www.elsevier.com/locate/cplett

Chemical Physics Letters 405 (2005) 240–245

Ab initio direct dynamics studies on the reaction Br + SiH4

Hui Zhang a,b, Jing-yao Liu a, Ze-sheng Li a,*, Li Sheng a, Jia-yan Wu a, Chia-chung Sun a

a Institute of Theoretical Chemistry, State Key Laboratory of Theoretical and Computational Chemistry, Jilin University, Changchun 130061, PR Chinab School of Chemical and Environmental Engineering, Harbin University of Science and Technology, Harbin 150080, PR China

Received 18 October 2004; in final form 3 November 2004

Abstract

The dynamical properties of the reaction Br + SiH4 ! products have been investigated theoretically. The optimized geometries,

frequencies and energies of reactants, transition states and products are calculated at the MP2/6-311G(d,p) and MP2/6-311G(2d,p)

levels. The energy profiles are refined by performing a series of single-point energy calculations at the MP4(SDQ)/6-311+G(2df,2p)//

MP2/6-311G(d,p) level. The rate constants are calculated by using canonical variational transition state theory (CVT) incorporating

with the small-curvature tunneling (SCT) correction in the temperature range 200–3000 K, and the results are in excellent agreement

with the available experimental values. H-abstraction reaction channel is the major channel for the title reaction.

� 2005 Elsevier B.V. All rights reserved.

1. Introduction

Silane is considered as an importantmaterial in plasma

chemical vapor deposition (CVD) and in semiconductor

manufacturing process. The use of volatile silicon com-

pounds may lead to their emission into the atmosphere,

where they can be removed by reactions with a variety

of reactive species. A number of investigations involving

attack by different atoms and free radicals, Cl [1–4], Br

[1–5], I [5], Si [6], O(3P) [7–11], O(1D) [12], H [13–15]and OH [9,16] have been reported. The reactions of Si,

O(3P), O(1D) andHwith SiH4 have been investigated the-

oretically [6,11,13,14]. Br atom is known to be an impor-

tant atmospheric species and is very efficient in destroying

ozone layer in the stratosphere and for the greenhouse ef-

fects [17]. The kinetics of the reaction Br + SiH4 ! prod-

ucts has attracted attentions experimentally [1,2,5]. Ding

andMarshall [1] studied the reaction employing the time-resolved atomic resonance fluorescence spectroscopy

technique. The measured rate constants were presented

by the expression of k = (9.0 ± 1.5) · 10�11exp [(�17.0

± 0.6) kJ mol�1/RT] cm3 molecule�1 s�1 over tempera-

0009-2614/$ - see front matter � 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2005.02.051

* Corresponding author. Fax: +86 0431 8498026/8945942.

E-mail address: zeshengli@mail.jlu.edu.cn (Z. Li).

ture range 295–575 K, which are in good agreement

with those of k = (1.6 ± 0.6) · 10�10exp[(�18.0 ± 1.3)kJ mol�1/RT] cm3 molecule�1 s�1 given by Seetula et al.

[5] over the temperature range 298–483 K. The rate con-

stant of title reaction determined by Niki et al. [2] was

1.0 · 10�13 cm3 molecule�1 s�1 at 298 K. This value is

excellent in accord with those of k = 9.4 · 10�14 cm3 mol-

ecule�1 s�1 given by Ding and Marshall [1] and

k = 1.1 · 10�13 cm3 molecule�1 s�1 given by Seetula

et al. [5] at 298 K. Niki et al. [2] discussed the mechanismfor the title reaction. They thought it can proceed through

H-atom abstraction and Br-atom displacement, i.e.

Brþ SiH4 ! SiH3 þHBr ðR1Þand

Brþ SiH4 ! SiH3BrþH ðR2ÞFurthermore, the reaction Br + SiH4 has been used as

a source of SiH3 radicals in kinetic experiments. To our

best knowledge, little theoretical attention has been paid

to the reaction of Br atoms with SiH4.

The main aim of this Letter is to investigate the mech-

anism for the title reaction and perform a direct ab initio

dynamics study on the rate constants of the title reactionover a wide temperature range 200–3000 K. The

H. Zhang et al. / Chemical Physics Letters 405 (2005) 240–245 241

information on an accurate potential energy surface,

including geometries, energies, gradients, and force con-

stants of the stationary points (reactants, transition

states, and products) and some extra points along the

minimum energy path (MEP), is obtained directly from

ab initio electronic structure calculations. Subsequently,by means of the POLYRATE 9.1 program [18], the rate

constants are calculated using the variational transition

state theory (VTST) proposed by Truhlar and co-

workers [19,20]. The comparison between theoretical

and experimental results is discussed.

2. Computational method

In the present work, the equilibrium geometries and

frequencies of the stationary points (reactants, products

and transition states) are optimized at the restricted or

unrestricted second-order Møller–Plesset perturbation

(MP2) [21–23] level with the 6-311G(d,p) basis sets

[24,25] by using the GAUSSIAN 03 program package

[26]. In order to quantify the sensitivity to the basisset, the optimizations are also performed at the MP2

level using the 6-311G(2d,p) basis set. At the MP2/6-

311G(d,p) level, the minimum energy path (MEP) is

obtained by intrinsic reaction coordinate (IRC) theory

with a gradient step-size of 0.05 (amu)1/2 bohr. Further-

more, at 16 selected points (8 points in the reactant

channel, 8 points in the product channel) along the

MEP, the force constant matrices as well as the har-monic vibrational frequencies are calculated. In order

to obtain more accurate reaction energies and barrier

heights, the single-point energy calculations are per-

Table 1

Calculated and experimental geometrical parameters (distances in angstroms

Species Geometrical parameters M

SiH4(Td) r(SiH) 1

SiH3(C3V) r(SiH) 1

\HSiH 1

HBr(C1V) r(HBr) 1

SiH3Br(C3V) r(SiBr) 2

r(SiH) 1

\BrSiH 1

\HSiH 1

SiH3–H–Br(C3V) r(SiH 0) 1

r(H0Br) 1

r(SiH) 1

\H0SiH 1

\HSiH 1

Br–SiH3–H(CS) r(SiBr) 2

r(SiH 0) 1

r(SiH) 1

\H0SiBr 5

\HSiBr 9

L = dr(SiH 0)/dr(H0Br) 3

a Experimental values from Ref. [15].b Experimental values from Ref. [29].

formed at the spin-projected fourth-order Mø11er–Ples-

set perturbation theory (MP4) [27] with single, double

and quadruple substitutions (SDQ) level using the 6-

311+G(2df,2p) basis set at the MP2/6-311G(d,p) and

MP2/6-311G(2d,p) optimized geometries, respectively.

Then the energy profile is further refined by a series ofsingle-point calculations along the MEP at the

MP4(SDQ)/6-311+G(2df,2p)//MP2/6-311G(d,p) level.

This initial information on the potential energy sur-

face (PES) is used to evaluate rate constants by means

of the POLYRATE 9.1 program [18]. The theoretical rate

constants and activation energies are calculated by

canonical variational transition state theory (CVT)

incorporating small-curvature tunneling (SCT) correc-tion methods proposed by Truhlar and co-workers

[20,28] over the temperature range 200–3000 K.

3. Results and discussions

3.1. Stationary points

The optimized geometric parameters of the reactant

(SiH4), products (SiH3, SiH3Br and HBr) and the

transition states at the MP2/6-311G(d,p) and MP2/6-

311G(2d,p) levels of theory and the available experimen-

tal values [15,29] are listed in Table 1. From Table 1, we

can see that the theoretical geometric parameters

obtained with the two basis sets are in excellent agree-

ment with the experimental values. The largest deviationbetween the theoretical and the experimental bond

lengths is 0.009 A for r(Si–H) in SiH4, and the largest

deviation of the bond angles is 0.6� for \HSiH in

and angles in degrees) of stable structures and transition state

P2/6-311G(d,p) MP2/6-311G(2d,p) Expt.

.475 1.472 1.481a

.475 1.473 1.477a

11.2 111.0 110.6

.412 1.412 1.414b

.228 2.253

.469 1.466

08.4 108.0

10.5 110.9

.900 1.861

.544 1.561

.471 1.468

06.2 105.9

12.5 112.8

.445 2.463

.670 1.685

.474, 1.476 1.471, 1.472

7.1 57.6

1.6, 117.1 91.3, 116.9

.13 2.50

242 H. Zhang et al. / Chemical Physics Letters 405 (2005) 240–245

SiH3. The transition state (TS1) for H-abstraction

reaction (R1) has C3v symmetry, while the transition

state (TS2) for Br-displacement reaction R2 has CS

symmetry. For H-abstraction reaction, we employ the

parameter L [30], which is defined as the ratio between

the elongation of the Si–H 0 bond and the elongationof the H 0–Br bond, i.e., L = dR(Si–H 0)/dR(H 0–Br), to re-

flect the reactant-like (L < 1) or product-like (L > 1)

character of the transition state. At the two levels, the

calculated values of L are 3.1 and 2.5 for reaction R1,

indicating that the transition states are product-like,

i.e., the reaction proceeds via a late transition state.

This late character in TS1 as expected for an endoer-

gic reaction is in keeping with Hammond�s postulate[31].

Table 2 gives the harmonic vibrational frequencies of

the reactants, products, and transition state at the MP2

level using the 6-311G(d,p) and 6-311G(2d,p) basis sets

as well as the corresponding available experimental re-

sults [15,29,32] for comparison. For the species SiH4,

SiH3, SiH3Br and HBr, the calculated frequencies at

the two levels are in good agreement with the experi-mental values with the largest deviation of 7.2%. The

transition states are confirmed by normal-mode analysis

to have only one imaginary frequency, which takes the

values of 365 (486) cm�1 for R1 and 369 (386) cm�1

for R2 at the MP2/6-311G(d,p) and MP2/6-311G(2d,p)

levels.

Table 2

Calculated and experimental frequencies (cm�1) of stationary points

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

SiH4 974, 974, 974, 1017, 1017, 2327, 2331,

2331, 2331

956, 956, 956

2330

SiH3 819, 979, 979, 2304, 2336, 2336 807, 966, 966

HBr 2741 2737

SiH3Br 436, 666, 666, 993, 996, 996, 2346,

2359, 2359

418, 648, 648,

SiH3–H–Br 365i, 193, 193, 667, 667, 755, 844,

970, 970, 2326, 2361, 2361

486i, 176, 176

2324, 2358, 2

Br–SiH3–H 369i, 153, 595, 773, 846, 914, 1000,

1063, 1275, 2299, 2314, 2325

386i, 149, 562

2301, 2314, 2

a Ref. [32].b Ref. [15].c Ref. [29].

Table 3

Reaction enthalpies ðDH 0298Þ and forward potential barriers (DEf) (kcal/mol)

MP2/6-311G(d,p) MP2/6-311G(2d,p) MP4(SDQ

MP2/6-31

ðDH0298Þ (R1) 2.42 1.29 3.41

DEf + ZPE (R1) 3.62 1.98 3.17

ðDH0298Þ (R2) �2.86 �4.37 �0.82

DEf + ZPE (R2) 17.43 14.08 14.75

Experimental values derived from heats of formation (in kcal/mol): SiH4, 8.2

�8.72 [29]; H, 52.15 [29].

The reaction enthalpies ðDH 0298Þ and potential barri-

ers (DE) with zero-point energy (ZPE) correction calcu-

lated at the MP2/6-311G(d,p), MP2/6-311G(2d,p),

MP4(SDQ)/6-311+G(2df,2p)//MP2/6-311G(d,p), and

MP4(SDQ)/6-311+G(2df,2p)//MP2/6-311G(2d,p) levels

are listed in Table 3. The reaction enthalpies, whichare 3.41 and �0.82 kcal/mol, respectively, for reactions

R1 and eqr2 at the MP4(SDQ)//MP2/6-311G(d,p) level,

show excellent mutual agreement with the ones of 3.40

and �0.82 kcal/mol obtained at the MP4(SDQ)//MP2/

6-311G(2d,p) level. And both of them agree well with

the corresponding experimental values of 4.28 ± 0.60

and �1.54 kcal/mol derived from the standard heats of

formation (SiH4, 8.21 kcal/mol [29]; Br, 26.76 kcal/mol[29]; SiH3, 47.97 ± 0.60 kcal/mol [5]; SiH3Br,

�18.72 kcal/mol [29]; HBr, �8.72 kcal/mol [29]; H,

52.15 kcal/mol [29]). The potential barrier height are

3.17 kcal/mol for reaction R1 and 14.75 kcal/mol for

reaction R2 obtained at the MP4(SDQ)//MP2/6-

311G(d,p) level, and the corresponding results are 2.77

and 14.51 kcal/mol when using the MP2/6-311G(2d,p)

optimized geometries. It is seen that at the two higher-levels the potential barrier heights of H-abstraction reac-

tion R1 are much lower than that of Br-displacement

reaction R2 by more than 10 kcal/mol, and this shows

that H-abstraction channel R1 is the absolute dominant

over the displacement channel R2 for the Br + SiH4

reactions. Thus we perform the rate constant

2d,p) Expt.

, 1010, 1010, 2327, 2330, 2330, 914a, 975, 2187, 2191

, 2297, 2327, 2327 773b, 933, 2150, 2180

2649c

962, 983, 983, 2348, 2361, 2361 430a, 633, 930, 950, 2196, 2200

, 566, 669, 669, 826, 959, 959,

358

, 753, 782, 899, 976, 1053, 1214,

325

with ZPE correction for the reaction at MP4//MP2 level of theory

)/6-311+G(2df,2p)//

1G(2d,p)

MP4(SDQ)/6-311+G(2df,2p)//

MP2/6-311G(d,p)

Expt.

3.40 4.28 ± 0.60

2.77

�0.82 �1.54

14.51

1 [29]; Br, 26.76 [29]; SiH3, 47.97 ± 0.60 [5]; SiH3Br, �18.72 [29]; HBr,

Fig. 1. Classical potential energy (VMEP), zero-point energies (ZPE),

and vibrational adiabatic potential energy ðV Ga Þ as a function of the

reaction coordinate, s, at the MP4(SDQ)//MP2 level.

Fig. 2. Generalized normal-mode vibrational frequencies as a function

of the reaction coordinate, s.

H. Zhang et al. / Chemical Physics Letters 405 (2005) 240–245 243

calculations only for the H-abstraction reaction

Br + SiH4 ! SiH3 + HBr. For purpose of comparison,

we use the formula Ea = DE* + RT = V* + DZPE +

DE(T) + RT as a simple estimation of the activation

energy [33], where V* and DE(T) represent the potentialbarrier height and thermal energy correction, respec-tively. Theoretical activation energy at T = 298 K for

R1 is estimated to be 4.71 kcal/mol at the MP4(SDQ)//

MP2/6-311G(d,p) level, which is excellent consistent

with the corresponding experimental values of

4.07 ± 0.14 and 4.31 ± 0.31 kcal/mol by Ding and Mar-

shall [1] and Seetula et al. [5], respectively. It should be

pointed out that the quenching of the energetic effect

of the spin–orbit coupling is probably very general forreactions of Cl and other halogen atoms. Truhlar and

co-workers [34,35] have analyzed this spin–orbit issue.

Spin–orbit coupling stabilizes the Br atom by

3.51 kcal/mol, and the spin–orbit coupling at the transi-

tion state is probably very small. The limited level of

electron correlation (MP4(SDQ)) tends to overestimate

reaction barriers heights for hydrogen transfers by

about 4 kcal/mol. Thus, the effects of neglecting spin–or-bit coupling and using a low-level of electron correlation

(MP4(SDQ)) roughly cancel and give good agreement

with experiment.

3.2. Minimum energy path

Since the geometries, frequencies, and energies of the

stationary points obtained at the MP2/6-311G(d,p) levelare consistent with those obtained at the MP2 level

using the 6-311G(2d,p) basis set, we can conclude that

the potential energy surface information obtained at

the MP2/6-311G(d,p) level are reliable. In the following

rate constant calculations, low-level calculations of

some extra-points along the MEP are performed at the

MP2/6-311G(d,p) level. Fig. 1 depicts the classical

potential energy curve, VMEP(s), the ground-statevibrational adiabatic potential energy curve, V G

a ðsÞ,and the zero-point energy (ZPE) curve as a function

of the intrinsic reaction coordinate s ((amu)1/2 bohr)

at the MP4(SDQ)/6-311+G(2df,2p)//MP2/6-311G(d,p)

level of theory. For the title reaction, the maximum posi-

tions of VMEP(s) and V Ga ðsÞ in the energy curve are the

same, and the ZPE curve is almost unchanged as s varies

except that there is a gentle drop from s = �0.5–0.5 amu1/2 bohr. To analyze this behavior in greater

detail, we give the variations of the generalized normal

modes vibrational frequencies along the MEP in

Fig. 2. In the negative limit of s, the frequencies are asso-

ciated with the reactants, and in the positive limit of s,

the frequencies are associated with the products. Most

of these modes are considered as spectator modes since

these frequencies do not change significantly in goingfrom the reactants to products, and they involve

motions not directly involved in the reaction. The two

lowest vibrational frequencies are the transitional

modes, which at the asymptote correspond to free rota-

tions and translations of the reactions, and they present

a maximum near the transition state. As shown in Fig. 2,

mode 4 is referred as the �reactive mode�, which connects

the stretching of Si–H bond in the reactant region with

the stretching of the H–Br bond in the product region,and it drops dramatically in the region from s = �0.5–

0.5 (amu)1/2 bohr as the reaction proceeds. This mode

is directly involved in the hydrogen transfer. Moreover,

because this dramatic drop of the reactive mode near the

saddle points is compensated partially by the two tran-

sitional modes, the ZPE shows small change with s.

Fig. 3. Computed CVT/SCT rate constants as a function of 103/T and

available experimental data.

244 H. Zhang et al. / Chemical Physics Letters 405 (2005) 240–245

3.3. Rate constants

The rate constants are calculated by canonical

variational transition state theory (CVT) with a

small-curvature tunneling (SCT) correction for the title

reaction in a wide temperature range from 200 to3000 K at the MP4(SDQ)//MP2 level of theory. The

calculated results and available experimental results

are displayed in Table 4 and Fig. 3. It is shown that

for the reaction SiH4 + Br, the variational effect, i.e.,

the ratio between the variational CVT and conven-

tional TST rate constant, is important in the lower

temperature range. The ratios of k(CVT)/k(TST) are

0.40 at 200 K and 0.76 at 400 K. Furthermore, theCVT and CVT/SCT rate constants are nearly the same

over the whole temperature range, which indicates that

the SCT correction is small. Our theoretical CVT/SCT

rate constants are in better agreement with the avail-

able experimental values in the experimental tempera-

ture range, the ratios of k(CVT/SCT)/k(expt) are

0.95, 0.95, 1.01 and 1.25 at 297, 333, 472 and 570 K,

respectively. In the temperature range 295–575 K, thetheoretical activation energy of 4.81 kcal/mol derived

from our calculated rate constants shows excellent

accordance with the experimental value of

4.07 ± 0.14 kcal/mol given by Ding and Marshall [1]

and 4.31 ± 0.31 kcal/mol given by Seetula et al. [5].

The good agreement between theoretical and experi-

mental rate constants and between theoretical and

experimental activation energies indicates that thepresent calculations can provide reliable prediction of

the rate constants for the title reaction at higher tem-

peratures. The three-parameter fits for the CVT/SCT

Table 4

Forward reaction rate constants (cm3 molecule�1 s�1) of title reaction

in the temperature range 200–3000 K

T (K) TST CVT CVT/SCT Ref. [1]

200 7.29 · 10�15 2.93 · 10�15 2.56 · 10�15

250 4.38 · 10�14 2.31 · 10�14 1.93 · 10�14

295 1.39 · 10�13 8.58 · 10�14 7.22 · 10�14 7.95 · 10�14

297 1.45 · 10�13 9.02 · 10�14 7.60 · 10�14 8.01 · l0�14

333 3.00 · 10�13 2.04 · 10�13 1.72 · 10�13 1.81 · 10�13

378 6.34 · 10�13 4.68 · 10�13 3.95 · 10�13 4.80 · 10�13

420 1.14 · 10�12 8.88 · 10�13 7.46 · 10�13 5.66 · 10�13

422 1.17 · 10�12 9.13 · 10�13 7.67 · 10�13 6.70 · 10�13

472 2.09 · 10�12 1.72 · 10�12 1.44 · 10�12 1.43 · 10�12

526 3.58 · 10�12 3.05 · 10�12 2.55 · 10�12 2.21 · 10�12

569 5.19 · 10�12 4.53 · 10�12 3.78 · 10�12 2.80 · 10�12

570 5.23 · 10�12 4.57 · 10�12 3.81 · 10�12 3.06 · 10�12

600 6.63 · 10�12 5.85 · 10�12 4.83 · 10�12

800 2.27 · 10�11 2.11 · 10�11 1.81 · 10�11

1000 5.36 · 10�11 5.09 · 10�11 4.50 · 10�11

1500 2.11 · 10�10 2.06 · 10�10 1.90 · 10�10

2000 4.94 · 10�10 4.85 · 10�10 4.57 · 10�10

2400 8.07 · 10�10 7.95 · 10�10 6.90 · 10�10

3000 1.41 · 10�9 1.39 · 10�9 1.23 · 10�9

rate constants for the reaction in the temperature

range from 200 to 3000 K give the expressionas follows: k = 6.24 · 10�17T2.17exp(�1566.94/T) cm3

molecules�1 s�1.

4. Conclusion

In this Letter, the reaction Br + SiH4 ! products

have been studied by ab initio direct dynamics method.Two transition states, one for H-abstraction and the

other for Br-displacement, are located at the MP2 level

with the 6-311G(d,p) and 6-311G(2d,p) basis sets,

respectively. The calculated potential barriers at the

MP4(SDQ)/6-311+G(2df,2p)//MP2/6-311G(d,p) and

MP4(SDQ)/6-311+G(2df,2p)//MP2/6-311G(2d,p) levels

show that the major reaction channel is H-abstraction

leading to product SiH3 + HBr. For the title reaction,the theoretical rate constants are calculated by canonical

variational transition state theory (CVT) incorporating

small-curvature tunneling (SCT) correction methods in

the temperature range 200–3000 K at the MP4(SDQ)/

6-311+G(2df,2p)//MP2/6-311G(d,p) level. The calcu-

lated CVT/SCT rate constants and activation energy

are in excellent agreement with the available experimen-

tal values.

Acknowledgements

The authors thank Prof. Donald G. Truhlar for pro-

viding the POLYRATE 9.1 program. This work is sup-

ported by the National Science Foundation of China

(20333050, 20303007), Doctor Foundation by the Minis-try of Education, Foundation for University Key

Teacher by the Ministry of Education, and Key subject

H. Zhang et al. / Chemical Physics Letters 405 (2005) 240–245 245

of Science and Technology by the Ministry of Education

of China.

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