+ Ethylene Reaction: A Trajectory Surface Hopping Study

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A: Kinetics and Dynamics 3

Dynamics of the C(P) + Ethylene Reaction: A Trajectory Surface Hopping Study Mrinmoy Mandal, Subhendu Ghosh, and Biswajit Maiti J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b01386 • Publication Date (Web): 20 Mar 2018 Downloaded from http://pubs.acs.org on March 22, 2018

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The Journal of Physical Chemistry

Dynamics of the C(3P) + Ethylene Reaction: A Trajectory Surface Hopping Study Mrinmoy Mandal, Subhendu Ghosh, Biswajit Maiti* Department of Chemistry, Institute of Science, Banaras Hindu University, Varanasi-221005

ABSTRACT: Direct dynamics trajectory surface hopping (DDTSH) method has been employed to study the reaction of C(3P) with ethylene (C2H4). Our trajectory simulations show that at a reagent collision energy of 7.36 kcal/mol, there are two possible product channels: propargyl (H2CCCH) + H and carbene (CH2) + acetylene (HCCH). Estimated branching ratios based on trajectory propagations indicates that propargyl radical formation is the dominant channel contributing (94.1±5.2) % of the overall products formation with (5.9±1.7)% contribution from the minor CH2 + HCCH channel. These findings are consistent with earlier experimental observations and theoretical predictions that propargyl (H2CCCH) formation is the dominant channel for the C(3P) + C2H4 collision reaction. Our trajectory simulations however, unravel five distinctly different dynamical pathways unlike earlier experimental and theoretical predictions of only two pathways proposed for the formation of propargyl radical and three different dynamics are followed for the CH2 + HCCH channel (this channel was not detected experimentally). The computed translational energy distribution for the propargyl + H channel is narrower and showed peak maximum at a lower energy compared to experimental one. While centre of mass product angular distribution based on our trajectory propagation is nearly isotropic in nature indicating formation of long-lived intermediate complexes, the experimental one was reported to be backward-forward distributed with more intensity in the forward direction indicating the

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formation of an osculating complex. Our trajectory surface hopping calculations confirms that the effect of intersystem crossing (ISC) is not important for the title reaction presumably because of weak spin-orbit coupling values (< 10 cm-1) for the (C + C2H4) system. No trace of cyclic products formation was obtained from our trajectory simulations, which however was predicted to be a minor (2%) product channel, experimentally.


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1. INTRODUCTION The reaction of triplet carbon, C(3P) with ethylene, C2H4(X 1Ag) produces nearly exclusive propargyl radical, H2CCCH (X 2B1) and is considered to be one of the most important reaction in combustion flame.1-6 Beside combustion the propargyl isomer is expected to exist in interstellar7, 8 and planetary environments.4 Specifically, the C(3P) + C2H4(X 1Ag) reaction is a key reaction to predict the growth of carbon containing molecules, such as formation of polycyclic aromatic hydrocarbons (PAHs) that is believed to proceed through reactions of the propargyl radical.9 This simplest reaction follows complex multichannel dynamical pathways. The possible primary channels are:3, 4 C(3P)+C2H4 (X 1Ag) → H2CCCH(X 2B2) + H(2S1/2)

∆ = − 45.3 ± 2.0 kcal/mol

→ c-H2CCCH(X 2A´ )+ H(2S1/2)

∆ = −5.0 kcal/mol

→ c-HCCHCH(X 2A´) + H(2S1/2)

∆ = −13.6 kcal/mol

→

H3CCC(X 2A1) + H(2S1/2)

∆ = −8.1 kcal/mol

→

HCCCH(3B1) + H2(X 1∑g+ )

∆ = −51.1 kcal/mol

→ c-C3H2(X 1A1) + H2(X 1∑g+)

∆ = −67.9 kcal/mol

→ C2H2(1∑g+) + CH2(X 3B1)

∆ = −33.7 kcal/mol

→ C2H(2∑+) + CH3(X2A2)

∆ = −19.6 kcal/mol

It was proposed4 that at the initial step of the C(3P)+C2H4 (X 1Ag) reaction the electrophilic carbon atom attacks the π-orbital of the C2H4 molecule yielding cyclopropylidene with no entrance barrier. The cyclopropylidene then isomerizes to triplet allene by ring opening. Elimination of a hydrogen atom from the triplet allene produces propargyl radical almost exclusively as the major product. One should note that the singlet allene being most stable



intermediate10 there is a possibility of intersystem crossing (ISC) in the C(3P)+C2H4 (X 1Ag) reaction. The importance of this triplet-singlet spin non-conserving root is not explored yet.

Studies11, 12 of the O(3P) + C2H4 (X 1Ag) reaction, a similar type to the C(3P)+C2H4 (X 1Ag) reaction, demonstrated that the electrophilic oxygen attacks one of the carbon atom of the C2H4

. . molecule forms an energetic triplet biradical OCH2CH2 which in turn can go to the singlet state through ISC followed by products formation. This dynamical path was predicted to be as important as ~50% of the overall reaction at collision energies in the range 4.0 – 12.9 kcal/mol.

Earlier theoretical studies of the C(3P)+C2H4 (X 1Ag) reaction by Mebel and co-workers4 have mainly been confined to quantum chemical calculations of the stationary points and energetics along the reaction pathways. Their investigation indicates the presence of many minima associated with various isomers of C3H4 which lead to a large number of energetically allowed product channels. They have performed RRKM calculations to find out the branching fraction of the different product channels. Their results show that at an initial internal energy 9.2 kcal/mol above the reactant level the propargyl radical (H2CCCH) + H channel accounts for 98% of the overall products while the formation of CH2(3B1) + C2H2 contributes 2% of the reaction products and negligible contribution from other channels. They also concluded that 91% of the propargyl radical out of 98% comes from the triplet allene (H2CCCH2) and rest only 7% comes from the venylmethylene (H2CCHCH). These results are close to the experimentally reported H atom elimination branching ratio of 92% in bulk condition at 300 K.5 Using the crossed molecular beam technique both Kaiser et al.6 and Geppert et al.3 concluded that C3H3(propargyl) + H is the major product channel of the C(3P)+C2H4 (X 1Ag) reaction. For the formation of propargyl 4 ACS Paragon Plus Environment

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(H2CCCH) radical Kaiser et al.6 suggested two microchannels with different dynamics after an initial attack of the C(3P) to the π-bond of the C2H4 via a transition state located at the centrifugal barrier. The first one, arising from ring opening of the initially formed c-C3H4 (cyclopropylidene) to triplet allene and decomposing to propargyl with weak coupling between the initial and final orbital angular momenta, contributes to an isotropic center-of-mass(CM) angular distribution indicating formation of long-lived intermediate complexes. The second one contributes ~10% of the scattering signal, resulting from A-like rotations of cyclopropylidene adduct followed by ring opening to triplet allene with a strong initial and final orbital angular momentum correlation, give rise to a forward scattered CM angular distribution. An improved experimental study by Casavecchia and co-workers3 however did not support these observations. In addition, varying the initial collision energy, they proposed a second source of H atom formation channel through the formation of less stable C3H3 (propyn-1-yl and/or cyclopropenyl) isomer(s) for the same reaction. Later, using molecular beam in conjunction with H-atom Doppler spectroscopy the C(3P)+C2H4 (X 1Ag) reaction dynamics was investigated by Costes and co-workers13 at low collision energies, 0.17 and 1.3 kcal/mol and reiterated the predictions made by Casavecchia and co-workers.3 Recently Chin et al.2 using crossed molecular beam investigated the velocity distribution of C3H3 radicals produced by the C(3P)+C2H4 (X 1Ag) reaction. Time-of-flight spectra of the C3H3 radical were measured using two photoionization energies 9.5 and 11.6 eV. The time-of-flight and laboratory angular distributions for the two sets of data remain unchanged indicating only one C3H3 isomer formation and the isomer was identified as propargyl radical based on its photoionization spectrum. Most recent flow tube study1 of the C(3P)+C2H4 (X 1Ag) reaction carried out in a flow tube reactor at 332 K and 4 Torr under multiple collision conditions detected propargyl radical as the sole molecular product.



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Above discussion clearly demonstrates that there exist controversies about the mechanism and product branching of the formation of the propargyl radical from the C(3P)+C2H4 (X 1Ag) reaction based on experimental as well as theoretical predictions and also about the formation of other products. Mebel and co-workers4 gave a good account of the reaction mechanism based on stationary points calculations along the reaction path. Stationary points on the potential energy surfaces however, are not sufficient for proposing the actual reaction path or reaction mechanism specifically when multiple electronic states are involved. Wherever feasible, dynamics calculations are desirable for quantitative prediction of the reaction mechanism, the product branching, and for visualization of chemical processes. Dynamical simulations of multichannel nonadiabatic processes however, are challenging as these involve the determination of multiple surfaces and their couplings, and a suitable description of nuclear motion subject to these surfaces. In the present study we therefore, have used direct dynamics trajectory surface hopping method14 to describe ISC. We have also computed the branching ratios and product angular distributions to get more insight into the reaction processes of the C(3P)+C2H4 (X 1Ag) reaction.

2. ELECTRONIC

STRUCTURE

AND

DIRECT

DYNAMICS

CALCULATIONS

In our direct dynamics trajectory surface hopping (DDTSH) calculations a classical molecular dynamics code is interfaced with Gaussian 09 computer program15 to compute potential energies and gradients on-the-fly. The potential energies of the triplet and singlet ground electronic states and gradients were computed at the UB3LYP/6-31G(d,p) level of theory. To find out the accuracy of the potential energy surfaces used in our calculations we have performed geometry 6 ACS Paragon Plus Environment

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optimizations for the stationary points along the major reaction channels. The intermediates were characterized by all nonzero real frequencies, whereas transition states by only one imaginary frequency. Fig. 1 represents the triplet and singlet PESs of the C(3P)+C2H4 reaction along different reaction channels. Energies of the triplet and singlet stationary points are computed relative to the energy of the separated reactants C(3P) + C2H4 (X 1Ag) inclusive of zero point energies.

The C(3P) atom initially attacks one of the carbon atoms of ethylene forming

CCH2CH2 biradical (i0) with no entrance barrier. This biradical either very quickly converted to cyclic-C3H4 (i1) or to vinylmethylene (i4) through TS3. Another possibility is that the C(3P) atom initially adds to the ethylene π-bond yielding triplet cyclopropylidene without an entrance barrier.

The cyclic-C3H4 is bound by 57.24 kcal/mol with respect to the separated triplet reactants C(3P)+C2H4 at the UB3LYP/6-31G(d,p) level of theory. Mebel and co-workers4 reported this value to be 51.7 kcal/mol at the G2M level, while at the CCSD(T)/6-311+G(3df,2p)//B3LYP/6311G(d,p) level of theory,2 the stabilization value is calculated to be 52.1 kcal/mol. One should note that our computed stabilization energy of the cyclic-C3H4 is more closer to the experimentally reported enthalpy of formation of 64.77 kcal/mol.6 Cyclopropylidene (cyclicC3H4) can isomerize to distorted triplet allene (i2) by ring opening through TS2.

This

isomerization is hindered by a barrier of 13.85 kcal/mol which is very comparable to the value of 13.4 kcal/mol reported by Le et al.4 at the G2M level and of 14.0 kcal/mol at the CCSD(T)/6311+G(3df,2p)//B3LYP/6-311G(d,p) by Chin et al.2 The triplet allene (i2 or i3) can transform to vinylmethylene (i4) by 1,2-H migration through TS7 with a barrier of 50.16 kcal/mol. This barrier was calculated to be 49.7 kcal/mol at the CCSD(T)/6-311+G(3df,2p)//B3LYP/6-



311G(d,p) level2 and at the G2M level4 as well. Our calculated stabilization energy of the triplet vinylmethylene (i4) of 88.2 kcal/mol at the UB3LYP/6-31G(d,p) level is very comparable with the experimental enthalpy of formation of 86.99 kcal/mol.6 At the G2M level4 this stabilization value was computed to be 80.8 kcal/mol, while at the CCSD(T)/6-311+G(3df,2p)//B3LYP/6311G(d,p) level2 this value is of 81.5 kcal/mol. Triplet vinylmethylene (i4) then can undergo either C-C bond breaking leading to triplet carbene, CH2(X 3B1) and acetylene (HCCH) with an exit channel barrier of 60.1 kcal/mol or H atom elimination from the middle carbon forming H2CCCH with a barrier of 42.8 kcal/mol. These exit channel barriers are reported to be of 53.7 and 41.6 kcal/mol, respectively, at the G2M level.4

The singlet carbon, C(1D) reacts with ethylene forms singlet cyclopropylidene (c-C3H4) which is bounded by 69.98 kcal/mol with respect to the separated triplet reactants, C(3P) + C2H4 at the UB3LYP/6-31G(d,p) level of theory. This value is very comparable to 72.39 kcal/mol computed at G2M level of theory by Mebel and co-workers.10 The singlet cyclopropylidene can form singlet allene by ring opening. The allene is the most stable intermediate in the singlet PES and it is stabilized by an energy of 137.91 kcal/mol compared to the triplet reactants, C(3P) + C2H4. This stabilization energy is very close to the experimental16 enthalpy of formation of 137.4 kcal/mol and computed10 137.85 kcal/mol (at the G2M level of theory) when compared with the triplet reactants, C(3P) + C2H4.

From the above discussion it can be concluded that the UB3LYP method with 6-31g(d,p) basis set provides highly accurate ground singlet and triplet potential energy surfaces for the C(3P,1D)


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+ C2H4 reaction. Therefore, our trajectory simulation would lead to reasonably accurate predictions based on the UB3LYP/6-31g(d,p) PESs.

We have computed spin-orbit coupling (SOC) matrix elements at each time step of a trajectory to calculate hopping probability between the triplet and singlet states by interfacing our dynamics code with GAMESS suits of program.17 The spin-orbit coupling calculation scheme is similar to that reported by Ghosh et al.18 For the completeness however, we summarize the procedure in brief.

The molecular orbitals (MOs) were generated from a four-state state-

averaged CASSCF(6,6) calculation using an aug-cc-pVDZ basis set. The four states included in the SOC calculations are 1 3A = 0, ±1 and 1 1A = 0 as we are interested in the lowest energy triplet-singlet ISC only. The SOC elements are generally imaginary. To make them real we have adapted a procedure proposed by Hoffmann and Schatz.19 In this method new symmetry-adapted triplet wave functions are generated from three components of a triplet wave function as given below: 3

Ψ z = i 3 Ψ (M s = 0 )

3

Ψx =

{

3

Ψ (M s = 1) + 3 Ψ (M s = − 1)}

3

Ψ

{

3

Ψ (M s = 1) − 3 Ψ (M s = − 1)}

y

1 2 i = 2

In this new representation, the SOC matrix elements

1

Ψ Hso 3 Ψ are real valued that are used

to construct a real valued Hamiltonian. We have computed an average SOC value between the singlet and triplet states by summing up the squares of the three singlet–triplet coupling elements divided by 3 (where 3 is the number of nonzero matrix elements) and then taking the square root: 9 ACS Paragon Plus Environment


V13 =

∑

1

3

ψ H so ψ j

2

/3

j = x, y , z

The calculated average value of the SOC constant values between the first triplet and singlet states are found to be very low, less than 10 cm-1.

To study the ISC mechanism in the C(3P) + C2H4 we have employed the direct dynamics quasiclassical version of trajectory surface hopping(DDTSH) method in conjunction with Tully’s fewest switches algorithm20 to compute triplet-singlet hopping probabilities. This DDTSH method is very similar to the one used previously.14 To match the experimental cross molecular beam condition of Casavecchia and coworkers,3 trajectories were initiated on the ground triplet state at a reagent collision energy of 7.36 kcal/mol. The polyatomic reactant ethylene (C2H4) is prepared in its ground singlet electronic and rovibrational state by running an intramolecular trajectory starting from its equilibrium geometry. Kinetic energy of each normal mode of ethylene (C2H4) is made equal to the corresponding zero point energy. The trajectory is integrated for large number of vibrational periods. The initial conditions are then generated from this trajectory by choosing impact parameter between attacking carbon and vibrating ethylene (C2H4) molecule randomly with a center-of-mass distance 15 a0 and a sampled maximum impact parameter 10 a0 . All the trajectories were propagated using a 10 a.u. (0.24 fs) integration step.

3. RESULTS AND DISCUSSION We have run a batch of 355 trajectories and propagated up to a maximum time of 400000 a.u.(9600 fs). Number of trajectories completed in different product channels is collected in Table I. The reaction proceeds through a long-lived intermediate complex (C3H4) with different 10 ACS Paragon Plus Environment

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isomeric form. Out of total 355 trajectories that were propagated, 181 (51%) trajectories are reactive leading to products through different pathways. Out of the total reactive trajectories 169 (~93%) trajectories ended up in H2CCCH+H channel which eventually was found to be the major product channel.3,

4

Remaining 12 (7%) reactive trajectories lead to the CH2+HCCH

channel, a minor product channel.

From our trajectory simulation we find that the product H2CCCH+H channel can be formed through different pathways. The propargyl (H2CCCH) radical can either come from triplet allene (i2 or i3) or venylmethylene (i4) after H atom elimination. The triplet allene can be formed in two different ways: (I) the electrophilic C(3P) initially attacks one of the carbon atoms of ethylene forming very short-lived addition complex (i0) which instantly converted to cyclopropylidene (i1), which in turn forms triplet allene (corresponding animation of a trajectory is shown in Fig. 2, path (a)), (II) initially triplet C(3P) attacks at the middle of the C=C bond forming triplet cyclopropylidene (i1), with no barrier, which then forms triplet allene through ring opening (a related animated trajectory is given in Fig. 2, path (b)). We should mention here that the former allene formation path (path (a)) is dominant one with ~34% contribution while later path (path (b)) contributes ~23% of the total H atom formation.

The formation of the propargyl (H2CCCH) radical by dissociation of H atom from venylmethylene follows three different pathways: (1) the C(3P) initially attacks one of the carbon atoms of ethylene leading to an

addition complex (i0) which quickly gets converted to

venylmethylene through H atom migration as can be seen from an animation given in Fig. 2, path (c), (2) the C(3P) gets inserted into one of the C-H bonds of ethylene forming venylmethylene



(i4) directly without any reaction barrier (see Fig. 1 and also animation in Fig. 2, path (d)), and (3) an addition complex (i0) formed initially, due to the addition of the C(3P) at any one of the C atoms of the ethylene, is converted to cyclopropylidene (i1) which isomerizes to triplet allene (i3, i4) by ring opening and then the allene again isomerizes to venylmethylene by 1,2-H migration (an animated trajectory is provided in Fig. 2, path (e) for clarification). While path (c) contributes about 33% and path (d) contributes ~10%, very small contribution was observed due path (e).

The formation of CH2+C2H2 products by C-C bond cleavage of venylmethylene (i4) is another important product channel. Our trajectory simulations indicate that formation of this venylmethylene (i4) can take place by two different initial approach of the C(3P) towards ethylene: (A) addition of the C(3P) to one of the carbon atoms of ethylene forming addition complex (i0) followed by a H atom shift leading to venylmethylene (a trajectory representing this path is demonstrated in Fig. 3, path (a)). One more possibility in this approach is that addition complex (i0) quickly forms cyclopropylidene which then converted to triplet allene by ring opening and then isomerizes to venylmethylene (i4) (this trajectory is shown in Fig. 3, path (b)), and (B) insertion of the C(3P) into one of the C-H bonds of ethylene directly leading to venylmethylene (a representative trajectory is given in Fig. 3, path (c)). One should note that the addition pathway (A) is dominant over the insertion pathway (B).

It is worth mentioning that none of the trajectories ended in the H2 + H2CCC product channel following triplet state dynamics presumably because of higher energy exit channel barrier4 compared to H + H2CCCH channel. If at all molecular H2 forms from the C(3P) + C2H4 (X 1Ag) reaction, it would form following the spin-forbidden ISC pathway near at cyclopropylidene (i1)


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(see Fig. 1) followed by formation of the singlet allene.10 This path is however, unlikely to be followed due to very weak spin-orbit coupling interactions between the ground triplet and the first excited singlet states as can be anticipated from our computed spin-orbit coupling values (less than 10 cm-1) and also from trajectory propagations; no trajectory started on the triplet state hops to the singlet state, perhaps due to relatively short life-time of the triplet c-C3H4 intermediate (i1) region where there are possibilities of ISC (see Fig. 1) to the singlet surface. One should note on the other hand, that despite necessarily the week spin-orbit interactions with an average value of 35 cm-1 in the O(3P) + C2H4 reaction the ISC was as important as ~50% due to repeated access of the singlet-triplet crossing seam arising presumably from longer life-time of

. . the initially formed triplet biradical OCH2CH2 .11, 12

We have calculated reaction cross section based on our trajectory simulations for channel j using the following expression 2 2π bmax σj = N

N

bl

∑b l =1

Pjl

max

where bl is the impact parameter of trajectory l with the maximum sampled impact parameter is

bmax , N is the total number of trajectory propagated, and P is the characteristic function for jl trajectory l. Pjl is 1 if the trajectory leads to channel, j otherwise it is taken to be 0. Our estimated reaction cross section (σj) for channel H2CCCH+H is (95.5±5.3) and for

channel CH2+HCCH is (6.0±1.7) . Therefore, branching ratio ∑

for the reaction channel

H2CCCH+H is (94.1±5.2) % and for channel CH2+HCCH is (5.9±1.7) %. These results are very 13 ACS Paragon Plus Environment


much comparable to the absolute branching ratio of (92.0±4.0)% for H2CCCH+H channel in a bulk condition at room temperature.5 It is worth pointing out here that crossed-molecular beam experiment at = 7.36 kcal/mol by Casavecchia and co-workers3 predicted 86% propargyl formation with 14% (cyclic C3H3 + H3CCC) products. Our trajectory propagations however, show no indication of formation of either cyclic C3H3 or H3CCC products.

We have calculated the product translational energy distribution for H+H2CCCH channel and plotted in Fig. 4 (upper panel) along with the experimental product translational energy distribution (lower panel) reported by Casavecchia and coworkers3 for comparison. Our calculated distribution shows a peak maximum at about 29.5 kJ/mol (~7.06 kcal/mol) and extends up to 147.9 kJ/mol (35.35 kcal/mol). The average release of product translational energy ∼(9.42±0.52) kcal/mol corresponds to the average fraction of translational energy

+ Ethylene Reaction: A Trajectory Surface Hopping Study

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