Experimental and Theoretical Investigation of Triple Fragmentation

Article pubs.acs.org/JPCA

Experimental and Theoretical Investigation of Triple Fragmentation in the Photodissociation Dynamics of H2CO Nicholas Hobday, Mitch S. Quinn, Klaas Nauta, Duncan U. Andrews, Meredith J. T. Jordan,* and Scott H. Kable* School of Chemistry, University of Sydney, Sydney NSW 2006, Australia S Supporting Information *

ABSTRACT: The photodissociation dynamics of H2CO molecules at energies bracketing the triple fragmentation threshold were investigated using velocity map ion imaging of the H-atom fragments. An algorithm was developed to model the experimental results as a two-step process: initially barrierless C−H bond fission on the S0 potential energy surface to form H + HCO, followed by secondary fragmentation of those HCO radicals with sufficient internal energy to overcome the small exit channel barrier on the HCO surface to form H + CO. Our model treats the first step using phase space theory (PST) and the second using a combined PST-impulsive model, with a tunneling correction. Experimentally, triple fragmentation reaches 25% of the radical (H + HCO) channel photochemical yield at energies about 1500 cm−1 above the barrier for breaking the second bond. In addition, the triplet (T1) channel appears to reduce in importance after the barrier on the T1 surface is exceeded, slowly decreasing to 7000 cm−1 of available energy.

I. INTRODUCTION Triple fragmentation (3F) can be defined as the production of three photofragments after the absorption of a single photon. This topic was first discussed in the 1920s in the decomposition of azomethane.1 It became of significant intellectual interest throughout the early days of laser photochemistry in the 1970s and 1980s, starting with a pioneering study of the photodissociation of Cd(CH3)2 by Bersohn and co-workers.2 The lessons from those studies are used consistently in 3F experiments to the present day. There are two reviews by Maul and Gericke (MG) that summarize 3F and review the literature up until 2000.3,4 Early researchers were interested in the dynamics of breaking two bonds (or three if a cyclic compound), and concepts of concerted, asynchronous, and stepwise have been extensively discussed. Concerted (or symmetric concerted in MG) is defined to be an inherent part of the electronic orbital rearrangement involved in the reaction. Famous examples include glyoxal, where there is a 4-center transition state, forming the new H−H bond, while cleaving the two C−H bonds in an orbitally concerted mechanism.5 The cyclic compounds, sym-triazine6,7 and sym-tetrazine,8,9 break three ring bonds in a concerted fashion to form 3HCN or 2HCN + N2, respectively. A stepwise, or sequential, dissociation occurs in two distinct kinetic steps. In this case, one bond is broken first to liberate two fragments, one of which has sufficient energy to undergo further fragmentation. In a definitional sense, the lifetime of the intermediate is longer than its rotational period (see below). The dynamics and hence kinetics of the first and second bond © 2013 American Chemical Society

breaking processes are completely independent, except inasmuch as the first step determines the range of energy and linear and angular momentum with which the second process starts. Stepwise triple fragmentation was first described for acetyl iodide,10 and the photodissociation of many other halogenated species (for example, halogenated alkanes,11−15 alkenes,16−19 alcohols,20,21 carbonyls,22,23 and carboxylic acids24) fall into this category. In each case, the weak carbon−halogen bond is broken first. Because the halogen atom has no internal degrees of freedom, the cofragment can be born very hot and undergoes spontaneous secondary decomposition. Stepwise triple fragmentation has also been observed in alkanes,25 alkenes,26 and carbonyl compounds.27,28 One distinctive characteristic of a stepwise reaction is that the hot intermediate has a lifetime longer than its rotational period, and therefore, the second step is isotropic. The asynchronous mechanism is intermediate between the concerted and stepwise. In this case, the bonds break separately, but the second bond is breaking while the two primary fragments are still in the vicinity of each other. Consequently, the dynamics of all three fragments are intertwined, at least in a nuclear (kinematic) sense, even though the electronic motion of the two steps may be decoupled. The photodissociation of phosgene (Cl2CO) to CO + 2Cl is an example where there are Special Issue: Curt Wittig Festschrift Received: May 18, 2013 Revised: July 18, 2013 Published: July 19, 2013 12091

dx.doi.org/10.1021/jp404895y | J. Phys. Chem. A 2013, 117, 12091−12103

The Journal of Physical Chemistry A

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Figure 1. Energy level schematic showing the potential energy surfaces and vibrational states of H2CO and HCO involved in this work. The H2CO vibrational levels in S1 are a representation of the states excited, while the HCO states represent all available vibrational states of HCO, up to the dissociation barrier. The figure defines four energy regions where the reaction dynamics change (see text).

two distinct Cl-atom speed components, but the CO fragment is preferentially forward scattered, which clearly shows that the transient ClCO fragment has not had sufficient time to rotate before the second Cl departs.29 Another example is the photodissociation of azomethane,30 where the two C−N bonds are cleaved within the rotational period of the parent molecule, but two distinct CH3 populations are observed. The kinematics of the stepwise triple fragmentation of photodissociating molecules was first described by Riley and Kroger10 for acetyl iodide. This description was based on Hershbach and co-workers’ theory of long-lived collision complexes, which itself was based on reactive scattering in nuclear fission.31 Riley and Kroger’s kinematic analysis, including full angular distributions, was extended in a series of papers by Grice and co-workers and reviewed by Grice in 1995.32 The 1997 review of 3F by MG extends the kinematic treatment from solely stepwise to include concerted and asynchronous processes.3 Strauss and Houston also provide a discussion of the difference between stepwise and asymmetric concerted dissociations using a maximum entropy approach.33 Speed distributions from ion-imaging experiments have also been modeled previously, for example, in North and coworkers’ study of the photodissociation dynamics of ClONO2.34 They used a Monte Carlo forward-convolution to fit their imaging data, allowing analysis of the secondary dissociation of the NO3 fragment. Recently, we presented the results of a 3F model where both the first and second steps occurred on a barrierless potential energy surface.35 Our model assumed that the dynamics of each step would be characterized by phase space theory (PST). In that paper, we demonstrated that the secondary fragments can be very cold, in both translational and rotational degrees of freedom. We compared the predictions of our model with previous experimental studies of the photodissociation of acetaldehyde and methyl formate, concluding that, in the case of methyl formate, 3F provided a viable mechanism for the observed distribution of energy. Our simple model also predicted that 3F should become increasingly important with increasing energy above the 3F threshold.

The purpose of this article is to extend the previous model by including the possibility of a small barrier in the exit channel, and by including tunneling through that barrier. We originally planned to benchmark the branching fraction of 3F as a function of energy against experimental data. However, despite the large body of previous work on triple fragmentation, we have found no systematic study of the energy dependence of the process. Therefore, to benchmark our model, we have also carried out an experimental study of 3F in a simple system: the triple fragmentation of formaldehyde, H2CO, to produce 2H + CO. This system has the advantage that it has been studied extensively at lower excitation energy, although 3F has not been studied previously. This system also has the advantage that both two-body and three-body processes can be probed by measuring a single product: the H atom. A. Brief History of H2CO Photodissociation. The photochemistry of H2CO has been extensively studied over the past few decades and we provide only a brief description here. The interest has been motivated in part by the atmospheric importance of H2CO, as well as the simple fact that it is almost the ideal prototypical polyatomic molecule, being both experimentally and theoretically tractable. The S0 − S1 absorption spectrum of H2CO covers a range of 28,000 to 40,000 cm−1 (360−250 nm).36 Following excitation from S0 to S1 H2CO can fluoresce or undergo internal conversion (IC) back to S0, or intersystem crossing (ISC) to T1. At these energies there are a number of dissociation channels, on both S0 and T1, which are listed below in order of increasing threshold energy, as indicated: H 2CO + hν → H 2 + CO (TS channel, 27700 cm−1 [ref 37])

(R1)

H 2CO + hν → H 2 + CO (roaming channel, 30120−30240 cm−1 [ref 38])

(R2)

H 2CO + hν → H + HCO (radical channel, 30327.6 cm−1 [ref 39]) 12092

(R3)



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suggest tunneling may play a significant role at low temperatures, in some cases reducing the effective barrier height to below 15 meV (∼120 cm−1).54,55 The aims of this study are 2-fold. First, we extend measurements of the photodissociation dynamics of H2CO through, and significantly above, the threshold for triple fragmentation. The dynamics of H atom production are determined at 23 energies from 30375 cm−1, which is just above the threshold for HCO + H, to 37 441 cm−1, where we are limited by the very weak absorption cross-section of H2CO. The data are concentrated at energies just below and above the 3F threshold. Second, we use the experimental data to benchmark and extend the double PST model that we developed previously.35 We add the effect of the barrier in the exit channel in the second (HCO → H + CO) step and allow tunneling through this barrier.

H 2CO + hν → H + HCO (triplet channel, 31900 ± 1000 cm−1 [refs 40 and 41]) (R4)

H 2CO + hν → H + H + CO (3F, 36070 cm−1, incl. 700 cm−1 barrier [refs 42 and 43])

(R5)

Molecular products are formed through a well-known transition state (TS) over a barrier that is estimated to be 27 700 ± 300 cm−1 above the S0 zero-point level (or about 2500 cm−1 below the C−H bond-dissociation energy).37 Following the pioneering work of van Zee et al.,44 a second molecular dissociation channel, R2, was identified that bypasses the conventional transition state and has since been termed the roaming channel.38,45,46 This mechanism is now fairly well understood to involve an interplay of the radical dissociation channel and the molecular channel where the molecule begins to dissociate along the simple bond-fission coordinate, but has insufficient energy in this coordinate to fully dissociate and the two radical fragments have time to roam around each other and react to form molecular products. Reactions R3−R5 are relevant to this work because they produce H-atom fragments. Figure 1 shows representations of the potential energy profiles for these three reactions. Barrierless C−H bond fission on S0 leads to the formation of an H atom and a formyl radical, HCO, with an energetic threshold of 30 327.6 ± 0.9 cm−1.39 The dynamics of this pathway are statistical and modeled well by PST.39,47 Radical products can also be produced on the (T1) triplet surface following ISC from S1. Here, dissociation occurs over a barrier, the height of which was first experimentally bracketed to 31 900 ± 1000 cm−1 by Moore and co-workers.41 The presence of a barrier on T1 produces a markedly different product state distribution with low rotational and vibrational excitation and higher translational energy40,48−51 compared to the statistical distribution for the radical products originating on S0. This difference in product state distributions has been used to experimentally distinguish R3 and R4 and to show that R4 becomes important at energies around 31 540 cm−1 and, above 32330 cm−1, reaction on T1 dominates the dynamics.40,48−51 Previous studies of the translational energy distribution of dissociated hydrogen atoms are consistent with these results, while also illustrating that the relative importance of the S0 and T1 mechanisms, R3 and R4, is highly dependent on the initially excited S1 state.40,49,51,52 Despite the vast number of theoretical and experimental studies on the photodissociation of H2CO, few studies have been performed at wavelengths 5285 cm−1 (see below). We attribute this cold component to the opening up of the 3F channel as discussed further in the next two sections. At higher excitation energies, this cold component also broadens and shifts to higher velocities, as expected.

Eavail = E int(HCO) − Ediss(HCO)

(1)

Dissociation of HCO has a small barrier of Ebarr ≈ 700 cm−1 in the exit channel.53 The product state distributions of this secondary process are modeled by dividing the available energy into two reservoirs, using an approach that has been described previously.69−71 The barrier energy is distributed to the product fragments impulsively, while the energy above the barrier is distributed statistically using PST, analogously to the first programming step. Impulsive models72 provide a simple means to calculate the energy imparted to products as they fall down a steep potential energy hill. Although such simple models have received some criticism,73,74 others have argued that they can provide useful insight for comparing with experimental data.75 We adopt a simple impulsive model that assumes that the sudden release of the reaction exoergicity manifests itself as an impulse. Short-range forces act between the fragments as they dissociate, thus dissociation occurs suddenly, on a time-scale 12096



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angular momentum is set to that arising from the first PST step. For the final velocity of the secondary products, we make the assumption that the two velocity vectors, the velocity of the HCO intermediate and the velocity of its dissociation products, are independent. This is reasonable given that one of the definitions of stepwise is that the intermediate survives for longer than a rotational period. In this limit, the final velocity of the secondary H atom dissociation products is the vector sum of vi, the HCO parent velocity from the first fragmentation, and vjtot, from the second fragmentation where we consider vjtot to be randomly distributed with respect to vi. Finally, as pointed out previously,35 it is important to appropriately weight the degeneracy of the secondary dissociation states such that the sum of all the secondary contributions equals the degeneracy of the primary dissociation step from which they derived. Technical and programmatic details of the double PSTimpulsive model are described in more detail in the Supporting Information.

short with respect to bending motions. Fragment rotation is then obtained by conservation of angular momentum and energy, assuming that the fragments originate from the transition state (TS) configuration at the top of the barrier. The standard impulsive model gives the portion of Ebarr that becomes angular momentum, Erot, as Erot

⎛ ⎜ 1 = E barr ⎜1 − bimp2μ ⎜ 1+ I ⎝

⎞ ⎟ ⎟⎟ ⎠

(2)

where bimp is the impulsive exit channel impact parameter for CO + H, I is the moment of inertia of CO, and μ is the reduced mass of the H and CO fragments. The impact parameter, bimp, is defined as the perpendicular distance between the CO center of mass and the CH bond vector, that is, bimp = xc‐o‐m sin θ

(3)

where θ is the HCO bond angle, and xc‑o‑m is the distance between the C atom and the CO center of mass. Both bimp and I have been obtained at the optimized transition state (TS) geometry, calculated at the CCSD/6-311++G(2df,p) level of theory76−82 and given in Table S2 of the Supporting Information. We allow the HCO bond angle, θ, to vary using the appropriate weighting from the one-dimensional harmonic wave function that describes the TS bending normal mode. Once the rotational energy, Erot, is known, the translational energy from the impulsive reservoir is simply the difference between the barrier height and the CO rotational energy:

Etrans = E barr − Erot

V. DISCUSSION There are three aspects to the H-atom speed distributions that are apparent in Figure 3, two of which have been reported previously, and one that is new to this work. As this paper is chiefly concerned with the triple fragmentation region, we consider the distributions above and below the 3F threshold separately. A. Dissociation below 3F. Triplet versus Singlet Yields. Figure 4 shows a number of the measured H-atom speed distributions for selected excitation energies in regions (i) and (ii) of Figure 1. On the right-hand side of the figure, the distributions have been converted to kinetic energy (KE) distributions. We stress that the KEs in the figure are those for the H atom alone; they are not total kinetic energy release (TKER) values because this quantity cannot be inferred when three fragments are produced, as is the case above the 3F threshold. Overlapping the data in the figure are the results of PST calculations. For the lowest energy (Eavail = 47 cm−1) the populations of the very few populated product states are shown as a stick distribution. As discussed above, the H atom speed is blurred in the ionization step due to the recoil kinetic energy of the departing electron. A continuous speed distribution is obtained by convoluting the calculated PST speed distribution with a Gaussian function to represent this 400 m s−1 recoil velocity of the H+ ion. The continuous speed distribution is then converted to a continuous energy distribution, both indicated by the thick blue lines in Figure 4. At the lowest energy considered, the convoluted distributions provide a very good fit to the experimental data. Consequently, we have convoluted all other PST distributions with the same broadening function. As the available energy is increased through the triplet barrier, the dynamics become dominated by reaction R4 on the T1 surface.40,48−51 The experimental distributions now show a significantly greater population of faster H atoms, and the PST model is a poor representation of the data. Reaction on T1 proceeds over a barrier that is ∼23 kJ mol−1 in the exit channel,88 which provides a much larger kick to the H atom than dissociation on the barrierless, S0 surface. Both experimental data40,48−51 and quasi-classical trajectories50 show that HCO fragments born on T1 are internally much colder than those from S0, with very little population in either excited vibrational states, or high J, K rotational states. Consequently, by conservation of energy, there will be very

(4)

The energy for the statistical reservoir is defined as the difference between the total available energy for the second dissociation and the energy required to surmount the barrier. This statistical energy is partitioned into rotational, translational, and vibrational degrees of freedom using the standard implementation of PST.68 The final rotational state of the CO fragment, Jtot, is obtained by adding the impulsive angular momentum, Jimp, to the angular momentum from the statistical reservoir, Jstat, assuming both are in the same direction. HCO fragments with insufficient energy to surmount the potential barrier to CO + H, but in excess of the required thermochemical energy, may still form these products by tunneling. We have used the unsymmetrical Eckart model83,84 to account for the probability that an excited HCO fragment approaching the barrier will tunnel through, corrected as suggested by Garrett and Truhlar.85,86 The force constant and reduced mass required in calculating the tunneling probabilities were again obtained from the ab initio calculation at the TS geometry. On the basis of the time frame of the reaction and previously calculated HCO line widths,42,87 we consider the tunneling correction as a scaling factor. The energy of the impulsive contribution is the residual exit channel energy, partitioned into rotation and translation as previously. The total velocity imparted to each fragment during the secondary dissociation is simply the sum of the impulsive and statistical translational components, assuming that the impulsive and statistical processes produce velocity vectors in the same direction. Finally, the final rotational and translational energy of the secondary products needs to be calculated from the resultant of the first and second dissociation processes. Angular momentum is explicitly included in the second PST calculation; the HCO 12097



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Figure 5. H atom yield via the singlet (reaction R3) and triplet (reaction R4) pathways relative to the total radical yield (R3 + R4 + R5) as inferred from fitting the PST model to the low H atom speed/ kinetic energy components of the experimental distributions, shown in Figure 4.

conical intersections at energies similar to this.89−91 An S1/S0 CI would bypass the triplet thereby lowering the triplet yield. A T1/S0 crossing seam would likewise remove triplet population efficiently, again reducing the triplet yield. However, accessing a crossing seam would likely result in a rapid drop in triplet yield over a narrow energy window. The observed loss of triplet yield occurs relatively slowly, over approximately 5000 cm−1. We hypothesize that this reduction in triplet yield is the result of slow changes in the S1/S0 or S1/T1 coupling matrix elements. The accepted explanation for the strong, state-dependent fluctuations at energies near the triplet barrier is that there is a dense continuum of background S0 states, but a sparse, structured set of triplet states. When the S1 state is resonant with a background triplet state S1 → T1, ISC dominates, while S1 → S0 IC dominates when they are out of resonance. As the energy increases above the triplet barrier, the background triplet states become more dense and the lifetime broadens. Therefore, there will be smaller variation in the S1/T1 ISC probability, with smaller observed fluctuations in the T1 yield. As energy increases further, however, the coupling efficiency will weaken, as there is less overlap between the vibrationally excited S1 and T1 states, and IC to S0 will become more probable due to the larger density of states on the S0 surface. These effects will cause a slow reduction in triplet yield, as observed in Figure 5. This explanation assumes that the dominant mechanisms for ISC are Franck−Condon and density-of-states overlaps. Theoretically, however, it has been suggested that ISC is dominated, at higher energies, by spin− orbit interactions, and that these increase with increasing energy.91 Bowman and co-workers predict that the triplet yield should rise steadily from about 30% at 32 000 cm−1 to more than 80% of the total radical yield near 37 000 cm−1.91 The experimental data, however, suggests that the triplet-like component of the H-atom speed distributions diminishes at higher energies, in favor of singlet-like dynamics.

Figure 4. Several speed and kinetic energy distributions in regions (i) and (ii), lying below the threshold for triple fragmentation. The results of a PST calculation are shown in red (individual states) and blue (broadened and binned). The model results correspond to reaction R3, and the difference between the observed distributionand the model is attributed to triplet reaction R4.

little population of slow H atoms from the T1 pathway. If we use this information and assume that there is in fact zero population of slow H atoms from T1, we can infer that the observed population of slow H atoms arises only from reaction on S0. In all cases shown in Figure 4, the shape of the slow component of the H-atom speed distribution appears to be well modeled by PST. This then allows us to determine the fraction of H atom flux arising from reaction on S0 and, by difference, the fraction arising from reaction on T1. The H atom yield (%) arising from reaction on the S0 and T1 surfaces is shown as a function of energy in Figure 5. The triplet yield rises quickly near the T1 barrier. It has been reported several times previously that the S0 and T1 yields are highly fluctuating in the region of the barrier40,48−51 and our yields likewise fluctuate strongly. As the energy increases beyond the barrier, the triplet yield drops gradually and the fluctuations also diminish. At Eavail > 5000 cm−1, the triplet yield has reduced to consistently 5000 cm−1, the singlet and triplet yields do not sum to unity because a third pathway, triple fragmentation, turns on (vide infra). The overall reduction in triplet yield with energy has not been reported before. There have been theoretical reports of 12098



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B. Dissociation above the 3F Threshold. Figure 6 shows several H atom speed and kinetic energy distributions for energies in regions (iii) and (iv) as defined in Figure 1. We reiterate that the H atom kinetic energy is not the TKER, but the energy of solely the H atom. The lowest energy distributions in Figure 6 resemble the highest energy distributions in Figure 4; there is no rapid change in dynamics as the 3F threshold is passed. However, with increasing energy a new feature at low speed and kinetic energy grows in.

Figure 7. For Eavail = 6943 cm−1, H-atom speed distributions and calculations for (a) no secondary fragmentation; (b) secondary fragmentation with no barrier in the HCO exit channel; (c) including the effect of a 700 cm−1 exit channel barrier; and (d) allowing tunneling through the barrier. See text for discussion of calculations.

energy in excess of the barrier treated statistically, as explained above and in more detail in the Supporting Information. The speed distribution for the second H atom (dashed line) is constrained to a minimum speed corresponding to the kinetic energy release from the exit channel barrier. When added to the distribution of the primary H atom, the model (solid line) now underestimates the slow H-atom speed component. This could be due to an overestimate of the barrier height, although the value we have used is based on experiment and is consistent with high level theoretical calculations.42,53,55 Any impulsive model, however, will give a sharp cutoff at low H atom speeds. The experiment shows a more gradual decrease, and we thus assume that the slow secondary H atoms are more likely to arise via tunneling through the exit channel barrier. If we include tunneling, as described in the theory section and the Supporting Information, the H-atom speed distribution in Figure 7d is obtained. Again, the red dashed line shows the speed distribution of the second H atom alone. Comparison with Figure 7c shows that tunneling increases the yield of slower H atoms. When combined with the primary H-atom distribution, the model now provides a respectable fit to the experimental data. The slow H atoms are still slightly underestimated, which might point to more tunneling than we have included and/or a slightly lower exit channel barrier. We note, however, that the speed distributions arising from our double PST-impulsive model contain no adjustable parameters. Tunneling has been modeled using parameters obtained from the optimized CCSD/6-311++G(2df,p) transition state (see

Figure 6. H atom speed and kinetic energy distributions for several levels above the triple fragmentation threshold. The solid blue line is the double PST-impulsive calculation with a tunneling correction, analogous to Figure 7d). The red dashed line is a single PST calculation (no secondary fragmentation), analogous to Figure 7a). The red distribution corresponds to H atoms produced via mechanisms R3 + R5, while the excess yield arises from the second H atom from R5.

Figure 7 shows the H-atom speed distributions for Eavail = 6943 cm−1. The solid blue line in the top panel, Figure 7a, shows results from a PST calculation for only H2CO → HCO + H, as used in Figure 4, that is triple fragmentation is not modeled. Clearly, the new component is not fit by this calculation. In Figure 7b, we use our recently published double PST model.35 In this model, the primary HCO fragment is allowed to undergo secondary fragmentation when its internal energy is in excess of the H−CO bond strength. The model assumes a barrierless secondary process. The solid blue curve shows the results of this calculation and the red, dashed line shows the speed distribution of the secondary H atoms alone. While this calculation shows a distinct second, slow component to the H-atom speed distribution, the slow component is overestimated due to the neglect of the exit channel barrier. In Figure 7c, the effect of the exit channel in included by modeling the exit channel energy release as impulsive with 12099



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Supporting Information), and there is scope to either improve this calculation or to fit the tunneling parameters to the experimental data. Speed and kinetic energy distributions calculated using our double PST-impulsive model are shown at a range of energies above the 3F threshold in Figure 6. Again, these calculations have no adjustable parameters and indicate that our model fits the experimental data over the experimental energy range. The yield of 3F products can be estimated using a similar, but slightly more complex, approach to the one used above to estimate the triplet yield. For Eavail > 5000 cm−1, the higher H atom speed/energy component of the experimental distributions has been modeled using a PST calculation of the primary dissociation step, that is H2CO → HCO + H, with no secondary fragmentation. This model result contains contributions from both mechanisms R3 and the first H atom from R5 and is shown as the red dashed line in Figure 6. The residual population at low H atom speed/energy is assumed to arise from the second H atom in R5. To calculate the yield of each radical channel, R3−R5 above, it must be recognized that the total H atom yield (e.g., the experimental H atom data in Figure 6) is equal to the sum of the yields from R3 +R4 + 2R5 because R5 yields two H atoms. The simple, one-step PST model (dashed line) contains contributions equivalent to R3 + R5 as indicated in Figure 6. (R4 + R5) is determined by subtracting the fitted curve (R3 + R5) from the total curve (R3 + R4 + 2R5). R4 and R5 are determined trivially because the speed distribution for the second 3F step (R5) is very slow, whereas the triplet component (R4) is very fast. None of the distributions in Figure 6 show a significant component from R4. The results of this fitting are shown in Figure 8, where the 3F yield is plotted as a function of available energy. The smooth

line through the data shows the results of the double PSTimpulsive calculation. Both the model and data show a rapid increase in 3F yield as a function of energy. By 1500 cm−1 over the 3F threshold, the 3F yield is about 25% of the total radical yield. The model does appear to slightly underestimate the experimental data, which is likely to be due to underestimation of the tunneling, overestimation of the exit channel barrier, or errors in the partitioning of energy in the impulsive calculation. Nonetheless, as a zero adjustable parameter model, our model captures the trend in the experimental data very well.

VI. CONCLUSIONS We have measured the speed distributions of H atoms resulting from the photolysis of H2CO at a wide range of energies across the S1−S0 absorption spectrum. We have developed a theoretical model to help understand and interpret the underlying features in the experimental distributions. The model combines PST with an impulsive model and tunneling corrections to obtain H-atom speed distributions that include both the initial H2CO → H + HCO and secondary HCO → H + CO dissociation steps. There are three main conclusions in this article. First, comparison of a normal PST model and the experimental distributions allows us to distinguish between singlet and triplet pathways and to discover that the triplet mechanism slowly diminishes in importance for energies in excess of the triplet barrier. The second conclusion is that triple fragmentation becomes increasingly important as the threshold energy is exceeded. Within ∼15 kJ mol−1 of the threshold, the 3F yield reaches ∼25%. The secondary H atom is also much slower than the primary H atom. Finally, a double PST model, with a small impulsive contribution to the second step and a correction for tunneling provides an excellent fit to the experimental data, spanning over 7000 cm−1 of available energy. There are no adjustable parameters in the model; the parameters are all provided by spectroscopic data or ab initio calculations.

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ASSOCIATED CONTENT

S Supporting Information *

Detailed description of the triple fragmentation model and its implementation, including all the parameters used in the phase space theory, impulsive, and tunneling components. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (M.J.T.J.); scott.kable@ sydney.edu.au (S.H.K.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Australian Research Council (DP 1094559). We gratefully acknowledge the expert assistance of Professor Scott Reid and Dr. Alan Maccarone in helping to set up the ion imaging spectrometer and discussions with Professor Tim Schmidt and Ms. Gabrielle de Wit about aspects of this work.

Figure 8. Triple fragmentation yield, R5/(R3 + R4 + R5), as a function of energy. The yield was found by fitting the single PST distribution to the high speed component of the H-atom speed distribution, as shown in Figure 7, and subtracting this from the observed speed distribution. The solid red line is the result of double PST-impulsive calculations with tunneling corrections. The model slightly underestimates the experimental 3F yield, which is attributed to more tunneling or a lower barrier than predicted theoretically. 12100



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Experimental and Theoretical Investigation of Triple Fragmentation

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