Quasiclassical trajectory study of H+SiH₄ reactions in full-dimensionality reveals atomic-level mechanisms

Abstract

This work elucidates new atomic-level mechanisms that may be common in a range of chemical reactions, and our findings are important for the understanding of the nature of polyatomic abstraction and exchange reactions. A global 12-dimensional ab initio potential energy surface (PES), which describes both H+SiH₄ abstraction and exchange reactions is constructed, based on the modified Shepard interpolation method and UCCSD(T)/cc-pVQZ energy calculations at 4,015 geometries. This PES has a classical barrier height of 5.35 kcal/mol for abstraction (our best estimate is 5.35 ± 0.15 kcal/mol from extensive ab initio calculations), and an exothermicity of −13.12 kcal/mol, in excellent agreement with experiment. Quasiclassical trajectory calculations on this new PES reveal interesting features of detailed dynamical quantities and underlying new mechanisms. Our calculated product angular distributions for exchange are in the forward hemisphere with a tail sideways, and are attributed to the combination of three mechanisms: inversion, torsion-tilt, and side-inversion. With increase of collision energy our calculated angular distributions for abstraction first peak at backward scattering and then shift toward smaller scattering angles, which is explained by a competition between rebound and stripping mechanisms; here stripping is seen at much lower energies, but is conceptually similar to what was observed in the reaction of H+CD₄ by Zare and coworkers [Camden JP, et al. (2005) J Am Chem Soc 127:11898–11899]. Each of these atomic-level mechanisms is confirmed by direct examination of trajectories, and two of them (torsion-tilt and side-inversion) are proposed and designated in this work.

The A+BC type reactions have long served as benchmarks in the development of the kinetics and dynamics theories of chemical reactions (1–5). However, behavior of polyatomic reactions may be qualitatively different from what has been deduced from studies of atom–diatom dynamics. For example, a major reaction path, which does not follow the intrinsic reaction coordinate, has recently been found by Hase et al. (6) in their quasiclassical trajectory (QCT) study on the F⁻+CH₃OOH reaction. Another example is the reaction of H+CH₄ (and its isotopic variants), for which recent investigations (7) have focused on the new stripping mechanism observed by Zare and coworkers (8–9). The rebound mechanism is well-known for the H+D₂ reaction (10–11), and a lot of polyatomic H abstraction reactions, including H+CD₄, have long been considered to proceed through this mechanism. However, in the recent combined experimental and theoretical studies on the reaction of H+CD₄ (9, 12), the stripping mechanism was proposed, in which the velocity of incoming H atom is perpendicular to the C-D bond and the HD product is carried into the forward hemisphere. The stripping mechanism was further confirmed by Bowman and coworkers (13) using the QCT method.

The H+SiH₄ reaction is an analogue to H+CH₄, and both abstraction and exchange reactions can happen; i.e.,

Unlike the H+CH₄ abstraction reaction, which is nearly thermoneutral, the H+SiH₄ abstraction reaction R1 is exothermic by ≈13 kcal/mol, and regarded as a prototype of exothermic polyatomic H abstraction reactions. Also, as we will demonstrate, both reactions 1 (R1) and 2 (R2) could happen at collision energies above ≈12.5 kcal/mol, therefore the H+SiH₄ reaction is actually a better candidate for studying the competition between abstraction and exchange than H+CH₄, for which the exchange channel is not open at collision energies <35 kcal/mol (noninversion exchange not open at <60 kcal/mol) (14).

In this work, a global 12-dimensional potential energy surface (PES) that describes both abstraction and exchange reactions for the SiH₅ system is constructed, and detailed QCT calculations for both reactions R1 and R2 on this ab initio PES are performed, which yield insights into the reaction mechanism. The computed product angular distributions indicate that the abstraction reaction is a combination of rebound and stripping. More importantly, here we propose that the H+SiH₄ exchange reaction is a combination of three mechanisms, inversion, torsion (more exactly, torsion-tilt), and side-inversion as demonstrated in Fig. 1. The interesting dynamical features for exchange can be explained with these atomic-level mechanisms. These findings are helpful for our understanding of the nature of polyatomic reactions, which goes beyond the atom–diatom pictures, and would have implications for a number of fields ranging from fundamental reaction dynamics to atmospheric and organic chemistry.

Fig. 1.

The inversion, torsion, and side-inversion mechanisms of the H+SiH₄ exchange reaction.

The H+SiH₄ reaction is important in the thermal decomposition of monosilane (15) and plays a significant role in chemical vapor deposition processes used in semiconductor industry and for the production of ceramic materials (16). The kinetics of reaction R1 has been extensively studied experimentally in the past decades (refs. 17–19 and references therein). However, few have investigated the detailed state-resolved dynamics, which underscores the need to perform detailed dynamical calculations. Furthermore, Bersohn and coworkers (20) examined reaction R2 (and isotopic substitutions) with a laser-induced fluorescence technique at a collision energy of ≈2 eV and the integral cross-section (ICS) for H+SiD₄ → SiD₃H+D was determined as ≈0.36 Ų. They inferred that the exchange channel proceeds through an inversion mechanism. Several theoretical investigations have been reported on H+SiH₄ reactions, although earlier ab initio calculations were limited to the small regions around a few stationary points and the minimum energy path (MEP) (18, 21–23). So far there have been two PESs reported (24, 25) for the SiH₅ system, but both of them could only describe reaction R1: Espinosa–García et al. (24) developed an analytic semiempirical PES in 1998; more recently, Wang et al. (25) constructed a 12-dimensional ab initio PES based on the modified Shepard interpolation method (26–28) and ≈1,300 ab initio reference points. The latter PES was designed for thermal conditions, and further variational transition state theory (25) and QCT (29) calculations yielded rate constants in good general agreement with experiment for reaction R1.

Results and Discussion

Ab Initio Calculations.

In the construction of high-quality ab initio PESs, it is very important to choose ab initio methods and basis sets properly. Extensive high-level ab initio calculations were performed to check the convergence of the barrier height and exothermicity for reaction R1 with respect to various basis sets and methods for treating electron correlation, and the main calculation results are summarized in Table S1. The reaction enthalpies at 0 K computed with different methods are extremely close to one another at the complete-basis-set (CBS) limit, which are between −12.70 and −12.80 kcal/mol, in nice agreement with experiment (30, 31). Generally the classical barrier height is not very sensitive to the extension of one-electron basis set, and at the CBS limit, different methods produce barrier heights in the range of 5.25–5.49 kcal/mol. In addition, the obtained barrier heights with cc-pVnZ and aug-cc-pVnZ (Dunning's augmented correlation-consistent polarized valence n zeta) basis sets are very similar at the CBS limit, indicating that the addition of diffuse functions is unimportant if a larger basis set is applied. The computed classical barrier height for reaction R1 has basically reached convergence, and our best estimate of it is 5.35 kcal/mol with the largest error being estimated to be just ≈0.15 kcal/mol. Based on our calculation results and convergence analysis, we conclude that the spin-unrestricted coupled cluster method with single and double excitations and triple excitation correction (UCCSD(T)) with the cc-pVQZ basis set is a suitable level for energy calculations required for the PES construction. At the UCCSD(T)/cc-pVQZ level, the computed classical barrier height is 5.34 kcal/mol, in excellent agreement with our best estimate. Also, the computed reaction enthalpy at 0 K is −13.15 kcal/mol, and is very close to the experimental value of −12.9 ± 1.1 kcal/mol (30, 31).

Geometries of various stationary points have been optimized at the UCCSD(T)/cc-pVQZ level. The obtained transition-state (TS) geometry for reaction R1 (Fig. 2A) is similar to that reported before (25) at the UQCISD/cc-pVTZ level. Two TSs for reaction R2 are determined: one is of D_3h symmetry (Fig. 2B) with a barrier height of 12.25 kcal/mol, and the other is of C_s symmetry (Fig. 2C) with a barrier height of 12.57 kcal/mol. These values are evidently lower than those from earlier ab initio calculations (22). The inversion and side-inversion mechanisms involve the D_3hTS, whereas the torsion mechanism proceeds through the C_s TS. We found a new van der Waals (vdW) complex, which is shown in Fig. 2D. More details about it and other two vdW complexes for reaction R1 are given in SI Appendix.

Fig. 2.

The geometries of stationary points in the SiH₅ system optimized at the UCCSD(T)/cc-pVQZ level. (A) Abstraction transition state (TS). (B) Exchange TS of D_3h symmetry. (C) Exchange TS of C_s symmetry. (D) vdW complex for exchange channel. R₁ and R₂ are defined here for use in other places. Bond lengths and angles are in ängstroms and degrees, respectively.

Twelve-Dimensional ab Initio PES.

To perform various detailed dynamical studies, we constructed a global 12-dimensional ab initio PES suitable for the study of both abstraction and exchange reactions in the SiH₅ system. The energy calculations were performed using UCCSD(T)/cc-pVQZ at 4,015 carefully selected geometries, and the modified Shepard interpolation method (26–28) was applied. This new PES (see Methods for more details) is referred to as the Bian–Cao–Liu–Wang–Sun (BCLWS) surface hereafter.

Properties of the three TSs on the BCLWS surface are presented in Table S2. The barrier height for reaction R1 is 5.35 kcal/mol, in close agreement with our ab initio value of 5.34 kcal/mol. The barrier heights for reaction R2 on the BCLWS surface are 12.27 kcal/mol (D_3h TS) and 12.62 kcal/mol (C_s TS), in very good agreement with our corresponding UCCSD(T)/cc-pVQZ calculation values. These low exchange barriers reported here are significantly different from those for reaction R2a, for which the exchange barrier height (for inversion) is 36.37 kcal/mol on the ZBB3 PES (13) and 38.1 kcal/mol as reported in earlier ab initio calculations (22). Furthermore, the BCLWS surface has vdW complexes in the entrance and exit valleys (see SI Appendix).

Various contour plots were made to check the quality of the BCLWS surface and three typical plots are shown in Fig. 3. The region of abstraction reaction is shown in Fig. 3A, in which the TS and MEP regions could be seen. It is clear that the contour lines are smooth and the potential is physically reasonable in various regions. We can also notice that the location of saddle point is closer to the H+SiH₄ reactant, indicating an early barrier. It should be noted that the “saddle point” in Fig. 3B does not correspond to the D_3h exchange TS, because the inversion of configuration contributes evidently to the reaction coordinate whereas the energy in Fig. 3B is minimized with respect to all other coordinates. This explains why the “barrier height” in Fig. 3B is somewhat less than 12.27 kcal/mol. Fig. 3C is for reaction R2 via the torsion mechanism. In this case, the saddle-point region basically corresponds to the C_s exchange TS region, which is shown to be relatively flat.

Fig. 3.

Contour plots of the BCLWS surface in the regions of abstraction (A), inversion exchange (B), and noninversion exchange (C) reactions as functions of R₁ and R₂ (defined in Fig. 2 A–C, respectively), where the energy is minimized with respect to all other coordinates. The contours are in kcal/mol relative to the H+SiH₄ asymptote.

Excitation Function for Abstraction.

Detailed QCT calculations were performed for both reactions R1 and R2 on the BCLWS surface with the reactant SiH₄ being fixed in its rovibrational ground state. Fig. 4 shows the excitation function for reaction R1 and it can be seen that, the ICSs increase quickly with collision energy at lower energies, which is consistent with the early abstraction barrier. At higher energies the increase slows down gradually, and >22.5 kcal/mol the ICSs start dropping slightly, which suggests a decrease tendency at even higher collision energies. In contrast to reaction R1a, much larger ICSs are obtained here at the same collision energy. This is understandable, because reaction R1 has a much lower barrier than reaction R1a [14.8 kcal/mol for barrier height (32)].

Fig. 4.

Excitation function for the H+SiH₄ abstraction reaction. The solid line with squares displays the QCT results, whereas the dotted line with circles gives the ZPE-corrected QCT results.

Two kinds of quantum effects, namely the zero-point energy (ZPE) and tunneling effects, may influence the results, and the latter is not taken into account in the present QCT calculations. ICSs with and without the ZPE correction (see Methods and ref. 33) are compared in Fig. 4, which indicates that the ICSs are sensitive to the ZPE correction. This may result from the fact that both the barrier height (5.35 kcal/mol) and TS ZPE (18.97 kcal/mol) are comparable to collision energies. Because of the light H atom, the tunneling effects are expected to be strong for reaction R1, however, normally these effects need to be considered only at collision energies lower than ≈6 kcal/mol. In view of the fact that the computed rate constant on the WSB surface (29) is somewhat lower than the experimental data, and the barrier height on the BCLWS surface is more accurate, we deduce that the QCT calculations on the BCLWS surface would yield better agreement with experiment (17–19) for thermal rate constant. Of course, it should be noted that at temperatures <500 K, the tunneling effects may increase the QCT rate constant.

H₂ Angular Distributions and Mechanisms for Abstraction.

We see from Fig. 5Left that the H₂ angular distribution is dominated by scattering in the backward direction at the collision energy of 6.5 kcal/mol, and the most striking feature is, with the increase of collision energy from 6.5 to 17.5 kcal/mol, a double-peak structure appears and the sideways peak shifts toward small scattering angles. This angular distribution shift suggests the existence of two competitive reaction mechanisms: rebound and stripping.

Fig. 5.

Three-dimensional H₂ (H) product flux surface plots in center-of-mass (c.m.) velocity space for the H+SiH₄ abstraction (Left) and exchange (Right) reactions at different collision energies. The forward scattering (θ = 0°) is defined along the H-atom reactant beam direction. The contour intensities are not normalized.

The rebound mechanism is well-known for this kind of H abstraction reaction, in which the incident H″ atom is directed along a Si—H′ bond and the H′H″ product rebounds backward. The stripping mechanism was proposed in a combined experimental and theoretical study on the reaction of H+CD₄ (9, 12). As for reaction R1, the rebound mechanism dominates at low collision energies, whereas at high collision energies, the incoming H atom has more energy to get over the angular-momentum barrier, and thus it becomes easier for the H atom to attack SiH₄ from the side face, and strip one H from SiH₄, and the H₂ product is carried into the forward hemisphere, as is the stripping mechanism. Because of the increasing contribution from the stripping mechanism, at 17.5 kcal/mol, H₂ products scatter sideways and peak in the perpendicular direction (see Fig. 5), and qualitatively, the shape of the angular distribution is analogous to what has been observed (9) for the D-substituted reaction R1a at the collision energy of 27.8 kcal/mol using the photoloc technique. In this respect, reaction R1 is similar to reaction R1a, and may be used as another example of the newly observed stripping mechanism. The intriguing feature of reaction R1 is, the stripping plays an important role at collision energies as low as 10.5 kcal/mol (see Fig. 5).

Our calculations indicate that the influence of ZPE correction on angular distribution is small, consistent with previous conclusions for reaction R1a. However, the tunneling effects may influence the results as well. It has been found (4) that the forward scattering in the F+H₂ reaction is enhanced in quantum mechanics by tunneling through the combined centrifugal and potential energy barrier. Thus, we infer that, for reaction R1, the tunneling effects may produce more forward-scattered H₂ products, but could not change the main feature of angular distribution shown in Fig. 5.

Excitation Function for Exchange.

Our calculated ICSs for reaction R2 are shown in Fig. 6. For comparison, the results from the inversion and torsion mechanisms are also shown in this figure. The contribution of the side-inversion mechanism is very small and included in the results indicated as inversion. The near-threshold behavior is revealed in Fig. 6 Upper Left, from which we can notice an evident dip along the curve, which is a reflection of two mechanisms. At collision energies <13.1 kcal/mol, only the inversion mechanism is effective, but >13.1 kcal/mol the torsion mechanism occurs and leads to a sharp increase of the total exchange ICS in the energy range of 13.1–13.5 kcal/mol. This unusual behavior should be able to be observed in experiment as an evidence for the coexistence of two mechanisms. Furthermore, it is remarkable that the ICS for torsion is larger than that for inversion particularly at higher collision energies. Although the inversion mechanism is slightly more favored energetically, torsion is predominant if judged from the dynamic factor such as steric angles available for the approach of H atom reactant.

Fig. 6.

Excitation function for the H+SiH₄ exchange reaction. The solid line with squares displays the ZPE-corrected QCT results for total exchange reaction. The dashed line with circles is from the torsion mechanism, whereas the dotted line with triangles from the inversion and side-inversion mechanisms. (Upper Left) An amplified view of the low-energy near-threshold region.

At the average relative energy of 2.08 eV, the ICS for H+SiD₄ → SiD₃H+D was determined as ≈0.36 Ų by Bersohn and coworkers (20). This implies that the ICS for reaction R2 should be somewhat greater than 0.36 Ų, because the three lighter nonreacting H atoms could move faster to reach the trigonal-bipyramidal TS. Fig. 6 shows that, at collision energies up to 24.5 kcal/mol, our computed ICSs for reaction R2 are <1.0 Ų; in addition, normally the ICS will be lowered to some extent if the collision energy is raised to ≈2 eV, which is beyond the scope of the present calculations (the BCLWS surface is designed for collision energies <26 kcal/mol). So our computed ICSs are well consistent with the experimental measurements in ref. 20.

H Angular Distributions and Mechanisms for Exchange.

In contrast to that for abstraction, the angular distribution for exchange predominately falls in the forward hemisphere (Fig. 5 Right). At the collision energy of 13.5 kcal/mol, the H angular distribution dominates by scattering in the forward direction, consistent with the inversion mechanism; meanwhile, although the sideways peak is weak, a double-peak structure is clearly presented, which suggests the existence of two mechanisms. Interestingly, with the increase of collision energy from 13.5 to 20.0 kcal/mol, the two peaks merge into one and its shape gradually changes. The understanding of these delicate changes requires a detailed study of the reaction mechanism.

Based on our QCT calculations on the BCLWS surface, we propose that the H+SiH₄ exchange reaction proceeds through a combination of three mechanisms, inversion, torsion, and side-inversion as shown in Fig. 1. These mechanisms are also confirmed by direct observation of trajectories in our calculations. Inversion would yield forward-scattered H atoms, whereas the H atoms are scattered sideways and forward via torsion. In addition, after side-inversion, H products peak at the scattering angle θ = 90°.

The first mechanism is inversion and shown in Fig. 1A, in which the incident H atom moves along the threefold axis and when it approaches H₃SiH with the C_3v symmetry maintained, the three nonreacting H atoms would make an inversion, passing through the trigonal-bipyramidal TS. Afterward, the H product goes forward to conserve the linear momentum. Inversion and noninversion exchange channels were suggested for reaction R2a by Morokuma et al. (14), although at much higher energies. The inversion mechanism in reaction R2 was first inferred in experiment by Bersohn and coworkers (20), and its existence is now confirmed by our QCT modeling.

The second mechanism is torsion (or torsion-tilt) as called by us. As shown in Fig. 1B, the incoming H′ atom is biased from the threefold axis toward one of the Si—H bonds, and during the approaching process, the plane determined by H′, Si and H contains the C₃ axis, and the Si—H bond tilts toward the forward direction, meanwhile, the nonreacting SiH₃ group makes a torsion movement with the C_3v symmetry retained. The typical torsion angle is found to be ≈70°. More exactly, this mechanism should be termed as torsion-tilt, through which the H product is scattered sideways and forward with θ < 90°. It should be noted that θ is much smaller than expected due to the tilt movement of the breaking Si—H bond. This mechanism would involve the C_s transition state and is consistent with the noninversion mechanism already known (14); however, the previous viewpoint that there is a retention of configuration needs to be changed.

The third mechanism is side-inversion, which we recognize and denominate. As shown in Fig. 1C, the incident H atom is directed along one twofold axis in SiH₄ and approaches one side of the two nonreacting H atoms, which are then pushed to invert to the other side with a triangle formed, meanwhile the remaining two H atoms moves up and down respectively, forming a trigonal-bipyramidal TS in the sideways direction. Afterward, one of the sideways H atoms goes out in the perpendicular direction. Clearly, this mechanism would yield H products, which peak at sideways, consistent with the sideways tail seen in Fig. 5. Compared with the inversion and torsion mechanisms, the number of trajectories that follow this mechanism is minor in the collision-energy range considered here.

To obtain further insights into the reaction mechanisms, we have compared the results from the inversion and torsion mechanisms carefully. As shown in Fig. 7, the peaks of H angular distribution for inversion appear always in the forward direction, however, those for torsion initially appear at a larger scattering angle, and then shift toward smaller angles with increase of collision energy. On passing from a collision energy of 13.5 to 24.5 kcal/mol, the angular distribution for torsion changes from peaking at ≈64° to ≈36°. This distribution-peak shift with collision energy is the most important feature, and could be well understood according to the torsion mechanism shown in Fig. 1B. With increase of collision energy the tilt movement of the breaking Si—H bond is enhanced, which could cause smaller and smaller scattering angles. Consequently, at high collision energies, the torsion mechanism is also characteristic of forward scattering, and the scattered H fragments appear seldom at larger angles. Then, the inference of Bersohn et al. (20) about reaction mechanism based on their experiment is probably incomplete, because they assumed that a direct attack of the H atom on a Si-D bond would cause the D atom to recoil at a fairly large angle. In addition, they did not imagine that reaction R2 could proceed through more than one mechanism (20). According to the tendency shown in Fig. 7, we deduce that at very high collision energies, the distribution peak will further shift to even smaller scattering angles <36°, in qualitative agreement with the experimental observation by Bersohn and coworkers (20), which indicates the scattering angles being in the range of 0–36.5° at the average collision energy of ≈48 kcal/mol.

Fig. 7.

H-atom product scattering angle-c.m. velocity polar maps for the H+SiH₄ exchange reaction via the inversion (Left) and torsion (Right) mechanisms at different collision energies. The forward scattering (θ = 0°) is defined along the H-atom reactant beam direction. For each pair of maps at the same collision energy the contour intensities are normalized, whereas at different collision energies the intensities are not normalized.

In addition, we have investigated the impact parameter dependence of reaction probability for reaction R2 via the two mechanisms. A typical result is presented in Fig. S1, and it shows that, b = 0 Å is most favored for inversion, and as for torsion, the probability peak appears at b = 0.6 Å, which is close to 0.74 Å (a half of the Si—H bond length in SiH₄). This is interesting and could be easily understood with the help of Fig. 1B. Furthermore, the product rotational distribution for the two mechanisms has been explored, and is shown in Fig. S2. Clearly, the inversion mechanism leads to a colder SiH₄ rotational distribution, and the torsion one promotes the rotational excitation of the SiH₄ product (see SI Appendix for more).

Conclusions

Detailed QCT calculations for both the H+SiH₄ abstraction and exchange reactions are performed on the BCLWS surface, which is an accurate global 12-dimensional ab initio PES constructed in this work. The excitation functions and product angular distributions are investigated in detail at various collision energies, and our QCT studies provide insights into the reaction mechanism. The dynamical behavior of the SiH₅ system presents a complex and interesting picture. There exists a competition between the abstraction and exchange channels, and, in each of them, two or more reaction mechanisms are involved, which depend on collision energy, impact parameter and orientation of the incoming H atom with respect to the Si—H bond. Our work elucidates the detailed mechanisms and the main findings are summarized below.

The abstraction reaction is a combination of rebound and stripping mechanisms. The rebound mechanism dominates at low collision energy, yielding the backward-scattered H₂, whereas the stripping mechanism becomes dominant at high collision energy with the sideways-scattered H₂ being yielded. The stripping mechanism is dynamically similar to what was recently observed in H+CD₄ by Zare and coworkers, and H+SiH₄ could serve as another example of stripping that appears at much lower collision energies.

The exchange reaction is the combination of three mechanisms: inversion, torsion-tilt, and side-inversion. Inversion is dominative at small impact parameter and low collision energy, yielding forward-scattered H products, whereas torsion is favored for intermediate impact parameters and at high collision energies, with H products being scattered sideways and forward. The shift of angular-distribution peak with collision energy toward smaller scattering angles can be explained by the tilt movement of the breaking Si—H bond. Inversion was first inferred in experiment by Bersohn and coworkers, and its existence is confirmed by our QCT modeling. At high collision energies, both the torsion and inversion mechanisms bias the angular distribution in the forward direction, in qualitative agreement with the previous experimental observation by Bersohn and coworkers. The side-inversion mechanism plays a minor role in the current collision-energy range, and would result in a H angular distribution peaking in the perpendicular direction. The latter two mechanisms are recognized and designated by us, and may be common in a range of polyatomic exchange reactions.

The new reaction mechanisms revealed in this work would be very beneficial for developing various theoretical models to study polyatomic abstraction and exchange reactions, and would extend our understanding of elementary reaction dynamics. It is our hope that the present theoretical study will stimulate further experimental research on this interesting system.

Methods

More details on the methods are described in SI Appendix.

Ab Initio Calculations.

The UCCSD(T), RCCSD(T) and icMRCI+Q/CASSCF calculations were carried out using the MOLPRO 2002.6 package (34), whereas the UQCISD calculations were performed with the Gaussian 03 package (35).

Potential Energy Surface Construction.

The modified Shepard interpolation method proposed by Collins and coworkers (26–28) was applied, in which the PES is given by an interpolation of second-order Taylor expansions centered at data points scattered throughout the configuration space. To determine the position and number of the reference data points properly is very important for the quality of the interpolated PES. We used a combined scheme to select the geometries and check the convergence, and both abstraction and exchange channels were considered. Approximately 3,000 reference points were selected based on classical trajectory simulations, and additionally several hundred points were selected according to physical considerations, particularly the analysis of potential contour plots. QCT calculations were performed to check the convergence of the interpolated PES with respect to the number of points in the dataset. A typical plot is shown in Fig. S3, which indicates that the exchange reaction probability is converged with small variations for datasets with >3,000 points. Several large QCT calculations were also performed to ensure the cross section is converged.

Finally, we achieved a reference dataset with 4,015 points, based on which the interpolated PES is believed to be able to describe the energy range <45 kcal/mol relative to the H+SiH₄ asymptote. The 1,300 reference geometries for the previous surface (25) were included as a subset of the present geometry set. At the 4,015 chosen reference geometries, the UCCSD(T)/cc-pVQZ calculations were performed to obtain the electronic energies, whereas the gradients and Hessians were computed at the UQCISD/cc-pVTZ level. The error introduced by using the derivatives at a relatively low level is small, and the validity of this kind of approximation was demonstrated in ref. 36 for the OH₃ system. The above choice reflects a balance between CPU time and accuracy, nevertheless, the amount of computer time expended is still substantial, and the final reference dataset with 4,015 points took ≈7.6 years of single-CPU time on our 64-bit Opteron server.

Quasiclassical Trajectory Calculations.

QCT calculations were performed using a custom- designed version of VENUS96 (37, 38) code modified to incorporate our PES. The QCT method has been described in literature (39–41), and some details concerning the present study are given here and in SI Appendix. For all trajectories, the initial SiH₄ molecule is set in its ground rovibrational state using fixed normal mode energy sampling (41), and the integration time step is 0.05 fs. The maximum value of the impact parameter (b_max) was estimated by calculating batches of 3,000 trajectories at fixed values of b and systematically increasing the value of b until no reactive trajectories were obtained. To ensure that all reactive trajectories can be collected, b_max,ab (b_max for abstraction) of 3.5 Å and b_max,ex (b_max for exchange) of 1.8 Å were used. For different collision energies, batches of 12,000–30,000 trajectories were calculated with b being sampled from b = b_max,abβ^1/2 (β is a random number in the [0, 1] interval), and to improve the statistics of calculations for exchange reaction, additional batches of 12,000–35,000 trajectories were calculated with b being sampled from b = b_max,exβ^1/2. To correct the ZPE leakage, we used a nonactive method (33), which follows the genuine QCT approach but discards all of the reactive trajectories that fulfill one of the following conditions: (i) the initial total energy is lower than the sum of the classical energy and harmonic ZPE of the saddle point; (ii) the vibrational energy of the products is lower than the sum of their ZPEs. Trajectories from the inversion and torsion mechanisms were separated in this work. We found that the minimum distance (R_L) between the incoming H atom and the leaving one could be used to distinguish between the two mechanisms: Reactive trajectories with R_L > 2.7 Å follow the inversion mechanism, whereas those with R_L < 2.0 Å obey the torsion mechanism. The number of reactive trajectories out of the above range was small, and these trajectories could be distinguished by viewing their animations, including those undergoing side-inversion.