Quasiclassical trajectory study of H�SiH4 reactionsin full-dimensionality reveals atomic-level mechanismsJianwei Caoa,b, Zhijun Zhanga,b, Chunfang Zhanga,b, Kun Liua, Manhui Wanga, and Wensheng Biana,1

aBeijing National Laboratory for Molecular Sciences, State Key Laboratory of Molecular Reaction Dynamics, Institute of Chemistry, ChineseAcademy of Sciences, Beijing 100190, China; and bGraduate University of Chinese Academy of Sciences, Beijing 100049, China

Edited by Richard N. Zare, Stanford University, Stanford, CA, and approved June 30, 2009 (received for review April 10, 2009)

This work elucidates new atomic-level mechanisms that may becommon in a range of chemical reactions, and our findings areimportant for the understanding of the nature of polyatomic abstrac-tion and exchange reactions. A global 12-dimensional ab initio po-tential energy surface (PES), which describes both H�SiH4 abstractionand exchange reactions is constructed, based on the modified Shep-ard interpolation method and UCCSD(T)/cc-pVQZ energy calculationsat 4,015 geometries. This PES has a classical barrier height of 5.35kcal/mol for abstraction (our best estimate is 5.35 � 0.15 kcal/molfrom extensive ab initio calculations), and an exothermicity of �13.12kcal/mol, in excellent agreement with experiment. Quasiclassicaltrajectory calculations on this new PES reveal interesting features ofdetailed dynamical quantities and underlying new mechanisms. Ourcalculated product angular distributions for exchange are in theforward hemisphere with a tail sideways, and are attributed to thecombination of three mechanisms: inversion, torsion-tilt, and side-inversion. With increase of collision energy our calculated angulardistributions for abstraction first peak at backward scattering andthen shift toward smaller scattering angles, which is explained by acompetition between rebound and stripping mechanisms; here strip-ping is seen at much lower energies, but is conceptually similar towhat 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 ofthese atomic-level mechanisms is confirmed by direct examination oftrajectories, and two of them (torsion-tilt and side-inversion) areproposed and designated in this work.

potential energy surface � reaction dynamics

The A�BC type reactions have long served as benchmarks in thedevelopment of the kinetics and dynamics theories of chemical

reactions (1–5). However, behavior of polyatomic reactions may bequalitatively different from what has been deduced from studies ofatom–diatom dynamics. For example, a major reaction path, whichdoes not follow the intrinsic reaction coordinate, has recently beenfound by Hase et al. (6) in their quasiclassical trajectory (QCT)study on the F��CH3OOH reaction. Another example is thereaction of H�CH4 (and its isotopic variants), for which recentinvestigations (7) have focused on the new stripping mechanismobserved by Zare and coworkers (8–9). The rebound mechanism iswell-known for the H�D2 reaction (10–11), and a lot of polyatomicH abstraction reactions, including H�CD4, have long been con-sidered to proceed through this mechanism. However, in the recentcombined experimental and theoretical studies on the reaction ofH�CD4 (9, 12), the stripping mechanism was proposed, in whichthe velocity of incoming H atom is perpendicular to the C-D bondand the HD product is carried into the forward hemisphere. Thestripping mechanism was further confirmed by Bowman and co-workers (13) using the QCT method.

The H�SiH4 reaction is an analogue to H�CH4, and bothabstraction and exchange reactions can happen; i.e.,

Abstraction: H� � SiH43 HH� � SiH3 [R1]

H� � CH43 HH� � CH3 [R1a]

Exchange: H� � SiH43 SiH3H� � H [R2]

H� � CH43 CH3H� � H. [R2a]

Unlike the H�CH4 abstraction reaction, which is nearly thermo-neutral, the H�SiH4 abstraction reaction R1 is exothermic by �13kcal/mol, and regarded as a prototype of exothermic polyatomic Habstraction reactions. Also, as we will demonstrate, both reactions1 (R1) and 2 (R2) could happen at collision energies above �12.5kcal/mol, therefore the H�SiH4 reaction is actually a better can-didate for studying the competition between abstraction and ex-change than H�CH4, for which the exchange channel is not openat collision energies �35 kcal/mol (noninversion exchange not openat �60 kcal/mol) (14).

In this work, a global 12-dimensional potential energy surface(PES) that describes both abstraction and exchange reactions forthe SiH5 system is constructed, and detailed QCT calculations forboth reactions R1 and R2 on this ab initio PES are performed,which yield insights into the reaction mechanism. The computedproduct angular distributions indicate that the abstraction reactionis a combination of rebound and stripping. More importantly, herewe propose that the H�SiH4 exchange reaction is a combination ofthree mechanisms, inversion, torsion (more exactly, torsion-tilt),and side-inversion as demonstrated in Fig. 1. The interestingdynamical features for exchange can be explained with theseatomic-level mechanisms. These findings are helpful for our un-derstanding of the nature of polyatomic reactions, which goesbeyond the atom–diatom pictures, and would have implications fora number of fields ranging from fundamental reaction dynamics toatmospheric and organic chemistry.

The H�SiH4 reaction is important in the thermal decompositionof monosilane (15) and plays a significant role in chemical vapordeposition processes used in semiconductor industry and for theproduction of ceramic materials (16). The kinetics of reaction R1has been extensively studied experimentally in the past decades(refs. 17–19 and references therein). However, few have investi-gated the detailed state-resolved dynamics, which underscores theneed to perform detailed dynamical calculations. Furthermore,Bersohn and coworkers (20) examined reaction R2 (and isotopicsubstitutions) with a laser-induced fluorescence technique at acollision energy of �2 eV and the integral cross-section (ICS) forH�SiD43 SiD3H�D was determined as �0.36 Å2. They inferredthat the exchange channel proceeds through an inversion mecha-nism. Several theoretical investigations have been reported onH�SiH4 reactions, although earlier ab initio calculations werelimited to the small regions around a few stationary points and theminimum energy path (MEP) (18, 21–23). So far there have beentwo PESs reported (24, 25) for the SiH5 system, but both of themcould only describe reaction R1: Espinosa–García et al. (24)developed an analytic semiempirical PES in 1998; more recently,

Author contributions: J.C., Z.Z., C.Z., K.L., M.W., and W.B. performed research; J.C., Z.Z., andC.Z. analyzed data; W.B. designed research; and W.B. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

1To whom correspondence should be addressed. E-mail: bian@iccas.ac.cn.

This article contains supporting information online at www.pnas.org/cgi/content/full/0903934106/DCSupplemental.

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Wang et al. (25) constructed a 12-dimensional ab initio PES basedon the modified Shepard interpolation method (26–28) and �1,300ab initio reference points. The latter PES was designed for thermalconditions, and further variational transition state theory (25) andQCT (29) calculations yielded rate constants in good generalagreement with experiment for reaction R1.

Results and DiscussionAb Initio Calculations. In the construction of high-quality ab initioPESs, it is very important to choose ab initio methods and basis setsproperly. Extensive high-level ab initio calculations were performedto check the convergence of the barrier height and exothermicity forreaction R1 with respect to various basis sets and methods fortreating electron correlation, and the main calculation results aresummarized in Table S1. The reaction enthalpies at 0 K computedwith different methods are extremely close to one another at thecomplete-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 theextension of one-electron basis set, and at the CBS limit, differentmethods 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 polarizedvalence n zeta) basis sets are very similar at the CBS limit, indicatingthat the addition of diffuse functions is unimportant if a larger basisset is applied. The computed classical barrier height for reaction R1has basically reached convergence, and our best estimate of it is 5.35kcal/mol with the largest error being estimated to be just �0.15kcal/mol. Based on our calculation results and convergence analysis,we conclude that the spin-unrestricted coupled cluster method withsingle and double excitations and triple excitation correction(UCCSD(T)) with the cc-pVQZ basis set is a suitable level forenergy calculations required for the PES construction. At theUCCSD(T)/cc-pVQZ level, the computed classical barrier height is5.34 kcal/mol, in excellent agreement with our best estimate. Also, thecomputed reaction enthalpy at 0 K is �13.15 kcal/mol, and is very closeto the experimental value of �12.9 � 1.1 kcal/mol (30, 31).

Geometries of various stationary points have been optimized atthe 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 aredetermined: one is of D3h symmetry (Fig. 2B) with a barrier heightof 12.25 kcal/mol, and the other is of Cs symmetry (Fig. 2C) with a

barrier height of 12.57 kcal/mol. These values are evidently lowerthan those from earlier ab initio calculations (22). The inversion andside-inversion mechanisms involve the D3hTS, whereas the torsionmechanism proceeds through the Cs TS. We found a new van derWaals (vdW) complex, which is shown in Fig. 2D. More detailsabout it and other two vdW complexes for reaction R1 are given inSI Appendix.

Twelve-Dimensional ab Initio PES. To perform various detailed dy-namical studies, we constructed a global 12-dimensional ab initio PESsuitable for the study of both abstraction and exchange reactions in theSiH5 system. The energy calculations were performed usingUCCSD(T)/cc-pVQZ at 4,015 carefully selected geometries, and themodified Shepard interpolation method (26–28) was applied. This newPES (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 presentedin Table S2. The barrier height for reaction R1 is 5.35 kcal/mol, inclose agreement with our ab initio value of 5.34 kcal/mol. Thebarrier heights for reaction R2 on the BCLWS surface are 12.27kcal/mol (D3h TS) and 12.62 kcal/mol (Cs TS), in very goodagreement with our corresponding UCCSD(T)/cc-pVQZ calcula-tion values. These low exchange barriers reported here are signif-icantly different from those for reaction R2a, for which the ex-change barrier height (for inversion) is 36.37 kcal/mol on the ZBB3PES (13) and 38.1 kcal/mol as reported in earlier ab initio calcu-lations (22). Furthermore, the BCLWS surface has vdW complexesin the entrance and exit valleys (see SI Appendix).

Various contour plots were made to check the quality of theBCLWS surface and three typical plots are shown in Fig. 3. Theregion of abstraction reaction is shown in Fig. 3A, in which the TSand MEP regions could be seen. It is clear that the contour lines aresmooth and the potential is physically reasonable in various regions.We can also notice that the location of saddle point is closer to theH�SiH4 reactant, indicating an early barrier. It should be notedthat the ‘‘saddle point’’ in Fig. 3B does not correspond to the D3hexchange TS, because the inversion of configuration contributesevidently to the reaction coordinate whereas the energy in Fig. 3Bis minimized with respect to all other coordinates. This explains whythe ‘‘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,

Fig. 1. The inversion, torsion, and side-inversion mechanisms of the H�SiH4

exchange reaction.

Fig. 2. The geometries of stationary points in the SiH5 system optimized at theUCCSD(T)/cc-pVQZ level. (A) Abstraction transition state (TS). (B) Exchange TS ofD3h symmetry. (C) Exchange TS of Cs symmetry. (D) vdW complex for exchangechannel. R1 and R2 are defined here for use in other places. Bond lengths andangles are in angstroms and degrees, respectively.

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the saddle-point region basically corresponds to the Cs exchange TSregion, which is shown to be relatively flat.

Excitation Function for Abstraction. Detailed QCT calculations wereperformed for both reactions R1 and R2 on the BCLWS surfacewith the reactant SiH4 being fixed in its rovibrational ground state.Fig. 4 shows the excitation function for reaction R1 and it can beseen that, the ICSs increase quickly with collision energy at lowerenergies, which is consistent with the early abstraction barrier. Athigher energies the increase slows down gradually, and �22.5kcal/mol the ICSs start dropping slightly, which suggests a decreasetendency at even higher collision energies. In contrast to reaction R1a,much larger ICSs are obtained here at the same collision energy. Thisis understandable, because reaction R1 has a much lower barrier thanreaction R1a [14.8 kcal/mol for barrier height (32)].

Two kinds of quantum effects, namely the zero-point energy(ZPE) and tunneling effects, may influence the results, and thelatter 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 sensitiveto the ZPE correction. This may result from the fact that both thebarrier height (5.35 kcal/mol) and TS ZPE (18.97 kcal/mol) arecomparable to collision energies. Because of the light H atom, the

tunneling effects are expected to be strong for reaction R1, how-ever, normally these effects need to be considered only at collisionenergies lower than �6 kcal/mol. In view of the fact that thecomputed rate constant on the WSB surface (29) is somewhat lowerthan the experimental data, and the barrier height on the BCLWSsurface is more accurate, we deduce that the QCT calculations onthe BCLWS surface would yield better agreement with experiment(17–19) for thermal rate constant. Of course, it should be noted thatat temperatures �500 K, the tunneling effects may increase theQCT rate constant.

H2 Angular Distributions and Mechanisms for Abstraction. We seefrom Fig. 5 Left that the H2 angular distribution is dominated byscattering in the backward direction at the collision energy of 6.5

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 andR2 (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.

Fig. 4. Excitation function for the H�SiH4 abstraction reaction. The solid linewith squares displays the QCT results, whereas the dotted line with circles givesthe ZPE-corrected QCT results.

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 (� � 0°) is definedalong the H-atom reactant beam direction. The contour intensities are notnormalized.

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kcal/mol, and the most striking feature is, with the increase ofcollision energy from 6.5 to 17.5 kcal/mol, a double-peak structureappears and the sideways peak shifts toward small scattering angles.This angular distribution shift suggests the existence of two com-petitive reaction mechanisms: rebound and stripping.

The rebound mechanism is well-known for this kind of Habstraction reaction, in which the incident H atom is directed alonga SiOH� bond and the H�H product rebounds backward. Thestripping mechanism was proposed in a combined experimentaland theoretical study on the reaction of H�CD4 (9, 12). As forreaction R1, the rebound mechanism dominates at low collisionenergies, whereas at high collision energies, the incoming H atomhas more energy to get over the angular-momentum barrier, andthus it becomes easier for the H atom to attack SiH4 from the sideface, and strip one H from SiH4, and the H2 product is carried intothe forward hemisphere, as is the stripping mechanism. Because ofthe increasing contribution from the stripping mechanism, at 17.5kcal/mol, H2 products scatter sideways and peak in the perpendic-ular direction (see Fig. 5), and qualitatively, the shape of the angulardistribution is analogous to what has been observed (9) for theD-substituted reaction R1a at the collision energy of 27.8 kcal/molusing the photoloc technique. In this respect, reaction R1 is similarto reaction R1a, and may be used as another example of the newlyobserved stripping mechanism. The intriguing feature of reactionR1 is, the stripping plays an important role at collision energies aslow as 10.5 kcal/mol (see Fig. 5).

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

Excitation Function for Exchange. Our calculated ICSs for reactionR2 are shown in Fig. 6. For comparison, the results from theinversion and torsion mechanisms are also shown in this figure. Thecontribution of the side-inversion mechanism is very small andincluded in the results indicated as inversion. The near-thresholdbehavior is revealed in Fig. 6 Upper Left, from which we can notice

an evident dip along the curve, which is a reflection of twomechanisms. At collision energies �13.1 kcal/mol, only the inver-sion mechanism is effective, but �13.1 kcal/mol the torsion mech-anism occurs and leads to a sharp increase of the total exchange ICSin the energy range of 13.1–13.5 kcal/mol. This unusual behaviorshould be able to be observed in experiment as an evidence for thecoexistence of two mechanisms. Furthermore, it is remarkable thatthe ICS for torsion is larger than that for inversion particularly athigher collision energies. Although the inversion mechanism isslightly more favored energetically, torsion is predominant if judgedfrom the dynamic factor such as steric angles available for theapproach of H atom reactant.

At the average relative energy of 2.08 eV, the ICS forH�SiD43 SiD3H�D was determined as �0.36 Å2 by Bersohnand coworkers (20). This implies that the ICS for reaction R2should be somewhat greater than 0.36 Å2, because the threelighter nonreacting H atoms could move faster to reach thetrigonal-bipyramidal TS. Fig. 6 shows that, at collision energiesup to 24.5 kcal/mol, our computed ICSs for reaction R2 are�1.0 Å2; in addition, normally the ICS will be lowered to someextent if the collision energy is raised to �2 eV, which isbeyond the scope of the present calculations (the BCLWSsurface is designed for collision energies �26 kcal/mol). So ourcomputed ICSs are well consistent with the experimentalmeasurements in ref. 20.

H Angular Distributions and Mechanisms for Exchange. In contrast tothat for abstraction, the angular distribution for exchange predom-inately falls in the forward hemisphere (Fig. 5 Right). At thecollision energy of 13.5 kcal/mol, the H angular distribution dom-inates by scattering in the forward direction, consistent with theinversion mechanism; meanwhile, although the sideways peak isweak, a double-peak structure is clearly presented, which suggeststhe existence of two mechanisms. Interestingly, with the increase ofcollision energy from 13.5 to 20.0 kcal/mol, the two peaks mergeinto one and its shape gradually changes. The understanding ofthese delicate changes requires a detailed study of the reactionmechanism.

Based on our QCT calculations on the BCLWS surface, wepropose that the H�SiH4 exchange reaction proceeds through acombination of three mechanisms, inversion, torsion, and side-inversion as shown in Fig. 1. These mechanisms are also confirmedby direct observation of trajectories in our calculations. Inversionwould yield forward-scattered H atoms, whereas the H atoms arescattered sideways and forward via torsion. In addition, afterside-inversion, H products peak at the scattering angle � � 90°.

The first mechanism is inversion and shown in Fig. 1A, in whichthe incident H atom moves along the threefold axis and when itapproaches H3SiH with the C3v symmetry maintained, the threenonreacting H atoms would make an inversion, passing through thetrigonal-bipyramidal TS. Afterward, the H product goes forward toconserve the linear momentum. Inversion and noninversion ex-change channels were suggested for reaction R2a by Morokuma etal. (14), although at much higher energies. The inversion mecha-nism in reaction R2 was first inferred in experiment by Bersohn andcoworkers (20), and its existence is now confirmed by our QCTmodeling.

The second mechanism is torsion (or torsion-tilt) as called by us.As shown in Fig. 1B, the incoming H� atom is biased from thethreefold axis toward one of the SiOH bonds, and during theapproaching process, the plane determined by H�, Si and H containsthe C3 axis, and the SiOH bond tilts toward the forward direction,meanwhile, the nonreacting SiH3 group makes a torsion movementwith the C3v symmetry retained. The typical torsion angle is foundto be �70°. More exactly, this mechanism should be termed astorsion-tilt, through which the H product is scattered sideways andforward with � � 90°. It should be noted that � is much smaller thanexpected due to the tilt movement of the breaking SiOH bond. This

Fig. 6. Excitationfunctionfor theH�SiH4 exchangereaction.Thesolid linewithsquares displays the ZPE-corrected QCT results for total exchange reaction. Thedashed line with circles is from the torsion mechanism, whereas the dotted linewith triangles from the inversion and side-inversion mechanisms. (Upper Left) Anamplified view of the low-energy near-threshold region.

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mechanism would involve the Cs transition state and is consistentwith the noninversion mechanism already known (14); however, theprevious viewpoint that there is a retention of configuration needsto be changed.

The third mechanism is side-inversion, which we recognize anddenominate. As shown in Fig. 1C, the incident H atom is directedalong one twofold axis in SiH4 and approaches one side of the twononreacting H atoms, which are then pushed to invert to the otherside with a triangle formed, meanwhile the remaining two H atomsmoves up and down respectively, forming a trigonal-bipyramidal TSin the sideways direction. Afterward, one of the sideways H atomsgoes out in the perpendicular direction. Clearly, this mechanismwould yield H products, which peak at sideways, consistent with thesideways tail seen in Fig. 5. Compared with the inversion andtorsion mechanisms, the number of trajectories that follow thismechanism is minor in the collision-energy range considered here.

To obtain further insights into the reaction mechanisms, we havecompared the results from the inversion and torsion mechanismscarefully. As shown in Fig. 7, the peaks of H angular distribution forinversion appear always in the forward direction, however, those fortorsion initially appear at a larger scattering angle, and then shifttoward smaller angles with increase of collision energy. On passingfrom a collision energy of 13.5 to 24.5 kcal/mol, the angulardistribution for torsion changes from peaking at �64° to �36°. Thisdistribution-peak shift with collision energy is the most importantfeature, and could be well understood according to the torsionmechanism shown in Fig. 1B. With increase of collision energy the

tilt movement of the breaking SiOH bond is enhanced, which couldcause smaller and smaller scattering angles. Consequently, at highcollision energies, the torsion mechanism is also characteristic offorward scattering, and the scattered H fragments appear seldom atlarger angles. Then, the inference of Bersohn et al. (20) aboutreaction mechanism based on their experiment is probably incom-plete, because they assumed that a direct attack of the H atom ona 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 proceedthrough more than one mechanism (20). According to the tendencyshown in Fig. 7, we deduce that at very high collision energies, thedistribution peak will further shift to even smaller scattering angles�36°, in qualitative agreement with the experimental observationby Bersohn and coworkers (20), which indicates the scatteringangles being in the range of 0–36.5° at the average collision energyof �48 kcal/mol.

In addition, we have investigated the impact parameter depen-dence of reaction probability for reaction R2 via the two mecha-nisms. 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 probabilitypeak appears at b � 0.6 Å, which is close to 0.74 Å (a half of theSiOH bond length in SiH4). This is interesting and could be easilyunderstood with the help of Fig. 1B. Furthermore, the productrotational distribution for the two mechanisms has been explored,and is shown in Fig. S2. Clearly, the inversion mechanism leads toa colder SiH4 rotational distribution, and the torsion one promotesthe rotational excitation of the SiH4 product (see SI Appendix formore).

ConclusionsDetailed QCT calculations for both the H�SiH4 abstraction andexchange reactions are performed on the BCLWS surface, which isan accurate global 12-dimensional ab initio PES constructed in thiswork. The excitation functions and product angular distributionsare investigated in detail at various collision energies, and our QCTstudies provide insights into the reaction mechanism. The dynam-ical behavior of the SiH5 system presents a complex and interestingpicture. There exists a competition between the abstraction andexchange channels, and, in each of them, two or more reactionmechanisms are involved, which depend on collision energy, impactparameter and orientation of the incoming H atom with respect tothe SiOH bond. Our work elucidates the detailed mechanisms andthe main findings are summarized below.

The abstraction reaction is a combination of rebound andstripping mechanisms. The rebound mechanism dominates at lowcollision energy, yielding the backward-scattered H2, whereas thestripping mechanism becomes dominant at high collision energywith the sideways-scattered H2 being yielded. The stripping mech-anism is dynamically similar to what was recently observed inH�CD4 by Zare and coworkers, and H�SiH4 could serve asanother example of stripping that appears at much lower collisionenergies.

The exchange reaction is the combination of three mechanisms:inversion, torsion-tilt, and side-inversion. Inversion is dominative atsmall impact parameter and low collision energy, yielding forward-scattered H products, whereas torsion is favored for intermediateimpact parameters and at high collision energies, with H productsbeing scattered sideways and forward. The shift of angular-distribution peak with collision energy toward smaller scatteringangles can be explained by the tilt movement of the breaking SiOHbond. Inversion was first inferred in experiment by Bersohn andcoworkers, and its existence is confirmed by our QCT modeling. Athigh collision energies, both the torsion and inversion mechanismsbias the angular distribution in the forward direction, in qualitativeagreement with the previous experimental observation by Bersohnand coworkers. The side-inversion mechanism plays a minor role inthe current collision-energy range, and would result in a H angulardistribution peaking in the perpendicular direction. The latter two

Fig. 7. H-atom product scattering angle-c.m. velocity polar maps for theH�SiH4 exchangereactionvia the inversion (Left) andtorsion (Right)mechanismsatdifferent collisionenergies. Theforwardscattering (� �0°) isdefinedalongtheH-atom reactant beam direction. For each pair of maps at the same collisionenergy the contour intensities are normalized, whereas at different collisionenergies the intensities are not normalized.

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mechanisms are recognized and designated by us, and may becommon in a range of polyatomic exchange reactions.

The new reaction mechanisms revealed in this work would bevery beneficial for developing various theoretical models to studypolyatomic abstraction and exchange reactions, and would extendour understanding of elementary reaction dynamics. It is our hopethat the present theoretical study will stimulate further experimen-tal research on this interesting system.

MethodsMore details on the methods are described in SI Appendix.

Ab Initio Calculations. The UCCSD(T), RCCSD(T) and icMRCI�Q/CASSCF calcula-tions were carried out using the MOLPRO 2002.6 package (34), whereas theUQCISD calculations were performed with the Gaussian 03 package (35).

Potential Energy Surface Construction. The modified Shepard interpolationmethod proposed by Collins and coworkers (26–28) was applied, in which the PESis given by an interpolation of second-order Taylor expansions centered at datapoints scattered throughout the configuration space. To determine the positionand number of the reference data points properly is very important for thequality of the interpolated PES. We used a combined scheme to select thegeometries and check the convergence, and both abstraction and exchangechannels were considered. Approximately 3,000 reference points were selectedbased on classical trajectory simulations, and additionally several hundred pointswere selected according to physical considerations, particularly the analysis ofpotential contour plots. QCT calculations were performed to check the conver-genceof the interpolatedPESwithrespect to thenumberofpoints in thedataset.A typical plot is shown in Fig. S3, which indicates that the exchange reactionprobability is converged with small variations for datasets with �3,000 points.Several large QCT calculations were also performed to ensure the cross section isconverged.

Finally, we achieved a reference dataset with 4,015 points, based on which theinterpolated PES is believed to be able to describe the energy range �45 kcal/molrelative to the H�SiH4 asymptote. The 1,300 reference geometries for the previ-ous surface (25) were included as a subset of the present geometry set. At the4,015 chosen reference geometries, the UCCSD(T)/cc-pVQZ calculations were

performed to obtain the electronic energies, whereas the gradients and Hessianswere computed at the UQCISD/cc-pVTZ level. The error introduced by using thederivatives at a relatively low level is small, and the validity of this kind ofapproximation was demonstrated in ref. 36 for the OH3 system. The above choicereflects a balance between CPU time and accuracy, nevertheless, the amount ofcomputer time expended is still substantial, and the final reference dataset with4,015 points took �7.6 years of single-CPU time on our 64-bit Opteron server.

Quasiclassical Trajectory Calculations. QCT calculations were performed using acustom- designed version of VENUS96 (37, 38) code modified to incorporate ourPES. The QCT method has been described in literature (39–41), and some detailsconcerning the present study are given here and in SI Appendix. For all trajecto-ries, the initial SiH4 molecule is set in its ground rovibrational state using fixednormal mode energy sampling (41), and the integration time step is 0.05 fs. Themaximum value of the impact parameter (bmax) was estimated by calculatingbatches of 3,000 trajectories at fixed values of b and systematically increasing thevalue of b until no reactive trajectories were obtained. To ensure that all reactivetrajectories can be collected, bmax,ab (bmax for abstraction) of 3.5 Å and bmax,ex

(bmax for exchange) of 1.8 Å were used. For different collision energies, batchesof 12,000–30,000 trajectories were calculated with b being sampled from b �bmax,ab�1/2 (� is a random number in the [0, 1] interval), and to improve thestatistics of calculations for exchange reaction, additional batches of 12,000–35,000 trajectories were calculated with b being sampled from b � bmax,ex�1/2. Tocorrect the ZPE leakage, we used a nonactive method (33), which follows thegenuine QCT approach but discards all of the reactive trajectories that fulfill oneof the following conditions: (i) the initial total energy is lower than the sum of theclassical energy and harmonic ZPE of the saddle point; (ii) the vibrational energyof theproducts is lower thanthesumoftheirZPEs.Trajectories fromthe inversionand torsion mechanisms were separated in this work. We found that the mini-mum distance (RL) between the incoming H atom and the leaving one could beused to distinguish between the two mechanisms: Reactive trajectories with RL �2.7 Å follow the inversion mechanism, whereas those with RL � 2.0 Å obey thetorsion mechanism. The number of reactive trajectories out of the above rangewas small, and these trajectories could be distinguished by viewing their anima-tions, including those undergoing side-inversion.

ACKNOWLEDGMENTS. This work was supported by National Natural ScienceFoundation of China Grants 20733005 and 20673127, the Chinese Ministry ofScienceandTechnology,andtheChineseAcademyofSciences.Manycalculationswere performed at Network Information Center, Chinese Academy of Sciences.

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