12122
J. Phys. Chem. 1993, 97, 12122-12126
Photodissociation of Iodobenzene Molecular Ion: Investigation of Entropy Bottleneck in Ionic Systems Yong Hymn Yim and Myung So0 Kim' Department of Chemistry and Research institute of Molecular Sciences, Seoul National University, Seoul 151-742, Korea Received: April 15, 1993; In Final Form: September IO. 1993'
Photodissociation kinetics of iodobenzene molecular ion has been investigated by mass-analyzed ion kinetic energy spectrometry (MIKES). A method has been devised to correct for the influence of collisional relaxation of the molecular ion occurring in the ion source on the rate constant. Theoretical analysis of the present rate-energy data on a nanosecond time scale together with previous microsecond data has found no firm evidence to support the transition state switching from an orbiting transition state to a tight transition state, especially a t internal energy well above the threshold. A t internal energy near the threshold, the transition-state switching has been found possible when the best literature value of 2.38 eV was used as the energy barrier. If the energy barrier is adjusted to a slightly higher value (2.46 eV), however, such a possibility can be ruled out. More accurate determination of the energy barrier and the measurement of the rate constant on a longer time scale are needed to clear the situation near the threshold.
each other and switching to TTS is expected a t higher energy. TSS was theoretically predicted18 and observed19 for neutral Investigation of the reaction rate and the internal energy systems. However, occurrence of TSS in ion reactions is still a disposal is of great importance for understanding the detailed matter of controversy.20 Even though TSS in ion reactions was kinetics and dynamics of unimolecular ion dissociations. Nureported for systems possessing multiple-well potentials,17 they merous experimental methods have been devised for this were not the observations of entropy bottlenecks. purpose,I-l0 and the theoretical developments have led to better Lifshitz et alaz1suggested that the halogen radical loss reactions descriptions for observed rate constants and product-state of halobenzene radical cations should be good candidates for distributions. Direct trajectory calculations on a potential energy determining the importance of entropy bottlenecks in ionic surface" may provide the most accurate theoretical results. systems. In addition to the fact that the reactions are known to Unfortunately, however, they are practically impossible at the proceed via single-well potential surfaces, well-known thermomoment except for very simple systems. Statistical approaches, chemical data22 for these reactions provide additional advantages such as Rice-Ramsperger-Kassel-Marcus (RRKM) theory12and in the theoretical calculations. The rate constant for the phase space theory (PST),13 provide accessible calculations for dissociation of bromobenzene ion was calculated by microcalarger systems. The majority of the unimolecular ion dissociations nonical VTST and compared with the previous experimental investigated so far have been interpreted successfully within the results.2' However, the experimental data available were confined frameworkof RRKM theory or quasi-equilibrium theory (QET).14 to those for dissociations occurring on microsecond or longer One of the major difficulties in the use of RRKM-QET lies time scales. It was concluded that the reaction proceeded via in the characterization of the transition state. For reactions OTS over the internal energy range considered and that TSS did proceeding via loose transition states, Klots' r e f ~ r m u l a t i o nof l~~ not occur. Also, accurate measurement of the rate constant at RRKM-QET in terms of statistical PST removes this difficulty high energy was proposed to find evidence for TSS. In this regard, by postulating an orbiting transition state (OTS). A more general it is thought to be of particular importance to obtain rateconstants formalism with rigorous energy and angular momentum conon a nanosecond time scale. servations has been developed by Chesnavich and B o ~ e r s . l ~ ~ - ~ Recently, we developed a new method to determine the rate PST has been successful for predicting product-state distributions constant for photodissociation (PD) of polyatomic ions on a in many cases. However, PST provides only an upper bound to nanosecond time scale.I0 In the present work, the dissociation the dissociation rate constantl3c due to the assumption of OTS. kinetics of iodobenzene molecular ion has been investigated using Within the statistical framework, the variational criterion15J6 this technique. which locates the transition state at the position of the minumum flux from reactant to product is expected to provide a better C6H5I'' C6H5' I' (1) estimate for the rate constant. This is the essential concept in Experimental results are compared with various theoretical the variational transition state theory (VTST). The variational calculations, and the importance of entropy bottleneck in criterion is particularly important for a reaction without any unimolecular ion dissociation is discussed. pronounced maximum in the potential energy surface. In this case, the location of the transition state is determined by a delicate balance between entropic and enthalpic effects. As a result, Experimental Section transition-state switching (TSS)" from an OTS to a tight The experimental setup has been described in detail elsetransition state (TTS) may appear as the internal energy of the whereIOJ3 and will be reviewed only briefly here. A doublereactant increases. Namely, dominance of the enthalpic effect focusing mass spectrometer with reversed geometry (VG Anaat low internal energy favors the transition state at large distance lytical Model ZAB-E) modified for PD study was used together between products (at OTS), while the two effects may offset with 514.5- and 488.0-nm lines of an argon ion laser (Spectra Physics Model 164-09). Ions formed by charge exchange in the * Author to whom correspondence should be addressed. ion source and accelerated to 8 keV were mass-analyzed by the *Abstract published in Advance ACS Abstracts, October 15, 1993.
Introduction
+
0022-3654/93/2091- 12122304.00/0
0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12123
Photodissociation of Iodobenzene Molecular Ion magneticsector. Then, the ion beam was crossed with thechopped laser beam perpendicularly in the field region of an electrode assembly. The translational kinetic energies of the fragment ions were analyzed by the electric sector. This is so-called massanalyzed ion kinetic energy spectrometry (MIKES). Since the MIKE spectrum contains contributions from metastable dissociation and collision-induced dissociation by residual gas, phasesensitive detection was adopted to record the MIKE spectrum originating from photodissociation, namely, the PD-MIKE spectrum. CS2 was used as a reagent gas for charge-exchange ionization. The temperature of the ion source chamber was maintained at 110 OC.
Results and Discussion
TRANSLATIONALENERGY, eV
A. Analysis of PD-MIKE Band Shape. To determine the photodissociation rate constant, a high voltage was applied on the electrode assembly. The spectrum thus obtained was called the field-on PD-MIKE spectrum in the previous work. Details of the method used to evaluate the rate constant by analyzing the PD-MIKE band shape have been reported already.10.23a Only the major features of the procedure will be reviewed as a means to describe the minor modification made in the present work. For PD occurring in the field region of the electrode assembly, the translational energy of a product ion after exiting the field region changes depending on the site of its formation or the dissociation time. Taking h(K,t)as the MIKE peakshape function for the product generated a t time t, the overall field-on PDMIKE band shape was expressed as below in the previous work.
Figure 1. Field-on PD-MIKEspectrum for reaction 1 obtained at 1 kV of appliedvoltagewith 5 14.5-nmexcitation. Experimental andcalculated
resultsareshownassolid lines and filledcircles,respectively. Thepre-ssures of reagent gas used for charge exchange are (a) 0.03 and (b) 0.14 Torr in ion source.
h
0.90 .
8v?
Y
M 0
v
M
0.89
-
0
I
H ( K ) = J P ( t ) h(K,t) d t Here, K is the translational energy scale in the MIKE spectrum and P(t) is the probability density for dissociation occurring a t time t. Since the dissociation was observed from parent ions possessing a range of internal energy, the following expression was used for an energy distribution function: P,(k(E)) = 2-
exp(-a(1og k - log k,)')
(3)
Here, k, is the most probable rate constant and cy is a constant related to the width of the distribution. Then, the following equation was used in the previous treatment to account for the random lifetime di~tribution:'~
P(r) 0: JP,(k(E))ke-k'
dk
(4)
It was realized in the present work, however, that the integration over the internal energy, not the rate constant, should be made because PE(k(E)) is the energy distribution. Namely,24
P(t)
Q
JP,(k(E))
k(E)
dE
(5)
Considering that a decent linear relation exists between log k and E, a better approximation than eq 4 is obtained as follows:
P ( t ) 0: JP,(k(E))
e-&(,)'dk
Equation 6 resulted in a factor-of-2 increase in the rate constant compared to eq 4. Field-on PD-MIKE spectra obtained at 1 kV of appliedvoltage using 514.5-nm excitation are shown in Figure 1. Here, peak A and its tail correspond to photoproducts generated before the exit electrode of the electrode assembly, while the photoproducts generated after exiting the electrode assembly appear as peak B. k, and cy were determined through the best fit to experimental data by the method described above. In the case of PD-MIKE data shown in Figure la, for example, the best k, and cy values
o%bO
0.05
0.10
0 L5
ION SOURCE PRESSURE (torr) Figure 2. Values of log(1og k,) vs the pressure of reagent gas used for
charge-exchange ionization. Filled circles represent exprimental log(log &), data, and the solid line is obtained from linear regression of four low-pressure log(1og k,) data. were 9.32 X lo7 s-I and 4.5, respectively. The PD-MIKE band shapes calculated with the best-fit parameters are also shown in Figure 1. B. Correctionfor the Collisional Relaxation in the Ion Source. In the previous study on the photodissociation of n-heptane ion?5 the possibility of internal energy lowering in high-pressurechargeexchange ionization was noted. This was thought to occur due to the collisional relaxation in the ion source. Since the internal energy of the iodobenzene molecular ion generated by charge exchange with CS2*+is much larger than that of the n-heptane ion, the influence of the collisional relaxation may be more significant in the present case. The lower internal energy of the iodobenzene molecular ion generated a t higher pressure in the ion source results in a smaller average rate constant. The PDMIKE band shapes shown in Figure l a and 1b were obtained for the molecular ion generated a t 0.03 and 0.14 Torr of ion source pressure, respectively. The stronger 3 peak relative to A at the high,er source pressure means that the rate constant is smaller at the higher source pressure. This suggests the possibility of collisional relaxation of the molecular ions before they exit the ion source. In Figure 2, k, values obtained from the band shape analysis at several ion source pressures are shown. One might expect that thecollisional relaxation can be removed by simply lowering the ion source pressure. However, it is not possible to reach such a condition because charge exchange is not effective, and direct ionization of iodobenzene molecule by electron impact interferes at such a low pressure. It was attempted in the
Yim and Kim
12124 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 ,"
I
I
TABLE I: Molecular Parameters Used in PST and VTST calculations
Vibrational Frequencies," cm-1 C6H51'+ (reactant ion)b 3065,3060,3050(2), 3030,1575(2), 1470, 1435, 1320, 1260 1175,1158,1068,1060,1015,999,980,963,904,837,730 684,654,' 613,449,398,266,220,d 166d
CsHs+ (OTS)c 3060(3), 3050(2), 1600(2), 1490(2), 1330,1310,1180(2), 1150 1040,1010,990(2), 975,850(2), 700,670,600(2), 410(2)
I
2.0
2.5
3.0
3.5
4.0
I
4.5
Rotational Constants] cm-I c~H~I*+ 0.046 C6HS+ 0.1517 Polarizability, 10-24 cm3 18 4.8
INTERNAL ENERGY (eV)
Figure 3. Rate-cnergy dependence for reaction 1, RRKM-QET calculations: (- - -) with EO = 2.335 eV and AS* = 6.4 eu (Dannacher et a1.,27efittingof photoionization breakdown data on a microsecond time scale), (-) with EO = 2.38 eV and AS* = 7.44 eu (Malinovich and Lifshitz,2* fitting of photoionization breakdown data on a microsecond time scale). Filled circles represent the present data, and sizes of circles represent error limits for the rate constants. PST calculationsin the zero angular momentum limit: (-) with EO= 2.38 eV and (- * -) with Eo = 2.46 eV.
present work to obtain the collisional relaxation-free k, by extrapolating the high-pressure data to the zero-pressure limit. In Figure 2, k,at pressure higher than 0.1 Torr is rather insensitive to the source pressure, indicating that the energy relaxation is more or less completed. Faulk and co-workers' suggested that exponential collisional relaxation be a reasonable first approximation. Considering that a decent linear relation exists between log k and E in a narrow internal energy range, log(1og kc) was plotted versus ion source pressure as shown in Figure 2. Then the collisional relaxation-free k, was estimated by linearly extrapolating the data in the pressure range 0.02-0.08 Torr. The average rate constants thus obtained were (1.3 f 0.2) X lo8 and (2.1 f 0.5) X lo8 s-l, respectively, for PD with 514.5- and 488.0-nm laser lines. Since charge-exchange ionization was used to generate molecular ion, its internal energy after photoexcitation is given by
Ei,=RE+Eth+ h v - I E
(7) provided that the collisional relaxation is not involved. Hence, the extrapolated k, value corresponds approximately to the rate constant at the most probable internal energy, Ein*. Here, R E is the recombination energy of CS2'+ and IE is the ionization energy for iodobenzene. Their best literature values are 10.07 and 8.685 eV, respectively.26 Ethis the thermal vibrational internal energy of the molecular ion at 110 OC. The thermal internal energy distribution was estimated as p r e v i o ~ s l y , l and ~ . ~ the ~ most probable value was found to be 0.12 eV. C. Rate-Energy Dependence. The fragmentation of iodobenzene molecular ion has been studied intensively on the time scale from millisecond to microsecond.I.22J7 Various information on the rate-energy relation and the thermochemical data for the reaction are available. Although the reported experimental rate constants display some discrepancies, two recent measurements by Dannacher et al.27e and Malinovich and Lifshitz22 are reasonably well-matched. These investigators reported the results of RRKM-QET fitting of the photoionization breakdown data. Using the same best-fit parameters adopted by the above investigators, RRKM-QET calculations have been carried out here. Calculations here have been extended to higher internal energy than considered previously to compare with the present experimental data obtained on the nanosecond time scale. The results are shown in Figure 3. Since the iodine loss reaction was the only channel observed in the present photodissociation, the rate constant obtained from the extrapolation described in the
a Numbers in the parentheses denote the degeneracies of vibrational modes. Reference 27d. Reaction coordinate. Bending mode frequencies. e Reference 3 1. /Estimated values. t Reference 32.
previous section is equivalent to the rate constant of the channel. The present result displays good agreement with RRKM-QET calculations as shown in Figure 3. It is well-known that RRKM-QET fitting of rate-energy data is virtually a two-parameter problem, namely, the energy barrier (EO)and the activation entropy (AS*).This arises because the rateconstant remains nearly the same regardless of the frequencies of individual oscillators as long as AS* is kept constant. In the R R K M 4 E T calculation by Malinovich and Lifshitz,22 the energy barrier of 2.38 eV and the activation entropy of 7.44 eu were used. It was thought that this corresponded to a totally loose transition state because the activation entropy was the same as that for OTS. At low internal energy, however, calculations show that the rate constant varies with the actual frequencies used, especially those for the low-frequency vibrations, even when AS* is fixed. This may arise because the high-frequency vibrational modes are not populated effectively at low internal energy, while AS*,the canonical equivalent entropy of activation, is calculated at 1000K. This suggests that AS*may not be a sufficient criterion for the looseness of a reaction. In this regard, PST calculation has been performed with the energy barrier of 2.38 eV which is the best literature value.22 Molecular parameters for this calculation are shown in Table I. Since the above RRKM-QET and VTST calculations, to be described later, were carried out in the zero angular momentum limit, PST calculation was done also at the same limit for comparison. It is seen that the PST rate constant gets larger than the RRKM-QET one almost immediately after the threshold. In view of RRKM-QET and PST calculations, the experimental rate-energy relation seems to indicate that the reaction proceeds via a transition state which is tighter than OTS even at an internal energy which is slightly higher than the threshold. It is to be noted that accurate measurement of the rate constant on a millisecond time scale will be very helpful to resolve the issue near the threshold. As far as the energy barrier is taken as an adjustable parameter, a good fit can be achieved between PST calculation and experimental rate-energy relation measured on a nanosecond to high microsecond time scale. Namely, the result of the PST calculation with a 2.46-eV energy barrier (shown in Figure 3) displays an excellent agreement with the experimental data. Hence, if the energy barrier of the reaction is 2.46 eV, the experimental data indicate that the reaction proceeds via an OTS over the entire energy range considered here. That is, the transition state switching to TTS does not occur, and the entropy bottleneck is not important in this ionic reaction. More accurate measurement of the energy barrier is required to test the validity of such a possibility. Accepting that 2.38 eV is the accurate value for the energy barrier,22 the VTST calculation proposed by Lifshitz et a1.21 has
Photodissociation of Iodobenzene Molecular Ion
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12125
L
I
2.0
I
2.5
3.0
3.5
4.0
J
29bo
4.5
INTERNAL ENERGY (eV)
Figure 4. Rate-energy dependence for reaction 1: ( 0 ) the present experimental result; VTST calculations, (-) with (I = 0.5 using eq 8 and (- -) with b = 2.5 using eq 9. The hatched region represents the region between two RRKM-QET calculations shown in Figure 3 which are the best fits to the experimental data on a microsecond time scale reported previously.22-27C
2950
3000
3050
31’00
31’50
TRANSLATIONAL ENERGY (eV)
Figure 5. Experimentalfield-off PD-MIKE spectrum for reaction 1 with 514.5-nm excitation.
been attempted in an effort to fit the experimental data over the expanded time range. In the VTST calculation, two C-I bending vibrations of CsHsI*+ (Table I) were taken as the transitional modes and were treated as hindered rotors with the barrier height Vo(r). The following expression for the barrier height proposed previously which is a decreasing function with distance along the reaction coordinate was used in the initial attempt: v 0 ( r ) = V, exp[-u(r - re)’] Here, Ve and re are the equilibrium barrier height and the equilibrium bond length, respectively; a is an adjustable parameter. Loosening of the transitional modes occurs earlier (at smaller r ) for larger a, while it occurs later for smaller u. As shown in Figure 4, however, a good fit with the experimental data could not be achieved with Vo(r) in eq 8 . A decent fit was possible (Figure 4) when the following Lorentzian type was used as the barrier height:
(9) Here, b is a parameter which plays the same role as a. Comparison with the PST rate-energy relation shows that the present VTST results mean transition-state switching from OTS to TTS occurs just above the reaction energy barrier in this ionic reaction. It is to be mentioned, however, that the transition state called TTS is tight when compared to OTS only. The high entropy of activation means that this is also a relatively loose transition state. At any rate, it is important to note that the entropy bottleneck can influence the dynamics of an ionic reaction beginning a t the internal energy slightly higher (
