Investigation of the Prototype Silylene Reaction, SiH2 + H 2O (and D2O): Time-Resolved Gas-Phase Kinetic Studies, Isotope Effects, RRKM Calculations, and Quantum Chemical Calculations of the Reaction Energy Surface

Article abstract of DOI:10.1021/jp036431w

Time-resolved kinetic studies of the reaction of silylene, SiH ₂, with H₂O and with D₂O have been carried out in the gas phase at 296 and at 339 K, using laser flash photolysis to generate and monitor SiH₂. The reaction was studied over the pressure range 10-200 Torr with SF₆ as bath gas. The second-order rate constants obtained were pressure dependent, indicating that the reaction is a third-body assisted association process. Rate constants at 339 K were about half those at 296 K. Isotope effects, k_H/k_D. were small averaging 1.076 ± 0.080, suggesting no involvement of H- (or D-) atom transfer in the rate determining step. RRKM modeling was undertaken based on a transition state appropriate to formation of the expected zwitterionic donor-acceptor complex, H₂Si ... OH₂. Because the reaction is close to the low pressure (third order) region, it is difficult to be definitive about the activated complex structure. Various structures were tried, both with and without the incorporation of rotational modes, leading to values for the high-pressure limiting (i.e., true second-order) rate constant in the range 9.5 × 10^-11 to 5 × 10^-10 cm³ molecule^-1 s^-1. The RRKM modeling and mechanistic interpretation is supported by ab initio quantum calculations carried out at the G2 and G3 levels. The results are compared and contrasted with the previous studies.

Full text of DOI:10.1021/jp036431w

J. Phys. Chem. A 2003, 107, 11049-11056
11049
Investigation of the Prototype Silylene Reaction, SiH2 + H2O (and D2O): Time-Resolved
Gas-Phase Kinetic Studies, Isotope Effects, RRKM Calculations, and Quantum Chemical
Calculations of the Reaction Energy Surface
Rosa Becerra
Instituto de Quimica-Fisica “Rocasolano”, C.S.I.C., C/Serrano 119, 28006 Madrid, Spain
J. Pat Cannady
Dow Corning Corporation, P.O. Box 995, Mail 128, Midland, Michigan 48686-0995
Robin Walsh*
Department of Chemistry, UniVersity of Reading, Whiteknights, P.O. Box 224,
Reading, RG6 6AD United Kingdom
ReceiVed: August 14, 2003; In Final Form: October 8, 2003
Time-resolved kinetic studies of the reaction of silylene, SiH2, with H2O and with D2O have been carried out
in the gas phase at 296 and at 339 K, using laser flash photolysis to generate and monitor SiH2. The reaction
was studied over the pressure range 10-200 Torr with SF6 as bath gas. The second-order rate constants
obtained were pressure dependent, indicating that the reaction is a third-body assisted association process.
Rate constants at 339 K were about half those at 296 K. Isotope effects, kH/kD, were small averaging 1.076
( 0.080, suggesting no involvement of H- (or D-) atom transfer in the rate determining step. RRKM modeling
was undertaken based on a transition state appropriate to formation of the expected zwitterionic donor-
acceptor complex, H2Si‚‚‚OH2. Because the reaction is close to the low pressure (third order) region, it is
difficult to be definitive about the activated complex structure. Various structures were tried, both with and
without the incorporation of rotational modes, leading to values for the high-pressure limiting (i.e., true second-
order) rate constant in the range 9.5 × 10-11 to 5 × 10-10 cm3 molecule-1 s-1. The RRKM modeling and
mechanistic interpretation is supported by ab initio quantum calculations carried out at the G2 and G3 levels.
The results are compared and contrasted with the previous studies.
Introduction
with the reversible formation of a zwitterionic donor acceptor
complex, viz.
Silylenes are of importance because they are implicated in
the thermal and photochemical breakdown mechanisms of
silicon hydrides and organosilanes, as well as being key
intermediates in CVD. Time-resolved kinetic studies, carried
out in recent years, have shown that the simplest silylene, SiH2,
reacts rapidly and efficiently with many chemical species.1,2
Examples of its reactions include Si-H bond insertions and
CdC and CtC π-bond additions.3 We have investigated the
H2Si + OH2 f H2Si‚‚‚OH2
(1,-1)
By means of RRKM calculations, the second-order rate
constants measured in the presence of argon (bath gas) were
extrapolated to give an estimated rate constant at the high-
pressure limit of 1.3 × 10-9 cm3 molecule-1 s-1. The RRKM
model employed an Eo value (approximately the binding energy
of the complex) of 64.9 kJ mol-1 compared with a quantum
4-18
kinetics and mechanisms of a number of reactions of SiH2
chemical (ab initio) calculated value of 52.3 kJ mol-1 20
.
including several of the prototype processes such as SiH2 +
SiH4,7 SiH2 + C2H4 ,6 and SiH2 + C2H2.5 Reactions of silylenes
with lone pair donors are another important reaction type,3 not
least because in the case of O donors they lead to formation of
the Si-O bond, the key linkage in silicone polymers. We have
already studied the kinetics and potential energy surfaces of
several reactions of SiH2 with carbonyl containing com-
pounds.12,14-16,18 In this paper, we turn our attention to SiH2 +
H2O, which may reasonably be considered the prototype reaction
of silylene with an n-type (lone pair) donor.
Although there is a reasonable self-consistency in the conclu-
sions of this work, the extrapolated second order rate constant
is particularly high, as are others found by the King and
Lawrance group for reactions of SiH2 with other O donors.19,21
For reactions of SiH2 with other species thought to be occurring
at the collision rate, we have measured rate constants in the
range 3-5 × 10-10 cm3 molecule-1 s-1 6,7,12
,
but nothing higher
than this.
We were thus stimulated to reinvestigate this system at room
temperature, but also to investigate it at higher temperatures.
To throw the maximum light on this system, we have investi-
gated the reaction of SiH2 with D2O as well to obtain isotope
effects. We additionally decided to reinvestigate the potential
energy surface most recently studied by Heaven, Metha, and
Alexander, King and Lawrance (AKL)19 have recently studied
the kinetics of this reaction at 294 K and found it to be a pressure
dependent, third-body assisted association process, consistent
* To whom correspondence should be addressed.
10.1021/jp036431w CCC: $25.00 © 2003 American Chemical Society
Published on Web 11/14/2003

11050 J. Phys. Chem. A, Vol. 107, No. 50, 2003
Becerra et al.
Buntine (HMB)20 and earlier by others.22-24 A preliminary report
of our work has appeared.25
Experimental Section
Equipment, Chemicals, and Method. The apparatus and
equipment for these studies have been described in detail
previously.7,26 Only essential and brief details are therefore
included here. SiH2 was produced by the 193 nm flash
photolysis of phenylsilane (PhSiH3) using a Coherent Compex
100 exciplex laser. Photolysis pulses were fired into a variable
temperature quartz reaction vessel with demountable windows,
at right angles to its main axis. SiH2 concentrations were
monitored in real time by means of a Coherent 699-21 single-
mode dye laser pumped by an Innova 90-5 argon ion laser and
operating with Rhodamine 6G. The monitoring laser beam was
multipassed between 32 and 48 times along the vessel axis,
through the reaction zone, to give an effective path length of
up to 1.8 m. A portion of the monitoring beam was split off
before entering the vessel for reference purposes. The monitoring
laser was tuned to 17259.50 cm-1, corresponding to a known
strong vibration-rotation transition26,27 in the SiH2 A(1B1) r
X(1A1) absorption band. Light signals were measured by a dual
photodiode/differential amplifier combination, and signal decays
were stored in a transient recorder (Datalab DL910) interfaced
to a BBC microcomputer. This was used to average the decays
of between 5 and 30 photolysis laser shots (at a repetition rate
of 0.5 or 1 Hz). The averaged decay traces were processed by
fitting the data to an exponential form using a nonlinear least
squares package. This analysis provided the values for first-
order rate coefficients, kobs, for removal of SiH2 in the presence
of known partial pressures of substrate gas.
Gas mixtures for photolysis were made up, containing
between 1.3 and 3.1 mTorr of PhSiH3, 0-12 Torr of H2O (or
D2O), and inert diluent (SF6) up to total pressures of between
10 and 200 Torr. Pressures were measured by capacitance
manometers (MKS, Baratron).
Figure 1. Second-order plots for the reaction of SiH2 + H2O at various
total pressures. (O) 10 Torr, (9) 30 Torr, (4) 100 Torr, (b) 200 Torr.
(a) T ) 296 K. (b) T ) 339 K.
All gases used in this work were thoroughly degassed prior
to use. PhSiH3 (99.9%) was obtained from Ventron-Alfa
(Petrarch). H2O (99.99%) was from local supply softened and
demineralized, and D2O (99.9%) was from Aldrich. Sulfur
hexafluoride, SF6, (no GC-detectable impurities) was from
Cambrian Gases.
Results
Kinetics. Preliminary experiments established that, for a given
reaction mixture, decomposition decay constants, kobs, were not
dependent on the exciplex laser energy (45-70 mJ/pulse, routine
variation) or number of photolysis shots (up to 30 shots). The
constancy of kobs (5 shot averages) showed no effective depletion
of reactants. Higher pressures of precursor were required at the
higher temperature because signal intensities decreased with
increasing temperature. However, at each temperature, the
precursor pressure was kept fixed. For each system (either SiH2
+ H2O or SiH2 + D2O) at each temperature, a series of
experiments was carried out at each of the four total pressures
in the range 10-200 Torr. At each pressure (SF6 diluent), four
to eight runs (of 5-30 laser shots each) at different H2O or
D2O pressures were carried out at each temperature. The results
of these experiments are shown in Figures 1 and 2. These figures
demonstrate, within reasonable experimental scatter, first the
linear dependence of kobs with substrate pressure expected for
second order kinetics and second the strong overall pressure
dependence of rates and therefore of the second-order rate
constants. The second order rate constants derived from the
gradients of these plots by least-squares fitting are shown in
Table 1. The error limits are single standard deviations and are
fairly small. As well as showing that the rate constants increase
with increasing pressure, these results also show that they
decrease with temperature (just as has been found in similar
Ab Initio Calculations. The electronic structure calculations
were performed with the Gaussian 98 software package.28 All
structures were determined by energy minimization at the
MP2)Full/6-31G(d) level. Transition state structures were
characterized as first-order saddle points by calculation of the
Hessian matrix. Stable structures, corresponding to energy
minima, were identified by possessing no negative eigenvalues
of the Hessian, whereas transition states were identified by
having one and only one negative eigenvalue. The standard
Gaussian-3 (G3) compound method29 was employed to deter-
mine final energies for all local minima. For transition states,
four single-point energy determinations were carried out at the
MP2 geometry, viz., QCISD(T)/6-31G(d), MP4/6-31+G(d),
MP4/6-31G(2df,p), and optimized MP2) full/GTlarge, and the
values were combined according to the G3 procedure.29 The
identities of the transition state structures were verified by
calculation of intrinsic reaction coordinates30 (IRC) at the
MP2)Full/6-31G(d) or B3LYP/6-31G(d) levels. Reaction bar-
riers were calculated as differences in G3 enthalpies at 298.15
K. These calculations were also carried out using the G2 method
for comparison purposes.31

Investigation of the SiH2 + H2O (and D2O) Reaction
J. Phys. Chem. A, Vol. 107, No. 50, 2003 11051
Figure 3. Pressure dependence of the second-order rate constants for
SiH2 + H2O at 296 K (9) and 339 K (3). Lines are RRKM fits
corresponding to different transition states: TSa (;, - - -), TSb
(-‚-‚, ‚‚‚‚). See text for details.
pressure was 200 Torr. At higher pressure, the SiH2 signals were
partially quenched, and reliable decays were impossible to
obtain. The temperature range of 40 K is insufficient to obtain
reliable Arrhenius parameters, but from the average decrease
in rate constant between 296 and 339 K, an activation energy
of ca -14 ((5) kJ mol-1 is calculated.
The overall pressure dependences for the SiH2 + H2O system
are plotted in Figures 3-5 where they are compared with the
results of RRKM (Rice, Ramsperger, Kassel, Marcus) calcula-
tions for various transition state models. The pressure depend-
ences for SiH2 + D2O were very similar and are not shown.
The pressure and temperature effects are consistent with those
of a third body assisted association process although not as
extensive as those obtained in other such reaction systems of
silylene.5-7,9,12,13,15 The RRKM calculations32 are described in
the next section.
RRKM Calculations. The pressure dependence of an as-
sociation reaction corresponds exactly to that of the reverse
unimolecular dissociation process providing there are no other
perturbing reaction channels. The ab initio calculations do not
suggest any such channel, and so we have carried out RRKM
calculations on the unimolecular dissociation of the zwitterion,
donor-acceptor complex, H2Si‚‚‚OH2, viz.
Figure 2. Second-order plots for the reaction of SiH2 + D2O at various
total pressures. (O) 10 Torr, (9) 30 Torr, (4) 100 Torr, (b) 200 Torr.
(a) T ) 296 K. (b) T ) 339 K.
TABLE 1: Experimental Second-Order Rate Constants for
SiH2 + H2O and D2O at 296 and 339 K and Various
Pressures
P/Torr
k (H2O)a
k (D2O)a
kH/kD
T ) 296K
10
30
100
200
1.40 ( 0.09
2.35 ( 0.15
5.10 ( 0.19
6.76 ( 0.24
1.32 ( 0.06
2.16 ( 0.07
4.44 ( 0.14
6.61 ( 0.56
1.061 ( 0.083
1.088 ( 0.078
1.149 ( 0.056
1.023 ( 0.093
T ) 339K
10
30
100
200
0.863 ( 0.037
1.08 ( 0.03
1.92 ( 0.14
3.33 ( 0.24
0.828 ( 0.063
1.048 ( 0.062
1.80 ( 0.04
1.042 ( 0.091
1.030 (0.067
1.066 ( 0.081
1.148 ( 0.095
2.90 ( 0.12
a Units: 10-12 cm3 molecule-1 s-1
.
SiH2 association reactions5-7,9,12-15). The rate constants for SiH2
+ D2O are very similar in magnitude to those for SiH2 + H2O
although there is a discernible isotope effect, favoring the latter
reaction.
H2Si‚‚‚OH2 f H2Si + OH2
(-1)
In this study, the rate measurements were limited to two
temperatures, viz., 296 and 336 K. At higher temperatures, the
quality of the reaction decay traces became poorer (signal decays
not exponential with slow return to baseline). This is probably
due to the onset of reversibility, as observed by AKL in the
SiH2 + MeOH19 and SiH2 + Me2O21 reaction systems. The
pressure range was dictated by practical considerations. The
lowest pressure of 10 Torr was governed by the need to have
sufficient substrate pressure to observe reaction. The highest
Because the H2Si‚‚‚OH2 molecule has not been isolated, let
alone studied, we are forced to make estimates of the necessary
parameters for these calculations. This has been done as follows.
First the ab initio calculations were used to calculate the
statistical mechanical standard entropies, S°, of the species
involved in the equilibrium reaction (1,-1). The values obtained,
S°(SiH2) ) 207 J K-1 mol-1 and S°(H2O) ) 188 J K-1 mol-1
,
are in good agreement with literature.33 The value for S°(H2-

11052 J. Phys. Chem. A, Vol. 107, No. 50, 2003
Becerra et al.
Figure 5. Comparison of RRKM calculated curves for four different
TS models at 296 K (data points, b). All models correspond to log-
(A/s-1) ) 15.0: a. TSb, vibs only; b. TSb with internal rotation replacing
torsion; c. TSb and reactant molecule with internal rotation replacing
torsion; d. TSb with active external rotation.
Figure 4. Comparison of RRKM calculated curves for three different
critical energies at 296 K (data points, b). For each curve, the value of
Eo/kJ mol-1 is given.
Si‚‚‚OH2) was 270 J K-1 mol-1, leading to a ∆S°(-1,1) value
of + 125 J K-1 mol-1. Using the relationship, ln(A-1/A1) )
∆S°(-1,1)/R where A-1 and A1 are the respective dissociation
and association A factors (and with modification of ∆S° (-1,1)
to molecular concentration units at 298 K) leads to A-1/A1 )
3.10 × 1025 molecule cm-3. This value was used to constrain
the magnitude of the dissociation A factor, A-1, as follows.
Typical values of A factors for SiH2 association reactions which
occur with high collisional efficiency are ca. 1.0 × 10-10 cm3
previous systems.6,7,9,12,15 The parameters used in the initial
RRKM calculations are shown in Table 2. This lists the
molecular vibrational wavenumbers for H2Si‚‚‚OH2 obtained
from the ab initio calculations corrected by the 0.893 factor
appropriate to this level. The values for the two transition states
TSa and TSb were obtained by adjustment of the wavenumbers
for the five modes associated with OH2 and SiH2 group rocking
and wagging and the Si‚‚‚O torsion. The Si-O stretching mode
was taken as the reaction coordinate. Although these wave-
number adjustments are somewhat arbitrary, it is well-known
that the outcome of the calculations is not sensitive to precise
values as long as the entropy of activation (i.e., the magnitude
of the A factor) is correctly matched. It is worth pointing out
that these TS assignments are essentially vibrational, in that all
modes are treated as harmonic oscillators. Exploration of other
possibilities is considered later. In modeling the collisional
molecule-1 s-1 1,2
Thus, to cover the possibilities of both looser
.
and tighter than normal A factors, values of 3.0 × 10-10 and
3.0 × 10-11 cm3 molecule-1 s-1 were chosen for A1. These
values correspond to values of A-1 of ca. 1.0 × 1016 s-1 and
1.0 × 1015 s-1 respectively, at 296 K. These values are both
lower than the ca. 4 × 1016 s-1 used by AKL.19 A slight
lowering of A by 10-0.06 ()0.87) was imposed on the transition
states at 339 K concordant with our modeling findings in
TABLE 2: Molecular and Transition State Parameters for RRKM Calculations for Decomposition of the H2Si‚‚‚OH2 Adduct
TS complex
parameter
O-H str(2)
molecule
TSa (296 K)
TSa (339 K)
TSb (296 K)
TSb (339 K)
3715
3613
1965
1918
1611
997
3715
3613
1965
1918
1611
997
3715
3613
1965
1918
1611
997
3715
3613
1965
1918
1611
997
3715
3613
1965
1918
1611
997
Si-H str(2)
OH2 bend
SiH2 bend
Si-O str
OH2 wag
776
509
rxn coord
102
rxn coord
120
rxn coord
180
rxn coord
190
OH2 rock
SiH2 wag
408
651
100
130
105
130
150
200
150
235
SiH2 rock
257
154
70
40
75
45
100
110
Si‚‚‚O torsion
75
80
A/s-1
1.0 × 1016
8.8 × 1015
1.0 × 1015
8.7 × 1014
Eo/kJ mol-1
Z/10-10 cm3 molec-1 s-1
65
65
54
54
4.38
4.46
4.38
4.46

Investigation of the SiH2 + H2O (and D2O) Reaction
J. Phys. Chem. A, Vol. 107, No. 50, 2003 11053
deactivation process, we have used a weak collisional (step-
ladder) model,32 because there is considerable evidence against
the strong collision assumption.34 The average energy removal
parameter, ∆E down, which determines the collisional efficiency
was taken as 12.0 kJ mol-1 (1000 cm-1), similar to that used
in previous systems (with SF6 bath gas6,15). The calculations
were fairly insensitive to this value, because effectively, at
lowish temperatures, this corresponded to close to strong
collisions. They are however significantly stronger than those
for Ar bath gas, viz., 3.8 kJ mol-1 (320 cm-1), used in the
calculations (and experiments) of AKL.19
or downward (in the case of an external rotation). We do not
agree with AKL19 that treating the low wavenumber torsional
vibration as an internal rotation cannot be made to fit our, or
indeed their, results provided A and Eo are appropriately chosen.
What these calculations show is that incorporation of such
∞
modes will alter the k1 value. Because this is experimentally
unknown (and not measurable under the present conditions),
the precise choice of correct model is impossible. Only limits
on the combinations of parameters can be set.
Ab Initio Calculations. The potential energy surface for this
reaction has been recently studied by HMB20 at the MP2/6-
311++G(d,p) and other levels of theory. Our objective, apart
from providing an energy surface for interpretation of the
experimental results, was to see whether the standard Gaussian
compound method (G2 and G3 procedures) would come close
to the results of this earlier study. As expected, we found three
stable species (or combination of species), viz., (i) H2Si‚‚‚OH2,
the initial complex of SiH2 + H2O, (ii) SiH3OH (silanol), the
lowest energy species on the surface, and (iii) H2 + HSiOH
(hydroxysilylene in both cis (c) and trans (t) forms). In addition,
we have located five transition states, TS1 leading from H2Si‚
‚‚OH2 to SiH3OH, TS2c/TS2t leading from H2Si‚‚‚OH2 to H2
+ HSiOH (c and t) via H2 elimination, and TS3c/TS3t
connecting SiH3OH to H2 + HSiOH (c and t). The transition
states for H2 elimination from H2Si‚‚‚OH2 and from SiH3OH
are clearly different from one another.
The critical energy, Eo, was treated as a semi-adjustable
parameter, because there is insufficient information to use it to
fit the data unambiguously. Thus, the range of values considered
was 48-66 kJ mol-1 (11.6-15.8 kcal mol-1) centered around
the ab initio value calculated both by us and in previous
work.19,20 Figure 3 shows the results of two sets of calculations
at each temperature of study: the first set with the higher A
factors (TSa) and Eo ) 65 kJ mol-1; the second with the lower
A factors (TSb) and Eo ) 54 kJ mol-1. The curves are positioned
to match the data at the pressures of study (as far as is possible).
Two features are immediately apparent. First, the fit to experi-
ment is not particularly good for either set of curves. This will
be discussed later. Second, the two pairs of curves diverge
significantly from one another at the high-pressure limits.
Because the high-pressure limiting values of the second-order
rate constants, k1∞, for SiH2 + H2O are not known, this cannot
The structures of all species are shown in Figure 6, and their
enthalpy values are listed in Table 3 as well as being represented
on the potential energy (enthalpy) surface in Figure 7.
It is worth noting that both TS1 and TS2c/TS2t lie above the
threshold energy for reaction, although TS3c/TS3t lie below it.
be used as a criterion to select which fit is best. The following
∞
argument, in our view, tends to favor the lower values of k1
.
The temperature dependence of k1∞, regardless of which TS is
used, indicates a reduction of value from 296 to 339 K of
between 0.80 and 0.70 (10-0.10 to 10-0.15) corresponding to Ea
of between -4 and -7 kJ mol-1. Thus, the activation energy
term, e-Ea/RT, of the rate constant at 296 K corresponds to a
factor of between 5 and 17. Assuming a value of 10 in
combination with each of the assumed A factors leads to values
for k1∞ of 3 × 10-9 cm3 molecule-1 s-1 for the loose transition
state, TSa, and 3 × 10-10 cm3 molecule-1 s-1 for the tight
Discussion
General Comments, Rate Constant Comparisons, and
Isotope Effects. The main experimental purpose of this study
was to measure the rate constants and their temperature and
pressure dependences for the reactions of SiH2 + H2O and SiH2
+ D2O. This has been accomplished and extends the work of
AKL19 who studied SiH2 + H2O at 294 K only. Our study was
limited to two temperatures by problems of reversibility at higher
temperatures. Our results are compared with those of AKL19 in
Table 4. A direct comparison is not possible because the reaction
is pressure dependent and we have used a stronger collision
partner (SF6) than AKL,19 who used Argon. The rate constants
differ by a factor of ca. 3 which is reasonable for the difference
in efficiencies of the two bath gases. A comparison of the
experimental results is shown graphically in Figure 8. The
negative temperature dependence of the SiH2 + H2O reaction
mirrors that of the SiH2 + CD3OD reaction also studied by
AKL19 as well as that of many other silylene reactions studied
in our labs.5-7,9,12,14,15,17
The isotope effects, kH/kD, shown in Table 1 are quite small
and, within experimental error, are independent of both tem-
perature and pressure, averaging 1.076 ( 0.080. There is no
sign of any trend. These are typical values for secondary isotope
effects and are reminiscent of the values we found previously15,18
in the SiH2/SiD2 + CH3CHO reaction. They certainly support
a mechanism in which there is no participation of a migrating
H (or D) in the rate determining step. These effects are discussed
again in the next but one section.
∞
transition state, TSb. The k1 values found from the modeling
3
lie in the range 1.6-5.0 × 10-10 cm molecule-1 s-1. Thus,
the tighter TS offers the greatest self-consistency. Because it
can be argued that this outcome depends on Eo, we present in
Figure 4 the effect of altering Eo on these results (for the tighter
TSb). The values of Eo chosen were 48, 54, and 66 kJ mol-1
.
∞
The comparison is made at 296 K. Clearly, k1 is lowered by
increasing Eo and raised by lowering Eo. The looser TSa could
∞
be made to produce a lower value for k1 by increasing Eo. A
value of ca. 77 kJ mol-1 would produce a more self-consistent
result, but this is further away from the ab initio value.
Last, because AKL19 employed a Gorin-type model with
certain modes of the loose transition state considered as
2-dimensional internal hindered rotors, we decided to try to
introduce the effects of rotation, within the confines of our
operational program. This was done first by converting the
torsional mode in TSb to an internal rotation. However, because
this altered the entropy of activation, small changes in the
rocking mode wavenumbers were also made to maintain a
constant A factor. Another calculation was done in which the
torsions of both the reactant molecule and TSb complex were
treated as internal rotations. A third calculation was done in
which the vibrational TSb was assumed to include an active
overall rotation. The results of these calculations are shown in
Figure 5. Clearly any of these offer as good a fit as one another
but alter the k1∞ value upward (in the case of internal rotations)
Ab Initio Calculations and the Mechanism. The intermedi-
ate species and the transition states together with their structures
and energy values are in close agreement with those found by
HMB.20 A comparison of energy values is shown in Table 3.

11054 J. Phys. Chem. A, Vol. 107, No. 50, 2003
Becerra et al.
Figure 7. Potential energy (enthalpy) surface for the reaction of SiH2
+ H2O. All enthalpies are calculated at the G3 level.
Figure 6. Ab initio MP2)Full/6-31G(d) calculated geometries of local
minimum structures and transition states on the SiH2 + H2O energy
surface. Selected distances are given in Å, and angles are in degrees.
TABLE 3: Ab Initio G3 and G2 Enthalpies for SiH4O
Species of Interest in the SiH2 + H2O Reaction
Figure 8. Comparison of pressure dependences of second-order rate
constants for SiH2 + H2O at 296 K: b, this work; 0, data of ref 19.
Lines are RRKM fits based on TSb but with different collisional
molecular
species
G3
G2
enthalpya relativeb enthalpya relativeb HMBb,c
deactivation step sizes, ∆E down: s, 1000 cm-1; ‚‚‚‚, 300 cm-1
.
SiH2 + H2O
H2Si‚‚‚OH2
TS1
H3SiOH
TS2c
-366.831971
-366.853159
-366.822067
0
-366.492167
0
-53
+32
0
-53
+39
-56 -366.512523
+26 -366.480122
TABLE 4: Comparison of Measured Second-Order Rate
Constantsa for SiH2 + H2O at Ambient Temperatures
-366.948156 -305 -366.606833 -301 -294
-366.825414
-366.825837
+17 -366.482423
+16 -366.482975
+32
+26
+38
+37
P/Torr
this workb
P/Torr
AKLc
TS2t
H2 + HSiOH(c) -366.880365 -127 -366.538782 -122 -111
H2 + HSiOH(t) -366.880393 -127 -366.538885 -123 -112
TS3c
TS3t
10
30
100
200
1.40
2.35
5.10
6.76
50
100
150
200
0.67
1.44
1.99
2.55
-366.845726
-366.846611
-36
-38
a Ho (298 K) values in Hartrees. b Relative energy in kJ mol-1
.
a Units of k: 10-11 cm3 molecule-1 s-1
19. T ) 294 K.
.
b T ) 296 K. c Reference
c Reference 20.
For comparisons with earlier theoretical calculations, the reader
is referred to Table 3 of the HMB paper.20 The only points we
have added are those of TS3c and TS3t, which were previously
found by Zakariah and Tsang.24 What our results show is that
there are two potential routes to formation of H2 + HSiOH (c
and t) from H2Si‚‚‚OH2, one direct and the other via SiH3OH.
However, the important point for the results of the present work
is that all pathways from H2Si‚‚‚OH2 to products have barriers

Investigation of the SiH2 + H2O (and D2O) Reaction
J. Phys. Chem. A, Vol. 107, No. 50, 2003 11055
in excess of the threshold energy for redissociation to SiH2 +
H2O, reaction (-1). Thus, our calculations confirm the fact that,
after reaction 1 has occurred, there is no easy pathway for the
reaction to continue further. The calculations thus support the
experimental findings of a pressure dependent association
reaction, without involvement of an H-transfer process in the
rate determining step. The calculations provide the value for
Eo, the dissociation (or critical) energy for the RRKM modeling
studies.
those of the SiH2 + ROR′ systems. AKL19 have rationalized
this modeling outcome by arguing that, in the case of reaction
of SiH2 with O-donor molecules, there may be a long-range
interaction giving rise to higher than usual reaction cross
sections. Furthermore, they rationalize a positive activation
energy by involving a centrifugal potential barrier which is
important because of the extended nature of the Si‚‚‚O bond
and the weak binding energy of the zwitterion complex.
Although we have no evidence against these propositions, we
remain cautious about them, because it seems possible to us
that the SiH2 + ROR′ systems can nevertheless be explained
within the framework of loose but normal transition states which
seem to fit other SiH2 reaction systems5-10,12,15,17,18 and also
GeH2 reaction systems36-42 where more weakly bound com-
plexes are generally involved.
RRKM Modeling Studies. Before discussing the results of
the calculations in detail, we show that our RRKM modeling
can be made to fit the results of AKL.19 Using TSb (and Eo )
54 kJ mol-1), we repeated one calculation at 296 K but with
∆E down ) 3.6 kJ mol-1 (300 cm-1), a reasonable value for Ar
bath gas. The result is shown in Figure 8 where it can be seen
that good agreement with the experimental data of AKL19 is
It should be added that we have not undertaken variational
transition state theory calculations of the isotope effects because
of the lack of information about the activated complex. We could
have attempted this, as we did for the SiH2 (SiD2) + CH3CHO
reaction.18 However, the exercise undertaken in that work, with
a better defined activation complex set of structures, demon-
strated that the isotope effects for different degrees of freedom
were largely self-canceling, leading to values of kH/kD in the
range of 1.005-1.122 at the temperatures and pressures of the
present work. The calculations in that work combined the high
pressure limiting values, 1.097 (296 K) and 1.135 (339 K), with
the pressure dependent values (inverse isotope effect) which
reduced them by up to 10%. Such an outcome in the present
study would be entirely consistent with the experimental results.
Finally, it is interesting to note the conclusion that, in the
gas-phase both in this and related systems,19,21 the reaction
effectively stops at the zwitterion stage; that is, the zwitterion
is the actual reaction product! The idea of such species as
intermediates in reactions of silylenes with O-donor molecules
goes back to the 1980s and the solution studies of Weber’s
group.43-45 Clearly in solution, the zwitterions find ways to react
further, and the solvent plays an important role. In the gas phase,
the fate of the zwitterions is unclear. We suspect a wall or
otherwise catalyzed reaction, which is too slow to affect our
measurements.
obtained. The calculation (from Figure 3) with ∆E
) 12
down
kJ mol-1 (1000 cm-1) is also shown for comparison.
The calculations presented here show that a number of
activated complex models can be made to fit (approximately)
the experimental data. There are, however, two problems. First,
the fit to the data (regardless of model) is not very good. The
models all show that in the region of measurement the reaction
is approaching its third order region of pressure dependence.
The experimental rate constants, particularly at the lower
pressures (10 and 30 Torr) do not show such a strong trend
with pressure. Increases in k1 are less than a factor of 2, whereas
the pressure change is a factor of 3. It should be acknowledged
that, at 10 Torr, the substrate H2O or D2O forms a significant
proportion of the total gas mixture and differences of collision
efficiency between SF6 and H2O (or D2O) may play a role. The
measurements of AKL19 fit their (and our) RRKM calculations
better, but the lowest pressure used was 50 Torr and their total
pressure range was necessarily limited (50-200 Torr) because
of the low collision efficiency of the argon bath gas. The
behavior we observe can sometimes arise in complex systems
when a non-pressure-dependent competing side reaction be-
comes significant at low pressures. Although this remains
possible, the occurrence of a direct reaction to SiH3OH or H2
+ HSiOH can be ruled out, not only because the PE surface
shows the barriers to be too high but also because such processes
involve H-migration and therefore primary isotope effects would
become evident at low pressures. Thus, we believe there is some,
as yet unexplained, experimental contribution to the rate.35 The
second problem concerns the RRKM model. Our modeling
shows that the data can be fitted within a range of loose
transition states and corresponding critical energies. These
models incorporate both internal rotational modes and overall
active rotations. None of the fitting is definitive, because we
do not have reliable information about the activated complex.
This arises in this system because the high-pressure limit which
would provide such information does not occur until pressures
that are ca. 104-105 times those accessible in our experiments.
Because of their preference for a Gorin-type model, AKL19
Acknowledgment. R.B. and R.W. thank Dow Corning for
a grant in support of the experimental work. R.B. also thanks
the Spanish DGICYT for support under Projects BQU2000-
1163-C02-01 and BQU2002-03381.
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∞
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