Theoretical study on the reaction of SiH(CH3)3 with SiH3 radical

Theoretical Study on the Reaction of SiH(CH3)3with SiH3 Radical

HUI ZHANG,1 GUI-LING ZHANG,1 JING-YAN LIU,2 MIAO SUN,1 BO LIU,1 ZE-SHENG LI2

1College of Chemical and Environmental Engineering, Harbin University of Science andTechnology, Harbin 150080, People’s Republic of China

2Institute of Theoretical Chemistry, State Key Laboratory of Theoretical and ComputationalChemistry, Jilin University, Changchun 130023, People’s Republic of China

Received 31 October 2007; Revised 30 April 2008; Accepted 2 May 2008DOI 10.1002/jcc.21047

Published online 19 June 2008 in Wiley InterScience (www.interscience.wiley.com).

Abstract: The multiple-channel reactions SiH3 1 SiH(CH3)3 ? products are investigated by direct dynamics

method. The minimum energy path (MEP) is calculated at the MP2/6-311G(d,p) level, and energetic information is

further refined by the MC-QCISD (single-point) method. The rate constants for individual reaction channels are cal-

culated by the improved canonical variational transition state theory with small-curvature tunneling correction over

the temperature range of 200–2400 K. The theoretical three-parameter expression k(T) 5 2.44 3 10223T3.94

exp(24309.55/T) cm3/(molecule s) is given. Our calculations indicate that hydrogen abstraction channel R1 from

SiH group is the major channel because of the smaller barrier height among five channels considered.

q 2008 Wiley Periodicals, Inc. J Comput Chem 30: 236–242, 2009

Key words: gas-phase reaction; transition state; rate constants

Introduction

Silane and its methyl-substituted homolog are considered as im-

portant reagents in plasma chemical vapor deposition and in the

semiconductor manufacturing process. Tetramethylsilane is fre-

quently used as a solvent. The use of volatile silicon compounds

may lead to their emission into the atmosphere, where they can

be removed by reactions with a variety of reactive species such

as hydroxyl, nitrate radicals, and silane radicals. For most hydro-

carbons, hydrogen abstraction by radicals is one of the major

channel for their removal in the atmosphere.1,2 For reaction

SiH(CH3)3 1 SiH3, the hydrogen atom can be abstracted from

SiH group and CH3 group, the hydrogen atom can also be sub-

stituted from SiH group, and CH3 can be abstracted by SiH3 rad-

ical; as a result, five reaction pathways are feasible, denoted as

R1, R2a, R2b, R3, and R4, respectively. The calculations indi-

cate that two reaction routes exist in the reaction channel R2,

namely ‘‘in-plane hydrogen abstraction’’ (channel R2a) and

‘‘out-of-plane hydrogen abstraction’’ (channel R2b), both path-

ways lead to the same products, as follows:

SiH3þSiHðCH3Þ3 ! SiðCH3Þ3þSiH4 ðR1Þ! SiHðCH3Þ2CH2þSiH4 ðR2a andR2bÞ! SiH3SiðCH3Þ3þH ðR3Þ! SiHðCH3Þ2þSiH3CH3 ðR4Þ

In 1980, the rate constants have been studied of the reverse

reaction R-1 SiH3 1 SiH(CH3)3 ? Si(CH3)3 1 SiH4 at 298 K

with the value of 1.08 3 10217 cm3/(molecule s) using a rela-

Additional Supporting Information may be found in the online version of

this article.

Contract/grant sponsor: National Natural Science Foundation of China;

contract/grant numbers: 20333050, 20303007, 50743013

Contract/grant sponsor: Doctor Foundation, The Ministry of Education

Contract/grant sponsor: Foundation for University Key Teacher, Depart-

ment of Education of Heilongjiang Province; contract/grant numbers:

1151G019, 1152G010

Contract/grant sponsor: Key Subject of Science and Technology, The

Ministry of Education of China

Contract/grant sponsor: Key Subject of Science and Technology, Jilin

Province

Contract/grant sponsor: SF, Academe of Harbin of China; contract/grant

number: 2007RFXXG027

Contract/grant sponsor: SF, Heilongjiang Province of China; contract/

grant number: LBH-Q07058

Contract/grant sponsor: Natural Science Foundation of Heilongjiang

Province; contract/grant numbers: TA2005-15, B200605

Correspondence to: B. Liu; e-mail: [email protected]

q 2008 Wiley Periodicals, Inc.

tive rate method by Cornett et al.3 Because measurements were

done mostly at the lower temperature range of practical interest

and no experimental information is available on the branching

ratios of the title reaction, theoretical investigation is desirable

to give a further understanding of the mechanism of this multi-

ple channel reaction and to evaluate the rate constant at high

temperatures. To the best of our knowledge, no previous theoret-

ical work has been performed on this reaction.

In this article, dual-level direct dynamics method4–8 is

employed to study the kinetics of the SiH3 1 SiH(CH3)3 reac-

tion. The potential energy surface information, including geome-

tries, energies, gradients, force constants of all the stationary

points (reactants, products, and transition states), and some extra

points along the minimum energy path (MEP), is obtained

directly from electronic structure calculations. Single-point ener-

gies are calculated by the MC-QCISD method.9 Subsequently,

by means of the POLYRATE 9.1 program,10 the rate constants

of these reaction channels are calculated by the variational tran-

sition state theory (VTST)11,12 proposed by Truhlar and co-

workers. The comparison between the theoretical and experi-

mental results is discussed. Our results may be helpful for

further experimental investigations.

Computational Method

In the present work, the equilibrium geometries and frequencies

of all the stationary points (reactants, products, and transition

states) are optimized at the restricted or unrestricted second-

order Møller-Plesset perturbation (MP2)13–15 level with the 6-

311G(d,p) basis set. The MEP is obtained by intrinsic reaction

coordinate theory with a gradient step-size of 0.05 (amu)1/2

bohr. Then, the first and second energy derivatives are obtained

to calculate the curvature of the reaction path and the general-

ized vibrational frequencies along the reaction path. In order to

obtain more accurate energies and barrier heights, the energies

are refined by the MC-QCISD method (multicoefficient correla-

tion method based on quadratic configuration interaction with

single and double excitations MC-QCISD method proposed by

Fast and Truhlar)9 based on the MP2/6-311G(d,p) geometries.

All the electronic structure calculations are performed by the

GAUSSIAN03 program package.16

VTST11,12 is employed to calculate the rate constants by the

POLYRATE 9.1 program.10 The theoretical rate constants for

each reaction channel over the temperature range of 200–2400

K are calculated by the improved canonical variational transition

state theory (ICVT)17 incorporating small-curvature tunneling

(SCT)18,19 contributions proposed by Truhlar and coworkers.17

For the title reaction, most of the vibrational modes are treated

as quantum-mechanical separable harmonic oscillators, except

for a few lower modes. The hindered-rotor approximation of

Truhlar and Chuang20,21 is used for calculating the partition

function of the five transitional state modes. The curvature com-

ponents are calculated by using a quadratic fit to obtain the de-

rivative of the gradient with respect to the reaction coordinate.

Since SiH(CH3)3 is C3v symmetry, there are ‘‘in-plane hydrogen

abstraction’’ and ‘‘out-of-plane hydrogen abstraction’’ for reac-

tion channel R2, and the symmetry factor r 5 3, 6 for the reac-

tion channels R2a and R2b are taken into account in the rate

constant calculation. The total rate constants k are calculated

from the sum of the individual rate constants, i.e., k 5 k1 1 k21 k3 1 k4, where k2 5 k2a 1 k2b.

Results and Discussions

Stationary Points

The optimized geometries of the reactants (SiH3 and

SiH(CH3)3), products (Si(CH3)3, SiH(CH3)2CH2, SiH4, SiH3-

Si(CH3)3, SiH(CH3)2, and SiH3CH3), and transition states (TS1,

TS2a, TS2b, TS3, and TS4) calculated at the MP2/6-311G(d,p)

level are presented in Figure 1, along with the available experi-

mental values.22,23 The theoretical geometric parameters of

SiH3, SiH4, and SiH3CH3 are in good agreement with the corre-

sponding experimental values.22,23 Figure 1 shows that the tran-

sition state TS1 has C3v symmetry and the transition states

TS2a, TS2b, TS3, and TS4 have the same symmetry, C1. When

symmetries of TS2a and TS3 are restricted to Cs and C3v, the

corresponding frequencies have five and four imaginary frequen-

cies at the same level, respectively. In TS1, TS2a, TS2b, TS3,

and TS4 structures, the breaking bonds Si—H, C—H, C—H,

Si—H, and Si—C increase by 24%, 39%, 39%, 15%, and 23%

compared to the equilibrium bond length in SiH(CH3)3; the

forming bonds Si—H, Si—H, Si—H, Si—Si, and Si—C stretch

by 16%, 11%, 11%, 2%, and 17% over the equilibrium bond

lengths in isolated SiH4, SiH3Si(CH3)3, and SiH3CH3, respec-

tively. The elongation of the breaking bond is larger than that of

the forming bond, indicating that TS1, TS2a, TS2b, TS3, and

TS4 of the title reaction are all product-like, i.e., all the five

reaction channels will proceed via ‘‘late’’ transition states, which

is consistent with Hammond’s postulate,24 applied to for an

endothermic reaction.

Table 1 lists the harmonic vibrational frequencies of the reac-

tants, products, and transition states calculated at the MP2/6-

311G(d,p) level as well as the available experimental

values.22,25,26 For the species SiH3, SiH4, and SiH3CH3, the cal-

culated frequencies are in general agreement with the experi-

mental values, with the largest deviation within 9%. The five

transition states are all confirmed by normal-mode analysis to

have one and only one imaginary frequency, which corresponds

to the stretching modes of coupling between breaking and form-

ing bonds. And the values of those imaginary frequencies are

1420i cm21 for TS1, 1513i cm21 for TS2a, 1504i cm21 for

TS2b, 806i cm21 for TS3, and 1127i cm21 for TS4.

Energetics

The reaction enthalpies (DH0298) and potential barrier heights

(DETS) with zero-point energy (ZPE) corrections for R1, R2a,

R2b, R3, and R4 reaction channels calculated at the MC-

QCISD//MP2/6-311G(d,p) level are listed in Table 2. The cal-

culated values agree well with corresponding experimental one.

The theoretical value at 298 K of DH0298, 3.1 kcal/mol for reac-

tion R1, is in good agreement with the corresponding experi-

mental value 3.3 6 1.7 kcal/mol, which was derived from the

standard heats of formation (SiH(CH3)3, 239.00 6 0.96 kcal/

237Theoretical Study on the Reaction of SiH(CH3)3 with SiH3 Radical

Journal of Computational Chemistry DOI 10.1002/jcc

mol27; SiH4, 8.21 kcal/mol28; SiH3, 47.97 6 0.60 kcal/mol29;

Si(CH3)3, 4.07 6 1.67 kcal/mol30), indicating that the values

calculated at the MC-QCISD//MP2/6-311G(d,p) level may be

reliable. Thus, we use MC-QCISD//MP2/6-311G(d,p) method to

calculate the potential energy barriers as well as the energies

along the MEP in the following studies. From Table 2, it is also

shown that the five individual reaction channels are all endother-

mic reactions, consistent with the discussion mentioned earlier

of Hammond’s postulate.24

Table S1 lists the calculated bond dissociation energies

(D0298) of the Si—H and C—H bonds in SiH2(CH3)2 and

SiH(CH3)3, along with several experimental data31–33 of Si—H

bond dissociation energy. The D0298 (Si—H) value of SiH(CH3)3

with 92.82 kcal/mol obtained at the MC-QCISD//MP2/6-

311G(d,p) level shows good consistency with the previous liter-

ature results, 94.82 6 0.48,31 91.24 6 1.67,32 and 90.28 6 1.43

kcal/mol.33 At the same level, the D0298 (C—H) values are

100.29 kcal/mol in SiH(CH3)3 and 101.23 kcal/mol in

SiH2(CH3)2. No comparison between theory and experiment

can be made due to the lack of the experimental D0298 (C—H)

value in SiH2(CH3)2 and SiH(CH3)3. The good agreement

between theoretical and experimental D0298 (Si—H) implies that

the MC-QCISD//MP2/6-311G(d,p) level is a suitable method

to compute the bond dissociation energies and our calculated

D0298 (C—H) value may be expected to provide reliable refer-

ence information for future laboratory investigations. The dis-

sociation energy of the Si—H bond in SiH2(CH3)2 is more

than 1 kcal/mol smaller than that of the Si—H bond in

SiH(CH3)3, which means that the H-abstraction channel of

SiH2(CH3)2 1 SiH3 ? SiH(CH3)2 1 SiH4 proceeds more

effectively than that of SiH(CH3)3 1 SiH3 ? Si(CH3)3 1SiH4. The dissociation energies of the Si—H bond are 9 and 7

kcal/mol smaller than those of the C—H bond in SiH2(CH3)2and SiH(CH3)3, respectively, indicating that the H-abstraction

channel from Si—H bond may be in favor of the abstraction

from C—H bond.

A schematic potential energy diagram of the SiH3 radicals

with SiH(CH3)3 reaction with ZPE corrections obtained at the

MC-QCISD//MP2/6-311G(d,p) level is plotted in Figure 2.

Note that the energy of reactant is set to zero for reference. The

values in parentheses are calculated at the MP2/6-311G(d,p)

level and include the ZPE corrections. The potential barrier

height of reaction channel R1 (10.25 kcal/mol) and is much

lower than the ones of R2a (17.85 kcal/mol), R2b (18.19 kcal/

mol), R3 (31.36 kcal/mol), and R4 (39.02 kcal/mol) at the MC-

QCISD//MP2/6-311G(d,p) level. The reaction route of the

abstraction from the in-plane hydrogen (R2a) has a lower barrier

than the out-plane hydrogen (R2b) route. At the same time, the

former reaction path R1 is less endothermic than the later by

about 7.46, 11.05, and 1.01 kcal/mol for R2a (or R2b), R3, and

R4, respectively, and as a result, the former reaction path R1 is

more thermodynamically and kinetically favorable than the later.

Thus, we infer that reaction channel R1 is the dominant channel

for the title reaction. TS4 is higher than TS3 by about 7.7 kcal/

Figure 1. Optimized geometries of the reactants, products, and transition states at the MP2/6-

311G(d,p) level. The values in parentheses are the experimental values (ref. 22 for SiH3 and SiH4,

and ref. 23 for SiH3CH3). Bond lengths are in angstroms and angles are in degrees.

238 Zhang et al. • Vol. 30, No. 2 • Journal of Computational Chemistry


Table 1. Calculated and Experimental Frequencies (in cm21) for the Reactants, Products, and Transition

States for the Title Reaction at the MP2/6-311G(d,p) Level.

Species MP2/6-311G(d,p) Expt.

SiH3 2354, 2354, 2319, 986, 986, 824 2180, 2150, 933, 773a

SiH(CH3)3 3215, 3215, 3215, 3210, 3209, 3209, 3111, 3111, 3111, 2280, 1513, 1504, 1504, 1495, 1495,

1490, 1350, 1340, 1340, 952, 952, 908, 882, 882, 729, 729, 706, 637, 637, 633, 239, 200,

200, 169, 169, 142

Si(CH3)3 3222, 3222, 3222, 3197, 3197, 3197, 3101, 3101, 3100, 1508, 1498, 1498, 1491, 1491, 1485,

1342, 1330, 1330, 902, 897, 897, 749, 749, 715, 706, 706, 618, 227, 197, 197, 156, 156,

132

SiH(CH3)2CH2 3327, 3225, 3216, 3216, 3215, 3214, 3113, 3113, 2267, 1508, 1503, 1497, 1495, 1472, 1346,

1339, 948, 945, 893, 863, 764, 755, 728, 697, 645, 635, 564, 252, 210, 199, 173, 158, 91

SiH4 2354, 2354, 2354, 2345, 1019, 1019, 975, 975, 975 2191, 2187, 975, 914b

SiH3Si(CH3)3 3209, 3209, 3209, 3205, 3205, 3205, 3105, 3105, 3105, 2303, 2303, 2294, 1512, 1501, 1501,

1493, 1493, 1488, 1346, 1334, 1334, 993, 993, 954, 892, 892, 887, 793, 793, 716, 716,

711, 640, 514, 514, 427, 207, 198, 198, 174, 174, 148, 131, 131, 78

SiH(CH3)2 3227, 3227, 3207, 3207, 3111, 3110, 2282, 1501, 1498, 1493, 1489, 1343, 1335, 934, 908,

896, 758, 714, 661, 630, 529, 201, 156, 132

SiH3CH3 3228, 3228, 3125, 2327, 2327, 2325, 1501, 1501, 1351, 1008, 1008, 992, 921, 921, 715, 531,

531, 204

2982, 2898, 2169, 2160, 1403, 1260,

980, 940, 868, 700, 540, 187c

TS1 3214, 3214, 3213, 3198, 3198, 3198, 3102, 3102, 3101, 2318, 2318, 2293, 1508, 1498, 1498,

1491, 1491, 1486, 1342, 1330, 1330, 1043, 1043, 986, 986, 905, 891, 891, 854, 743, 743,

710, 708, 708, 618, 301, 200, 200, 186, 186, 175, 151, 151, 127, 11, 11, 9, 1420i

TS2a 3277, 3214, 3214, 3212, 3211, 3181, 3112, 3112, 2334, 2329, 2311, 2267, 1508, 1502, 1496,

1493, 1448, 1346, 1339, 1146, 1138, 991, 988, 952, 948, 941, 898, 889, 872, 755, 730,

712, 706, 644, 635, 565, 455, 291, 239, 216, 203, 198, 166, 151, 65, 48, 25, 1513i

TS2b 3277, 3217, 3215, 3210, 3209, 3180, 3111, 3110, 2334, 2331, 2313, 2279, 1507, 1501, 1495,

1493, 1448, 1345, 1337, 1141, 1137, 991, 988, 964, 944, 931, 902, 897, 875, 783, 745,

722, 681, 643, 637, 555, 461, 273, 239, 214, 203, 187, 172, 154, 61, 40, 24, 1504i

TS3 3230, 3229, 3226, 3214, 3213, 3206, 3111, 3111, 3110, 2305, 2305, 2285, 1523, 1513, 1511,

1494, 1486, 1483, 1338, 1319, 1308, 1010, 987, 985, 904, 899, 888, 881, 841, 760, 718,

707, 595, 560, 559, 513, 495, 484, 306, 185, 176, 138, 121, 117, 84, 83, 67, 806iTS4 3382, 3370, 3212, 3212, 3201, 3200, 3175, 3106, 3105, 2306, 2305, 2274, 2253, 1504, 1499,

1494, 1489, 1404, 1400, 1342, 1334, 1073, 1065, 989, 987, 922, 899, 889, 842, 772, 764,

716, 659, 626, 565, 374, 366, 237, 195, 153, 150, 143, 140, 133, 54, 44, 39, 1127i

aRef. 23.bRef. 26.cRef. 27.

Table 2. The Reaction Enthalpies at 298 K (DH0298), the Barrier Heights TSs (DETS) (kcal/mol) with

Zero-Point Energy (ZPE) Correction for the Reactions of SiH3 Radical with SiH(CH3)3 at the

MC-QCISD//MP2/6-311G(d,p) Level Together with the Experimental Value.

MC-QCISD//MP2 Expt.

DH0298 SiH3 1 SiH(CH3)3 ? Si(CH3)3 1 SiH4 (R1) 3.07 3.31 6 1.67

SiH3 1 SiH(CH3)3 ? SiH(CH3)2CH2 1 SiH4 (R2a) 10.66

SiH3 1 SiH(CH3)3 ? SiH(CH3)2CH2 1 SiH4 (R2b) 10.66

SiH3 1 SiH(CH3)3 ? SiH3SiH(CH3)2 1 H (R3) 15.91

SiH3 1 SiH(CH3)3 ? SiH(CH3)2 1 SiH3CH3 (R4) 3.68

DETS1ZPE SiH3 1 SiH(CH3)3 ? Si(CH3)3 1 SiH4 (R1) 10.25

SiH3 1 SiH(CH3)3 ? SiH(CH3)2CH2 1 SiH4 (R2a) 17.85

SiH3 1 SiH(CH3)3 ? SiH(CH3)2CH2 1 SiH4 (R2b) 18.19

SiH3 1 SiH(CH3)3 ? SiH3SiH(CH3)2 1 H (R3) 31.36

SiH3 1 SiH(CH3)3 ? SiH(CH3)2 1 SiH3CH3 (R4) 39.02

Experimental value derived from the standard heats of formation (in kcal/mol): SiH(CH3)3, –39.00 6 0.96 kcal/

mol;25 SiH4, 8.21 kcal/mol26; SiH3, 47.97 6 0.60 kcal/mol27; Si(CH3)3, 4.07 6 1.67 kcal/mol.28



mol, which means that reaction R3 is more preferable, but reac-

tion R4 is 11.0 kcal/mol less endothermic than reaction R3;

thus, reaction R4 becomes more important in thermodynamic

than R3 as the temperature increases, and as a result of a larger

rate constant of reaction R4 at high temperature. The potential

barrier height of reaction channel SiH2(CH3)2 1 SiH3 ?SiH(CH3)2 1 SiH4 (9.87 kcal/mol) is lower than the one of

SiH(CH3)3 1 SiH3 ? Si(CH3)3 1 SiH4 (10.25 kcal/mol) at the

MC-QCISD//MP2/6-311G(d,p) level. Thus, the rate constants of

the former channel may be faster than the latter one.

Rate Constants

Dual-level dynamics calculations4–8 of the title reaction are car-

ried out at the MC-QCISD//MP2/6-311G(d,p) level. The rate

constants of the individual channel, k1, k2, k3, and k4, are eval-

uated by conventional transition state theory (TST), the ICVT,

and the ICVT with the SCT contributions in a wide temperature

range from 200 to 2400 K. The TST, ICVT, ICVT/SCT rate

constants of k1 and the reverse reaction rate constants k21 are

given in Table 3 along with the available experimental results.3

The calculated rate constant value of k21 at 298 K, 2.68 310217 cm3/(molecule s), is in good agreement with the available

experimental value,3 1.08 3 10217 cm3/(molecule s), and the

ratio of kICVT/SCT/kexptl is 2.48 at 298 K. The theoretical ICVT/

SCT rate constant of reaction channel SiH(CH3)3 1 SiH3 ?Si(CH3)3 1 SiH4 is 7.02 3 10220 cm3/(molecule s), which is

smaller than the one [5.30 3 10218 cm3/(molecule s)] of reac-

tion channel SiH2(CH3)2 1 SiH3 ? SiH(CH3)2 1 SiH4 at 298

K. Theoretical activation energy (Ea) is estimated based on the

calculated ICVT/SCT rate constants, and it is found that the cor-

responding Ea value for reaction channel SiH2(CH3)2 1 SiH3 ?SiH(CH3)2 1 SiH4, 7.49 kcal/mol, is lower than that for reaction

channel SiH(CH3)3 1 SiH3 ? Si(CH3)3 1 SiH4 (11.11 kcal/

mol) in 200–600 K. Those are consistent with a qualitative

assessment based on the bond dissociation energies and the

potential energy barrier heights of the two reactions.

The ICVT/SCT rate constants of the four channels and over-

all rate constants are plotted against the reciprocal of tempera-

ture in Figure 3. Seen from Figure 3, it is shown that the ICVT

Figure 2. Schematic potential energy surface for the title reaction

system. Relative energies are calculated at the MC-QCISD//MP2/6-

311G(d,p) 1 ZPE level [in (kcal/mol)]. The values in parentheses

are calculated at the MP2/6-311G(d,p) 1 ZPE level.

Table 3. Calculated TST, ICVT, and ICVT/SCT Rate Constants [cm3/(molecule s)] of the Reaction Channel

R1, k1, and the Reverse Reaction Channel R-1, k21, in the Temperature Region 200–2400 K at the

MC-QCISD//MP2/6-311G(d,p) Level.

T (K)

k1 k21

TST ICVT ICVT/SCT TST ICVT ICVT/SCT

200 5.22 3 10224 2.84 3 10224 1.36 3 10223 2.59 3 10220 1.41 3 10220 6.76 3 10220

225 1.22 3 10222 6.42 3 10223 2.23 3 10222 2.53 3 10219 1.34 3 10219 4.65 3 10219

250 1.57 3 10221 8.04 3 10222 2.23 3 10221 1.63 3 10218 8.35 3 10219 2.32 3 10218

298 6.90 3 10220 3.38 3 10220 7.02 3 10220 2.64 3 10217 1.29 3 10217 2.68 3 10217

350 1.41 3 10218 6.62 3 10219 1.14 3 10218 2.50 3 10216 1.18 3 10216 2.02 3 10216

400 1.30 3 10217 5.95 3 10218 9.04 3 10218 1.34 3 10215 6.14 3 10216 9.33 3 10216

450 7.72 3 10217 3.45 3 10217 4.81 3 10217 5.24 3 10215 2.34 3 10215 3.27 3 10215

500 3.34 3 10216 1.46 3 10216 1.92 3 10216 1.63 3 10214 7.13 3 10215 9.36 3 10215

600 3.27 3 10215 1.39 3 10215 1.69 3 10215 9.77 3 10214 4.16 3 10214 5.04 3 10214

700 1.82 3 10214 7.59 3 10215 8.74 3 10215 3.85 3 10213 1.61 3 10213 1.85 3 10213

800 7.02 3 10214 2.88 3 10214 3.21 3 10214 1.15 3 10212 4.73 3 10213 5.27 3 10213

900 2.11 3 10213 8.55 3 10214 9.32 3 10214 2.84 3 10212 1.15 3 10212 1.26 3 10212

1000 5.27 3 10213 2.12 3 10213 2.27 3 10213 6.08 3 10212 2.45 3 10212 2.62 3 10212

1200 2.26 3 10212 8.96 3 10213 9.40 3 10213 2.07 3 10211 8.21 3 10212 8.61 3 10212

1500 1.11 3 10211 4.32 3 10212 4.45 3 10212 8.06 3 10211 3.15 3 10211 3.25 3 10211

2000 6.58 3 10211 2.53 3 10211 2.58 3 10211 3.84 3 10210 1.48 3 10210 1.50 3 10210

2400 1.80 3 10210 6.87 3 10211 6.95 3 10211 9.38 3 10210 3.59 3 10210 3.63 3 10210



and TST rate constants of four reaction channels are nearly the

same in the whole temperature region, which indicates that the

variational effect is almost negligible. And the tunneling effect

of four reaction channels, i.e., the ratio between ICVT/SCT and

ICVT rate constants, plays an important role at the lower tem-

peratures and is negligible at high temperatures. For example,

the ratios of k(ICVT/SCT)/k(ICVT) are 4.79, 9.37, 5.84, and

4.13 3 102 at 200 K for R1, R2, R3, and R4, respectively, and

while they are 1.22, 1.27, 1.25, and 1.57 at 600 K, respectively.

Figure 3 shows that it can also be found that the values of k1is much larger than those of k2, k3, and k4 by about 2–7, 9–24,

and 10–29 orders of magnitude in the temperature range of 200–

600 K, and the total rate constants are almost equal to reaction

R1. Thus, on the basis of our calculation the hydrogen abstrac-

tion channel R1 to yield Si(CH3)3 and SiH4 is the major reaction

channel over the whole temperature range, while the other three

reaction channels R2, R3, and R4 are always minor pathways

over the temperature range of 200–2400. This is in line with the

potential energy barrier heights and the reaction enthalpies

results calculated earlier. The ratios of k3/k4 are 4.6 3 104, 2.5

3 102, and 3.3 at 200, 350, and 600 K, respectively. This mean

reaction R3 is the more important channel in the lower tempera-

ture region, which is in accordance with its kinetic superiority.

However, the rate constant is mainly affected not by kinetics but

by thermodynamics with the increase in temperature. Thus, reac-

tion R4 becomes more and more competitive as the temperature

increases. It is seen that when the temperature goes above 743

K, the CH3-abstraction channel R4 has more important contribu-

tion to the overall rate constant. This is consistent with the

prediction in the Energetics section.

To further understand the reaction mechanism of the title

reaction, the temperature dependence of branching ratios, k1/(k11 k2 1 k3 1 k4), k2/(k1 1 k2 1 k3 1 k4), k3/(k1 1 k2 1 k3 1k4), and k4/(k1 1 k2 1 k3 1 k4), is calculated and exhibited

against the reciprocal of temperature in Figure 4. It can be seen

that the H-abstraction channel R1 from SiH group is to dominate

the reaction over the whole temperature region. The values of

k1/(k1 1 k2 1 k3 1 k4) are greater than or equal to 98% in the

temperature range of 200–1000 K. This is consistent with the

inferences made from the potential barrier heights of these reac-

tion channels. For reaction R2, on increasing the temperature,

the contribution of k2 to the overall rate constant increases grad-

ually, for instance, the ratios k2/(k1 1 k2 1 k3 1 k4) are up to

2–15% from 1000 to 2400 K, i.e., the reaction channel R2

becomes more and more competitive with the increase in tem-

perature; therefore, the H-abstraction channel R2 from CH3

group should be considered when the temperature increases.

Because of the limited experimental knowledge on the

kinetics of the title reaction, we hope that our present study may

provide useful information for future laboratory investigations.

For convenience of future experimental measurements, the three-

parameter fits of the ICVT/SCT rate constants of four reaction

channels and the whole reaction in the temperature range from

200 to 2400 K are performed and the expressions are given as

follows [in unit of cm3/(molecule s)]:

k1ðTÞ ¼ 6:77 3 10�23T3:80 expð�4363:50=TÞ

k2ðTÞ ¼ 2:56 3 10�24T4:18 expð�7708:18=TÞ

k3ðTÞ ¼ 1:15 3 10�25T3:97 expð�14591:22=TÞ

k4ðTÞ ¼ 1:39 3 10�27T5:15 expð�17275:82=TÞ

kðTÞ ¼ 2:44 3 10�23T3:94 expð�4309:55=TÞ

Conclusion

In this article, the multichannel reactions SiH3 1 SiH(CH3)3 ?products are studied by a dual-level direct dynamics method.

The potential energy surface information is obtained at the MP2/

6-311G(d,p) level, and energies of the stationary points and a

few extra points along the MEP are refined at the MC-QCISD

level. For the title reaction, five reaction channels are identified;

Figure 3. The ICVT/SCT rate constants calculated at the MC-

QCISD//MP2/6-311G(d,p) level for four reaction channels and the

total rate constants k [in cm3/(molecule s)] versus 1000/T between

200 and 2400 K.

Figure 4. Calculated branching ratios for the title reaction versus

1000/T between 200 and 2400 K.



hydrogen abstraction reaction from SiH group R1 is the major

pathway. The rate constants for five reaction channels are calcu-

lated by the ICVT incorporating SCT correction at the

MC-QCISD//MP2 level. The calculated results show that the

tunneling effect plays an important role in the calculation of rate

constants. The overall ICVT/SCT rate constant, k, is in good

agreement with the available experimental value. The three-pa-

rameter rate–temperature formulae for the SiH3 1 SiH(CH3)3reaction in the temperature range from 200 to 2400 K are fitted

and given as follows [in cm3/(molecule s)]:

kðTÞ ¼ 2:44 3 10�23T3:94 expð�4309:55=TÞ

Acknowledgments

The authors thank Professor Donald G. Truhlar for providing

POLYRATE 9.1 program.

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Theoretical study on the reaction of SiH(CH3)3 with SiH3 radical