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The Roaming Atom: Straying from the Reaction Path in Formaldehyde Decomposition

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Science  12 Nov 2004:
Vol. 306, Issue 5699, pp. 1158-1161
DOI: 10.1126/science.1104386

Abstract

We present a combined experimental and theoretical investigation of formaldehyde (H2CO) dissociation to H2 and CO at energies just above the threshold for competing H elimination. High-resolution state-resolved imaging measurements of the CO velocity distributions reveal two dissociation pathways. The first proceeds through a well-established transition state to produce rotationally excited CO and vibrationally cold H2. The second dissociation pathway yields rotationally cold CO in conjunction with highly vibrationally excited H2. Quasi-classical trajectory calculations performed on a global potential energy surface for H2CO suggest that this second channel represents an intramolecular hydrogen abstraction mechanism: One hydrogen atom explores large regions of the potential energy surface before bonding with the second H atom, bypassing the saddle point entirely.

As chemical kinetic theory has evolved from Eyring's work in the 1930s through the Rice-Ramsperger-Kassel-Marcus (RRKM) and related statistical approaches, the transition-state concept has remained paramount. Reactants are assumed to proceed along the lowest energy pathway to products, with the configuration at the energetic maximum of this pathway termed the transition state. The properties of the transition state, in particular its geometry and vibrational frequencies, have profound importance for determining the rate of reaction, so studies of reaction rate theory have focused mainly on elucidating these properties. Absent from this paradigm is the possibility of two or more distinct pathways to the same products. We present here a combined theoretical and experimental study of formaldehyde (H2CO) dissociation that supports two distinct active pathways to H2 and CO products. Whereas the dominant pathway involves a conventional transition state, the alternative pathway is an intramolecular hydrogen abstraction that avoids the transition state region entirely. These results, considered with recent work on the CH3 + O (1) and O + C2H6 (2) reactions and other cases in which regions of deep potential energy wells are avoided in reaction (3), suggest that transition-state theories are incomplete in their description of chemical reactivity.

The study of unimolecular dissociation of vibrationally excited molecules in the ground electronic state has been central to the development of transition-state theories, and the nature of the transition state itself has been the focus of many of these studies (4, 5). Formaldehyde has literally become a textbook example (6) with which to study these issues. It is one of the simplest molecules in which to examine the correlation between rotational and vibrational excitation in the products. Moreover, laser excitation efficiently prepares H2CO on the ground electronic state with specific amounts of internal energy.

Moore and co-workers have explored the unimolecular reaction dynamics of formaldehyde in great depth (712). In studies of both H2 and CO product state distributions and state-resolved H2 Doppler profiles, they found about 65% of the available energy is released in translation; the rest of the energy is partitioned between strong CO rotational excitation and modest H2 vibrational excitation. They found little energy in CO vibrational excitation or in rotational excitation of H2. All of these observations could be accounted for qualitatively by a skewed transition-state structure in which both hydrogen atoms are on the same side of the CO molecule. These results have also been accounted for semiquantitatively by quasi-classical trajectory calculations which were initiated at this transition state (1316).

However, one subtle feature of the measurements did not fit well with this conventional understanding of the dynamics. At energies above 30,300 cm–1, H2CO can undergo an alternative dissociation to H + HCO (the radical channel). In a prescient paper, van Zee et al. noted (12) that, at energies below this threshold, the CO rotational state (jCO) distributions were simply Gaussian-shaped, peaking near jCO = 45, and were well understood to arise from energy and angular momentum conservation given the nature of the transition state and the exit channel interactions. However, above the threshold for the H + HCO dissociation channel, the CO rotational distributions exhibited a shoulder toward lower rotational levels. van Zee and co-workers proposed two possible explanations for the low-jCO component. One explanation was that at higher energies the transition-state region may sample additional geometries that lead to reduced exit impact parameters, hence lower rotational excitation in the CO and higher overall translational and vibrational energy. The second possibility was that the low jCO was related to the opening of the radical channel and thus a distinct new pathway to formation of molecular products via intramolecular hydrogen abstraction.

To resolve this issue, we performed high-resolution direct current (DC) slice imaging (17) measurements of specific CO rovibrational levels after dissociation of formaldehyde above the threshold for the radical channel. These images provide the correlated H2 vibrational distributions with vibrational and partial rotational resolution. The experimental measurements are combined with quasiclassical trajectory calculations performed on a new, high-level, global potential energy surface for H2CO (18).

The ion imaging experiment (19, 20) involves laser excitation of formaldehyde in a molecular beam under collisionless conditions to the first electronically excited singlet state at 30,340.1 cm–1 (21), one of several dissociation energies used by van Zee et al. This excitation includes one quantum in the CO stretch and three in the out-of-plane bend. Internal conversion then produces a distribution of vibrationally excited ground-state molecules that dissociate some picoseconds later (22). The product, CO, is probed in the dominant ground vibrational state on specific rotational levels by using DC slice imaging. By using weak DC electric focusing fields and resonant multiphoton ionization, we are able to image the central slice through the recoiling product spheres. This yields high-resolution state-resolved velocity distributions (Fig. 1). These images represent the velocity distributions for specific indicated quantum states of the CO product, and the structure in the images reflects the internal energy distribution of the H2 co-product for the particular CO level being probed because the total energy is fixed by the photolysis laser.

Fig. 1.

DC sliced images of CO (v = 0) after dissociation of H2CO at 30,340.1 cm–1 excess energy for the CO product rotational levels jCO = 40 (A), jCO = 28 (B), and jCO = 15 (C).

In the image for jCO = 40 (Fig. 1A), the rings represent formation of the H2 coproduct in vibrational states (v) from 0 to 3 with substantial translational energy release. Integration of the data in the images and conversion from velocity to total energy yields the translational energy distribution (Fig. 2A, solid line). This resulting H2 vibrational distribution peaks at v = 2 with the bulk of the available energy appearing in translation, consistent with Moore's measurements. The image obtained for jCO = 28 (Fig. 1B) reveals a bimodal internal energy distribution in the H2 co-product, strongly suggesting a distinct dissociation mechanism. This rotational level is intermediate between the peak of the rotational distribution and the low-jCO shoulder reported by van Zee et al. The corresponding translational energy distribution (Fig. 2B), showing partial rotational resolution of the correlated H2, reveals that the slower CO product is formed in conjunction with H2 in vibrational levels up to v = 7. Lastly, the image for jCO = 15 (Fig. 1C) in the region of the low-jCO shoulder reported by van Zee et al. shows only the slow component, and the translational energy distribution (Fig. 2C) is quite similar to the slow part of the distribution in Fig. 2B: In this case, we see only formation of highly internally excited H2 up to v = 7 and rotational state j = 13.

Fig. 2.

(A to C) Solid lines are experimental translational energy distributions obtained from the corresponding images in Fig. 1. Dashed lines are translational energy distributions obtained from the trajectory calculations. Markers indicate positions for correlated H2 (v and j = 1) vibrational levels for v from 0 to 4 and odd rotational levels for H2 v from 5 to 7. P(ET) is the probability of a given translational energy (ET) (arbitrary units).

The accompanying trajectory calculations were performed on a new H2CO potential energy surface (18) constructed from least squares fits to roughly 60,000 high-level ab initio points, followed by a smooth joining of these fits. The surface contains the molecular (H2 + CO) and radical (H + HCO) dissociation channels as well as the cis and trans isomers of HCOH. The relevant energetics of this surface, including corrections for harmonic zero-point energy, are 28,633 cm–1 for the barrier to the molecular channel and 30,325 cm–1 for the radical channel, in very good agreement with experiment.

Quasi-classical trajectories on this surface were calculated at a total energy corresponding to the experiment based on a harmonic estimate of the zero-point energy of 5844 cm–1. Two sets of trajectories were performed: In one the initial molecular geometry was set at the formaldehyde minimum, and in the other one CH bond was initially stretched to a distance of 2.1Å, about twice the equilibrium value (23). Roughly 40,000 trajectories were performed for each initial geometry with zero total angular momentum. The generation of initial conditions for these trajectories followed the standard method (1316), and the usual histogram binning procedure was used to obtain final vibration/rotation (v/j) distributions of the H2 and CO products. The results from the two sets of calculations are identical within the statistical uncertainties of each, confirming the robustness of the results. The translational energy distributions obtained from the calculations (Fig. 2, dashed lines) are in near-quantitative agreement with the experimental data for each CO rotational level. The calculations also yield probabilities for dissociation to given levels of CO rotational and H2 vibrational excitation, both summed over CO vibrational levels (Fig. 3A) and restricted to vCO = 0 (Fig. 3B). In both cases, there is a bimodal distribution in vH2, with a major peak at vH2 = 1 and a smaller peak at vH2 = 6. Further in accord with experiment, the vibrationally excited H2 correlates with a CO rotational distribution peaked near jCO = 10; the vibrationally cold H2 is formed with rotationally excited CO (peaked near jCO = 45). Calculations have also been done at five energies spanning a 3000-cm–1 energy range centered at the energy of the experiment. At the lowest energy, the low-jCO shoulder in the CO rotational distribution is near zero relative to the peak value (jCO = 42), and this contribution grows monotonically as the energy increases. Correspondingly, the second peak in the bimodal vH2 distribution is nearly zero relative to the first peak at low vH2. The branching ratio for the molecular channel decreases monotonically from roughly 1.0 to 0.2 (24). Thus, whereas the high-v H2 and low-jCO component of the molecular channel increases with energy, the branching ratio of the molecular products decreases. These results are consistent with the dissociation energy dependence of the low-jCO shoulder reported by van Zee et al.

Fig. 3.

State correlations obtained from the trajectory calculations: (A) CO (all v and j) compared with H2 (v) and (B) CO (v = 0 and j) compared with H2 (v).

One compelling feature of these calculations is that trajectories may be examined directly for insight into the associated dynamics. A typical trajectory leading to jCO = 41 and vH2 = 1 (movie S1) proceeds via the skewed transition state, and the corresponding reaction path is closely followed. In contrast, a trajectory leading to jCO = 7and vHH = 6 (movie S2) involves one H atom nearly detaching via the H + HCO channel, although lacking sufficient energy for complete dissociation. The H atom meanders in the broad attractive space of the H + HCO surface, far from the reaction path, until it abstracts the other hydrogen atom to yield highly vibrationally excited H2 and rotationally cold CO. Figure 4 shows six frames of movie S2, illustrating the “roaming” mechanism.

Fig. 4.

Six frames of a sample trajectory leading to CO (jCO = 7) and H2 (vH2 = 6) at the indicated times after initiation.

These two trajectories illustrate the dramatically distinct mechanisms underlying the bimodal correlated state distribution seen in the experimental images and trajectory calculations. In one case, we have what may be described as the conventional dissociation pathway involving the well-characterized transition state. For this dominant mechanism, transition-state theories are appropriate and may be used to predict the dissociation rates and product state distributions. For the second case, we find compelling evidence in support of van Zee's conjecture invoking the H + HCO channel. This pathway is analogous to recently calculated trajectories for the O + CH3 reaction (1) involving near H elimination followed by intramolecular H abstraction, which accounted for CO yields seen experimentally.

We suspect this roaming atom mechanism is a common pathway. A key question remaining is whether diatomic products besides H2, or even polyatomic products, may be formed by such a mechanism. It may be more common for the roaming species to be a hydrogen atom that can rapidly explore the accessible regions of the surface. Perhaps, however, an atom or group besides H could be the abstraction target.

Supporting Online Material

www.sciencemag.org/cgi/content/full/1104386/DC1

Movies S1 and S2

References and Notes

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