Time-resolved gas-phase kinetic, quantum chemical and RRKM studies of reactions of silylene with cyclic ethers

Article abstract of DOI:10.1021/jp908289h

Time-resolved kinetic studies of silylene, SiH₂, generated by laser flash photolysis of phenylsilane, have been carried out to obtain rate constants for its bimolecular reactions with oxirane, oxetane, and tetrahydrofuran (THF). The reactions were studied in the gas phase over the pressure range 1 - 100 Torr in SF₆ bath gas, at four or five temperatures in the range 294-605 K. All three reactions showed pressure dependences characteristic of third-body-assisted association reactions with, surprisingly, SiH₂ + oxirane showing the least and SiH₂ + THF showing the most pressure dependence. The second-order rate constants obtained by extrapolation to the high-pressure limits at each temperature fitted the Arrhenius equations where the error limits are single standard deviations: log(k_oxirane^∞/cm³molecule ^-1s^-1) = (-11.03 ± 0.07) + (5.70 ± 0.51) kJ mol^-1/RT ln 10 log(k_oxirane^∞/cm ³molecule^-1s^-1 = (-11 17 ± 0.11) + (9.04 ± 0.78) kJ mol^-1/RT in 10 log(k_THF ^∞/cm³molecule^-1s^-1 = (-10.59 ± 0.10) + (5.76 ± 0.65) KJ mol^-1/RT in 10 Binding-energy values of 77, 97, and 92 kJ mol^-1 have been obtained for the donor - acceptor complexes of SiH₂ with oxirane, oxetane, and THF, respectively, by means of quantum chemical (ab initio) calculations carried out at the G3 level. The use of these values to model the pressure dependences of these reactions, via RRKM theory, provided a good fit only in the case of SiH₂ + THF. The lack of fit in the other two cases is attributed to further reaction pathways for the association complexes of SiH₂ with oxirane and oxetane. The finding of ethene as a product of the SiH₂ + oxirane reaction supports a pathway leading to H ₂Si=O + C₂H₄ predicted by the theoretical calculations of Apeloig and Sklenak.

Full text of DOI:10.1021/jp908289h

784
J. Phys. Chem. A 2010, 114, 784–793
Time-Resolved Gas-Phase Kinetic, Quantum Chemical and RRKM Studies of Reactions of
Silylene with Cyclic Ethers
Rosa Becerra,*,† J. Pat Cannady,‡ Olivia Goulder,§ and Robin Walsh*,§
Instituto de Quimica-Fisica ‘Rocasolano’, C.S.I.C., C/Serrano 119, 28006 Madrid, Spain, Dow Corning
Corporation, P.O. Box 994, Mail CO1232, Midland, Michigan, 48686-0994, and Department of Chemistry,
UniVersity of Reading, Whiteknights, P.O. Box 224, Reading, RG6 6AD, U.K.
ReceiVed: August 27, 2009; ReVised Manuscript ReceiVed: NoVember 18, 2009
Time-resolved kinetic studies of silylene, SiH2, generated by laser flash photolysis of phenylsilane, have
been carried out to obtain rate constants for its bimolecular reactions with oxirane, oxetane, and tetrahydrofuran
(THF). The reactions were studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at
four or five temperatures in the range 294-605 K. All three reactions showed pressure dependences
characteristic of third-body-assisted association reactions with, surprisingly, SiH2 + oxirane showing the least
and SiH2 + THF showing the most pressure dependence. The second-order rate constants obtained by
extrapolation to the high-pressure limits at each temperature fitted the Arrhenius equations where the error
limits are single standard deviations:
log(ko∞xirane⁄cm3molecule-1s-1) ) (-11.03 ( 0.07) + (5.70 ( 0.51) kJ mol-1 ⁄ RT ln 10
log(ko∞xetane⁄cm3molecule-1s-1) ) (-11.17 ( 0.11) + (9.04 ( 0.78) kJ mol-1 ⁄ RT ln 10
log(kT∞HF⁄cm3molecule-1s-1) ) (-10.59 ( 0.10) + (5.76 ( 0.65) kJ mol-1 ⁄ RT ln 10
Binding-energy values of 77, 97, and 92 kJ mol-1 have been obtained for the donor-acceptor complexes of
SiH2 with oxirane, oxetane, and THF, respectively, by means of quantum chemical (ab initio) calculations
carried out at the G3 level. The use of these values to model the pressure dependences of these reactions, via
RRKM theory, provided a good fit only in the case of SiH2 + THF. The lack of fit in the other two cases is
attributed to further reaction pathways for the association complexes of SiH2 with oxirane and oxetane. The
finding of ethene as a product of the SiH2 + oxirane reaction supports a pathway leading to H2SidO + C2H4
predicted by the theoretical calculations of Apeloig and Sklenak.
Introduction
by Moiseev and Leigh.22,23 In our own laboratories,24,25 com-
plexes of SiMe2 with Me2O and with tetrahydrofuran (THF)
were invoked to explain biexponential kinetic behavior in their-
gas phase reactions. Complexes of SiH2 itself with O-donor
molecules have not been seen directly, but from gas-phase
kinetic studies, the evidence includes (i) reversibility of reaction9
and (ii) third-body-assisted association processes,5-9 both
consistent with formation of weakly bound adducts with binding
energies of 54-65 kJ mol-1 (H2Si· · ·OH2)6 and 88 kJ mol-1
(H2Si · · · OMe2)9 consistent with theoretically calculated
values.6,9,16,26-28
Silylenes are of importance because they are implicated in
the thermal and photochemical breakdown mechanisms of
silicon hydrides and organosilanes and they are key intermedi-
ates 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.1-3 Examples of its
reactions include SisH bond insertions, CdC, and CtC π-bond
additions.4 Because it has an empty p orbital in its A1 ground
1
state, SiH2 is particularly reactive with lone-pair donor molecules
such as H2O (D2O),5-7 MeOH (CD3OD),5 and Me2O.8,9 There
is little doubt that such reactions, in their initial steps, form
donor-acceptor complexes with zwitterionic character. Origi-
nally, such complexes were invoked by Weber and his
group10-15 to account for their findings in kinetic and mecha-
nistic studies of SiMe2 in solution. Their existence was supported
by the theoretical calculations of Raghavachari et al.16 Soon
after that, a number of specific complexes of silylenes were
isolated in frozen matrices by the groups of Ando17,18 and
West.19,20 They have also been directly detected by time-resolved
kinetic means in solution by Levin et al.21 and more recently
In the gas phase, the complexes themselves appear to have
relatively long lifetimes and, for the most part, do not readily
rearrange to other products despite the apparently straightforward-
looking isomerization process 1 shown below:
It appears that the energy barriers to the 1,2 migration of X
(X ) H or Me) from O to Si are too high to be easily
surmounted. (An H2O catalyzed version of reaction 1 (X ) H)
has been observed,7 viz., a bimolecular reaction. This is the
analogue of solvent catalyzed process 1 in solution.)6,16,26-28
* Corresponding authors.
† Instituto de Quimica-Fisica ‘Rocasolano’.
‡ Dow Corning Corporation.
§ University of Reading.
10.1021/jp908289h  2010 American Chemical Society
Published on Web 12/22/2009

Studies of Reactions of Silylene with Cyclic Ethers
J. Phys. Chem. A, Vol. 114, No. 2, 2010 785
Other unimolecular processes also have barriers that rule out
their occurrence.6,28 One way in which such complexes might
be encouraged to react further is by incorporation of strain
energy into their structures. To this end, we decided to embark
on a kinetic study of the reaction of SiH2 with oxirane (cyclo-
CH2CH2Os) and oxetane (cyclo-CH2CH2CH2Os). In order to
provide a benchmark, we also included the reaction of SiH2
with THF (cyclo-CH2CH2CH2CH2Os), a relatively unstrained
cyclic ether. These reactions have not previously been inves-
tigated experimentally. In addition, we have undertaken quantum
chemical calculations of the binding energies of SiH2 with each
of these molecules. Apeloig and Sklenak29 have shown, in a
previous study of SiH2 + oxirane, that there is a relatively low-
energy pathway leading to formation of silanone, viz.:
) 133.3 N m-2). The substrate pressure ranges were as follows:
oxirane, 0-940 mTorr; oxetane, 0-680 mTorr; THF, 0-800
mTorr. Pressures were measured by capacitance manometers
(MKS, Baratron). All gases used in this work were frozen and
rigorously pumped to remove any residual air prior to use.
PhSiH3 (99.9%) was obtained from Ventron-Alfa (Petrarch).
Oxirane was obtained from Cambrian gases (99.7%). Oxetane
was obtained from Aldrich (99.7%). THF was obtained from
BDH (99.5%). Sulfur hexafluoride, SF6, (no GC-detectable
impurities) was obtained from Cambrian Gases. GC purity
checks were carried out both with a 3 m silicone oil column
(OV101) operated at 60 °C and with a 3 m Porapak Q operated
at 120 °C. The latter column was also used for end-product
analyses. N2 was used as carrier gas, and detection was by FID.
Detection limits for impurity peaks were better than 0.1% of
the principal component.
SiH2 + oxirane f complex f H2SiO + C2H4 (2)
The ethers used in this study show weak absorptions at 193
nm, and it was found in preliminary experiments, by GC
analysis, that decomposition of a few percent occurred under
the conditions of these studies. Without a longer-wavelength
absorbing precursor for SiH2, we were unable to avoid this
problem. The consequences of this are considered in the Results
section.
Ab Initio Calculations. The electronic-structure calculations
were performed with the Gaussian 98 software package.34 All
structures were determined by energy minimization at the
MP2)Full/6-31G(d) level. Stable structures, corresponding to
energy minima, were identified by possessing no negative
eigenvalues of the Hessian. [Transition states which would have
been identified by having one negative eigenvalue were not
sought in this study.] The standard Gaussian-3 (G3) compound
method35 was employed to determine final energies for all local
minima. Harmonic frequencies were obtained from the values
calculated at the HF/6-31G(d) level adjusted by the correction
factor 0.893 appropriate to this level.36
The occurrence of reaction 2 is consistent with the findings
of a previous study of SiMe2 + oxirane from our laboratories.25
As well as the measurement of rate constants for these
reactions, a key aspect of the present study is to obtain their
pressure dependences and to undertake modeling via Rice-
Ramsperger-Kassel-Marcus (RRKM) theory30 in order to test
the consistency with quantum-chemically calculated binding
energies of the complexes. For book-keeping purposes, we use
the following reaction numbering system:
SiH2 + oxirane f products
SiH2 + oxetane f products
(3)
(4)
(5)
SiH2 + tetrahydrofuran f products
Experimental Section
Equipment, Chemicals and Method. The apparatus and
equipment for these studies have been described in detail
previously.31,32 Only essential and brief details are therefore
included here. SiH2 was produced by the 193 nm flash photolysis
of phenylsilane (PhSiH3) by using a Coherent Compex 100
exciplex laser. (An Oxford Lasers KX2 exciplex laser was used
in some early experiments.) Photolysis pulses (beam cross
section 4 cm × 1 cm) 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
36 times along the vessel axis, through the reaction zone, to
give an effective path length of 1.5 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
Results
Kinetics. Preliminary experiments established that, for given
reaction gas mixtures in each of the three reaction systems,
decomposition decay constants, kobs, were not dependent on the
exciplex laser energy within the normal routine range of
variation (50-80 mJ/pulse). There was also no dependence on
the number of photolysis laser shots (up to 15 shots). The
constancy of kobs (five shot averages) showed that there was no
effective depletion of reactants. Higher pressures of precursor
were required at the higher temperatures because signal intensi-
ties decreased with increasing temperature. However, for the
purposes of rate constant measurement at a given temperature,
the precursor pressure was kept fixed.
For each reaction system, at each temperature of study and
at 10 Torr total pressure, a series of experiments was carried
out to investigate the dependence of kobs on reactant partial
pressure (at least five different values). The purpose of these
experiments was to establish the second-order nature of the
kinetics. In addition, again for each reaction system at each
temperature of study, another series of runs was carried out
in which total pressures were varied by addition of SF6 to
values in the range 1-100 Torr, in order to investigate the
dependences of rate constants on total pressure. The data were
obtained in the same way as those at 10 Torr, although in
these experiments, only three or four substrate partial
pressures were tried at each total pressure (because second-
order behavior was established at 10 Torr). The pressure
range was limited by practical considerations. Above ca. 100
R
cm-1, corresponding to the known Q0,J (5) strong rotation
1
1
transition32,33 in the SiH2 A B1(0,2,0) r X A1(0,0,0) vibronic
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 5-15 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 by using a nonlinear least-squares
package. This analysis provided the values for first-order rate
constants, kobs, for removal of SiH2 in the presence of known
partial pressures of substrate gas.
˜
˜
Gas mixtures for photolysis were made up containing between
1.6 and 6.9 mTorr of PhSiH3, variable pressures of substrate
and inert diluent (SF6) to total pressures of 1-100 Torr (1 Torr

786 J. Phys. Chem. A, Vol. 114, No. 2, 2010
Becerra et al.
Figure 2. Pressure dependence of second-order rate constants for
reaction 3, SiH2 + oxirane, in the presence of SF6 at five temperatures
(indicated). Curves are eyeball fits (see text).
Figure 1. Second-order plots for reaction of SiH2 + oxirane:
temperatures for each set of data are marked in the figure.
TABLE 1: Second-Order Rate Constants for SiH2 +
Oxirane over the Range 294-605 K, at 10 Torr Total
Pressure and Infinite Pressure (by Extrapolation)
T/K
ka,b
k∞a,c
294
356
397
481
605
9.23 ( 0.29
6.25 ( 0.35
4.61 ( 0.17
2.86 ( 0.12
1.92 ( 0.16
10.0 ( 1.0
6.3 ( 0.6
5.0 ( 0.5
3.5 ( 0.35
3.2 ( 0.3
a Units: 10-11 cm3 molecule-1 s-1
.
b Single standard deviations.
c Estimated (10%.
Torr, transient signals became too small to be measured
reliably, and below 1 Torr, pressure measurement uncertain-
ties became significant. The particular results for each
reaction system are given below.
Figure 3. Arrhenius plots of second-order rate constants for reaction
3, SiH2 + oxirane in SF6: O, 10 Torr; b, infinite pressure. Line is LSQ
fit to k∞ values.
Oxirane and oxetane absorb 193 nm radiation weakly and
undergo small amounts of photochemical decomposition (see
below). The percentage product yields are at most a few
percent, and although products such as C2H4 are reactive
toward SiH2, the small amounts produced are unlikely to
affect the SiH2 decays beyond existing experimental error.
Kinetics of SiH2 + Oxirane. This reaction was investigated
over the temperature range 294-605 K. The second-order
rate plots are shown in Figure 1 for the five temperatures
studied. It can be seen that reasonably linear plots are
obtained, and the second-order rate constants at 10 Torr,
obtained by least-squares fitting to these plots, are given in
Table 1. The error limits are single standard deviations. It
should be noted that the rate constants decrease with
increasing temperature. The pressure dependences of these
rate constants are plotted in Figure 2, in log-log plots for
convenience. Although the rate constants show some pressure
dependence, it is relatively small. We were not able to model
this pressure dependence (see later); therefore, the fits are
empirical. With this in mind, the values for the high-pressure
limiting rate constants, also shown in Table 1, clearly have
a higher uncertainty (estimated at (10%). Figure 3 shows
an Arrhenius plot of the rate constants obtained here both at
10 Torr and at infinite pressure. A linear least-squares fit to
the infinite pressure values corresponds to the Arrhenius
equation, where the uncertainties are again single standard
deviations:
log(k∞3 /cm3molecule-1s-1) ) (-11.03 ( 0.07) +
(5.67 ( 0.50) kJ mol-1/RT ln 10
Because of the unknown uncertainties involved in extrapola-
tion, we would estimate that these Arrhenius parameters may
have maximum uncertainties of (0.5 (log A∞) and (3.6 kJ
mol-1 (Ea).
Kinetics of SiH2 + Oxetane. This reaction was investigated
over the temperature range 296-594 K. The second-order rate plots
are shown in Figure 4 for the five temperatures studied. It can be
seen that reasonably linear plots are obtained, and the second-order
rate constants at 10 Torr, obtained by least-squares fitting to these
plots, are given in Table 2. It may be noted that the rate constants
again decrease with increasing temperature. The pressure depend-
ences of these rate constants are plotted in Figure 5. The rate
constants show more pressure dependence than for the SiH2 +
oxirane system, but we were again unable to model it (see later);
therefore, the fits are empirical. The values for the high-pressure
limiting rate constants, also shown in Table 2, again have a higher
uncertainty (estimated). Figure 6 shows an Arrhenius plot of the
rate constants obtained here both at 10 Torr and at infinite pressure.
A linear least-squares fit to the infinite pressure values corresponds
to the Arrhenius equation, where the uncertainties are again single
standard deviations:

Studies of Reactions of Silylene with Cyclic Ethers
J. Phys. Chem. A, Vol. 114, No. 2, 2010 787
log(k∞4 /cm3molecule-1s-1) ) (-11.17 ( 0.11) +
(9.04 ( 0.78) kJ mol-1/RT ln 10
Because of the unknown uncertainties involved in extrapola-
tion, we would estimate that these Arrhenius parameters may
have maximum uncertainties of (0.7 (log A∞) and (5.0 kJ
mol-1 (Ea).
Kinetics of SiH2 + THF. This reaction was investigated over
the temperature range 294-398 K. The temperature range
for this study was more limited because decay traces showed
end absorptions above 400 K. The second-order rate plots
Figure 6. Arrhenius plots of second-order rate constants for reaction
4, SiH2 + oxetane in SF6: 4, 10 Torr; 2, infinite pressure. Line is
LSQ fit to k∞ values.
are shown in Figure 7 for the four temperatures studied. It
can be seen that reasonably linear plots are obtained, and
the second-order rate constants at 10 Torr, obtained by least-
squares fitting to these plots, are given in Table 3. The error
limits are single standard deviations. It may be noted that
the rate constants again decrease with increasing temperature.
The pressure dependences of these rate constants are plotted
in Figure 8. The rate constants show more pressure depen-
dence than for the SiH2 + oxetane, and in this case, we were
able to model it (see later); therefore, the fits are those
calculated by RRKM theory.30 The values for the high-
Figure 4. Second-order plots for reaction of SiH2 + oxetane:
temperatures for each set of data are marked in the
figure.
TABLE 2: Second-Order Rate Constants for SiH2 +
Oxetane over the Range 296-594 K, at 10 Torr Total
Pressure and Infinite Pressure (by Extrapolation)
T/K
ka,b
k∞a,c
296
340
398
477
594
15.7 ( 1.0
8.77 ( 1.00
7.04 ( 0.21
4.08 ( 0.19
2.38 ( 0.09
25 ( 2.5
16 ( 1.6
12.5 ( 1.3
6.3 ( 0.6
4.0 ( 0.4
a Units: 10-11 cm3 molecule-1 s-1
.
b Single standard deviations.
c Estimated (10%.
Figure 7. Second-order plots for reaction of SiH2 + THF: temperatures
for each set of data are marked in the figure.
TABLE 3: Second-Order Rate Constants for SiH2 + THF
over the Range 294-398 K, at 10 Torr Total Pressure and
Infinite Pressure (by Extrapolation)
T/K
ka,b
k∞a,c
294
323
357
398
10.14 ( 0.35
6.09 ( 0.17
3.37 ( 0.12
1.73 ( 0.08
28 ( 2.8
21 ( 2.1
18.6 ( 1.9
14.8 ( 1.5
Figure 5. Pressure dependence of second-order rate constants for
reaction 4, SiH2 + oxetane, in the presence of SF6 at five temperatures
(indicated). Curves are eyeball fits (see text).
a Units: 10-11 cm3 molecule-1 s-1
.
b Single standard deviations.
c Estimated (10%.

788 J. Phys. Chem. A, Vol. 114, No. 2, 2010
Becerra et al.
Figure 10. Ab initio, MP2)full/6-31G(d) calculated geometries of
the complexes formed by SiH2 with oxirane, oxetane, and THF. Selected
distances are given in angstroms, and angles are given in degrees. For
simplicity, H atoms have been omitted from the rings.
peak was observed (apart from benzene from PhSiH3 photolysis)
which eluted at 2.0 min and was identified as C2H4. Under these
conditions, its peak corresponded to 30% of the residual oxirane
(based on peak area). Blank experiments showed that only 0.3%
of C2H4 was formed from oxirane alone.
SiH2 + Oxetane. A mixture of 0.6 Torr PhSiH3, 1.0 Torr
oxetane, and 10 Torr SF6 was subjected to 200 shots of 193
nm laser radiation (50 mJ/pulse) and then analyzed by GC
(Porapak Q column at 150 °C). Despite the formation of small
amounts of some small molecules (e.g. C2H4) from oxetane
alone, no product peaks were detected with retention times
between those of oxetane itself and benzene, suggesting that
stable end products of SiH2 with oxetane were not formed under
these conditions.
Figure 8. Pressure dependence of second-order rate constants for
reaction 5, SiH2 + THF, in the presence of SF6 at five temperatures
(indicated). Curves are RRKM fits (see text).
Quantum Chemical (ab initio) Calculations. These were
limited to calculation of the structures and stabilities of the
adducts, that is the donor-acceptor complexes, of SiH2 to
each of the three cyclic ethers of interest, viz., oxirane,
oxetane, and THF. Exploration of the potential energy
surfaces for decomposition of these complexes was beyond
the scope of the present study. Structures were determined
at the MP2)Full/6-31G(d) level, and energies were calculated
at the G3 level. Structures are shown in Figure 10, and the
energies are shown in Table 4.
It can be seen from Figure 10 that the Si atom of the SiH2
group is not coplanar with the CsOsC plane of any of the
cyclic ethers, consistent with the Si bonding to one of the lone
pairs of the O atom. The orientation of the SiH2 group is skew
to the ring37a in all cases, presumably because this minimizes
nonbonded interactions.37b The Si · · ·O bond lengths are all ca.
0.4 Å longer than those of a normal SisO bond (e.g. 1.63 Å in
(SiH3)2O)) and reflect the relatively weaker nature of the
donor-acceptor bonds. The energy values (Table 4) indicate
that Si· · ·O bonds in the complexes of oxetane and THF are
comparable and slightly stronger than that of the complex with
oxirane. Interestingly, the latter complex has the longest Si · · ·O
bond.
RRKM Calculations (General). In order to judge whether
the observed pressure dependences are consistent with associa-
tion processes alone, we have undertaken RRKM calculations30
of the reverse decomposition processes of the complexes. This
was to enable us to assess the potential significance of further
mechanistic steps of the complexes in these reactions. A general
Figure 9. Arrhenius plots of second-order rate constants for reaction
5, SiH2 + THF in SF6: 0, 10 Torr; 9, infinite pressure. Line is LSQ
fit to k∞ values.
pressure limiting rate constants, also shown in Table 3, have
uncertainties related to this fitting. Figure 9 shows an
Arrhenius plot of the rate constants obtained here both at 10
Torr and at infinite pressure. A linear least-squares fit to the
infinite pressure values corresponds to the Arrhenius equa-
tion, where the uncertainties are again single standard devia-
tions:
log(k∞5 /cm3molecule-1s-1) ) (-10.59 ( 0.10) +
(5.76 ( 0.65) kJ mol-1/RT ln 10
The uncertainties involved in extrapolation performed by
using RRKM theory are less than those without its aid. Thus,
we would estimate that these Arrhenius parameters may have
maximum uncertainties of (0.3 (log A∞) and (2.0 kJ mol-1
(Ea).
TABLE 4: Theoretical Values for Energy, Enthalpy and
Free Energy of Complexes of SiH2 with Cyclic Ethers,
Calculated at the G3 Level
Species
∆E(0 K)
∆H(298 K)
∆G(298 K)
End-Product Analyses. These could only be carried out for
experiments at room temperature.
SiH2 + Oxirane. A mixture of 0.5 Torr PhSiH3, 1.2 Torr
oxirane, and 50 Torr SF6 was subjected to 150 shots of 193 nm
laser radiation (70 mJ/pulse) and then analyzed by GC (Porapak
Q column at 120 °C). Under these conditions, one major product
SiH2 + oxirane
H2Si· · ·oxirane
SiH2 + oxetane
H2Si· · ·oxetane
SiH2 + THF
0
-77
0
-97
0
0
-79
0
-99
0
0
-39
0
-56
0
H2Si· · ·THF
-92
-94
-53

Studies of Reactions of Silylene with Cyclic Ethers
J. Phys. Chem. A, Vol. 114, No. 2, 2010 789
SCHEME 1
TABLE 5: Molecular and Transition-State Parameters for
RRKM Calculations for Decomposition of the SiH2 · · ·THF
Complex at 294 K
SiH2 · · ·THF complex TS-a(5)
ν˜/cm-1
2930(8)
1912(2)
1485(4)
1346(4)
1235(2)
1170(3)
1074(1)
1009(1)
980(1)
942(1)
865(5)
725(1)
670(1)
668(1)
555(1)
236(1)
219(1)
179(1)
134(1)
77(1)
2930(8)
1912(2)
1485(4)
1346(4)
1235(2)
1170(3)
1074(1)
1009(1)
980(1)
942(1)
865(5)
668(1)
555(1)
219(1)
179(1)
158(1)
54(1)
mechanism for reactions 3-5 is shown in Scheme 1. If the
mechanism involves only steps (a), (-a) and collisional stabiliza-
tion, RRKM theory should be able to provide a fit. But if step
(b) is occurring, this will not be the case.
The RRKM calculations were carried out in combination with
a collisional deactivation model (also called the master-equation
method) in a manner similar to that of previous work.6,7,31,38-52
Because experimental details of the structures and vibrational
wavenumbers of the molecules of interest here are not available,
we have taken most of the necessary information from the output
of the theoretical calculations. These provide the vibrational
wavenumbers of the silylene complexes but not the transition
states. The vibrational assignments of the transition states were
obtained by the same procedure as previously,6,7,31,38-52 based
on adjustment of the vibrational wavenumbers of each complex
to match the A factor for its decomposition.53 The latter were
calculated by use of the microscopic reversibility relationship,
ln(A-a/Aa) ) ∆So-a,a/R, where A-a and Aa are the decomposition
and combination A factors (i.e., A-a is what is required, Aa is
the experimental, infinite pressure, value measured here (see
below)) and ∆S-o a,a is the entropy change. The values for ∆So-a,a
were also obtained from the thermodynamic output of the
theoretical calculations, although because of the approximations
used in the procedure, they were corrected for the vibrational
wavenumber factor (0.893). Uncertainties in entropy values
derived in this way are unlikely to be beyond ca. (4 J K-1
mol-1; therefore, values of log(A-a/s-1) should be good to (0.2.
There is one complication in this procedure, viz., obtaining log
Aa values requires the use of the calculated RRKM curves to
match experiment in order to extrapolate rate constants to infinite
pressure. This is dealt with by refinement, viz., an initial
(approximate) extrapolation is made, leading to a first-round
choice of parameters. RRKM-calculated curves are then fitted
to experimental data by matching their curvature, which in turn
leads to improved values for the extrapolated infinite pressure
rate constants and thereby an improved, second-round choice
of Arrhenius parameters, Aa and Ea(a).
31(1)
18(1)
10(1)
35(1)
725
1
78
reaction coordinate/cm-1
path degeneracy
Eo(critical energy)/kJ mol-1
collision number (in SF6): ZLJ/10-10
cm3 molecule-1 s-1
5.17
TABLE 6: Temperature-Dependent Parameters Used in
RRKM Calculations for Decomposition of the SiH2 · · ·THF
Complex
T/K
294
323
357
398
TS-a(5) wavenumbers/cm-1
158
54
31
18
10
159
55
32
19
11
162
57
34
21
11
164
58
35
22
12
ZLJ(SF6)/10-10 cm3 molecule-1 s-1
5.17 5.23
5.31
5.40
position transition state, TS-a(5), at room temperature (294 K),
are shown in Table 5. Some of the higher-value vibrational
wavenumbers have been grouped together (both for the complex
and the transition state). This does not affect the results. The
wavenumber values for the transitional modes at other temper-
atures are given in Table 6. Fitting to the data was accomplished
by using Eo(5) as an adjustable parameter and by matching the
curvatures of the calculated pressure-dependent curves to
experiment. The curves at all four temperatures were used for
this fitting. The resultant optimal value for Eo(5) was 78 kJ
mol-1. Despite an element of judgment involved in this process,
we estimate that the maximum uncertainty in this value is (10
kJ mol-1. Adjusted for thermal energy, the value for Eo(5)
corresponds to E-a(5) ) 83 ( 10 kJ mol-1. This can be
converted to ∆H°(298 K) by using the microscopic reversibility
relationship, ∆H°(298 K) ) E-a(5) - Ea(5) + RT. The value
of 92 ( 10 kJ mol-1 was obtained for ∆H°(298 K). This is in
excellent agreement with the value of 94 kJ mol-1 from the
quantum chemical calculations. The results of the calculations
are shown in Figure 8 where they are compared with experiment.
RRKM Calculations for SiH2 + Oxirane. Details of the
vibrational assignment for the donor-acceptor complex and for
The wavenumbers of the transitional modes for each reactant
molecule (i.e. each silylene complex) were adjusted systemati-
cally at each temperature to match the entropy of activation
and, thereby, the A-a value. Although the value of A-a was fixed,
this had the effect of introducing variational character, because
the derived wavenumber values were different at each temper-
ature. Details of assignments and the choice of critical energy
for each reaction are discussed below. We have assumed, as
previously, that geometry changes between reactant and transi-
tion state do not lead to significant complications. In modeling
the collisional deactivation process, we have used a weak
collisional (stepladder) model,30 because there is overwhelming
evidence against the strong-collision assumption.54 The average
energy removal parameter, 〈∆E〉down, which determines the
collision efficiencies, was taken as 12.0 kJ mol-1 (1000 cm-1
)
for SF6 for each reaction system. Further details of the
calculations for each reaction system are considered below. For
convenience, those for reaction 5 are considered first.
RRKM Calculations for SiH2 + THF. The vibrational
assignment for the donor-acceptor complex and for its decom-

790 J. Phys. Chem. A, Vol. 114, No. 2, 2010
Becerra et al.
Discussion
Kinetic Comparisons. The main experimental purpose of
the present work was to study the kinetics of the reactions of
SiH2 with cyclic ethers for the first time and to investigate the
temperature and pressure dependences of the second-order rate
constants. This has been accomplished. All three reactions
studied are found to be pressure dependent and to have negative
temperature dependences, that is, rate constants which decrease
with increasing temperature. This is characteristic of most
silylene association reactions.1-3 There is no previous work on
reactions 3-5 with which to compare these results. However,
there is kinetic data for the reaction of SiH2 with Me2O,9 the
prototype silylene + ether reaction. Comparisons are tricky,
however, because all reactions of this type are pressure-
dependent, and the true bimolecular rate constants are only
obtainable by extrapolation to high pressures. This has been
done in all the cases cited here, and the infinite pressure
Arrhenius parameters obtained are shown in Table 7. Because
of the uncertainties of extrapolation, maximum error limits are
given. For the three reactions studied here, the A factors are all
similar in magnitude but slightly lower than those (log(A/cm3
molecule-1 s-1) ) ca. -10.0) found for SiH2 addition reactions
to π-bonds,39-41,45,51,52 the other general class of silylene
association reactions. The values for Ea are slightly more
negative than those (-1.7 to -3.4 kJ mol-1) for the SiH2
additions to π-bonds. Although the value for SiH2 + oxetane
(reaction 4) looks rather more negative than the others (reactions
3 and 5), the rate-constant data for this reaction were the hardest
to extrapolate; therefore, the error limits are the largest. For the
reference reaction, viz., SiH2 + Me2O, the Arrhenius parameters9
appear anomalous. Not only is the A factor exceptionally high,
but the activation energy is positive. To obtain these values,
once again, extrapolation of rate constants was necessary, in
this case to considerably higher pressures (106-107 Torr) than
those needed for reactions 3-5 (103-105 Torr). The Arrhenius
parameters become more uncertain the lengthier the extrapola-
tion, and although Alexander, King, and Lawrance (AKL)9
modeled their pressure dependence by using RRKM theory, we
have shown that, in a similar study of SiH2 + H2O,6 extrapola-
tion of such data is very dependent on precise details of the
transition-state models. Thus, we suspect that the Arrhenius
parameters for SiH2 + Me2O may be in error (see below). For
reactions 3-5, the data are consistent with single-step reactions
Figure 11. Comparison of pressure dependence of rate constants for
SiH2 + oxirane at 294 K. Experiment, O; RRKM theory, line.
Figure 12. Comparison of pressure dependence of rate constants for
SiH2 + oxetane. Experiment: O, 296 K; g, 594 K. RRKM theory lines
at same temperatures (indicated).
its decomposition transition state, TS-a(3), at room temperature
(294 K), are given in the Supporting Information. The Eo(3)
value (67 kJ mol-1) was chosen to be consistent with the
theoretically calculated value for ∆H°(298 K) (75 kJ mol-1).
The results of the calculation at 294 K are compared with
experimental results in Figure 11. Because there is clearly no
agreement with the experimental values, no further calculations
were carried out on this system.
RRKM Calculations for SiH2 + Oxetane. Details of the
vibrational assignment for the donor-acceptor complex and
for its decomposition transition state, TS-a(4), at 296 and
594 K, are given in the Supporting Information. The Eo(4)
value (82 kJ mol-1) was chosen to be consistent with the
theoretically calculated value for ∆H°(298 K) (99 kJ mol-1).
The results of the calculation at 296 K are compared with
experimental results in Figure 12. Because the difference with
experiment was small, a further calculation was carried out
at 594 K. This is also compared with experimental results in
Figure 12, where there is clearly no agreement. No further
calculations at other temperatures were carried out on this
system.
TABLE 7: Arrhenius Parameters for Elementary Silylene
Reactions with Ethersa
log(A/cm3
reaction
molecule-1 s-1
)
Ea/kJ mol-1
ref
SiH2 + oxirane
SiH2 + oxetane
SiH2 + THF
-11.0 ( 0.5
-11.2 ( 0.7
-10.6 ( 0.3
-7.6 ( 0.4
-5.7 ( 3.6
-9.0 ( 5.0
-5.8 ( 2.0
+9.3 ( 2.8
this work
this work
this work
9
SiH2 + Me2O
a High-pressure limiting values.
TABLE 8: Rate Constants, Lennard-Jones Collision
Numbers, and Collision Efficiences for Elementary Silylene
Reactions with Ethers at Room Temperature
b
reaction
ka,b
ZLJ
efficiency/%
SiH2 + oxirane
SiH2 + oxetane
SiH2 + THF
1.0
2.5
2.8
5.23
5.79
5.20
5.04
19
43
45
SiH2 + Me2O
8.09
160
a High-pressure limiting values. b Units: 10-10 cm3 molecule-1 s-1
.

Studies of Reactions of Silylene with Cyclic Ethers
J. Phys. Chem. A, Vol. 114, No. 2, 2010 791
SCHEME 2
with no energy barrier. The small negative activation energies
probably arise through conservation of angular momentum
considerations such as those known to occur in radical associa-
tion processes.30
We have also calculated the Lennard-Jones collision num-
bers at 298 K for these reactions (from parameters given in the
Supporting Information) and thereby the collision efficiencies.
These are shown in Table 8. The collision efficiencies for the
reactions 4 and 5 compare reasonably well with values for
silylene addition reactions, which lie in the range 64-82%,52,55
but the 19% value for reaction 3 seems a bit low. Because the
reactive site in these cyclic ethers represents a fraction of the
surface space of these ethers which diminishes as they increase
in size, it might have been expected that the efficiency for
reaction 3 would be greater than that for the other two reactions.
The reason for this is not obvious. Once again, the value for
SiH2 + Me2O looks anomalous, but AKL9 have argued that its
reaction cross-section may be larger than calculations based on
Lennard-Jones values because of long-range interactions. AKL9
have presented a model in which the centrifugal potential
associated with rotation of the complexes, in cases where they
possess weak binding energies, can lead to positive energy
barriers in certain situations. However, although we cannot refute
this model, we remain unconvinced of its validity (mainly
because, in our experience of heavy carbene reactions,1-3 no
other example needing such a model has been found). What is
needed is a more direct measurement of the true (limiting high
pressure) rate constant for SiH2 + Me2O (and, indeed, SiH2
with other O-donors).
has almost no effect on the binding energies of these
complexes, because both oxirane and oxetane are much more
strained than THF and Me2O has no strain at all. What is
more illuminating are the values for the orbital ionization
energies obtained from photoelectron spectroscopy. The
lowest ionization energy is that for an oxygen lone-pair
electron in all cases. The values (in eV) are 10.57 (oxirane),58
9.63 (oxetane),59 9.74 (THF),58 and 9.70 (Me2O).58 The
significantly higher value for oxirane indicates the greater
stability of its nO orbital and presumably, therefore, its lesser
availability for bonding. This may explain why the binding
energy of the H2Si · · · oxirane complex is only ca 80% of the
binding energies of the other two cyclic complexes, although
the H2Si · · · OMe2 complex lies awkwardly in between.
Pressure-Dependences, RRKM Calculations and Mech-
anisms. As a generalization, we should expect that, for three
members of a class of molecules undergoing the same
association process, rate constant pressure-dependences would
get less as the molecules increase in size. This is because,
for the initially formed, vibrationally excited adducts, ap-
proximately the same (released) energy is distributed over
increasing vibrational phase space, leading to longer lifetimes
and a greater likelihood of being collisionally quenched at a
given pressure. This reduces the probability of redissociation
of an adduct and puts the reaction nearer to its bimolecular
limit. Reactions 3-5 of SiH2 with oxirane, oxetane, and THF
exhibit the opposite trend! The reaction of SiH2 with oxirane
shows the least pressure dependence, whereas the reaction
of SiH2 with THF shows the most. Among the three reactions,
only 5 has been successfully modeled here by RRKM theory
(Figure 8). For reaction 3, SiH2 + oxirane, RRKM modeling
fails by large factors, which increase as pressure is reduced,
even at 294 K (Figure 11). For reaction 4, SiH2 + oxetane,
RRKM modeling gives a reasonably close fit at 296 K but
again fails significantly at 594 K (Figure 12). There is,
however, a fairly simple explanation for this, viz., that for
the complexes of SiH2 with oxirane and oxetane, there are
decomposition pathways, as well as redissociation; that is,
kb (in Scheme 1) is not negligible for either reaction.
One other comparison is worth mentioning. In earlier
studies, Baggott et al.25 measured rate constants for the
analogous reactions of SiMe2. However, strict comparisons
with the present work are not possible, because studies were
(a) limited to room temperature (295 K), (b) carried out in
Argon diluent and (c) pressure-dependence studies were only
carried out for SiMe2 + oxirane. With this in mind, values
for the rate constants for SiMe2 (in 5 Torr Ar; units, cm3
molecule-1 s-1) were 4.2 × 10-12 (oxirane), 3.3 × 10-11
(oxetane), and 2.9 × 10-12 (THF). These are all smaller than
their SiH2 analogues (Tables 1-3) as expected for the
generally less reactive SiMe2.2,3 In solution, the rate constant
for SiMe2 + THF is 2.9 × 10-11 cm3 molecule-1 s-1 2,3
,
which
shows that solvent effects can enhance the rate constants for
these processes.
Quantum Chemical Calculations and Stabilities of Com-
plexes. The only previous calculation on any of these systems
was carried out by Apeloig and Sklenak (AS)29 for the
complex of SiH2 + oxirane. The structure and geometry of
the H2Si · · · oxirane complex found by us is very similar to
that obtained by AS at the QCISD/6-31G** and MP2/6-
31G** levels.56 Similarly, our value for the binding energy
(∆E(0 K), see Table 4) of 77 kJ mol-1 is in good agreement
with those found by AS, viz., 71 kJ mol-1 (QCISD/6-31G**
level) and 84 kJ mol-1 (MP2/6-31G** level). There are no
values in the literature for comparision for the other two
complexes. However, for reference, the prototype, unstrained
complex of SiH2 with MeOMe has calculated values for its
binding energy of 84.3 kJ mol-1 (MP2/6-311++G(d,p)
level)28 and 82.9 kJ mol-1(MP2/6-311+G** level),9 which
are in reasonable agreement with experiment9 (88.4 kJ mol-1).
For the cyclic ethers, strain enthalpies are available from
group additivity57 and have values (in kJ mol-1) of 115
(oxirane), 110 (oxetane), and 28 (THF). It would appear from
these numbers that strain in the cyclic rings of these ethers
For the reaction of SiH2 with oxirane, it is significant that
we have found C2H4 as a substantial product. Apeloig and
Sklenak29 have already shown that there is a low-barrier process
from the H2Si· · ·oxirane complex leading to H2SidO + C2H4.
The mechanism proceeds by sequential OsC bond fission, via
the intermediacy of the •SiH2OCH2CH2• diradical, as shown in
Scheme 2.
Starting from SiH2 + oxirane, the process is barrierless
overall. This is consistent with our kinetic finding of a negative
activation energy. The slight pressure dependences indicates that
only small fractions of initially formed complexes are stabilized
at any temperature and that the majority decomposes under all
experimental conditions. The reaction mechanism for SiH2 with
oxirane parallels that found earlier for SiMe2 with oxirane.25
It is not difficult to believe that the H2Si· · ·oxetane complex
should also have a relatively easy decomposition pathway, on
account of the strain energy in the oxetane ring. Following the

792 J. Phys. Chem. A, Vol. 114, No. 2, 2010
Becerra et al.
SCHEME 3
work of Gu and Weber,12 who investigated the products of
SiMe2 + oxetane, the mechanism shown in Scheme 3 seems
likely.
CTQ2006-10512. We also thank Sarah Bowes for help with
some of the experiments.
Supporting Information Available: Details of vibrational
assignments for the SiH2 · · ·oxirane and SiH2 · · ·oxetane com-
plexes and their decomposition transition states, Lennard-Jones
parameters for molecules of interest. This material is available
free of charge via the Internet at http://pubs.acs.org.
We were unable to detect any end products at room
temperature from the reaction of SiH2 with oxetane. However,
because the experimental rate-constant pressure-dependence
measurements were quite closely fitted by the RRKM
modeling at 296 K, this suggests that there was little or no
decomposition of H2Si · · · oxetane at this temperature. The
lack of fit at other temperatures shows that decomposition
to other products takes place to an increasing extent as the
temperature is raised. This implies a small effective energy
barrier for this process. The slight differences in strain energy
of the 3-and 4-membered rings may mean that it is slightly
harder to break the initial OsC bond in the oxetane complex
than in the oxirane one, although there are clearly other
mechanistic differences in the decomposition pathways of
these two complexes. It would appear that the factors
governing the behavior of silylene · · · oxetane complexes are
quite subtle because SiMe2 is able to react with oxetane in
solution at room temperature to produce products.12 Of
course, this may be due to solvent effects, although in the
gas phase, the reaction of SiMe2 with oxetane at 298 K was
found to be particularly fast.25
The fact that the pressure-dependent kinetic behavior of the
SiH2 + THF reaction 5 conforms to RRKM theory (with the
calculated binding energy) shows that, when the cyclic ether
has little or no strain energy, there is insufficient driving force
for further reaction, either isomerization or decomposition of
the complex. This is consistent with what is known about the
reaction of SiH2 with acyclic ethers.9,28 The Me2Si· · ·THF
complex is similarly stable, both in solution23 and in the gas
phase.25
References and Notes
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The experimental kinetics studies carried out here show
that SiH2 reacts fairly rapidly with all three cyclic ethers,
viz., oxirane, oxetane, and THF, in pressure-dependent
reactions to form the Lewis acid-base association complexes.
This is supported by quantum chemical calculations. For SiH2
+ oxirane, the detection of C2H4 as product shows that the
complex is largely decomposed. For SiH2 + oxetane,
disagreement between RRKM calculations and experiment
also indicates that the complex decomposes at temperatures
above ambient. For SiH2 + THF, agreement between RRKM
calculations and experiment shows that the complex is stable.
The existence of breakdown pathways for the SiH2 complexes
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Acknowledgment. R.B. and R.W. thank Dow-Corning for a
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Ministerio de Educacion y Ciencia for support under Project

Studies of Reactions of Silylene with Cyclic Ethers
J. Phys. Chem. A, Vol. 114, No. 2, 2010 793
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(37) (a) This means that one of the Si-H bonds lies above and between
the two O-C bonds when the complex is viewed along the Si-O bond. (b)
A second structure for the H2Si· ·oxirane complex was found, in which
the SiH2 group is anti- to the oxirane ring plane. This is 4 kJ mol-1 less
stable than the skew structure.
(38) Baggott, J. E.; Frey, H. M.; Lightfoot, P. D.; Walsh, R.; Watts,
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(53) In this procedure, the internal rotations around the SisO bonds
have been treated as harmonic vibrations. Because these are among the
modes in the transition states which are adjusted to match the activation
entropies, ∆S‡, and thereby the A factors, this approximation should make
little difference.
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