Photodissociation dynamics of n-butylbenzene molecular ion

Article abstract of DOI:10.1021/jp9605818

Photodissociation dynamics of n-butylbenzene molecular ion has been investigated on a nanosecond time scale. The rate constants for production of C₇H₈^?+ and C₇H₇⁺, their branching ratios, and the kinetic energy release distributions have been determined by the photodissociation method using mass-analyzed ion kinetic energy spectrometry. The branching ratios have been found to be in excellent agreement with the previously established results. All the experimental data could be explained with statistical theories such as Rice-Ramsperger-Kassel-Marcus (RRKM) and phase space theories. RRKM fittings for these reactions have been improved. The present result supports the previous suggestion that the dissociation to C₇H₈^?+ occurs via a stepwise McLafferty rearrangement.

Full text of DOI:10.1021/jp9605818

J. Phys. Chem. 1996, 100, 13367-13374
13367
ARTICLES
Photodissociation Dynamics of n-Butylbenzene Molecular Ion
,
†
Seong Tae Oh, Joong Chul Choe,* and Myung Soo Kim*
Department of Chemistry and Center for Molecular Catalysis, Seoul National UniVersity,
Seoul 151-742, Korea, and Department of Chemistry, UniVersity of Suwon, Kyunggi 445-743, Korea
X
ReceiVed: February 27, 1996
Photodissociation dynamics of n-butylbenzene molecular ion has been investigated on a nanosecond time
•+
+
scale. The rate constants for production of C
H
7 8
7 7
and C H , their branching ratios, and the kinetic energy
release distributions have been determined by the photodissociation method using mass-analyzed ion kinetic
energy spectrometry. The branching ratios have been found to be in excellent agreement with the previously
established results. All the experimental data could be explained with statistical theories such as Rice-
Ramsperger-Kassel-Marcus (RRKM) and phase space theories. RRKM fittings for these reactions have
•
+
been improved. The present result supports the previous suggestion that the dissociation to C
via a stepwise McLafferty rearrangement.
7
H
8
occurs
ions.7
-14
For example, non-RRKM nature in the dissociation
1. Introduction
of photoexcited tert-butylbenzene ion has been observed through
The kinetics of unimolecular ion dissociation has been a
1
2
PD-MIKES investigation.
Dissociation of n-butylbenzene ion has been the focus of
subject of general interest in chemistry and related fields. In
particular, the successful interpretation of breakdown patterns
in the mass spectra of polyatomic molecules with the quasi-
equilibrium theory (QET) led to the establishment of mass
1
5-28
intensive research effort
ever since the pioneering ion-beam
15-17
photodissociation experiments by Beynon and co-workers.
In particular, the branching ratio for the production of m/z 91
and 92 was found to depend sensitively on the photon energy,
suggesting its use as a thermometer for determining the internal
energy.
1
spectrometry as a useful analytical technique. The quasi-
equilibrium theory, which is mathematically equivalent to the
microcanonical Rice-Ramsperger-Kassel-Marcus (RRKM)
theory for unimolecular dissociation, is usually referred to as
RRKM-QET.2 Breakdown patterns utilized to test RRKM-
QET in the early days were basically determined by the relative
magnitudes of rate constants of various reaction channels.
Instead of these, measurement of the rate constant for the
dissociation of energy-selected polyatomic ions would be more
useful for the test of RRKM-QET and its application to the
study of reaction mechanism. Some experimental techniques
such as photoelectron-photoion coincidence (PEPICO) spec-
,3
C7H8•+ (m/z 92) + C3H6
(1)
n-C6H5C4H9•+
+
•
C
7
H
7
(
m
/
z
9
1
)
+
C
3
H
7
(2)
In fact, such a sensitive dependence is expected because the
rate-energy dependences for the two reactions, reaction 1
occurring via a rearrangement (McLafferty) and reaction 2
occurring via a simple bond cleavage (R), are widely different.
However, the above ion-beam results were found to be
inconsistent with later investigations with charge exchange
4
trometry and photodissociation in ion cyclotron resonance (PD-
5
ICR) spectrometer have been developed for the above purpose.
However, these techniques which have made tremendous
contribution to the study of the kinetics and dynamics of
unimolecular ion dissociation over the years allow rate constant
measurement on milli- to microsecond time scale only. Re-
19
ionization by Harrison and Lin and with PD-ICR by Dunbar
21
and co-workers. The latter investigators attempted an RRKM-
6
cently, we have developed a technique based on the mass-
QET fit to explain their 91/92 ratios and suggested that shifting
the energy scale of the ion-beam results to higher energy by
analyzed ion kinetic energy spectrometry (MIKES) of photo-
dissociation products in a double-focusing mass spectrometer,
namely PD-MIKES, which allows rate constant measurement
on a nanosecond time scale. Hence, combining the rate-energy
data available from the above techniques, it is now possible to
investigate a unimolecular ion dissociation over 6 orders of
magnitude in time scale. In addition to the rate constant, the
kinetic energy release distribution (KERD) can be measured
also with PEPICO and PD-MIKES, which provides useful
information on the exit channel dynamics. This advantage has
been utilized for the studies of dissociation of various molecular
1
.5-2 eV would bring them into reasonable accord with other
results. That is, this amount of energy would correspond to
the internal energy of the parent ions being photoexcited.
The most detailed investigation so far on the kinetics and
dynamics of n-butylbenzene ion dissociation has been carried
27
out by Baer et al. using PEPICO. The 91/92 branching ratio
was measured over an internal energy range 2-6.5 eV, and the
rate constant for the production of m/z 92 fragment ion was
determined over a narrow internal energy range corresponding
5
6
-1
to rate constant of 10 -10 s . Even though the measured
1/92 ratios were in reasonable agreement with the charge
9
*
Authors to whom correspondence should be addressed.
University of Suwon.
Abstract published in AdVance ACS Abstracts, July 1, 1996.
19,20
21
†
exchange ionization
and PD-ICR results, the rate constants
X
were found to be larger by 2 orders of magnitude than predicted
S0022-3654(96)00581-3 CCC: $12.00 © 1996 American Chemical Society

13368 J. Phys. Chem., Vol. 100, No. 32, 1996
Oh et al.
by Dunbar and co-workers.21 An RRKM-QET fit of the above
data was utilized to investigate the reactions. In particular, the
stepwise occurrence of the McLafferty rearrangement leading
•+
to 92 was inferred from the rate result together with the kinetic
2
8
energy release data reported by Holmes and Osborne.
Our instrumentation for PD-MIKES bears some resemblance
to Beynon’s,15 even though details of the technique are quite
different. Hence, we have felt it necessary to investigate the
91/92 ratio problem to see if the results are in accord with the
results from well-established methods such as PEPICO. Also,
nanosecond rate-energy data and KERD available from the
present investigation have been utilized here to deepen our
understanding of the kinetics and dynamics of reactions 1 and
2.
2. Experimental Section
The experimental setup has been described in detail else-
6
where and will be reviewed only briefly here. A double
focusing mass spectrometer with reversed geometry (VG
Analytical Model ZAB-E) modified for photodissociation study
was used. n-Butylbenzene ions generated by charge exchange
in the ion source and accelerated to 8 keV were mass-analyzed
by the magnetic sector. Then, the ion beam was crossed with
the laser beam in the field region of an electrode assembly
located near the intermediate focal point of the instrument. The
Figure 1. MIKE spectra for dissociation of n-butylbenzene ion: (a)
metastable ion decomposition; (b) field-off photodissociation at 488.0
nm. m/z of the fragment ion corresponding to each peak is indicated.
607.5 nm output of a dye laser (Spectra Physics Model 375B)
and the 514.5 and 488.0 nm lines of an argon ion laser (Spectra
Physics Model 164-09) were used. The translational kinetic
energy of the fragment ions was analyzed by the electric sector.
This is called the mass-analyzed ion kinetic energy spectrometry.
Since a MIKE spectrum contains contributions from metastable
ion decomposition (MID) and collision-induced dissociation by
residual gas, phase-sensitive detection was adopted to record a
MIKE spectrum originating from photodissociation, namely, a
PD-MIKE spectrum. To improve the quality of a MIKE
spectrum, signal averaging was carried out for repetitive scans.
Errors quoted in this work were estimated from several duplicate
experiments at 95% confidence limits. For the photodissociation
experiment, CS2 was used as the reagent gas for charge exchange
ionization. The ion source chamber was maintained at 140 °C.
For the MID experiment, 70 eV electron ionization was used
at an ion source temperature of 200 °C.
3. Results
It is well-known that the production of the m/z 92 ion
dominates the dissociation of n-butylbenzene ion on a micro-
second time scale.27 In the MID-MIKE spectrum of n-
butylbenzene ion recorded in this work, the m/z 92 peak has
been found to constitute more than 97% of the total daughter
ion. The m/z 91 ion was hardly observable as shown in Figure
Figure 2. PD-MIKE spectra for dissociation of n-butylbenzene ion
obtained at 1.5 kV applied on the electrode assembly: (a) 488.0 and
1a. On the other hand, both the peaks at m/z 91 and 92 appear
prominently in PD-MIKE spectra as shown in Figure 1b. The
spectrum in the figure was recorded without the applied voltage
on the electrode and is called a field-off PD-MIKE spectrum.
Substantial noise appears at the m/z 92 position in this spectrum
due to the presence of a strong metastable background,
prohibiting a reliable determination of the branching ratio. This
difficulty can be overcome by recording a field-on PD-MIKE
spectrum, namely a spectrum obtained with a high voltage
applied at the electrode assembly. Field-on PD-MIKE spectra
with 1.5 kV applied voltage are shown in Figure 2. With the
applied voltage, the PD-MIKE spectra tail toward lower
translational energy, which is due to a distribution of time delay
between photoexcitation and dissociation. The tailing is more
severe with 607.5 nm excitation than with 488.0 nm because
(
b) 607.5 nm excitations. Experimental and calculated results are shown
as filled circles and solid curves, respectively. m/z of the fragment ion
corresponding to each peak is indicated.
the lifetime is longer in the former. Relative abundances of
the m/z 91 and 92 ions can not be determined readily from the
field-on PD-MIKE spectra, however, because the two peaks are
not well resolved. At the three excitation wavelengths used in
this work, the combined intensities of the m/z 91 and 92 ions
were ∼90% of the total daughter ion yields. The remainder
was mostly due to the m/z 105 peak, which was not useful for
kinetic analysis because of a poor signal-to-noise ratio. The

Photodissociation Dynamics of n-Butylbenzene Molecular Ion
J. Phys. Chem., Vol. 100, No. 32, 1996 13369
TABLE 1: The 91/92 Branching Ratios and Dissociation
Rate Constants Derived from PD-MIKES Peaks
rate constant (10 s-1)
8
λa (nm) Eb (eV) 91/92 ratio
totalc
m/z 91d
m/z 92e
607.5
514.5
488.0
3.71 0.72 ( 0.16 1.8 ( 0.5 0.68 ( 0.25 0.94 ( 0.35
4.08 1.15 ( 0.10 5.9 ( 1.0 2.8 ( 0.6
4.21 1.30 ( 0.10 7.5 ( 1.6 3.8 ( 1.0
2.5 ( 0.5
2.9 ( 0.8
a
Photodissociation wavelength. b Average internal energy of the
c
molecular ion after absorption of a photon. Average total dissociation
d
+
rate constant. Average rate constant for the production of C H .
7 7
e
•+
7 8
Average rate constant for the production of C H .
Figure 3. Plots of (a) log (log k) and (b) log (91/92 ratio) vs the
pressure of the reagent gas in the ion source used for charge exchange
ionization; 488.0 nm excitation. Filled circles represent experimental
data. The solid lines are obtained from linear regression of experimental
data.
method to determine the 91/92 ratio and the photodissociation
rate constant simultaneously via peak shape analysis is described
below.
The PD-MIKE peak shapes can be analyzed as described in
detail previoulsy,6 the only difference being that overlapping
of peaks from two channels instead of one should be taken into
account. The overall PD-MIKE peak shape obtained with an
applied voltage is expressed as a weighted sum of h(K;t), which
is the peak shape function for the dissociation occurring at time
t.
,10
Figure 4. Kinetic energy release distributions in dissociation of
•+
n-butylbenzene ion: (a) metastable ion decomposition to C H ;
7 8
•
+
+
7
H(K) )
∫
P(t) h(K;t) dt
(3)
photodissociation to (b) C
H
7 8
and (c) C
7
H
at 488.0 nm. Experi-
mental results are shown as filled circles. Theoretical (phase space
theory) are shown as solid curves. Bars represent error limits.
Here, K is the translational energy scale in the MIKE spectrum
and P(t) is the probability density for dissociation at time t.
In our previous photodissociation studies, 10,11,13 lowering of
the internal energy of the molecular ions due to collisional
relaxation in the ion source was observed and a method was
devised to correct for its influence on the measured rate constant.
Following the same procedure, the collisional relaxation-free
rate constant was estimated by extrapolating the high-pressure
data to the zero-pressure limit. An example is shown in Figure
The relation between P(t) and the rate constant distribution was
described previously.10 Then, the latter can be determined via
regression. The PD-MIKE contour to be analyzed here consists
of two peaks, m/z 91 and 92, and this fact must be incorporated
into eq 3. It will be assumed that P(t) is the same for the two
reaction channels, which means that the two reactions occur
competitively. This assumption will be further discussed later.
Then, taking the 91/92 ratio, â, as an adjustable parameter, the
following expression for h(K;t) has been used.
3
a for a set of rate constant data obtained at 488.0 nm. In
addition to the rate constant, the 91/92 branching ratio has been
found to depend on the ion source pressure also. A semi-log
plot of the experimental ratio has been drawn as shown in Figure
h(K;t) ) h (K;t) + âh (K;t)
(4)
9
2
91
3
b and the collisional relaxation-free ratio has been estimated
hi(K;t) is the normalized peak shape function for dissociation
to mi/z ion at time t, which can be estimated from the
corresponding field-off spectrum. After determining â and rate
constant distribution via regression, the peak contour was
recalculated. For example, the recalculated contours are shown
in Figure 2, a and b, demonstrating successful analyses. The
by linear extrapolation of the high-pressure data to the zero-
pressure limit. The total rate constants and the 91/92 ratios
thus obtained are summarized in Table 1. The individual rate
constants for reactions 1 and 2 evaluated from their branching
ratios and the total rate constants are also listed in the same
table.
91/92 ratios in these cases are 1.20 and 0.50, respectively, and
Kinetic energy release distributions (KERDs) have been
the average rate constants evaluated from the distributions are
determined from MIKE peak profiles using a well-established
8
8
-1
29
6.0 × 10 and 1.3 × 10 s . The internal energy distribution
method.
For a more reliable determination of KERD in
originating from the thermal energy necessitates the use of a
distribution rather than a single value of the rate constant, which
will be discussed later.
metastable ion decomposition (MID), a MIKE spectrum for MID
occurring inside the cell located near the intermediate focal point
30
has been obtained by floating the cell at high voltage (1.5 kV).

13370 J. Phys. Chem., Vol. 100, No. 32, 1996
Oh et al.
TABLE 2: Thermochemical Data
∆
H°f298a
(kJ/mol)
∆H°f0b
(kJ/mol)
IEc
(eV)
species (structure)
d
32e
8.66e
n-C
n-C
6
H
H
5
C
C
4
H
H
9
-13.2
•
+
822e
e
6
5
4
•
9
867
+
d
f
C
6
H CH
cyclohexadiene ion)
6
2
(5-methylene-1,3-
934
914
897
957
g
f
937
+
h
h
C
6
H
5
CH
2
(benzyl ion)
919
•
d
d
n-C
H
3 7
100.5
115
i
f
9
8
5.0
6.6
109
j
f
101
d
f
C
3
H
6
(propene)
20.2
33
a
Heat of formation at 298 K. Heat of formation at 0 K. c Ionization
b
d
e
f
energy. Reference 31. Reference 27. Values converted from 298
Figure 5. Internal energy distributions of n-butylbenzene ions in the
ion source, P (E), generated by charge exchange ionization and at the
s
K data. Reference 21. h Reference 38. Reference 39. Reference 40.
g
i
j
laser-ion beam crossing point, P(E).
The KERD in MID to m/z 92 ion thus determined is shown in
Figure 4a. KERDs in photodissociation have been evaluated
from field-off PD-MIKE spectra. The outer halves of the two
MIKE peaks for m/z 91 and 92 ions have been used to minimize
the interference between the two. KERDs in photodissociation
were rather insensitive to the ion source pressure, making it
unnecessary to correct for the collisional relaxation effect.
KERDs in photodissociation to m/z 92 and 91 at 488.0 nm are
shown in Figure 4, b and c, respectively.
molecular ions. This distribution for the molecular ions getting
photoexcited can be estimated by the random lifetime distribu-
2
tion.
P(E) ) P (E) exp[-k(E)τ]
(6)
S
Here, τ is the flight time of the molecular ion to the laser-ion
beam crossing point which is estimated to be 30 ( 2 µs at 8
keV acceleration energy in the ion source. The rate-energy
dependence, k(E), can be taken from the data reported by Baer
4. Discussion
2
7
A. Internal Energy. The internal energy of the molecular
et al. P(E) thus estimated is shown in Figure 5. The average
internal energy evaluated from P(E) is 1.67 eV. Adding the
photon energy results in the average total internal energy of
the photoexcited ion, which is 3.71, 4.08, and 4.21 eV at 607.5,
514.5, and 488.0 nm excitations, respectively. The average
internal energy of the molecular ions undergoing MID has been
ion generated by charge exchange ionization which was used
1
0
in the photodissociation study is well approximated by
E ) RE - IE + Eth
(5)
7
provided that collisional relaxation is not involved. Here, RE
is the recombination energy of CS2• and IE is the ionization
energy for n-butylbenzene. Their best literature values are
estimated similarly, which is 1.70 eV.
+
B. The 91/92 Branching Ratio. This ratio increases with
the molecular ion internal energy according to all the previous
investigations using various methods.
3
1
27
15-21,27
1
0.07 and 8.66 eV, respectively. (Thermochemical data are
summarized in Table 2.) Eth is the thermal internal energy at
40 °C. Its distribution has been calculated with the molecular
Among these
2
7
previous reports, data obtained by Baer et al. with PEPICO
are thought to be the most reliable. The previous ion-beam
1
6
15
parameters in Table 3 as previously. The internal energy
distribution, Ps(E), for the molecular ions in the ion source thus
estimated is shown in Figure 5. Essentially all the molecular
ions possess internal energies higher than the critical energy of
photodissociation results were reported as a function of the
photon energy only, disregarding the internal energy of the
molecular ions getting photoexcited. We also do not have much
confidence in the charge exchange ionization results
19,20
because
2
7
∼
1 eV for reaction 1 which is the least endoergic channel.
some needed calibrations such as the correction for the colli-
sional relaxation were not made. The results from the PD-ICR
Hence, dissociation of some molecular ions during the flight
between the ion source and the laser-ion beam crossing point
will alter the internal energy distribution for the surviving
2
1
work agree reasonably well with the PEPICO results. The
91/92 ratios obtained in the present work are compared with
TABLE 3: Molecular Parameters Used in the Calculations of Thermal Energy Distribution, Rate Constants, and KERDs
vibrational frequencies (cm-1)
a
•
+b
n-C
6
H
5
C
4
H
9
3000(14), 1460(11), 1260(7), 1060(10), 910(6), 730(5), 590(2), 435(4), 265(4), 180, 90(2)
3000(13), 1460(11), 1260(7), 1060(10), 910(6), 730(5), 590(2), 500(4), 340(4), 260, 135(2)
3000(14), 1460(11), 1260(7), 1060(10), 910(5), 730(5), 560(2), 320(4), 150(4), 120, 70(2)
3010(8), 1510(6), 1240(7), 1010(7), 790(5), 570(2), 430(2), 340, 210
2940(7), 1480(7), 1210(5), 1045(4), 940(4), 730(4), 485(4), 370
2930(7), 1420(6), 1250(3), 1080(2), 960(2), 860, 740, 340, 230
•
•
+
(TS1)c
C
C
C
C
6
6
7
7
H
5
5
8
7
C
C
4
H
H
9
+
(TS2)d
H
H
H
4
9
•
+e
+f
•g
n-C
3
H
6
7
h
C
3
H
3091, 3017, 2991, 2973, 2953, 2932, 1653, 1459,1443, 1419, 1378, 1298, 1174, 1045, 990,
945, 914, 912, 575, 428, 188
rotational constant (cm-1)
i
polarizability (10 cm3)
i
-24
•+
n-C
6
H
5
C
H
4 9
0.035
0.097
0.099
0.441
0.507
•
+
C
C
7
H
8
+
7
H
7
•
n-C
C H
3 6
3
H
7
5.8
6.2
a
Numbers in parentheses denote the degeneracies of vibrational modes. Reference 27. c Transition state for the production of C
b
•+. d Transition
H
7 8
+
e
f
g
state for the production of C H . Values obtained from the frequencies for toluene from ref. 34. Reference 38. Values obtained from the
frequencies for n-propyl halides from ref. 41. Reference 35. Estimated values.
7 7
h
i

Photodissociation Dynamics of n-Butylbenzene Molecular Ion
J. Phys. Chem., Vol. 100, No. 32, 1996 13371
ment via a distonic ion intermediate (DII) as shown in Scheme
1
. The reaction occurs on a double-well potential energy
surface, the first step being rate-determining while the second
step determines the KERD.
As the first step to investigate the dynamics of this reaction,
the KERD determined in this work is compared with the
prediction from a statistical theory. The phase space theory
32
formalism which is easily applicable to dissociation occurring
via a loose transition state without a reverse barrier would be
adequate for this purpose.
E-E0-T
n(T;J,E) ∝
∫
F(E - E - T - R)P(T,J,R) dR (7)
0
Rm
Here, n(T;J,E) is the KERD at a given angular momentum J
and internal energy E. The root-mean-square average J value
Figure 6. The 91/92 branching ratio as a function of n-butylbenzene
ion internal energy. The present photodissociation results are shown
as filled circles (b). The PEPICO results of Baer et al. (0) and PD-
ICR results of Dunbar and co-workers (4) are also shown. The solid
curve represents the theoretical result calculated from the rate-energy
curves in Figures 7 and 8 at 298 K.
3
3
evaluated at the ion source temperature has been used. F and
P are the product vibrational and angular momentum state
densities, respectively. R is the product rotational energy and
Rm is its minimum. E0 is the reaction critical energy which
may be set equal to the reaction endoergicity at 0 K under the
assumption of an extremely loose transition state. According
to Scheme 1, 5-methylene-1,3-cyclohexadiene ion and propene
are the reaction products. The heat of formation of the ionic
product is not well established. The values of E0 estimated from
the PEPICO and PD-ICR data in Figure 6. The original PD-
2
1
ICR data reported by Dunbar and co-workers have been
corrected for the thermal energy. Agreement among the data
is remarkable considering that the three methods being compared
operate on totally different principles. The results render a
partial support to the general validity of the present PD-MIKES
techniques, the method for the internal energy estimation in
particular.
2
1,31
two recent heats of formation data
(Table 2) are 1.07 and
1
.27 eV. E0 of 1.17 eV, average of the two, has been used in
the present calculation. KERDs have been calculated at various
internal energies and averaged over the internal energy distribu-
tions for the molecular ions undergoing MID and photodisso-
It has been generally accepted that the 91/92 ratios reported
by Beynon and co-workers15 in the photodissociation of
34,35
ciation, respectively. The molecular parameters
used in the
n-butylbenzene ion generated by 70 eV electron ionization
deviate from other results due to the neglect of the internal
energy of the ion getting photoexcited. In this regard, we have
measured the 91/92 ratios in PD-MIKES of molecular ions
generated by 70 eV electron ionization also. These are 0.23,
calculations are listed in Table 3. Theoretical KERDs shown
in Figure 4a,b agree with the experimental ones virtually within
error limits, respectively. It is to be noted that rearrangement
reactions usually display kinetic energy releases much larger
3
6
than statistical predictions. Hence, the above results indicate
that the separation of the ionic and neutral products in reaction
0.54, and 0.66 at 607.5, 514.5, and 488.0 nm excitations, re-
spectively. These values are smaller than reported by Beynon
and co-workers. Such a difference is thought to arise from the
fact that ions are irradiated perpendicularly near the intermediate
focal point in the present experiment while the entire second
field-free region was irradiated by Beynon and co-workers.
Comparing the present results with the solid curve in Figure 6
which is the energy dependent 91/92 ratio obtained through
RRKM-QET fitting to be described later, the average internal
energies of 3.14, 3.60, and 3.74 eV are estimated for the
photoexcited molecular ions with 607.5, 514.5, and 488.0 nm,
respectively. (Since the solid curve has been estimated at 298
K, the additional rotational energy of 0.02 eV at 473 K, the ion
source temperature in this photodissociation experiment, is
added.) Then, subtracting the photon energies, the average
internal energies of molecular ions getting photoexcited esti-
mated from 607.5, 514.5, and 488.0 nm experiments become
1
occurs via a loose transition state without a significant reverse
barrier over a microsecond to nanosecond time scale, in
agreement with Scheme 1.
The rate constant for this reaction has been calculated with
2
,3
the RRKM-QET formalism.
q
W (E - E )
0
k(E) ) σ
(8)
hF(E)
q
Here, F is the density of states of the reactant ion, W is the
state sum at the transition state, and σ is the reaction path
degeneracy. Since the difference in the external rotational
moments of inertia between the reactant and the transition state
is generally ignored, the rotational energy has not been included
in the estimation of the ion internal energy. In a usual RRKM
fitting of rate-energy data for a particular channel, the critical
1.10, 1.19, and 1.20 eV, respectively. The molecular ions
q
energy and the activation entropy at 1000 K (∆S ) are treated
getting photoexcited possess ∼1.16 eV of internal energy, the
value being remarkably consistent in the three experiments. This
suggests overall validity of the present method again. Also,
this supports the argument that the neglect of the ion internal
energy in the previous ion-beam photodissociation experiment
was responsible for its mismatch with other data.
37
as two parameters to be adjusted. These two parameters have
been varied to fit both the present and PEPICO rate constant
data. Assuming that the isomerization in Scheme 1 is the rate-
determining step, a C-H stretching mode (3000 cm ) has been
taken as the reaction coordinate and σ of 2 has been used. Even
-1
2
7
-1
C. Production of C7H8•+. As was pointed out in an earlier
though Baer et al. took a 910 cm mode as the reaction
section, the rate-energy dependence for this channel measured
SCHEME 1
with PEPICO27 required the participation of a tight transition
2
8
state while the KERD measured by Holmes and Osborne
indicated dissociation via a loose transition state. To accom-
modate these apparently conflicting results, Baer et al. suggested
that the reaction occur by the stepwise MaLafferty rearrange-

13372 J. Phys. Chem., Vol. 100, No. 32, 1996
Oh et al.
Figure 7. Rate-energy dependence for the dissociation of n-
Figure 8. Rate-energy dependence for the dissociation of n-
•+
butylbenzene ion to C
7
H
8
. The present photodissociation results are
+
butylbenzene ion to C
7
H
7
. The present photodissociation results are
shown as filled circles (b). The PEPICO results of Baer et al. (0) are
also shown. The theoretical result (RRKM-QET) is shown as a solid
shown as filled circles (b). The rate-energy data estimated from the
curve in Figure 7 and the 91/92 ratios of Baer et al. (0) and Dunbar
and co-workers (4) are also shown. The theoretical result (RRKM-
curve. Rate parameters used in the calculation are E ) 1.12 eV and
0
q
∆
S ) -5.49 eu. Bars represent error limits.
QET) is shown as a solid curve. Rate parameters used in the calculation
q
are E
0
) 1.61 eV and ∆S ) 7.28 eu. Bars represent error limits.
coordinate and used σ of 1, variation of these parameters has
not been important. The best fit was achieved when E0 of 1.12
eV and ∆S of -5.49 eu has been used, as shown in Figure 7.
wide internal energy range. These data are plotted in Figure 8
together with the nanosecond data obtained in this work. It is
to be noted that the present data follow the same general trend
as the PEPICO and PD-ICR data, supporting the overall validity
of the present approach.
q
The vibrational frequencies used to achieve the above fit are
listed in Table 3. The critical energy used is slightly larger
27
than 0.99 eV adopted by Baer et al. but is similar to 1.1 eV
estimated by Dunbar and co-workers.21 ∆Sq of -5.49 eu
All the above data have been considered for RRKM-QET
fitting for this reaction. The best fit was obtained when E0 of
indicates that the reaction occurs via a tight transition state over
the microsecond to nanosecond time scale. Conflicting indica-
tions from KERD and rate-energy data suggest the participation
q
1
.61 eV and ∆S of 7.28 eu were used, as shown in Figure 8.
-1
The C-C stretching mode at 910 cm was taken as the reaction
coordinate. The vibrational frequencies used in the calculation
are listed in Table 3. The critical energy of 1.61 eV is the same
as reported by Baer et al. while ∆S is larger than 3.5 eu
reported by these investigators. ∆S of 7.28 eu obtained in this
of a multiple-well potential in reaction 1, as shown in Scheme
q
1
. ∆S of -10.9 eu reported by Baer et al. through RRKM-
2
7
q
QET analysis of PEPICO data seems to be a little extreme
compared to results in other rearrangement reactions. The value
of the extended range made possible by our rates in the
nanosecond region is clearly evident. Whereas the PEPICO
data, covering only a 1 order of magnitude range of rates could
q
work indicates that the reaction occurs via a very loose transition
state by a simple bond cleavage and the most likely products,
at least initially, are benzyl ion and n-propyl radical. For such
a reaction, the critical energy will approach the reaction
endoergicity very closely. The thermochemical data for the
above products are not well established. The reaction endoer-
q
not distinguish between ∆S of -11 and -5, the combined data,
covering over 3 orders of magnitude in rate constants, permit
us to establish a much more reliable entropy of activation. The
internal energy distribution for the photoexcited molecular ion
has been recalculated using the rate-energy relation obtained
here. Its average is 0.01 eV larger than the previous estimation
based on the rate data of Baer et al., which is negligible
compared to the experimental error limits.
3
1,38-40
gicity estimated from the thermochemical data
in Table
2
varies in the range 1.59-1.73 eV. E0 of 1.61 eV determined
in this work compares very well with the thermochemical data
and is in excellent accord with the large value of ∆S .
q
For a simple bond cleavage occurring statistically via a very
loose transition state without a significant reverse barrier, the
phase space theory is expected to provide a good description
Accepting Scheme 1 for this reaction, E0 of 1.12 eV obtained
from RRKM-QET fit corresponds to the critical energy for the
isomerization step. This value is comparable in magnitude to
the endoergicity (1.07-1.27 eV) of the overall reaction. This
means that the critical energies for the forward and backward
reactions of the distonic ion intermediate are comparable, which,
in turn, suggests the possibility of reversible occurrence of the
first step in Scheme 1. Then, the measured rate constant may
not correspond to the forward rate constant as assumed in the
above analysis. Such a possibility will be probed later in this
section after completing the analysis for reaction 2.
38,41
for KERD. The molecular parameters
used in the calculation
are listed in Table 3. KERD in photodissociation is in excellent
agreement with the calculated result as shown in Figure 4c.
E. A Stepwise McLafferty Rearrangement Mechanism.
As was mentioned earlier, the isomerization step in the
McLafferty rearrangement can occur reversibly and it is
necessary to study how this affects the data analysis described
above. The kinetic scheme for the major reactions investigated
so far can be written as follows. The expressions for the rates
D. Production of C7H7 . Unlike the production of C7H8•+,
microsecond rate-energy data are not available for this channel.
Using only the nanosecond data obtained in this work, however,
may not allow a reliable RRKM-QET fitting. Hence, with the
rate-energy curve for reaction 1 determined above and the
branching ratios reported from PEPICO27 and PD-ICR studies,
the rate constants for reaction 2 have been estimated over a
+
k1
k2
k3
n-C6H5C4H9•+
+
C6H6CH2CH2 CHCH3
•
C7H8•+ + C3H6
(DII)
(9)
k4
C7H7+ + C3H7•
21
of production of C7H8•+ and C7H7+ can be found elsewhere42

Photodissociation Dynamics of n-Butylbenzene Molecular Ion
J. Phys. Chem., Vol. 100, No. 32, 1996 13373
That is, the appearance rates of C7H7+ and C7H8•+ are
determined by k1 + k4 and their branching ratio by k4/k1, in
agreement with the kinetic treatment made in this work and by
Baer et al. It is to be noted that the above simple treatment is
not generally applicable to competing consecutive reactions. For
example, if DII is more stable than estimated by Kuck, the above
limiting situation may not hold especially in a low internal
energy region. Then, k1 and/or k4 cannot be determined from
the experimental rates without the knowledge of k2 and k3.
5
. Conclusions
Photodissociation of n-butylbenzene ion has been found to
occur competitively to C7H8•+ and C7H7+ on a nanosecond time
scale. The transition state structures inferred from the measured
•+
rate-energy relation and the KERD for the production of C7H8
were different. The controversy could be resolved by assuming
that the reaction occurs consecutively via a distonic ion
intermediate, in agreement with Baer et al. The reaction seems
Figure 9. Rate-energy dependences for the four channels in reaction
. See text for details.
9
27
to be a stepwise McLafferty rearrangement in which isomer-
and can be written as below if DII is not present initially.
ization via a γ-hydrogen rearrangement is followed by R-cleav-
d[C H •+]
age to 5-methylene-1,3-cyclohexadiene ion and propene. On
k k
7
8
1
3
-λ t
+
-λ t
the other hand, the production of C7H7+ which is dominant at
-
)
(e -e
)
(10)
dt
λ+ - λ
-
higher internal energy occurs by a simple bond cleavage to
benzyl ion and n-propyl radical.
+
d[C H ]
7
7
Combining previous microsecond rate-energy data and the
branching ratios with the nanosecond data, RRKM-QET fitting
could be improved as manifested by more reasonable values of
)
dt
k4
-
-λ t
+
-λ t
q
[
(λ - k - k )e
- (λ - k - k )e ] (11)
∆S . Successful analysis with the statistical theories also means
+
1
4
-
1
4
λ+ - λ
-
that the dissociation occurs on the potential energy surface of
the ground electronic state even though photoabsorption initially
leads to an excited electronic state(s). The quasi-equilibrium
hypothesis generally made for the dissociation of polyatomic
ions seems to hold in this case. This is in contrast with the
photodissociation of one of its isomers, tert-butylbenzene ion,
where
λ )
(
1
2
/2
[(k + k + k + k ) ( (k + k - k - k ) + 4k k ]
1
2
3
4
x
2
3
1
4
1 2
1
2
which displayed apparent non-RRKM-QET behavior.
(
12)
The excellent agreement of the 91/92 ratio determined in this
work with the previous PEPICO and PD-ICR results indicates
the overall validity of the present PD-MIKES technique, the
method for the internal energy estimation in particular. Also,
this is the first time that overlapping PD-MIKE peaks arising
from two competing channels have been successfully analyzed.
To arrive at simplified versions of the above rate equations
applicable to the present case, it is necessary to have estimates
of the magnitudes of k1, k2, k3, and k4. k1 and k4 have been
evaluated already in this work, namely the rates of production
•
+
+
of C7H8 and C7H7 , respectively. To evaluate k2 and k3,
thermochemical and structural information on DII is needed.
According to Kuck,43 the heat of formation at 298 K of DII is
roughly 887 kJ/mol which is ∼65 kJ/mol higher than that of
the n-butylbenzene ion. The critical energies for the reverse
isomerization and dissociation of DII evaluated from this value
Acknowledgment. This work was supported financially by
the Ministry of Education, Republic of Korea, by Center for
Molecular Catalysis and Korea Science and Engineering Foun-
dation, and by the Non Directed Research Fund, Korea Research
Foundation.
q
are 0.45 and 0.50 eV, respectively. Since ∆S is mostly
determined by the tightness (or looseness) of the transition state,
it seems to be reasonable to use -5.49 eu in the calculation of
k2, which is the same value used for k1. Since the dissociation
of DII is presumed to occur via a very loose transition state as
References and Notes
(
1) Levsen, K. Fundamental Aspects of Organic Mass Spectrometry;
Verlag Chemie: Weinheim, Germany, 1978.
2) Forst, W. Theory of Unimolecular Reactions; Academic Press: New
York, 1973.
q
indicated by KERD analysis, ∆S of 7.28 eu, which is the value
(
used for k4, has been adopted for k3. The rate-energy relations
k1(E)-k4(E) are shown in Figure 9. At the internal energy range
investigated by PEPICO, PD-ICR, and the present PD-MIKES
technique, the relation k1, k4 , k2 , k3 holds. In this limiting
case, eqs 10 and 11 are simplified as below.
(3) Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; Wiley-
Interscience: New York, 1972.
(
4) Baer, T. AdV. Chem. Phys. 1986, 64, 111. Booze, J. A.; Schweins-
berg, M.; Baer, T. J. Chem. Phys. 1993, 99, 4441. Riley, J.; Baer, T. J.
Phys. Chem. 1993, 97, 385. Booze, J. A.; Feinberg, T. N.; Keister, J. W.;
Baer, T. J. Chem. Phys. 1994, 100, 4294.
d[C H •+]
(5) Dunbar, R. C. J. Phys. Chem. 1987, 91, 2901. Gotkis, Y.; Naor,
M.; Laskin, J.; Lifshitz, C.; Faulk, J. D.; Dunbar, R. C. J. Am. Chem. Soc.
7
8
≈
≈
k exp[-(k + k )t)]
(13)
(14)
1
1
4
1
993, 115, 7402. Lin, C, Y.; Dunbar, R. C. J. Phys. Chem. 1994, 98, 1369.
dt
Weddle, G. H.; Dunbar, R. C.; Song, K.; Morton, T. H. J. Am. Chem. Soc.
1
995, 117, 2573.
+
(6) Choe, J. C.; Kim, M. S. J. Phys. Chem. 1991, 95, 50.
d[C H ]
7
7
(
7) Choe, J. C.; Kim, M. S. Int. J. Mass Spectrom. Ion Processes 1991,
107, 103.
8) Choe, J. C.; Kim, M. S. J. Phys. Chem. 1992, 96, 726.
k exp[-(k + k )t)]
4
1
4
dt
(

13374 J. Phys. Chem., Vol. 100, No. 32, 1996
Oh et al.
(
9) Yim, Y. H.; Kim, M. S. Int. J. Mass Spectrom. Ion Processes 1993,
(27) Baer, T.; Dutuit, O.; Mestdagh, H.; Rolando, C. J. Phys. Chem.
1988, 92, 5674.
1
23, 133.
(
(
(
(
10) Yim, Y. H.; Kim, M. S. J. Phys. Chem. 1993, 97, 12122.
(28) Holmes, J. L.; Osborne, A. D. Org. Mass Spectrom. 1981, 16, 236.
(29) Yeh, I. C.; Kim, M. S. Rapid Commun. Mass Spectrom. 1992, 6,
115; 293.
11) Yim, Y. H.; Kim, M. S. J. Phys. Chem. 1994, 98, 5201.
12) Cho, Y. S.; Choe, J. C.; Kim, M. S. J. Phys. Chem. 1995, 99, 8645.
13) Cho, Y. S.; Kim, M. S.; Choe, J. C. Int. J. Mass Spectrom. Ion
(30) Kim, Y. H.; Kim, M. S. Rapid Commun. Mass Spectrom. 1991, 5,
Processes 1995, 145, 187.
14) Hwang, W. G.; Kim, M. S.; Choe, J. C. J. Phys. Chem. 1996, 100,
227.
15) Mukhtar, E. S.; Griffiths, I. W.; Harris, F. M.; Beynon, J. H. Int.
J. Mass Spectrom. Ion Phys. 1981, 37, 159.
16) Griffiths, I. W.; Mukhtar, E. S.; March, R. E.; Harris, F. M.; Beynon,
J. H. Int. J. Mass Spectrom. Ion Phys. 1981, 39, 125.
17) Griffiths, I. W.; Mukhtar, E. S.; Harris, F. M.; Beynon, J. H. Int.
J. Mass Spectrom. Ion Phys. 1982, 43, 283.
18) Welch, M. J.; Pereles, D. J.; White, E. Org. Mass Spectrom. 1985,
0, 425.
2
5.
(
(
31) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin,
9
R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17, Suppl. 1.
32) Chesnavich, W. J.; Bowers, M. T. In Gas Phase Ion Chemistry;
Bowers, M. T., Ed.; Academic Press: New York, 1979; Vol. I, Chapter 4.
(
(
(
Chesnavich; W. J.; Bowers, M. T. Prog. React. Kinet. 1982, 11, 137.
(
33) Choe, J. C.; Kim, B. J.; Kim, M. S. Bull. Korean Chem. Soc. 1989,
(
1
0, 167.
(
(
(
(
34) Draeger, J. A. Spectrochim. Acta 1985, 41A, 607.
(
35) Dewar, M. J. S.; Ford , G. P. J. Am. Chem. Soc. 1977, 99, 1685.
36) Lee, T. G.; Park, S. C.; Kim, M. S. J. Chem. Phys., in press.
37) Lifshitz, C. AdV. Mass Spectrom. 1989, 11, 713.
2
5
1
4
(19) Harrison, A. G.; Lin, M. S. Int. J. Mass Spectrom. Ion Phys. 1983,
1, 353.
(20) Nacson, S.; Harrison, A. G. Int. J. Mass Spectrom. Ion Processes
(38) Baer, T.; Morrow, J. C.; Shao, J. D.; Olesik, S. J. Am. Chem. Soc.
985, 63, 325.
1988, 110, 5633.
(21) Chen, J. H.; Hays, J. D.; Dunbar, R. C. J. Phys. Chem. 1984, 88,
(39) Holmes, J. L.; Lossing, F. P.; Maccoll, A. J. Am. Chem. Soc. 1988,
110, 7339.
759.
(
(
(
22) Uechi, G. T.; Dunbar, R. C. J. Chem. Phys. 1990, 93, 1626.
23) Uechi, G. T.; Dunbar, R. C. J. Chem. Phys. 1993, 98, 7888.
24) McLuckey, S. A.; Sallans, L.; Cody, R. B.; Burnier, R. C.;Verma,
(40) Rosenstock, H. M.; Draxl, K.; Steiner, B. W.; Herron, J. T. J. Phys.
Chem. Ref. Data 1977, 6, Suppl. 1.
(41) Shimanouchi, T.; Matsuura, H.; Ogawa, Y.; Harada, I. J. Phys.
Chem. Ref. Data 1978, 7, 1323.
S.; Freiser, B. S.; Cooks, R. G. Int. J. Mass Spectrom. Ion Phys. 1982, 44,
2
15.
(
42) Baer, T.; Brand, W. A.; Bunn, T. L.; Butler, J. J. Faraday Discuss.
Chem. Soc. 1983, 75, 45.
43) Kuck, D. Mass Spectrom. ReV. 1990, 9, 187.
(25) Dawson, P. H.; Sun, W. F. Int. J. Mass Spectrom. Ion Phys. 1982,
4
(
Mass Spectrom. Ion Processes 1986, 68, 71.
JP9605818