# 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 for chemical reactions using the corrections of Zero Curvature Tunneling (ZCT) and of Small Curvature Tunneling (SCT) methods are reported. The general procedure is implemented and used with high quality ab initio computations and semi-classical reaction probabilities along the Minimum Energy Path (MEP). The approach is based on a vibrational adiabatic reaction path and is applied to the H + Si(CH$_3$)$_4$ $\rightarrow$ H$_2$ +Si(CH$_3$)$_3$CH$_2$ reaction and its isotopically substituted variants. All the degrees of freedom are optimized and harmonic vibrational frequencies and zero-point energies are calculated at the MP2(full) level with the cc-pVTZ basis set. Single point energies are calculated at a higher level of theory with the same basis set, namely CCSD(T, full). The influence of the Basis Set Superposition Error (BSSE) on the energetics is tested. The method is further exploited to predict primary and secondary Kinetic Isotope Effects (KIEs and SKIEs respectively). Rate constants computed with the ZCT and SCT methods over a wide temperature range [180-2000 K] show important quantum tunneling effects at low temperatures when compared to rates obtained from the purely classical Transition State Theory (TST) and from the Canonical Variational Transition state theory (CVT). For the H + Si(CH$_3$)$_4$ reaction, they are given by the following expressions: k(TST/ZCT)=9.47 10$^{-19}$ $\times$ T$^{2.65}$ exp(-2455.7/T) and k(CVT/SCT)=7.81 10$^{-19}$ $\times$ T$^{2.61}$ exp[(2704.2/T) (in cm$^3$molec$^{-1}$s$^{-1}$). These calculated rates are in very good agreement with available experiments. <sub><sub><sup><sub><sub><sub><sub><sub><sub><sub><sub><sub><sub><sub>The Journal of Physical Chemistry A 01/2014; · 2.77 Impact Factor - SourceAvailable from: Yi Zhao[Show abstract] [Hide abstract]

**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,

Page 3

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.

Page 5

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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