Theoretical study on the reaction CX3 + SiH(CH3)3 (X = H, F)

DOI: 10.1002/jcc.21964

Theoretical Study on the ReactionCX3 1 SiH(CH3)3 (X 5 H, F)

Hui Zhang,[a] Liu Yang,[a] Jing-Yao Liu,[b] and Ze-Sheng Li*[c,d]

Theoretical investigations are carried out on the multiple-channel

reactions, CH3 þ SiH(CH3)3 ! products and CF3 þ SiH(CH3)3 !products. The minimum energy paths (MEP) are calculated at the

MP2/6-311 þ G(d,p) level, and energetic information is further

refined by the MC-QCISD (single point) method. The rate

constants for major reaction channels are calculated by the

canonical variational transition state theory (CVT) with small-

curvature tunneling (SCT) correction over the temperature range

200–1500 K. The theoretical rate constants are in good

agreement with the available experimental data and are found to

be k1a(T) ¼ 1.93 � 10�24T3.15exp(�1214.59/T) and k2a(T) ¼ 1.33

� 10�25T4.13exp(�397.94/T) (in unit of cm3molecule�1s�1). Our

calculations indicate that hydrogen abstraction channel from SiH

group is the major channel due to the smaller barrier height

among five channels considered. VC 2011 Wiley Periodicals, Inc.

J Comput Chem 33: 203–210, 2012

Keywords: gas-phase reaction � transition state � rate constants

Introduction

Silane and its methyl-substituted homolog are considered as

important reagents in plasma chemical vapor deposition (CVD)

and in the semiconductor manufacturing process. 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. For reactions CX3 þ SiH(CH3)3 (X ¼H, F), the hydrogen atom can be abstracted from SiH group

and CH3 group, the hydrogen atom in SiH group can also be

substituted by CH3 or CF3, and CH3 can be abstracted by CX3radical, as a result, five reaction pathways are feasible, denoted

as R1a (R2a), R1b1 (R2b1), R1b2 (R2b2), R1c (R2c), and R1d

(R2d), respectively. The calculations indicate that two reaction

routes exist in the reaction channel R1b (R2b), namely ‘‘in-

plane hydrogen abstraction’’ (channel R1b1 or R2b1) and ‘‘out-

of-plane hydrogen abstraction’’ (channel R1b2 or R2b2), both

pathways lead to the same products, as follows:

CH3 þ SiHðCH3Þ3 ! SiðCH3Þ3 þ CH4 ðR1aÞ! SiHðCH3Þ2CH2 þ CH4 ðR1b1 and R1b2Þ! SiðCH3Þ4 þ H ðR1cÞ! SiHðCH3Þ2 þ C2H6 ðR1dÞ

CF3 þ SiHðCH3Þ3 ! SiðCH3Þ3 þ CHF3 ðR2aÞ! SiHðCH3Þ2CH2 þ CHF3 ðR2b1 and R2b2Þ! SiðCH3Þ2CF3 þ H ðR2cÞ! SiHðCH3Þ2 þ CH3CF3 ðR2dÞ

Five papers have reported about experimental kinetic data

on the reaction of CX3 þ SiH(CH3)3 (X ¼ H, F). In 1967, the

Arrhenius parameters have been determined by photolysing

azomethane in admixture with the organosilicon compound in

the gas phase CH3 þ SiH(CH3)3 ! Si(CH3)3 þ CH4 by Kerr

et al.[1] over the temperature range 330–445 K, the value is

7.97 � 10�18 cm3molecule�1s�1 at 350 K. In 1969, Arrhenius

parameters have been obtained for the above-mentioned reac-

tion by Morris et al.[2] using same method. Arrhenius expres-

sion of 3.64 � 10�13exp[–32,759(J/mol)/RT] cm3molecule�1s�1

is given over the temperature range 348–498 K, the value is

5.03 � 10�18 cm3molecule�1s�1 at 350 K. After 1 year, rate

constants for reaction CF3 þ SiH(CH3)3 ! Si(CH3)3 þ CHF3have been determined in the temperature range 323–476 K by

the same group,[3] the value is 1.01 � 10�15 cm3molecule�1s�1

at 350 K. In 1973 and 1978, kinetic data were also evalua-

ted by two groups, Berkley[4] and Arthur,[5] for the reaction

CH3 þ SiH(CH3)3 ! Si(CH3)3 þ CH4, Arrhenius expressions are

8.14 � 10�13exp[–34,754 6 2087(J/mol)/RT] (302–486 K) and

2.09 � 10�13exp[–30,182 6 906(J/mol)/RT] (345–526 K)

cm3molecule�1s�1, respectively. The rate constants are 5.29 �10�18 and 6.55 � 10�18 cm3molecule�1s�1 at 350 K, respec-

tively. Comparison of the reference results about reaction R1a

shows that they are in good consistency.

Because measurements were done mostly at the lower tem-

perature range of practical interest and no experimental infor-

mation is available on the higher temperature of the title reac-

tion, theoretical investigation is desirable to give a further

[a] H. Zhang, L. Yang

College of Chemical and Environmental Engineering, Harbin University of

Science and Technology, Harbin 150080, People’s Republic of China

Fax: 86-0451-86392708, E-mail: [email protected]

[b] J.-Y. Liu

Institute of Theoretical Chemistry, Jilin University, Changchun 130023,

People’s Republic of China

[c] Z.-S. Li

Academy of Fundamental and Interdisciplinary Sciences, Department of

Chemistry, Harbin Institute of Technology, Harbin 150080, People’s Republic

of China

[d] Z.-S. Li

School of Sciences, Beijing Institute of Technology, Beijing 100081, People’s

Republic of China, E-mail: [email protected]

Journal of Computational Chemistry VC 2011 Wiley Periodicals, Inc. 203

ORIGINAL ARTICLES

understanding of the mechanism of this multiple channel reac-

tion and to evaluate the rate constant at high temperatures.

To the best of our knowledge, no previous theoretical work

has been performed on the kinetics of the title reactions.

In this paper, dual-level direct dynamics method[6–10] is

employed to study the kinetics of the CH3 þ SiH(CH3)3 !Si(CH3)3 þ CH4 and CF3 þ SiH(CH3)3 ! Si(CH3)3 þ CHF3 reac-

tions. The potential energy surface information, including

geometries, energies, gradients, force constants of all the sta-

tionary points (reactants, products, and transition states), and

some extra points along the minimum energy path (MEP), is

obtained directly from electronic structure calculations. Sin-

gle-point energies are calculated by the MC-QCISD

method.[11] Subsequently, by means of the POLYRATE 9.7 pro-

gram,[12] the rate constants of the two reaction channels are

calculated by the variational transition state theory

(VTST)[13,14] proposed by Truhlar and co-workers. The com-

parison between the theoretical and experimental results is

discussed. Our results may be helpful for further experimental

investigations.

Figure 1. Optimized geometries of the reactants, products, and transition states at the MP2/6-311 þ G(d,p) level. The values in parentheses are the experi-

mental values (Ref. [28] for CF3, CH3, C2H6, CHF3, and CH4). Bond lengths are in angstrom and angles are in degree.

H. Zhang et al.

Journal of Computational Chemistry204 http://wileyonlinelibrary.com/jcc

Computational Method

In the present work, we used dual-level (X//Y) direct dynamics

method[6–10] to study the kinetic nature of the title reactions.

The equilibrium geometries and frequencies of all the station-

ary points (reactants, products, and transition states) are

optimized at the restricted or unrestricted second-order

Møller–Plesset perturbation (MP2)[15–17] level with the 6-

311þG(d,p) basis set. Molecular electrostatic potentials[18] of

SiH(CH3)3, CH3, and CF3 radicals are calculated at the same

level and plotted using gOpenMol 2.32.[19] The MEP is

obtained by intrinsic reaction coordinate (IRC) theory with a

gradient stepsize of 0.05 (amu)1/2 Bohr. Then, the first and sec-

ond energy derivatives are obtained to calculate the curvature

Table 1. Calculated and experimental frequencies (in cm21) for the reactants, products, and transition states for the title reaction at

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

Species MP2/6-311 þ G(d,p) Expt.

CH3 3362, 3362, 3169, 1446, 1446, 459 3171, 3004, 1403a

CF3 1272, 1272, 1106, 711, 516, 516 1260, 1089, 703, 512a

SiH(CH3)3 3164, 3164, 3164, 3160, 3159, 3159, 3068, 3068, 3067, 2262, 1485, 1476, 1476, 1468, 1468,

1462, 1319, 1308, 1308, 938, 938, 889, 865, 865, 728, 728, 690, 636, 625, 625, 241, 200,

200, 165, 165, 141

Si(CH3)3 3170, 3170, 3170, 3146, 3146, 3146, 3056, 3056, 3056, 1478, 1469, 1469, 1462, 1462, 1456,

1312, 1299, 1299, 884, 879, 879, 743, 743, 700, 697, 697, 622, 228, 196, 196, 155, 155, 136

CH4 3211, 3211, 3211, 3074, 1575, 1575, 1363, 1363, 1363 3019, 2917, 1534b

SiH(CH3)2CH2 3270, 3172, 3165, 3165, 3165, 3164, 3070, 3070, 2248, 1480, 1475, 1469, 1466, 1438, 1315,

1307, 935, 930, 876, 846, 761, 744, 727, 681, 647, 622, 554, 251, 209, 199, 170, 155, 87

SiH(CH3)2 3175, 3175, 3156, 3155, 3067, 3066, 2265, 1472, 1470, 1464, 1461, 1312, 1303, 921, 892, 878,

755, 702, 664, 618, 527, 202, 152, 132

C2H6 3173, 3173, 3152, 3152, 3078, 3078, 1523, 1523, 1522, 1522, 1446, 1420, 1238, 1238, 1032,

833, 833, 330

2985, 2969, 1468, 1388,

1190, 822b

Si(CH3)4 3157, 3157, 3157, 3155, 3155, 3155, 3155, 3155, 3062, 3062, 3062, 3062, 1483, 1483, 1483,

1466, 1466, 1463, 1463, 1463, 1319, 1303, 1303, 1303, 899, 899, 899, 840, 840, 715, 715,

715, 689, 689, 689, 602, 227, 227, 227, 182, 182, 168, 168, 168, 134

2971, 2914, 1429, 1257, 914,

886, 743, 686c

CHF3 3221, 1424, 1424, 1176, 1176, 1151, 704, 513, 513 3036, 1372, 1152, 1117, 700,

507b

CH3CF3 3220, 3220, 3114, 1506, 1506, 1463, 1318, 1249, 1249, 992, 992, 841, 610, 546, 546, 371, 371,

253

Si(CH3)3CF3 3171, 3171, 3171, 3164, 3163, 3163, 3071, 3071, 3071, 1483, 1475, 1475, 1464, 1464, 1460,

1322, 1311, 1311, 1246, 1099, 1099, 888, 888, 887, 787, 787, 728, 722, 722, 702, 640, 523,

523, 394, 296, 296, 195, 195, 190, 150, 150, 123, 119, 119, 43

TS1a 3276, 3276, 3163, 3163, 3162, 3152, 3151, 3151, 3113, 3062, 3062, 3061, 1483, 1473, 1473,

1465, 1465, 1459, 1453, 1453, 1314, 1302, 1302, 1302, 1115, 1115, 1096, 878, 873, 873,

746, 746, 702, 702, 692, 633, 458, 458, 427, 208, 196, 196, 162, 162, 140, 53, 53, 24, 1453i

TS1b1 3258, 3255, 3197, 3163, 3163, 3161, 3160, 3114, 3105, 3068, 3067, 2250, 1481, 1474, 1471,

1468, 1464, 1463, 1419, 1375, 1356, 1313, 1306, 1185, 985, 940, 920, 874, 872, 756, 752,

722, 708, 657, 647, 618, 559, 458, 335, 261, 202, 200, 164, 149, 92, 49, 26, 1854i

TS1b2 3258, 3255, 3195, 3165, 3164, 3159, 3158, 3112, 3105, 3067, 3066, 2258, 1480, 1475, 1470,

1468, 1465, 1464, 1419, 1378, 1350, 1312, 1305, 1186, 985, 936, 919, 893, 866, 782, 746,

730, 717, 648, 633, 610, 566, 456, 334, 241, 212, 195, 168, 153, 81, 52, 43, 1855i

TS1c 3274, 3262, 3225, 3225, 3160, 3159, 3151, 3151, 3080, 3062, 3062, 3056, 2236, 1476, 1472,

1471, 1470, 1466, 1460, 1363, 1358, 1312, 1303, 1148, 1146, 1137, 936, 913, 880, 861, 772,

739, 726, 699, 663, 618, 574, 300, 272, 268, 239, 188, 151, 137, 76, 72, 53, 1256i

TS1d 3221, 3214, 3206, 3184, 3176, 3176, 3157, 3157, 3077, 3074, 3065, 3065, 1839, 1488, 1487,

1483, 1471, 1465, 1464, 1455, 1449, 1302, 1281, 1237, 1140, 933, 905, 854, 840, 818, 752,

739, 726, 693, 678, 617, 592, 512, 328, 320, 249, 231, 145, 129, 98, 91, 79, 769i

TS2a 3168, 3168, 3167, 3156, 3155, 3155, 3065, 3065, 3065, 1482, 1472, 1472, 1464, 1464, 1458,

1318, 1305, 1305, 1215, 1215, 1116, 1088, 1088, 877, 877, 875, 745, 745, 734, 697, 697,

697, 629, 510, 510, 306, 201, 201, 170, 159, 159, 135, 124, 124, 34, 34, 9, 1361i

TS2b1 3195, 3165, 3165, 3164, 3163, 3112, 3070, 3070, 2261, 1480, 1476, 1470, 1465, 1435, 1426,

1390, 1318, 1310, 1213, 1200, 1138, 972, 940, 917, 877, 869, 752, 738, 734, 711, 691, 644,

631, 565, 515, 498, 404, 260, 204, 203, 168, 157, 123, 106, 64, 47, 12, 1957i

TS2b2 3193, 3168, 3167, 3162, 3160, 3110, 3070, 3068, 2273, 1480, 1474, 1469, 1465, 1442, 1426,

1389, 1316, 1307, 1212, 1204, 1137, 978, 934, 913, 891, 867, 777, 745, 729, 717, 683, 643,

631, 553, 515, 497, 411, 235, 217, 176, 168, 154, 129, 109, 58, 37, 13, 1966i

TS2c 3237, 3228, 3164, 3164, 3156, 3156, 3066, 3066, 3024, 2260, 1475, 1469, 1465, 1459, 1346,

1342, 1315, 1307, 1253, 1247, 1119, 1097, 1093, 917, 912, 879, 848, 769, 712, 684, 659,

625, 613, 519, 515, 366, 360, 218, 199, 159, 144, 140, 135, 130, 64, 50, 20, 1125i

TS2d 3207, 3200, 3185, 3183, 3179, 3170, 3083, 3080, 3076, 1604, 1495, 1487, 1483, 1468, 1459,

1451, 1310, 1280, 1260, 1158, 1155, 1018, 912, 874, 870, 855, 762, 735, 721, 697, 634, 561,

543, 530, 517, 500, 286, 262, 244, 209, 186, 143, 129, 95, 80, 70, 49, 1165i

a Ref. [29]. b Ref. [30]. c Ref. [31].

Theoretical Study on the Reaction CX3 þ SiH(CH3)3 (X ¼ H, F)

Journal of Computational Chemistry http://wileyonlinelibrary.com/jcc 205

of the reaction path and the generalized vibrational frequencies

along the reaction path. To obtain more accurate energies and

barrier heights, the energies are refined by the MC-QCISD

method (multi-coefficient correlation method based on quad-

ratic configuration interaction with single and double excita-

tions proposed by Fast and Truhlar)[11] based on the MP2/6-311

þ G(d,p) geometries. The reaction enthalpies are refined by per-

forming single-point energy calculations at the MC-QCISD level

with the thermal enthalpy corrections obtained at the MP2

level. All the electronic structure calculations are performed by

the GAUSSIAN03 program package.[20]

VTST[13,14] is employed to calculate the rate constants by

the POLYRATE 9.7 program.[12] The theoretical rate constants

for the two reaction channels over the temperature range

200–1500 K are calculated by the canonical variational transi-

tion state theory (CVT)[21–23] incorporating small-curvature tun-

neling (SCT)[24,25] contributions proposed by Truhlar and co-

workers.[21] Euler steepest descents (ESD) algorithm was used

to follow the MEP in POLYRATE calculations. For the two reac-

tions, most of the vibrational modes are treated as quantum-

mechanical separable harmonic oscillators except for the low-

est modes. The hindered rotor approximation of Truhlar and

Chuang[26,27] is used for calculating the partition function of

the two transitional state modes. The curvature components

are calculated by using a quadratic fit to obtain the derivative

of the gradient with respect to the reaction coordinate.

Results and Discussions

Stationary points

The optimized geometries of the reactants (CH3, CF3, and

SiH(CH3)3), products (Si(CH3)3, SiH(CH3)2CH2, CH4, Si(CH3)4,

SiH(CH3)2, C2H6, CHF3, Si(CH3)3CF3, and

CH3CF3), and transition states (TS1a, TS1b1,

TS1b2, TS1c, TS1d, TS2a, TS2b1, TS2b2, TS2c,

and TS2d) calculated at the MP2/6-311 þG(d,p) level are presented in Figure 1, along

with the available experimental values.[28] The

theoretical geometric parameters of CF3, CH3,

C2H6, CHF3, and CH4 are in good agreement

with the corresponding experimental val-

ues.[28] Figure 1 shows that the transition

states have the same symmetry, C1. In TS2a,

TS2b1, TS2b2, TS2c, and TS2d structures, the

breaking bonds SiAH, CAH, CAH, SiAH, and

SiAC increase by 9, 17, 17, 6, and 17% com-

pared to the equilibrium bond length in

SiH(CH3)3; the forming bonds CAH, CAH,

CAH, CASi, and CAC stretch by 42, 27, 27, 7,

and 27% over the equilibrium bond lengths

in isolated CHF3, Si(CH3)3CF3, and CH3CF3,

respectively. The elongation of the breaking

bond is smaller than that of the forming

bond, indicating that the above-mentioned

reaction channels are all reactant-like, i.e., all

the five reaction channels will proceed via

‘‘early’’ transition states, which is consistent

with Hammond’s postulate,[29] applied to an exothermic

reaction.

Table 1 lists the harmonic vibrational frequencies of the

reactants, products, and transition states calculated at the

MP2/6-311 þ G(d,p) level as well as the available experimental

values.[30–32] The scaling factor is 1 in our calculations. For the

species CH3, CF3, CH4, C2H6, Si(CH3)4, and CHF3, the calculated

frequencies are in agreement with the experimental values

with the largest deviation within 6%. The 10 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 forming

bonds. And the values of those imaginary frequencies are

1453i cm�1 for TS1a, 1854i cm�1 for TS1b1, 1855i cm�1 for

TS1b2, 1256i cm�1 for TS1c, 769i cm�1 for TS1d, 1361i cm�1

for TS2a, 1957i cm�1 for TS2b1, 1966i cm�1 for TS2b2, 1125i

cm�1 for TS2c, and 1165i cm�1 for TS2d.

Energetics

The reaction enthalpies (DH0298) and potential barrier heights

(DETS) with zero-point energy (ZPE) corrections for 10 reaction

channels calculated at the MC-QCISD//MP2/6-311 þ G(d,p)

level are listed in Table 2. The calculated values agree well

Table 2. The reaction enthalpies at 298 K (D H0298), the barrier heights TSs (DETS) (kcal/mol) with

zero-point energy (ZPE) correction for the reactions of CX3 radical with SiH(CH3)3 at the

MC-QCISD//MP2/6-311 1 G(d,p) level together with the experimental value.

MC-QCISD//MP2 Expt.

D H0298 CH3 þ SiH(CH3)3 ! Si(CH3)3 þ CH4 (R1a) –10.47 –9.61 6 2.63

CH3 þ SiH(CH3)3 ! SiH(CH3)2CH2 þ CH4 (R1b1) –2.79

CH3 þ SiH(CH3)3 ! SiH(CH3)2CH2 þ CH4 (R1b2) –2.79

CH3 þ SiH(CH3)3 ! Si(CH3)4 þ H (R1c) 0.63

CH3 þ SiH(CH3)3 ! SiH(CH3)2 þ C2H6 (R1d) 2.70

CF3 þ SiH(CH3)3 ! Si(CH3)3 þ CHF3 (R2a) –13.14 –11.10 6 2.63

CF3 þ SiH(CH3)3 ! SiH(CH3)2CH2 þ CHF3 (R2b1) –5.46

CF3 þ SiH(CH3)3 ! SiH(CH3)2CH2 þ CHF3 (R2b2) –5.46

CF3 þ SiH(CH3)3 ! Si(CH3)3CF3 þ H (R2c) –2.25

CF3 þ SiH(CH3)3 ! SiH(CH3)2 þ CH3CF3 (R2d) –11.29

DETS þ ZPE CH3 þ SiH(CH3)3 ! Si(CH3)3 þ CH4 (R1a) 10.37

CH3 þ SiH(CH3)3 ! SiH(CH3)2CH2 þ CH4 (R1b1) 14.23

CH3 þ SiH(CH3)3 ! SiH(CH3)2CH2 þ CH4 (R1b2) 14.46

CH3 þ SiH(CH3)3 ! Si(CH3)4 þ H (R1c) 28.20

CH3 þ SiH(CH3)3 ! SiH(CH3)2 þ C2H6 (R1d) 46.42

CF3 þ SiH(CH3)3 ! Si(CH3)3 þ CHF3 (R2a) 3.78

CF3 þ SiH(CH3)3 ! SiH(CH3)2CH2 þ CHF3 (R2b1) 9.02

CF3 þ SiH(CH3)3 ! SiH(CH3)2CH2 þ CHF3 (R2b2) 9.46

CF3 þ SiH(CH3)3 ! Si(CH3)3CF3 þ H (R2c) 20.65

CF3 þ SiH(CH3)3 ! SiH(CH3)2 þ CH3CF3 (R2d) 33.69

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

6 0.96 kcal/mol;[32] CH4, –17.88 kcal/mol;[33] CH3, 34.80 kcal/mol;[34] Si(CH3)3, 4.07 6 1.67 kcal/

mol;[34] CF3, –112.32 kcal/mol;[34] CHF3, –166.49 kcal/mol.[34]

Table 3. Calculated and experimental bond dissociation energies in

SiH(CH3)3 at 298 K (kcal/mol) at MC-QCISD//MP2/6-311 1 G(d,p) level.

SiH(CH3)3 Expt.

Do298 (SiAH) 92.87 94.8260.48;a 91.2461.67;b 90.28 6 1.43c

Do298 (CAH) 100.41

a Ref. [35]. b Ref. [36]. c Ref. [37].

H. Zhang et al.


with corresponding experimental one. The theoretical value at

298 K of D H0298, –10.47 kcal/mol for reaction R1a and –13.14

kcal/mol for reaction R2a, are in good agreement with the cor-

responding experimental values –9.61 6 2.63 and –11.10 6

2.63 kcal/mol, which were derived from the standard heats of

formation (SiH(CH3)3, –39.00 6 0.96 kcal/mol;[33] CH4, –17.88

kcal/mol;[34] CH3, 34.80 kcal/mol;[35] Si(CH3)3, 4.07 6 1.67 kcal/

mol.[35] CF3, –112.32 kcal/mol;[35] CHF3, –166.49 kcal/mol;[35]),

indicating the values calculated at the MC-QCISD//MP2/6-311

þ G(d,p) level may be reliable. Thus, we use MC-QCISD//MP2/

6-311 þ G(d,p) method to calculate the potential energy bar-

riers 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 of R2 are all exothermic reactions, consistent

with the discussion above of Hammond’s postulate.[29]

Table 3 lists the calculated bond dissociation energies (Do298)

of the SiAH and CAH bonds in SiH(CH3)3, along with several

experimental data[36–38] of SiAH bond dissociation energy. The

Do298 (SiAH) value of SiH(CH3)3 with 92.87 kcal/mol obtained at

the MC-QCISD//MP2/6-311 þ G(d,p) level shows good consis-

tency with the previous literature results, 94.82 6 0.48,[36]

91.24 6 1.67,[37] and 90.28 6 1.43 kcal/mol.[38] At the same

level, the Do298 (CAH) values are 100.41 kcal/mol in SiH(CH3)3.

No comparison between theory and experiment can be made

due to the lack of the experimental Do298 (CAH) value in

SiH(CH3)3. The good agreement between theoretical and ex-

perimental Do298 (SiAH) implies that the MC-QCISD//MP2/6-311

þ G(d,p) level is a suitable method to compute the bond dis-

sociation energies and our calculated Do298 (CAH) value may

be expected to provide reliable reference information for

future laboratory investigations. The dissociation energy of the

SiAH bond is 7.54 kcal/mol smaller than that of the CAH

bond in SiH(CH3)3, indicating that the H-abstraction channel

from SiAH bond may be in favor of the abstraction from CAH

bond.

The schematic potential energy diagrams of CH3 þSiH(CH3)3 ! products and CF3 þ SiH(CH3)3 ! products reac-

tions with ZPE corrections obtained at the MC-QCISD//MP2/6-

311 þ G(d,p) level are plotted in Figures 2 and 3, respectively.

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

The values in parentheses are calculated at the MP2/6-311 þG(d,p) level and also include the ZPE corrections. The potential

barrier height of reaction channel R1a (10.37 kcal/mol) and is

much lower than the ones of R1b1 (14.23 kcal/mol), R1b2

(14.46 kcal/mol), R1c (28.20 kcal/mol), and R1d (46.42 kcal/mol)

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

of the abstraction from the in-plane hydrogen (R1b1) has a

lower barrier than the out-plane hydrogen (R1b2) route. At the

same time, the former reaction channel R1a is more exother-

mic than the later ones by about 7.53, 13.90, and 10.78 kcal/

mol for R1b1 (or R1b2), R1c, and R1d, respectively, and as a

result, the former reaction channel R1a is more thermodynami-

cally and kinetically favorable than the later ones. The reaction

channel R1a will dominate the products Si(CH3)3 and CH4 for-

mation for the reaction CH3 þ SiH(CH3)3, and the later paths

will be negligible. Similar case can be found in the reaction

CF3 þ SiH(CH3)3 ! products, which indicates that the reaction

channels R2b, R2c, and R2d will also be negligible. Thus we

perform the rate constant calculations only for the H-abstrac-

tion from SiH group R1a and R2a reaction channels.

Rate constants

Dual-level dynamics calculations[6–10] of R1a and R2a reaction

channels are carried out at the MC-QCISD//MP2/6-311 þG(d,p) level. The rate constants of the two channels, k1a, and

k2a, are evaluated by conventional transition state theory

Figure 2. Schematic potential energy surface for the reaction CH3 þSiH(CH3)3. Relative energies are calculated at the MC-QCISD//MP2/6-311 þG(d,p) þ ZPE level [in (kcal/mol)]. The values in parentheses are calculated

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

Figure 3. Schematic potential energy surface for the reaction CF3 þSiH(CH3)3. Relative energies are calculated at the MC-QCISD//MP2/6-311 þG(d,p) þ ZPE level [in (kcal/mol)]. The values in parentheses are calculated

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



(TST), the canonical variational transition state theory (CVT),

and the CVT with the small-curvature tunneling (SCT) contribu-

tions in a wide temperature range from 200 to 1500 K. The

CVT/SCT rate constants of k1a and k2a are plotted against the

reciprocal of temperature in Figure 4 and given in Table 4

along with the available experimental results.[1–5] The calcu-

lated rate constant value of k1a is in good agreement with the

available experimental value.[1,3–5] For example, the ratios

of kCVT/SCT/kexptl are 0.79, 1.24, 1.18, and 0.96 at 350 K for

Refs. [1, 2, 4 and 5], respectively. For reaction channel R2a, the

theoretical CVT/SCT rate constant is in good agreement with

the available experimental values.[3] The ratio of kCVT/SCT/kexptlremains within a factor of approximately 1.34–0.80 over the

temperature range 350–475 K, the ratio is 1.01 at 400 K. The

theoretical CVT/SCT rate constant of reaction channel CH3 þ

SiH(CH3)3 ! Si(CH3)3 þ CH4 (R1a) is 6.26 � 10�18

cm3molecule�1s�1, which is smaller than the one (1.38 �10�15 cm3 molecule�1s�1) of reaction channel CF3 þ SiH(CH3)3! Si(CH3)3 þ CHF3 (R2a) at 350 K. Theoretical activation

energy (Ea) is estimated based on the calculated CVT/SCT rate

constants, and it is found that the corresponding Ea value for

reaction channel R2a, 4.24 kcal/mol, is lower than that for

reaction channel R1a (4.96 kcal/mol) in 350–500 K, which is in

accordance with its kinetic superiority. Those are consistent

with a qualitative assessment based on the potential energy

barrier heights of the two reactions.

Table 5 lists the tunneling factors for reaction R1a and R2a.

It can be seen that the tunneling factors are important at

lower temperatures for both reactions R1a and R2a. For exam-

ple, the tunneling factors are

2.77 (4.92), 2.25 (3.63), 1.30

(1.54), and 1.19 (1.32) for R1a

(R2a) at 200, 250, 400, and

500 K, respectively.

Due to the limited experi-

mental knowledge on the

kinetics of the title reaction,

we hope that our present

study may provide useful

information for future labo-

ratory investigations. For

convenience of future exper-

imental measurements, the

three-parameter fits of the

CVT/SCT rate constants of

the two reaction channels in

the temperature range from

200 to 1500 K are performed

and the expressions are

given as follows (in unit of

cm3molecule�1s�1):

Table 4. Calculated CVT/SCT rate constants (cm3molecule21s21) of the reaction channel R1a, k1a, and R2a, k2a, in

the temperature region 200–1500 K at the MC-QCISD//MP2/6-311 1 G(d,p) level together with the corresponding

experimental value.

T (K) k1a(CVT/SCT) kRef.[1] kRef.[3] kRef.[4] k2a(CVT/SCT) kRef.[2]

200 7.52 � 10�20 6.00 � 10�17

225 2.19 � 10�19 1.20 � 10�16

250 5.33 � 10�19 2.19 � 10�16

298 2.06 � 10�18 5.49 � 10�16

325 3.80 � 10�18 2.11 � 10�18 9.29 � 10�16 5.48 � 10�16

350 6.26 � 10�18 5.03 � 10�18 5.29 � 10�18 6.55 � 10�18 1.38 � 10�15 1.01 � 10�15

375 9.79 � 10�18 1.07 � 10�17 1.17 � 10�17 1.31 � 10�17 1.99 � 10�15 1.73 � 10�15

400 1.46 � 10�17 2.08 � 10�17 2.36 � 10�17 2.40 � 10�17 2.78 � 10�15 2.76 � 10�15

425 2.11 � 10�17 3.74 � 10�17 4.36 � 10�17 4.09 � 10�17 3.79 � 10�15 4.16 � 10�15

450 2.95 � 10�17 6.30 � 10�17 7.52 � 10�17 6.57 � 10�17 5.07 � 10�15 6.00 � 10�15

475 4.01 � 10�17 1.00 � 10�16 1.23 � 10�16 1.00 � 10�16 6.66 � 10�15 8.32 � 10�15

500 5.32 � 10�17 1.52 � 10�16 1.47 � 10�16 8.60 � 10�15

525 6.95 � 10�17 2.23 � 10�16 2.08 � 10�16 1.09 � 10�14

600 1.40 � 10�16 2.10 � 10�14

700 3.01 � 10�16 4.38 � 10�14

800 5.68 � 10�16 8.17 � 10�14

900 9.82 � 10�16 1.40 � 10�13

1000 1.58 � 10�15 2.26 � 10�13

1200 3.52 � 10�15 5.08 � 10�13

1500 9.11 � 10�15 1.33 � 10�12

Table 5. Tunneling factors for reaction R1a and R2a.

T (K) R1a R2a

200 2.7728E þ 00 4.9197E þ 00

225 2.2538E þ 00 3.6274E þ 00

250 1.9401E þ 00 2.8890E þ 00

298 1.6017E þ 00 2.1415E þ 00

325 1.4884E þ 00 1.9055E þ 00

350 1.4106E þ 00 1.7482E þ 00

375 1.3505E þ 00 1.6298E þ 00

400 1.3030E þ 00 1.5381E þ 00

425 1.2648E þ 00 1.4656E þ 00

450 1.2336E þ 00 1.4072E þ 00

475 1.2076E þ 00 1.3595E þ 00

500 1.1859E þ 00 1.3198E þ 00

525 1.1674E þ 00 1.2865E þ 00

600 1.1262E þ 00 1.2133E þ 00

700 1.0915E þ 00 1.1529E þ 00

800 1.0694E þ 00 1.1153E þ 00

900 1.0545E þ 00 1.0901E þ 00

1000 1.0440E þ 00 1.0724E þ 00

1200 1.0304E þ 00 1.0498E þ 00

1500 1.0193E þ 00 1.0316E þ 00

Figure 4. The CVT/SCT rate constants calculated at the MC-QCISD//MP2/6-

311 þ G(d,p) level for two reaction channels rate constants k1a and k2a (in

cm3molecule�1s�1) versus 1000/T between 200 and 1500 K.

H. Zhang et al.


k1aðTÞ ¼ 1:93� 10�24T3:15 expð�1214:59=TÞk2aðTÞ ¼ 1:33� 10�25T4:13 expð�397:94=TÞ

Reactivity trends

The molecular electrostatic potential is an important tool to

analyze molecular reactivity because it can provide the infor-

mation about local polarity. Figure 5 gives the distribution of

the molecular electrostatic potential. There, the most negative

and positive potentials are assigned to be blue and red,

respectively, and the color spectrum is mapped to all other

values by linear interpolation. The more negative potential

region (more blue) will be more favored for the electrophilic

to attack at. It is found that in molecule SiH(CH3)3, the H

atoms of SiH group bear stronger negative potential (green)

than the H atoms of CH3 groups (red), indicating that the H

atoms can be more easily attacked by the electrophilic. Note

that the C atom of CF3 radical is encircled by marked positive

potential; therefore, the CF3 radical is more preferably to

attack the H atom of SiH group in SiH(CH3)3 comparing to the

CH3 group. From these results, we could infer that the H-

abstraction reaction channel from SiH group and CH3-abstrac-

tion reaction channel in SiH(CH3)3 with CF3 radical could occur

more easily than with CH3 radical. As a result, the reaction rate

constants increase in the order of CH3 þ CH3SCH3 < CF3 þCH3SCH3. This is in line with the potential energy barrier

heights, bond dissociation energies, and the rate constant

results calculated above.

Conclusion

In this paper, the multi-channel reactions CX3 þ SiH(CH3)3 !products (X ¼ H, F) are theoretically investigated. The poten-

tial energy surface information is obtained at the MP2/6-311 þG(d,p) level, and energies of the stationary points and a few

extra points along the minimum energy path are refined at

the MC-QCISD level. For the title reaction, five reaction chan-

nels are identified; hydrogen abstraction reaction from SiH

group R1a (R2a) is the major pathway. The rate constants for

the two reaction channels are calculated by the CVT incorpo-

rating SCT correction at the MC-QCISD//MP2 level. The calcu-

lated results show that the CVT/SCT rate constants, k1a and

k2a, are in good agreement with the corresponding available

experimental values. The three-parameter rate–temperature

formulae for the two reaction channels in the temperature

range from 200 to 1500 K are fitted and given as follows (in

cm3molecule�1s�1):

k1aðTÞ ¼ 1:93� 10�24T3:15 expð�1214:59=TÞk2aðTÞ ¼ 1:33� 10�25T4:13 expð�397:94=TÞ

Acknowledgments

The authors thank Professor Donald G. Truhlar for providing POLY-

RATE 9.7 program. This work is supported by the National Natural

Science Foundation of China (20973077 and 20973049), the Pro-

gram for New Century Excellent Talents in University (NCET), the

Doctor Foundation by the Ministry of Education, the Foundation for

the Department of Education of Heilongjiang Province (1152G010,

11551077), the Key subject of Science and Technology by the Minis-

try of Education of China, the SF for leading experts in academe of

Harbin of China (2011RFJGS026).

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Received: 26 February 2011Revised: 12 July 2011Accepted: 14 September 2011Published online on 1 November 2011

H. Zhang et al.


Documents

Theoretical study on the reaction CX3 + SiH(CH3)3 (X = H, F)