Kinetic study on the H + SiH4 abstraction reaction using an ab initio potential energy surface.
ABSTRACT Variational transition state theory calculations with the correction of multidimensional tunneling are performed on a 12-dimensional ab initio potential energy surface for the H + SiH(4) abstraction reaction. The surface is constructed using a dual-level strategy. For the temperature range 200-1600 K, thermal rate constants are calculated and kinetic isotope effects for various isotopic species of the title reaction are investigated. The results are in very good agreement with available experimental data.
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ABSTRACT: Thermal rate constants and kinetic isotope effects for the title reaction are calculated by using the quantum instanton approximation within the full dimensional Cartesian coordinates. The obtained results are in good agreement with experimental measurements at high temperatures. The detailed investigation reveals that the anharmonicity of the hindered internal rotation motion does not influence the rate too much compared to its harmonic oscillator approximation. However, the motion of the nonreactive methyl group in C(2)H(6) significantly enhances the rates compared to its rigid case, which makes conventional reduced-dimensionality calculations a challenge. In addition, the temperature dependence of kinetic isotope effects is also revealed.Physical Chemistry Chemical Physics 09/2011; 13(43):19362-70. · 4.20 Impact Factor
Page 1
THE JOURNAL OF CHEMICAL PHYSICS 134, 024315 (2011)
Kinetic study on the H+SiH4abstraction reaction using an ab initio
potential energy surface
Jianwei Cao,1,2,a)Zhijun Zhang,1,2,a)Chunfang Zhang,1,2Wensheng Bian,1,b)and
Yin Guo3,c)
1Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Molecular Reaction Dynamics,
Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
2Graduate University of the Chinese Academy of Sciences, Beijing 100049, China
3Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078, USA
(Received 27 June 2010; accepted 11 August 2010; published online 12 January 2011)
Variational transition state theory calculations with the correction of multidimensional tunneling are
performed on a 12-dimensional ab initio potential energy surface for the H + SiH4abstraction reac-
tion. The surface is constructed using a dual-level strategy. For the temperature range 200−1600 K,
thermal rate constants are calculated and kinetic isotope effects for various isotopic species of the
title reaction are investigated. The results are in very good agreement with available experimental
data. © 2011 American Institute of Physics. [doi:10.1063/1.3521477]
I. INTRODUCTION
The H + SiH4reaction is important in the mechanism of
the thermal decomposition of monosilane.1It also plays a sig-
nificant role in chemical vapor deposition processes used in
thesemiconductorindustryaswellasfortheproductionofce-
ramic materials.2–4As a prototype of exothermic polyatomic
hydrogen abstraction reactions, the H + SiH4abstraction re-
action has been investigated by experimentalists and theoreti-
cians for several decades. Experimentally, the rate constants
were measured with a wide variety of methods;5–15most stud-
ies were carried out at room temperature, and only a few re-
cent ones by Arthur et al.5,6and Goumri et al.7were con-
ducted on the temperature dependence of the rate constant.
The measured rate constants reported by different groups
or obtained by different techniques varied significantly at
room temperature, ranging from 2.0 × 10−13to 85.0 × 10−13
cm3molecule−1s−1; this range was recently reduced to
2.0 × 10−13to 4.0 × 10−13cm3molecule−1s−1.5–11More-
over, a few experimental studies on the kinetic isotope effects
(KIEs) have been reported,5,10,12–15and they were focused on
the KIEs at room temperature.
On the theoretical side, several investigations have been
reported on the title reaction.7,16–24Most of the previous
ab initio calculations were limited to the small regions
around a few stationary points and the minimum energy
path (MEP),7,16–19and thermal rate constants were computed
using the transition state theory (TST)7,18or variational tran-
sition state theory (VTST)19approaches. In 1998, Espinosa-
García et al.20
constructed an analytic semiempirical
potential energy surface (PES) for the H + SiH4abstraction
reaction and computed thermal rate constants and KIEs us-
ing VTST. Employing the same PES, Wang et al.21also cal-
culated thermal rate constants and KIEs using the quantum
a)These authors contributed equally to this work.
b)Electronic mail: bian@iccas.ac.cn.
c)Electronic mail: yin.guo@okstate.edu.
instanton (QI) method.25Both the VTST and QI calcula-
tions on the semiempirical PES yielded KIEs that deviate sig-
nificantly from experimental measurements. In 2006, Wang
et al.22constructed a global 12-dimensional ab initio PES for
the H + SiH4abstraction reaction with the modified Shepard
interpolation method,26–28and both VTST22and quasiclas-
sical trajectory (QCT)23calculations on this surface yielded
thermal rate constants in good general agreement with exper-
iment. More recently, we constructed a global 12-dimensional
ab initio PES24that describes both abstraction and exchange
reactions for the H + SiH4 system based on the modified
Shepard interpolation method and high-level ab initio calcu-
lations at carefully chosen reference geometries. The energy
values were computed at the spin-unrestricted coupled clus-
ter method with single and double excitations and triple exci-
tation correction and Dunning’s correlation-consistent polar-
ized valence quadruple-zeta basis set [UCCSD(T)/cc-pVQZ]
level, whereas the gradients and Hessians were computed at
the lower spin-unrestricted quadratic configuration interac-
tion method with all single and double excitations and Dun-
ning’s correlation-consistent polarized valence triple-zeta ba-
sis set (UQCISD/cc-pVTZ) level due to the prohibitive com-
putational cost. Further detailed QCT calculations24for both
abstraction and exchange reactions on this PES were per-
formed, and they revealed interesting features of detailed
dynamical quantities and underlying new atomic-level mech-
anisms. However, this PES is not suitable for VTST calcu-
lations, which involve the evaluation of the Hessian matrix
along the reaction path and require very smooth derivative
surfaces.
In this study, the previous ab initio PES for the H + SiH4
abstraction reaction is modified by using a dual-level strategy
that employs two levels of electronic-structure calculations.
In addition to the modified Shepard interpolation, we also
use the local interpolating moving least-squares (L-IMLS)
method29here as it does not require the ab initio gradients and
Hessians. We then perform the VTST calculations of thermal
rate constants and KIEs for the H + SiH4abstraction reaction
0021-9606/2011/134(2)/024315/8/$30.00 © 2011 American Institute of Physics
134, 024315-1
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024315-2Cao et al.J. Chem. Phys. 134, 024315 (2011)
on this new PES. The IMLS method has been applied to three-
and four-atom systems so far. The application to the present
six-atom system provides a test and an example of the appli-
cability of the IMLS method to larger systems.
The paper is organized as follows: In Sec. II, we describe
the construction of the PES and computational details of the
VTST calculations. In Sec. III, we present the properties of
the PES as well as the results and discussion of the calcu-
lated thermal rate constants and the KIEs. The conclusions
are given in Sec. IV.
II. THEORETICAL METHODS
A. Potential energy surface
The present PES is a modification of the previous
ab initio surface for the H + SiH4 abstraction reaction. It
is constructed using a dual-level strategy. The idea of the
dual-level strategy is to use two levels of ab initio calculations
so as to reduce the number of high-level points needed for
fitting. The basic scheme of the dual-level strategy is as
follows. First, a set of lower-level ab initio points is generated
to construct a reference surface V0. Then a set of higher-level
points is generated and the data set of the differences of the
two levels is used to generate a surface of the difference ?V
= Vhigh− Vlow. The final potential V is the sum of the two,
V = V0+ ?V.
Since the difference surface ?V is flatter than V itself
and thus requires fewer data points to achieve a given ac-
curacy, the computational cost is reduced with the use of a
smaller set of high-level points. The dual-level strategy was
first proposed by Nguyen et al.,30and it was employed re-
cently for the FH2system using spline31and for the H2CN
system using the L-IMLS method.32
In this study, UQCISD/cc-pVTZ and UCCSD(T)/cc-
pVQZ were used as the lower- and higher-level methods, re-
spectively. Although we did not apply a correlation scaling
method33to achieve the one-electron basis set limit, it was
shown that24the present UCCSD(T)/cc-pVQZ scheme yields
similar results to those obtained with the complete basis-set
extrapolation. The reference surface V0was constructed with
the modified Shepard interpolation method using a reference
data set with 3356 UQCISD/cc-pVTZ points including ener-
gies, gradients, and Hessians, which are sufficient for describ-
ing the H + SiH4abstraction reaction.24Since it is too costly
to obtain the gradients and Hessians at the UCCSD(T)/cc-
pVQZ level, the difference surface ?V was generated us-
ing the second-degree local-IMLS method by fitting only the
difference of the lower- and higher-level ab initio energies.
The UCCSD(T)/cc-pVQZ set contains 3356 ab initio energy
points. More details of the construction of the present PES are
given in the accompanying supplementary material.34
(1)
B. Variational transition state theory
The VTST35,36is employed for the calculations of ther-
mal rate constants and KIEs. The details of the theory can be
foundintheliterature.35–37Thecalculationsareperformedus-
ing the POLYRATE program, version 9.3,38which has been
used to predict the rate constants and KIEs on various PESs
successfully.39–42On the present PES, the reaction path is
calculated starting from the saddle-point geometry and go-
ing downhill to both the asymptotic reactant and product
channels in mass-scaled Cartesian coordinates by the Page-
McIver methods.43Different step sizes are tried until varia-
tional rate constants are converged, and a step size around
0.003 bohr used for the gradient is found to be reasonable.
The generalized normal-mode analysis is performed every
0.03 bohr along the MEP using a set of redundant curvi-
linear internal coordinates44which includes all the possible
bond lengths and bond angles. The improved canonical vari-
ational theory (ICVT)35,45plus the small-curvature tunneling
(SCT) correction46is suitable for this system whose reaction
path curvature is not large. Tests show that results from dif-
ferent VTST methods are, in general, quite close to one an-
other over the whole temperature range considered. The ther-
mal rate constants and KIEs reported here are those from the
ICVT/SCT calculations.
III. RESULTS AND DISCUSSION
A. Properties of the PES
The geometrical parameters and frequencies for reac-
tants, products, and the saddle point obtained from the
present PES are listed in Table I, along with the re-
sults obtained from the semiempirical surface of Ref. 20,
on which the previous kinetic studies were carried out,
the previous ab initio surface of Ref. 22, UCCSD(T)/cc-
pVQZ ab initio calculations, as well as experimental data.
As shown in Table I, the geometrical parameters for vari-
ous stationary points from the present surface are in very
good agreement with those from our UCCSD(T)/cc-pVQZ
ab initio calculations, and similar to those from the pre-
vious ab initio surface of Ref. 22. Except for the imag-
inary frequency, the differences in vibrational frequencies
between the present surface and UCCSD(T)/cc-pVQZ ab ini-
tio calculations are less than 10 cm−1. The imaginary fre-
quency from the present surface (1237i cm−1) is smaller
than those from the semiempirical surface (1301i cm−1)
and the previous ab initio surface (1333i cm−1), indicating a
slightly thicker barrier. Furthermore, the lengths of the Si-Hc
and Hc-Habonds (defined in the upper right panel of Fig. 1)
for the abstraction TS on the present surface are 1.5936 and
1.1568 Å, respectively, while on the semiempirical surface
the corresponding values are 1.711 and 0.957 Å. Therefore,
the abstraction TS on the present surface is more reactantlike
than that on the semiempirical surface, and the reaction will
proceed via a more evident early barrier. The classical barrier
height on the present surface is 5.34 kcal/mol, which is very
close to our best estimate value of 5.35 ± 0.15 kcal/mol.24
The present surface is a hypersurface in 12 dimensions,
and various two-dimensional cuts into the hypersurface are
helpful in evaluating the quality of the surface. Typical cuts
of the present PES and the difference surface ?V are shown
in Figs. 1 and 2, respectively, which are contour plots as
functions of R1, the distance between the Haand Hcatoms,
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024315-3Kinetic study on the H+SiH4reaction J. Chem. Phys. 134, 024315 (2011)
TABLE I. Reactants, products, and transition state properties (distances in angstroms, angles in degrees, and frequencies in cm−1) for the H + SiH4abstrac-
tion reaction on different surfaces along with the data from UCCSD(T)/cc-pVQZ calculations and experiment.
Stationary pointsParametersSemiempirical surfacea
Previous surfaceb
UCCSD(T)/ cc-pVQZPresent surface Expt.
SiH4(Td)
R(Si-H)
Frequencies
1.432
2119(t2)
2062(a1)
1113(e)
843(t2)
1.4816
2269(t2)
2261(a1)
985(e)
933(t2)
1.4798
2265(t2)
2261(a1)
983(e)
930(t2)
1.4798
2258(t2)
2251(a1)
980(e)
926(t2)
1.481c
2191(t2)d
2187(a1)
975(e)
914(t2)
SiH3(C3v)
R(Si-H)
?HSiH
Frequencies
1.4781.4828
111.2
2259(e)
2227(a1)
949(e)
789(a1)
0.7426
4410(σg)
1.4818
1.5987
1.1506
180.0
110.3
2266(e)
2248(a1)
1152(a1)
987(e)
951(e)
891(a1)
284(e)
1333i(a1)
1.4807
111.3
2262(e)
2230(a1)
941(e)
769(a1)
0.7419
4403(σg)
1.4801
1.5936
1.1570
180.0
110.3
2265(e)
2250(a1)
1162(a1)
977(e)
941(e)
882(a1)
275(e)
1277i(a1)
1.4807
111.2
2259(e)
2220(a1)
942(e)
773(a1)
0.7418
4418(σg)
1.4800
1.5936
1.1568
179.9
110.3
2262(e)
2248(a1)
1159(a1)
980(e)
943(e)
882(a1)
280(e)
1237i(a1)
1.468e
110.5e
2185(e)f
2136(a1)
929(e)
735(a1)
0.7414c
4404(σg)c
2185(e)
2130(a1)
819(e)
669(a1)
0.741
4404(σg)
1.477
1.711
0.957
180.0
109.8
2075(e)
2054(a1)
1235(a1)
964(e)
845(e)
822(a1)
396(e)
1301i(a1)
H2
R(H-H)
Frequencies
R(H-Hb)
R(H-Hc)
R(Hc-Ha)
?SiHcHa
?HbSiHb?
Frequencies
TS (C3v)
aFrom Ref. 20.
bFrom Ref. 22.
cFrom Ref. 47.
dFrom Ref. 48.
eFrom Ref. 49.
fSiH3: 2185 from Ref. 50(a), 2136 from Ref. 50(b), 929 from Ref. 50(c), and 735 from Ref. 50(d).
and R2, the distance between the Si and Hcatoms (see the up-
per right panel of Fig. 1), with the other coordinates fixed at
the geometry of the abstraction TS. It can be seen from Fig. 1
that the contour lines are smooth and the potential is physi-
cally reasonable in various regions. It is also easy to see that
the location of the saddle point is close to the H + SiH4re-
actant, indicating an early barrier. In Fig. 2, we can see that
the difference surface ?V is smooth and much flatter than the
PES itself.
Figure 3 depicts the classical potential energies along the
MEP, VMEP, and the ground-state vibrationally adiabatic po-
tential, VG
ergy, as functions of reaction coordinate s on the present sur-
face. As shown, the VG
MEP one. The VG
on the present surface, while on the semiempirical surface20
the location of the VG
viously, a large difference in the variational effect can be ex-
pected between the two surfaces.
a, which is the sum of VMEPand the zero-point en-
a curve is somewhat wider than the
amaximum is located at s = −0.128 bohr
amaximum is at s = 0.227 bohr. Ob-
B. Thermal rate constants
The thermal rate constants in the temperature range of
200–1600 K obtained with the present surface are listed in
Table II. We notice the following: (i) The rate constants of
CVT and ICVT are the same and they are lower than those
of TST, especially at low temperatures, indicating an evident
variational effect. (ii) The CVT/SCT rate constants agree with
the ICVT/SCT ones within 3% over the temperature range
shown. (iii) At low temperatures, the tunneling contribution
is very important in the title reaction, where a light atom is
transferred. For instance, tunneling accounts for about 94%
and 71% of the total reactivity at 200 and 300 K, respec-
tively, and the proportion decreases to about 4% at 1600 K.
(iv) ICVT/SCT-ISPE (interpolated single point energies)51
results are obtained by evaluating the minimum energy path
(MEP) on the reference surface V0and then correcting the
energies at the high level [UCCSD(T)/cc-pVQZ]. As shown,
the ICVT/SCT-ISPE results are close to the ICVT/SCT ones
within 3.5% over the temperature range. This is understand-
ablesincethestructuresalongtheMEParefortunatelysimilar
at the lower and higher levels for this reaction, which is par-
tially supported by the similar TS structures from the present
and previous ab initio surfaces (see Table I). In this case, the
MEP of the lower level with the energies corrected is a good
approximation to the higher-level MEP.
We show in Fig. 4 the Arrhenius plots of thermal rate
constants obtained in this work with the ICVT/SCT method
Page 4
024315-4Cao et al.J. Chem. Phys. 134, 024315 (2011)
FIG. 1. A contour plot of the present surface as a function of R1and R2
with the other coordinates fixed at the transition state geometry. As shown
in the figure, R1denotes the distance between the Hcand Haatoms, and
R2denotes the distance between the Si and Hcatoms. The contours are in
kcal/mol relative to the H + SiH4asymptote.
(shown by a solid line) on the present surface, together with
experimental6,7,9,11and previous theoretical results.18–22It
can be seen that the calculated rate constants are in very
good agreement with experimental results at higher temper-
atures, but somewhat smaller than those of experiments at
lower temperatures. In view of the high accuracy of the
present ab initio PES, we suppose that the tunneling at
lower temperatures may have been underestimated by the
present ICVT/SCT scheme, leading to smaller rate constants,
since in this scheme it is still impossible to take the tunnel-
ing of the newly observed stripping mechanism24into ac-
count. We note that the limitations of local dynamics ap-
proaches were pointed out in a recent study on the X + CH4
(X = H, O, Cl) reactions,52and thus further global dynami-
cal calculations on the present PES would be helpful to as-
FIG. 2. A contour plot of the difference surface ?V as a function of R1and
R2(defined in Fig. 1) with the other coordinates fixed at the transition state
geometry. The contours are in kcal/mol relative to the difference between the
lower- and higher-level H + SiH4asymptote.
FIG. 3. Classical potential energy (VMEP) and ground-state vibrationally adi-
abatic potential energy (VG
a) as functions of the reaction coordinate s.
sess the importance of those effects beyond the TST-based
scheme.
We note that the present rate constants are larger than
those obtained from the previous ab initio surface of Ref.
22. This is understandable since the barrier height of the
present surface (5.34 kcal/mol) is somewhat lower and of
higher precision than the previous value of 6.01 kcal/mol,
which leads to more accurate thermal rate constants. It turns
out that the difference between the present results and previ-
ous CVT/SCT ones on the semiempirical PES20is not sig-
nificant, but this may result from an error cancellation. Al-
though the classical barrier height does not show large dif-
ferences for the present and semiempirical PESs (5.34/5.13
kcal/mol for the two PESs, respectively), the topologies of
these two PESs in the abstraction barrier region are quite
different, and the vibrational frequencies of the saddle point
on the present surface differ evidently from those on the
FIG. 4. The thermal rate constants for the H + SiH4→ SiH3+ H2reaction
as a function of 1000/T, where the solid line corresponds to the ICVT/SCT
results on the present surface. Several experimental (in symbols, from
Refs. 6, 7, 9, and 11) and previous theoretical (in lines, from Refs. 18–22)
results are also presented.
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024315-5Kinetic study on the H+SiH4reactionJ. Chem. Phys. 134, 024315 (2011)
TABLE II. Thermal rate constants (in cm3molecule−1s−1) for the H + SiH4abstraction reaction.
T (K) TST CVTCVT/SCTICVT ICVT/SCTICVT/SCT-ISPEa
200
250
300
350
400
450
500
600
700
800
1000
1200
1400
1600
1.04 × 10−15
1.08 × 10−14
5.38 × 10−14
1.75 × 10−13
4.33 × 10−13
8.99 × 10−13
1.64 × 10−12
4.23 × 10−12
8.70 × 10−12
1.54 × 10−11
3.69 × 10−11
7.01 × 10−11
1.16 × 10−10
1.74 × 10−10
8.75 × 10−16
9.66 × 10−15
4.93 × 10−14
1.63 × 10−13
4.11 × 10−13
8.61 × 10−13
1.58 × 10−12
4.12 × 10−12
8.50 × 10−12
1.51 × 10−11
3.62 × 10−11
6.89 × 10−11
1.14 × 10−10
1.71 × 10−10
1.59 × 10−14
5.84 × 10−14
1.68 × 10−13
3.98 × 10−13
8.08 × 10−13
1.46 × 10−12
2.42 × 10−12
5.48 × 10−12
1.04 × 10−11
1.76 × 10−11
3.98 × 10−11
7.33 × 10−11
1.19 × 10−10
1.76 × 10−10
8.75 × 10−16
9.66 × 10−15
4.93 × 10−14
1.63 × 10−13
4.11 × 10−13
8.61 × 10−13
1.58 × 10−12
4.12 × 10−12
8.50 × 10−12
1.51 × 10−11
3.62 × 10−11
6.89 × 10−11
1.14 × 10−10
1.71 × 10−10
1.59 × 10−14
5.95 × 10−14
1.72 × 10−13
4.08 × 10−13
8.27 × 10−13
1.49 × 10−12
2.47 × 10−12
5.61 × 10−12
1.07 × 10−11
1.80 × 10−11
4.05 × 10−11
7.44 × 10−11
1.20 × 10−10
1.78 × 10−10
1.62 × 10−14
6.16 × 10−14
1.78 × 10−13
4.16 × 10−13
8.36 × 10−13
1.50 × 10−12
2.47 × 10−12
5.55 × 10−12
1.05 × 10−11
1.76 × 10−11
3.95 × 10−11
7.23 × 10−11
1.17 × 10−10
1.73 × 10−10
aThe ICVT/SCT-ISPE (interpolated single point energies) results are obtained by evaluating the minimum energy path at the lower level with the reference surface V0, and then
correcting it with the energies at the UCCSD(T)/cc-pVQZ level.
semiempirical surface. For example, the vibrational frequen-
cies for bending along Si-Hc-Haaxis (defined in the upper
right panel of Fig. 1) are 280 and 396 cm−1on the present
and semiempirical surfaces, respectively. Compared to the
semiempirical surface, the present PES has (i) an earlier sad-
dle point, which is closer to the reactant region, and (ii) a flat-
ter bending potential, which allows more reactive trajectories.
TheabovedifferencesinthetwoPESsinfluencethecomputed
KIEs, as presented in the next section.
C. Kinetic isotope effects
The KIEs at different temperatures have been investi-
gated for the following isotope reactions:
H + SiH4→ SiH3+ H2,
(R1)
D + SiH4→ SiH3+ HD,
(R2)
H + SiD4→ SiD3+ DH,
D + SiD4→ SiD3+ D2.
The KIEs are defined as the ratio of the rate constants
of the unsubstituted reaction (R1) to the different substituted
reactions (R2), (R3), and (R4). The ICVT/SCT results on the
present surface, and the previous CVT/SCT20and QI21results
on the semiempirical surface, are listed in Table III for com-
parison. Further insight into the origin of the KIEs could be
obtained from a factor analysis. The KIE factorizes as39,53
(R3)
(R4)
KIE =ηtransηrotηvibηtunηvar,
where ηtransis the ratio of the relative translational partition
functions, ηrot is from rotation, ηvib is from vibration, ηtun
is the ratio between tunneling factors κSCT(H)/κSCT(D), and
ηvaris the ratio of KIEs calculated using variational and con-
ventional TST. The factors for the present KIEs are listed in
Tables IV–VI.
(2)
It can be seen from Table III that the present KIEs
of (R1)/(R2) predicted by the ICVT/SCT calculations are
greater than 1 over the whole temperature range. In contrast,
the results obtained by the previous CVT/SCT20and QI21cal-
culations on the semiempirical surface have an “inverse” be-
havior, i.e., the KIEs of (R1)/(R2) are smaller than 1, which
differ from the experimental measurements qualitatively. All
available experimental data measured with different methods
for KIEs of (R1)/(R2) are greater than 1.10,13,15Our computed
value of 1.91 at room temperature is somewhat larger than
the experimental value (1.3 ± 0.3).13However, the experi-
mental rate constants for R2 range from (1.9 ± 0.4) × 10−13
to (3.9 ± 0.7) × 10−13cm3molecule−1s−1,2,5,13,15and if we
apply the most recent experimental rate constant8for R1
to the calculation of the ratio, the deduced higher limit for
(R1)/(R2) KIEs is (1.8 ± 0.4). Thus, more precise experimen-
tal measurements on rate constants for R2 are required to ver-
ify our prediction. The large difference between the present
and previous theoretical results can be explained by a factor
analysis. We see from Table IV that the variational contribu-
tions in the present results are quite different from those re-
ported in Ref. 20. In particular, our variational contribution
factor of 1.61 at 300 K is much larger than the value of 0.64
obtained in previous calculations on the semiempirical sur-
face, which mainly accounts for the KIE being less than 1 on
that surface. Therefore, the difference results from different
topologies in the TS region on the two PESs, and the present
PES is based on high-level ab initio calculations and should
be more reliable.
For the KIEs of (R1)/(R3), our value (2.51) at room tem-
perature is in excellent agreement with the experimental value
(2.4 ± 0.2),5and much smaller than the values obtained in
previous calculations on the semiempirical surface (9.81 from
CVT/SCT calculations20and 8.57 from QI calculations,21re-
spectively). The comparison also shows that our computed
KIEs are smaller than those obtained on the semiempirical
surface for the temperature range 200–1000 K. Comparing
the factors listed in Table V, we find that both vibrational and
tunneling contributions make the present results better than
Page 6
024315-6Cao et al.J. Chem. Phys. 134, 024315 (2011)
TABLE III. Kinetic isotope effects at different temperatures computed using the present and semiempirical surfaces.
KIE (R1)/(R2)a
KIE (R1)/(R3)a
KIE (R1)/(R4)a
Semiempirical surfaceSemiempirical surface Semiempirical surface
T(K)This workb
CVT/SCTc
QId
This workb
CVT/SCTc
QId
This workb
CVT/SCTc
200
250
300
3.37
2.32
1.91
0.69
0.65
0.71
0.563.48
2.89
2.51
33.60
16.63
9.81
30.1010.00
5.83
4.21
10.85
6.42
4.540.738.57
Expt. value: 1.3 ± 0.3e
Expt. value: 2.4 ± 0.2f
350
400
450
500
600
700
800
1000
1200
1400
1600
1.73
1.62
1.56
1.52
1.47
1.45
1.44
1.43
1.43
1.43
1.44
0.73
0.76
0.79
0.81
0.84
0.86
2.25
2.07
1.92
1.80
1.65
1.55
1.48
1.38
1.32
1.29
1.26
6.72
5.07
4.08
3.46
2.72
2.32
3.40
2.93
2.61
2.40
2.11
1.94
1.82
1.69
1.61
1.56
1.53
3.57
3.01
2.64
2.39
2.06
1.85
0.774.39
0.85
0.90
0.92
0.94
0.95
3.11
2.41
2.15
1.78
1.640.90 1.801.58
a(R1)denotesthereactionH + SiH4→ SiH3+ H2;(R2)denotesthereactionD + SiH4→ SiH3+ HD;(R3)denotesthereactionH + SiD4→ SiD3+ DH;(R4)denotesthereaction
D + SiD4→ SiD3+ D2.
bCalculated using the ICVT/SCT method.
cFrom Ref. 20.
dFrom Ref. 21.
eThe experimental value from Ref. 13; other experimental values: 1.1 ± 0.3 from Ref. 15; 1.14 from Ref. 10.
fThe experimental value from Ref. 5, at room temperature (295–305 K); other experimental values: 2.8 ± 0.5 at 305 K from Ref. 14.
the previous ones.20The vibrational contributions depend sig-
nificantly on the vibrational frequencies along the reaction
path. At 300 K, the vibrational contribution factor is 3.82 for
the previous CVT/SCT calculations, while this value is 2.25
in the present case. Furthermore, in the case of the semiem-
pirical surface, the KIE at 300 K has a tunneling contribu-
tion factor of 2.00, whereas for the present surface the KIE at
300 Khas alow tunneling contribution factor of 0.88. The low
tunneling contributions in the present results can be explained
by the fact that the zero-point-inclusive barrier height is lower
for reaction (R1) (4.56 kcal/mol for R1 and 5.15 kcal/mol for
R3 on the present PES), and thus tunneling should be more
important for R3.
For the KIEs of (R1)/(R4), the present ICVT/SCT
results are slightly smaller than the previous CVT/SCT
ones,20and both results are larger than the deduced
value13of 1.8 ± 0.1 at room temperature. The deduced
value is obtained by the experimental value of (4.6 ± 0.3)
TABLE IV. Factor analysis of the kinetic isotope effects of (R1)/(R2) at different temperatures.
ηvib
ηtun
ηvar
T (K) This worka
CVT/SCTb
This worka
CVT/SCTb
This worka
CVT/SCTb
200
250
300
350
400
450
500
600
700
800
1000
1200
1400
1600
0.35
0.41
0.46
0.50
0.52
0.55
0.56
0.58
0.60
0.61
0.62
0.63
0.64
0.64
0.19
0.25
0.31
0.35
0.38
0.42
0.44
0.46
0.48
2.50
1.73
1.44
1.30
1.22
1.17
1.13
1.09
1.06
1.05
1.03
1.02
1.02
1.01
3.85
1.39
1.95
1.64
1.45
1.33
1.26
1.16
1.10
2.17
1.81
1.61
1.50
1.42
1.37
1.34
1.29
1.27
1.25
1.24
1.24
1.24
1.24
0.51
0.59
0.64
0.70
0.76
0.79
0.82
0.86
0.88
0.521.030.93
aCalculated using the ICVT/SCT method. ηtransand ηrotare independent of temperature, and their values are 2.70 and 0.66,
respectively.
bFrom Ref. 20, ηtransand ηrotare 2.69 and 0.67, respectively.
Page 7
024315-7Kinetic study on the H+SiH4reactionJ. Chem. Phys. 134, 024315 (2011)
TABLE V. Factor analysis of the kinetic isotope effects of (R1)/(R3) at different temperatures.
ηvib
ηtun
ηvar
T (K)This worka
CVT/SCTb
This worka
CVT/SCTb
This worka
CVT/SCTb
200
250
300
350
400
450
500
600
700
800
1000
1200
1400
1600
3.90
2.81
2.25
1.91
1.69
1.54
1.42
1.27
1.17
1.11
1.03
0.98
0.96
0.94
8.55
5.30
3.82
3.01
2.50
2.20
1.92
1.65
1.49
0.76
0.83
0.88
0.91
0.93
0.94
0.95
0.97
0.98
0.98
0.99
0.99
0.99
1.00
3.11
2.45
2.00
1.71
1.52
1.40
1.32
1.20
1.14
0.85
0.90
0.92
0.94
0.95
0.96
0.97
0.98
0.98
0.98
0.98
0.99
0.99
0.99
0.94
0.96
0.97
0.97
0.97
0.98
1.00
1.01
1.01
1.251.061.02
aCalculated using the ICVT/SCT method. ηtransand ηrotare independent of temperature, and their values are 1.01 and 1.37,
respectively.
bFrom Ref. 20, ηtransand ηrotare 1.01 and 1.33, respectively.
× 10−13cm3molecule−1s−1for R1 and the calculational
value of 2.6 × 10−13cm3molecule−1s−1for R4, which is
very approximate. Clearly, new experimental measurements
are highly desirable to verify the theoretical predictions. Nev-
ertheless, as shown in Table VI, although the final KIEs are
similar,thefactorizationsofthecontributionsarequalitatively
different for the two surfaces. The present results have lower
tunneling and larger variational contribution factors over the
whole temperature range.
In summary, we believe that the predictions of the VTST
calculations on the present surface are more accurate than
those on the semiempirical surface for the following reasons:
(i) The topologies in the barrier region revealed by the present
surface are based on high-level ab initio calculations, whereas
those of the latter surface are basically semiempirical;20(ii)
the KIE results on the present surface are in very good agree-
ment with available experimental values, while those on the
semiempirical surface differ from experiment evidently.
IV. CONCLUSIONS
We have performed detailed VTST calculations of ther-
mal rate constants and KIEs over a broad temperature range.
The PES employed is a newly constructed 12-dimensional
ab initio interpolated surface that is a modification of the
previous ab initio surface for the H + SiH4abstraction reac-
tion by a dual-level strategy. It is encouraging to see that the
computed ICVT/SCT rate constants are in very good agree-
ment with the available experimental measurements. As for
KIEs, which are very sensitive to the features of PES, better
TABLE VI. Factor analysis of the kinetic isotope effects of (R1)/(R4) at different temperatures.
ηvib
ηtun
ηvar
T (K)This worka
CVT/SCTb
This worka
CVT/SCTb
This worka
CVT/SCTb
200
250
300
350
400
450
500
600
700
800
1000
1200
1400
1600
1.34
1.13
0.99
0.90
0.83
0.78
0.74
0.68
0.64
0.62
0.58
0.56
0.55
0.54
1.48
1.20
1.10
0.98
0.86
0.81
0.75
0.70
0.64
3.01
2.00
1.61
1.42
1.31
1.24
1.19
1.13
1.09
1.07
1.04
1.03
1.02
1.02
4.98
3.08
2.27
1.85
1.61
1.44
1.35
1.21
1.13
0.90
0.93
0.95
0.96
0.97
0.98
0.99
0.99
1.00
1.00
1.00
1.01
1.01
1.01
0.53
0.63
0.68
0.74
0.78
0.81
0.84
0.89
0.90
0.601.050.95
aCalculated using the ICVT/SCT method. ηtransand ηrotare independent of temperature, and their values are 2.73 and 1.01,
respectively.
bFrom Ref. 20, ηtransand ηrotare 2.72 and 1.01, respectively.
Page 8
024315-8Cao et al.J. Chem. Phys. 134, 024315 (2011)
agreements with available experimental values are achieved
than before, indicating the accuracy of the present surface.
More experimental studies on the temperature dependence of
KIEs are needed to verify the theoretical calculations. It will
be a topic of our future research to perform global dynamical
calculations on the present ab initio PES.
ACKNOWLEDGMENTS
This work is supported by National Natural Science
Foundation of China (Grant No. 20733005), Chinese
Academy of Sciences (KJCX2.YW.H17), and Chinese Min-
istry of Science and Technology (Grant No.2007CB815204),
and the DoD EPSCoR program through the Office of Naval
Research (for Y.G.). Some of the computations were carried
out at Virtual Laboratory of Computational Chemistry, Com-
puterNetworkInformationCenteroftheChineseAcademyof
Sciences. The authors would like to thank Professor Donald
G. Truhlar for providing the POLYRATE 9.3 program.
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