Temperature dependence of the rate constants and branching ratios for the reactions of Cl- (D2O)1-3 with CH3Br and thermal dissociation rates for Cl-(CH3Br)

Article abstract of DOI:10.1021/ja960872u

The rate constants and products for the reactions of Cl^-(D₂O)(n) + CH₃Br (n = 1-3) have been measured. The n = 1 reaction was studied from 238 to 478 K. The rate constant is well described by k = (6.0 x 10^-10) exp(-1270/T) cm³ s^-1. We determined the reaction mechanism to be ligand switching to produce Cl^-(CH₃Br) followed by thermal decomposition of the complex. Cl^-(CH₃Br) decomposition produces greater than 90% Br^- + CH₃Cl with the remainder being Cl^- + CH₃Br. The Cl^-(CH₃Br) + He rate constant is well described by k = (4.5 x 10^-10) exp(-2260/T) cm³ s^-1. RRKM theory was used to model the decomposition of Cl^-(CH₃Br). The results are consistent with our experimental results if a central barrier height of 22.5 kJ mol^-1 is used. The n = 2 and 3 reactions also proceed by ligand switching followed by thermal decomposition. The n = 2 reaction was studied from 203 to 298 K. The rate constant is well-described by (4.4 x 10^-9) exp(-1329/T) cm³ s^-1. The main product observed was Cl^-(D₂O) with a smaller amount of Cl^-(D₂O)(CH₃Br) also detected. The n = 3 reaction was studied from 188 to 203 K. The reaction was about a factor of 1.8 faster than the n = 2 reaction. The main product was Cl^-(D₂O)₂ with smaller amounts of Cl^-(D₂O)₂(CH₃Br) and Cl^-(D₂O)(CH₃Br) also observed.

Full text of DOI:10.1021/ja960872u

J. Am. Chem. Soc. 1997, 119, 577-584
577
Temperature Dependence of the Rate Constants and Branching
Ratios for the Reactions of Cl-(D2O)1-3 with CH3Br and
Thermal Dissociation Rates for Cl-(CH3Br)
John V. Seeley,†,‡ Robert A. Morris,‡ A. A. Viggiano,*,‡ Haobin Wang,§ and
William L. Hase§
Contribution from Phillips Laboratory, Geophysics Directorate, Ionospheric Effects DiVision
(GPID), 29 Randolph Road, Hanscom AFB, Massachusetts 01731-3010,
and Department of Chemistry, Wayne State UniVersity, Detroit, Michigan 48202
ReceiVed March 18, 1996X
Abstract: The rate constants and products for the reactions of Cl-(D2O)n + CH3Br (n ) 1-3) have been measured.
The n ) 1 reaction was studied from 238 to 478 K. The rate constant is well described by k ) (6.0 × 10-10
)
exp(-1270/T) cm3 s-1. We determined the reaction mechanism to be ligand switching to produce Cl-(CH3Br)
followed by thermal decomposition of the complex. Cl-(CH3Br) decomposition produces greater than 90% Br- +
CH3Cl with the remainder being Cl- + CH3Br. The Cl-(CH3Br) + He rate constant is well described by k ) (4.5
× 10-10) exp(-2260/T) cm3 s-1. RRKM theory was used to model the decomposition of Cl-(CH3Br). The results
are consistent with our experimental results if a central barrier height of 22.5 kJ mol-1 is used. The n ) 2 and 3
reactions also proceed by ligand switching followed by thermal decomposition. The n ) 2 reaction was studied
from 203 to 298 K. The rate constant is well-described by (4.4 × 10-9) exp(-1329/T) cm3 s-1. The main product
observed was Cl-(D2O) with a smaller amount of Cl-(D2O)(CH3Br) also detected. The n ) 3 reaction was studied
from 188 to 203 K. The reaction was about a factor of 1.8 faster than the n ) 2 reaction. The main product was
Cl-(D2O)2 with smaller amounts of Cl-(D2O)2(CH3Br) and Cl-(D2O)(CH3Br) also observed.
Introduction
effects involving SN2 reactions has a long history.19-25 In
general, solvation is thought to stabilize the reactants more
than it does the transition state located at the central barrier.19
As a result, the relative barrier height increases and the frac-
tion of reaction adducts which dissociate to regenerate the
reactants increases at the expense of those that are transformed
into products. Thus, rate constants are often observed to
decrease substantially with increasing solvation. Previous
solvation studies on the Cl- + CH3Br reaction have focused
on solvents other than water. Bohme and Raksit21 and Giles
and Grimsrud26 both found that the addition of a variety of
organic solvent molecules to Cl- greatly reduced the reaction
rate.
The gas-phase SN2 reaction of Cl- + CH3Br has been well
studied experimentally and theoretically.1-15 This reaction is
believed to proceed along a double-well potential energy surface
with a central barrier that separates the entrance and exit channel
complexes. Although statistical theories, such as RRKM theory,
have been used to model SN2 reactions,8 the Cl- + CH3Br
reaction has been shown2-4,13-18 to be inadequately described
by such theories.
The goal of this work was to study the effects of hydra-
tion of Cl- on its reaction with CH3Br. Interest in solvation
* Author to whom correspondence should be addressed.
† Air Force Geophysics Scholar.
We find that hydration also slows down the SN2 channel.
However, instead of the reaction stopping upon solvation, the
reaction mechanism changes to ligand switching. In addition,
we find that the Cl-(CH3Br) product of the Cl-(D2O) + CH3-
Br reaction can be observed in our flow tube, allowing the
thermal breakup rate of Cl-(CH3Br) to be determined as a
function of temperature. We have performed RRKM calcula-
tions to complement our experimental results.
‡ Phillips Laboratory.
§ Wayne State University.
X Abstract published in AdVance ACS Abstracts, January 1, 1997.
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J. Am. Chem. Soc. 1993, 115, 12079.
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S0002-7863(96)00872-4 CCC: $14.00 © 1997 American Chemical Society

578 J. Am. Chem. Soc., Vol. 119, No. 3, 1997
Seeley et al.
Experimental Section
The experiments were performed in a variable-temperature selected
ion flow tube (VT-SIFT). The apparatus has been described in detail
elsewhere,27 and only information pertinent to the present experiments
will be discussed. Cl-(H2O)n or Cl-(D2O)n ions were produced using
a supersonic expansion ion source. Ions were formed by expanding a
mixture of Ar and H2O or D2O, held at about 4 atm of total pressure,
through a 25-µm orifice and then ionizing the gas just downstream of
the expansion with an electron filament (ThO2/Ir). CF2Cl2 was added
immediately downstream of the expansion. The CF2Cl2 was entrained
in the expansion to produce Cl-(H2O)n ions in a manner similar to that
used by Johnson and colleagues.28 The ions were sampled by a blunt
skimmer and passed into a quadrupole mass filter.
To study the reactions of Cl-(D2O) or Cl-(H2O), we injected that
particular cluster ion into the flow tube and obtained signals of ∼50-
90% purity, the remainder being Cl- due to dissociation. Less
dissociation was seen at lower temperatures. To study Cl-(D2O)n with
n g 2, we used three techniques, all of which produced the same
experimental results: (1) We injected Cl-(D2O)n and obtained about
20% Cl-(D2O)n and 80% Cl-(D2O)n-1. (2) We injected Cl-(D2O)n+1
at a higher injection energy chosen to dissociate one of the solvent
molecules upon injection. This allowed the ion of interest to be nearly
80% of the total ion current at low temperatures, while smaller amounts
were obtained at higher temperatures. (3) We injected a broad
distribution of large clusters by turning the DC off in the upstream
quadrupole and setting that quadrupole to allow only Cl-(D2O)n>4 ions
to be injected. The flow tube temperature was then set so that all
clusters larger than the desired cluster thermally decomposed in the
upstream portion of the flow tube. At room temperature this resulted
in about 15% Cl-(D2O)2 and 85% Cl-(D2O). At 233 K, this resulted
in 97% Cl-(D2O)2, 2% Cl-(D2O), and <1% Cl-(D2O)3. At 200 K,
the resulting distribution was 55% Cl-(D2O)3 and 45% Cl-(D2O)2 with
a negligible amount of Cl-(D2O). The last technique gave the largest
signals since many clusters in the primary distribution compressed into
1 or 2 main peaks. Only the reactions of the cluster with the largest
value of n and reasonable signal intensity were studied using this
method.
Figure 1. Arrhenius plot of the rate constants for the reactions of
Cl-(D2O)0-3 and Cl-(H2O) with CH3Br.
Table 1. Experimental Product Percentages for the Reaction of
Cl-(D2O) + CH3Br
exptl valuesa
temp (K)
% Br-
% (BrCH3Cl)-
% (BrCH3Cl)(D2O)-
241
273
298
328
363
77
88
94
98
99
20
12
6
2
1
3
a Does not include the Cl- channel.
correction is minimized by taking data under low-resolution conditions,
and the branching fractions are expected to be accurate to within 5-10
percentage units.
Results
Both H2O and D2O were used for n ) 1. In order to avoid the
mass coincidence problem of 35Cl-(H2O) with OH-(H2O)2, we adjusted
Figure 1 shows an Arrhenius plot of the rate constants for
the reactions of Cl-(D2O)0-3 and Cl-(H2O) with CH3Br. The
rate constants for n ) 0 are taken from a previous study.2 We
did remeasure the n ) 0 rate constants at several temperatures
and obtained excellent agreement with these previous results.
The n ) 0 reaction produces only Br- and shows the negative
temperature dependence that is typical of ion-molecule reac-
tions, including most SN2 reactions.10,31,32
the upstream quadrupole to inject only 37Cl-(H2O). For Cl-(H2O)n>1
,
the requisite high resolution of the upstream quadrupole resulted in
considerable mass discrimination and insufficient signal intensity for
kinetics studies. Thus for n > 1, data are available only for D2O
clusters.
The reactant ions are thermalized by undergoing approximately
50 000 collisions before reaching the port where CH3Br is injected.
The CH3Br was added without purification. At low temperatures the
reactant inlet was heated to prevent freezing in the inlet line.29 The
CH3Br had extremely low levels of reactive impurities. In particular,
we found that the maximum HBr concentration was approximately 100
parts per million (ppm).25 This is important since some of the rate
constants reported here occur on only 1 in 103 collisions and therefore
an HBr impurity substantially larger than 100 ppm would affect the
results.
In order to minimize the breakup of clusters during sampling, we
biased our sampling orifice at only 2.5 V and the next electrode at
<25 V. Based on our analysis of the kinetics data (see the Results
section), these settings allowed the Cl-(D2O) clusters to be sampled
with <5% breakup. This small amount of breakup did not affect our
ability to determine rate constants; however, it limited the determination
of the Cl-(CH3Br) decomposition branching fractions.
Addition of one water molecule to Cl- changes the temper-
ature dependence from negative to positive. The n ) 1 reaction
was studied from 238 to 478 K. No difference is found whether
the ligand is H2O or D2O, i.e. we find no isotope effect. Using
both the H2O and D2O data sets, the n ) 1 rate constant is well
described by the Arrhenius equation k ) (6.0 × 10-10) exp(-
1270/T) cm3 s-1, which corresponds to an activation energy of
10.3 kJ mol-1 and a room temperature rate constant of 9 ×
.
10-12 cm3 s-1 Three product ions were observed: Br-,
Cl-(CH3Br), and, at the lowest temperature, Cl-(CH3Br)(D2O)
or Cl-(CH3Br)(H2O). We write the product as Cl-(CH3Br) and
not Br-(CH3Cl) for reasons given below. Table 1 gives the
observed product fractions as a function of temperature. In the
presence of CH3Br, the Cl- signal decayed more slowly when
Cl-(D2O) was injected into the tube than when only Cl- was
injected into the flow tube. Thus, it is probable that Cl- is a
minor product of the Cl-(D2O) + CH3Br reaction or that a
Uncertainty in the absolute rate constants is estimated as 25%, and
the uncertainty in the relative rate constants is 15%.30 Product branching
fractions were calculated without a mass discrimination correction. The
(27) Arnold, S. T.; Morris, R. A.; Viggiano, A. A. J. Chem. Phys 1995,
103, 9242.
(28) Posey, L. A.; DeLucca, M. J.; Campagnola, P. J.; Johnson, M. A.
J. Phys. Chem. 1989, 93, 1178.
(29) Viggiano, A. A.; Dale, F.; Paulson, J. F. J. Chem. Phys. 1988, 88,
2469.
(30) Viggiano, A. A.; Morris, R. A.; Dale, F.; Paulson, J. F.; Giles, K.;
Smith, D.; Su, T. J. Chem. Phys. 1990, 93, 1149-1157.
(31) Magnera, T. F.; Kebarle, P. In Ionic Processes in the Gas Phase;
Almoster Ferreira, M. A., Ed.; D. Reidel Publishing: Boston, 1984; pp
135-157.
(32) Ikezoe, Y.; Matsuoka, S.; Takebe, M.; Viggiano, A. A. Gas Phase
Ion-Molecule Reaction Rate Constants Through 1986; Maruzen Company,
Ltd.: Tokyo, 1987.

Reactions of Cl-(D2O)n + CH3Br
J. Am. Chem. Soc., Vol. 119, No. 3, 1997 579
portion of the Cl-(D2O) and Cl-(CH3Br) dissociate upon
sampling to produce Cl-.
The reaction enthalpies of the possible product channels are
listed below
Cl-(H2O) + CH3Br
f Br- + CH3Cl + H2O
f Cl- + CH3Br + H2O
f Cl-(CH3Br) + H2O
f Cl-(H2O)(CH3Br)
f Br-(H2O) + CH3Cl
∆H° ) + 25 kJ mol-1
∆H° ) + 62 kJ mol-1
∆H° ) + 9.6 kJ mol-1
∆H° ) ?
∆H° ) - 27.8 kJ mol-1
(1)
Thermodynamic data are taken from Lias et al.,33 Keesee and
Castleman,34 McMahon et al.35 and Li et al.36 Although the
Br-(H2O) product channel is exothermic, Br-(H2O) was not
observed over the entire temperature range of this study. It may
be possible that Br-(H2O) is produced Via the SN2 mechanism
and subsequently dissociates to Br- and H2O. However, in a
previous study25 we were able to observe significant quantities
of Br-(H2O) produced by the OH-(H2O) + CH3Br reaction at
temperatures ranging from 163 to 477 K. Hence, the complete
absence of Br-(D2O) for the Cl-(D2O) + CH3Br reaction
indicates that this channel is negligible. The lack of an isotope
effect also suggests that an SN2 mechanism is not operative:
O’Hair et al. found significant isotope effects in the SN2
reactions of F-(H2O) and F-(D2O) with methyl halides.37 The
10.3 kJ mol-1 activation energy observed for reaction 1 most
closely matches the endothermicity of the ligand switching
reaction to form Cl-(CH3Br) and is substantially lower than
the endothermicity of the SN2 channel to form Br- directly.
Our results indicate that the Cl-(D2O) + CH3Br reaction
proceeds by a ligand switch to form Cl-(CH3Br) which then
partially dissociates to Br- and some Cl-. Thus, we propose
the following two-step mechanism
Figure 2. Count rates Vs [CH3Br] at 300 K with and without D2O
added. The lines are exponential fits to the Cl-(D2O) signals.
both reduced when D2O is added. Similar results were obtained
for a variety of D2O concentrations. These results all support
the proposed mechanism, showing that the direct SN2 channel
is small or nonexistent. The fact that D2O scavenges the
dissociating complex to form Cl-(D2O) also shows that the
complex is correctly written as Cl-(CH3Br) and not Br-(CH3Cl).
The breakup rate of the Cl-(CH3Br) complex can be
determined from the Cl-(D2O) and Cl-(CH3Br) signals obtained
as a function of [CH3Br] (in the absence of added D2O). We
have used a computer program which implements a variable-
step fourth-order Runge-Kutta algorithm to integrate the rate
equations resulting from reactions 2 and 3 as a function of [CH3-
Br]. This program performs a ø2 minimization by varying the
values of k2, k3, and the Cl-(D2O) signal at t ) 0. The value
of the Cl-(CH3Br) signal was assumed to be zero at t ) 0.
This approach produced excellent fits to the data, including k2
values that agreed well with the values taken in the usual
manner. Figure 3 contains a set of typical plots. The resulting
thermal dissociation rate constants, k3, are shown in Figure 4
as an Arrhenius plot. We estimate that the rate constants have
an absolute accuracy of (40% and a relative accuracy of (20%.
The relative error bars are shown in the Figure 4. The
Cl-(D2O) + CH3Br f Cl-(CH3Br) + D2O
(2)
(3)
f Br- + CH Cl + He
-
Cl (CH3Br) + He
3
f Cl- + CH3Br + He
To test this mechanism, we added D2O to the He in sufficient
quantities to allow the exothermic ligand exchange reaction
dissociation rate constant is well-described by k3 ) (4.5 × 10-10
)
exp(-2260/T) cm3 s-1 which corresponds to an activation
energy of 18.8 kJ mol-1. The error in the activation energy is
estimated as (2.5 kJ mol-1 based on taking the 20% error at
the lowest and highest temperatures.
Cl-(CH3Br) + D2O f Cl-(D2O) + CH3Br
(4)
to scavenge some of the Cl-(CH3Br) and compete with thermal
dissociation (reaction 3), but not enough to affect the initial
Cl- to Cl-(D2O) ratio. The plot of the relevant ion signals Vs
[CH3Br] from such a test at 300 K is shown in Figure 2. Signals
corresponding to Cl-(D2O), Br-, and Cl-(CH3Br) with and
without added D2O are shown. The D2O concentration, 3 ×
1011 cm-3, is enough to convert only a small fraction of the
Cl- (approximately 10-4) to Cl-(D2O).32 With added D2O, the
slope of the decay of the Cl-(D2O) signal is a factor of 3.5 less
than without added D2O, indicating that Cl-(D2O) is regenerated
by reaction 4. In addition, the Br- and Cl-(CH3Br) signals are
In deriving the thermal decomposition rate constants we
assumed that only helium was responsible. At the highest flow
rates of CH3Br used, the fraction of CH3Br in the tube was
only 0.005. Assuming a â0, the low-pressure collision ef-
ficiency, of 1 for CH3Br results in a maximum error of only
25%. Most of the data were taken with less than this flow rate
of CH3Br, and most likely â0 is considerably less than 1;38,39
these facts indicate that the assumption causes a negligible error.
We also used this approach to estimate the dissociation
branching fractions of the Br- and Cl- product channels of
reaction 3. In this case we included the effect of the reaction
of Cl- with methyl bromide,
(33) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin,
R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17, Suppl. 1, 1-861.
(34) Keesee, R. G.; Castleman, A. W., Jr. J. Phys. Chem. Ref. Data 1986,
15, 1011.
(35) McMahon, T. B. Personal communication.
(36) Li, C.; Ross, P.; Szulejko, J. E.; McMahon, T. B. J. Am. Chem.
Soc. In press.
Cl- + CH3Br f CH3Cl + Br-
(5)
The Cl-, Cl-(D2O), Br-, and Cl-(CH3Br) data points were fitted
(37) O’Hair, R. A. J.; Davico, G. E.; Hacaloglu, J.; Dang, T. T.; DePuy,
C. H.; Bierbaum, V. M. J. Am. Chem. Soc. 1994, 116, 3609-3610.
(38) Troe, J. J. Chem. Phys. 1977, 66, 4745.
(39) Tardy, D. C.; Rabinovitch, B. S. Chem. ReV. 1977, 77, 369.

580 J. Am. Chem. Soc., Vol. 119, No. 3, 1997
Seeley et al.
Figure 5. Count rates Vs [CH3Br] at 300 K. The lines are the model
fits to the data as described in the text.
of k5 was assumed to be proportional to k2, with the propor-
tionality constant determined from the Arrhenius expressions
shown in Figure 1. A typical fit to the data is shown in Figure
5. This analysis indicated that the fraction of Br- produced
from reaction 3 was 90% and the fraction of Cl- produced was
10%. However, it is probable that a small portion of Cl-(D2O)
and Cl-(CH3Br) clusters break up upon sampling to produce
Cl-. If sampling breakup is also included in the model then
equally good fits are obtained for 100% of the reaction
proceeding Via the Br- channel with a 4% breakup upon
sampling. Thus, our data place limits on the Cl- formation
channel at 0-10%.
We studied the reactions of Cl-(D2O)2,3 over more limited
temperature ranges. The n ) 2 reaction was studied from 203
to 298 K. The n ) 2 rate constants were fit by k ) (4.4 ×
10-9) exp(-1329/T) cm3 s-1 corresponding to an activation
energy of 11.5 kJ mol-1. This value is slightly larger than the
activation energy observed for the n ) 1 reaction. The n ) 3
reaction was studied at 188 and 203 K. The main ionic product
for both n ) 2 and 3 was Cl-(D2O)n-1. No hydrates of Br-
were observed. In analogy to the mechanism for Cl-(D2O),
we propose the following mechanism for Cl-(D2O)2,3
,
Cl-(D2O)n + CH3Br f Cl-(D2O)n-1(CH3Br) + D2O (6)
followed by
Figure 3. Typical plots used to determine the rate constants for the
decomposition of Cl-(CH3Br). The circles represent the Cl-(D2O) signal
and the squares represent the Cl-(CH3Br) signal.
Cl-(CH3Br)(D2O)n-1 + He
f Cl-(D2O)n-1 + CH3Br + He
f Cl-(D2O)n-2(CH3Br) + D2O + He
(7)
For n ) 2, 95% Cl-(D2O) and 5% Cl-(D2O)(CH3Br) were
observed as products at 233 K, while 50% Cl-(D2O) and
50% Cl-(D2O)(CH3Br) were observed at 203 K. The temper-
ature dependence associated with these products is consistent
with the proposed mechanism, i.e. reaction 7 is considerably
slower at lower temperatures. For n ) 3, 90% Cl-(D2O)2,
8% Cl-(D2O)2(CH3Br), and 2% Cl-(D2O)(CH3Br) were ob-
served as products at 203 K, and 90% Cl-(D2O)2, 5%
Cl-(D2O)2(CH3Br), and 5% Cl-(D2O)(CH3Br) were observed
at 188 K.
RRKM Modeling of Cl-(CH3Br) Dissociation
Figure 4. Arrhenius plot of the rate constant for the decomposition of
Cl-(CH3Br).
Rice-Ramsperger-Kassel-Marcus (RRKM) theory40-43 cal-
culations were performed for Cl-(CH3Br) dissociation in the
by integrating the rate equations resulting from reactions 2, 3,
and 5, and varying the values of k2, k3, the reaction 3 branching
fraction, and the Cl- and Cl-(D2O) signals at t ) 0. The value
(40) Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; Wiley-
Interscience: London, 1972.

Reactions of Cl-(D2O)n + CH3Br
J. Am. Chem. Soc., Vol. 119, No. 3, 1997 581
low-pressure limit, to give a more detailed analysis of the results
in Figure 4 and to determine the branching ratio for Cl-(CH3Br)
dissociation to Cl- and Br-. According to RRKM theory, the
thermal unimolecular rate constant in the low-pressure limit may
be expressed as40-42,44
J
max(E)
â0ω
E
k0(T) )
∞dE
(2J + 1) F(E,J) exp -
(8)
∫
∑
E0
(
)
Q
kBT
J)0
where â0 is the low-pressure collision efficiency,38-42,44-47
ω
is the collision frequency, Q is the vibrational/rotational partition
function for the unimolecular reactant, and F(E,J) is the
reactant’s density of states. E0 is the unimolecular threshold,
and Jmax(E) is the largest value of J for which the reaction can
occur for energy E. If the reactant is treated as a symmetric
top, with the rotational quantum number K treated as ac-
tive,44,48,49 F(E,J) is given by
Figure 6. Potential energy surface for the reaction of Cl- + CH3Br
from Wang et al. Added to the graph is the barrier height derived from
the thermal decomposition experiments reported here. Approximate
energy distributions for experiments performed on this system are given
on the axis as (a) chemical reaction at low pressure, (b) chemical
reaction at 640 Torr, (c) the reacting part of the thermal decomposition
experiments (note the tail goes slightly above zero), (d) distribution
range of decaying states in the Graul and Bowers experiments and
collisional activation of the exit well complex, and (e) distribution range
of decaying states in collisional activation of the entrance well complex.
J
F(E,J) )
F(E,J,K)
(9)
∑
K ) -J
with
F(E,J,K) ) F[E - Er(J,K)]
where Er(J,K) is the symmetric top rotational energy.
(10)
The energies and vibrational frequencies used to evaluate
eq 8 are those for the analytic potential energy function
PES1(Br), derived from ab initio calculations to represent the
Cl- + CH3Br f ClCH3 + Br- reaction.12 The minimum
energy pathway from this work is shown in Figure 6. The
classical well depth for Cl-(CH3Br) on PES1(Br) is -44.89 kJ
mol-1. Using harmonic frequencies to approximate the CH3Br
and Cl-(CH3Br) zero-point energies50 gives a Cl-(CH3Br) f
Cl- + CH3Br 0 K dissociation energy, D0, of 42.3 kJ mol-1
,
which agrees with the measured value of 42 ( 4 kJ mol-1 10
.
The transition state for Cl-(CH3Br) f Cl- + CH3Br is
variational,51-56 and the counteracting effects of the increased
transitional mode bending frequencies and the more attractive
radial potential as Cl- and CH3Br associate results in a
unimolecular dissociation threshold E0 equal to the above
dissociation energy D0.
(41) Forst, W. Theory of Unimolecular Reactions; Academic Press: New
York, 1973.
(42) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recom-
bination Reactions; Blackwell: London, 1990.
(43) Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics. Theory
and Experiment; New York: Oxford, 1996.
(44) Zhu, L.; Chen, W.; Hase, W. L.; Kaiser, E. W. J. Phys. Chem. 1993,
97, 311.
(45) Chan, S. C.; Rabinovitch, B. S.; Bryant, J. T.; Spicer, L. D.;
Fujimoto, T.; Lin, Y. N.; Paulou, S. P. J. Phys. Chem. 1970, 74, 3160.
(46) Fujimoto, T.; Lin, Y. N.; Paulou, S. P. J. Phys. Chem 1970, 74,
3160.
Figure 7. Plot of RRKM rate constant divided by the experimental
rate constant Vs temperature for the thermal decomposition of Cl-(CH3Br).
Plotted are least-squares fits for several assumed values of the branching
into Cl-. Several other values of the Cl- branching fraction were
performed but not included in the graph for clarity. The ideal is the
horizontal line through 1.
Equation 8 was used to calculate k0(T) values for Cl-(CH3Br)
dissociation to Cl- + CH3Br and ClCH3 + Br-. The threshold
energy E0 for the latter dissociation channel is given by the
central barrier height on the potential energy surface. This
threshold was adjusted so that varying fractions of Br- and Cl-
were produced. For a particular threshold these fractions vary
with temperature. To determine an absolute (not relative) value
for the decomposition rate constant, He and Cl-(CH3Br) were
assigned collision diameters of 2.2 and 8.5 Å,45 respectively,
to give ω ) (14.8 × 107)P Torr s-1 and the collision efficiency
â0 was taken as an adjustable parameter. The thermal dissocia-
tion rates were normalized by adjusting the â parameter so that
the calculations matched the 300 K experimental point. Figure
7 shows the theoretical result obtained in this manner divided
by the experimental value as a function of temperature for
(47) Troe, J. J. Phys. Chem. 1979, 83, 114.
(48) Zhu, L.; Hase, W. L. Chem. Phys. Lett. 1990, 175, 117.
(49) Aubanel, E. E.; Wardlaw, D. M.; Zhu, L.; Hase, W. L. Int. ReV.
Phys. Chem. 1990, 10, 249.
(50) The harmonic model should give an accurate zero-point energy
difference for CH3Br and Cl-(CH3Br), since there is very little shifting in
the vibrational frequencies in going from the reactant to complex.
(51) Bunker, D. L.; Pattengill, M. J. Chem. Phys. 1968, 48, 772.
(52) Hase, W. L. J. Chem. Phys. 1972, 57, 730.
(53) Hase, W. L. In Modern Theoretical Chemistry, Vol. 2, Dynamics
of Molecular Collisions; Miller, W. H., Ed.; Plenum: New York, 1976; p
121.
(54) Hase, W. L. Acc. Chem. Res. 1983, 16, 258.
(55) Hase, W. L.; Wardlaw, D. M. In AdVances in Bimolecular Collisions;
Ashfold, M. N. R., Baggott, J. E., Ed.; Royal Society of Chemistry: London,
1989; p 171.
(56) Wardlaw, D. M.; Marcus, R. A. AdV. Chem. Phys. 1988, 70, 231.

582 J. Am. Chem. Soc., Vol. 119, No. 3, 1997
Seeley et al.
Table 2. Calculated Branching into Cl- for the Thermal
+ Br- reaction path,63,64 it is very likely that the most important
tunneling paths will not follow the reaction path, but involve
multidimensional “corner cutting”.65-67 Determining an ac-
curate tunneling correction will require extensive potential
energy surface modeling in the vicinity of the central barrier
between the two complex minima. Therefore, at this time we
leave such a detailed calculation to future work. It is of interest
that there has been no consideration of tunneling in presentations
outlining RRKM calculations for thermal systems at low
pressure.40-42 The only careful study of this effect appears to
be for vinyl radical decomposition, for which tunneling at low
pressures was found to be very important.68
This comparison shows that an RRKM model, which neglects
tunneling and uses a central barrier height lower than the ab
initio barrier, fits the temperature dependence of the data
extremely well. Finally, the above RRKM calculation uses a
harmonic density of states. The anharmonic density is ap-
proximately two times larger,69 and using this density would
require a â0 two times smaller to fit experiment.
The measured activation energy of 18.8 ( 2.5 kJ mol-1 is
smaller than the effective barrier of 22.5 kJ mol-1 derived from
the RRKM calculations. This is expected for thermal dissocia-
tion reactions in the low pressure limit.17,18 The principle behind
this is that the activation energy is the average energy of reacting
molecules minus the average energy of reactants. In the low-
pressure limit the average energy of reacting molecules is just
above the critical energy for reaction, i.e. significantly smaller
than this same energy for a Boltzmann distribution. In the high-
pressure limit we would find the activation energy approximately
equal to the central barrier height to Cl-(CH3Br) f Br- + CH3-
Cl dissociation.
Dissociation of Cl-(CH3Br)
temp (K)
Cl- product (%)
241
273
298
328
363
0.3
0.8
1.5
2.7
4.8
various fractions of Cl- produced. A straight line with no slope
represents the best fit to the data. From Figure 7 it can be seen
that the fit with 1.5% Cl- at 298 K gives the best reproduction
of the experimental temperature dependence with a value of
1% at 298 K only slightly worse. Values as close as 0.5 and
2% give clearly negative and positive slopes, respectively. The
1.5% Cl- fit results in a value for the Cl-(CH3Br) f Br-
+
CH3Cl threshold of 22.5 kJ mol-1 and the value chosen for â0
is 2.0 × 10-2. The barrier height is shown in Figure 6 as ∆E
thermal. For Cl- fractions of 1 and 2% at 298 K, the threshold
values are 21.0 and 23.7 kJ mol-1, respectively. We report this
number as 22.5 ( 2.5 kJ mol-1. The fraction of Cl- produced
in the decomposition was calculated to increase with increasing
temperature as expected, and the results are listed in Table 2.
Since the Cl-(CH3Br) f Cl- + CH3Br dissociation threshold
is 42.3 kJ mol-1 for these calculations, the above fitted threshold
of 22.5 ( 2.5 kJ mol-1 for Br- formation suggests the threshold
energy difference ∆E0 for Cl- and Br- formation is 19.8 kJ
mol-1. This value for ∆E0 is significantly larger than the values
in the range of 4.6 to 6.3 kJ mol-1 derived14 by using different
statistical models to fit the experimental 300 K, low-pressure
Cl- + CH3Br f ClCH3 + Br- rate constant.1 These smaller
values for ∆E0 are similar to the ab initio values of 4.2 and 6.7
kJ mol-1 determined from MP2/PTZ+57 and G2(+)58 calcula-
tions, respectively.
The above comparisons indicate the Cl-(CH3Br) f ClCH3
+ Br- barrier derived here of 22.5 kJ mol-1 may be ∼15 kJ
mol-1 lower than the actual barrier. This is larger than our 2.5
kJ mol-1 uncertainty in our experimental activation energy for
the overall decomposition. The origin(s) of this discrepancy is
unclear. One might want to consider non-statistical effects for
Cl-(CH3Br) decomposition, which may make RRKM theory,
i.e. eq 8, invalid for calculating k0(T). However, this seems
unlikely since non-RRKM effects are more prevalent at high
pressure, when collisional quenching competes with intramo-
lecular vibrational energy redistribution (IVR).53,59 On the other
hand, the low pressure and long time between collisions (∼10-7
s) suggest that a dynamical process not included in calculating
k0(T) for Cl-(CH3Br) f ClCH3 + Br-, i.e. tunneling through
the central barrier, may be important. Using eq 8, with a
tunneling correction, to fit the experimental Cl- to Br-
branching ratio will require a central barrier height higher than
the value of 22.5 kJ mol-1 derived here without tunneling. In
the bimolecular reaction the energy is greater than that of the
barrier and tunneling would not be important.
Discussion
For the Cl-(D2O)n + CH3Br system, we find that the SN2
mechanism is only important for the n ) 0 case. For n > 0 we
observe ligand switching presumably because the relative height
of the central barrier becomes too high for the SN2 mechanism
to be efficient. This result is to be expected because the barrier
crossing efficiency for the n ) 0 case is already quite low (1%)
and the relative height of the central barrier is believed to
increase with increasing hydration level.19
Ligand switching mechanisms have not been previously
reported for the reactions of hydrated ions with methyl halides.
However, previous studies have mostly focused on reactions
involving F- or OH-. At low levels of hydration, F- and OH-
form substantially stronger bonds with water than does Cl-.34
As a result ligand switching with hydrates of F- and OH- is
probably much more endothermic. The ab initio studies of
Morokuma and co-workers70,71 support this statement. They
calculate that the reaction OH-(H2O) + CH3Cl f Cl-(CH3Cl)
+ H2O is endothermic by 57 kJ mol-1, while the reaction
Cl-(H2O) + CH3Cl f Cl-(CH3Cl) + H2O is endothermic by
only 4 kJ mol-1
.
Calculating an accurate correction for low-pressure tunneling
through the central barrier will require evaluating state specific
tunneling rates,60-62 which are thermally averaged. Also,
because of the sharp curvature for the Cl-(CH3Br) f ClCH3
(63) Cho, Y. J.; Vande Linde, S. R.; Zhu, L.; Hase, W. L. J. Chem.
Phys. 1992, 96, 8275.
(64) Wang, H.; Hase, W. L. Chem. Phys. Submitted for publication.
(65) Marcus, R. A.; Coltrin, M. E. J. Chem. Phys. 1977, 67, 2609.
(66) Garrett, B. C.; Truhlar, D. G.; Wagner, A. F.; Dunning, T. H. J.
Chem. Phys. 1985, 78, 440.
(57) Hu, W.-P.; Truhlar, D. G. J. Am. Chem. Soc. 1995, 117, 10726.
(58) Glukhovtsev, M. N.; Pross, A.; Radom, L. J. Am. Chem. Soc.
Submitted for publication.
(59) Meagher, J. F.; Chao, K. J.; Barker, J. R.; Rabinovitch, B. S. J.
Phys. Chem. 1974, 78, 2535.
(60) Miller, W. H. J. Am. Chem. Soc. 1979, 101, 6810.
(61) Kato, S.; Morokuma, K. J. Chem. Phys. 1980, 72, 206.
(62) Forst, W. J. Phys. Chem. 1983, 87, 4489.
(67) Garrett, B. C.; Joseph, T.; Truong, T.; Truhlar, D. G. Chem. Phys.
1989, 136, 271.
(68) Knyazev, V. D.; Slagle, I. R. J. Phys. Chem. Submitted for
publication.
(69) Peslherbe, G. H.; Wang, H.; Hase, W. L. J. Chem. Phys. 1995, 102,
5626.
(70) Morokuma, K. J. J. Am. Chem. Soc. 1982, 104, 3732.
(71) Ohta, K.; Morokuma, K. J. Phys. Chem. 1985, 89, 5845.

Reactions of Cl-(D2O)n + CH3Br
J. Am. Chem. Soc., Vol. 119, No. 3, 1997 583
Two previous studies of solvated chloride ions with methyl
bromide have been made. Bohme and Raksit21 studied the
reactions of Cl-(S)n with CH3Br, where S ) CH3OH, C2H5-
OH, CH3COCH3, HCOOH, and CH3COOH. They found that
the reaction rate constants were too low for accurate measure-
ment for n g 1 and did not observe ligand switching. Giles
and Grimsud26 found that solvation of Cl- by CHCl3 also
inhibits the reaction with CH3Br and, similarly, did not find
evidence for ligand switching. However, the experimental
systems used in these studies produced solvated clusters by
adding solvent directly to the reaction mixture. Hence, any
Cl-(S)n-1CH3Br produced would be quickly converted back into
Cl-(S)n by the high levels of solvent in the flow (analogous to
reaction 5). It is interesting to note that as the hydration levels
of F-, OH-, and Cl- are increased their water binding energies
become similar. Thus, it is possible that ligand switching
reactions will be observed for large (n > 3) hydrates of F- and
OH-.
Our study of the thermal dissociation of Cl-(CH3Br) indicates
that when the complex is formed Via Cl-(H2O) + CH3Br, it
dissociates through the Br- channel with a branching fraction
greater than 90%. Several previous studies have also focused
on the Cl-(CH3Br) complex due to its role as the initial
intermediate in the unsolvated Cl- + CH3Br reaction. At low
pressure (0.4 Torr) the Cl- + CH3Br reaction proceeds at 1%
of the collision rate. Thus, 99% of the Cl-(CH3Br) collision
complexes dissociate back into Cl- and CH3Br, while 1% of
the complexes dissociate into Br- and CH3Cl. At high pressure
(640 Torr of N2) the reaction proceeds at 3% of the collision
rate, which corresponds to 97% of the complexes dissociating
to Cl- and CH3Br.
Since Cl-(CH3Br) formation is endothermic, the complex is
likely to be near the bottom of the well. However, the lifetime
of the Cl-(CH3Br) cluster is long enough (>0.1 ms) to allow
thousands of collisions with the bath gas to establish a
Boltzmann distribution truncated by the thermal dissociation
process. The dominance of the Br- channel indicates that the
majority of the complexes have energies less than the threshold
for separating Cl- and CH3Br. It also should be noted that the
large difference between the dissociation branching ratios
obtained from complexes prepared Via Cl-(D2O) + CH3Br and
those prepared in the high pressure kinetics study Via Cl-
+
CH3Br indicates that the atmospheric pressure study had not
reached the high-pressure limit.
The collisional activation (CAD) experiments have less-well-
defined distributions. Cyr et al.5 estimated that the complex
had an average energy of 0.65 eV and a width on the order of
1 eV. This distribution should have substantial populations of
Cl-(CH3Br) complexes both below and above the threshold
dissociating to Cl- + CH3Br. Thus their estimated energy
distribution and equally divided product distribution are con-
sistent.
The metastable decay experiments of Graul and Bowers3,15
produced little or no Cl-, indicating that few of the dissociating
complexes have an energy above the Cl- + CH3Br asymptote,
and hence, their energy spread is likely to be similar to that
obtained from the Cl-(D2O) + CH3Br reaction, although the
distribution may be different.
The results reported here demonstrate that RRKM theory can
model the dissociation of Cl-(CH3Br) when it is formed by the
Cl-(D2O) + CH3Br reaction if a smaller central barrier is used.
In contrast, previous experimental2 and theoretical14 studies
indicate that the breakup of Cl-(CH3Br) cannot be modeled by
RRKM theory when formed by the Cl- + CH3Br reaction. This
difference is most likely due to the lifetimes of the resulting
complexes. Complexes produced by Cl- + CH3Br have
energies substantially above the threshold for dissociating to
Cl- + CH3Br or Br- + CH3Cl and have lifetimes on the order
of picoseconds13 which is apparently insufficient to allow the
energy to be randomly dispersed. In addition, complexes in
high-J states may have an increased probability for nonstatistical
behavior. Complexes produced by Cl-(D2O) + CH3Br reactions
are initially formed at energies below the threshold for dis-
sociating to either Cl- + CH3Br or Br- + CH3Cl. These
complexes may dissociate by tunneling or be further activated
by collisions with He. The tunneling lifetime is expected to be
sufficiently long for energy to be randomly distributed.
Two previous studies have isolated the Cl-(CH3Br) complex
and directly monitored its dissociation products. Cyr et al.5
prepared Cl-(CH3Br) in a supersonic expansion and activated
the complex in a single high-energy collision (2.5 keV) with
Ar. They observed the complex to dissociate with equal
probability Via the Cl- and Br- product channels. Graul and
Bowers3,15 prepared a metastable beam of Cl-(CH3Br) which
dissociated primarily Via the Br- channel and estimated that
the Cl- channel had a branching fraction of less than 1%. They
also performed a collisional activation experiment and obtained
good agreement with the work of Cyr et al.5
These differing results can be qualitatively reconciled by
examining the energy of the complex in each experiment. The
approximate energy distributions of each experiment are shown
on the y axis in Figure 6. The curve marked (a) in Figure 6
represents a Boltzmann distribution of energies of the reactants
for the Cl- + CH3Br reaction. Trajectory calculations predict
that the complex formed from the bare ion reaction has a lifetime
of approximately 10 ps.13 For the low-pressure (0.5 Torr) flow
tube experiments, collisions occur approximately every 5 ns.
Thus, collisional cooling of the complex does not occur, and
the energy distribution of the complex is very similar to
distribution (a). Because the distribution lies substantially above
the dissociation energy for either channel, the complex dissoci-
ates Via the more entropically favored Cl- channel 99% of the
time.
Graul and Bowers have also reported nonstatistical effects
in their study of the dissociation of metastable Cl-(CH3Br).3,15
They found that the kinetic energy release by metastable
Cl-(CH3Br) upon dissociation was 0.05-0.1 eV less than
predicted by phase space theory. Metastable dissociation was
observed to take place on the order of microseconds, a time
similar to the thermal dissociation experiment. Therefore, the
barrier needed to fit the thermal dissociation data should apply.
This implies that the distribution in the metastable decay
experiment would be about 15 kJ mol-1 less energetic than used
in the phase space calculations, about the same as the difference
between the experimental results and the phase space calcula-
tions. The results would still be nonstatistical but due to
tunneling through the barrier instead of incomplete energy
randomization.
The high-pressure kinetics study of the Cl- + CH3Br
reaction4 has the same energy distribution for reactants, but
collisions with the complex occur approximately every 50 ps.
Thus, the complex is cooled slightly by collisions. Curve (b)
in Figure 6 is an estimate of the distribution. The lower energy
causes more of the complexes to dissociate Via the Br- channel.
If the above is true, the following picture emerges: For
energies above the dissociation limit to Cl- and CH3Br, the
lifetime of the collision complex is short (∼picoseconds),
nonstatistical behavior occurs, and most of the dissociation is
The distribution of the complex formed from the Cl-(D2O)
+ CH3Br ligand switching reaction is represented by curve (c).

584 J. Am. Chem. Soc., Vol. 119, No. 3, 1997
Seeley et al.
Via the Cl- channel. As the energy is lowered, the lifetime
increases to microseconds, as evidenced by the metastable decay
experiments. Statistical theories using an effective barrier
adequately describe the results, and the complex predominantly
dissociates through the Br- channel.
The hypothesis that statistical theories work well for SN2
reactions when the lifetime is long and do not when the lifetime
is short is consistent with other work from our laboratory on
SN2 reactions. We have found nonstatistical kinetics in systems
involving methyl halides.2,72 Several theoretical studies involv-
ing halide ion reactions with methyl halides have shown that
the lifetimes are short.13,63 In contrast, statistical behavior was
found for reactions involving species other than methyl ha-
lides.16,17 For these reactions, we observed that a fraction of
the reactivity proceeds by association. The association sets the
lifetime of the complex in the 10-7 s range.
Conclusions
We have studied the reactions of Cl-(D2O)n)1-3 with CH3-
Br. We find that the SN2 channel is negligible and that ligand
switching becomes the main pathway. The shutdown of the
SN2 channel is consistent with past work that indicates solvation
greatly hinders this mechanism.19-25 The ligand switching
products were observed to thermally dissociate in the helium
buffer gas. For n ) 1, the ligand switching produces the
entrance well complex, Cl-(CH3Br), which then dissociates to
produce mainly Br-. RRKM calculations were carried out to
fit the data. The barrier was adjusted to match the thermal
dissociation rate, and excellent agreement was found when a
barrier height of 22.5 ( 2.5 kJ mol-1 was used. This calculated
barrier is significantly smaller than the ab initio barrier12 and
that obtained by modeling the Cl- + CH3Br reaction.3,14,15 This
leads us to speculate that tunneling may be important in the
thermal decomposition experiments.
Acknowledgment. The PL authors thank John Williamson
and Paul Mundis for technical support. Helpful discussions with
Roger Meads, Susan Arnold, Caroline Dessent, and Mark
Johnson are gratefully acknowledged. The research was sup-
ported by the Air Force Office of Scientific Research and the
National Science Foundation.
JA960872U
(72) Su, T.; Morris, R. A.; Viggiano, A. A.; Paulson, J. F. J. Phys. Chem.
1990, 94, 8426.