J. Phys. Chem. 1991, 95,6473-6481 example, the splitting for the (l,O,l) level is 17. Note that the splitting for the (0,3,0)level, in the three.-mode calculation, is 2 while that for the (0,3)level, in the two-mode calculation at r = re, is 0.6 (from ref 15). In part, the larger splitting for the three-mode calculation may be attributed to the greater zero-point energy for the three-mode Hamiltonian and the correspondingly lower adiabatic potential barrier for hydrogen atom exchange. We now consider results for H'60'80, which we compare to those for H " W 6 0 . As expected, the 0-0 stretch fundamental is smaller by a factor approximately equal to the square root of the relative reduced masses of the oxygen atoms, and the 0-H stretch and bend fundamentals are both slightly smaller. The splitting for the 0-0stretch fundamental is not measurable, but it is measurable for all other vibrational levels and, in particular, for both the 0-H stretch and bend fundamentals (10 and 1, respectively). Summary and Discussion
In this paper we have calculated vibrational levels for H 0 2 using the DMBE 111 surface of Varandas, Brandao, and Q~intales.~ We have considered vibrational levels up to and slightly above the potential barrier for hydrogen atom exchange. The calculated fundamentals for all three vibrational modes are significantly smaller than the experimentally determined fundamentals, and the calculated successive spacings for progressions in all three vibrations show that the potential surface is strongly anharmonic. It would Seem that, in incorporating the experimentally determined force field data into the DMBE I11 surface, this strong anharmonicity has not been taken into account. For the two-mode calculations, except for the (2,O) level, the splittings of all vibrational levels increase as the 0-0distance increases. However, as the oxygen atoms separate, hydrogen atom exchange must ultimately become more difficult, and these results must therefore be specific to the range of r values that have been considered in this paper. These results must also be specific to the potential surface and are evidently a consequence of the fact that the saddle point region is located at a small R value that is
6473
not easily accessed by the zeroth-order 0 - H bend motion. Our results indicate that the zeroth-order 0-H bend motion more effectively acceSSeS the saddle point region for slightly larger 0-0 distances. Apparently, the zeroth-order 0 - H stretch motion (in combination with the zeroth-order 0-H bend motion) is even more effective in accessing this region for slightly larger r values since the rate of increase of the splitting is greater for the (1,l) level than for either the (0,3)or (0,4) levels. Complicating a definitive statement in this regard is the existence of a secondary potential minimum at the linear O-H-O geometry for significantly larger 0-0distances. It is clear from eq 1 that there is a singularity in the triatomic ( J = 0) Hamiltonian for R = 0. For the three-mode calculations, the calculated splittings are not measurable for any of the fundamentals for H'60'60, but for H'60'80 they are measurable for the 0 - H stretch and bend fundamentals (10 and 1 cm-', respectively). The larger splittings for H'60180at low energies may be qualitatively understood as resulting from the dynamical nonequivalence of the 160-H and I80-H stretch and bend vibrations. As expected, energy in the 0-H bend vibration is of primary importance in promoting hydrogen atom exchange. However, energy in the 0 - H or 0-0 stretch vibration is also important in combination with the 0-H bend vibration (and in combination with one another). On the basis of the two-mode calculations, we infer that the 0-0stretch vibration is important in promoting hydrogen atom exchange primarily because it creates nuclear geometries in which the saddle point region is more effectively accessed by the zeroth-order ( F H bend motion.
Acknowledgment. We thank NSERC (Canada) for partial funding of this work and McGill University and the University of Ottawa for grants of computer time. We thank Herong Yang (McGill University Computer Centre) for program modifications that made these calculations possible for the total number of basis functions used. Regis@ NO. HOZ, 3170-83-0;H,12385-13-6.
Cluster Beam Analysis via Photoionization J. R. Grover,* Department of Chemistry, Brookhaven National Laboratory, Upton, New York 11973
W . J. Herron, M. T. Coolbaugh, W. R. Peifer, and J. F. Garvey Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14214 (Received: February 12, 1991; In Final Form: April 9, 1991)
A photoionization method for quantitatively analyzing the neutral products of free jet expansions is described. The basic principle is to measure the yield of an ion characteristic of each component cluster at a photon energy just below that at which production of the same ion from larger clusters can be detected. Since there is then no problem with fragmentation, the beam density of each neutral cluster can be measured in the presence of larger clusters. Although these measurements must be done in the test ions' onset regions where their yields are often quite small, the technique is made highly practicable by the large intensities of widely tunable vacuum-ultraviolet synchrotron light now available at electron storage rings. As an example, the method is applied to the analysis of cluster beams collimated from the free jet expansion of a 200:l ammonia-chlorobenzenemixture.
Introduction Syntheses of neutral clusters in jet expansions are now widely the method is very convenient and used in research, hause applicable to a tremendous range of compositions. A serious drawback, however, is that such expansions always produce mixtures of clusters, so that for many experiments a knowledge of the relative amounts of the different cluster species becomes necessary. Analysis is usually attempted via mass spectrometry
following electron impact ionization, although results obtained by this method are subject to distortions, often ruinous, due to extensive dissociative ionization of the clusters (fragmentation).'-' (1) Henka. W. 2.Narurforsch. A 1962, 17, 786-789. Acra (2)19,8, Herrmann, 61, 453-487. A,; Leutwylcr, S.; Schumacher, E.;Woste,
L. Hefu. Chim.
(3) Lee, N.; Fenn, J. B. Rev. Sci. Insfrum. 1918,19, 1269-1272. Fenn, J. B.; Lea, N. Reu. Sci. Instrum. 1982.53. 1494-1495.
0022-36S4/91/209S-6473302.50/00 1991 American Chemical Society
Grover et al.
6474 The Journal of Physical Chemistry, Vol. 95, No. 17, 1991
4 ONSET (N +1) HIGHEST ONSET (N)
PROBE ION SIGNAL
i
m
-------
*
PHOTON ENERGY
Figure 1. Diagram of photon energy scan used to measure the relative beam density of a given cluster. The onset of probe ions from the cluster to be analyzed is indicated as onset (N) and as onset (N 1) from the next larger cluster.
+
Several other techniques for the analysis of beams of neutral clusters have been reported: laser spectro~copy,~-'~ angle- plus velocity-resolved crossed-beam s~attering,'~ photoelectron spectroscopy,16electron beam diffraction,17laser Rayleigh scattering.17 Of these, the elegant crossed-beam scattering method has been the most productive and has already been used to provide a wealth of information, namely, probabilities of cluster fragmentation by electron impact, pressure and nozzle diameter scaling functions for cluster production, and photodissociation studies. The laser methods, often very effective indeed for specially selected systems, cannot, as yet, be generally applied. The method employing photoelectron spectroscopy is limited to mixtures of very few components, and it is difficult to see how this can be improved. Methods that exploit electron beam diffraction or laser Rayleigh scattering are presently limited to large clusters and are only sensitive to size, not composition. The molecular scattering method is the most general, but it is restricted to masses smaller than a few hundred daltons and requires rather large mass differences between the clusters. Many chemically interesting clusters, such as (C,H5CI),(NH3),, cannot, therefore, be well analyzed by this method at the present time. In addition, a machine similar to that in Buck's laboratory demands a significant dedication of resources, the acquisition of which may be difficult. For all these reasons, we found it advisable to develop an additional, complementary analytical technique, which is presented in this paper. It seemed possible that the tunable vacuum-ultraviolet photon beams available at electron storage rings offered a good opportunity to develop an analysis method of general applicability, and which would not be restricted to only one or a very few sites.I8 (4)Stace, A. J.; Shukla, A. K. Inr. J . Muss. Specrrom. Ion Phys. 1980, 36, 119-122. ( 5 ) Geraedts, J.; Setiadi, S.;Stolte, S.;Reuss, J. Chem. Phys. Leu. 1981, 78, 277-282. (6)Stephan, K.;Mark, T. D. Inr. J . Muss Specrrom. Ion Phys. 1983,47, 195-198; Chem. Phys. Letr. 1982,90, 51-54. (7) Gough, T.E.; Miller, R. E. Chem. Phys. Lert. 1982, 87, 280-283. (8)Amirav, A.; Even, U.; Jortner, J. J . Chem. Phys. 1981,75,2489-2512. (9)Geraedts, J.; Stolte, S.; Reuss, J. Z . Phys. A 1982. 304, 167-304. (IO) Smalley, R. E.; Wharton, L.; Levy, D. H. J . Chem. Phys. 1977,66, 2750-275 I. ( 1 1 ) Hopkins, J . 9.; Powers, D. E.; Smalley, R. E. J . Phys. Chem. 1981, 85, 3739-3742. (12) Even, U.; Amirav, A.; Leutwyler, S.; Ondrechen, M. J.; BerkovitchYellin, Z.; Jortner, J. Furuduy Discuss. Chem. Soc. 1982, 73, 153-172. (13)Leutwyler, S.; Even, U.; Jortner, J. Chem. Phys. Leu. 1982, 86, 439-444. (14)Rademann, K.;Brutschy, 9.; Baumgirtel, H. Chem. Phys. 1983,80, 129-145. (15) Buck, U.; Meyer, H. Phys. Reo. Lcrr. 1984,52, 109-112. Buck, U.; Meyer, H. Ber. Bunsen-Ges. Phys. Chem. 1984.88, 254-256. Buck, U.J . Phys. Chem. 1988,92, 1023-1031 and references therein. (16) Tomoda, S.;Achiba, Y.; Nomoto, K.; Sato, K.; Kimura, K. Chem. Phys. 1983, 74, 1 13-1 20. Tomoda, S.;Kimura, K. Bull. Chem. SOC.Jpn. 1983,515, 1768-1771. (17) For a review of these techniques see: Kappes, M.; Leutwyler, S. In Atomic und Moleculur Beam Methods; Scoles. G., Ed.; Oxford University Press: London, 1988;Vol. I , pp 398-399.
For illustration, the application of the technique to be described to the expansion of chlorobenzene seeded in ammonia is used. Although this method has already been exploited to analyze the expansion products of several different gas mixtures,Iga the chlorobenzene/ammonia system has been analyzed the most comprehensively. Also, chlorobenzene-ammonia clusters should be good candidates for methods that employ laser spectroscopy, and this invites future independent verification.
Explanation of the Method The method requires a probe ion that originates in the cluster one wants to measure. Thus, preliminary experiments are carried out for each kind of cluster in the mixture to select the photoionization product most suitable to represent it. The onset energyZofor that product, N, is carefully measured and checked against the literature whenever possible. Then, using the known onset energy, we can set up a coarse scan using three photon energies, depicted by the open circles in Figure 1. Only three energies are used to minimize the amount of time needed for the measurement. The lowest energy is set just below the onset and serves to measure the background. The middle energy is well above the known onset but just below the lowest onset of the same ion from larger clusters, N 1 or larger. This latter onset is above the onset of N by the binding energy of a neutral moiety to the investigated cluster. The highest energy is then set high enough above the middle energy to provide a warning if production of the probe ion from larger clusters is likely to be important. If there is danger of a significant contribution from larger clusters, it will be evident as a sharp increase with nozzle pressure of the ratio of yields at the highest and middle energies, so that if necessary the measurement scan can be repeated using lower energies. The relative yield of the probe ion at the middle energy is then proportional to the relative density of the corresponding neutral cluster, completely free of contributions from fragmentation. Once the pressure dependencies of the beam densities of the various components are known, their quantitative relationship with respect to each other can be calculated from the abovemeasured data plus the pressure dependencies of the monomers and of the total mass transported by the beam.
+
Experimental Section Apparatus. The experiments were carried out with the photoionization mass spectrometer described in refs 19b-d and made use of a tunable vacuum-ultraviolet beam provided by the National Synchrotron Light Source a t Brookhaven National Laboratory. A sonic nozzlez1was used to emphasize small clusters; its orifice diameter was 0.0102 cm. To eliminate second-order radiation, a lithium fluoride filter 0.20 cm thick was used. Selection of Probe Iom. Simple qualitative experiments were first carried out using high photon energies, 21 and 18 eV (584 and 700 A), to find, by trial and error, the conditions in which the desired clusters for a planned series of measurements are best produced, in this case C6HSCI.NH3and C6HSC1(NH3)2.When the gas mixture was too rich in chlorobenzene, the ions produced from the heteroclusters could not be seen because they were overwhelmed by ions produced from chlorobenzene and its homoclusters. This point was checked by examination of the products (18) Most electron storage rings are set up to accommodate general users. For a list of such facilities see: Winick, H. Synchrotron Rudiut. News March/April 1989,2 (2), 25. (19)(a) Grover, J. R.; Waken, E. A.; Arneberg. D. L.; Santandrca, C. Chem. Phys. Leu. 1988,146,305-309. (b) White, M. G.; Grover, J. R. J . Chem. Phys. 1983,79,4124-4131.(c) Grover, J. R.; Walters, E. A.; Newman, J. K.; White, M. G.J . Am. Chem. Soc. 1985, 107, 7329-7339. (d) Grover, J. R.; Walters, E. A. J . Phys. Chem. 1986,90, 6201-6210. (e) Walters, E. A,; Grover, J. R.; White, M. G.; Hui, E. T. J. Phys. Chem. 1985, 89,3814-3818. ( f ) Grover, J. R.; Walters, E. A.; Newman, J. K.; White, M. G. J . Am. Chem. SOC.1990,112,6499-6506. (g) Grover, J. R.; Walters, E. A.; Clay, J. T.; Willcox, M. V. Submitted for publication. (h) Grover, J. R.; Hagenow, G.; Walters, E. A. Manuscript in preparation. (20) In the experiment described here, the "onset energy" is that photon energy at which the ion in question first becomes detectable. This energy is therefore not necessarily the ion's adiabatic threshold. (21)Hagena, 0.F.; Obert, W. J . Chem. Phys. 1972, 56, 1793-1802.
I.
-
. . . . -.
. ,
.
..
cluster Beam ~narysisvia rnotoionization
The Journal of Physical Chemistry, Vol. 95, No. 17, 1991 6475
of chlorobenzeneargon expansions, in which (C6H5C1)2+and the fragmentation products of (C6H5C1)2are formed strongly. The proportion of chlorobenzene in the ammonia was therefore systematically reduced until the heterodimer-derived ions could be clearly observed and then further reduced until they were essentially free of interference from the homoclusters. The resulting mixture was 200:l ammonia-hlorobenzene, produced by bubbling ammonia at 2400 Torr through chlorobenzene temperature-controlled at 25.0 OC. After establishing the expansion conditions, a wide mass scan at high energy (2 1 eV) and high nozzle pressure ( 1700 Torr) was used to identify and inventory all of the ions arising from the jet expansion products. Possible candidates for probe ions for each cluster of interest were identified from this information. The pressure dependence of these candidate ions was then measured at a photon energy of 21 eV, and some of the results are shown in Figure 2a,b. (Ions from the homodimer (C6HSC1)2 were now sufficiently reduced as to be essentially undetectable.) These data were used to refine the selection of probe ions for the analysis. Close to their low-pressure ends the curves fall into families that correlate with the smallest clusters from which the ions can be produced. In some cases this is difficult to see in Figure 11 I I I I I I I I 1 1 2 because of the logarithmic scale. However, the family to which 0 300 600 '900 1200 a given ion belongs is readily identified if plots are made of the NOZZLE PRESSURE (Torr) ratios of its yield to the yields of ions belonging to the various possible families. The correct family is that for which the ratio is independent of pressure close to the low-pressure end. 100 'BH; From Figure 2a one sees that NH2+ and NH3+ belong to one family, for monomeric ammonia, that NH4+and (NH3)2t belong to another family, for dimeric ammonia, which rises at higher pressures than do the monomers, and that (NH3)2H+belongs to still another, for (NH,),. To represent (NH3)2, NH4+ seems preferable to (NH3)2+ because it is much more intense. The curve for NH4+rises at lower pressures than do the curves for the ions t O P 1 that must be made from homotrimers and larger clusters of ammonia, and this is evidence that at 21 eV NH4+is indeed produced from the dissociative photoionization of ammonia d i m e r ~ , 2 ~as- ~ ~ well as from larger clusters (as substantiated by electron impact i o n i ~ a t i o n ~ ~ )Similar . considerations lead to the selection of 0.1 (NH3)2H+ to represent (NH,), and (NH3),H+ to represent (NH,),. To analyze for C6HSCI.NH3,Figure 2b shows three candidates: C6H&1+, CeHsNH3+, and (C~HSCI*NH~)+. The most intense is C6H5CI+. (The curve for C6H5Cl+represents only that C6HSCl+ produced from clusters26 and is therefore symbolized by [C6H5CI+],.) However, [C6H5CI+],is not suitable for a probe c because it cannot be measured accurately in the presence of large A yields of C6H5CI+from direct ionization of monomeric C6H5Cl, ' ' 0.001 especially at low nozzle pressures. Of the remaining two ions 0 300 600 900 1200 belonging to this family of curves, C6H5NH3+is significantly the NOZZLE PRESSURE (Torr) more intense. C6HSNH3+rises at lower pressures than do ions Figure 2. Inventory scans at 584 A (21 eV) of ion yield versus nozzle that must be made from larger heteroclusters, which verifies that pressure for molecular beams collimated from expansions of the 200:l it is indeed made from the h e t e r ~ d i m e r . ~ * s ~ ~ chlorobenzene-ammonia mixture: (a) ions including only ammonia or its fragments; (b) ions including chlorobenzene or its fragments. The curve for C6H5+ appears in both panels to help provide perspective. (22) Ceyer, S.T.; Tiedemann, P. W.; Mahan, E. H.; Lee, Y.T. J . Chem.
t
I
I
/
L
€
I
P h p . 1979, 70, 14-17. (23) Kamke, W.; Herrmann, R.; Wang, Z.; Hcrtel. I. V. Z . Phys. D 1988, 10,491-497. (24) Some workers have expressed doubt that ions are ever made from neutral dimers. It is difficult to understand how this belief originated, for it would mean that electron or photon impact with dimers leads only to neutral products. We detected ions from every homo- and heterodimer that we have studied. (25) Buck, U.; Lauenstein, Ch. J . Chem. Phys. 1990, 92, 4250-4255. (26) The presence of cluster-produced C6H5CIt in the inventory data is clearly revealed by the pressure dependence of the yield ratio [C6H5Clt]/ [C6Hf]. The formation of C6Hs+requires enough energy to break the strong carbon-chlorine bond, which is much more energy than that needed to break the weak van der Waals bond. The production of C6Hs+from C ~ H & ~ N H I and larger clusters is therefore suppressed"'" so that the increase of the ratio is due to the production of C6H5CItfrom clusters. After suitable normalization the production of C6H5+or C6H4+can be used to estimate the production of C6H5CI* from monomeric C6H5CI,and [C6HsCI+],can then be calculated by subtraction.Iw (27) Jonkman, H. T.; Even, U.; Kommandeur, J. J. Phys. Chem. 1985,89, 4240-4243.
'
1
1
I
1
1
Distinguishable symbols are used for many of the data points to help guide the eye for a given ion. The curve labeled [C6H5CI+], represents the yield of C6H5CI+ that arises from the dissociative ionization of clusters; i.e., the yield of C6HsCI+ from C6HsCI monomer has been subtracted.
It is important to be sure that the probe ion is not also a product of another cluster having the same number of molecules but a different composition. For example, C6H5Cl+could be made either from C6H5CbNH,or from (C6H5CI),. However, sometimes one of the possible reactions does not interfere; e.&, (C6H6)2 does not produce C6H6+ ions until photon energies greatly exceed the appearance p ~ t e n t i a l . ' ~ ~ * ~ (28) (a) Maeyama, T.; Mikami, N. J . Am. Chem. Soc. 1988, 110, 7238-7239. (b) Maeyama, T.; Mikami, N. J . Phys. Chem. 1990, 94, 6973-6977. (29) Brutschy, B. J . Phys. Chem. 1990, 94, 8637-8647.
6476 The Journal of Physical Chemistry, Vol. 95, No. 17, 1991
Grover et al.
TABLE I: Comparison of the M ~ u n Onset d Eaegs with tbe Results of Prior Work and of "acbemical
cluster
probe ion
this work
ref 22
9.509 9.096
9.59 9.15 9.03
Calcul.tioas onset enerw. eV ref 23 ref 28b thermochem" 9.54 9.14 9.02
9.36+ 8.88
8.926 8.664 a
8.87+
References 30 and 3 1. I
I
I
,
I
TABLE II: Probe lolls Used, Their Oapets, and Photon Ewrgies Cbosen for the Measurewats, Backgrounds,and Ratio Tests
photon energy. eV mle NH
cluster
a
(NH3)2 (NH3)3 (NH3)4
C6HsCIeNH3 C,jH&l(NH3)2
18 35 52 94 146
9.509 9.096 9.02' 8.926 8.664
9.671 9.225 9.150 9.057 8.775'
9.450 9.024 8.952 8.862 8.592
ratio test 9.903 9.436 9.357 9.260 8.965
'Reference 23. bThis measurement was carried out at 8.965 eV. The counting statistics are much better than at 8.775 eV, and the ratio test indicates negligible contributions from larger clusters (see Figure
:"
5d).
, 9.40
used onset measurement background
9.40 ENERGY (Ev)
9.56
9.06 ENERGY (Ev)
9.26
Figure 3. Photoionization yield curves in the onset regions, for production from neutral clusters of ammonia, of (a) NH4+,200 Torr nozzle pressure;
(b) (NH&H+, 700 Torr. In (a), the dashed line shows the shape of the hot bands to be expected for a thermal excitation of 300 K, and the solid line is a visual straight-line fit. The line's intercept corresponds to the onset (N) defined in Figure 1. In (b) arrows mark the photon energies used for measurement (Le., the middle energy of Figure 1) and background; the energy used for the ratio test (Le., the highest energy of Figure 1) is off scale to the right.
After the most promising of the candidate probe ions had been selected, their effective energy onsets were examined. Only ions with reasonably sharp onsets can be used. This is exemplified for NH4+ and (NH&H+ in Figure 3a,b. Since both ions display unambiguous onsets, both were retained as candidate probes for the beam analysis. Possible probe ions for other clusters were chosen in the same way.
Literature Verification of Probe Ion Selection. Comparisons of the measured onsets with literature values and with known thermochemistry are shown in Table I. The values for (NH3),,H+ agree very well with those in refs 22 and 23; they are systematically slightly lower because the high photon intensity available a t Brookhaven's U-1 1 line allows the onset to be delineated more sharply than could be done before. The value for C6HsNH3+is consistent with that reported in ref 28b. Thermochemical calc u l a t i o n ~for ~ ~ both * ~ ~NH4+ and C6HSNH3+are close to, and consistent with, the onsets. The calculated onsets must be increased by the dimer dissociation energies (symbolized in Table I by +), and this will bring them well within the combined uncertainties of data and calculations. It seems entirely possible that acceptable probe ions do not exist for some clusters. However, in our experience to date, which is admittedly limited, this problem has not yet been encountered. !Wection of Scan Energies. For each cluster, the three photon energies for the analysis scan were now selected. The lowest energy measures background and is set just below the measured onset. The value of the middle energy was chosen such as to produce probe ions only from the smallest possible cluster, but with as high a yield as possible. Measurement of the lowest onset of the probe ion from a larger cluster is normally quite difficult (e.g., see Figure 8 of ref 190, and it was therefore estimated as follows. One expects, as a rough rule of thumb, that the energy required to separate a monomer unit from a trimer will cause the probe ion's onset energy from the trimer to be larger than that from the dimer by about double the dissociation energy of the dimer (e.& ref 32). Most dissociation energies of dimers comprised of polyatomic molecules are in the neighborhood of 1.5-5 kcal mol-'. More complex separations, such as of a dimer from a tetramer, require even more energy. Analogous reasoning applies to probe ions for clusters larger than dimers. The middle energy was therefore set very conservatively in the region 0.13-0.17 eV (3-4 kcal mol-') above the onset energy. The highest energy was used to warn of possible important contributions to the probe ion intensity from larger clusters. It was set 0.17-0.22 eV (4-5 kcal mol-') above the middle energy. If the ratio of the probe ion yield at the highest energy to the yield at the middle energy rises sharply with increasing pressure, there may be significant contributions from (30) Rosenstock, H. M.;Draxl, K.;Steiner, B.W.; Herron, J. T. J . Phys. No. I ) , 1-783. (31) Lias, S.G.; Liebman, J. F.; Levin, R. D. J . Phys. Chem. Ref Dura
Chem. Ref Data 1977,6 (Suppl.
1984, 13, 695-808. (32) Van de Waal,
B. W. Chem. Phys. Lett. 1986, 123, 69-72.
The Journal of Physical Chemistry, Vol. 95, No. 17. 1991 6477
Cluster Beam Analysis via Photoionization
!
0.
q3
indicating that the behavior of the apparatus is reproducible in this respect. We believe the drop is due to scattering of the beam by background gas in the collimator chamber.
Effects Possibly Causing Falsification
5
1
300
600
1200
900
NOZZLE PRESSURE (Torr) I
I
I
I
I
I
I
I
I
I
I
I
I
/
NOZZLE PRESSURE (Torr)
Figure 4. (a) Nozzle pressure dependence of the total amount of matter passing through the skimmer per unit time: 0 and W, Ar; A, He; +, N,; 0, 90% o2+ 10% C6H6; 0 , CF,Br (all normalized at 600 Torr). (b) Nozzle pressure dependence of the total amount of matter present in the molecular beam in the ionization region.
fragmentation of larger clusters at the middle energy; vide infra. It is then necessary to repeat the measurement with lower values of the middle and highest energies. Table I1 presents the probe ion chosen (via its m / e value) for each neutral cluster, plus its measured onset, and the energies used for the background, measurement (middle energy), and ratio test (highest energy). The background and measurement energies for (NH3)*H+are illustrated in Figure 3b by arrows. Total Target Mass of Beam. Analysis for the relative amounts of the different clusters in the beams requires a knowledge of the pressure dependence of the total mass being presented to the ionizing radiation. This was estimated by measurement of the increase in pressure of the interaction chamber under stable conditions, as the n d e pressure is systematically increased. Nude ion gauges were used; essentially this technique is just a variant of the stagnation gauge method. The results are shown in Figure 4a,b. Figure 4a shows the increase in pressure of the collimator chamber (Le., the differentially pumped space between the skimmer and the collimator) as the nozzle pressure is increased. The normalized results of many different experiments, carried out at many different times and with many different gases, established that in our apparatus the rate of mass delivery through the skimmer is linear up to 1200 Torr of nozzle pressure. For argon the nominal pressure (i.e., instrument readout uncorrected for gas identity) is 5 X IC5Torr at 1000 Torr. Figure 4b shows the corresponding pressure in the interaction chamber (Le., after the collimator), which is essentially proportional to the rate of mass delivery via the molecular beam. Here the nominal pressure increase for argon reaches 1 X lV at a nozzle pressure of loo0 Torr. The pressure rises linearly to about 500 Torr but slowly deviates below the extrapolation of this line as the nozzle pressure rises, reaching 80% of the linear prediction at 1000 Torr. The results of two argon runs are shown, carried out 2 years apart,
A probe ion might be produced at the measurement energy from larger clusters than the one for which it was selected because of the effects of Franck-Condon factors, thermal excitation, the kinetic shift, or exothermic intracluster reaction. These possibilities are discussed in this section, and a test for such falsification is described. Adverse Franck-Condon Factors. Low Franck-Condon factors at threshold would cause the effective onset to be higher than the adiabatic appearance potential, possibly driving it so high that the middle energy would exceed the appearance potential for production of the probe ion from a larger cluster. However, the latter onset is also subject to Franck-Condon factors. In general, one expects the onsets' apparent energy shifts to grow larger as the cluster grows larger because configurational effects associated with the extra monomers are more likely to hinder than to accommodate the reaction. That is one reason why product ion onsets from clusters always become more gradual as clusters become larger.33 Thus, even if the middle energy is chosen larger than the appearance energy for the larger cluster because of an upshift at the onset, one expects little or no interference from this source. The larger cluster's onset is shifted higher by a still greater energy. Autoionization is pertinent to onset shifts. The onsets of dimer parent ions usually correspond to the adiabatic thresholds because of autoionization.lw*MThey are therefore often excellent probe ions for neutral dimers, e.g., (1 ,3-C4H6.So2)+ to representI9' 1,3-C4H6-S02.No such effect has yet been identified that compensates for the Franck-Condon upshifts for the onsets of parent ions from larger clusters, although structure due to Penning ionization has been reported for (C6H6-Ar,)+, n = 1-4, produced from cluster beams collimated from jet expansions of benzene seeded into argon.35 Low-lying isomers of a cluster and its ion might affect its onset. Each combination of neutral and ionic isomers will have its own characteristic Franck-Condon onset, the lowest of which will be the one observed. Whether that will decrease or increase the difference between the onsets of the probe ion from the cluster being measured and of the same ion from the next larger cluster will vary from problem to problem and cannot be predicted at the present time. However, we believe this effect will nearly always be negligibly small. Thermal Excitation of the Clusters. If the clusters contain excitation energy, the appearance potentials of the probe ions from larger clusters would be decreased. Contributions from the larger clusters might then appear at the middle energy and thus interfere with the measurement. However, the cluster whose density is being measured would also be excited since both clusters are being produced in the same jet expansion. In particular, clusters that differ by only a single monomer should have similar temperatures, with that of the larger cluster being slightly lower than that of the smaller.36 The smaller cluster's effective onset for producing the probe ion would be correspondingly lowered, as would, then, the middle energy chosen for the analysis. In effect, the whole pattern would simply be shifted to lower energies and the problem essentially eliminated. A second reason that thermal excitation should not be a serious problem is that the clusters are usually too cool. Evidence for thermally excited clusters would be hot bands of characteristic shape in the clusters' onset regions. To show the approximate size of the expected effect, such a band, (33) Ng, C. Y.Ada Chem. Phys. 1983, LII, 263-362. (34) Dehmer, P. M.;Pratt, S . T. J. Chem. Phys. 1982, 76, 843-853; J . Chem. Phys. 1982, 77, 4804-4817. Pratt, S. T.; Dehmer, P. M . J . Chem. Phys. 1983, 78, 6336-6338. (35) Kamke, B.; Kamke, W.; Wang, Z.; RUhl, E.;Brutschy, B. J . Chem. P h p . 1987,86, 2525-2529. (36) Bauer, S.H.; Chiu, N.-S.; Wilcox, C. F.,Jr. J . Chem. Phys. 1986, 85, 2029-2037.
6478 The Journal of Physical Chemistry, Vol. 95, No. 17, 1991 measured in a separate experimentlgh(on C6F6). was normalized to the data for NH4+ and coplotted as a dashed line in Figure 3a. The relative sharpness of the observed onset for NH4+shows that the effective temperature of (NH3)2 was much less" than 300 K (Le.,
