50
J . Phys. Chem. 1991, 95, 50-56 versions highlights the importance of making equivalent state to state comparisons when discussing the properties of these complex excited state systems. In the earlier data based on complexes of Os", there were varying amounts of contributions to k,, from upper MLCT states, for example." From the intercept of the plot in Figure 3, Po = 5.8 X I O l 4 cm-I. On the basis of this value, the assumption that huk = 300 cm-l for the promoting mode,IOand eq 4c, it is possible to calculate a value of 91 cm-'i2 for ck. From this value and eq 5, the
vk = (hwk/2)"2ck In(k,,x
Is)
Figure 3. Plot of In [F(calcd)] vs In (knrX Is). In the correlation the slope was fixcd at I . The intercept is -34 f 0.5 and R = 0.96.
state decay at 157 K involves a MLCT state or states of common orbital origin. A more significant, quantitative correlation also exists between In (knr X Is) and In [F(calc)], eq 4b. The correlation is shown in Figure 3. The quality of the correlation is especially impressive when it is realized that the data extend over a factor of 30 in T and 3600 cm-' in emission energy. The fact that this correlation is also considerably improved over earlier room temperature
-
(5)
magnitude of the electronic interaction integral is Vk 1120 cm-I. In the earlier correlation, based on polypyridyl complexes of Os", a value of vk 1300 cm-' was found by using the same procedure. There are large uncertainties in both values.
-
Acknowledgment is made to the Department of Energy under Grant No. DE-FG05-86ER13633 for support of this research, K.R.B. acknowledges sabbatical leave support from Yarmouk University, Irbid, Jordan. Registry No. ci~-[Ru(bpy)~(py)Cl]', 47690-98-2; cis-[Ru(bpy),(NHJ),I2+, 56993-98-7; [Ru(bpy),(en)I2', 47597-15-9; [Ru(bpy),-
(Pz4B)]', 130168-47-7;~is-[Ru(bpy),(NMI),]~',85719-79-5; cis-[Ru(bpy),(pyd),]*+, 85719-80-8;cis-[Ru(bpy),(py),12', 63338-38-5; [Ru(bpy)J2', 15158-62-0; ~is-[Ru(bpy)~(lnh)~]", 130168-48-8.
Photodissociation Kinetics of the p-Nitrotoluene Molecular Ion on a Nanosecond Time Scale Joong Chul Choe and Myung So0 Kim* Department of Chemistry, Seoul National University, Seoul I51 -742, Korea (Received: April 30, 1990; In Final Form: July 11, 1990)
An experimental method has been developed to study photodissociation kinetics for polyatomic ions on a nanosecond time scale. Details of the method are described. The method has been applied to the photodissociation of the p-nitrotoluene molecular ion. Experimental rate constants were in good agreement with the Rice-Ramsperger-Kassel-Marcus (RRKM) calculation. Kinetic energy release of the photodissociation was also investigated. The experimental kinetic energy release distribution could be well explained by phase space theory.
I. Introduction When molecules are ionized in the source of a mass spectrometer, they may undergo various competing consecutive reactions. The resulting ion fragmentation pattern, which is called the mass spectrum, is of great practical importance for structural determination. Rosenstock et al.' developed a statistical model, the so-called quasi-equilibrium theory (QET), to describe the mass spectral patterns. The mathematical formalism of QET is essentially the same as that of Rice-Ramsperger-Kassel-Marcus (RRKM) theory.2 which is referred to more frequently in the unimolecular reactions of neutral molecules. QET was tested initially by comparing its predictions with the fragmentation patterns. Namely, spectral patterns were calculated by using rate constants that were evaluated theoretically for various competing consecutive reaction^.'.^ It is obvious, however, that direct comparison of rate constants instead of product abundances will be more useful for the understanding of dissociation processes. Various experimental methods have been devised to measure the dissociation rate constants for precursor ions with specified internal energy. For example, Andlauer and Ottinger4 utilized charge-exchange scattering between neutral and ion beams oc'To whom all correspondence should be addressed.
0022-3654/91/2095-0050$02.50/0
curring within the accelerating field of an ion source to measure the rate constants on the nanosecond time scale. More recently, the photoelectron-photoion coincidence (PEPICO) technique5 has been developed to study the dissociation of energy-selected polyatomic ions. Using this powerful technique, one can measure rate constants for ion dissociations on the microsecond time scale as a function of precursor internal energy. In addition, dynamically important information such as the kinetic energy release (KER) is available from the experiment. Photodissociation (PD) of polyatomic ions has been investigated since the early 1 9 6 0 ~However, ~ it was Dunbar's work since the early 1970s using the ion cyclotron resonance (ICR) spectrometer that has provided impetus for research in this area. Structures and fragmentation mechanisms of various polyatomic ions have (1) Rosenstock, H. M.; Wallenstein, M. B.; Wahrhaftig, A. L.; Eyring, H. Proc. Nall. Acad. Sci. U.S.A. 1952, 38, 667. (2) Robinson, P. J.; Holbrook, K.A. Unimolecular Reactions; Wiley: New York, 1972. (3) Vestal, M. L. J . Chem. Phys. 1965, 43, 1356. (4)Andlauer, B.; Ottinger, C. Z . Narurforsch. 1972, 27A, 293. (5) Baer, T. In Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic: New York, 1979; Vol. 1, Chapter 5. (6) Dunbar, R. C. In Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic: New York, 1979; Vol. 2, Chapter 14.
0 199 1 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 51
Photodissociation of p-Nitrotoluene Ion ARGON ION L A S E R
--'q
MIRRORS
CHOPPER
WINDOW
v
DI
I
LENS
DZ I
D3
COLLISION CELL
COLLECTOR
SOURCE
Figure 1. Schematic diagram of the VG ZAB-E mass spectrometer modified for photodissociation study.
LASER
BEAM
Figure 2. Schematic diagram of the collision cell assembly modified for
been investigated with photodissociation in ICR spe~trometer.'~ More recently, it was demonstrated that commercial double-focusing mass spectrometers could be used for photodissociation study after minor modifications. For example, Carrington and co-workersI0 reported Doppler-free spectroscopy of polyatomic ions using an ion beam photodissociation technique. Beynon and co-workers11*12 investigated kinetics and mechanisms of ion fragmentation using tandem mass spectrometric techniques available with a double-focusing mass spectrometer. Bowers and c o - ~ o r k e r sused ' ~ ~ a~ similar ~ technique to investigate the dissociation dynamics of loosely bound ion-molecule (atom) clusters. I n the present work, an attempt has been made to develop a method to measure the photodissociation rate constants of polyatomic ions on a nanosecond time scale. Details of the method and the results of its application to the following reaction will be described. F"3
11. Experimental Section
A double-focusing mass spectrometer with reversed geometry (VG Analytical Model ZAB-E) modified for photodissociation study was used in this work (Figure 1). Three windows W 1, W2, and W3 installed on the flight tube of the instrument are for collinear irradiation of the ion beam in the first and the second field-free regions and cross-beam irradiation in the second field-free region, respectively. In the present work, the laser (Spectra Physics Model 164-09 argon ion laser) was directed along the z axis through W3 for cross-beam photodissociation of the ion beam which was mass-selected by the magnetic sector. A typical laser power used was 1-2 W, and the polarization was kept along the x axis. The standard convention is adopted here for the definition of laboratory coordinates. Namely, the x axis is defined as the direction along the central ion trajectory and the z axis is the direction of the magnetic field in the magnetic sector. T h e y axis (7) Dunbar,R. C.; Kim, M. S.; Olah, G. A. J . Am. Chem. SOC.1979,101, 1368. (8) Kim, M. S.; Dunbar, R. C.; McLafferty, F. W. J . Am. Chem. SOC. 1978, 100, 4600. (9) Chen, J. H.;Dunbar, R. C. Int. J . Mass Spectrom. Ion Processes 1986, 72, 115.
(IO) Carrington, A.; Milverton, D. R. J.; Sarre, P. J. Mol. Phys. 1976,32, 297. ( I I ) Harris, F. M.; Mukhtar, E. S.; Griffiths, I. W.; Beynon, J. H. Proc. R. SOC.London 1981, A374, 461. (12) Mukhtar, E. S.; Griffiths, 1. W.;March, R. E.; Harris, F. M.; Beynon, J. H. Int. J . Mass Spectrom. Ion Phys. 1981, 41, 61. (13) Jarrold. M. F.; Illies, A. J.; Bowers, M. T. J . Chem. Phys. 1983, 79, 6086. (14) Kim, H. S.; Jarrold, M. F.; Bowers, M. T. J . Chem. Phys. 1986, 84, 4882.
photodissociation study. is taken along the direction perpendicular to both the x and z axes. Daughter ions produced by the fragmentation of mass-selected parent ions were detected by scanning the electric sector potential. This is the so-called mass-analyzed ion kinetic energy spectrometry (MIKES) in mass spectrometry. To study the kinetics of ion fragmentation on a nanosecond time scale, two parallel disk electrodes D2 and D3 (Figure 2) separated by 1 cm were installed. Each electrode has a diameter of 7 cm and has a slit (10 mm X 1 mm) in the center. High voltage could be applied to D2 which was connected electrically to the collision cell, and D3 was grounded. Electric field calculations using the SIMION programI5 showed that the effect of field penetration could be ignored for the present purpose. Translational energy of the daughter ions produced by photodissociation in this region will be discussed in the next section. The laser beam was made to cross the ion beam at a position between these electrodes, where it was focused to a spot size of -0.02 mm. At the top and bottom of the ion beam, the laser spot diameter was estimated to be -0.1 mm. Charge-exchange ionization was used to produce the molecular ion of p-nitrotoluene with rather well-defined internal energy. For this purpose, CS2 and N2 were introduced to the chemical ionization (CI) source by means of the septum and gas inlets, respectively. Reagent gas pressure in the CI source was -0.2 Torr, and the volume ratio of the gases was CS2/N2 0.25 as recommended.I6 The source was maintained at 200 'C, filament emission current was 0.5 mA, and an accelerating voltage of 8 kV was employed. The molecular ion of nitrobenzene, which was used for time zero calibration (to be discussed later), was generated by 70-eV electron ionization (EI). The ion source temperature was 200 OC, and a trap current of 200 pA was maintained. To detect weak PD signals superimposed on a strong metastable decomposition background, the laser beam was modulated with a chopper (EG&G Model 125A), and phase-sensitive detection (EG&G Model 5208 lock-in amplifier) was employed. Output from the lock-in amplifier was transmitted to the mass spectrometer data system (VG Model 11-2505). To improve the quality of a PD/MIKE spectrum, signal averaging was carried out for repetitive scans. Errors quoted in this work were estimated from several duplicate experiments at a 95% confidence limit. All the chemicals used in this work were of the best grade commercially available.
-
111. Principle of the Method
When photodissociation occurs in the region between D2 and D3 (Figure 2) h
ml+ 2 m,+*
-
m2+
+ m3
(2)
the translational energy of the daughter ion (mz') changes depending on the site of dissociation. Since the ion velocity at 8 (15) Dahl, D. A,; Delmore, J. E. EGG-(3-7233, 1988, Rev. 2. (16) Meot-Ner, M.; Hamlet, P.; Hunter, E. P.; Field, F. H. J . Am. Chem. SOC.1978, 100, 5466.
52 The Journal of Physical Chemistry, Vol. 95, No. 1, 1991
Choe and Kim
keV is approximately IO7 cm/s, the transit time is 1 ns per 0.1 mm (laser beam diameter at the top or the bottom of the ion beam). When 1 k V is applied to the D2 electrode, this length corresponds to a IO-V potential difference. Since the electric sector in the present instrument has an energy resolution better than 1 eV, a timc resolution of 1 ns can be achieved, in principle, by analyzing the translational energy of the daughter ion. In addition to kinetic considerations, the in-field PD/MIKE band shape is influenced by various factors such as the inherent MIKE peak profile and the internal energy distribution for the parent ions. A. Dissociation Time us Translational Energy. Since the time dependence of photodissociation appears as a broadening of the MIKES profile, namely, the translational energy distribution for the daughter ions, a proper relation between the time scale and the translational energy should be established first. The origin of the x axis is taken as the crossing point between the x axis and the D2 electrode (Figure 2). Suppose that the parent ion which was photoexcited at xo dissociates at x according to reaction 2 . The translational energy of m l + at x is given by K , ( x ) = eV - eV’(d - x ) / d (3)
been devised to obtain the KER distribution (KERD, n ( T ) ) from the MIKES profile. According to the algorithm reported in ref 20, which is essentially the same as that of Jarrold et aI.,l9 the area-normalized peak shape function centered at K , (eq 8 ) is related to n ( T ) as follows
-
where eV is the ion accelerating energy in the source, V’is the potential applied to D2, and d is the spacing between electrodes D2 and D3. I f the dissociation occurs at x without any kinetic energy release, the translational energy of m2+ at x is given by K2b) = (mdm~)K~(x)
Y I = m I ,/ 4m2m3K~
(10)
Here K 1 is the parent ion translational energy. A function proportional to the first derivative of h , ( t ) was defined as follows: 1 dhl(t) g,(c) = - - -
-
YI de Then the coordinate transformation c ( T / Y ~ ) converted ’/~ gl(c) into n ( T ) . To find the exact functional dependence of h,(c) on the parent ion translational energy, the following function will be defined
Then from eq 9 one obtains
(4)
Due to further acceleration by the field, the translational energy of m2+ at the exit electrode (D3) becomes
K2&) = ( m 2 / m l ) e V + ( m 3 / m 1 ) e V ’ ( d- x ) / d
where
h,(c) = (Y11’2/2)lf(m)
-f(r1c2)1
(13)
Since n(T) usually falls off exponentially at large T,f(T) is nearly an exponentially decreasing function also. Hence
(5)
h,(c) = - ( Y 1 1 / 2 / 2 ) f ( Y l e 2 )
(14)
This is the translational energy analyzed by the electric sector. The transit time between xo and x which corresponds to the lifetime of a particular parent ion can be evaluated from the velocity of the parent ion and the acceleration ( a = e V ’ / d m , ) by the field:
For the dissociation of the parent ion with an arbitrary translational energy, K , the peak shape function will be designated h ( t ) . Then, the coordinate transformation
t = (uI(x) - o l ( x 0 ) ) / a= ( { ( 2 / m l ) [ e v -eV’(d - ~ ) / d l ) ~-/ ’ 1 ( 2 / m l ) [ e v -eV’(d - ~ O ) / d l ) ~ / ~ ) / ( e V ’ / (d6m) , )
with
Substituting eq 5 into eq 6, a relation between the time of dissociation and the daughter ion translational energy is obtained
results in the following relation:
Equation 7 can be used for interconversion between the translational energy scale in a MIKE spectrum and the time scale. For this conversion the zero-time position, namely, the position of interaction between the laser and the ion beam, needs to be known accurately. This can be achieved by recording a PD/MIKE spectrum for a reaction occurring faster than the nanosecond time scale. B. MIKE Peak Profile. It has been discussed so far that the daughter ions formed at different positions in the field region appear at different translational energies in the MIKE spectrum (eq 5). In addition to the peak position, its profile is also affected by the position of dissociation. This is because the magnitude of the peak broadening observed in the MIKE spectrum depends on the translational energy of the parent ion. To account for this effect, peak broadening in the absence of the applied field (V’ = 0) will be considered first. In the absence of the applied field, the daughter ion peak in the MIKE spectrum is centered at the following translational energy K2 = ( m 2 / m 1 ) e V (8) This peak is symmetrically broadened due to the kinetic energy release (KER, T ) in the dissociation. Various technique^"-*^ have ( 1 7) Holmes, J. L.; Osborne, A. D. Int. J . Mass Spectrom. Ion Pbys. 1977, 23. 189. (18) Mendez-Amya, A.; Brenton. A. G.;Szulejko, J. E.; Beynon, J. H. Proc. R. Soc. London 1980, A373, 13.
-
(Y/71)l/26
(15)
= m12/4m2m3K
(16)
= (Y/Yl)1/2hl[(Y/Yl)1’2€l
(17)
In the present work, the PD/MIKE peak shape was obtained in the absence of the applied field (V’ = 0). Then the expected peak shape for the dissociation occurring at x in the presence of the field was calculated from the field-free peak shape via eq 17. It was shown that the position of dissociation, the translational energy of the parent ion dissociating at this position, and the transit time are interrelated. Hence, the expected peak shape for the dissociation occurring at x will be designated h(t,t). The coordinate transformation t E - K2d(x) (18) converts h(c,t) into h(E,t),which is the expected normalized peak shape in the MIKE spectrum. Here E represents the translational energy in the MIKE spectrum. C. PDIMIKE Band Shape. I ( t ) will be defined as the probability density for dissociation occurring at time t after photoexcitation. When the dissociation is described by a single rate constant k , I ( t ) is given by +
I ( t ) = ke-k‘ (19) k represents the total rate constant for the dissociation of the parent ion. k is the sum of individual rate constants when competing reactions (19) Jarrold, M. F.; Illies, A. J.; Kirchner, N. J.; Wagner-Redeker, W.; Bowers, M. T.; Mandich, M. L.; Beauchamp, J. L. J . Phys. Cbem. 1983.87, 2213. ( 2 0 ) Choe, J. C.; Kim, B. J.; Kim, M. S. Bull. Korean Cbem. Soc. 1989,
-10.- (21) .161. -Levsen, K. Fundamental Aspects of Organic Mass Spectrometry;
Verlag Chemie: Weinheim, 1978.
The Journal of Physical Chemistry, Vol. 95, No. 1 , 1991 53
Photodissociation of p-Nitrotoluene Ion
5550
5600
TRANSLATIONAL
5650
ENERGY,
eV
Due to the thermal internal energy distribution for the parent ions generated in the source, dissociation rate constants are expected to display a certain distribution also. In the general case, [ ( I ) may be expressed as
1
P(k)ke-kfd k
(20)
Here P ( k ) is the probability distribution for the rate constant. The overall PD/MIKE band shape for dissociation occurring between the electrodes D2 and D3 can now be expressed as follows:
H ( E ) = I f 0d Z ( f ) h(E,t) d t
5300
5380
TRANSLATIONAL
Figure 3. Experimental PD/MIKE peaks for reaction I . Solid curve was obtained with 2 kV of applied voltage (V?. Dashed curve is the field-free (V' = 0) result converted according to eqs 17 and 18. Laser wavelength was 514.5 nm.
I(?) =
5220
(21)
Here td is the transit time of the parent ion from xo to d . The following procedure was used to obtain Z(t) from the overall band shape. First of all, h(E,t)'s were calculated at constant time interval from the field-free PD/MIKE peak shape. Then Z(t) was calculated through band fitting using h(E,t)'sas the basis functions for regression analysis.
IV. Results and Discussion A. Time Zero Calibration. The first step in the analysis of a PD/MIKE band shape is to relate the daughter ion translational energy to the transit time (eq 7). For this purpose, accurate knowledge of the time zero position (xo), namely, the position of the laser beam/ion beam crossing, is needed. In the present work, photodissociation of nitrobenzene molecular ion was utilized for time zero calibration:
ENERGY,
eV
Figure 4. Experimental field-free PD/MIKE spectrum for reaction with 488.0-nm excitation.
t W
t-
5
W
-c>
4:
J W
Q
I
,
4800
4950
TRANSLATIONAL
I
ENERGY,
5100 eV
Figure 5. PD/MIKE spectrum for reaction I obtained at -2 kV of
applied voltage with 488.0-nm excitation. Experimental result is shown as open circles. Solid curve denotes the calculated result using k, = 1.6 X
lo8 s-' and a = 4.8.
Based on a previous study of this reaction,22the lifetime of the photoexcited nitrobenzene molecular ion is expected to be 1 ns or less. A PD/MIKE band shape for this reaction obtained with 2 kV of applied field ( V ? is shown in Figure 3. The very symmetric nature of the band shape indicates that the dissociation occurred faster than could be resolved with the present technique. Also shown in the figure is the field-free (V' = 0) PD/MIKES profile which was converted according to eqs 17 and 18. Maximum positions of these two bands could be made to coincide by using an xo value of 0.251 f 0.004 cm in eq 5 . The in-field PD/MIKES profile is slightly broader than that of the converted field-free PD/MIKE peak. The additional band broadening for the former may be attributed to incorrect alignment of the laser beam along the z axis. In the case shown in Figure 3, it was estimated that the laser beam was tilted by ~ 0 . from 3 ~the z axis. At this tilting angle, the xo positions at the top and the bottom of the ion beam are expected to differ by -0.05 mm. This
difference is small enough for nanosecond time resolution. In the actual experiment, the laser beam was aligned such that satisfactory coincidence could be achieved between the two PD/ MIKES profiles. Then the PD/MIKES experiment was carried out for the desired reaction. Duplicate experiments showed that the procedure was adequate for the present purpose. B. Photodissociation Kinetics. A field-free PD/MIKE spectrum for reaction 1 is shown in Figure 4. The small peak on the low-energy side of the main peak is due to the H N 0 2 loss reaction from the molecular ion. The intensity of this side peak was less than 6% of the main peak when the 488.0- or 514.5-nm line of the laser was used. In the peak shape analysis, only the highenergy half of the main peak was used. In-field PD/MIKES experiments were carried out using a range of applied potential (V' = -2.5, -2, -1.5, and 2 kV). Figure 5 shows a PD/MIKE spectrum obtained at -2 kV of applied voltage with the 488.0-nm laser line. Substantial tailing of the band toward high translational energy is readily noticeable. It was reported previously that the dissociations of weakly bound diatomic molecular ions could be induced by a strong electric field.23 Even though the potential applied in the present experiment was not thought to be high enough to induce dissociation reaction, the following experiments were carried out to verify this point. First of all, unimolecular decomposition of p-nitrotoluene
(22) Nishimura, T.; Das, P. R.; Meisels, G. G. J . Chem. Phys. 1986, 84, 6190.
(23) (a) Bjerre, N.; Keiding, S.R. Phys. Rev. Lett. 1986, 56, 1459. (b) Carrington, A.; McNab, I. R.; Montgomerie, C. A. Ibid. 1988, 61, 1573.
C6H5NO2'+-k C6H5N02'**
-
C6H5+ + 'NO2 (22)
54
The Journal of Physical Chemistry, Vol. 95, No. I, 1991
Choe and Kim
T
0
10 TRANSIT
20 TIME,
30
40
nsec
Figure 6. I(!) functions obtained from the PD/MIKE band shape analysis. Laser wavelength was 488.0 nm. Open and closed circles are data obtained with -2 and -1.5 kV of applied voltage, respectively. Bars represent error limits.
molecular ion was observed without laser irradiation. Regardless of the magnitude of the applied potential, the resulting metastable spectra could be interpreted in terms of well-established methods.24 Namely, no evidence was found for the occurrence of field-induced dissociation in the metastable reaction. Secondly, the integrated intensity of the fragment ion peak in the PD/MIKE spectrum was measured. The fact that the peak intensity was the same within experimental error regardless of the applied potential seemed to exclude the possibility of field-induced reaction. The in-field PD/MIKE band shape was treated according to the method described in the previous section. In the calculation, 25 basis functions sampled at equal time intervals were used. f(t) functions thus obtained were the same within experimental error regardless of the magnitude of the potential adopted in this work. I(?) functions obtained at -2 and -1.5 kV of applied voltage are shown in Figure 6 as semilog plots with respect to time. A semilog plot of I ( t ) from a perfect experiment will appear as a straight line (eq 19) if dissociation occurs with a single rate constant. To account for the apparent nonlinearity of the I ( f ) functions in Figure 6, various factors such as time zero calibration, tilting of the laser beam, electric field penetration, the number of basis functions, etc.. have been reevaluated. All these efforts failed to explain tailing of [ ( t ) functions in the long time limit. Hence, it was concluded that the tailing occurred due to the dominance of slow reactions in the long time limit. The following Gaussian function was used as the probability distribution for the rate constant: P ( k ) = 2 ( ( ~ / 7 r ) ' /exp[-a(log ~ k - log k,)2]
(23)
In this function, log k was used instead of k because the rate constant increases very rapidly with the parent ion internal energy. k, is the most probable rate constant, and CY is a constant related to the width of distribution. The P(k) function was determined through a best fit to the experimental f(t) function. The P ( k ) function thus obtained was used to calculate the in-field PD/ MIKE band shape. The calculated PD/MIKE band shape is shown in Figure 5 together with the experimental one. k, and a values used in the calculation were 1.6 X lo8 s-I and 4.8, respectively. A slight disagreement between the raw and the calculated band shapes in the low translational energy region seems to be mainly due to the laser beam tilting and the HNO, loss reaction. The P ( k ) function described above is presented in Figure 7. The most probable rate constants, k,, have been evaluated from several duplicate experiments. These were (1.7 f 1 .O) X (24) (a) Howells, S.;Brenton, A. G.;Beynon, J. H. In?. J . Mass Spectrom. Ion Phys. 1980, 32, 379. (b) Hudson, C. E.; Koppe, J. A.; McAdoo, D. J . In!. J . Mass Spectrom. Ion Processes 1987, 75, 137.
7
8
9
IO
LOG I k / s e c - ' )
Figure 7. P ( k ) functions. Solid curve was obtained from experiment (eq 23, k , = 1.6 X IO" s-I and a = 4.8). Error limit is shown. Dashed curve is the theoretical result. See text for details.
lo8 and (1.4 f 0.8) X lo8 s-I respectively for photodissociations with the 488.0- and 514.5-nm lines of the argon ion laser. From the relative intensities of peaks in PD/MIKE spectrum, the loss of 'NO2 was found to be the dominant channel (-94%) in the photodissociation of the p-nitrotoluene molecular ion. Hence, after correcting for the branching ratios, the rate constants for the reaction 1 become (1.6 f 1.0) X lo8 and (1.3 f 0.8) X IO8 s-' respectively for photodissociation at 488.0 and 5 14.5 nm. According to RRKM-QET, the microcanonical rate constant for unimolecular dissociation is given by2
Here Einand Eoare the ion internal energy and the critical energy for dissociation, respectively. d is the sum of states from the zero-point energy to Ein- Eo in the transition state. p(Ein)is the density of states for the parent ion at energy E,. u is the reaction path degeneracy. Since charge-exchange ionization was used to generate the molecular ion, its internal energy after photoexcitation is given by Ei, = RE + Eth h~ - 1E (25) Here RE is the recombination energy of CS
