Crossed Molecular Beams and Quasiclassical Trajectory Surface

Article pubs.acs.org/JPCA

Crossed Molecular Beams and Quasiclassical Trajectory Surface Hopping Studies of the Multichannel Nonadiabatic O(3P) + Ethylene Reaction at High Collision Energy Nadia Balucani,† Francesca Leonori,† Piergiorgio Casavecchia,*,† Bina Fu,*,‡ and Joel M. Bowman§ †

Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, 06123 Perugia, Italy State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China § Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States ‡

ABSTRACT: The combustion relevant O(3P) + C2H4 reaction stands out as a prototypical multichannel nonadiabatic reaction involving both triplet and singlet potential energy surfaces (PESs), which are strongly coupled. Crossed molecular beam (CMB) scattering experiments with universal soft electron ionization mass spectrometric detection have been used to characterize the dynamics of this reaction at the relatively high collision energy Ec of 13.7 kcal/mol, attained by crossing the reactant beams at an angle of 135°. This work is a full report of the data at the highest Ec investigated for this reaction. From laboratory product angular and velocity distribution measurements, angular and translational energy distributions in the center-of-mass system have been obtained for the five observed exothermic competing reaction channels leading to H + CH2CHO, H + CH3CO, CH3 + HCO, CH2 + H2CO, and H2 + CH2CO. The product branching ratios (BRs) have been derived. The elucidation of the reaction dynamics is assisted by synergic full-dimensional quasiclassical trajectory surface-hopping calculations of the reactive differential cross sections on coupled ab initio triplet/singlet PESs. This joint experimental/theoretical study extends and complements our previous combined CMB and theoretical work at the lower collision energy of 8.4 kcal/mol. The theoretically derived BRs and extent of intersystem crossing (ISC) are compared with experimental results. In particular, the predictions of the QCT results for the three main channels (those leading to vinoxy + H, methyl + HCO and methylene + H2CO formation) are compared directly with the experimental data in the laboratory frame. Good overall agreement is noted between theory and experiment, although some small, yet significant shortcomings of the theoretical differential cross section are noted. Both experiment and theory find almost an equal contribution from the triplet and singlet surfaces to the reaction, with a clear tendency of the degree of ISC to decrease with increasing Ec and with theory slightly overestimating the extent of ISC.

1. INTRODUCTION

O(3P) + C2H4 → CH 2CHO + H ΔH00 = −17.0 kcal/mol

The reaction between ground-state oxygen atoms O(3P) and ethylene has attracted a great deal of attention over many decades from both experimentalists and theoreticians, because of its importance in combustion and atmospheric chemistry.1,2 This reaction, involving multiple potential energy surfaces (PESs) of different spin multiplicity and exhibiting a variety of competitive product channels, can be considered as a prototypical polyatomic nonadiabatic multichannel reaction which, as such, is of great interest to both experimental and theoretical kineticists and dynamicists (see refs 3 and 4, and references therein). The title reaction has the following thermodynamically allowed product channels: © XXXX American Chemical Society

(1)

→ CH 2 + CH 2O

ΔH00

= −6.6(−5.4) kcal/mol

(2)

→ CH3CO + H

ΔH00

= −23.5 kcal/mol

(3)

→ CH 2CO + H 2

ΔH00 = −85.1(−84.2) kcal/mol

(4)

→ CH3 + HCO

ΔH00 = −28.8(−27.9) kcal/mol

(5)

→ CH4 + CO

ΔH00

(6)

= −116.7(−117.4) kcal/mol

Special Issue: Dynamics of Molecular Collisions XXV: Fifty Years of Chemical Reaction Dynamics Received: August 16, 2015 Revised: September 28, 2015

A

DOI: 10.1021/acs.jpca.5b07979 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

completion at the experimentally relevant collision energy, Ec, of 12.9 kcal/mol. In addition, again because of the computational effort, only relatively short-lived trajectories could be propagated to completion (a maximum of 4000 steps, roughly 1 ps). Nevertheless, the results of these calculations were in qualitative agreement with CMB experimental data in showing the significance of the intersystem crossing and motivated us to investigate these complex dynamics in far more detail and to make more detailed comparisons with CMB reactive scattering data. Recently, we reported a detailed account of extensive QCTSH calculations of the O(3P) + C2H4 reaction using fulldimensional ab initio PESs for the singlet and triplet states and their coupling, together with accurate CMB experiments at the collision energy of 8.4 kcal/mol.3,4 The very good agreement between theory and experiment given in that work represented the most comprehensive and significant comparison between theory and experiment for a reaction system of this complexity and importance, including nonadiabatic effects. Both theory and experiment found almost equal contributions from the two PESs to the reaction. Detailed comparisons at the level of center-of-mass (CM) angular and translational energy distributions between theory and experiment were presented for the three primary channel products, CH3 + HCO, H + CH2CHO, and CH2 + H2CO. The agreement between experimental and theoretical CM functions was very good, implying that theory had reached the capability of describing complex multichannel nonadiabatic reactions. However, some small differences were noted between experimentally and theoretically derived differential cross sections in the CM system, but direct comparisons of the theoretical predictions with the laboratory data, which is a most sensitive test, was not carried out. In this article, we extend these joint experimental/theoretical studies of the O(3P) + C2H4 reaction dynamics at the higher collision energy of 13.7 kcal/mol, focusing on the detailed dynamics of the various product channels, on the collision energy dependence of the branching ratios for the various product channels and of the extent of the ISC. Some of the results obtained from the analysis of the CMB scattering data at Ec = 13.7 kcal/mol were anticipated in previous publications,4,13 in particular in ref 4, where the BRs were reported together with those obtained from QCT-SH calculations performed at a collision energy of 12.9 kcal/mol, which is very close to the experimental one. The present article is a full account of all the experimental data and their analysis and of the detailed QCTSH calculations at Ec = 13.7 kcal/mol. The paper is organized as follows. In section 2, we describe the CMB experiments at Ec = 13.7 kcal/mol, and summarize the experimental results and their analysis. In section 3, details of the QCT surface hopping methodology are given. The experimental differential cross section results for the five observed reaction channels are discussed in section 4, where they are also compared with the results of surface hopping calculations on the coupled triplet-singlet PESs. These results include branching ratios and yields of products formed on the triplet and singlet PESs. Finally, in section 5 we give a summary of our results and conclusions.

The exothermicities at 0 K are taken from recent quantumchemical calculations;5 numbers in parentheses are experimental values.6 Because the differences between experimental and theoretical values are of the order of 1 kcal/mol, we adopted the theoretical values for all channels. Notably, although channels 1 and 2 are expected to occur on the triplet PES, channels 3−6 involve non adiabatic pathways, i.e., intersystem crossing (ISC) from the triplet to the singlet PES. The reaction has been studied very extensively from the kinetics standpoint. A survey of previous kinetics work, mostly at room temperature, and the history of the branching ratios (BRs) at 300 K have been critically surveyed in our previous experimental/theoretical study at lower collision energy (see Table 1 in ref 4). It should be noted that most kinetics characterizations of the channel yields have been conducted at room temperature, which is far from the typical conditions of combustion. Measurements of BRs at high temperature, of interest in combustion, are needed for an accurate modeling of hydrocarbon combustion. These quantities can be more readily provided by dynamics experiments as a function of relative translational energy. However, to identify the primary products of all reaction channels and determine their BRs, it is necessary to study all open channels under the same experimental conditions and with the same degree of accuracy. The most suitable detection technique to do so is the “universal” massspectrometric method relying on sof t electron ionization4,7 or soft photoionization.8,9 This technique can be used in both kinetics and dynamics experiments, but unambiguous product detection can be best pursued in crossed molecular beam (CMB) experiments, where the reactions are investigated under single collision conditions (under which secondary or wall collisions are avoided). Previous CMB work on the title reaction using both hard and sof t electron ionization has been summarized in our previous publication on this reaction.4 A common and intriguing aspect of O(3P) reactions with molecular species is that the reactants approach on a triplet PES that intersects a singlet PES, which usually contains stable intermediates. Intersystem crossing is then possible from the triplet to the singlet PES, making the dynamics that involve motion on the underlying singlet PES different from those involving motion only over the triplet PES.4 Both kinetics10 and dynamics11−13 studies of O(3P) reactions with unsaturated hydrocarbons, such as ethylene and higher alkenes, have long since provided clear indication that ISC is significant also in reactive systems not involving heavy atoms, such as O(3P) + light unsaturated hydrocarbons, with the notable exception of O(3P) + acetylene.14 The investigation of chemical reactions involving ISC presents challenges to both theory and experiment, because of the complexity of these systems. In fact, in contrast to studies of simpler three-atom nonadiabatic reactions (such as F(2P) + H2), which can be done by both quantum-mechanical and quasiclassical trajectory (QCT) scattering methods,15 theoretical studies of nonadiabaticity (i.e., ISC) in complex polyatomic reactions, such as O(3P) + unsaturated hydrocarbons, are rare. Pioneering work was performed on O(3P) + C2H4 by Schatz and co-workers,16 who performed a direct-dynamics calculation of this two-state reaction, including spin−orbit coupling. Due to the large computational effort required by this approach, a fairly lowlevel of electronic structure, i.e., unrestricted density functional theory/B3LYP with the 6-31G(d,p) basis, was used. Even so, only 545 trajectories (of which only 143 were reactive) using a simple “surface hopping” (SH) method, were propagated to

2. EXPERIMENTAL METHOD AND RESULTS The CMB apparatus with the critical improvement of soft electron−ionization detection and variable crossing beam setups have been described elsewhere.13,17 For the present B


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Figure 1. (lhs) Dots: LAB angular distributions measured at m/z = 42 (top panel) and m/z = 15 (bottom panel) (error bars representing ±1 standard deviation are indicated, when visible outside the dots) for the reactions O(3P,1D) + C2H4 at Ec = 13.7 kcal/mol. The solid black curve represents the calculated total angular distribution when the weighted best-fit CM functions of Figure 3 are used for the O(3P) and O(1D) contributions. The separate contributions to the calculated global LAB angular distributions are also shown ((see legend and text) (solid and dashed lines are contributions from O(3P) and O(1D), respectively). Red solid line: CH2CHO from O(3P). Blue solid line: CH3 from O(3P). Blue dashed line: CH3 from O(1D). Green olive solid line: CH2CO from O(3P). Green olive dashed line: CH2CO from O(1D). Orange solid line: CH3CO from O(3P). Dark cyano solid line: CH2 from O(3P). (rhs) Comparison of the experimental data with the prediction of the QCT-SH angular and translational energy distributions obtained at Ec = 13.7 kcal/mol for the O(3P) + C2H4 → CH3 + HCO channel (top panel) and the O(3P) + C2H4 → CH2CHO + H channel (bottom panel), while keeping for all other channels the best-fit functions and the same relative weights for the various channels as in the best-fit shown in the lhs. Symbols are as in the lhs. (Lower part): velocity vector (Newton) diagram of the experiment showing the 135° crossing angle geometry. Here the various circles delimit the maximum velocity that the indicated products can attain if all the available energy is channeled into product translation. The circles for CH3 and CH2CO formation from O(1D) are also depicted.

experiment the high collision energy Ec of 13.7 kcal/mol has been achieved by crossing the two supersonic beams of the reactants at 135° under single collision conditions in a scattering chamber kept at about 3 × 10−6 mbar in operating conditions. We recall that for a generic beam intersection angle γ, Ec= 1/2μ(v12 + v22 − 2v1v2 cos γ), where μ is the reduced mass of the system and v1 and v2 are the colliding beam velocities. The angular and velocity distributions of the reaction products are recorded by a ultrahigh-vacuum (10−11 mbar) detector equipped with a tunable electron impact ionizer, a quadrupole mass filter and an off-axis (90°) electron multiplier.

The whole detector unit can be rotated in the plane of the two beams around their intersection axis (Θ = 0° represents the direction of the atomic oxygen beam). The velocity of reactants and products is derived using single-shot and pseudorandom, respectively, time-of-flight (TOF) analysis. A continuous supersonic beam of atomic oxygen was obtained by means of a radio-frequency (RF) discharge beam source,18 in which 200 mbar of a 5% O2/He gas mixture were discharged through a 0.25 mm diameter water cooled quartz nozzle at 310 W of RF power; peak velocity and speed ratio were 2739 m/s and 4.9, respectively. The supersonic beam of C


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Figure 2. Open circles: LAB time-of-flight distributions measured at m/z = 42 at six indicated LAB angles (lhs panels), m/z = 15 at four indicated LAB angles (central panels) and m/z = 14 at the indicated LAB angle (rhs panels) for the reactions O(3P,1D) + C2H4 at Ec = 13.7 kcal/mol. The solid black curve represents the calculated total TOF distributions when using the weighted (as in Figure 1) best-fit CM functions of Figure 3 for the O(3P) and O(1D) contributions. The separate contributions to the calculated global TOF distributions at each LAB angle are also shown (line and color notations as in Figure 1).

ethylene was generated by expanding through a 100 μm diameter stainless-steel nozzle kept at room temperature 550 mbar of neat ethylene; beam peak velocity and speed ratio were 808 m/s and 6.3, respectively. The laboratory frame (LAB) angular distributions, N(Θ), were obtained by modulating at 160 Hz by a tuning-fork chopper the C2H4 beam for background subtraction and by taking the chopper-on minus the chopper-off counts (typical counting times per each angle were 30 s and typically 5−6 angular scans were measured and averaged). TOF distributions, N(Θ,t), of the products were obtained at selected laboratory angles using the pseudorandom (cross-correlation) TOF method with a dwell time of 6 μs/channel; the flight length was 24.3 cm (counting times varied from 30 to 120 min depending upon the signal intensity). From measurements of LAB N(Θ) and N(Θ,t) distributions of the possible reaction products we retrieve the product angular, T(θ), and translational energy, P(E′T), distributions in the center-of-mass (CM) frame. Branching ratios are derived by a multichannel fit of the LAB data using the best-fit CM functions and estimated (when not available) ionization cross sections and fragmentation patterns, as described in ref 4.

We take into account that our O atom beam contains, in addition to O(3P), about 5% of O(1D), as from a Stern− Gerlach characterization, when using a 5% O2 in He precursor gas mixture and about 300 W of RF power.18 Pulsed CMB work on this reaction at Ec = 3.0 kcal/mol with VUV photoionization detection has clearly shown that even small concentrations of O(1D) can contribute to the reactive signal at the masses corresponding to the CH3 (5) and CH2CO (4) channels.8,9 In particular, Lee et al.9 have determined that the cross section for the reaction O(1D) + C2H4 → CH3 + HCO is about 90 times larger than that of the O(3P) reaction at Ec = 3 kcal/mol. From the analysis of our LAB data at Ec = 8.4 kcal/ mol the ratio of O(1D)/O(3P) cross sections for CH3 formation was found to reduce to about 38, and at Ec = 13.7 kcal/mol to about 24, in line with the fact that the reactivity of O(3P) increases (because of the entrance barrier to reaction), whereas that of O(1D) decreases (being the reaction barrierless and dominated by long-range attractive forces). We found a reduction of the O(1D) contribution also for the CH2CO + H2 forming channel: the reactivity of O(1D) is about 18 times that of O(3P) at Ec = 8.4 and about 13 times at Ec = 13.7 kcal/mol, to be compared with the value of 38 found by Lee et al.9 at Ec = 3.0 kcal/mol. D


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The Journal of Physical Chemistry A In the present study at Ec = 13.7 kcal/mol, reactive signals have been observed at the mass-to-charge ratio m/z = 43, 42, 29, 15, and 14; however, product angular and TOF distributions have been measured only at m/z = 42, 15, and 14. For m/z = 15 and 14 it was mandatory to use soft ionization with 17 eV electron energy to suppress interferences arising from the dissociative ionization of the elastically/inelastically scattered C2H4 reactant beam (the appearance energies of CH 3 + and 13,12 CH 2 + from C 2 H 4 are 17 and 18 eV, respectively6). From the above measurements, which extend and complement our previous experiments at the lower Ec of 8.4 kcal/ mol,3,4 we have been able to unambiguously detect products from the five reaction pathways (1−5) (all channels then, with the exception of the CO + CH4 channel (6)the latter channel was observed to occur neither in our CMB studies at Ec = 8.4 kcal/mol nor in those of Lee et al. at Ec = 3 kcal/mol), characterize their dynamics, and determine their branching ratios. As discussed previously,3,4 the vinoxy product is detected at m/z = 42 because the parent ion CH2CHO+ (m/z = 43) is not very stable and fragments heavily to m/z = 42, especially at electron (or photon) energies higher than 12.5 eV.9,13 Consequently, all measurements of product angular and TOF distributions for the CH2CHO and CH3CO channels were carried out at the daughter ion m/z = 42, at which signal from also ketene (as parent ion) contributes. The CH3 and CH2 channels were probed at m/z = 15 and m/z = 14, respectively. The angular distributions, measured at m/z = 42 and m/z = 15 in a wide laboratory angular range (from 10° to 90°), are presented in Figure 1-lhs, top and bottom panels, respectively, together with the best-fit curves (see below). In the lower part of Figure 1 the velocity vector (so-called Newton) diagram of the experiment is also shown, with the circles delimiting the maximum speed that the various indicated products can attain by assuming that all the available energy for each channel (given by Ec − ΔH00) is channeled into recoil energy. The entire set of TOF distributions at selected LAB angles are shown in Figure 2 for m/z = 42 at six angles (left panel), m/z = 15 at four angles (center panel), and m/z = 14 at Θ = 34° (close to the center of mass angle) (right panel), together with the best-fit curves (see below). The reported LAB angular and TOF distribution at m/z = 42 have been obtained using 60 eV electron energy, whereas the data at m/z = 15 and 14 have been measured using 17 eV electrons. The m/z = 42 angular and TOF distributions were equally well measured at 17 eV electron energy for signal calibration purposes (not shown); in this case the fast shoulder in the TOF spectra due to ketene formation is somewhat more intense than at 60 eV, because ketene fragments to daughter ions relatively less at 17 eV than at 60 eV. The data at m/z = 15 carry the fingerprints of both principal channels, that is, H + CH2CHO (vinoxy) (via its daughter ions CH3+) and HCO + CH3 (via the parent ion CH3+). In fact, under the conditions of the present experiment, signal at m/z = 15 can only originate from the CH3 product (parent ion) (5) and the CH2CHO product (1) (that dissociates strongly to the daughter ion CH3+ even at this low electron energy). On the basis of energy and linear momentum conservation, the broad intense peak of the angular distribution, centered at the CM angle and exhibiting a clear backward−forward feature (Figure 1-lhs-top panel), and the slow intense peak of the TOF spectra (bimodal at the CM angle, Θ = 30°, where the TOF resolution is higher) (Figure 2, center panel) can be unambiguously

attributed to the heavy vinoxy radical product, whereas the two wide wings of the angular distribution and the fast broad peak distributed at around 100 μs of the TOF spectra arise from the methyl radical coming from both the O(3P) + C2H4 → CH3 + HCO and the O(1D) + C2H4 → CH3 + HCO reactions, as also found at lower Ec.4 The data recorded at m/z = 42, instead, carry the fingerprint of products from the three channels H + CH2CHO (via the daughter ion C2H2O+), H + CH3CO (acetyl) (via the daughter ion C2H2O+), and H2 + CH2CO (ketene) (via its parent ion). As for the m/z = 15 data, the relative contributions in the LAB angular distribution m/z = 42 (Figure 1-lhs-bottom panel) are disentangled through TOF measurements at selected LAB angles, as can be seen in Figure 2 (left panels). These spectra exhibit (i) a dominant peak, analogous to the main peak observed at m/z = 15, which is mainly due to dissociative ionization of vinoxy; (ii) a fast peak, which appears as a shoulder on the main peak and is unambiguously attributed, on the basis of energy and linear momentum conservation, to the ketene product from the channel CH2CO+H2; (iii) a small component, peaked at the CM velocity, which is attributed to formation of the acetyl radical from the channel CH3CO + H with a very small recoil energy. In addition, a contribution from O(1D) reaction is also present on the ketene channel; notably, to the contrary of what found at Ec = 8.4 kcal/mol4 (and also in the CMB study of Lee et al.9 at Ec = 3 kcal/mol), there was no need to invoke the CH2CO + H + H channel (however, a small contribution of this three-body channel could well be embedded into the small acetyl contribution, without possibility of disentangling it). The contribution of the CH3CO + H channel from O(3P) is also clearly inferred from the shape of the angular distribution at m/z = 42, as discussed below. We remark that, as already found at Ec = 8.4 kcal/mol, also at this higher Ec a comparison of the detailed shape of the angular distributions (measured in a fine grid of angles, i.e., every 2°) and of also the TOF spectra at m/z = 15 and 42 leads to an unambiguous determination of the CH3CO + H channel, which in contrast could not be identified in the study of Lee et al.9 at Ec = 3 kcal/mol in pulsed CMB experiments with soft PI detection, because of the coarse angular distributions obtained in those experiments by integration of the TOF spectra measured every 10°. We note that the likely reason the acetyl channel was not identified in Lee et al.’s experiments is that it represents a minor channel and this cannot be easily observed in TOF spectra at the parent mass just above its ionization threshold; on the contrary, it also cannot be readily observed at the daughter ion m/z = 42 using higher ionization energies in the presence of another dominant channel (the vinoxy channel). In contrast, a minor channel can more readily be observed in high-resolution angular distributions, measured with small error bars, especially when the channel is characterized by a very small recoil energy, because its intensity is strongly enhanced in the LAB frame, around the CM, due to the nature of the CM-to-LAB v/u2 (where v and u are the LAB and CM velocities of the detected product, respectively) Jacobian transformation.19 In fact, as can be seen from Figure 1lhs, whereas the m/z = 15 angular distribution has a clear dip at the CM angle (where the dominant contribution arises from dissociative ionization of vinoxy), that of m/z = 42 has a significantly less pronounced dip, because of the presence of an additional small contribution (with respect to that of vinoxy), just centered at the CM angle, i.e., that due to the acetyl product (see continuous green curve in Figure 1-lhs-bottom E


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The Journal of Physical Chemistry A panel). Furthermore, in the TOF spectra at the CM angle of 30° (Figure 2) the contribution of the CH3CO + H channel in the spectrum at m/z = 42 determines the clear difference with respect to the shape of the spectrum at m/z = 15 (to which only the vinoxy channel contributes around the CM velocity). The TOF data at m/z = 14 (Figure 2-right panel) exhibit, in addition to contributions from fragmentation of the ketene, vinoxy and acetyl products, very clearly also a fast peak that can only correspond, on the basis of energy and linear momentum conservation, to methylene formation from the channel CH2 + H2CO (formaldehyde). A small contribution to this fast peak comes also from fragmentation of the CH3 product, but this is small considering that the appearance energy of CH2+ from CH3 dissociative ionization is 15.1 eV.6 This was readily estimated from the known EI cross section as a function of electron energy of CH3 leading to CH3+ and CH2+ + H.6 Because of the many contributions to the reactive signal at m/z = 14, the sensitivity to the CM angular and translational energy distributions of the CH2 + H2CO channel is much lower than that, for instance, of the CH3 + HCO and CH2CHO + H channels. Nevertheless, from the TOF data at an angle close to the CM angle, considering that the CM functions for all the other contributing channels have been determined from data recorded at other masses, it has been possible to derive meaningful CM angular and translational energy distributions also for the CH2 channel (see below). It should be noted that the CH2 channel was not observed by Lee et al.9 at Ec = 3 kcal/ mol, whereas it had been clearly observed in their previous experiment at Ec = 6 kcal/mol.8 As described elsewhere,4,13,17 data analysis assumes a CM differential cross section I(θ,E′T) for each channel that is separable in the product of two parts: one depending only on the CM scattering angle, T(θ), and the other only on the product translational energy, P(E′T) (coupling between these two functions is weak under our experimental conditions). The total CM differential cross section at a given m/z is obtained by a weighted sum of the I(θ,E′T) for the various channels contributing to the signal at that m/z value: ICM(θ ,E′T ) = Σiαi[Ti(θ ) Pi(E′T )]

(7)

using a forward-convolution program with instrumental and experimental parameter inputs, along with a T(θ), a P(E′T), and a relative weight α for each channel i. The two CM functions and the relative weight for each channel were iteratively adjusted until calculated LAB angular distributions and TOF spectra matched those from experiment (Figures 1 and 2). The best-fit T(θ)’s and P(E′T)’s for the five channels from the O(3P) reaction leading to CH2CHO (1), CH2 (2), CH3CO (3), CH2CO (4), and CH3 (5) formation, as well as those for the two channels from the O(1D) reaction leading to formation of CH2CO + H2 and CH3 + HCO at Ec = 13.7 kcal/mol are depicted in Figure 3. These CM functions contain detailed information on the O(3P) + C2H4 and O(1D) + C2H4 reaction dynamics and on the extent of the intersystem crossing occurring in the O(3P) + C2H4 reaction. The O(3P) reaction dynamics, from both experiment and theory, and at the same time the reaction dynamics of O(1D) relative to the methyl and ketene forming channels will be discussed in section 4, where the experimental results will be compared with the theoretical predictions from the present QCT surface-hopping dynamical calculations on coupled multidimensional ab initio triplet and singlet PESs, which are described next.

Figure 3. Best-fit center-of-mass angular, T(θ) (lhs panels), and translational energy, P(E′T) (rhs panels), distributions for all channels (five) used in the best fits of Figures 1 and 2 at Ec = 13.7 kcal/mol. Line and color notations are as in Figures 1 and 2. Solid and dashed arrows indicate the total available energy for each product channel from the O(3P) and O(1D) reactions, respectively.

3. QUASICLASSICAL TRAJECTORY (QCT) SURFACE HOPPING CALCULATIONS The quasiclassical trajectory surface-hopping calculations for the O(3P) + C2H4 reaction were carried out at the collision energy of 13.7 kcal/mol on the basis of a triplet and singlet PES in a similar way as reported previously.3,4 Both triplet and singlet PESs were fit by a permutationally invariant polynomial approach20,21 based on high-level ab initio energy points. Figure 4 shows schematics of the singlet and triplet PESs, including the stationary-point structures and energies relative to the reagents O(3P) + C2H4 (with vibrational zero-point energies not included). As seen, there are many local minima, saddle F


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Figure 4. Schematic of triplet (a) and singlet (b) potentials employed in the present study. The fitted energies are in kcal/mol, relative to the reactants O(3P) + C2H4, and those shown in parentheses are from direct ab initio calculations of RCCSD(T)/aug-cc-pVTZ theory. All the energies are shown without vibrational zero-point energy correction. The biradical region, enclosed by the ellipse, is where the majority of surface hops occurs.

points, and product channels for the two PESs. Due to the complexity of the PESs for this system, the fitting is challenging to describe accurately all the stationary points and reaction channels. The comparisons made for the energies obtained from the current PESs and RCCSD(T)/AVTZ calculations show good agreement among them. These PESs have been used in surface hopping trajectory calculations of the title reaction. The trajectories were initiated from O(3P) + C2H4 on the triplet PES with C2H4 in the ground rovibrational state. Initial coordinates and momenta of C2H4 were obtained by randomly sampling the normal coordinates and momenta. Adjustments were then made to the momenta to enforce zero

angular momentum of C2H4. The initial distance of the O atom from the center of mass of C2H4 was (x2 + b2)1/2, where b is the impact parameter and x was set to 10 bohr. The orientation of C2H4 was randomly sampled, and b was scanned from 0 to bmax (where the reaction probability is zero) with a step size of 0.5 bohr. The value of bmax is 4.5 bohr for the collision energy of 13.7 kcal/mol. The trajectory surface hopping method employed is a modified version of the well-known Tully fewest-switches trajectory surface hopping algorithm with the extension of the time uncertainty algorithm,22−24 which has been successfully applied to simulate the three-state photodissociation dynamics of H2CO.25 The diabatic representation G


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significantly “sideways” peaked with a broad plateau centered at about 120° and extending between 90° and 150°; in addition, the T(θ) overall exhibits significantly more intensity in the forward direction with respect to the backward direction. The sideways shape in this angular range is similar to that derived previously by us at Ec = 8.4 kcal/mol, but with respect to the lower Ec, the forward (θ = 0°) to backward (θ = 180°) intensity ratio is now significantly more pronounced, being 1.0/0.5 with respect to 0.82/0.70. This increasing forward/backward intensity ratio with increasing Ec is typical of an “osculating complex” behavior.26,27 Notably, a pronounced sideways bump in the T(θ) was also derived by Lee et al.9 at Ec = 3 kcal/mol, but at this much lower Ec, the sideways peaking occurs at larger angles (peaking at around 150°) and the T(θ) exhibits the same intensity at the two poles, indicating that at this low Ec the ratio between the complex lifetime, τ, and its rotational period, τrot, is larger than 5−6, typical of a long-lived complex behavior.26,27 According to the “osculating model” of chemical reactions26,27 the increasing asymmetry toward the forward direction with increasing Ec indicates that the complex starts to osculate already at Ec = 8.4 kcal/mol (that is, the complex lifetime is of a few rotational periods). Notably, the average diradical lifetime in the QCT calculations at Ec = 13.7 kcal/mol is roughly 2.8 ps on the triplet PES, and 8.9 ps on the singlet PES. The QCT value of 2.8 ps on the triplet PES is comparable to the complex rotational period of a few picoseconds and therefore corroborates the significant backward/forward asymmetry T(180°)/T(0°) = exp(−τrot/2τ) = 0.5 for the vinoxy (Figure 3) which corresponds, within the osculating model, to τ/τrot ∼ 1. The preference for the sideways scattering reflects the preferential emission of the H atom from the triplet CH2CH2O intermediate complex nearly orthogonal to the plane of the three heavy atoms (CCO), as recently discussed in some detail,3,4 and similarly to what observed in the related F + C2H4 → CH2CHF + H reaction.28 However, the main characteristic of the CM angular distribution of vinoxy at this high Ec is the presence of a pronounced sideways bump superimposed on an asymmetric distribution strongly forward biased. Likely, different ranges of impact parameter b give rise to different angular scattering of the CH2CHO product, with small b values responsible mainly for the backward scattering, intermediate b values giving rise to sideways scattering and large b values to forward scattering. The shifting of the sideways scattering bump to smaller scattering angles with increasing Ec is what one would expect (in a direct reaction) when increasingly larger impact parameters contribute to the reaction. The product translational energy distribution P(E′T) for the CH2CHO + H channel has a maximum at 7.2 kcal/mol and extends up to about 28 kcal/mol (Figure 3). The average amount of energy released into product translation is 12 kcal/ mol, which corresponds to an average fraction ⟨f T⟩ of 0.39 of the total available energy, ETOT (ETOT = Ec − ΔH00 = 25.4 kcal/ mol). This fraction is somewhat lower than that derived at Ec = 8.4 kcal/mol (where ⟨f T⟩ = 0.43) and implies that about 61% of the available energy goes into internal excitation of the vinoxy product; that is, the extra translational (collision) energy when going from 8.4 to 13.7 kcal/mol is mostly channelled into internal excitation of the products. We note that the coupling between the P(E′T) and T(θ) functions is negligible at this Ec within the resolution of our experiment. Anyway, the assumption of separability between P(E′T) and T(θ) in the data analysis does not affect the conclusions of this work. Our

is used for the coupled two states of the title reaction, and the potential energy matrix is expressed as ⎡ V11 V21 ⎤ ⎢ ⎥ ⎣ V12 V22 ⎦

(8)

where V11 and V22 are the potential energies of singlet and triplet energies and V12 (=V21) represents the SO coupling between the singlet and triplet states. There are actually two singlet and two triplet states that are close in energy in the biradical region, and thus there are a total of 12 states that are spin−orbit coupled. Instead of considering this complex coupled-state picture, we followed Schatz and co-workers16 and used an average value of the magnitude of 12 SO coupling elements for each configuration and considered coupling only between the singlet and triplet PESs described above. In our surface hopping calculations, we used a constant of 35 cm−1 for the SO coupling between singlet and triplet PESs except in the asymptote regions where the SO couplings are zero. We did verify the validity of this choice for the calculations, which was discussed in detail previously.4 Roughly 170 000 trajectories were run for each b using the Bulirsch−Stoer integration scheme with adaptive step size for a maximum time of 300 ps, and a total of roughly 1.3 million trajectories were run. The trajectories were terminated when one of the internuclear distances became larger than 13 bohr. We found all of the trajectories ended up dissociating into various products using the maximum propagation time we set. For a specific product channel, the ZPE constrained analysis that considered trajectories in which each of the products has at least the corresponding ZPE was performed.

4. COMPARISON BETWEEN EXPERIMENTAL AND THEORETICAL RESULTS AND DISCUSSION 4.1. Experimental Results. The CM angular and translational energy distributions derived for the reaction channels involved in the O(3P) + C2H4 reaction and depicted in Figure 3 form the basis for the discussion of the reaction dynamics. In doing so, we refer to the detailed schematic of the triplet and singlet PESs of the reaction shown in Figure 4. Here, we will comment briefly also on the best-fit functions for the O(1D) reactions that are contributing to products coming from also the O(3P) reactions. One relevant issue is whether O(1D) can contribute to products formed on the triplet PES via singlet → triplet ISC. As discussed in the previous section, all trajectories are initiated on the triplet PES (O(3P) + C2H4); because we have not initiated trajectories also on the singlet PES (O(1D) + C 2 H 4 ), theoretically we have not obtained dynamical information on the O(1D) + C2H4 reaction dynamics. This was outside the scope of the present paper. However, we have commented elsewhere4 that O(1D) is not expected to contribute to the main CH3 + HCO product channel via singlet−triplet CH2CH2O ISC; in fact, as considered in the data analysis, CH3 can only be formed from the O(1D) + C2H4 reaction directly on the singlet PES (from singlet acetaldehyde), and from the O(3P) + C2H4 reaction via triplet → singlet CH2CH2O ISC. We have also commented previously that O(1D) also does not contribute to the CH2CHO + H channel via singlet → triplet ISC.4 4.1.1. CH2CHO + H Channel (1). The best-fit CM functions derived for the reaction channel O(3P) + C2H4 → CH2CHO + H are shown in the second row of panels of Figure 3. As seen, the CM angular distribution, T(θ), of the vinoxy product is H


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Table 1. Product Branching Ratios of the O(3P) + C2H4 Reaction at Three Different Collision Energies, as from Kinetics and Dynamics Studies, and from QCT-SH Calculations at Ec = 8.4 and 13.7 kcal/mol

a

product:

CH2CHO

CH2

CH3CO

CH2CO

CH3

reference:

vinoxy

methylene

acetyl

ketene

methyl

kinetics exptsa (∼300 K) (Ec ∼ 0.9 kcal/mol) CMB exptsa (Ec = 8.4 kcal/mol) theory (QCT-SH)a (Ec = 8.4 kcal/mol) CMB expts (this work) (Ec = 13.7 kcal/mol) theory (QCT-SH) (this work) (Ec = 13.7 kcal/mol)

0.39 ± 0.10 0.30 ± 0.06 0.27 0.33 ± 0.07 0.33

0.06 ± 0.03 0.20 ± 0.05 0.08 0.21+0.02−0.08 0.11

0.03 ± 0.01 0.11 0.02 ± 0.01 0.07

0.019 ± 0.001 0.13 ± 0.04 0.05 0.13 ± 0.03 0.04

0.53 ± 0.04 0.34 ± 0.09 0.49 0.31 ± 0.08 0.45

See ref 4.

corresponding best-fit functions are shown in Figure 3-top panel: as can be seen, the T(θ) function of the CH2CO product from O(3P) is backward−forward symmetric and isotropic and is similar to that derived by us at Ec = 8.4 kcal/mol and by Lee et al.9 at Ec = 3 kcal/mol. The symmetry of the T(θ) indicates that the reaction is proceeding via a long-lived complex mechanism. In fact, the formation of singlet ketene implies an ISC process that leads the initially formed triplet biradical to a singlet biradical that can isomerize to very stable singlet acetaldehyde (Figure 4), which in turn, because of its high internal energy content, can undergo a four-center H 2 elimination process leading to formation of ketene. The T(θ) of ketene from O( 1D), which was backward−forward symmetric at Ec = 8.4 kcal/mol, is forward peaked at higher Ec (here the sensitivity to the backward peak is, however, very low), indicating that the intermediate complex starts to osculate.26,27 The P(E′T) of the CH2CO + H2 channel from O(3P) peaks at about 40 kcal/mol and extends to about 90 kcal/mol (ETOT = 98.8 kcal/mol); the average fraction of energy released in translation is ⟨f T⟩ = 0.45, a value somewhat higher than that (⟨f T⟩ = 0.36) derived at Ec = 8.4 kcal/mol; however, the shapes of the P(E′T) are similar at the two Ec’s. The P(E′T) for the corresponding O(1D) reaction peaks at about 65 kcal/mol and extends up to about 140 kcal/mol (ETOT ∼ 143 kcal/mol); the average fraction of energy released in translation is 0.49, somewhat larger than for O(3P), and also larger than the value (0.41) observed at Ec = 8.4 kcal/mol. The peaking at very high energy indicates that the elimination of H2 requires to overpass a very high exit potential barrier; theory calculates a barrier of 60 kcal/mol with respect to products (Figure 4). 4.1.4. CH2 + H2CO Channel (2). The best-fit CM functions for this channel are shown in Figure 3 (fourth row of panels from top). These products can be formed adiabatically on the triplet PES (Figure 4). The T(θ) of methylene is backward− forward distributed with a pronounced polarization and a pronounced forward bias, consistent with an osculating complex mechanism. The P(E′T) peaks at about 10 kcal/mol and has an average amount of energy in translation of about 9 kcal/mol, corresponding to a fraction of ⟨f T⟩ ∼ 0.5 (the total available energy is 20 kcal/mol). This high fraction of energy in translation indicates the existence of a high exit potential barrier and this is consistent with the calculations of the PES that find an exit barrier of about 6 kcal/mol with respect to the product asymptote (Figure 4). 4.1.5. CH3CO + H Channel (3). The best-fit CM functions for the acetyl forming channel is shown in Figure 3-bottom panels. The T(θ) of acetyl is backward−forward distributed with a slight backward bias and a considerable degree of polarization, consistent with a long-lived/osculating complex mechanism.26,27 The P(E′T) is characterized by a narrow peak

experimental data are very sensitive to the rising and peaking of the P(E′T) function, but significantly less to its falloff and cutoff value. The comparison between the simulations of the LAB data using the QCT-SH results (section 4.3) and the best-fit curves will exemplify the sensitivity of the data to the shape of both the T(θ) and P(E′T) functions. All previous CMB studies of this reaction, including that of Schmoltner et al.,11 agree on the sideways aspect of the vinoxy angular distribution and that the P(E′T) function of this channel peaks away from zero, which are indications that the ejection of the H atom occurs outside of the plane of the CCO heavy atoms overpassing a sizable exit potential barrier; this is theoretically calculated to be 8.3 kcal/mol (Figure 4). 4.1.2. CH3 + HCO Channel (5). This channel can be formed from the O(3P) and O(1D) reactions. The corresponding CM best-fit functions for both reactions are shown in Figure 3 (third raw of panels from top). As can be seen from the figure, the T(θ) of the CH3 product from O(3P) is backward−forward distributed, with a pronounced forward bias, and strongly polarized (i.e., its intensity at 90° is much lower than at the two poles, especially at 0°). The CH3 T(θ) from O(1D) on the singlet PES is similar to some extent, but with a significantly stronger forward bias. In both cases the reaction is proceeding via an osculating complex mechanism (as for the vinoxy channel), with the complex lifetime of the O(1D) reaction being shorter than that of the O(3P) reaction because of the higher total energy of the singlet complex formed from O(1D). The trend with Ec, as shown by the results at the lower Ec = 8.4 kcal/mol,4 confirms the osculating complex mechanism. The polarization of the angular distribution reflects the partitioning of the total angular momentum and indicates a coplanar type reaction, as recently discussed.3,4 The P(E′T)’s obtained at Ec = 13.7 kcal/mol witness a modest fraction (0.21 for O(3P) and 0.24 for O(1D)) of the total available energy released as product recoil energy. These fractions are slightly larger than those observed at Ec = 8.4 kcal/ mol (0.14 for O(3P) and 0.22 for O(1D)) and are in line with those derived by Lee et al.9 at Ec = 3 kcal/mol (f T = 0.087 for O(3P) and 0.081 for O(1D)). It is interesting to note that the internal excitation of the CH3 and HCO products is extremely high in the case of the O(1D) reaction, where about 80% of the total available energy (87.9 kcal/mol at Ec = 13.7 kcal/mol) is anticipated to go in internal energy. The fact that the various CMB studies of the reaction channel O(3P) + C2H4 → CH3 + HCO find a P(E′T) that rises quickly and peaks at low values of translational energy indicates the absence of an exit potential barrier, and this is confirmed by the theoretical calculations of the PES (Figure 4) and by the present QCT calculations (section 4.3). 4.1.3. CH2CO + H2 Channel (4). Also this channel can originate from both the O(3P) and O(1D) reactions. The I


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two channels coming from the triplet state, CH2CHO + H and CH2 + H2CO, increase slowly with the increase of collision energy; the former increases from 27% to 33%, and the latter increases from 8% to 11%. Notably, the theoretical predictions as a function of Ec, while slightly overestimating the experimental CH3 yield at high Ec and underestimating that of CH2CHO at low Ec, do exhibit the same qualitative trend with Ec observed in the experiment. Theory predicts the ketene and acetyl yields to be nearly constant with Ec, whereas the CH2 yield to increase with Ec, in qualitative agreement with the experiment. Overall, the variation of branching ratios of these products with the collision energy is not pronounced. As shown in Figure 8b of ref 4, the computed branching ratio of channels arising from the singlet PES (via ISC) tends to decrease slightly, whereas the branching ratio of those arising from the triplet PES tends to increase slightly, as expected on the basis of a shorter lifetime of the intermediate complex with increasing Ec and consequent lower probability of ISC. From the experiment, although the extent of ISC decreases slightly as the collision energy increases, within the error bars it can be considered nearly constant, at least in the investigated energy range. Both theory and experiment indicate that the collision energy is not playing a very significant role in the branching ratios. A similar situation was found to occur also for the O(3P) + C2H2 reaction.14 4.3. Detailed Comparison of the Main Channels at Ec = 13.7 kcal/mol. Here we will focus on the dynamics information at Ec = 13.7 kcal/mol. As the vinoxy, the CH3, and the CH2 channels account for more than 80% of the total products (Table 1), a comparison of the detailed dynamics of these channels from experiment and theory (PESs and dynamics) is interesting and useful. Figure 5 shows the comparisons between theory and experiment for the T(θ) and P(E′T) distributions for the three channels, CH2CHO + H,

with a steep rising and a maximum at only 2 kcal/mol, and then it decays with a tail up nearly the limit of energy conservation for the O(3P) reaction. Because the total available energy is 37 kcal/mol for channel (3), the average fraction of energy in translation is small (⟨f T⟩ ∼ 0.2). This P(E′T) is in line with that derived at the lower Ec of 8.4 kcal/mol.4 It should be noted that the acetyl channel has not been observed in the studies by Lee et al. at Ec = 3 kcal/mol9 and 6.4 kcal/mol.8 4.2. Branching Ratios and Extent of Intersystem Crossing. One of the most useful pieces of information desirable on the dynamics of a multichannel reaction is the branching ratio of the various channels. The derivation of the BRs at Ec = 8.4 and 13.7 kcal/mol from the experimental data and from the QCT-SH calculations has been discussed in detail in ref 4. The experimental and theoretical BRs are summarized in Table 1, together with those derived from kinetics studies at 300 K. The behavior of the BRs as a function of collision energy from both experiment and theory was examined in graphical form in our previous paper.4 It should be noted that the QCTSH results at Ec = 12.9 kcal/mol (reported in ref 4) and at Ec = 13.7 kcal/mol are essentially the same. As discussed there, there are not major variations of the experimental product yields with increasing Ec (see ref 4). When the yields of products coming from the triplet PES and from the singlet PES were added up, the triplet and singlet yields as a function of Ec were also examined. Experimentally, it appears that the yield of triplet products (vinoxy and methylene) increases slightly with increasing Ec, from a fraction of 0.50 ± 0.10 at Ec = 8.4 kcal/mol to 0.54 ± 0.10 at Ec = 13.7 kcal/mol, whereas the opposite holds for the singlet products (CH3, ketene, and acetyl) whose fraction decreases from 0.50 ± 0.10 at Ec = 8.4 kcal/mol to 0.46 ± 0.10 at Ec = 13.7 kcal/mol. However, although the slight trend with Ec appears to be clear (see Figure 8 in ref 4), the fractions can be considered to be nearly constant within the error bars of ±0.10. This nearly constant behavior with the variation of Ec is perhaps not too surprising considering that the probability of ISC is proportional to the complex lifetime, and this remains long (i.e., of the order of the rotational period) even at the highest Ec of 13.7 kcal/mol. It should be noted that a slight decrease of ISC with increasing Ec correlates nicely with a slight decrease of the complex lifetime as Ec increases. This kind of behavior with Ec was also found for the related reaction C(3P) + C2H2, both experimentally and theoretically.29 Theoretically, it has been found that the ISC between the triplet and singlet PESs occurs very efficiently. We recall that formation of CH3 + CHO and CH3CO + H on the triplet PES is prevented at the experimental collision energies by a high isomerization barrier (∼12 kcal/mol above the reactant asymptote) from the initial biradical adduct to triplet acetaldehyde (Figure 4). As seen from Table 1, the QCT calculated CH3 channel is dominant, accounting for about 50% of the total products at the three energies (see also ref 4). As the collision energy increases from 8.4 to 13.7 kcal/mol, the fraction of CH3 channel decreases a bit, roughly from 49% to 45%. The same trend can be found for another channel CH3CO, which is also coming from the singlet PES; in fact, the branching ratio of CH3CO + H decreases from about 11% to 7% with the increasing energy. The branching ratio of CH2CO + H2 product formed on the singlet PES is very small, remaining a constant of about 4% for varied energies. In contrast, we can find that the fractions of

Figure 5. Center-of-mass translational energy distributions (rhs) of H + CH2CHO (top), CH3 + HCO (middle), and CH2 + H2CO (bottom), and angular distributions (lhs) of CH2CHO (top), CH3 (middle), and CH2 (bottom) as obtained by theory (dashed-dotted lines) and experiment (continuous lines) for the O(3P) + C2H4 reaction at Ec = 13.7 kcal/mol. Arrows indicate the total available energy for the various channels (for CH3 + HCO it is 42 kcal/mol and therefore falls outside the graph range). J


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The Journal of Physical Chemistry A CH3 + HCO, and CH2 + H2CO. As shown, the agreement between theory and experiment is overall good, but some small differences are present. To show the sensitivity of the experimental data to the CM functions, we have tested the reliability of the QCT predictions for each of the above three channels directly toward the experimental (LAB) data by using the theoretical CM functions in the simulation procedures (see below). As the pathway leading to CH3 + HCO on the singlet PES is barrierless, the statistical distributions of energies of different degrees of freedoms are responsible for this channel. Both theory and experiment show that a small fraction of the total available energy (Etot ∼ 42 kcal/mol) is released as translational energy, and this implies high internal (ro-vibrational) excitations of the molecular radical products. In our previous study at Ec = 8.4 kcal/mol we investigated whether CH3 or HCO is highly rotationally excited or vibrationally excited, and we concluded that most of the total available energy available is partitioned into vibrational excitation of CH3 or HCO. Similar findings hold also at Ec = 13.7 kcal/mol. Figure 5-middle panels show that there is a good agreement between the QCT predictions and experiment for this channel. Specifically, the theoretical P(E′T) rises a bit more slowly and peaks at a somewhat higher energy than the best-fit (BF) P(E′T). This should have the effect of accelerating a little bit or, rather, making the calculated TOF distribution on the low velocity side a little bit narrower with respect to experiment. Indeed, the effect can be appreciated in Figure 7 where, because of less intensity on the low velocity side of the QCT CH3 TOF distribution, there is a resulting lower intensity between the CH3 (fast) peak and the CH2CHO (slow) peak. Note that the peak of the CH3 TOF distribution from QCT does not move in an appreciable manner to higher velocities with respect to the BF curve, because the overall difference is small between the BF and QCT P(E′T)’s and, in addition, there is a slight compensatory effect due to the fact that the QCT T(θ) is slightly less polarized and more symmetric with respect to the BF one (Figure 5). Regarding the CH3 T(θ), the QCT one is qualitatively similar to the best-fit one, just slightly less polarized and less forward biased. This should have mainly the effect of a predicted slightly lower forward intensity in the LAB frame angular distribution, as can be appreciated in Figure 1-rhs-upper panel. However, the differences between the QCT and BF LAB angular and translational energy distribution for the CH3 + HCO channel are small and can be considered to fall only slightly outside the estimated experimental error bars of the BF functions. Regarding the CH2CHO + H channel, as can be seen from Figure 5-rhs-top panel, there is quite a good agreement between theory and experiment for the P(E′T) function: in fact they both peak at the same energy value; however, the theoretical curve is a bit narrower than the experimental one and in particular it rises a little bit too fast and declines a little bit too soon. The sensitivity of the data for this channel is very high, and in fact, the effect of these small differences is that the calculated TOF distributions are clearly slower than the experiment at all the angles, as can be seen in Figure 6. Furthermore, the fact that the P(E′T) rises too early has the effect of removing the incipient bimodality in the TOF spectra, clearly visible at the four smaller angles (Figure 6-rhs) and especially the bimodality in the angular distribution (Figure 1rhs-lower panel). In conclusion, although the P(E′T) from QCT calculations resembles closely the experimental P(E′T), it

Figure 6. Comparison between experiment and theory in the LAB frame. (lhs) best fit of TOF distributions at m/z = 42 (as in Figure 2). (rhs) simulation of the TOF distributions at m/z = 42 using the T(θ) and P(E′T) functions for the vinoxy channel obtained from the QCTSH calculations and depicted in Figure 5.

falls well outside the experimental error bars, which are quite small for the H-elimination channel. The comparison of the T(θ) distributions also evidence significant differences between theory and experiment for this channel. Although at a first look the two T(θ) curves exhibit some similar sideways scattering (Figure 5-lhs-top panel), the theoretical curve is significantly less asymmetric, has a wider sideways plateau and does not have a dip at around 45°. These differences, together with the somewhat less energetic P(E′T) have the very pronounced effect of producing a LAB angular distribution, which is strongly peaked at the CM angle rather than being bimodal, and that is narrower and more backward biased with respect to experiment (Figure 1-rhs-bottom panel). That is, the experimental data are very sensitive to the rise and width of the P(E′T), and to the detailed shape of the T(θ), in particular the forward−backward asymmetry. In conclusion, there is an K


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procedures to provide an analytical PES) and perhaps the use of quasiclassical trajectories to describe the light H atom dynamics for a polyatomic reaction of this complexity. For the CH2 + H2CO channel the agreement between experiment and theory is also overall very good, as can be seen from Figure 5-bottom panels. In particular, the theoretical T(θ) is only less forward biased than experiment and the P(E′T) distributions has the same rise, being simply somewhat narrower than the experimental one. Because of the limited amount of experimental data at m/z = 14 (only one TOF spectrum at Θ = 34°, Figure 2), there is not much sensitivity to the degree of asymmetry of the T(θ)) whereas some sensitivity is present about the width of the P(E′T); in fact, the QCT P(E′T) is overall less energetic than the experimental one and the effect is to slow down a little bit the calculated TOF peak attributed to the CH2 product (Figure 8). The theoretical calculations for the CH2 + H2CO and CH2CHO + H channels support that the dynamics of the two channels is dominated by the exit channel barrier, with the P(E′T) of the former peaking at around 10 kcal/mol and the latter at around 7−8 kcal/mol, from both theory and experiment. Both P(E′T) distributions reach up to the total available energy of about 15 and 25 kcal/mol, respectively for CH2 and vinoxy channels; however, the theoretical results rise and go down a bit faster than the experimental results. As seen from Figure 5-lhs, the theoretical T(θ) distributions of the three product channels closely resemble the experimental ones. The CH2 angular distribution is backward−forward distributed with a forward bias and polarized. This indicates that in the reaction O(3P) + C2H4 the CH2 and H2CO coproducts depart on the same plane of the heavy C−C−O atoms at the transition state, which contains the initial relative velocity vr; that is, the final relative velocity v′r lies in the same plane of the initial vr and therefore the initial and final angular momentum Li and Lf, which are perpendicular to the scattering plane defined by vr and v′r, lie (parallel or antiparallel) on the

Figure 7. Comparison between experiment and theory in the LAB frame. (lhs) best fit of TOF distributions at m/z = 15 (as in Figure 2, but enlarged). (rhs) simulation of the TOF distributions at m/z = 15 using the T(θ) and P(E′T) functions for the methyl channel obtained from the QCT-SH calculations and depicted in Figure 5.

overall good qualitative agreement between experiment and theory, but from the quantitative point of view the data are extremely sensitive to minor details of the PES for this kinematically favored H-elimination channel and perhaps these details cannot be provided sufficiently accurate by the current ab initio electronic structure techniques (and related fitting

Figure 8. Comparison between experiment and theory in the LAB frame. (Top) best fit of TOF distributions at m/z = 14 (as in Figure 2). (Bottom) simulation of the TOF distributions at m/z = 14 using the T(θ) and P(E′T) functions for the methylene channel obtained from the QCT-SH calculations and depicted in Figure 5. L


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sensitivity of the experimental data to details of the PES is highest. The behavior of the P(E′T) distributions of CH2CHO + H and CH2 + H2CO, characterized by a large fraction of total available energy released in translation, supports that the dynamics of these two channels is dominated by the exit channel barrier on the triplet PES. In contrast, the pathway leading to CH3 + HCO on the singlet PES is barrierless on the exit channel, and a smaller fraction of total available energy is released as translational energy. For the CH2CHO channel we find a nearly isotropic angular distribution, with a broad, clear preference for sideways scattering from both theory and experiment. However, the experimental T(θ) is significantly more forward biased than the QCT-SH results, and this difference manifests itself very clearly in the LAB simulations. In contrast, the T(θ) for the CH3 and CH2 is backward−forward distributed, with a forward bias, and polarized. The very different peculiar shapes of the angular distributions for the three channels reflect a very different partitioning of the total angular momentum and correlation between the initial (reactant) and final (product) relative velocity vectors. Considering the good overall agreement between detailed theoretical and experimental results for the O(3P) + C2H4 reaction also at high Ec, we can conclude that QCT surfacehopping calculations, using reliable coupled multidimensional PESs, can yield reliable dynamical information for polyatomic multichannel reactions in which ISC plays an important role. It is certainly desirable to extend this kind of dynamical calculations to also more complex O(3P) + unsaturated hydrocarbon reactions, such as those with three-carbon alkynes and alkenes,7 such as propyne,30 allene,31 and propene,32,33 for which reactive scattering data of similar quality to those reported here for ethylene have been recently obtained. As a general conclusion, we can say that detailed CMB studies on multichannel reactions, possibly combined with synergic theoretical investigations, contribute to bridge the gap between crossed molecular beam dynamics and thermal kinetics research, by providing detailed information on the primary products and their branching ratios as a function of relative translational energy (temperature). This information for O(3P) + unsaturated hydrocarbons maybe particularly valuable for improving combustion as well as astrochemistry models.7,34

same plane. These relationships are similar to what was found and verified for the CH3 + HCO channel,3 with the two products leaving on the same plane of the heavy atoms. As shown in Figure 5, the CH3 angular distribution is backward− forward distributed and polarized, slightly favoring the forward scattering, and this is consistent with an “osculating complex” mechanism.26,27 The T(θ)’s for the CH2 and CH3 channels are different from that of the vinoxy channel, whose angular distribution is nearly isotropic, with some broad, clear preference for sideways scattering, indicating that the hydrogen atom is emitted from the decomposing collision complex nearly orthogonal to the plane of the heavy atoms at the transition state. As discussed in ref 4, because this is a Heavy + Heavy Light → Heavy Heavy + Light reaction, most of the initial orbital angular momentum (in this case J because ji is very small) goes into jf and, as a result, Lf, which is perpendicular to the final relative velocity v′r is small, and J (and hence jf because Lf is very small) tends to be along v′r. The sideways scattering of the CH2CHO product resembles the sideways scattering of the CH2CHF product observed in the well-known F(2P) + C2H4 reaction.28 These types of scattering were elegantly elucidated since the early days of reaction dynamics by Herschbach in the context of alkali atom reactions.26

5. SUMMARY AND CONCLUSIONS We have reported combined experimental and theoretical studies for the O(3P) + C2H4 multichannel nonadiabatic reaction at the relatively high collision energy of 13.7 kcal/mol. This work complements our previous combined experimental and theoretical studies at the lower collision energy of 8.4 kcal/ mol.3,4 ISC has been found to play an important role also at this high energy for the title reaction. From the full-dimensional, QCT surface hopping calculations on the coupled triplet and singlet PESs and CMB experiments, taking into account also kinetics results at room temperature, we have assessed the extent of ISC and the branching ratios for the various product channels as a function of collision energy. According to both experiment and theory, the variation of branching ratios of five product channels, CH2CHO + H, CH3CO + H, CH2CO + H2, CH3 + HCO, and CH2 + H2CO, with the collision energy is not pronounced. In particular, the branching ratio of channels arising from the singlet PES (via ISC) decreases slightly, whereas the branching ratio of those arising from the triplet PES increases slightly, as expected on the basis of a shorter lifetime of the intermediate complex with increasing Ec and consequently lower probability of ISC. Detailed comparisons were made between theory and experiment at Ec = 13.7 kcal/ mol for the translational energy and angular distributions of three most significant channels, CH2CHO + H, CH2 + H2CO, and CH3 + HCO, the former two occurring on the triplet PES and the latter on the singlet PES (following ISC from the triplet PES). The agreement between experimental and theoretical functions is overall good, indicating that theory has reached the capability of describing complex multichannel nonadiabatic reactions. However, small, yet significant, differences between the theoretical and the experimental angular and translational energy distributions exist, and the simulations in the LAB frame of the experimental observables using the theoretical functions fall outside the experimental error bars; this is especially well noticeable for the CH2CHO + H channel, for which the

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS N.B., F.L., and P.C. acknowledge financial support from the Italian “Ministero Istruzione, Università e Ricerca - MIUR (FIRB 2010-2011, Grant 2010ERFKXL). This work was supported in part by the EC COST Action CM0901 “Detailed Chemical Models for Cleaner Combustion” (2010-2013). N.B., F.L., and PC. thank G. Capozza and E. Segoloni for contributing to the early data collection. B.F. thanks the National Natural Science Foundation of China (21303197), Youth Innovation Promotion Association (2015143), and the M


Article

The Journal of Physical Chemistry A Chinese Academy of Sciences for financial support. J.M.B. thanks the US Department of Energy (DE-FG02-97ER14782) for financial support.

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Crossed Molecular Beams and Quasiclassical Trajectory Surface

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