Faraday Discuss. Chem. Soc., 1983, 75,45-55 Isomerizati on of Internal -energy- selected Ions BY TOMAS BAER, WILLI A. BRAND,* THOMAS L. Bum AND JAMES J. BUTLER? Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27514, U.S.A. Receiued 23rd December, 1982 Solutions of coupled differential equations for the decay rates of energy-selected ions which competitively dissociate and isornerize show that under appropriate circumstances two-component decay rates can be expected. Although the requirements for the observation of such non-exponential decay is rather restrictive, it has now been observed in a number of cases, including the dissociation of butene and pentene ions, as well as l,Coxathian, 1,4- dithian and dioxan. Photoelectron-photoion coincidence spectroscopy has been used to energy-select ions and to measure the rate of dissociation.Examples of such non-exponential decay rates are presented for the above-mentioned ions. INTRODUCTION Non-exponential or two-component decay resulting from competitive decay and internal conversion has been known for some time now for the case of ion fluorescence.l This effect can be observed in the case where the fluorescence rate and radiationless transition rate are comparable, and the ion is sufficiently small so that the probability for reconstitution of the excited electronic state and subsequent fluorescence is appreciable. A similar situation exists in the case of metastableion dissociation reactions. Metastable ions are those ions which dissociate during the time of mass analysis in a mass spectrometer.This generally means dissociating ions with life times of the order of microseconds. Two-, or perhaps multi-, component exponential decay has been observed in a few dissociations of metastable and in the case of propargyl chloride,2 CH3- CCCl+ , this was attributed to the competition between isomerization and dissociation. The dissociation of a series of energy-selected butene ions gave further evidence for the connection between isomerization and dissociation, and two-component decay ratesms We present here the mathematical analysis of the expected decay rates and some additional examples which we have recently discovered. Photoelectron-photoion coincidence (PEPICU) is a technique fur energy-selecting ions and measuring their dissociation rate, the branching ratio to the various products, and the translational energy released in the dissociation reaction.6 The principle of the experiment is based on the conservation of energy and momentum, which ensures that for a given photon energy the ion internal energy, E,, is given by EI = hv - E, + Eth in which E, is the energy of the departing photoelectron and Eth is the residual thermal energy of the ion as a resuIt of the initial thermal energy of the precursor neutral * Present address : Institut fiir Physikalische Chemie, Universitat Bonn, 5300 Bonn, West Germany.7 Present address: National Bureau of Standards, Washington D.C. 20234, U.S.A.46 ISOMERIZATION OF ENERGY-SELECTED IONS molecule. In large molecules such as brornobenzene Eth can be as much as U.1 eV.Two types of PEPICO experiments are being carried out in various laboratories. One employs a fixed-energy light source and the ion energy is selected by varying the electron energy with which the ion is ass~ciated.~-~ The other type is a threshold PEPICO experiment in which a variable-energy light source is used and only threshold photoelectrons are co11ected.2-6* 'Om The latter approach is utilized fur this study. EXPERIMENTAL In the threshold PEPICO experiment, electrons of nominally zero energy are measured in coincidence with ions. The experimental set-up is illustrated in fig. 1. The electron signal ELECTRONS t START To STOP DISCRIM- - - DELAY >PULSE h€IGHT 4 - INATOR DISCRI M - INATOR CONVERTER MULTICHANNEL I I I ANAWSER PDP 11/03 Fig.1. Experimental set-up fur the photoelectron-photoion coincidence spectrometer. provides the start for measuring the ion time-of-flight distribution, which in addition to its role as a mass-analyser contains a considerable amount of dynamical information. For instance, if a dissociation is accompanied by release of translational energy, the ion time-of- flight distribution will be symmetrically broadened. Metastable ions are identified by their asymmetric time-of-flight distributions, which arise from the dissociation of the ion during acceleration in the ionization region. ISOMERIZATION AND TWO-COMPONENT DECAY RATES Consider the potential-energy curve in fig. 2, which relates isomers A+ and B+ (the + signs are omitted in the fig.), each of which can dissociate to products PI and P2, respectively.These products could be either a single or several ion-neutral pairs. Furthermore PI and P2 could be the same or different products. Initially, ionization will take place to either A+ or B+ [eqn (l)], depending on the starting neutral isomer: A + k v + A + ( 1 4 €3 + hY --f B+. (1b)T. BAER, W. A. BRAND, T. L. BUNN AND J. J. BUTLER 47 Fig. 2. Model potential for a competitive dissociation/isomerization reaction. The reaction then proceeds via k2 A+ 7 B+ B+ A P2+ + N2. k Now the rate of production of P1+ and P2+ is (3) (4) In order to determine the rate, we need to know the time dependences of A+ and These are given by the coupled, linear, homogeneous differential equations (6). B+. (The plus sign indicating ions will not be included for the remainder of this paper.) (6) dA - = (-kl - k2) A + k3 B = alA + blB dt @ = k2A + (-k3 - k4) B = a2A + b2B.dt Solutions are of the form: A = ae-lf , B =pe-A'. Substituting these solutions into eqn (6) yields (7) This matrix equation only has solutions when the determinant of the 2 x 2 matrix is zero. This condition yields the following values of A: ' 2 = -+(a, + b2) & +d[(a, + b2I2 + 4a2b1 - 4a&]. (9) Now the general solutions for A and B are given by h e a r combinations of the + and - solutions of eqn (7) and (9), which result in:48 ISOMERIZATION OF ENERGY-SELECTED IONS The a and j3 coefficients are related by the conditions set by eqn (8). However, only the ratio of a and p is determined, so that we can arbitrarily set, say, the p coefficients equal to 1.Suppose that A is the initially formed ion, at an energy above the dissociation limit of both P, and P2. As a result B(t = 0) = 0 and A ( t ) and B(t) reduce to To go beyond eqn (10) we need to consider the initial conditions. Eqn (11) has been written with the slower rate term, A-, first. rates are not simple exponential functions. exponentials. limiting cases. The rate of product formation is given by eqn (5) and (1 1). It is evident that these Rather they are the sums or differences of Because A, are rather complicated, it is helpful to approximate them for various Case (A) then k2 x k3 9 kl x k4. This results in Suppose that isomerization is very fast compared with dissociation. We have Solving eqn (8) for the a in terms of the j3 leads to dP2 -- dt - kk44B = (e-IE-t - e-A+t).Because k3 x k2 and A+ 9 A-, the second terms, involving the fast rates, are neg- ligible at times other than t z 0, so that the two products are formed with the single rate of A-. This is expected for the conditions imposed, which imply a complete equilibration of isomers A and B prior to dissociation. A variation of this case is k2 > k3 so that L is just k4. These latter conditions are apparently the ones most frequently encountered, such as in the dissociation of isomers of C4H6+,12 C6H6+ ,13 C8H8+ l4 and C4H5N+.15 Case (B) We can imagine a situation in which isomerization of A is in competition with direct dissociation. That is, k, x k2 $ k3 = k4. The two rates derived from eqn (9) are This again yields a fast rate, A+, and a slow rate, A- x k3 z k4.The resulting decay rates are - dP2 dt = k4B = k4(e-a-t - e-A+t).T. BAER, W. A. BRAND, T. L. BUNN AND J. J. BUTLER 49 In this case ion A will produce P, with a two-component rate because the co- efficient for each rate is of the order of magnitude of the rate itself. On the other hand, the product P2 will be formed essentially at the slow rate. We will show with the accompanying examples, that conditions such as this are reasonable and can account for the observed two-component behaviour. Case ( C ) Suppose that photoionization initially produces ion B, and that the rate constants are as they were in case (B), namely k, z k2 9 k, = k4 so that ,l* are as in case (B). However, now A(t = 0) = 0 so that the rates of P1 and P2 production are given by It is evident that the product P, will be formed to any significant extent only with the slow rate because the coefficient of the fast rate is small.Similarly product P, can be formed only with the slow rate. Cases (B) and (C) therefore offer a convenient means of testing a two-component mechanism because if the most stable isomer is one which can be formed directly from a stable molecule, its decay rate can be shown to be one- component [case (C)]. Furthermore this rate should be equal to the slow component of the higher-energy isomer [case (B)]. EXPERIMENTAL RESULTS DISSOCIATION OF C5H10' The most clear-cut case of two-component decay to date has been found for the dissociation of energy-selected C,H,,+ isomers.16 Both 13C and deuterium labelling 1 1 Fig.3. Potential energies of three C5H10+ isomers and their dissociation to C3H6+ and C4H7+. The energies of the isomers and the dissociation limits are known. The isomerization barriers are only estimated.50 ISOMERIZATION OF ENERGY-SELECTED IONS studies have shown that extensive rearrangement of the ions prior to dissociation results in scrambling of the carbon and hydrogen atoms.17 In addition recent photo- dissociation studies of several C5H10+ isomers, initially produced by electron impact,18 as well as ion-molecule reaction and collisional-activation investigation l9 suggested that some of the ions rearrange to more stable isomers. However, none of the data lend themselves to a simple interpretation. Two reactions are energetically possible within 0.5 eV of the dissociation threshold. These involve the loss of CH3 and C2H4 to produce C4H7+ and C3H6+, respectively. The dissociation threshold to both of these ions lies essentially at the thermochemical dissociation limit, so that there is no reverse activation barrier. Fig.3 shows the energies relevant for the dissociation of three of the isomers. 11 12 13 I4 15 ion time of flight Fig. 4. Time-of-flight distributions C3Hd + and C4H7 + fragment ions originating from the indicated parent C5HI0+ ions. The solid lines are calculated time-of-flight distributions assuming the indicated rates, A- and d+ . The same values of d are used for both fragments. The energies are the 0 K absolute energies based on the common heat-of-formation scale.The time-of-flight distributions of fragments from the three isomers obtained at several ion internal energies are shown in fig. 4. These data are examples of the remarkable variety observed for all six isomers investigated over a range of internal energies. Not only do the ratios of the C3H6+ to C4H,+ signals vary from one isomerT. BAER, W. A. BRAND, T. L. BUNN AND J. J. BUTLER 51 to the next, but even for one isomer at a single energy it is evident that the two products are both produced with two-component rates. The thermochemistry of the C5H10+ isomers is well known.16*20*21 The cyclo- pentane ion, although quite stable as a neutral molecule, is less stable than the simple branched and linear pentenes. The most stable ion is 2-methylbut-2-ene.At all energies it decays via a one-component decay rate, as predicted for the case (C) type of dissociation. All other, higher-energy isomers are consistent with case (B) dissociation. That is, they decay via a two-component rate. The slow rate is the same for all ions at a given ion internal energy and it increases with ion energy. This slow rate is associated with the rate of dissociation from the lowest isomeric structure, that of the 2-met hylbut-2-ene ion. Because of the numerous isomeric structures which are involved in the dissociation, it is not very useful to analyse the data in more than a qualitative manner. There are too many unknown reaction steps, so that the actual mechanism is far more compli- cated than the models of fig. 2 or 3. DISSOCIATION OF C4HsOS' AND C4HsS2' The total rate of ion decay to several product ions can be measured by monitoring the time-of-flight distribution of any one of the fragments.For a number of ions, such as isomers of C6H6+,13 C4H5N+ l5 and dioxan (C4H802+),22 the measured total rate is the same regardless of which fragment ion is monitored. This is the situation expected when all dissociation paths originate from the same parent-ion structure, or at least if the various parent-ion structures are fully equilibrated. One notable exception has been the dissociation of CH3N02+ which was found to decay via two distinct rates to the products, NO+ + CH30 and CH30+ + NO,23 This observation is proof that at least two types of non-equilibrated precursor ions are involved in the dissociation.* In the case of the previously discussed C5H10 ions, the two parent ions correspond to the initially formed ion and its rearranged, lower-energy isomer.A similar situation apparently exists in the dissociation of C4HsOS and C4HsS2 ions except that the two parent ions produce different fragment ions so that each decay can be described by a single exponential. However, the rates (as shown in fig. 5) for the C4HsOS+ dissoci- ation are different. It corresponds to our rate model case (B), in which P1 and P, are different product ions. The rate data for C4HsS2 are very similar. The fragment C2H5S+ is produced at a rate which is ten times higher than that forming C3H2S2+ and C4H7S+. Very little information is available concerning the energies of the C4HsOS+ and C4HsS2+ isomers.However, we can learn something about them from a comparison of these ions with their oxygen analogues, C4Hs02+. A recent PEPICO study of dioxan 22 and two of its isomers, butanoic acid 24 and ethyl acetate 25 indicated that these three ions dissociate directly, withour prior isomerization. This is evident not only from the rate studies, but also from the fragments produced by each ion. Table 1 summarizes the major fragments from the three C4H802+ isomers, as well as those from C4HsOS+ and C4HsS2+. This table is very revealing. Consider the fragment ion C2H5X+, X = 0 or S. This is one of the three ions produced by dioxan near its dissociation limit. Although this ion is also formed in the dissociation of ethyl acetate, it is a minor product and the structures of the C2H50+ ions are probably not the same.It is significant that this product ion is formed by both C4HsOS+ and C4HsS2+ with a rate about ten times higher than the rate of parent-ion decay as * Meisels et al.23 analysed their results in terms of different electronic states. In view of our results and model presented here, it is likely that these electronic states refer to different CH,NO: structures, e.g. CH30-N=O+ and CH2-OH-NO+, the latter being more stable.52 ISOMERIZATION OF ENERGY-SELECTED IONS 3 I v) . 0 Y h 1 o6 1 o5 10.0 10.2 10.4 10.6 photon energyleV Fig. 5. Measured total C4H80S+ dissociation rates as a function of the ion internal energy. The solid line through the C2H5S+ points (0) is an R.R.K.M./Q.E.T. calculation assuming a 1,4-oxathian structure for both parent and transition-state ions (see tables 2 and 3).The solid line through the C4H6S+ (0 ) and C2H4S+ (0) and points is an R.R.K.M./Q.E.T. calcu- lation assuming an isomerized, lower-energy parent-ion structure (see text). measured by the appearance of the other fragments. Yet the fraction of C2H5S+ ions is only ca. 20%, and it is not energetically the first ion formed (table 2). All the more slowly formed fragment ions, such as C4H,S+, C3H2S2+ and C2H4SO+, are ones which are also produced in the butanoic acid and ethyl acetate ion dissociation. Table 1. Major fragments formed from C4H802+ isomers and C4H80S+ and C4H8SF+ n e u t r a l OH ocz H5 "The numbers in parentheses are the orders of the fragment ion appearance energies.The lowest is first.T. BAER, W. A. BRAND, T. L. BUNN AND J. J. BUTLER Table 2. 0 K onsets a for fragments from 1,4-oxathian (C4HSOS) product IE or AEo/eV C,H,OS + 8.53 i 0.02 C,H,jS+ + H20 9.73 * 0.05 C2H,SO+ + C2H4 9.79 & 0.05 C4H70+ + SH 9.78 f 0.08 CzH,S+ + CZHjO 9.85 * 0.05 C2H4S+ + CzH40 10.0 * 0.1 H2CS+ + C3H60 10.9 * 0.1 53 The 0 K onsets were obtained from the 298 K onset by adding 0.1 eV, the average C4H8US thermal energy, to the measured onset. The most stable of the three C4H802+ isomers investigated is the butanoic acid ion which, on the absolute (0 K) energy scale, has a heat of formation of 5.54 eV. In addition, both the ethyl acetate ion (5.68 eV) and its enol isomer (5 eV) are considerably more stable than the dioxan ion (6.23 eV).We can assume that a similar relation- ship holds for the sulphur analogues. (Such an analogy must, in fact, be made with considerable caution because the sdphur atom can cause the relative energies to vary considerably.) This analogy offers a simpIe explanation for the different rates observed in the dissociation of C,H,OS+ and of C,H,S,+ ions. The cyclic structure of these ions can be identified with isomer A in fig. 2. An as yet unknown isomer, which could be the thioacetate, the thiobutanoic acid or perhaps a combination of these, is isomer B. Whereas the barrier to isomerization in dioxan is large, it is evidently sufficiently small in the case of the sulphur analogues, so that direct dissoci- ation to C,H,S+ is in competition with rearrangement to the more slowly dissociating isomers.One test of this dissociation mechanism is the comparison of the experimental dissociation rates with those caIculated using the statistical theory of unimolecular decay (R.R.K.M.1Q.E.T.). We have done this for the case of C4H80S+. An activ- ation energy of 1.32 eV is obtained for the production of C,H,S+ from the data of table 2. The R.R.K.M./Q.E.T. calculation requires this activation energy, as well as the vibrational frequencies for the molecular ion and the transition state, as input. The vibrational frequencies of 1,4-oxathian 26 (table 3) were used for both the ion and Table 3. Molecular ion and transition-state frequencies (cm- ') for R.R.K.M.1Q.E.T. calculated dissociation rates of C&OS + Dissociation to C4H,S+ + SH ' 2980 2980 2980 2940 2910 2910 2880 2880 1720 1460 1460 1440 1410 1410 1370 1350 1260 1260 1180 1110 1090 1080 1000 950 940 770 760 590 545 460 413 378 226 226 210 106 Dissociation to CIHsS ' + C2H30 a 2970 2950 2950 2920 2970 2920 2860 2860 1460 1440 1420 1410 1390 1360 1320 1290 1270 1210 I200 1170 1110 1050 1010 1000 970 950 830 810 690 670 550 430 400 340 252 206 a The same frequencies were used for the molecular ions and the transition states.The 940 and 830 cm-' frequencies were the assumed reaction coordinates for the transition states of the two dis- sociation paths.54 ISOMERIZATION OF ENERGY-SELECTED IONS the transition state. This procedure gave a good fit for the previously studied dioxan dissociation, The solid Iine through the C,H,S+ points is the result of this calcu- Iation.A similar attempt was made to fit the C4H,S+ and C2H4SO+ points. Their slightly lower activation energies of 1-20 and 1.26 eV and the fact that the parent ion is reacting via two paths (a symmetry factor of 2) resulted in rates which are 2 to 3 orders of magnitude higher than experimentally observed. Clearly the C4H80S+ ion is isomerizing prior to dissociation to a lower-energy structure from which it wiIl decay more slowly, as suggested in case (B) of our model. A fitting of the calcuIated rates to our measured ones using the " loose " vibrational frequencies of table 3 and the parent-ion energy as an adjustable parameter suggests a value of 8.05 eV for the isomer (in contrast to 8.53 eV for 1,4-oxathian). CONCLUSION We have shown that under appropriate conditions two-component dissociation rates can be expected in sIowly fragmenting energy-selected ions.This complex behaviour can be ascribed to competition between isomerization and direct dissoci- ation. A11 of these cases are in accord with the statistical theory of unimolecular decay.. In fact if sufficient information concerning the dissociation path and energies were available, the rates could be calcdated with the theory. ExampIes of such dissociation/isomerization of energy-selected ions have now been found for the decay of the ions of C3H3Cl?g3 CH30N0,23 C4H8:p5 C5H10,16 and C4Hs- OS, C4H8S2. The Iatter data are presented here for the first time. We are grateful to the Department of Energy and the National Science foundation for financial support of this project.(a) J. P. Maier, Ace. Chern. Res., 1982,lS 1 ; (b) M. Allan, E. Kloster-Jensen and J. P. Maier, J. Chenz. Soc., Favaday Trans. I , 1977,73, 1417; (c) J. P. Maier and F. 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Soc., 1980, 102, 6774. l6 W. A. Brand and T. Baer, J. Am. Chem. Sac., to be submitted. l7 (a) D. P. Stevenson,J. Am. Chem. Soc., 1958,80,1571; (b) S. Meyerson, Appl. Spectrusc., 1968, l8 P. N. T. VanVelzen and W. J. Van der Hart, Chern. Phys., 1981,61, 335. l9 (a) T. Nishita and F. W. McLafferty, Urg. Mass Specfrom., 1977, 12, 7 5 ; (b) K. Levsen and J. 2o J. B. Pedley and J. Rylance, Sussex-NPL Compufer Analysed ThermochemicaI Ddia: Organic ti T, Baer, in Gas Phase Ion Chemisfry, ed. M. T. Bowers (Academic Press, New York, 1979), 155. 22, 30. Heimbrecht, Org. Mass Specfrom., 1977, 12, 131. and OrganarnetaIIic Compounds (University of Sussex, Sussex, 1977).T. BAER, W. A. BRAND, T. L. BUNN AND J. J. BUTLER 55 21 H, M. Rosenstock, K. Draxl, B. W. Steiner and J. T. Herron, J. Phys. Chern. Ref. Data, 1977,6, 22 M. L. Fraser-Monteiro, L. Fraser-Monteiro, J. J. Butler, T. Baer and J. R. Hass, J. Phys. Chem., 23 G. G. Meisels, T. Hsieh and J. P. Gillman, J. Chem. Phys., 1980,73,4126. 24 3. 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