Thermal dissociation of acetophenone molecular ions activated by infrared radiation

Article abstract of DOI:10.1021/jp970198i

The thermal dissociation of the molecular ions of acetophenone (C₆H₅COCH₃?⁺ → C₆H₅CO⁺ + ^?CH₃) and acetophenone-d₃ (C₆H₅COCD₃^?+ → C₆H₅CO⁺ + ^?CD₃) induced by broad band infrared radiation has been studied in the cell of an FT-ICR spectrometer. Rate constants in the range of 0.5-10 s^-1 have been obtained for the system of ions exposed to a radiation source equivalent to blackbody temperatures between 1100 and 1600 K. The unimolecular dissociation is almost pressure independent in the 4 × 10^-8 to 5 × 10^-7 Torr range indicating that the most important mechanism is of a noncollisional nature. Activation energies obtained from Arrhenius-type plots yield 46.6 ± 2.0 kJ mol^-1 for acetophenone and 44.9 ± 2.2 kJ mol^-1 for acetophenone-d₃. The dissociation process has been modeled by a Monte Carlo simulation and by numerical solution of the master equation of a process which takes into account interaction with the background radiation field through absorption and emission. These calculations reveal that meaningful activation energies can be obtained from these experiments even though the exact radiance viewed by the ions is not known. Solution of the master equation reveals that the experimental activation energies are consistent with a dissociation energy of 80.5 kJ mol^-1 for the acetophenone molecular ion. This result is used to derive a heat of formation of 745 kJ mor^-1 for the C₆H₅CO⁺ ion.

Full text of DOI:10.1021/jp970198i

4384
J. Phys. Chem. A 1997, 101, 4384-4391
Thermal Dissociation of Acetophenone Molecular Ions Activated by Infrared Radiation
Marcelo Sena and Jose´ M. Riveros*
Instituto de Qu´ımica, UniVersidade de Sa˜o Paulo, Caixa Postal 26077, Sa˜o Paulo, Brazil, CEP 05599-970
ReceiVed: January 13, 1997; In Final Form: March 27, 1997X
The thermal dissociation of the molecular ions of acetophenone (C6H5COCH3 f C6H5CO+ + CH3) and
•+
•
acetophenone-d3 (C6H5COCD3 f C6H5CO+ + CD3) induced by broad band infrared radiation has been
studied in the cell of an FT-ICR spectrometer. Rate constants in the range of 0.5-10 s-1 have been obtained
for the system of ions exposed to a radiation source equivalent to blackbody temperatures between 1100 and
1600 K. The unimolecular dissociation is almost pressure independent in the 4 × 10-8 to 5 × 10-7 Torr
range indicating that the most important mechanism is of a noncollisional nature. Activation energies obtained
from Arrhenius-type plots yield 46.6 ( 2.0 kJ mol-1 for acetophenone and 44.9 ( 2.2 kJ mol-1 for
acetophenone-d3. The dissociation process has been modeled by a Monte Carlo simulation and by numerical
solution of the master equation of a process which takes into account interaction with the background radiation
field through absorption and emission. These calculations reveal that meaningful activation energies can be
obtained from these experiments even though the exact radiance viewed by the ions is not known. Solution
of the master equation reveals that the experimental activation energies are consistent with a dissociation
energy of 80.5 kJ mol-1 for the acetophenone molecular ion. This result is used to derive a heat of formation
of 745 kJ mol-1 for the C6H5CO+ ion.
•+
•
Introduction
energies (less than 1 eV) are likely to undergo collisionless
induced dissociation by absorption of thermal radiation. A
The ability to promote the dissociation of gas-phase ions with
low-power cw CO2 lasers by sequential absorption of photons
is now well established.1 Infrared multiphoton dissociation
(IRMPD) becomes possible in these cases since ions trapped at
low pressures are exposed to the laser radiation for long
irradiation times (hundreds of milliseconds) and undergo
stepwise multiphoton absorption processes without significant
interference by collisions. While this kind of IRMPD of ions
can be described within the theoretical framework formulated
for infrared multiphoton excitation and dissociation processes,2
a more specific analysis of the kinetics of low-intensity infrared
laser induced photofragmentation of ions3 reveals two interesting
features: (i) dissociation energies can be extracted from
photofragmentation rate constants obtained as a function of laser
intensity, and (ii) under certain conditions, modeling of the
process is equivalent to that of an ensemble of ions subject to
irradiation by an incoherent blackbody source. The first aspect
has yet to be largely explored although rate constants of infrared
multiphoton induced photofragmentation have been used to
determine the pumping rate of ions to their dissociation limit4
and as a sensitive tool to differentiate between isomeric ions.5
The second idea parallels an early prediction by Beauchamp
and co-workers6 who claimed the distinct possibility of inducing
ion dissociation with incoherent infrared radiation.
particularly important aspect of the approach proposed by
Dunbar9 resides in the fact that valuable thermochemical data
can be derived from the kinetics of dissociation as a function
of temperature. This was in fact verified experimentally for
Cl-(H2O)2 and Cl-(H2O)3 ions.10 At present, a growing number
of molecular ions,11,12 loosely bound cluster ions,13-15 and ions
derived from biomolecules16,17 have been observed to undergo
collisionless thermal dissociation within the cell of FT-ICR
spectrometers. A comparison of techniques used in determining
the thermochemistry associated with dissociation processes
reveals that very reliable quantities can be obtained from
experiments dealing with thermal dissociation of ions.18
A preliminary communication from this laboratory11 reported
the dissociation of the covalently bound acetophenone molecular
ion, C6H5COCH3•+, induced by thermal radiation
C6H5COCH3•+ f C6H5CO+ + •CH3
(1)
This is an attractive case because reaction 1 represents a
common low-energy fragmentation pathway which has been
extensively characterized by mass spectrometry. For example,
the metastable transition and the kinetic energy release associ-
ated with reaction 1 suggest a negligible reverse activation
energy.19 Thus, determination of the activation energy for
reaction 1 provides a good estimate of the thermochemistry of
the process. The dissociation energy for reaction 1 has been
estimated to be anywhere from 37.6 to 84.9 kJ mol-1 from
appearance energy measurements.20 Yet, the reliability of the
appearance potential data is still questionable, and the heat of
formation of the benzoyl cation (C6H5CO+) remains unsettled.
Our initial measurements regarding the thermal radiation
induced dissociation of acetophenone molecular ions suffered
from poorly defined temperature and infrared radiation condi-
tions in the cell.11 Thus, a more elaborate experimental study
and theoretical modeling of the dissociation of acetophenone
and acetophenone-d3 (C6H5COCD3) molecular ions activated
by incoherent infrared radiation are presented in this paper in
The fact that near-ambient blackbody radiation could be
instrumental in promoting collisionless dissociation of ions was
first reported in 1994.7 Loosely bound ion-neutral complexes
were shown to suffer spontaneous dissociation in the cell of an
FT-ICR spectrometer in a process mediated by absorption of
thermal radiation from the surroundings. Furthermore, rate
constants were shown to display isotopic selectivity.8
A
comprehensive interpretation of these experiments was devel-
oped by Dunbar9 as an extension of his early work on low-
power IR laser dissociation of ions. The general conclusion of
this model is that medium sized ions with low dissociation
X Abstract published in AdVance ACS Abstracts, May 1, 1997.
S1089-5639(97)00198-9 CCC: $14.00 © 1997 American Chemical Society

Dissociation of Acetophenone Molecular Ions
J. Phys. Chem. A, Vol. 101, No. 24, 1997 4385
order to derive the thermochemistry of reaction 1. A simple
technique has been developed to promote ion dissociation with
a broad band infrared source which circumvents two important
problems in dealing with spontaneous dissociation of reactive
ions: (a) the need for a wide range variable temperature
spectrometer to obtain activation energies and (b) slow dis-
sociation rate constants at room temperatures which make the
kinetic characterization of reactive molecular and fragment ions
a complex procedure even at very low pressures. Modeling of
the process through a Monte Carlo simulation and numerical
solution of the master equation yield good agreement with the
experimental results and allow the dissociation energy to be
obtained for reaction 1. An extension of this work to the enol
form of the acetophenone molecular ion reveals that thermal
radiation activated dissociation can readily distinguish between
isomeric ions.
Experimental Section
Figure 1. Temperature calculated (eq 2) for the filament of the in situ
lamp as a function of electrical power dissipated on the tungsten wire.
Experiments were carried out in a Fourier transform ion
cyclotron resonance spectrometer interfaced to an IonSpec
Omega Data System (IonSpec, Irvine, CA). The basic design
of this instrument has been described previously.21
respect to the photon emission properties of the wire, the
resistivity was measured as a function of electrical power which
was controlled by varying the current. A least-squares fit of
the data (Figure 1) reveals that power dissipated on the filament
and temperature (as obtained from eq 2) follow a relationship
which closely resembles the blackbody Stefan-Boltzmann law
Ions are produced by electron impact from a heated rhenium
filament mounted on a ceramic block attached to a 1 in. cubic
cell and undergo cyclotron motion in a 1 T magnetic field of a
9 in. Varian electromagnet. The filament current of the ion
source can be operated continuously or in a pulsed mode in the
FT experiment. This latter mode allows the filament current
to be turned on only during ion formation and eliminates
possible postionization effects due to the light emitted by the
filament (see Experimental Results). The majority of the
experiments were carried out at electron energies in the vicinity
of 10 eV to minimize ion-molecule reactions. Molecular ions
of acetophenone were isolated at variable times after ion
formation (200-700 ms) by ejection of the m/z 105 (C6H5CO+)
and 106 (13CC5H5CO+) ions from the cell. The amplitude of
the ejection radio-frequency pulse was maintained at the lowest
level compatible with ejection of the ions. The m/z 121 ions,
a mixture of (C6H5COCH3)H+ and 13CC7H8O•+, were not
ejected in order to avoid any undesirable excitation of the
molecular ion (m/z 120). No difference was observed within
experimental error for the dissociation rate constant of the
molecular ion as a function of isolation delay time.
The temperature of the cell was measured with a calibrated
Pt wire thermometer placed below the bottom receiver plate of
the cell. The measured temperature in the pulsed filament
current experiments was typically 323 ( 5 K, which is 20-30
K lower than that of experiments with the filament current
operating continuously. The vacuum surrounding the cell is
provided with heating tapes which allow the temperature of the
cell to be raised to a maximum of 420 K.
A tungsten wire was installed inside the vacuum system but
outside of the ICR cell and about 0.5 cm from one of the
transmitter plates. These plates have a partial open structure
to allow for optical experiments. More recently, a new support
for the tungsten wire has been installed which allows the
distance to the cell to be varied. This wire can be heated through
an external circuit and act as an in situ lamp. Measurements
of the resistivity, F (µΩ cm), of the tungsten wire (obtained
from resistance measurements of the wire) can be transformed
into temperature of the tungsten wire, T (K), by the expression22
P(W) ) 1.8 × 10-13T4.13
This equation strongly suggests that the emissivity of the
filament in the temperature range essentially obeys one of the
important laws of a blackbody source.
Pressure was measured with an ion gauge located on the side
arm of a vacuum cross connecting the cell to the turbomolecular
pump. The absolute pressure has been calibrated over the years
using the CH4•+/CH4 reaction rate constant as a test case. This
procedure yields methane pressures which are higher by at least
a factor of 2 from those indicated by the ion gauge.23
Acetophenone (BDH Chemicals, Poole, England), 99.3%
acetophenone-d3, C6H5COCD3, (Isotec), and butyrophenone
(Aldrich) were subject to freeze, pump, and thaw cycles prior
to use. Their conventional mass spectra revealed no detectable
impurities. However, continuous baking of the vacuum system
for at least 3 days was necessary to reduce traces of water from
the spectrometer.
Impulse excitation24 was used for detection purposes since
this method has been observed in our laboratories to yield more
reliable relative intensities in the mass range of interest.
The kinetics of the CO2 laser infrared multiphoton fragmenta-
tion of the molecular ion was studied using a methodology
similar to that previously described.5 A tunable cw CO2 laser
(Synrad, Model 48-1) was used in these experiments, and
irradiation times were electronically controlled with a variable
Uniblitz shutter (Vincent Associates, Rochester, NY) triggered
by the FT software of the experiment. An entrance and exit
ZnSe window were installed in the vacuum system for these
experiments.
Experimental Results
Preliminary Experiments. The mass spectrum of acetophe-
none at low electron energies (10 eV or lower) exhibits the
molecular ion, C6H5COCH3 •+ (m/z 120), the fragment ion C6H5-
CO •+ (m/z 105), and the corresponding 13C species. Initial
experiments11 using electron impact ionization with a continu-
ously heated filament revealed that the molecular ions of
acetophenone undergo rapid spontaneous dissociation in the
T ) 103.898 + 38.04F - 0.0938F2 + 0.000024F3 (2)
In order to verify the significance of this temperature with

4386 J. Phys. Chem. A, Vol. 101, No. 24, 1997
Sena and Riveros
Figure 4. Dissociation rate constant of the acetophenone molecular
ion promoted by broad band infrared radiation from the internal tungsten
lamp as a function of nitrogen pressure used as a buffer gas.
Figure 2. Typical experiment (with ionization filament operating
continuously) showing spontaneous dissociation of the molecular ion
of acetophenone (m/z 120) to yield the benzoyl cation (m/z 105)
(reaction 1) at an acetophenone pressure of 4.9 × 10-8 Torr. Notice
that ion-molecule reactions leading to protonated acetophenone (m/z
121) are slow under these conditions.
remains lit only during the ionization period of the FT-ICR
experimental sequence. Thus, the dissociation illustrated in
Figures 2 and 3 is promoted by radiation emitted by the ionizing
filament. Further studies were then carried out exclusively in
the pulsed current mode for the ionizing filament.
The dissociation rate constant for reaction 1 is observed to
increase when the temperature of the cell is raised to 400 K by
heating the vacuum system. However, the rates of ion-
molecule reactions leading to m/z 121 are also observed to
increase significantly, a fact that may be due to considerable
water desorption from the walls of the vacuum system.
The fact that the rhenium filament used for ionization was
instrumental in promoting the dissociation of the acetophenone
molecular ions (Figures 2 and 3) led us to investigate the effect
of different radiation sources on the dissociation. For example,
rapid dissociation of the acetophenone molecular ion can be
achieved by continuous irradiation of the ions with an external
commercial infrared lamp. The rate of dissociation was
observed to decrease when a Ge filter was used to block the
visible components of the lamp, but the decrease was compa-
rable (within experimental error) to the infrared attenuation of
the Ge filter as measured by using a cw CO2 laser. This result
is a strong indication that the dissociation process is promoted
by absorption of infrared radiation. No dissociation was
observed when acetophenone molecular ions were exposed to
pulses of 532 nm light from the second harmonic of a Nd:YAG
laser.
Experiments Using Broad Band Infrared Radiation. The
tungsten wire installed outside the transmitter plate of the ICR
cell can act as an in situ lamp and a versatile source of infrared
radiation. Variation of the current applied to this tungsten wire
allows the intensity and distribution of the radiation to be varied
in almost near-blackbody fashion.
Experiments were then carried out with ions formed at low
electron energies (∼10 eV) while maintaining the tungsten wire
at a fixed temperature as determined by its power rating (eq 3).
Rate constants for the dissociation of the molecular ion were
generally obtained at pressures of 4.8 × 10-8 Torr. While this
pressure is considerably above the zero-pressure limit, the
collisional contribution to the overall process is negligible as
shown in Figure 4.
Figure 3. Dissociation rate constant determined as a function of
acetophenone pressures in experiments with different emission currents
of the ionizing filament under continuous heating (ions exposed to
different radiation temperatures): b emission current 4 µA; 9 emission
current 1.5 µA; 2 emission current 1.4 µA; 1 emission current 0.3
µA.
ICR cell according to reaction 1 (Figure 2). At low ionization
energies and at pressures of 4 × 10-8 Torr, dissociation was
observed to be much faster than ion/molecule reactions leading
to protonated acetophenone (m/z 121).25
Figure 3 shows typical plots of the dissociation rate constant
determined at different acetophenone pressures and for different
emission currents of the continuously heated ionizing filament.
Extrapolation of these data to zero pressure clearly suggests
that dissociation is essentially promoted by a noncollisional
mechanism. This same behavior is observed for experiments
carried out at fixed acetophenone pressures and variable
pressures of buffer gases like Ar and SF6.
Light emitted by the ionizing filament can be a critical factor
in experiments of this nature when carried out in a single-cell
arrangement. Unlike the results shown in Figures 2 and 3,
spontaneous dissociation of the acetophenone molecular ion is
much slower (kdiss ∼ 0.08 s-1) than the rate of ion-molecule
reactions leading to protonated acetophenone when the filament
Figure 5 displays the dissociation rate constant for the
acetophenone molecular ion obtained as a function of the power
supplied to the tungsten lamp. At low power, an almost linear
relationship is observed between rate constant and power. At

Dissociation of Acetophenone Molecular Ions
J. Phys. Chem. A, Vol. 101, No. 24, 1997 4387
Figure 7. Arrhenius plot for the dissociation rate constants of the
acetophenone-d3 molecular ion as a function of the equivalent blackbody
temperature of the tungsten lamp.
Figure 5. Dissociation rate constant for the acetophenone molecular
ion as a function of power of the in situ tungsten lamp.
derived from these two independent graphs spanning a large
range of radiation temperature.
The effectiveness of the dissociation induced by the tungsten
lamp can be compared with that promoted by an infrared laser.
The photofragmentation kinetics of the molecular ion of
acetophenone induced by a 1.5 W cw CO2 laser tuned to the
10.57 µm line yields a rate constant comparable to that obtained
with a 2.5 W tungsten lamp. Thus, the efficiency of incoherent
infrared radiation to promote ion dissociation fully confirms the
early predictions advanced in ref 6.
Model for Ion Dissociation Activated by Thermal Radia-
tion. Basic Model. The formal approach for describing ion
dissociation activated by continuous infrared light under colli-
sionless conditions has been discussed for the case of low-power
monochromatic radiation (CO2 laser for example)4 and for
blackbody radiation.9 The underlying theoretical model entails
an analysis of the time evolution of the vibrational content of
an ensemble of ions in the presence of a weak radiation field.
In the present case, the acetophenone molecular ion can be
represented by a collection of 45 harmonic oscillators exchang-
ing energy (absorption and emission) with the radiation field
as a function of time. While the vibrational frequencies for
neutral acetophenone and acetophenone-d3 are known,26 the
frequencies and the absorption and emission coefficients for the
molecular ions must be estimated from theoretical calculations
or by comparison with similar systems. Vibrational frequencies
for the acetophenone molecular ion were first estimated using
the semiempirical AM1 method contained in the Gaussian 92
suite of programs27 and used without corrections since appropri-
ate scaling factors for this level of calculation are not well
defined. Vibrational frequencies were also computed from
density functional and ab initio calculations at the Hartree-
Fock level using a 6-31G** basis set for comparison purposes.
While these frequencies are usually calculated within 10% of
the experimental values, the Einstein absorption and emission
coefficients which are obtained from calculated band intensities
are expected to be subject to much larger uncertainties in the
absence of correlation corrections.28
Figure 6. Arrhenius plot for the dissociation rate constants of the
acetophenone molecular ion as a function of the equivalent blackbody
temperature of the tungsten lamp.
higher powers (>6 W), and as rate constants become large,
experimental uncertainty increases since a large fraction of the
molecular ion population is depleted before ion isolation is
achieved. A very similar graph is obtained for the dissociation
rate constants of acetophenone-d3.
A more interesting result can be obtained by using the
temperature of the radiation source as the significant variable.
While the temperature of the radiation source can be obtained
from eq 2, the tungsten lamp can be treated as an approximate
blackbody provided the radiance is corrected to that of an
equivalent blackbody temperature. This correction entails a
well-known conversion of the radiation emitted by tungsten at
a certain temperature (T) to the equivalent integrated radiation
emitted by a blackbody at a temperature Tb, which is consider-
ably lower than that obtained from eq 2.22 The use of these
effective blackbody temperatures in Arrhenius-type plots is
shown in Figures 6 and 7 for the dissociation rate constants of
acetophenone and acetophenone-d3 respectively. The corre-
sponding activation energies obtained from these graphs yield
46.6 ( 2.0 kJ mol-1 for acetophenone and 44.9 ( 2.2 kJ mol-1
for acetophenone-d3, and their significance is discussed below.
The error quoted for these activation energies reflect exclusively
the standard deviation of a linear regression analysis of the data.
Excellent agreement is observed for the activation energies
Two independent approaches were developed to study the
time evolution of the acetophenone molecular ions: (1) a Monte
Carlo simulation of a random walk process along the vibrational
energy axis of the molecule and (2) solution of the appropriate
master equation. The initial objective of these calculations was
to estimate the dissociation rate constant expected for the
molecular ion of acetophenone exposed to blackbody radiation

4388 J. Phys. Chem. A, Vol. 101, No. 24, 1997
Sena and Riveros
at near-ambient temperature and to extract meaningful thermo-
chemical parameters from the temperature dependence of the
rate constants.
temperature. No significant differences were obtained in
calculated rate constant using AM1 or ab initio Hartree-Fock
calculated vibrational frequencies and intensities. These cal-
culated rate constants are about five times larger than the
estimated experimental value (0.08 s-1) obtained at this tem-
perature under pulsed filament current and with the in situ lamp
turned off. This result suggests that the assumed dissociation
energy is incorrect.
Monte Carlo Simulation. Our approach is based on a
treatment originally proposed by Kramers29 for chemical reac-
tions activated through collisions. In this model, energy
exchange between the radiation field and ions leads some of
the reactant ions to acquire eventually sufficient energy to cross
over the potential barrier for dissociation.30 The reaction rate
is then set equal to the rate of crossing, and a Monte Carlo
algorithm is used to simulate the random walk of internal
energy.31
For a given temperature, the initial internal energy and
vibrational configuration of the ion is chosen at random using
the probability distribution as a weight function. The probability
distribution function is represented in this case by a Boltzmann
distribution truncated at the dissociation threshold.9 Each ion
is then allowed to do a random walk in energy absorbing and
emitting thermal radiation, and dissociation is assumed to occur
instantaneously for ions with vibrational energies in excess of
the dissociation level (sudden death approximation). The
dissociation threshold was initially assumed to be 37 kJ mol-1
as suggested by the appearance potential measurements using
photoionization techniques.20d The sudden death approximation
can be corrected by incorporating explicitly the internal energy
dependence of the RRKM rate constants for ions with energies
just above the dissociation limit. However, this contribution is
negligible for the case of acetophenone and for the time scale
of the experiment.
Master Equation. The master equation approach for describ-
ing the process of ion dissociation is equivalent to the Monte
Carlo simulation except for the fact that the random character
of the process is hidden.30,31 For the present case, a discrete
form of the master equation31 was used with an energy grain
size of 50 cm-1
.
upper
dxi
dt
)
P x - P x
ji i
(6)
∑
ij
j
j)0
In eq 6, xj represents the ion population of a level with an energy
equal to j (an integer) × ∆ꢀ (the energy grain size). Transition
probabilities are defined by
Pij ) P(xi, t+δt|xj,t)
Pji ) P(xj,t+δt|xi,t)
(7a)
(7b)
and the probabilities Pij and Pji are assumed to be zero if the
energy difference between states i and j does not correspond to
the energy of a vibrational transition of the ion. If the energy
difference coincides with a transition connecting the two states,
these probabilities are identical to those used in the Monte Carlo
The actual simulation considers that every oscillator can
increase, decrease, or maintain unchanged its level of occupation
(n) during a given time interval (δt). The probability (P) of
these events for a level i can be represented by
simulation. The population of the upper limit in eq 6, xupper
,
refers to a state with an energy just above the dissociation
threshold and represents the fraction of population converted
to products
P(n+1,t0+δt|n,t0) ) 1 - exp[-BiF(νi,T)δt]
(3)
Equation 6 is usually written in matrix notation
P(n-1,t0+δt|n,t0) )
dx
dt
1 - exp{[-BiF(νi,T) - Ai]δt} (for n * 0) (4)
) Jx
(8)
A and B represent the Einstein coefficients obtained from the
calculated intensities, and the radiation density at the appropriate
frequency for a harmonic oscillator transition, F(νi,T), is assumed
to be the Planck distribution for a blackbody source:
where x is a column vector with elements (x0, x1, ..., xupper) and
the operator matrix J is defined by elements
J ) (-δ
P ) - (δ - 1)P
ij
(9)
∑
ij
ij
kj
ij
k)j
8πhν3
c3
hν
exp - 1
kT
-1
F(νi,T) )
(5)
Equation 9 can be solved by a series expansion
(
)
1
1
x(t) ) x(0) + Jx(0)t + J2x(0)t2 + J3x(0)t3 + ... (10)
These transition probabilities allow the behavior of an ion
undergoing random emission and absorption for every time step
δt to be simulated.
2! 3!
For small values of t, and correspondingly small values of
the J matrix elements, the linear term of eq 10 is a good
approximation to the solution of the master equation. The
approximate solution was then obtained with a corrector-
predictor method yielding the time evolution of the distribution
vector x including the number of dissociated ions. The internal
energy of the ions was again represented by a Boltzmann
distribution truncated at the dissociation energy for a given
temperature, and initial conditions were obtained through the
Beyer-Swinehart algorithm.33
Assuming again the dissociation energy of reaction 1 to be
equal to 37 kJ mol-1, the numerical solution of the master
equation yields a dissociation rate constant of 0.38 s-1 for the
acetophenone molecular ion and 0.43 s-1 for acetophenone-d3
at 346 K. These values are in excellent agreement with those
calculated by the Monte Carlo simulation.
This method was first tested with the dissociation channel
turned off. The time average of the energy yields excellent
agreement with that calculated from equilibrium statistical
mechanics and remains constant provided that intramolecular
vibrational redistribution (IVR) is explicitly included after every
time step. Thus, IVR was included among the vibrational modes
after every time step δt under the condition of constant total
energy. For calculations with the dissociation channel open,
500 simulations were typically performed for each temperature
and the rate constant was determined by a fitting process from
the resulting list of dissociation times.
Assuming the dissociation energy of reaction 1 to be equal
to 37 kJ mol-1, a dissociation rate constant of 0.40 s-1 was
calculated for the molecular ion of acetophenone at 346 K and
0.44 s-1 for the molecular ion of acetophenone-d3 at the same

Dissociation of Acetophenone Molecular Ions
J. Phys. Chem. A, Vol. 101, No. 24, 1997 4389
Figure 9. Calculated infrared spectrum of the molecular ion of
acetophenone with integrated intensities shown on the left-hand scale
(AM1 caclulation) and blackbody radiation distribution plotted at 350
and 1400 K with radiation densities shown on the right-hand scale.
Figure 8. Kinetics of the m/z 120 enol ion obtained from butyrophe-
none and under irradiation with the tungsten lamp. Notice that
protonation of butyrophenone (m/z 149) is much faster than dissociation.
process can be analyzed by either of our theoretical methods.
For example, calculations can be performed for a given radiation
source temperature and variable degrees of attenuation for the
blackbody radiation density effectively viewed by the ions.
Using the master equation approach, absolute rate constants are
found to be sensitive to the attenuation considered for the
radiation density (an essentially linear relationship). This is
obviously the expected type of behavior since it ultimately
reflects different ion temperatures. However, for a fixed
attenuation factor the variation of the absolute rate constants
with radiation source temperature reveals some very interesting
and useful results. For a hypothetical system similar to the
acetophenone molecular ion, and assuming a critical energy of
50 kJ mol-1, model calculations reveal that Arrhenius plots of
rate constants estimated for radiation densities (corresponding
to temperatures similar to those of Figures 6 and 7) attenuated
by as much as 94% yield at most a variation of less than 10%
in activation energy. Thus, while absolute rate constants are
critically dependent on radiation density, activation energies
obtained from Arrhenius plots are largely insensitive to the
actual radiation viewed by the ions but sensitive to the spectral
radiance distribution as a function of temperature. This conclu-
sion begins to break down at attenuation factors higher than
95%, presumably because superposition of the blackbody
radiation from the walls of the cell must be taken into
consideration.
The results of this calculation are supported by experiments
in which the tungsten wire is placed at different distances from
the cell. While the absolute values of the dissociation rate
constants are sensitive to the position of the tungsten wire,
actiVation energies obtained for different fixed positions of the
heated tungsten wire from plots similar to those in Figures 6
and 7 are similar within the quoted error.
The results of these model calculations suggest then that
activation energies obtained from plots like those shown in
Figures 6 and 7 can be can be used to recover the dissociation
energy of the molecular ion of acetophenone from master
equation calculations. This can be done by using the dissocia-
tion energy as a parameter to be adjusted in master equation
calculations of dissociation rate constants as a function of
temperature until the experimental activation energies are
reproduced. Using a constant attenuation factor of 94% for the
radiation density, master equation calculations for the acetophe-
none molecular ion reveal that a dissociation energy of 80.5 kJ
mol-1 is capable of reproducing the experimental activation
Calculation of Dissociation Energies and Thermochemistry.
The models described above can be used to extract thermo-
chemical parameters from experiments carried out as a function
of power, or temperature, of the light source provided proper
adjustments are made for the actual radiation density viewed
by the ions in experiments like those shown in Figures 5-7.
The heated tungsten wire can be considered as a gray body
source with an emittance lower than that of a true blackbody
source. At temperatures ranging from 1000 to 2000 K, the
emission is almost entirely in the infrared region (only 1% is
in the visible region), and the total radiance can be approximated
as being equal to that of a blackbody at an effective temperature
Tb (lower than the temperature of the filament).34 This
procedure was used in Figures 6 and 7 where the tabulated
temperatures refer to Tb. The blackbody-like behavior of the
light source is in fact confirmed by the measurements displayed
in Figure 1 which show the heated tungsten wire to follow a
near Stefan-Boltzmann-type law. While the light source can
then be reasonably approximated as a blackbody source, with
an effective blackbody temperature, the actual radiation density
sampled by the ions is dependent on the geometry of the lamp,
the geometry of the cell, and the distance between the ion cloud
and the light source. In principle, the effective radiation density
reaching the ion cloud could be estimated from geometric
considerations, but this procedure is subject to considerable
arbitrariness. Thus, calculated absolute rate constants for
dissociation promoted by the tungsten lamp using the procedures
outlined above are not expected to be very meaningful under
these conditions. However, the effectiveness of the higher
temperature radiation in promoting dissociation of the acetophe-
none molecular ion can be illustrated by comparing the
calculated infrared spectrum of the acetophenone molecular ion
and the radiation spectral distribution at a higher temperature.
Figure 9 shows the superposition of the calculated infrared
spectrum of the ion (AM1 calculation) with the blackbody
radiation distribution at 350 and 1400 K. It is clear from this
plot that the most intense vibrations of the molecular ion of
acetophenone (1450-1620 cm-1 and 3000-3200 cm-1) have
a particularly good overlap with the high-temperature radiation
spectral distribution.
The fact that the ion cloud samples only a fraction of the
radiation density emitted by the source implies that ions would
come to equilibrium at a much lower temperature than that of
the radiation source in the absence of the dissociation channel.
The consequences of this situation on the ion dissociation

4390 J. Phys. Chem. A, Vol. 101, No. 24, 1997
Sena and Riveros
energy of 46.6 kJ mol-1. For these calculations, the internal
energy of the ions was initially assumed to be at room
temperature. Under these condtions, an induction period of
about 500 ms is observed before ions undergo a dissociation
which can be represented by a simple exponential decay.
Simulations carried out with higher initial internal energies (from
350 to 600 K) reveal a decrease in the induction time, but the
steady state dissociation constant remains the same. An
induction period has no direct consequences on the experimental
rate constants since the experimental procedure involving the
use of pulsed filament currents for ionization and ion selection
requires at least 600 ms.
from the Arrhenius plots and consequently the dissociation
energies obtained from the master equation calculations and (b)
the accuracy of the ionization energy of acetophenone.
The present value obtained for the dissociation energy and
the heat of formation of the benzoyl cation can be compared
with several measurements reported in the 1970s. For example,
heats of formation of 753,20b 669,19a and 778 kJ mol-1 37 have
been proposed on the basis of the appearance potential of
electron impact experiments and are of questionable validity.
A more reliable result is probably the one obained from
appearance potential measurements of a variety of benzoyl
compounds by photoionization techniques20d which results in a
mean value of 705 ( 6 kJ mol-1 for the heat of formation of
the benzoyl cation. Yet, this last value must also be viewed
with caution because the low-intensity tail of the ion yield curves
is structure dependent, and participation of isolated electronic
states of the molecular ion located below the appearance
potential in the fragmentation process is still a distinct possibil-
ity. Furthermore, the threshold values derived in ref 20d were
not corrected for the thermal energy content of acetophenone.
We therefore believe that our result for the heat of formation
of the benzoyl cation is reliable within the limitations imposed
by the accuracy of our temperature measurements. It is
These calculations above allow us then to conclude that
C6H5COCH3•+ f C6H5CO+ + •CH3
D0 ) 80.5 ( 2.1 kJ mol-1
The error quoted for the dissociation energy was estimated from
solutions of the master equation with activation energies allowed
to vary between the error limits determined in Figures 6 and 7.
A more serious source of error in the determination of the
dissociation energy by the present procedure is the accuracy of
our temperature measurements which are derived from the
resistivity of the tungsten wire. The accuracy of these measure-
ments and the eventual contribution to the error in the
dissociation energy are difficult to assess at present without an
independent check for the temperature measurements.
An alternative procedure to verify the consistency betwen
the calculated dissociation energy and the activation energy
obtained for acetophenone is to estimate the dissociation energy
from the relationship previously proposed by Dunbar9 within
the context of Tolman’s theorem.
important to point out that significant differences (20 kJ mol-1
)
have already been reported between bond dissociation energies
obtained from thermal radiation induced dissociation and CID18
and those obtained by PEPICO techniques.38
Thermal Dissociation of C8H8O•+ Isomeric Ions. An
interesting application of the type of dissociation discussed in
this paper is its sensitivity toward ionic structure. The enol
•+
form of molecular ions of ketones, (C6H5C(OH)CH2
in
acetophenone) is known to be more stable than the keto isomer39
and can be independently generated from different precursors.
For example, butyrophenone, C6H5COCH2CH2CH3, provides
an easy way to generate the enol ion of acetophenone as a result
of a McLafferty rearrangement of the molecular ion.40
E0 ≈ Ea + E - 3.6 kJ mol-1
In this equation, E represents the average energy of the ions
calculated over the reaction depleted internal energy distribution
of the reagent ion. Calculation of E for the reaction depleted
ensemble of acetophenone ions yields E ) 40.3 kJ mol-1 for
a typical case of the tungsten wire at 1250 K and the radiation
density attenuated by 94%. This value then leads to Et ≈ 83.3
kJ mol-1, in excellent agreement with the value obtained from
the master equation calculations and consistent with similar
comparisons in other systems.10,12
Experiments carried out with the m/z 120 enol isomer ion
generated from butyrophenone, and under continuous irradiation
by the in situ tungsten lamp, reveal that C6H5C(OH)CH2
promotes proton transfer readily to neutral butyrophenone while
essentially no dissociation is observed in this case (Figure 8).
Such an observation is consistent with the much higher
dissociation energy for the enol form and the fact that it is prone
to undergo proton transfer reactions to substrates of high proton
affinity.
•+
The dissociation energy obtained from the master equation
approach can be compared with a value of 67 kJ mol-1 obtained
by ab initio calculations at the 6-31G** level. This theoretical
value is probably no better than (20 kJ mol-1 in the absence
of any corrections for electron correlation. Unfortunately, MP2
calculations for the acetophenone system proved infeasible with
our present computational facilities.
The calculated dissociation energy can also be used to
establish the appropriate thermochemistry for the benzoyl ion,
C6H5CO•+ The heat of formation of the molecular ion of
acetophenone is 809 kJ mol-1 assuming an adiabatic ionization
potential of 9.28 eV for acetophenone as obtained by photo-
ionization techniques.20d,35,36 The thermal corrections necessary
to calculate the heat of formation of C6H5CO+ at 298 K from
the dissociation energy, D0, are estimated to be 3 kJ mol-1 from
the ab initio calculations. On the basis of these assumptions,
the heat of formation of C6H5CO+ at 298 K is calculated to be
746 kJ mol-1. The error limits for this heat of formation cannot
be easily estimated because of two important limitations: (a)
the unknown accuracy of our temperature measurements
discussed above which affects the activation energies obtained
This particular feature in the acetophenone system can be
used as a powerful technique to establish the relative amount
of keto and enol ions generated in acetophenone.41
Discussion
The present experiments reveal that the molecular ion of
acetophenone can undergo readily thermal dissociation induced
by broad band incoherent infrared radiation. Modeling of the
process reveals that dissociation energies can be obtained from
our experiments using activation energies derived from Arrhe-
nius-type plots of the rate constants as a function of the
temperature of the radiation source. The modeling reveals that
these experiments yield meaningful activation energies even
though the radiation viewed by the ions represents only a
fraction of the radiation field of the lamp source.
A number of possible applications of the present methodology
can be envisioned by suitable experimental development. The
determination of dissociation energies by this method looks
particularly attractive for the case of reactive ions where larger
unimolecular dissociation rate constants are needed even if the

Dissociation of Acetophenone Molecular Ions
J. Phys. Chem. A, Vol. 101, No. 24, 1997 4391
(11) Sena, M.; Riveros, J. M. Rapid Commun. Mass Spectrom. 1994, 8,
1031.
(12) Lin, C.-Y.; Dunbar, R. C. J. Phys. Chem. 1996, 100, 655.
(13) Linnert, H. V.; Riveros, J. M. Int. J. Mass Spectrom. Ion Processes
1994, 140, 163.
(14) Schindler, T.; Berg, C.; Niedner-Schatteburg, G.; Bondybey, V. E.
Chem. Phys. Lett. 1996, 250, 301.
(15) Beyer, M; Berg, C.; Go¨rlitzer, H. W.; Schindler, T.; Achatz, U.;
Albert, G.; Niedner-Schatteburg, G.; Bondybey, V. E. J. Am. Chem. Soc.
1996, 118, 7386.
(16) Price, W. D.; Schnier, P. D.; Williams, E. R. Anal. Chem. 1996,
68, 859.
(17) Schnier, P. D.; Price, W. D.; Jockusch, R. A.; Williams, E. R. J.
Am. Chem. Soc. 1996, 118, 7178.
(18) Lin, C.-Y.; Dunbar, R. C.; Haynes, C. L.; Armentrout, P. B.; Tonner,
D. S.; McMahon, T. B. J. Phys. Chem. 1996, 100, 19659.
(19) (a) Elder, Jr, J. F.; Beynon, J. H.; Cooks, R. G. Org. Mass Spectrom.
1976, 11, 415; (b) Elder, Jr, J. F.; Beynon, J. H.; Cooks, R. G. Org. Mass
Spectrom. 1976, 11, 423.
experiments are carried out at lower pressures than those used
in this study. The ultimate accuracy in obtaining thermochemi-
cal parameters from these experiments depends on several
variables which have been repeatedly emphasized. For example,
the temperature of the lamp is assumed to be well represented
by eq 2 but ideally should be checked by independent methods
such as optical pyrometry. Furthermore, the tungsten lamp used
in our experiments is treated as a pseudoblackbody source
represented by an effective temperature. While the radiation
distribution closely resembles that of a blackbody, the color
temperature of tungsten is typically 30 K higher than the
temperature measured by eq 2. Thus, different radiation sources
could be used to ensure that the blackbody equivalency yields
consistent results. A second alternative would be to use
commercially available blackbody sources to eliminate any
possible effects from an uneven radiation density distribution.
Errors associated with the Einstein absorption and emission
coefficients obtained from theoretically calculated band intensi-
ties are difficult to estimate, but their effect is more important
in the calculation of absolute rate constants than in the variation
of the rate constant with temperature which is used to obtain
dissociation energies.
(20) (a) 48.2 kJ mol-1 obtained by: McLafferty, F. W.; Bente, P. F.;
Kornfeld, R.; Tsai, S.-C.; Howe, I. J. Am. Chem. Soc. 1973, 95, 2120. (b)
84.9 kJ mol-1 obtained by: Benoit, F. Org. Mass Spectrom. 1973, 7, 1407.
(c) 60.8 kJ mol-1 obtained in ref 19a. (d) 37.6 kJ mol-1 obtained by:
McLoughlin, R. G.; Traeger, J. C. Org. Mass Spectrom. 1979, 14, 434.
(21) Isolani, P. C.; Kida-Tinone, M. C.; Linnert, H. V.; Menegon, J. J.;
Riveros, J.M.; Tiedemann, P. W.; Franzin, R. L. Qu´ım. NoVa 1992, 15,
351.
(22) Forsythe, W. E. In International Critical Tables of Numerical Data,
Physics, Chemistry and Technology; Washburn, E. W., Ed., McGraw-Hill
Book Company: 1929; pp 245-247.
Finally, these experiments suggest the possibility of using
near-blackbody sources with infrared filters to obtain infrared
spectra of ions either by direct dissociation or in conjunction
with a CO2 laser in analogy with the two laser experiments
advocated by Eyler and co-workers.41 These experiments also
extend the application of thermal dissociation by infrared
dissociation and may be of particular interest in dealing with
ions derived from biomolecules.
(23) Linnert, H. V. Personal communication.
(24) (a) McIver, R. T., Jr.; Hunter, R. L.; Baykut, G. ReV. Sci. Instrum.
1989, 60, 400. (b) McIver, R. T., Jr.; Hunter, R. L.; Baykut, G. Int. J. Mass
Spectrom. Ion Processes 1989, 89, 343.
(25) The detailed electron energy dependence of the reactions leading
to protonated acetophenone will be discussed in a future publication.
However, reaction with traces of background water can also account for
the formation of the m/z 121 ion.
(26) Gambi, A.; Giorgani, S.; Passerini, A.; Visinoni, R.; Gherseti, S.
Spectrochim. Acta 1980, 36A, 871.
(27) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.;
Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M.
A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Blinkley,
J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.;
Stewart, J. J. P.; Pople, J. A. GAUSSIAN/92, Revision C; Gaussian, Inc.:
Pittsburgh, PA, 1992.
(28) See for example Wiberg, K. B.; Thiel, Y.; Goodman, L.; Leszc-
zynski, J. J. Am. Chem. Soc. 1995, 99, 13850.
(29) Kramers, H. A. Physica 1940, 7, 284.
(30) Montroll, W.; Shuler, K. E. AdV. Chem. Phys. 1958, 1, 361.
(31) (a) Gardiner, W. Handbook of Stochastic Methods for Physics,
Chemistry and the Natural Sciences; Springer Series in Synergetics. 13;
Springer-Verlag: Berlin, 1983. (b) Binder, K. Applications of the Monte
Carlo Method; Springer-Verlag: Berlin, 1984.
Acknowledgment. This work was supported by generous
grants from the Sa˜o Paulo Science Foundation (FAPESP Grant
94/4406) and the Brazilian Research Council (CNPq) through
its graduate fellowship (M.S.) and Senior Research fellowship
(J.M.R.) programs. We thank Jair J. Menegon for technical
support in setting up several of the experimental procedures
and Dr. Nelson H. Morgon for his guidance in the early stages
of the theoretical calculations. The authors are also indebted
to Prof. Robert C. Dunbar for drawing our attention to the
possible effects of the light emitted by the filament and to Prof.
J. L. Beauchamp for comments regarding the possibility of
extracting Arrhenius type plots from experiments carried out
as function of lamp power.
(32) Liboff, L. Kinetic Theory: Classical, Quantum, and RelatiVistic
Description; Prentice-Hall: Englewood Cliffs, NJ, 1990.
(33) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recom-
bination Reactions; Blackwell Scientific Publications: Oxford, 1990.
(34) (a) Moore, J. H.; Davis, C. C.; Coplan, M. A. Building Scientific
Apparatus; Addison-Wesley: Redwood City, CA, 1989; pp 197-200. (b)
Skoog, D. A.; Leary, J. A. Principles of Instrumental Analysis, 4th ed.;
Saunders College Publishing: Fort Worth, TX, 1992; p 75. (c) Willard, H.
H.; Merritt, L. L., Jr.; Dean, J. A. Instrumental Methods of Analysis; Van
Nostrand: Princeton, NJ, 1958; pp 31-32. (d) Zworykin, V. K.; Gramberg,
E. Photoelectricity and Its Applications; John Wiley and Sons: New York,
1949; pp 17-19, 408-409.
References and Notes
(1) Thorne, L. R.; Beauchamp, J. L. In Gas Phase Ion Chemistry, Vol
3: Ions and Light; Bowers, M. T., Ed.; Academic Press: Orlando, FL,
1984; pp 42-97.
(2) Lupo, D. W.; Quack, M. Chem. ReV. 1987, 87, 181.
(3) Dunbar, R. C. J. Chem. Phys. 1991, 95, 2537.
(4) Uechi, G. T.; Dunbar, R. C. J. Chem. Phys. 1992, 96, 8897.
(5) Gaumann, T.; Zhu, Z.; Kida, M. C.; Riveros, J. M. J. Am. Soc.
Mass Spectrom. 1991, 2, 372.
(6) Bomse, D. R.; Woodin, R. L.; Beauchamp, J. L. In AdVances in
Laser Chemistry; Zewail, A. H, Ed.; Springer-Verlag: Berlin, 1978; pp
362-373.
(7) Tho¨lmann, D.; Tonner, D. S.; McMahon, T. B. J. Phys. Chem. 1994,
98, 2002.
(35) Lias, S. G.; Liebman, J. F.; Levin, R. D.; Kafafi, S. A., NIST
Standard Reference Database 25, Structures and Properties Version 2.02;
NIST: Gaithersburg, MD, 1994.
(36) The most recent X-ray photoelectron spectrum of acetophenone
yields an IE of 9.38 eV. See: Distefano, G.; Granozzi, G.; Olivato, P. R.;
Guerrero, S. A. J. Chem. Soc., Perkin Trans. 2 1987, 1459.
(37) Helal, A. I.; Zahran, N. F. Org. Mass Spectrom. 1978, 13, 549.
(38) Szepes, L.; Baer, T. J. Am. Chem. Soc. 1984, 106, 273.
(39) Turecek, F. Tetrahedron Lett. 1986, 27, 4219 and references therein.
(40) Budzikiewicz, H.; Djerassi, C.; Williams, D. H. Mass Spectrometry
of Organic Compounds; Holden Day: San Francisco, CA 1967; p 155.
(41) Sena, M.; Riveros, J. M. Manuscript in preparation.
(42) Peiris, D. M.; Cheeseman, M. A.; Ramanathan, R.; Eyler, J. R. J.
Phys. Chem. 1993, 97, 7839.
(8) Tonner, D. S.; Tho¨lmann, D.; McMahon, T. B. Chem. Phys. Lett.
1995, 233, 324.
(9) Dunbar, R. C. J. Phys. Chem. 1994, 98, 8705.
(10) Dunbar, R. C.; McMahon, T. B.; Tho¨lmann, D.; Tonner, D. S.;
Salahub, D. R.; Wei, D. J. Am. Chem. Soc. 1995, 117, 12819.