Pressure and temperature dependence of the gas-phase reaction of silylene with dimethyl ether

Article abstract of DOI:10.1039/b100068n

Gas-phase reaction rate constants for the reaction of silylene with dimethyl ether Me₂O were determined at 294-441 K and 30-850 torr. Rate constants for the reaction (SiH₂ reacting with Me₂O) decreased with increasing temperature and increased with increasing pressure. The pressure and temperature dependence of the rate constants were modeled using an RRKM/master equation approach, which determined the rate for SiH₂ + Me₂O reaction from that of the unimolecular dissociation of the SiH₂-Me₂O complex. A comparison of the scaled MP2/6-311+G** vibrational frequencies for SiH₂ and Me₂O with experimental values showed that they lie within a few percent of each other. The calculations showed that an association complex forms between SiH₂ and Me₂O.

Full text of DOI:10.1039/b100068n

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Pressure and temperature dependence of the gas-phase reaction of
silylene with dimethyl ether
Ula N. Alexander,a Keith D. King*b and Warren D. Lawrancea
a School of Chemistry, Physics and Earth Sciences, Flinders University, GPO Box 2100,
Adelaide SA 5001, Australia
b Department of Chemical Engineering, Adelaide University, SA 5005, Australia.
E-mail: kking=chemeng.adelaide.edu.au
Received 2nd January 2001, Accepted 25th May 2001
First published as an Advance Article on the web 29th June 2001
Gas-phase reaction rate constants for the reaction of silylene, SiH , with dimethyl ether, CH OCH have been
2
3
3
determined over the temperature range 294È441 K and at total pressures of inert bath gas (Ar or SF ) over the
6
range 30È850 Torr. The second-order rate constants are pressure dependent, even up to the maximum pressure
investigated of 850 Torr, and the rate constants decrease with increasing temperature, indicating that the
reaction proceeds via the formation of a complex. At the highest temperature studied (441 K), the experimental
decay curves do not return to the baseline. This is attributed to the system reaching equilibrium, with SiH
being produced by dissociation of the complex, and provides direct experimental evidence for the formation of
2
the complex. Analysis of the decay curves provided an experimental determination of the equilibrium constant,
K
, at 441 K. The high-pressure rate constants, obtained by extrapolation of the experimental data using
eq
RRKM/master equation modelling, yield the Arrhenius parameters log (A/cm3 molecule~1 s~1) \ [7.6 ^ 0.4
and E \ 9.3 ^ 2.8 kJ mol~1. The RRKM/master equation modelling gives a well depth for the
a
SiH ÈCH OCH complex of 87 kJ mol~1. This compares with a value of 88.4 ^ 1.7 kJ mol~1 determined
2
3
3
from K at 441 K. Ab initio calculations, performed at the MP2/6-311&G** level of theory, give a well-depth
eq
for the complex of 82.9 kJ mol~1, in excellent agreement with this value.
HÈH bonds (hydrogen) and SiÈC bonds (substituted silanes) is
1. Introduction
much slower than insertion into SiÈH bonds (silanes) and
addition across multiple bonds (alkenes and alkynes). Exam-
ples of reactions showing a dependence of the reaction rate on
total pressure include SiH reaction with C H 11 and
Silylene, SiH , is a reactive intermediate important to a
2
number of industrial processes. For example, it is formed
when silanes are pyrolysed during the chemical vapour depo-
sition (CVD) process used to deposit thin silicon Ðlms onto
substrates during the manufacture of semi-conductor com-
ponents. The desire to determine the reactions and kinetic
behaviour of this key reactive intermediate within the silicon
CVD process has been a major force driving the interest in the
2
2 4
C H ,12 which are still pressure-dependent at 100 Torr, the
2
2
highest pressure accessed experimentally. N O and Me SiH10
are notable exceptions to the dependence of the reaction rate
on total pressure.
2
3
The reactions of SiH with organic analogues of water (e.g.,
2
study of SiH kinetics.1 Besides the industrial relevance of
methanol, MeOH and dimethyl ether, Me O) are of impor-
2
2
SiH kinetic studies, there is a desire to understand the funda-
tance to the study of silicone chemistry. They also represent
2
mental chemistry of the simplest silylene and how its reactions
an important class of reactions, namely SiH with n-donor
2
compare to its Group 4 analogues, CH and GeH .
bases. However, to date they have received little attention.10
2
2
Prior to 1985, silylenes were exclusively studied via indirect
methods such as end-product analyses and relative rates.2h4
These indirect studies are useful since they give a broad
picture of the reactivity of silylenes and provide grounding for
direct gas-phase experiments. Since 1985, direct time-resolved
techniques in the gas phase have allowed more detailed study
of the reaction kinetics,5 including direct insight into reaction
Preliminary kinetics studies within our group of the reactions
of SiH with D O and CD OD have led to some unpublished
2
2
3
data for these reactions at room temperature13 and, in con-
junction with WalshÏs group, we have reported the results of a
limited study of the reaction of SiH with Me O.14 We have
2
2
now studied the reaction of SiH with H O, MeOH and
Me O, and some deuterated analogues, D O and CD OD, in
2
2
2
2
3
intermediates. In addition to the direct study of SiH kinetics,
reactions of dimethylsilylene, SiMe , have also been studied in
detail, with the aim of determining the pressure and tem-
perature dependence of the second-order rate constants for
these reactions. The chosen reactants represent a series sys-
tematically substituted about the oxygen atom. We report
here on a detailed study of the temperature and pressure
dependence of SiH reaction with Me O; papers discussing
the other systems will follow.
The reaction of SiH with Me O is expected to occur via
the formation of a complex with signiÐcant charge transfer
character.15,16 The study by Becerra et al.14 conÐrmed this. In
the present work, RRKM/master equation modelling of the
2
2
some detail.6h8
The gas-phase reactions between SiH and selected small
2
inorganic molecules, alkanes, alkenes, alkynes and silanes
have been investigated with varying levels of detail. Reviews
such as those of Jasinski et al.9 and Becerra et al.10 provide a
summary of the SiH reactions that have been studied. The
general picture that emerges is that SiH reacts by insertion
into certain types of sigma bonds and by addition across
double and triple bonds. Insertion into CÈH bonds (alkanes),
2
2
2
2
2
2
DOI: 10.1039/b100068n
Phys. Chem. Chem. Phys., 2001, 3, 3085È3094
This journal is ( The Owner Societies 2001
3085

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experimental data and ab initio calculations are used to deter-
mine the well depth of the complex. In addition, we provide
experimental evidence for the formation of the complex
through the observation of equilibrium between the reactants
and complex at elevated temperatures.
limit for this reaction is reached at pressures in excess of
105È106 Torr.14 To allow accurate extrapolations to deter-
mine the high-pressure limit rate constant, k=, it is desirable
2
to undertake the kinetic measurements up to as high a total
pressure as possible. The experiments were performed up to
850 Torr, the highest pressure attainable with our present
apparatus. The SiH /Me O reaction was studied using two
2. Experimental details
2
2
bath gases, SF and Ar, and as expected the rate constants at
6
Experiments investigating reactions between SiH and Me O
a particular pressure are a†ected by the identity of the bath
2
2
were undertaken over the temperature range 294È441 K. The
experimental system is based on that used in our extensive
studies of CH (a 1A ) kinetics17h22 and GeH kinetics.23,24
gas, although of course k= should be independent of the bath
2
gas. The maximum pressure achievable with SF was lower
6
than that for Ar and was limited by the range of Ñow rates
2
1
2
The temperature-variable reaction cell is described in ref. 20.
attainable with the mass Ñow controllers.
We here give details pertinent to the SiH experiments.
2
SiH (0,0,0) was generated by 193 nm (ArF) excimer laser
3.1 Argon bath gas
2
photolysis of phenylsilane, PhSiH , and probed by a single
3
The experimental observable is the SiH relative concentra-
tion as a function of time following the photolysis laser pulse.
A typical decay trace recorded at 294 K for SiH /Me O in Ar
is shown in Fig. 1. Fits to such decay curves yield the pseudo-
frequency cw laser tuned to 17 259.50 cm~1 (vac) which coin-
2
cides with the rovibronic transition 1B (0,2,0) ^ 1A (0,0,0)
1
1
5
.25 193 nm photolysis of PhSiH produces SiH in both
2
2
05
3
2
the (0,0,0) and (0,1,0) vibrational states.26 Chu et al. have
shown that at total pressures above a few Torr collision-
induced relaxation of vibrationally excited silylene is rapid27
and, since our experiments are conducted at pressures [30
Ðrst-order rate constant, k , for the reaction.23 Typical plots
1
of k vs. reactant pressure at a high and a low total pressure
1
are shown in Fig. 2. Such plots give the second-order rate
constant, k , at each total pressure.
Torr, vibrational relaxation of the (0,1,0) SiH to (0,0,0) is not
expected to confound our measurements. This was conÐrmed
by testing that the rate constants obtained using 248 nm pho-
2
2
At the highest temperature studied, 441 K, the decay traces
collected at all total pressures (200È800 Torr) exhibited
unusual behaviour, with both a fast and a slow component in
the decay portion of the trace (see Fig. 3). The slow com-
ponent extends over much longer times than would be associ-
ated with removal of SiH by reaction with Me O, suggesting
tolysis, where much less (0,1,0) SiH is produced, were the
2
same as those obtained with 193 nm photolysis. Me O does
2
not absorb at the photolysis wavelengths of 193 and 248 nm.
The probe laser is split into reference and signal beams. The
signal beam is double passed through the reaction cell, giving
a total absorption path length of 2 m, and then focussed onto
one channel of a di†erential ampliÐer. The reference beam is
imaged onto the second channel, with the laser noise thereby
being subtracted from the resultant output. The output of the
di†erential ampliÐer is averaged (64È256 photolysis laser
shots) on a digital oscilloscope (Hewlett Packard 54510A) and
the averaged trace transferred to a computer for analysis. To
minimise non-silylene contributions to the signal, two sets of
2
2
that there is a mechanism leading to replenishment of SiH
2
under these conditions. These decay traces were Ðtted with an
exponential rise and double exponential decay to model the
fast and slow components of the overall decay portion of the
SiH traces.
2
If the reaction involves the formation of an intermediate
complex, the most straightforward mechanism for the
observed behaviour at 441 K involves equilibrium being
established between the reactants and the reaction complex.
In such a mechanism there would be rapid initial decay of the
decay traces are recorded; one with the laser tuned to a SiH
2
absorption (signal) and one with the laser detuned from SiH
2
SiH concentration but as more of the complex is formed the
2
rate of the reverse reaction increases and SiH reforms
(background). The background is subtracted from the signal
2
through dissociation of the complex. The SiH concentration
to provide the SiH decay signal. The experiment is performed
under conditions such that the reactions are pseudo-Ðrst order
2
2
would decay to a plateau at the equilibrium SiH concentra-
2
tion. Another loss mechanism for SiH , such as reaction with
2
and the silylene signal decays exponentially. With the excep-
tion of the highest temperature data, decay traces were Ðtted
to a bi-exponential function to account for both the rise and
the decay features. At the highest temperature of 441 K traces
did not return to the baseline. These traces were Ðtted with a
tri-exponential function having a rise and two decay times. A
minimum of three averaged traces were recorded and analysed
at each reactant pressure. The signal levels were found to
decrease with increasing total pressure.
another component of the mixture, di†usion from the obser-
The rate constants reported here were obtained with total
cell pressures of 30È850 Torr. The PhSiH pressure was typi-
3
cally 10È30 mTorr and the Me O pressure was typically
2
varied in the range 0.5È3.5 Torr. Ar and SF were used as the
6
bu†er gases with total pressures in the range 30È850 Torr (Ar)
and 30È150 Torr (SF ). The gases are Ñowed continuously
6
through the sample cell to prevent the build up of reaction
products. Gas Ñow rates are controlled using mass Ñow con-
trollers (MKS).
All chemicals were thoroughly degassed prior to use.
PhSiH (Aldrich, 99%), Me O (Aldrich, [99.99%), Ar (BOC,
3
2
[99.99%) and SF (BOC, 99.9%) were used as supplied.
6
3. Experimental results
Fig. 1 Typical average decay trace for SiH (10 mTorr of PhSiH
2
3
precursor) reacting with 0.5 Torr Me O at 400 Torr total pressure (Ar
2
RRKM/master equation calculations performed for the
SiH /Me O system have suggested that the high pressure
bath gas) and 294 K. The lower trace corresponds to the residuals
from a biexponential Ðt.
2
2
3086
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Baggott et al.7 have observed double exponential decay
behaviour for SiMe reacting with Me O, similar to our
2
2
observations for SiH , and presented the appropriate kinetic
2
scheme and expressions for the rate constants. The decay con-
stants extracted should show certain dependencies on reactant
concentration. k
should be linearly dependent on [Me O]
fast
2
while k
should be independent of this variable. Our data
slow
conform to this expectation, as shown in Fig. 4. A further test
is that (Ak ] Bk )/(A ] B), where A and B are the ampli-
fast
slow
tudes of the fast and slow components respectively, is predict-
ed to be independent of [Me O]. For SiMe ] Me O,
2
2
2
Baggott et al. observed this term to be dependent on [Me O],
2
contrary to expectations. In the analysis of our data we Ðnd
that the experimental uncertainties associated with the ratio
(Ak ] Bk )/(A ] B), coupled with a smaller [Me O]
fast
slow
2
range in our experiments, prevent us from determining
whether or not the ratio is dependent on [Me O]. However,
2
we will demonstrate later that the pre-equilibrium model is
consistent with the results of RRKM/master equation model-
ling and so eqn. (2) is expected to be relevant to our experi-
ments. We believe it likely that a pre-equilibrium situation is
also responsible for the experimental observations for the
SiMe ] Me O system, with the reason for BaggottÏs analysis
Fig. 2 Typical plots of the pseudo-Ðrst-order rate constants vs. reac-
tant pressure for the reaction of SiH with Me O. The data were
2
2
obtained at total pressures of 600 Torr (circles) and 60 Torr (squares)
at 294 K in Ar bath gas.
2
2
not conforming with model expectations being the high frac-
tion of Me O used, leading to this species playing a dual role
2
of reactant and bath gas.
vation region, or reaction of the complex to form products,
Rate constants for SiH reacting with Me O have been
would then be responsible for the slow decay of the SiH
2
2
2
signal. Qualitatively, the observed SiH time behaviour is con-
2
obtained up to an Ar pressure of 850 Torr at four tem-
peratures over the range 294È441 K (Table 1). The rate con-
stants reported for 441 K are those extracted from the fast
decay component of the overall decay trace, as discussed
above. The rate constants clearly decrease with increasing
temperature and increase with increasing pressure.
sistent with this picture. The dissociation rate of the complex
will increase with increasing temperature, and so the obser-
vation of this behaviour only at the highest temperature
studied is consistent with the proposed explanation.
Kinetic models for this type of reaction scheme predict a
It is usual to extrapolate fall-o† data to the high-pressure
limit using a LindemannÈHinshelwood form, or a modiÐed
version thereof. However, such extrapolations are only reliable
when the data are near the high-pressure limit. Earlier RRKM
calculations suggest that, even at the highest experimental
pressures D103 Torr, the reaction is a factor of D102È103
below the high pressure limit.14 Under these circumstances
such extrapolation of the data will not provide a meaningful
double exponential decay in the SiH concentration.7 If a pre-
2
equilibrium between reactants and complex is approached, the
sum of the fast and slow rate constants, k and k , in this
fast
slow
decay is related to the bimolecular rate constant, k , via
2
k
] k \ k [Me O] ] c
slow
where c is a constant. From the Ðts to the data, we Ðnd k
(1)
fast
2
2
slow
to be both small compared with k and approximately con-
estimate of k=. RRKM/master equation modelling has been
fast
stant with [Me O], as we illustrate below. Thus
2
used to obtain the high-pressure Arrhenius parameters (see
2
Section 4.2).
k
+ k [Me O] ] c@
(2)
fast
2
2
The negative temperature dependence seen in the data, i.e.
the reduction in the rate constant with increasing temperature,
where c@ \ c [ k
yields the second-order rate constant, k , from the slope.
is constant. A plot of k
vs. [Me O]
slow
fast
2
2
Fig. 3 Typical average decay trace for the high temperature (441 K)
reaction of SiH with Me O showing the raised baseline (10 mTorr
2
2
PhSiH , 2.5 Torr Me O in 200 Torr total pressure of Ar bu†er gas).
Fig. 4
k
(Ðlled circles) and k
(Ðlled triangles) variation with
Me O pressure. The data are for total pressures of 600, 700 and 800
3
2
fast
slow
The decay, which consists of 32 averages, is modelled with an expo-
nential rise and double exponential decay.
2
Torr in Ar bath gas.
Phys. Chem. Chem. Phys., 2001, 3, 3085È3094
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Table 1 Second-order rate constants, k , for the reaction of SiH
constraining the value of the critical energy for dissociation of
the complex.
2
2
with Me O at various temperatures and pressures (Ar bath gas)
2
The reactions a†ecting the SiH concentration can be mod-
k /10~11 cm3 molecule~1 s~1
2
2
elled as:
P/Torr
294 K
336 K
372 K
441 K
kf
SiH ] Me O ÈÈ SiH ÈMe O
30
60
3.54 ^ 0.1
5.24 ^ 0.04
6.62 ^ 0.1
7.91 ^ 0.3
9.70 ^ 0.3
10.8 ^ 0.4
11.5 ^ 0.1
12.7 ^ 0.7
14.0 ^ 0.6
15.8 ^ 0.9
14.4 ^ 0.5
17.3 ^ 0.7
16.4 ^ 0.8
16.6 ^ 0.8
2
2
2
2
kf
100
150
200
250
300
350
400
500
600
700
800
850
4.40 ^ 0.07
6.40 ^ 0.2
7.90 ^ 0.3
2.68 ^ 0.19
3.60 ^ 0.18
5.26 ^ 0.16
SiH ÈMe O ÈÈ SiH ] Me O
2
2
2
2
2.30 ^ 0.08
3.24 ^ 0.41
kp
SiH ÈMe O ÈÈ products
2
2
The reaction between SiH and PhSiH is not included as,
2
3
9.56 ^ 0.5
10.4 ^ 0.6
11.4 ^ 00.3
12.1 ^ 00.5
13.5 ^ 0.7
13.4 ^ 0.4
5.97 ^ 0.14
7.32 ^ 0.67
7.85 ^ 0.43
9.64 ^ 0.58
9.16 ^ 0.52
due to the low concentration of PhSiH , its rate is much
3
slower than that for the SiH /Me O reaction. k incorporates
4.37 ^ 0.62
4.25 ^ 1.10
5.25 ^ 0.45
2
2
p
any process that removes the complex, and hence SiH . The
2
SiH concentration at any time is described by considering
2
how the SiH and SiH ÈMe O concentrations change with
2
2
2
time:
d[SiH ]
2 t
\ [k [SiH ] [Me O] ] k [SiH ÈMe O]
2 t
f
2
t
r
2
2
t
dt
is typical of the behaviour of systems involving the formation
of an association complex.28
d[SiH ÈMe O]
2
2
t
\ k [SiH ] [Me O] [ k [SiH ÈMe O]
2 t
f
2
t
r
2
2
t
dt
3.2 Sulfur hexaÑuoride bath gas
[ k [SiH ÈMe O]
t
Results were obtained for the reaction of SiH with Me O at
p
2
2
2
2
294 and 438 K using SF as the bath gas (Table 2). SF has no
where [X] is the concentration of species X at time t. Under
6
6
t
signiÐcant absorption at the photolysis wavelengths of 193
pseudo-Ðrst-order conditions, [Me O] is constant and these
2
t
and 248 nm. The maximum pressure used in the SF experi-
equations reduced to:
6
ments was 150 Torr.
d[SiH ]
The SiH decay traces are of similar quality to that shown
in Fig. 1 for Ar bath gas and the plots of pseudo-Ðrst-order
rate constants vs. reactant pressure are similar to Fig. 2. The
2 t
2
\ [k [SiH ] ] k [SiH ÈMe O]
2 t
F
r
2
2
t
dt
d[SiH ÈMe O]
SiH decay traces at 438 K show the same raised baseline
2
2
t
\ k [SiH ] [ (k ] k )[SiH ÈMe O]
2 t
2
behaviour and fast and slow components as seen with Ar bath
F
r
p
2
2
t
dt
gas at 441 K. These decays were therefore treated in the same
manner as described above for the Ar case to extract the
second-order rate constants.
where k \ k [Me O], the t being omitted here as it is
F
f
2
redundant.
These equations can be solved analytically or by numerical
integration and Ðtted to the experimental decay curves. Over
a short time period, *t, they can be expressed as:
A comparison of the 294 K rate constants shows that those
for SF bath gas are approximately 1.4 times larger than the
6
values for Ar bath gas at the same total pressure. The
increased values for the rate constants arise from the increased
*[SiH ] \ ([k [SiH ] ] k [SiH R] )*t
collisional relaxation efficiency of the SiH ÈMe O complex by
2 t
F
2 t
r
2
t
2
2
SF compared to Ar. The rate constants obtained using both
*[SiH R] \ (k [SiH ] [ (k ] k )[SiH R] )*t
6
2
t
F
2 t
r
p
2
t
bath gases show a similar trend with total pressure. Our rate
\ [*[SiH ] [ k [SiH R] *t
constants with SF are uniformly lower than those reported
2 t
p
2
t
6
by Becerra et al.,14 with the di†erence being D15% at 50
Since [SiH ]
2 t`*t
\ [SiH ] ] *[SiH ] and [SiH R]
\
Torr.
2 t 2 t t`*t
2
[SiH R] ] *[SiH R] , the concentration of each species is
2
t
2
t
calculated from its concentration at the preceding time with a
set of initial values, [SiH ] and [SiH R] , as input. The
theoretical decay curves so obtained can be Ðtted to the
3.3 Extraction of the equilibrium constant at 441 K
2 0
2
0
As we have noted in Section 3.1, the decay traces at 441 K
display direct evidence for the formation of a pre-equilibrium.
These decay traces can be Ðtted to extract the equilibrium
constant for the system at this temperature. A direct experi-
mental measurement of the equilibrium constant helps to con-
strain the later RRKM/master equation calculations through
experimental curves with k , k and k as variables. We have
F
r
p
done this using a nonlinear least-squares Ðtting algorithm
(LevenbergÈMarquardt algorithm29). Since the experimental
decay traces include the production of SiH (0,0,0) (the rising
2
portion), which is not a feature of the model discussed here,
we Ðt the decays ignoring the Ðrst D10% of the decay after
time zero. *t values were checked to ensure convergence.
A typical Ðt to a SiH /Me O decay is shown in Fig. 5. We
2
2
Table 2 Second-order rate constants, k , for the reaction of SiH
Ðnd that the k values are consistent with those determined
2
2
with Me O at 294 and 438 K at various pressures (SF bath gas)
F
2
6
from the analysis of the experimental data discussed pre-
viously. The equilibrium constant, K , can be obtained from
k /10~11 cm3 molecule~1 s~1
eq
2
P/Torr
294 K
438 K
k
k
k /[Me O]
f
r
F
\
2
K
\
eq
k
30
60
100
150
4.66 ^ 0.06
7.25 ^ 0.08
9.19 ^ 0.08
10.99 ^ 0.15
0.96 ^ 0.07
1.45 ^ 0.11
2.13 ^ 0.09
È
r
K
should be independent of the total pressure at which the
eq
experiment is performed and hence also of the bath gas
used.30 The average value for K determined from the Ar
eq
3088
Phys. Chem. Chem. Phys., 2001, 3, 3085È3094

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and Me O allow a comparison of the calculated frequencies
2
with experimental values, thereby providing a check of their
accuracy, and also allow the stabilisation energy of the
complex to be determined.
4.1 Ab initio calculations
The initial geometry of each complex and reactant was found
using HartreeÈFock (HF) theory with a minimal basis set
(HF/6-31G**) and then reÐned with increasing complexity of
theory and basis set until the calculations were performed
with the Ðnal theory/basis set, MP2/6-311&G**. The harmo-
nic vibrational frequencies were scaled by the recommended
factor of 0.9496 before use in the statistical mechanical calcu-
lation of thermodynamic quantities and the RRKM calcu-
lations.32 No imaginary frequencies were found for any of the
structures, indicating that they correspond to local minima on
the relevant potential energy surfaces. A comparison of the
scaled MP2/6-311&G** vibrational frequencies for SiH and
2
Fig. 5 A typical Ðt to a high temperature SiH decay trace. The
Me O with experimental values shows that they lie within a
2
2
residuals (lower curve), which are the di†erence between the Ðt and
few percent of each other.
the decay trace (upper curve), illustrate the quality of the Ðt. The SiH
2
decay trace was obtained under conditions of 1.0 Torr Me O and 200
2
The calculations show that an association complex forms
between SiH and Me O. A representation of the complex
Torr total pressure in Ar bath gas at a temperature of 441 K. The Ðt
2
2
geometry is shown in Fig. 6. The geometry of the two halves
used *t of 1 ] 10~7 s and yielded k , k and k values of 5.06 ] 105,
F
r
p
1.00 ] 105 and 2.68 ] 104 s~1, respectively.
of the SiH ÈMe O complex are much the same as in the frag-
2
2
ments SiH and Me O. Key features are (i) SiÈH bond
2
2
length \ 0.1515 nm, (ii) SiÈO bond length \ 0.203 nm,
SiÈOÈC angle \ 111.38¡ and HÈSiÈO angle \ 87.9¡. The
HÈSiÈO angle is, as expected, based on an interaction between
the p-orbital of the Si atom and the lone pair on the O atom.
The calculated SiÈO bond length is longer than those found in
stable molecules. The reactant molecule is positioned perpen-
data is 2.2 ^ 0.7 ] 10~16 cm3 molecule~1 while that for the
SF data is 2.8 ^ 0.8 ] 10~16 cm3 molecule~1. Importantly,
6
within the experimental uncertainty the equilibrium constant
determined from the SF data is the same as that determined
6
from the Ar data.
The value for k was found to be ill-determined in the Ðtting
dicular to the HÈSiÈH plane, in keeping with SiH accepting
p
2
and this rate constant could take any value below 104 s~1
electron density into an empty p-orbital, which lies perpen-
without a†ecting how well the calculated curves Ðtted. This
dicular to the HÈSiÈH plane.
suggests that the process associated with k is slow and, coup-
The calculations show the electronic energy of the complex
to be stabilized by 97.2 kJ mol~1 compared with the reactants
and the di†erence in zero point energies, determined using
scaled ab initio harmonic frequencies, is 82.9 kJ mol~1. This is
slightly lower than the value of 84.3 kJ mol~1 recently report-
ed by Heaven et al.,33 whose calculations used a basis set with
more di†use functions because of their desire to compare the
behaviour of silylene with that of germylene. While this is
much lower than a typical chemical bond, it nevertheless indi-
cates that a signiÐcant bond is formed between the two moi-
eties. It is comparable, for example, to the critical energy for
dissociation of the propyl radical to form a methyl radical and
ethylene.34 The value of 82.9 kJ mol~1 compares favourably
with the value of 88.4 ^ 1.7 kJ mol~1 determined from the
high-temperature equilibrium constant.
p
ling this with the results of the ab initio calculations which
show a high barrier to rearrangement of the complex, we
suggest that the slow decay of SiH is associated with its di†u-
2
sion from the volume interrogated by the laser and/or its reac-
tion with other species rather than subsequent reaction of the
complex.
Having a value for K provides a check for the RRKM/
eq
master equation calculations that are presented later, in par-
ticular the value of the critical energy, E . Since the reaction
0
of interest involves a barrierless recombination, K is related
eq
to E via30
0
Qtr
AB
Q@
AB
A
A
E
B
0
K
\
exp
eq
Qtr Qtr Q@ Q@
k T
A
B
B
B
Here Qtr, Qtr and Qtr are the translational partition functions,
A
A
B
B
AB
while Q@ , Q@ and Q@ are the product of the electronic, vibra-
AB
tional and rotational partition functions. The value of K
eq
thus depends exponentially on E . Using parameters deter-
mined from ab initio calculations (see the following section) to
0
calculate the partition functions, an E value consistent with
0
the experimentally determined K can be calculated. With
eq
this approach we determine E to be 88.4 ^ 1.7 kJ mol~1.
0
4. Modelling the SiH /Me O system
2
2
The pressure and temperature dependence of the rate con-
stants have been modelled using an RRKM/master equation
approach. This determines the rate for the SiH ] Me O
2
2
reaction from that for the unimolecular dissociation of the
SiH ÈMe O complex. Ab initio calculations have been used to
2
2
supply the necessary input data for the RRKM calculations.
These calculations were performed for the SiH ÈMe O
2
2
complex and its constituents (SiH and Me O) using the
Fig. 6 A representation of the MP2/6-311&G** optimised geometry
of the SiH ÈMe O complex.
2
2
GAUSSIAN suite of programs.31 The calculations for SiH
2
2
2
Phys. Chem. Chem. Phys., 2001, 3, 3085È3094
3089

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Calculations of the SiH ] Me O system recently reported
are used instead of two-dimensional rotations did not repro-
duce the experimental behaviour. Consideration of steric hin-
drance between the fragments was not necessary in this model
due to the lack of bulky fragments and the relatively long
SiÈO bond length. The external moment of inertia that corre-
sponds to rotation about the SiÈO axis was treated as active
in both the molecule and the transition state. A vibrational
assignment and the structural and thermodynamic properties
for the SiH ÈMe O complex were obtained from the ab initio
2
2
by Heaven et al.33 have explored the reaction pathways
beyond the complex. They Ðnd the barrier to further reaction
of the complex to be signiÐcant (193.3 kJ mol~1). At the tem-
peratures of our experiment there is thus no possibility of
further reaction of the complex other than the channel leading
back to SiH and Me O. These ab initio predictions for
2
2
SiH ÈMe O are consistent with experiments for the methyl-
2
2
ated analogue of SiH , SiMe , which shows rearrangement
products for alcohols but not for Me O.7,35
2
2
2
2
calculations. The molecular parameters used in the RRKM
calculations are listed in Table 3.
2
In the master equation calculations an exponential-down
model for the energy transfer was employed:
4.2 RRKM/master equation modelling
The SiH ÈMe O Ðssion and SiH /Me O association reactions
2
2
2
2
1
C AE@ [ EBD
are described as:
P(E, E@) \
exp [
,
(E \ E@)
N(E@)
a
k~2
SiH ] Me O CD SiH ÈMe O
2
2
2
2
where E@ and E are the reactant energies before and after a
collision, respectively, N(E@) is a normalising factor and a is a
parameter related to the average downward energy transferred
k2
The bimolecular rate constant, k , is related to the
2
unimolecular rate constant, k , via the reaction equilibrium
~2
per collision, S*E
T. The value for S*E
T is the only
down
down
constant, K \ k /k . RRKM/master equation calculations
parameter varied in the master equation calculations. For Ar,
eq
2 ~2
were carried out using the UNIMOL program suite36 to
Becerra et al.38 found a constant value of 300 cm~1 applied
obtain k
values for total pressures ranging over those
covered experimentally and up to the high-pressure limit. K
over the range 298È665 K for the pressure dependence of SiH
reactions. This is consistent with values in the range 260È350
~2
2
eq
is determined in the usual manner from the partition functions
and enthalpy di†erence between reactants and products at 0
K37 (see Section 3.3 above). The bimolecular rate constant is
cm~1 at room temperature obtained from various kinetic and
energy transfer studies.30 Values of S*E
T for SF in SiH
down
6
2
reaction systems have been found to range from D800 to 1000
cm~1 over the temperature range 298 to D500 K and from
D700 to 900 cm~1 between D500 and 650 K.38h40 Based on
these previous studies, we have applied temperature-
then calculated from k and K
.
~2
eq
The RRKM calculations are performed using the Gorin
model, which has been extensively used for simple bond
Ðssion reactions producing fragments that do not show exten-
sive electronic rearrangement (resonance stabilization). In this
transition state model, the stretch in the breaking bond is
assigned as the reaction coordinate, the torsion around that
bond becomes a free rotation, and the four bending modes
that are destined to become external rotations of the products
are weakened. The internal modes of this ““looseÏÏ transition
state are simply the vibrations and rotations of the indepen-
dent product fragments, and the four low-frequency bending
modes associated with the breaking bond are considered to be
two two-dimensional internal rotations of the product frag-
ments that are hindered by some angular potential function.
The extent to which a fragment rotation in the transition state
is hindered due to the presence of the other fragment is
accounted for by reducing the moment of inertia of the free
rotor to an ““e†ectiveÏÏ moment of inertia for the hindered
rotor as determined by the hindrance angle.
independent S*E
T values for SF in the range 650È750
down
6
cm~1 and for Ar in the range 300È350 cm~1. It was found
that varying the S*E
T value over these ranges had only a
down
small e†ect on the predicted bimolecular rate constants.
Fig. 7 shows the calculated fall-o† curves with the experi-
mental data for Ar bath gas, while Fig. 8 shows the calculated
curves extrapolated to the high-pressure limit. Fig. 9 illus-
trates the corresponding Ðt for the SF experimental data. The
6
high-pressure limit rate constant, k~ , occurs at a total pressure
2
of D107 Torr. Our experimental data were obtained at pres-
sures below 103 Torr. The data are thus extrapolated to the
high-pressure limit over four orders of magnitude. The calcu-
lated fall-o† curves predict that the temperature dependence
of the rate constants switches at D105 Torr from being nega-
tive below this pressure to being positive above it. The log
A
and k~ values calculated at each temperature are given in
~2
2
Table 4. An Arrhenius plot of k~ yields the following param-
2
The input parameters for the RRKM/master equation cal-
culations are based largely on the results of the ab initio calcu-
lations. Having multiple temperature data was found to
provide a tight constraint on the Ðtting parameters. The vari-
able parameters in our approach are rs, the SiÈO bond length
in the transition state, E , the critical energy, and the lowest
0
frequency of the transition state. For the SiH ÈMe O
2
2
complex, the SiÈO bond stretch (ca. 440 cm~1) was selected as
the reaction coordinate, and this bond was lengthened from a
ground-state value of 0.230 nm to a transition-state value,
rs \ 0.400È0.525 nm, depending on the temperature. The
values used were 0.4, 0.45, 0.47 and 0.525 nm at temperatures
of 441, 372, 336 and 294 K, respectively. The transition state
becomes tighter as the temperature is increased. With
rs \ 0.525 nm at 294 K, A
\ 1017.30 s~1, a value within
~2, =
an acceptable range for simple Ðssion reactions (16 to 17.5).30
The SiÈO torsional motion was treated as a low frequency
vibration since treating it as a rotational motion leads to poor
Ðts to the pressure-dependent data because there is too high
an entropy in the transition state. Two CÈOÈSi bends and two
HÈSiÈO bends associated with the breaking SiÈO bond were
replaced by two-dimensional rotors. Calculations using the
alternate approach where low-frequency rocking vibrations
Fig. 7 The pressure-dependent second-order rate constants for the
SiH /Me O reaction in Ar bath gas at 294 (Ðlled circles), 336 (Ðlled
2
2
squares), 372 (Ðlled diamonds) and 441 K (Ðlled triangles) Ðtted with
the RRKM/master equation analysis (lines).
3090
Phys. Chem. Chem. Phys., 2001, 3, 3085È3094

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Table 3 RRKM parameters for the decomposition of the SiH ÈMe O complex
2
2
Reactant
Transition state
Frequencies/cm~1
3074
3062
3012
3010
2924
2920
2015
1960
1453
1443
1435
1428
1426
1400
1226
1162
1141
1121
1042
974
3026
3025
2937
2931
2877
2869
2049
2044
1465
1446
1435
1433
1425
1409
1220
1166
1153
1121
1084
1014
922
885
752
704
401
249
440
293
200
200
258
248
189
163
109
Rotational constants/cm~1a
Inactive external
Active external
0.109(1,2)
0.292(1,1)
0.028(1,2)
0.292(1,1)
Internal
SiH
7.602(1,2)b
0.321(2,2)b
17.3
2
Me O
2
log (A /s~1) at 294 K
=
Path degeneracy
1.0
Critical energy, E /kJ mol~1
87.0
0
Lennard-Jones parameters
p
, e
3.9, 164 (Ar bath gas)
4.7, 252 (SF bath gas)
LJ LJ
6
a Quantities in parentheses are symmetry number and dimension, respectively. b Rotational constants for rs \ 0.525 nm.
eters: log (A/cm3 molecule~1 s~1) \ [7.6 ^ 0.4 and E \ 9.3
a
^ 2.8 kJ mol~1.
It is important to note that one does not obtain a unique
set of parameters from the RRKM/master equation Ðts. For
Fig. 9 RRKM/master equation Ðt to experimental rate constants
obtained for the SiH /Me O reaction in SF bath gas at temperatures
2
2
6
of 294 (Ðlled circles) and 438 K (Ðlled squares). The RRKM param-
eters are those optimised to Ðt the data for Ar bath gas with changes
to the Lennard-Jones collision parameters and SE
T appropriate
down
for SF . A SE
T value of 700 cm~1 was used. The error bars for
6
down
the experimental data are smaller than the symbols shown. The results
(Ðlled triangles) of Becerra et al.14 at 296 K are shown for comparison.
Fig. 8 A plot of the pressure dependence of the rate constants calcu-
lated from the RRKM/master equation Ðt to the data shown in Fig. 7.
Phys. Chem. Chem. Phys., 2001, 3, 3085È3094
3091

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Table 4 Log A and k~ values determined from the RRKM/master equation Ðts to the experimental data at each of the temperatures studied
~2
2
Temperature/K
294
336
372
441
log (A /s~1)
17.30
8.09 ] 10~10
17.19
1.02 ] 10~9
17.12
1.14 ] 10~9
16.96
2.13 ] 10~9
~2
k~ /cm3 molecule~1 s~1
2
example, we Ðnd that the E value could vary from 85.4 to
87.0 kJ mol~1 (with, of course, compensating changes in the
other parameters) with similar quality Ðts obtained. While a
with the RRKM/master equation analysis than did the pre-
vious data. For this reason we believe the present data to be
more reliable than those presented previously.
0
S*E
T value for Ar of 320 cm~1 was used in the calcu-
The high-pressure limit values for the rate constants as
determined by the RRKM/master equation calculations are
highly unusual. An issue with the analysis is the large pressure
range over which the data are extrapolated to the high-
pressure limit. Because fall-o† curves approach the high-
pressure limit asymptotically, we quote pressure values for
which k /k= is 0.9. k /k= is predicted to be 0.9 at pressures of
1 ] 105, 3 ] 105, 6 ] 105 and 5 ] 106 Torr at temperatures of
294, 336, 372 and 441 K, respectively. Thus the extrapolation
to the high-pressure region is over D2È3 orders of magnitude
in pressure. Consequently, it is likely that the high-pressure
rate constants and the pressure values required to reach this
limit are not reliable. Nevertheless, the fact that the calcu-
lations produce such an unusual set of values leads to the
question of whether there are unusual features of the system
that might lead to it having behaviour that di†ers from the
norm.
down
lations, we Ðnd that values in the range 300È350 cm~1 give
similar results. At 441 K, the calculated K is 1.9 ] 10~16
eq
cm3 molecule~1. This compares with the experimentally deter-
mined values of 2.2 ^ 0.7 ] 10~16 cm3 molecule~1 and
2.8 ^ 0.8 ] 10~16 cm3 molecule~1 with Ar and SF as the
6
collision partners, respectively.
2
2
2 2
5. Discussion
The SiH /Me O reaction is expected to be similar to the
2
2
SiMe /Me O reaction. For the SiMe /Me O reaction, both
2
2
2
2
CÈH and CÈO bond insertion is possible but no reaction pro-
ducts corresponding to CÈO bond insertion have been
observed7,8 and CÈH insertion is unlikely.9,10 Ab initio calcu-
lated reaction proÐles34 show that rearrangement of the
SiH ÈMe O complex has too high an energy barrier to occur
2
2
with our experimental conditions. The previous experimental
study of the SiH /Me O reaction provided evidence for reac-
Trends that are a consistent feature of the RRKM calcu-
lations using a wide variety of parameters are: (i) the high-
pressure limit is reached at unusually high pressure (e.g., the
values obtained here compare with 105 Torr in ref. 14); (ii) the
reaction is very efficient, with indications that the high-
pressure limit rate constant is larger than the Lennard-Jones
collision rate constant (for comparison, the high-pressure rate
constant for the 1CH /Me O reaction is D1/3 of the
2
2
tion involving the formation of a stabilized SiH ÈMe O
2
2
complex as the only product.14
Our data provide further support for this. The negative
temperature dependence observed for the experimentally mea-
sured SiH /Me O second-order rate constants is the reverse
2
2
of the expected behaviour for most simple reactions. The
negative temperature dependence and the total pressure
dependence of the rate constants combine to reinforce the
presence of a complex mechanism. Particularly important is
the observation of decays that do not return to the baseline at
elevated temperatures (D440 K) as this is direct evidence for
complex formation and subsequent decay. The slow decay of
these curves to the baseline provides direct evidence for the
longevity of the complex. Analysis of these high-temperature
decay curves allows the equilibrium constant to be deter-
mined. This has provided an experimental measurement for
the well-depth of the complex. Behaviour similar to that seen
in our elevated temperature work has been seen for the analo-
gous reactions of SiMe with Me O7 and the cyclic ether,
2
2
Lennard-Jones collision rate constant41); (iii) in the high-
pressure limit the reaction is predicted to have a positive tem-
perature dependence over the range studied, indicating a
barrier to reaction. We have examined the system to explore
why it is displaying this unusual behaviour and, therefore,
when such unusual behaviour might be found in other
systems.
The high-pressure limit for the rate constant corresponds to
the situation where collisions can rapidly repopulate levels
depleted by reaction and hence there is a steady-state popu-
lation in the levels above dissociation. The larger the micro-
scopic rate constants for dissociation, the higher the pressure
required to reach the high-pressure limit because the col-
lisional energy transfer rate constants must exceed the disso-
ciation rate constants at the high-pressure limit. A very
high-pressure value required to reach for the high-pressure
limit thus implies unusually large microscopic rate constants
for unimolecular dissociation of the complex. The microscopic
rate constants, k(E), are given by RRKM theory as:30
2
2
tetrahydrofuran8 at lower temperatures, and with CH OH at
temperatures [421 K.10
3
The well-depth determined from the RRKM/master equa-
tion Ðts to the data is 87 kJ mol~1. This compares well with
the values calculated by ab initio methods (82.9 kJ mol~1)34
and from the experimentally determined 441 K equilibrium
constant (88.4 ^ 1.7 kJ mol~1). This value is, however, some-
what lower than the value of 96 kJ mol~1 determined in our
previous Ðt to a more limited data set.14 The availability of
the fall-o† data at elevated temperatures has provided a con-
straint that was absent in the earlier analysis. We noted pre-
P
E~E0os(E ) dE
`
`
0
k(E) \
ho(E)
viously that E was poorly constrained with a set of data at a
Here os(E ) is the density of states of the transition state at
0
`
single temperature. Note also that the value of 1017.7 s~1 at
energy E above the critical energy E , o(E) is the density of
`
0
294 K for A
calculated previously is higher than the
states of the molecular reactant and h is PlanckÏs constant.
Since the vibrational frequencies of the complex are not par-
ticularly unusual, the density of states will increase in the
usual way. However, a key di†erence between the complex
and the more usual unimolecular dissociations is the very low
critical energy for dissociation. Thus, while the numerator in
the RRKM rate constant expression is expected to vary with
increasing energy in a manner analogous to that for usual
~2, =
value of 1017.30 s~1 obtained here from the current set of
molecular and transition state parameters so the values for E
would be in much closer agreement for the same value of
0
A
.
~2, =
The rate constants obtained with SF bath gas in the
6
present work are consistently lower than those reported pre-
viously. We note that the new data provide a better match
3092
Phys. Chem. Chem. Phys., 2001, 3, 3085È3094

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systems, the denominator will be much smaller than usual due
calculation of Lennard-Jones collision frequencies is 0.42 nm.
to the lower energy (associated with the smaller value for E ).
This leads to the k(E) values being unusually large, and it
therefore follows that an unusually high value for the high-
pressure limit is required.
The SiÈO separation in the transition state places the SiH
0
2
and Me O further apart than this (D0.50 nm).
2
The calculations suggest that the rate constants revert to
the usual positive temperature dependence in the high-
pressure limit, i.e., they increase with increasing temperature.
The recombination reaction occurs on an e†ective potential
that is the sum of the intermolecular potential (approximated
In this context it is interesting to compare the values for
k(E) in the SiH /Me O system to those for other, more typical
2
2
systems. Consider, for example, the thermal decomposition of
phenylsilane, PhSiH which has been studied by OÏNeal et
al.42 This system has an E for dissociation into PhSiH and
as a one dimensional Morse oscillator in the RRKM
3
calculations) and a ““centrifugal potentialÏÏ associated with the
orbital angular momentum of the approaching reactants.30
The centrifugal term can act to set up a barrier to reaction.
We have calculated the value of the centrifugal term and the
potential energy term at the transition state positions at each
temperature for an impact parameter corresponding to the
transition state bond length. The potential is taken to be a
Morse function with the same parameters as used for the
RRKM calculations. The results of these calculations are
given in Table 5.
The feature that emerges from this calculation is that for the
294 to 372 K data the centrifugal barrier height exceeds the
decrease in the potential energy at the transition state, the net
result being a barrier between reactants and the association
product. As the temperature increases this barrier height is
reduced as the transition state moves in tighter and the
decrease in potential energy becomes much larger. As the tem-
perature increases eventually the decrease in the potential
energy at the transition state more than o†sets the increase
due to the centrifugal term and overall there is no barrier, as
we see in the calculations for 441 K. The presence of a barrier
will cause the rate to increase with increasing temperature
over the range of our experiments. While these calculations
are only indicative, they show that for a shallow well the e†ect
of the centrifugal term can be considerable. A key feature is
that the decrease in the potential energy at the transition state
is small and a barrier will also result with smaller values of the
impact parameter.
0
H
of 257 kJ mol~1 and at 1150 K a value of k /k= of 0.9 is
2
2 2
reached at D50 Torr total pressure. The contribution to the
dissociation rate of particular k(E) values can be estimated by
examining the function k(E) o(E)exp([E/kT ), where o(E) is
the density of states at energy E. Using the RRKM param-
eters reported by OÏNeal et al. it can be determined that this
function peaks at 13 000 cm~1 above the critical energy and
falls to 50% of the peak at 18 100 cm~1 above E , 20% at
0
21 400 cm~1 above E and 10% at 23 200 cm~1 above E .
0
0
The corresponding k(E) values are 1.5 ] 106, 1.8 ] 107,
6.4 ] 107 and 1.2 ] 108 s~1. The comparable values for the
SiH /Me O system at 294 K are as follows. The function k(E)
2
2
o(E)exp([E/kT ) peaks at 2700 cm~1 above E , where k(E) is
0
4.0 ] 109 s~1, drops to 50% by 3400 cm~1 above E where
0
k(E) is 2.5 ] 1010 s~1, to 20% by 3900 cm~1 above E where
0
k(E) is 6.0 ] 1010 s~1 and to 10% by 4200 cm~1 where k(E) is
9.4 ] 1010 s~1. At comparable points in the function the k(E)
values for SiH /Me O are D1È2 ] 103 larger than they are
2
2
for PhSiH decomposition. We thus expect the high-pressure
3
limit to be reached at pressures D1È2 ] 103 larger than is the
case for PhSiH decomposition, i.e. k /k= should be 0.9 at
3
2 2
pressures of D5 ] 104 to 1 ] 105 Torr. At 294 K k /k= is 0.9
2
2
at 1 ] 105 Torr. This comparison illustrates that the high
pressures required to reach the high-pressure limit for
SiH /Me O are a straightforward consequence of the k(E)
2
2
values being unusually large in this system.
The analysis presented above suggests that large high-
pressure limit pressures will be a general feature of systems
The unusual temperature dependence appears to arise
because the SiH ÈMe O bond is unusually weak and this is
with unusually low E values. Hippler and co-workers have
0
2
2
recently reported the results of an extensive series of studies of
coupled with the transition state being at large separation
where the potential energy is not much reduced from the
asymptotic value. The weak bond and large separation mean
that the centrifugal term can become important by creating a
barrier at low temperatures, leading to a positive temperature
dependence in this temperature regime. It is readily shown by
repeating the calculations of potential energy and centrifugal
barrier height for a system with a more typical dissociation
energy that the total energy is now negative over the full tem-
perature range of the experiment. Thus, at more typical values
of the dissociation energy there is no barrier since the centrifu-
gal term is now smaller than the decrease in the potential
energy at the transition state. This will also be the situation
where the well-depth is shallow but the transition state is at
smaller separations than for the SiH /Me O case.
the unimolecular decomposition of alkoxyl radicals.43,44
These species have relatively low E values. The recent work
0
concerns the isopropoxyl radical and includes data up to very
high pressures (D5 ] 104 Torr).43 E for this system is 63.7 kJ
0
mol~1. At 330 K the experimental rate constants reach 90%
of the high-pressure limit value reported by the authors at
2 ] 104 Torr. At 408 K the rate constant at the highest pres-
sure for which data are available (4.6 ] 104 Torr) is only 77%
of the high-pressure limit. This suggests that the 90% value is
in the 105È106 Torr range. The isopropoxyl radical system
which, like SiH ÈMe O, has a low E value, thus has high-
2
2
0
pressure limit values similar to those reported here for the
SiH /Me O system, consistent with our expectations based on
2
2
the analysis above.
2
2
A high efficiency for the reaction implies that it involves a
long-range attraction between the reactant species. This
appears to be a consequence of the large SiÈO bond length in
the transition state. The collision diameter that is used for the
As we discussed above, the weak bond was also responsible
for making the pressure dependence unusually high. A predic-
tion of our analysis is that similarly weakly bonded systems
will show unusual pressure and temperature behaviour.
Table 5 The values of the centrifugal and potential energy terms at the transition state positions at each temperature for an impact parameter
corresponding to the transition state bond length. The potential is a Morse function with the same parameters as used for the RRKM calcu-
lations
Temperature/K
294
336
372
441
Transition state bond length/nm
Centrifugal energy/cm~1
Potential energy/cm~1
Total energy/cm~1
0.525
258
0.47
295
0.45
327
0.40
387
[47
[125
[178
[430
211
170
149
[43
Phys. Chem. Chem. Phys., 2001, 3, 3085È3094
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23 U. N. Alexander, N. A. Trout, K. D. King and W. D. Lawrance,
Chem. Phys. L ett., 1999, 299, 291.
Acknowledgements
24 U. N. Alexander, K. D. King and W. D. Lawrance, Chem. Phys.
L ett., 2000, 319, 529.
This work was supported in part by the Australian Research
Council. UNA acknowledges the Ðnancial support provided
by an Australian Postgraduate Award. The help of the
Mechanical, Glassblowing and Engineering Workshop sta† at
Flinders University is gratefully acknowledged. We thank
Professor Robin Walsh for helpful correspondence.
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