threshold energies and n parameters extracted by the two approaches are directly comparable. Under conditions where the RRKM rates increase very rapidly for Eaval1 > EO (Le. for small clusters), simulations using the same parameters are superimposable in the threshold region. Further details are given by Sowa-Resat.28 RRKM correction for kinetic shifts has also been implemented by Ervin et al.34using a somewhat different approach involving direct numerical convolution of a LOC cross section function with a decay probability function. An advantage of our approach is that the energy transfer function is more closely related to the physics of the problem than the resulting cross section function. This makes it possible to include insight gained from model trajectory studies (e.g. those of Hase and c o - ~ o r k e r s ~which ~) systematically explore the effects of projectile/target mass ratios, potential stiffness, and cluster shape on the energy transfer. For the P(Etransf) function used here, the two approaches are essentially identical. The best fit thresholds (EO)and n parameters for each cluster dissociation channel are given in Table 1. We also give experimental appearance energies for each channel, so that the magnitude of the kinetic shifts can be seen by comparison with the EO results. From the sensitivity of the fits to the EO parameter, we estimate absolute uncertainties in the dissociation energies of f 0 . 2 eV for the small clusters and up to fO.5 eV for the largest C,+. The relative uncertainty for comparing energetics for diffemt cluster sizes is -0.1 eV. The increased absolute uncertainty for large clusters is largely a function of the unimolecular rate modeling discussed below. We want to stress that the trenddfeatures observed in the EOresults are also evident in the raw appearance energies and do not result from the fitting procedure. To illustrate the dependence of the dissociation thresholds on cluster size, we have plotted the lowest EO value for each cluster as an overlay in Figure 2.
J. Phys. Chem., Vol. 99, No. 27, 1995 10739
Dissociation Energies for C2-19+ Measured by CID Dissociation energies for clusters containing two to eight atoms show a pronounced evedodd alternation, but the average stability appears to be roughly constant at 5.5 eV. These are the cluster sizes where chemistry r e s ~ l t sshow ~ ~ , that ~ ~ our ion beam is predominantly composed of the linear isomer. For C,+ (n 2 10) where the reactivity shows the beam to be entirely composed of cyclic isomers, the stability has a quite different dependence on size. The stability peaks at 7.3 eV for CII + and then decreases markedly to under 5 eV for our largest clusters. Superimposed on this overall decline is an apparent periodicity of four, with the most stable clusters being CII+,CIS+, and (219'. To verify that C19+ is indeed a local maximum in stability, cross sections were also measured for CZO+,though not fit due to low signal levels. The observed CS-lossappearance energy of -3.5 eV is well below the lowest appearance energy for C19'. Fluctuations in abundance vs cluster size spectra are often interpreted as indicating that the more abundant sizes have enhanced stability. Although the abundance distribution is strongly dependent upon experimental conditions, we consistently observe more intense peaks for C3+, CII+, CIS+, and Clg', while c2+, c4+, c5+, and c6+ are less intense. s~milar distributions are observed for clusters formed by laser vaporization followed b a sp ersonic expansion.38 This appears to support a stability/mtensity correlation. Another unsurprising correlation is that the more stable clusters generally have smaller CID cross sections.
7.
IV. Unimolecular Rate Modeling
RRKM theory39was used to calculate dissociation rates as a function of Eavail,for use in the fitting process. Since the potential energy surfaces for carbon cluster dissociation are not known, it is necessary to make several assumptions regarding the transition state properties. We have assumed loose transition states$O i.e. no barriers in the dissociation exit channel. For the small, linear clusters this seems clearly justified. Dissociation is a simple bond scission, and there is no reason to expect a significant activation barrier for the reverse Cn-3+ C3 association. For the cyclic clusters, the dissociation is obviously more complicated, but for want of information, we continued with a loose transition state model. As discussed below, the experimental data seem to require a loose model, except perhaps for the smallest rings. The vibrational frequencies for both the parent cluster ions and dissociation products are available from ab initio calculations. For C2-5+, the vibrational frequencies of the parent ion were obtained from RHF/6-3Ig* (ROW) calculations using G A U S S V L N ~and ~~~ Frequencies for c6-1I + are from von Heldon et al.' For the larger sizes where the frequencies were not available, they were estimated by extrapolation from the frequencies for Cllf by adding an averaged value for one stretch and two bends for each additional atom. To test the sensitivity of the extracted EO values to assumptions regarding the transition state, we did a series of test calculations for Ce+, cl4+, and C19+, assuming various transition states lying between two limits of looseness. One extreme case was the orbiting or free rotor transition state, where the fragments are assumed to be essentially separated and the associated bending frequencies are converted to free rotations. This limit gives the fastest dissociation rates, the least kinetic shift, and therefore a upper limit on EO. The tightest model tested consisted of simply taking the vibrational frequencies for the parent cluster, dropping the CC stretch corresponding to the dissociation coordinate, and leaving all the rest unchanged. For small clusters such as Cs', the number of degrees of freedom is small, as are the resulting kinetic shifts. The
+
uncertainty from the RRKM modeling is therefore only -0.1 eV, well within the uncertainties from fitting. For C14+ the difference in EOvalues obtained from the extreme fits was 0.7 eV, and for C19+ the variation was 0.8 eV. The f0.5 eV uncertainty quoted above is largely due to this uncertainty in RRKM modeling. The EO values given in Table 1 are for a rather loose transition state, with most frequencies set equal to those in the fragments and 100 cm-l torsions for the bends associated with the dissociation coordinate. The resulting EO values should therefore be near upper limits, at least in so far as the effect of transition state looseness is concemed.
V. Discussion CID measurements give dissociation threshold energies, i.e. upper limits on the dissociation energy. In the absence of activation barriers for the reverse association reaction, the limits are expected to be close to the dissociation energy. For small carbon clusters it is possible to calculate dissociation energetics using standard thermochemical cycles and results from the literature. The heats of formation are available for cl-4+2o and for neutral C, containing up to seven atom^.'^-'^ Ionization potentials have been bracketed for c6-24+ by Bach et allowing additional Cnf dissociation energies to be calculated. For CS+,the IF' is taken from ab initio calculations of Rohlfing and c o - w ~ r k e r s . ~ ~ Table 1 compares our CID results with dissociation energies derived from the literature. For c2-4+ the agreement is excellent. For C5-7+ our dissociation energies are significantly lower than the literature values, and there also some qualitative discrepancies. For example, the literature-derivedvalues would predict that the lowest energy dissociation channel for C7+ is C3+ C4, while CID, metastable decay, and photodissociation experiments all favor C4+ C3. The discrepancies most likely reflect differencesin linear/cyclic isomer stability for the neutrals and ions. Our CID results are direct measurements on the ions, while the literature estimates are derived from AHf values for neutrals and Ips derived from charge exchange reactions of the ions. If the relative stability of the isomers change upon ionization, the estimates derived from the literature are likely to be in error. In Figure 3, we compare our results for the lowest energy dissociation channels for C2-9+ with the corresponding theoretical results of Raghavachari and Binkley?g5 In general, the agreement is excellent: all trends are reproduced and the absolute values are generally within a few tenths of an electron volt. We have also calculated the dissociation energies for neutral carbon clusters using AHf values from the literature.l7-I9 The neutral and cationic dissociation energies are surprisingly similar. showing the same striking evedodd alternation. For the neutral clusters, Pitzer and Clementi suggested a simplified n-bonding argument to explain the enhanced stability of the odd sizes. Since the clusters can accommodate four electrons in each n band orbital, for odd size C, the highest energy n orbital is filled, while for even size clusters it is half filled. This same argument applied to the cations, where the n orbital is always partially filled, would predict weaker evedodd altemations, in contrast with the data. It is not obvious why the strong alternation persists in the cation, but this would seem to suggest either that the n band filling argument is oversimplied or that the electron removed in the cation comes out of one of the terminal nonbonding orbitals, rather than from the n orbitals. The agreement between our CID results and metastable decay experimentsis not particularly good, even at the qualitative level. For example, both Radi et al.25 and Lifshitz et al.26find that Cl I + fragments primarily by loss of a single C atom, while we
+
+
10740 J. Phys. Chem., Vol. 99, No. 27, 1995 0 CID A Raghavachari a n d Binkley v NeutralC,
Sequential Mechanism
n - I
+
Sowa-Resat et al.
;
T
Concerted Mechanism
Figure 4. Schematic reaction coordinatesfor sequential and concerted mechanisms for dissociation of cyclic C,.' 2
4
6
8
N u m b e r of Atoms i n C l u s t e r
Figure 3. Comparison of CID thresholds from this work ( 0 ) with theoretical values from Raghavachari and Binkley (A) and experimental results for neutral clusters (see text). see C3 loss, as do photodissociation experiments.22 Binding energies were extracted from the metastable decay results using statistical phase space modeling. The dissociation energies extracted by Radi et al. and Lifshitz et al. are generally within an electron volt of ours; however, they did not observe the strong fluctuations in Eo with size. There are several differences between the experiments that are the likely source of disagreement. Our experiment probes dissociation at total energies near the dissociation threshold and is sensitive to dissociation during a 100-200 p s time scale. The metastable decay experiments are sensitive to a shorter time scale (< 10 p s ) and therefore can only observe dissociation from parent ions with enough excess energy to decompose quickly. For these higher excess energies, it is not unlikely that dissociation can occur into higher energy product channels, resulting in significantly different branching. It is also possible that statistical modeling of product recoil energy distributions does not accurately recover the true (and perhaps nonstatistical) intemal energy distribution of the dissociating ions and therefore gives inaccurate EOvalues. In contrast, the agreement of our Eo values with the energetics extracted from multicollision drift tube experiments by Shelimov et a1.I6 is quite good (as well as can be determined from the figure in their paper). We observe somewhat larger fluctuations in stability with cluster size, but the trends and the magnitudes of the dissociation energies are in excellent agreement. This appears to be a good validation of the assumptions used in analyzing the drift tube results. An important issue to address is the effects of geometric isomers on our measurements and their interpretation. We are fortunate that for C,+ we know how the isomer distribution from our source varies with cluster size. Isomer identification is based on the observation that the linear C,' are highly reactive, while the cyclic Cn+ are unreactive at low collision energies.8-" On the basis of our results for reaction of C,+ with deuterium,36 oxygen,43and nitrous oxide37we estimate the isomer composition as follows. For n = 2-6, the beam appears to be almost entirely composed of the reactive (linear) isomer, and for n 1 10 the clusters are entirely unreactive at low energies (cyclic). For C7'-C9+, there clearly are both linear and cyclic isomers present in the beam. The CID cross sections show some signs of multiple isomers as well. For most cluster sizes, the experimental cross sections rise out of the baseline noise reasonably quickly as collision energy is raised above the appearance energy (Figure 1). For
CS+, and to a lesser extent for C7+, the main rise in the cross section is preceded by a low-energy tail, extending for -0.5 eV. We believe that this low-energy tail is due to isomer contamination. For C9+ the cyclic isomer is more stable; therefore, we attribute the tail to the linear isomer and the main rise to the cyclic isomer. In fitting this energy dependence we are faced with a choice. The entire threshold region, including the tail, can be fit using anomalously large n parameter (2.78), giving EO = 5.6 eV. Alternatively, we can constrain the n parameter to the range found for the other clusters, thereby focusing the fitting on the main rise in the cross section. For purposes of comparison with other cluster sizes, the EOresults given in Table 1 are for fits constrained to n < 2.5. Constraining the fit actually makes relatively little difference. For Cg+ (the worst case) the n-constrained fit gives an EOonly 0.1 eV higher than the free fit, well within our uncertainty. In summary, we believe the EO values in Table 1 can be interpreted as follows. For C*+-C6+ they are the dissociation thresholds for the linear isomer. For C,+ (n 1 10) the thresholds are for the cyclic isomer. For the intermediate size range, the EOcorresponds to the main component of the beam, although it appears that the dissociation thresholds for both isomers are quite similar. The other isomer effect to consider is on the dissociation mechanism. Dissociation for the linear isomer presumably simply involves a single bond cleavage, and this suggests that there should be no significant activation barrier for the reverse association. In this case, our EOresults should be quite close to the thermodynamic dissociation energies, and the good agreement with both literature values and theory suggests that this is the case. The mechanism for the cyclic species is more problematic (Figure 4). First consider a large cluster such as cl6+,which fragments to both Cll+ and C13+. The parent cluster is large enough to be relatively unstrained, and both product clusters are in the size range where the cyclic isomer is substantially more stable. If the dissociation mechanism is a sequential process where the ring opens, loses C3 or Cs, and then subsequently recyclizes, we would expect a substantial activation barrier corresponding to the point along the dissociation coordinate where two CC bonds have been broken. The height of the barrier should be approximately 10 eV above the parent cluster energy, assuming CC bond strengths similar to those in the small clusters. Clearly this is inconsistent with our observation that the EO values for large C,+ are smaller than those for the linear clusters. (N.B.: in our RRKM modeling, we used a transition state near the loose extreme; use of a tighter model would result in even lower extracted EO values.) The measured EOvalues for the large Cn+,therefore, rather strongly support a concerted CID mechanism, where the C3 or Cs unit is pinched off the main ring. In Figure 4 this is drawn with a
J. Phys. Chem., Vol. 99, No. 27, 1995 10741
Dissociation Energies for C2-19~Measured by CID small barrier with respect to the product channel, but in fact there may well be no barrier at all. A likely mechanism for this process might be ring opening, followed by closure into a smaller ring with a C3 or C5 side chain that is lost as the ring closes. The only case where it seems that there might be a significant barrier is the small cyclic clusters, such as C,,+. Here the product cluster, Cgf, is small enough that it is strained. This may create a substantial barrier for the concerted mechanism and could partly account for the anomalously high dissociation threshold measured for Cll+ and Cl2+. It should be noted, however, that the same argument applies to CIO+,which does not show an elevated threshold. The 4-fold periodicity in the stability of the monocyclic isomer is reminiscent of conjugated ring systems. For ionic species, the Huckel aromaticity rule would predict added stabilization for clusters containing 4n 3 carbon atoms, while 1 atoms should be formally antiaroclusters containing 4n matic. On the basis of these predictions, the most stable clusters should be C ~ I +CIS+, , and C19+, and the lowest dissociation energies would be expected for CIS+and cl7+.This pattem is indeed observed, and the anomalously high stability of C II + is at least partly attributed to this electronic stabilization. A similar 4-fold periodicity has been observed in ion cyclotron resonance experiments measuring the rates for the reaction of c7-24' with benzene.44 The formally antiaromatic clusters were found to exhibit the greatest reactivity forming primarily a benzene adduct.
+
+
Acknowledgment. We would like to thank H. Resat for helpful discussions concerning development of the energy transfer function, and G. von Heldon for providing vibrational frequencies. S.L.A. acknowledges support from a Camille and Henry Dreyfus Foundation Teacher-Scholar award. This work was supported by the Mechanics and Energy Conversion Division of the US. Office of Naval Research (Grant N0001492J1202). References and Notes Pitzer, K. S.; Clementi, E. J . Am. Chem. Soc. 1959, 81, 4477. Hoffman R. Tetrahedron 1966, 22, 521. Ray, A. K. J . Phys. B 1987, 20, 5233. Raghavachari, K.; Binkley, J. S. J. Chem. Phys. 1987, 87, 2191. (5) Raghavachari, K.; Binkley, J. S. In The Physics and Chemistry of Small Clusters; Jena, P., Ed.; Plenum: New York, 1987; p 317. (6) von Helden, G.; Palke, W. E.; Bowers, M. T. Chem. Phys. Lett. 1993, 212, 247. (7) von Helden, G.; Gotts, N. G.; Palke, W. E.; Bowers, M. T. Int. J . Mass Spectrom. lon Processes 1994, 138, 33. (8) McElvnany, S. W. J. Chem. Phys. 1988, 89, 2063. (9) Parent, D. C.; McElvany, S. W. J. Am. Chem. SOC.1988,111,2393. (10) McElvany, S. W.; Nelson, H. H.; Baronavski, A. P.; Watson, C. H.; Eyler, J. R. Chem. Phys. Lett. 1987, 134, 214. (1) (2) (3) (4)
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