Roaming Dissociation of Ethyl Radicals - American Chemical Society

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Roaming Dissociation of Ethyl Radical Akira Matsugi J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 26 Nov 2013 Downloaded from http://pubs.acs.org on December 1, 2013

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The Journal of Physical Chemistry Letters

Roaming Dissociation of Ethyl Radical Akira Matsugi*

National Institute of Advanced Industrial Science and Technology, 16-1 Onogawa, Tsukuba, Ibaraki 305-8569, Japan.

Corresponding author

*E-mail: [email protected]

Notes

The author declares no competing financial interest.

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ABSTRACT Previous studies on the photodissociation of C2H5 reported rate constants for H-atom formation

several

orders

of

magnitude

smaller

than

that

predicted

by

Rice-Ramsperger-Kassel-Marcus (RRKM) theory. This Letter provides a potential explanation for this anomaly, based on direct trajectory calculations of C2H5 dissociation. The trajectories reveal the existence of a roaming dissociation channel that leads to the formation of C2H3 and H2. This channel is found to proceed over the ridge between the transition state of H-atom elimination and that of bimolecular H-abstraction. The formed C2H3 radical can subsequently dissociate to C2H2 and H atom; this secondary dissociation is suggested to be a potential reason for the unexpectedly slow H-atom formation observed in the photodissociation experiments.

TOC GRAPHIC:

KEYWORDS: ethyl radical; unimolecular dissociation; classical trajectory; roaming dynamics; RRKM theory


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MAIN TEXT Ethyl radical, C2H5, is an intermediate of central importance in hydrocarbon combustion,1 and consequently the kinetics of its thermal decomposition has been extensively studied.1–6 There have also been numerous studies carried out on the photodissociation process of C2H5 to elucidate its dissociation dynamics.7–13 Among them, time-resolved photodissociation experiments8,11 that accessed the 3s Rydberg band of C2H5 posed an as yet unresolved question: whether statistical models for reaction rates, such as Rice-Ramsperger-Kassel-Marcus (RRKM) theory,14,15 can explain the observed dissociation rates.

Upon excitation into the 3s state, some of the C2H5 radicals return to the ground electronic state, whereas others directly dissociate, with an excited-state lifetime of ≈ 20 fs.10,13 The energized C2H5 radicals that result from the fast internal conversion then dissociate on the ground-state potential energy surface (PES) to form C2H4 and H atom. The translational energy of the H atoms produced upon the photoexcitation of C2H5 at ca. 250 nm exhibits a bimodal distribution.9,11 This illustrates the competition between the dissociation directly from the 3s state of C2H5 and from the ground state. In the latter process, the fraction of energy released into translation, 〈T 〉, was determined to be 0.19,11 typical for statistical dissociation reactions. However, the microcanonical rate constant of this process has been reported to be ≈107 s−1,8,11 in contrast to that expected from RRKM theory, ≈1012 s−1.8 This unexpectedly small rate was derived from the observed temporal profile of H atoms; the profile showed a prompt rise within the time-resolution of the experimental setup (roughly 10 ns),11 followed by a slow rise which had a maximum at 100–200 ns.8,11 These measurements suggest that there is a 3 ACS Paragon Plus Environment


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component of unimolecular dissociation several orders of magnitude slower than that predicted by RRKM theory.

Motivated by this anomalous experimental observation, Bach et al.16,17 and Wagner et al.18 performed classical trajectory calculations on the dissociation of C2H5. The trajectory calculations of Bach et al. were carried out on a PES that was directly evaluated using density functional theory (DFT), and identified quasi-periodic trajectories that might explain the unusually long lifetime of energized C2H5 radicals. However, the actual lifetime of such trajectories could not be determined because of the limited time range of their calculation (up to 2 ps) compared with the experimental lifetime of 100−200 ns. Recently, Wagner et al.18 reported a trajectory study on the semi-empirical PES of C2H5 with an integration time up to as much as 100 ps. Although they found some indication of multiexponential decay at high excitation energies, the overall dissociation rates were consistent with RRKM theory and no evidence was found for lifetimes of more than a nanosecond. Similar conclusions had also been drawn in the earlier trajectory studies of Hase and co-workers.19–21

This Letter, reporting another classical trajectory study on C2H5 dissociation, aims to provide an alternative explanation for the unexpectedly slow H-atom formation from energized C2H5 radicals. The present trajectory calculations were carried out on a PES directly evaluated using the ωB97X-D hybrid DFT method22 with 6-31+G(d,p) basis set and spin-unrestricted approximation. The Gaussian 09 program23 was used for the DFT calculation. This method gave the zero-point energy (ZPE)-corrected reaction energy and reverse barrier height for the C2H5 → C2H4 + H2 reaction of 164.8 and 14.2 kJ mol−1, respectively. These are comparable to the QCISD(T)/complete basis set (CBS) 4 ACS Paragon Plus Environment

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values6 of 146.4 and 11.8 kJ mol−1, considering the high excitation energy used in the trajectory calculations. The initial conditions of the trajectories were generated by classical microcanonical sampling24 using the global minimum of C2H5 as a reference geometry. The excitation energy of 478.5 kJ mol−1 (corresponding to a wavelength of 250 nm) above the ZPE of C2H5 was randomly distributed among the normal modes with the constraint that all modes had to contain at least ZPEs. The phases of each vibrational mode were also randomly determined. Then, the normal-mode displacements and momenta were iteratively scaled with the constraint of zero total angular momentum so that the total vibrational energy matched the desired excitation energy to within 0.1 kJ mol−1. 3600 trajectories were integrated using the velocity Verlet algorithm with a time step of 0.2 fs, which gave typical root-mean-square of energy drifts of 0.1–0.5 kJ mol−1. The trajectory was terminated if the product pair reached a separation of 10 a.u. (5.3 Å).

The time profiles of the ensemble-averaged population of C2H5 and products are plotted in Figure 1. The dissociation time, tdis, was calculated as tdis = tsep − tdelay where

tsep is the time when the fragments reached a 10 a.u. separation, and tdelay is the delay time which is defined as tdelay = (rf − r0) / v where rf and r0 are the final and initial distances between the nuclei that correspond to the dissociating bond, and v is the relative velocity of the separating fragments. All of the trajectories dissociated within 12 ps. The C2H5 population decay exhibits single-exponential behavior and the least-squares fit to an exponential decay function (shown as a black dotted line in Figure 1) gives the dissociation rate constant, k1, of 6.8 × 1011 s−1, which is in good agreement with those obtained by RRKM theory8 and the trajectory calculation of Wagner et al.18



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The three product channels are found in the present calculation:

C2H5

→ C2H4 + H

(1a)

→ C2H3 + H2

(1b)

→ CH3 + 3CH2 (1c)

The dotted lines drawn for the product profiles in Figure 1 represent the exponential growth functions, φ [1 − exp(−k1t)], where φ is the branching fraction. These functions reproduce the observed time profiles of all three channels, indicating that the dissociation process can be described by a statistical model.

Figure 1. Time profiles of the ensemble-averaged population of C2H5 and products (solid lines) and the corresponding exponential decay and growth functions (dotted lines).


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As expected, C2H5 radicals predominantly dissociate to C2H4 + H (1a), with a branching fraction of 98.3% (3540 out of 3600 trajectories). For this channel, the fraction 〈T 〉 was calculated to be 0.22, which is comparable to the recent experimental value of 0.19.11 Several trajectories were found to experience one or more isomerization reaction (i.e., H-atom migration from the CH3 to CH2 group) before dissociation. This causes intramolecular H-atom scrambling. The fraction of H atoms eliminated that was initially located at the CH3 group, FH, was 0.80, reproducing the regioselectivity observed in the photolysis of CD3CH211 and reported in the trajectory study of Wagner et al.18 (note that Wagner et al. compared the calculated FH with an incorrect value of 0.95 ± 0.05; the actual fraction observed in the experiment11 was ≈ 80% for the dissociation of CD3CH2). As described above, the present trajectory calculation accurately reproduces the majority of the experimental observations, except for the anomalously large time constant for H-atom formation.

There are two minor product channels previously unidentified: C2H3 + H2 (1b) and CH3 + 3CH2 (1c), for which the branching fractions are 1.4% (50 out of 3600 trajectories) and 0.3% (10 out of 3600), respectively. Some trajectories lead to direct cleavage of the C–C bond, resulting in channel 1c, which is energetically accessible with an excitation at 250 nm11 but is significantly higher in energy than the other channels. Channel 1b, the primary focus of this Letter, is the direct elimination of H2 from C2H5, leading to the formation of vinyl radical, C2H3. The endothermicity of this channel is 189.8 kJ mol−1, calculated by ωB97X-D/6-31+G(d,p), which is only 25.0 kJ mol−1 higher in energy than channel 1a. However, no first-order saddle point could be located for channel 1b. Geometry optimizations were attempted to find the saddle point



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that correlates C2H5 and C2H3 + H2, but they converged to either the transition state (TS) of H-atom elimination (channel 1a) or to the TS of bimolecular H-abstraction reaction, C2H4 + H ⇄ C2H3 + H2. The non-existence of a first-order saddle point for channel 1b was also ascertained by Mebel et al.25 who argued that the unpaired σ electron of C2H3 cannot interact with the H–H bond of H2, and concluded that the insertion of C2H3 to H2 cannot occur directly. Nevertheless, the trajectory calculations suggest the presence of a small but discernible fraction of C2H3 + H2 products.

Inspection of the trajectories leading to channel 1b revealed that the dissociation proceeds over the ridge between the TS of channel 1a and that of the C2H4 + H ⇄ C2H3 + H2 reaction. Figure 2 illustrates the snapshots and time evolutions of selected bond lengths for a representative trajectory that dissociates to C2H3 + H2. In this trajectory, the dissociation process begins at 1500 fs and is completed at approximately 1580 fs. Before the dissociation occurs, the C–H stretch has larger amplitude than C–Hʹ (see snapshot (a) for atom labels). At 1500 fs, the H starts to detach from the C, resulting in a structure similar to the TS for H-atom elimination. However, lacking sufficient kinetic energy for direct H-atom elimination, the H remains at the C–H length of ≈ 2Å for several tens of femtoseconds before it then abstracts another H atom, labeled Hʹ, to form H2 and leave C2H3. While the H is distant from the C2H4 moiety, the C–Hʹ bond experiences several vibrational periods, and the abstraction takes place when the elongated C–Hʹ bond is coupled with the feasible H–C2H4 orientation and the vibrational phase of the CH2 wagging mode. This motion is closely related to the “roaming” dissociation mechanism,26,27 in which a radical fragment spends several hundred femtoseconds at near dissociation followed by intramolecular abstraction to


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give other products. Though studies on roaming dynamics have mainly been conducted on the dissociation of closed-shell species, a recent study demonstrated the existence of roaming dissociation pathways from radicals such as C2H4OH.28 Similar dynamics was also observed in an earlier study on the dissociation of CH3O formed in the CH3 + O reaction.29

Figure 2. Time evolutions of selected bond lengths for a trajectory producing C2H3 and H2 and snapshots of the trajectory at (a) 1500, (b) 1510, (c) 1520, and (d) 1530 fs.

The C2H3 radicals produced by the mechanism discussed above can undergo further dissociation to produce C2H2 and H atom: 9 ACS Paragon Plus Environment


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C 2 H3

→ C2H2 + H

(2)

To evaluate the rate of this secondary dissociation, the microcanonical rate constant for reaction 2, k2(E), was estimated by RRKM theory. The density and sum of states for C2H3 and the TS of reaction 2 were calculated by the modified Beyer-Swinehart algorithm15 using the rovibrational properties presented in ref. 6, which were computed by B3LYP/6-311++G(d,p) and QCISD(T)/cc-pVTZ, respectively. The rotation around the unique axis (K-rotor) was treated as an active rotor. For the barrier height (E0) and reaction energy (∆E), the QCISD(T)/CBS values6 of 163 and 145 kJ mol−1 (including ZPE), respectively, were adopted. A semiclassical tunneling correction was included by assuming the asymmetric Eckart potential determined using the imaginary frequency of TS.30–33 Figure 3 shows the RRKM rate constant and the distribution of internal (vibrations and K-rotor) energies of the C2H3 radicals produced from the C2H5 dissociation, Eint(C2H3). Although the distribution is not suitable for quantitative analysis because of the limited number of trajectories that produced C2H3, the appreciable fraction of C2H3 formed in the energy above ∆E indicates that H atoms can also be produced by this secondary dissociation. In particular, the C2H3 formed in a quasi-bound state (i.e., in the energy between ∆E and E0), which is in the middle of the histogram, can dissociate via tunneling with a rate constant similar to that for the slow-rise component of the H-atom profile observed following the photoexcitation of C2H5.11 Therefore, this secondary dissociation could be a potential explanation for the anomalously slow H-atom formation.


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Figure 3. Internal (vibrations and K-rotor) energy distribution of the C2H3 produced from the dissociation of C2H5 (histogram) and the microcanonical rate constant of reaction 2 (C2H3 → C2H2 + H), k2(E), calculated by RRKM theory (blue line). The vertical dotted lines show the ZPE-corrected barrier height (E0) and reaction energy (∆E) for reaction 2.

To summarize the previous experimental observations and present findings, the photoexcitation of C2H5 into the 3s state produces H atoms via: (i) direct dissociation of the 3s state of C2H5 with an excited-state lifetime of ≈20 fs,10 (ii) direct H-atom elimination from C2H5 on the ground-state PES with an RRKM lifetime of ≈1 ps, and (iii) the secondary dissociation pathway of C2H5 → C2H3 +H2 → C2H2 + H + H2 whose time constant is presumed to be much larger than those for (i) and (ii). In the photodissociation experiment,11 both of the (i) and (ii) channels might have been observed as the prompt rise of the H-atom signals, and the slow-rise component might be attributed to the H-atom formation from the channel (iii). Though the trajectory 11 ACS Paragon Plus Environment


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calculations suggest that the branching fraction to the third pathway is small, more detailed analysis is needed to quantitatively examine the contribution of this pathway. For example, the present study generated the initial conditions of the trajectory by microcanonical sampling, whereas in the experiments the energized C2H5 radicals are produced via internal conversion from the 3s state; therefore, the nascent rovibrational configuration of the ground-state C2H5 radicals is determined by the multi-state dynamics near the seam of the conical intersection. The minimum energy crossing point (MECP) between the 3s and ground states has been reported to have a non-classical C2v bridged structure in which one H atom is situated perpendicular to the C–C bond and located some distance from the center of the C–C bond.12,13 The minimal energy path leading to the MECP in the 3s state (see Figure 2 of ref. 12) indicates that internal conversion may preferentially excite the C–H stretching and CH2 wagging modes. Because these vibrational modes contribute to the non-TS dissociation pathway identified in the present study, such non-random excitation can significantly affect the branching fraction.

In conclusion, direct trajectory calculations on the C2H5 dissociation revealed the existence of a reaction pathway that is not associated with a first-order saddle point. This pathway directly eliminates H2 from C2H5 via the roaming mechanism, leading to the formation of C2H3 radicals. The produced C2H3 radicals can subsequently dissociate to C2H2 + H and this secondary dissociation may be a potential explanation for the unexpectedly slow H-atom formation previously observed in photodissociation experiments of C2H5. Further investigation is warranted to assess this hypothesis.


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TOC GRAPHIC 42x36mm (300 x 300 DPI)

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Figure 1. Time profiles of the ensemble-averaged population of C2H5 and products (solid lines) and the corresponding exponential decay and growth functions (dotted lines). 63x56mm (300 x 300 DPI)



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Figure 2. Time evolutions of selected bond lengths for a trajectory producing C2H3 and H2 and snapshots of the trajectory at (a) 1500, (b) 1510, (c) 1520, and (d) 1530 fs. 90x113mm (300 x 300 DPI)


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Figure 3. Internal (vibrations and K-rotor) energy distribution of the C2H3 produced from the dissociation of C2H5 (histogram) and the microcanonical rate constant of reaction 2 (C2H3 → C2H2 + H), k2(E), calculated by RRKM theory (blue line). The vertical dotted lines show the ZPE-corrected barrier height (E0) and reaction energy (DE) for reaction 2. 65x55mm (300 x 300 DPI)


Roaming Dissociation of Ethyl Radicals - American Chemical Society

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