J . Phys. Chem. 1994, 98, 2002-2004
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Spontaneous Unimolecular Dissociation of Small Cluster Ions, (H30+)L0and Cl-(H20), (n = 2-4), under Fourier Transform Ion Cyclotron Resonance Conditions Detlef Tholmann, D. Scott Tonner, and Terrance B. McMahon' Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada Received: July 26, 1993; In Final Form: November 2, 1993"
Unimolecular dissociation reactions of weakly bound cluster ions of the type H30+L, and Cl-(H20), (n = 2-4) have been examined under low-pressure conditions in a FT-ICR mass spectrometer. The loss of a ligand molecule occurs spontaneously and is pressure independent. For the species examined the observed rate constants range from 2.4 X 10-3 to 0.83 s-l. It is concluded that the ions gain the energy required for the dissociation by absorption of blackbody radiation.
Introduction
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Traditionally, the most commonly encountered unimolecular reactions observed in mass spectrometric experiments have been those of so-called metastable ions.' Typical time scales for metastable dissociations are 10-4-10-s s, which is much shorter than the time scale of an ICR experiment, and for this reason metastable dissociations are not usually observed with this technique. For large oligosaccharide molecular ions, however, metastable ion lifetimes of 2 ms have been recently reported in FT-ICR experiments.2 In addition, very long metastable ion lifetimes in the millisecond range have also been observed by Fisher and McMahon3 for chemically activated proton-bound dimers of diethyl ether, dimethyl ether, acetonitrile, and acetone formed in low-pressure association reactions. The dissociation of metastable, chemically activated, adduct ions has also been studied very recently by a new experimental technique in FTICR ~pectrometry.~ Ions trapped in an ICR cell for more than 10 ms, however, are usually regarded as stable species, exchanging energy mainly by collisions with the surrounding gas. The average time between collisions in an ICR cell at typical background pressures of mbar is in the range 10-40 s, which means that, on a time scale of seconds, the ions can be regarded as isolated species. Unimolecular dissociations of ionic clusters have been frequently observed to accompany bimolecular gas-phase reactions in a FT-ICR mass spectrometer.5 However, recent closer examination of these processes revealed that the spontaneous loss of a ligand molecule dominates under low-pressure conditions, when bimolecular reactions are slow and, therefore, not competitive with trueunimolecular dissociations. These unimolecular dissociations are certainly not due to metastable ions, as the time scale is in the range of tens to hundreds of seconds rather than, as outlined above, microseconds. The present study now shows that ions trapped for sufficiently long periods of time in an ICR cell may exchange energy with the surroundings by emission and absorption of blackbody radiation. In the case of weakly bound clusters energy absorbed from blackbody radiation can lead to unimolecular dissociation of the cluster. The time scale for this dissociation is on the order of several hundred seconds, Le., of the same order of magnitude as the trapping time capabilities of the high magnetic field FTICR apparatus. The present study reports the accurate determination of the true unimolecular rate constants for this slow, infraredinduced dissociation. 0
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Figure 1. Kinetics of the unimolecular loss of a HzO molecule from (H20)4H+ ions. The bath gas is CH, at a pressure of 1.5 X lo-' mbar.
Experimental Section All experiments were performed with a Bruker CMS 47 FTICR mass spectrometer equipped with a high-pressure external ion source described in detail previously.6 Positive cluster ions weregeneratedfroma mixtureofCHIwith 10-3-1.5%ofdimethyl ether (E) and/or water (W). Hydrated chloride ions, W,Cl- (n = 2,3) were produced from a mixture of CH4, C C 4 , and water. The pressure in the high-pressure ion source was kept at 3-4 mbar at a temperature of -30 OC. The background pressure in the ICR cell under these conditions was below 3 X 10-9 mbar. The ions were transferred into the ICR cell, and the cluster ion of interest was selected and trapped in the cell for up to 500 s, using standard radio-frequency ejection techniques. To examine the pressure dependence and to exclude any dissociation caused by excess kinetic energy of the cluster ions, various amounts of buffer gases, usually CH4, but also Ar and n-butane, were introducedinto theICRcellat pressuresof 10-8-10-6mbar. With careful choice of the ejection parameters and, if necessary, pulsed addition of CH4 prior to the reaction time, excess kinetic energy from the ejection process could be completely avoided or efficiently removed.' In this way a true, thermal ion energy distribution is readily obtained. The ion abundances were monitored as a function of time, and the apparent reaction rates were obtained by a least-squares fit of the data to the appropriate integrated rate laws. Reaction rate constants were obtained with reproducibilities better than 5%. A plot of the apparent rate constants vs the calibrated pressure of the bath gas yields the true unimolecular rate constant from the
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Figure 3. Temperature dependence of the sequential unimolecular dissociation of the EW3H+cluster ions (E = (CH&O, W = H20).Lines correspond to least-squares fits to the integrated rate equations for consecutive reactions.
Results and Discussion An example of kinetic data for a unimolecular dissociation reaction, the loss of a H20 molecule from the WdH+ cluster ion, is shown in Figure 1. The lines shown in the graph correspond to least-squares fits of the data to the exponential functions for a simple A B unimolecular reaction. The ion loss over a trapping time of 500 s a t 1.5 X mbar is insignificant ( le7mbar, of a small, but significant, bimolecular component. The latter contributes to the apparent rate constant as a pseudo-first-order, pressure-dependent reaction rate. In order to understand the mechanism of the bimolecular process, the pressure dependence of the apparent dissociation rate of the negative cluster ion W3Cl- shown in Figure 2 has been examined using different bath gases. The intercepts for each set of experiments are identical, giving the true unimolecular dissociation rate. The slopes are different, however, indicating that the bimolecular dissociation rates, kbi, vary with the nature of the bath gas. The values obtained for kbi (X10-12cm3 molecule-1s-1) are 3.0 f 0.2 (Ar), 6.7 f 0.2 (CH4), and 14 1 (n-butane). From a comparison of kbi(CH4) and kbi(Ar), it can be concluded that it is not excess kinetic energy transferred into internal energy of the cluster ion during a collision which leads to dissociation, but, rather, an exchange of internal energy. A kinetically excited cluster ion would gain more internal energy on a collision with Ar than with CH4, as the center-ofmass energy with Ar would be larger and Ar has no internal degrees of freedom. Therefore, the bimolecular component of the dissociation is the result of a Lindemann type activation mechanism.8 The unimolecular dissociation reaction rates obtained for several cluster ion systems of interest are summarized in Table 1 together with the corresponding relevant thermochemical data. The zero-pressure unimolecular dissociation rates vary from 2.4 X 10-3 to0.83 s-1 with the product cluster ions W3H+, EWH+, E*H+,and WCl- stable to >SO0 s. Some larger cluster ions, like WaH+, were also initially observed but could not be isolated in the ICR cell for sufficiently long periods of time to ensure complete thermalization because they are too short-lived at 25 "C and above. The question therefore arises as to what is the source of the energy required for these spontaneous, endoergic unimolecular dissociations. Excess internal energy from the ionization process can easily be excluded, because of the high-pressure conditions of the external ion source and its low temperature (-30 "C).
Furthermore, any initial excess internal energy would rapidly dissipate by radiative and collisional cooling in the course of the reaction, leading to a decreasing reaction rate throughout the course of the reaction. This is neuer observed, however, due to the efficient collisional cooling achieved by a pulse of CH4 gas admitted to the ICR cell, before the dissociation is monitored. All experiments show first-order, single-exponential decay of reactant ion intensities to zero. Thus, we conclude that the ions attempt to achieve thermal equilibrium with the walls of the ICR cell by absorption and emission of radiation. The fueling of unimolecular reactions by exchange of radiation was originally proposed by Perringin 1919, even before unimolecular behavior had ever been systematically characterized. The distribution of the blackbody radiation a t room temperature (298 K) shows a maximum a t 1035 cm-1 (3.0 kcal/mol). Compared to the binding energy of the ligands (about 12-22 kcal/mol), the maximum of the blackbody energy distribution, calculated from the Planck equation,1° is too low in energy to promote the dissociation. The distribution shows a considerable high-energy tail, however. At 3600 cm-1, the wavelength of the 0-H stretch vibration in H20, the energy density per unit wavelength of the blackbody radiation still is about 1%of the maximum value. Thus, by a process of absorption and emission of radiation on the time scale of the FT-ICR experiment, a certain number of vibrationally hot cluster ions will continuously be generated, and some of them will gain enough energy to dissociate. The ion population can therefore be represented by a truncated Boltzmann distribution as previously suggested by Dunbar11 in his studies of C02 laser-induced dissociation of gas-phase ions. For ions a t threshold energy the dissociation rate is given by a minimum rate constant, kfi,,, according to RRKM theory. For loss of H2O from (H20)2,3Cl-, kfin has been calculated to be on the order of 102-103 s-1. Therefore, it is the rate of energization of the cluster ions which must determine the overall rate of the unimolecular dissociation. The energization rate depends on the threshold energy, the temperature of the surroundings, and the IR absorption frequencies and intensities of the cluster ions. The dissociation rates show the anticipated increase with decreasing bond dissociation energy when similar ions are compared. For example, WsH+ and EW2H+ contain the same number of atoms and vibrational modes, but the former, which binds H2O 2.8 kcal mol-' more weakly, dissociates 15 times more rapidly than the latter. However, when ions with similar ligand bond dissociation energy which are different in either size or composition are compared, the unimolecular dissociation rates may be very different. For example, despite their relatively weak
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TABLE 1: Unimolecular Rate C~nstantsk d and Associated Thermochemical Data' (Literature Value in Parentheses) for the Loss of a Ligand from Cluster Ions (W = H20; E = (CH3)20) reaction kuni (s-') Iiif0298 (kcal mol-') AGO298 (kcal mol-') S O 2 9 8 (cal mol-' K-I) W5H+ W4Ht 0.49 0.01 13.9 (15.3)b 5.8 (5.S)b 27.2 (32.6)b W4H" W3Ht 4.6(i0.1) X l t 3 17.4 (17.5)b 9.6 (9.3)b 25.1 (27.3)b EWaH+- EW2Ht 0.23 f 0.03 12.9 (13.8)c 6.1 (6.2)' 22.7 (25.4)c 3.3(*0.3) X 16.7 (15.3)' 1.4 (7.5)c 31.1 (26.3)c EW2Ht EWH+ 0.44 f 0.07 14.3 (13.6)c 6.2 (6.3)' 27.2 (24.6)c E2W2Ht EzWH+ 12.4 (16.3)' 4.3 (4.7)' 27.2 (38.8)c E2WH+- E2H+ 0.83 i 0.2 E3WH+ E2WH+ 9.5(*1) x 10-2 21.7 (16.8)c 9.3 (8.9P 41.6 126.6Y 8.6(&1) X 11.8d 5.ld. ' 22.3d' WXI- W,Clw;a- wc12.4(i0:4) X l t 3 13.0d 6.6d 21.4d a Reference 17. b Reference 18. Reference 13. Reference 19. 4
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bonds, chloride-bound water clusters dissociate slowly. This can be regarded as being a direct result of the smaller size of these ions relative to the W,E,H+ species which results in a lower energization rate due to the much smaller number of normal modes of these cluster ions. A semiquantitative verification that the blackbody radiation hypothesis is a reasonable one to explain these observed unimolecular dissociations can be obtained from a calculation of the radiation absorption kinetics. Using an ion internal energy distribution which is a Boltzmann distribution truncated at the dissociation threshold energy together with the blackbody thermal radiation flux and a set of ion vibrational frequencies and integrated absorption intensities modeled by his "standard hydrocarbon", Dunbar12 has calculated theoretical unimolecular dissociation rate constants for species of the size and binding energies of our clusters. These calculations give rate constants which are only 1-2 orders of magnitude less than those experimentally observed here. Given that neither the frequencies nor the integrated absorption intensities of the "standard hydrocarbon" accurately represent those of our ion-polar molecule clusters, this agreement between theory and experiment can be regarded as excellent. A general feature of cluster ion energetics is that successive ligands are usually lessstrongly bound. In thecaseof the E2W*H+ ion, the first loss of a water molecule is slower than the second loss of W, Le., that from the E2WH+ ion (see Table l), even though the first water molecule lost was reported to be bound more weakly than the second.13 The unusually high entropy for the energetically favorable but mechanistically complex process E2WH+ E*H+,obtained by Kebarle, led us to reexamine these thermochemical data by pulsed ionization high-pressure mass spectrometry.14 Our data show, in contrast, that the first water molecule to be lost from E2W2H+ is indeed more strongly bound than the second. This can beunderstoodconsidering the structures of these complexes. Energy-resolved CID experiments of Graul and Squires's show that the E2WH+ ion consists of a core H30+ unit with two solvent dimethyl ether molecules bound via hydrogen bonds. A second water molecule thus can be bound to the remaining free H atom on the core water. The ease with which the core water can be removed from the E2WH+ ion results from a fast rearrangement and dissociation reaction to form the very stable protonated dimethyl ether dimer, E2H+. The effect of the temperature on the dissociation rate is demonstrated in Figure 3. At higher temperatures the energy density per unit wavelength of the blackbody radiation increases, and the maximum is shifted to higher energy. Therefore, the rate of energization of the cluster ions increases and so does the dissociation rate. A detailed study of the temperature dependence of the dissociation rates will be published separately.16 Thus, all of the data reported here support the existence of a mechanism for unimolecular dissociation which is truly pressure independent and which can most readily be rationalized by continuous energization of the cluster ion population via interaction with ambient, background blackbody radiation.
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Conclusion The present study shows that ions under low-pressureconditions attempt to establish a "thermal equilibrium" with the surrounding walls by exchange of radiation. For ions trapped in an ICR cell at pressures of mbar, this means that such ions cannot be regarded as isolated entities on the long (>1 s) time scale of ICR experiments. Thus, the experiments reported here describe a thermal population of ions in which those species in the highenergy end of the Boltzmann distribution of internal energies have sufficient energy to undergo unimolecular dissociation on a time scale which is rapid compared to the trapping time in the ICR cell. This part of the distribution is slowly replaced by a process of absorption of blackbody radiation from the cell walls. However, once repopulated, this part of the distribution also dissociates such that at all times the ion ensemble exhibits a truncated Boltzmann distribution of internal energies. Detailed studies of pressure, temperature, and composition effects on the unimolecular dissociation of weakly bound cluster ions will, be reported in future contributions from this laboratory.
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Acknowledgment. The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Centres of Excellence in Molecular and Interfacial Dynamics (CEMAID) is gratefully acknowledged. The authors thank Dr. Jan Szulejko for the high-pressure mass spectrometric determination of the bond dissociation energies of the protonbound clusters and Professor R. C. Dunbar for performing the calculations of radiation absorption kinetics, for stimulating discussions, and for his interest in this problem. References and Notes (1) Levsen, K. Fundamental Aspects of Organic Mass Spectrometry, 4th 4.; Verlag Chemie: Weinheim, 1978. (2) Ngoka,L.; Lebrilla, C. B.J. Am. Soc. MassSpectrom. 1993,4,210. (3) Fisher, J. J.; McMahon, T. B. In?.J. Mass Spectrom. Ion Processes 1990,100, 701. (4) Audier, H. E.; McMahon, T. B. J. Am. Chem. Soc., submitted.
( 5 ) (a) McMahon,T.B.;Herman,J.A.;Herman,K.Unpublishedresults. (b)Thblmann,D.;McMahon,T.B.Proceedingsofthe4lst~MSCon/ermce on Mass Spectrometry and Allied Topics, San Francisco, 1993. (6) Kofel, P.; McMahon, T. B. In?. J. Mass Spectrom. Ion Processes 1990, 98, 1. (7) For thermalization of ions in an ICR cell see: ThrSlmann, D.; Griitzmacher, H.-Fr. OSU ICRlIon Trap Newsletter 1992, 25. 17. (8) Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; Wiley-Interscience: London, 1972. (9) Perrin, J. Ann. Phys. 1919. 11, 5 . (10) Atkins, P. W. Molecular Quantum Mechanics, 2nd ed.; Oxford University Press: Oxford, 1983; p 7. (11) Dunbar, R. C. J. Chem. Phys. 1991, 95, 2537. (12) Dunbar, R. C. Private communication. (13) Hiraoka, K.; Grimsrud, E. P.; Kebarle, P. J. Am. Chem. Soc. 1974,
96, 3359. (14) For the instrumentation see: Szulejko, J. E.; McMahon, T. B. In?. J. Mass Spectrom. Ion Processes 1991, 109, 279. (15) Graul, S.T.; Squires,R. R.In?. J . Mass Spectrom. Ion Processes 1989, 94, 41. (16) Thalmann, D.; McMahon, T. B. To be published. (17) Szulejko, J. E. Unpublished results from this laboratory. (18) Grimsrud, E. P.; Kebarle, P. J. Am. Chem. Soc. 1973, 95, 7939. (19) Hiraoka, K.; Misuze, S.Chem. Phys. 1987, 118,457.
