SPECIAL FEATURE
Roaming is the dominant mechanism for molecular products in acetaldehyde photodissociation Brianna R. Heazlewood*, Meredith J. T. Jordan*, Scott H. Kable*†, Talitha M. Selby‡, David L. Osborn†§, Benjamin C. Shepler§, Bastiaan J. Braams§, and Joel M. Bowman†§ *School of Chemistry, University of Sydney, Sydney NSW 2006, Australia; ‡Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551-0969; and §Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, GA 30322
Reaction pathways that bypass the conventional saddle-point transition state (TS) are of considerable interest and importance. An example of such a pathway, termed ‘‘roaming,’’ has been described in the photodissociation of H2CO. In a combined experimental and theoretical study, we show that roaming pathways are important in the 308-nm photodissociation of CH3CHO to CH4 ⴙ CO. The CH4 product is found to have extreme vibrational excitation, with the vibrational distribution peaked at ⬇95% of the total available energy. Quasiclassical trajectory calculations on fulldimensional potential energy surfaces reproduce these results and are used to infer that the major route to CH4 ⴙ CO products is via a roaming pathway where a CH3 fragment abstracts an H from HCO. The conventional saddle-point TS pathway to CH4 ⴙ CO formation plays only a minor role. H-atom roaming is also observed, but this is also a minor pathway. The dominance of the CH3 roaming mechanism is attributed to the fact that the CH3 ⴙ HCO radical asymptote and the TS saddle-point barrier to CH4 ⴙ CO are nearly isoenergetic. Roaming dynamics are therefore not restricted to small molecules such as H2CO, nor are they limited to H atoms being the roaming fragment. The observed dominance of the roaming mechanism over the conventional TS mechanism presents a significant challenge to current reaction rate theory. reaction dynamics 兩 roaming mechanisms 兩 photochemistry 兩 quasiclassical trajectories 兩 transition state
S
ince its introduction by Eyring in 1935 (1), the concept of the ‘‘transition state’’ (TS) has been central to chemistry because the products, rates, and dynamics of a reaction are often determined by this special molecular configuration (2). For reactions with potential barriers, the TS is a transient molecular structure at the highest point along the minimum energy path connecting reactants to products and thus is a central construct in reaction rate theory and the classification of reaction types. In transition state theory (TST), the reaction rate coefficient is obtained from the ‘‘one-way’’ flux through a dividing surface containing the TS. In the more general variational version of TST, denoted VTST, the TS dividing surface is chosen to minimize the reactive flux. This theory is widely used in mathematical modeling of reaction rates in combustion, atmospheric, and biological chemistry, impacting fields as diverse as energy production (3), climate change (4), and enzyme function (5). Although the conventional transition state paradigm will remain essential to chemists, several reaction pathways have been reported in the last 8 years (6–13) in which it is not obvious how to use present implementations of TST or VTST. If such mechanisms are common, they may represent a significant challenge for reaction rate theories. In this report, we show that the ‘‘roaming atom mechanism’’ in formaldehyde (H2CO) dissociation (9) is not unique to H2CO but also occurs in acetaldehyde (CH3CHO) dissociation. Moreover, in CH3CHO, we find that the roaming mechanism is the dominant pathway to the molecular photodissociation products, CH4 ⫹ CO. The roamingatom pathway in H2CO photodissociation describes a mechanism that bypasses the conventional saddle-point TS to form the www.pnas.org兾cgi兾doi兾10.1073兾pnas.0802769105
molecular products H2 ⫹ CO. (Hereafter, ‘‘conventional saddlepoint TS’’ will be referred to as ‘‘conventional TS.’’) In a combined experimental and theoretical study, Townsend et al. (9) demonstrated two different pathways to molecular products. The dominant mechanism (⬇80%) was assigned to conventional dynamics along the minimum energy path through the well known conventional TS yielding H2 ⫹ CO. The remaining H2 ⫹ CO products arise from an entirely different mechanism, related to the radical channel. At energies near the H ⫹ HCO threshold, sufficient energy can be sequestered in internal modes of HCO such that the nearly free H atom cannot dissociate. Instead, this H atom ‘‘roams’’ around the HCO core at long range (3–4 Å), in a flat region of the potential energy surface (PES), eventually abstracting an H atom from HCO producing highly vibrationally excited H2. This type of ‘‘self abstraction’’ was observed earlier in an interesting direct-dynamics classical study of the CH3 ⫹ O reaction, where the H atom in the nearly formed H ⫹ H2CO product channel abstracts an H atom to give H2 ⫹ HCO (7). In 2006, Houston and Kable (HK) (10) proposed a second example of a roaming mechanism based on experimental CO(v, J) state distributions in the 308-nm photodissociation of CH3CHO. As in H2CO, excitation at 308 nm is followed by internal conversion, preparing highly vibrationally excited CH3CHO on the S0 surface, which dissociates to radical and molecular products (Fig. 1). The minimum energy path to the molecular products, CH4 ⫹ CO, has a well defined saddle-point transition state with energy 84 kcal䡠mol⫺1 above the CH3CHO minimum (see Fig. 1). The CO fragments, speculated by HK to arise from a roaming methyl (CH3) pathway, had little internal or translational energy, implying high excitation in the unobserved CH4 fragment. A preliminary quasiclassical trajectory (QCT) study by Shepler et al. (14) indicated that trajectories initiated from the conventional TS (representing exclusively the conventional TS pathway) produced a CO rotational distribution much hotter than experiment, whereas the distribution obtained from trajectories initiated from the equilibrium CH3CHO geometry are in good agreement with the HK experiment. More recent experiments at 248 nm suggested a greater contribution to the CH4 ⫹ CO roaming channel (12), although at this energy more than one pathway can lead to formation of CO, making interpretation of the experiment potentially ambiguous. Here, we report a combined experimental and theoretical study of the photodissociation of CH3CHO at 308 nm. These experiments probe the CH4 fragment that was not observed in the HK study (10). Together, the CH4 vibrational energy distriAuthor contributions: S.H.K., D.L.O., B.J.B., and J.M.B. designed research; B.R.H., M.J.T.J., T.M.S., D.L.O., B.C.S., and B.J.B. performed research; B.R.H., M.J.T.J., S.H.K., D.L.O., B.C.S., B.J.B., and J.M.B. analyzed data; and M.J.T.J., S.H.K., D.L.O., and J.M.B. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. †To
whom correspondence may be addressed. E-mail: kable㛭
[email protected],
[email protected], or
[email protected].
This article contains supporting information online at www.pnas.org/cgi/content/full/ 0802769105/DCSupplemental. © 2008 by The National Academy of Sciences of the USA
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CHEMISTRY
Edited by F. Fleming Crim, University of Wisconsin, Madison, WI, and approved May 15, 2008 (received for review March 19, 2008)
Fig. 1. Schematic diagram of the sum of electronic energies from G3 theory plus CCSD(T)/aug-cc-pVTZ harmonic zero-point energies of the CH3CHO system, relative to the acetaldehyde zero-point energy. At the energy of 308-nm excitation (red dashed line) both molecular and radical channels are open.
bution and the QCT calculations provide strong evidence for the dominance of the roaming CH3 mechanism in the molecular dissociation channel of CH3CHO. Results and Discussion The major photodissociation products of CH3CHO at 308 nm are CH3 ⫹ HCO, formed after intersystem crossing to the triplet (T1) surface (ref. 15 and references therein). All other products, including CH4 ⫹ CO, as illustrated in Fig. 1, are formed after internal conversion to the S0 surface. Although CH3 ⫹ HCO are also energetically allowed products on the S0 surface, they have not been experimentally observed, and the branching ratios between any of the products in Fig. 1 are unknown. We investigated the products of CH3CHO photodissociation using time-resolved Fourier transform infrared (FTIR) emission spectroscopy (16) [see supporting information (SI) Text]. Fig. 2A shows the emission of all IR-active photoproducts as a function of time after the laser pulse. Spectral intensity is indicated as a color scale. The P and R rotational branches of CO are clearly visible centered at 2,143 cm⫺1. Broad emission in the C–H stretch region at early time, spanning 2,400–3,100 cm⫺1, is indicative of a very highly vibrationally excited molecule. The first spectrum, obtained 1 s after the laser pulse, indicated by the dotted red line in Fig. 2 A, is shown in Fig. 2B. Emission from CO and HCO is clearly identified, as is the broad emission centered at ⬇2,600 cm⫺1. The HCO and CH3 products must be formed vibrationally cold at 308 nm (see Fig. 1), and both have been measured to have only a small fraction of population in excited vibrational states (15, 17). Consequently, the broad C–H emission cannot be attributed to HCO or CH3. Other potential sources of this emission (CH3CO, CH3CHO, CH2CO) are eliminated by similar arguments and additional measurements (see SI Text). This emission is assigned solely to ⌬v ⫽ ⫺1 CH-stretch emission (see Fig. S1) from very hot CH4. To improve the signal-to-noise ratio, the first five spectra (t ⫽ 1–5 s) were averaged and the emission truncated at ⬇2,300 cm⫺1 to exclude CO (Fig. 2C, dashed line). The HCO 1 emission was fit and subtracted, revealing the underlying CH4 3 emission profile (solid line).¶ The raw spectrum was deconvolved with the CH4 rotational contour and instrument resolution functions to
provide a pure vibrational emission spectrum (i.e., a spectrum at 0-K rotational temperature), as shown in Fig. 2D (see SI Text). The energy content of the CH4 fragment was extracted from the spectrum in Fig. 2D as follows. First, note that there are several million vibrational states accessible at the available energy (96.3 kcal䡠mol⫺1). Therefore, it is unfeasible to resolve individual emitting states in the spectrum. This large number of states suggests that a statistical, maximum entropy analysis of the emission is appropriate. To do this, we used the standard Dunham expansion for degenerate vibrational energies, and experimental spectroscopic constants (18) to estimate the state density by direct count. The emission intensity from each of these states was modeled by using harmonic Einstein A coefficients. We tested the assumptions in this model in several ways: (i) the model density of states was compared with known experimental frequencies and the best reported theoretical calculations, which are available up to ⬇9,000 cm⫺1 of vibrational energy; (ii) line-strengths were tested against our own theoretical calculations of CH-stretch local mode oscillator strengths up to 35,000 cm⫺1; and (iii) the effect of the spectroscopic constants on the Dunham expansion energies was checked by allowing each constant to vary by 25% (after which the resultant state densities became unphysical). A discussion of these benchmarking tests can be found in SI Text. With this model, emission frequencies from all initial states ⬍96.3 kcal䡠mol⫺1 were calculated and binned into 10-cm⫺1 intervals. The population of all states emitting into a single bin was treated as equally likely (the maximum entropy assumption), and the relative population in each bin was fit to the experimental spectrum (Fig. 2D, red dots). The model spectrum was reconvolved with the CH4 rotational profile and the instrument function (Fig. 2C, red dots) to compare with the original data (see SI Text). All states in the model were reordered according to the energy of the emitting state, with total population binned into 500-cm⫺1 energy intervals to smooth the energy distribution. The resultant CH4 vibrational energy distribution (Fig. 3) indicates that CH4 is produced with very high vibrational excitation. On average, 70 kcal䡠mol⫺1—that is 75% of the available energy—is distributed into CH4 vibration, with the distribution sharply peaked at ⬇95% of the available energy. This unusual distribution is not
¶The profile in Fig. 2C comprises emission from all populated CH
4 rotational and vibrational states. After 5 s, under our conditions, the rotational distribution should be nearly thermalized, whereas the vibrational population will be little affected. The overall spec-
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trum can therefore be viewed as a pure vibrational spectrum, convolved with a T ⬇ 400 K rotational contour and the 8-cm⫺1 instrument resolution.
Heazlewood et al.
SPECIAL FEATURE CHEMISTRY
Fig. 2. Time-resolved FTIR emission spectra of CH3CHO photodissociation. (A) Two-dimensional image of time-resolved infrared spectra. Cooling of vibrational populations due to collisions leads to blue-shifted spectra as a function of time. Rotational cooling narrows the width of individual vibrational bands. The red dashed line shows the position of the spectrum in B. (B) Spectrum 1 s after photodissociation, showing signatures of CO, HCO, and CH4. (C) CH4 emission with HCO and CO contributions removed. Red symbols, maximum entropy spectrum convolved with 400-K rotational and instrument response functions. (D) CH4 deconvolved vibrational emission spectrum (i.e., 0 K rotational temperature), binned at 10-cm⫺1 intervals.
easily interpreted in terms of the conventional transition state to CH4 ⫹ CO, which is known to have an exit barrier of ⬇90 kcal䡠mol⫺1 (see Fig. 1). In such cases, a large fraction of the exit barrier energy is normally converted into kinetic energy of the separating fragments (19) and hence cannot appear as internal energy. QCT calculations have been used to interpret and provide mechanistic insight into the nature of the dynamics that give rise to the observed CH4 vibrational distribution. QCT calculations were performed on PESs that were described in ref. 14. Briefly, 135,000 high-level ab initio energies储 were fit with permutationally invariant polynomials of total order five and six in terms of Morse variables of all internuclear distances (20, 21). As described in detail elsewhere (22), there 储135,000
ab initio points were computed with the coupled cluster method with single and double excitations and a perturbative treatment of triple excitations [CCSD(T)], using correlation consistent basis sets of double- and triple- quality.
Heazlewood et al.
are many stationary points and reaction products in this system. The topological challenge to fitting the PES in full dimensionality is considerable. Energies obtained for stationary points and fragment channels from the two PESs were benchmarked against new accurate ab initio electronic energy calculations [without zero-point energy (ZPE) or higher-order corrections] in Table 1. These benchmarks indicate that both the fifth- and sixth-order PESs faithfully describe the complexity of this system. Trajectories were run at a total energy corresponding to the experimental 308-nm excitation. The CH4 vibrational energy distribution was determined, as discussed in SI Text, for all trajectories yielding CH4 ⫹ CO. Trajectories initiated from the CH3CHO equilibrium geometry yielded distributions denoted ‘‘EQ Dynamics’’ in Fig. 3. A second set of QCTs, independent of an analytical PES representation, were performed with direct-dynamics calculations starting from the conventional TS for CH4 ⫹ CO formation, using standard microcanonical sampling of the phase-space dividing surface that contains the PNAS 兩 September 2, 2008 兩 vol. 105 兩 no. 35 兩 12721
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EQ Dynamics TS Direct Dynamics
Distribution
0.8
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0.4
0.2
0.0
0
10
20
30
40
50
60
70
80
90
100
CH Vibrational Energy (kcal/mol) 4
Fig. 3. Vibrational energy distributions of CH4 from experiment and two sets of QCT calculations described in the text. A dashed blue line is drawn through the direct dynamics points as a guide.
saddle-point (14, 23, 24). The CH4 vibrational energy distribution resulting from these trajectories is denoted ‘‘TS Direct Dynamics’’ in Fig. 3. The direct-dynamics trajectories calculations are very similar to those for CH3CHO dissociation at 248 nm previously reported by Kurosaki (24). Our results, although at lower total energy, are consistent with these earlier calculations. Because the trajectories initiated at the conventional TS provide, by definition, the internal energy distribution for the conventional TS pathway, we used them to estimate the contribution of this pathway to the experimental distribution. We did this by scaling the QCT TS distribution to agree with the low-energy tail of the experimental one. Calibrated in this way, we conclude that the experiment shows only 16 ⫾ 10% contribution from the conventional TS pathway to CH4 ⫹ CO, with the Table 1. Comparison of the fitted potential energy surfaces and ab initio benchmark electronic energy calculations (without ZPE or higher-level corrections) for selected stationary points on the CH3CHO surface relative to the acetaldehyde minimum (kcal䡠molⴚ1) Species 1. Acetaldehyde 2. Vinyl alcohol 3. Hydroxyethylidene 4. TS1 (1–2) 5. TS2 (1–3) 6. TS3 (2–3) 7. TS4 (1–10) 8. TS5 (3–10) 9. TS6 (1–11) 10. CH4 ⫹ CO 11. CH2CO ⫹ H2 12. CH3 ⫹ HCO 13. CH3CO ⫹ H 14. CH2CHO ⫹ H 15. CH3 ⫹ CO ⫹ H 16. CH2CH ⫹ OH
CCSD(T)/ CBS ⫹ CV
G3
Fifth-order PES
Sixth-order PES
0.0 9.1 50.8 70.8 83.0 75.5 87.5 110.9 86.0 ⫺2.0 35.2 90.8 95.6 102.5 110.5 124.5
0.0 9.6 51.2 70.7 82.9 76.3 87.2 111.8 86.9 ⫺2.7 33.9 89.4 94.0 101.1 107.8 123.7
0.0 13.5 54.0 72.4 87.2 87.6 84.8 102.6 91.8 ⫺2.5 43.5 91.0 100.9 103.7 104.7 141.7
0.0 15.0 53.4 72.5 85.6 81.6 96.1 108.0 95.1 ⫺1.6 37.1 94.0 100.5 103.9 106.0 142.0
The nomenclature for the TSs refers to the numbered species in the table. 12722 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0802769105
remaining 84 ⫾ 10% representing a non-TS, roaming mechanism.** By comparison, using the same scaling procedure for the EQ trajectories, the theoretical roaming fraction is estimated to be 94%. The experimental CH4 vibrational energy distribution is very different from the conventional TS direct-dynamics prediction (Fig. 3) but is well reproduced by the EQ dynamics. This apparent deviation from conventional TS dynamics contrasts with the situation for H2CO dissociation, where the roaming pathway is a minor component of the dynamics (25). In the acetaldehyde case, the majority of EQ trajectories do not approach the conventional TS to CH4 ⫹ CO products. The QCT calculations allow us to explore the nature of these roaming trajectories by visual inspection and also by analysis of configurations where the H atom transfer occurs (14). Three limiting types of roaming mechanisms have been identified, although there is a continuum between each. The dominant roaming mechanism is ‘‘CH3 roaming,’’ as conjectured by HK (10). Nine snapshots from one such trajectory initiated at the CH3CHO equilibrium geometry are shown in Fig. 4. The C–C bond is essentially broken after the first 78 fs and is never substantively reformed. The CH3 is essentially planar and remains so for the rest of the reaction. In this reference frame, the HCO moiety appears to rotate freely next to the CH3. After ⬇150 fs the two fragments approach each other again, with the formyl H atom oriented toward the CH3. The CH3 then strips the H atom, and the two fragments finally depart with the CH4 very highly excited. From the reference frame of a stationary HCO, the CH3 would appear to almost depart, then roam around past the O atom before approaching from the other side and stripping the H atom. This is an example of what we call a ‘‘CH3 roaming’’ trajectory. This trajectory and another example of a CH3 roaming trajectory are available as movies (Movies S1 and S2). Other ‘‘H roaming’’ pathways, in which the aldehyde-H atom nearly dissociates and roams around the CH3CO core, eventually abstracting the CH3 group, were also found. A third type of roaming trajectory involved the near three-body breakup (CH3 ⫹ H ⫹ CO) pathway. This last pathway, however, must be interpreted cautiously. The CH3 ⫹ H ⫹ CO channel is closed experimentally at 308 nm because of ZPE constraints; but the channel is accessible classically, and indeed three-body breakup QCTs were observed. These trajectories were discarded. Based on the C–C bond length distribution reported previously for EQ trajectories (14), the CH3 roaming fraction is estimated as 80% of the total CH4 ⫹ CO channel, while H roaming is a minor mechanism. It is not clear whether there exists a unique metric to define the CH3 roaming fraction; however, it is evident from experiment and theory that CH3 roaming dynamics dominate the conventional TS dynamics for CH3CHO photodissociation to CH4 ⫹ CO at 308 nm. This result arises because the CH3 ⫹ HCO asymptote and the conventional TS to CH4 ⫹ CO products are nearly isoenergetic, and the larger entropy of the radical channel compared with the ‘‘tight’’ molecular TS favors the roaming pathway. The dominant mechanism for CH4 ⫹ CO production is therefore abstraction of the HCO hydrogen by a roaming CH3 group and not the conventional TS mechanism. The H roaming channel, although present in the QCT dynamics, is less important than CH3 roaming. The analogous radical dissociation pathway for H roaming is H ⫹ CH3CO. From Table 1 it can be seen that this pathway lies 7–8 kcal䡠mol⫺1 above the conventional TS to CH4 ⫹ CO (⬇10 kcal䡠mol⫺1 on the fitted PESs). The QCT results indicate that this energy difference is the **We have performed a large number of tests on both experimental and theoretical datasets to explore the robustness of these branching ratios (see SI Text).
Heazlewood et al.
78 fs
102 fs
126 fs
150 fs
174 fs
198 fs
fFig
222 fs
246 fs
Fig. 4. Frames of a sample CH3 roaming trajectory leading to CH4 ⫹ CO via a roaming pathway described in detail in the text.
key feature in determining which roaming mechanism is dominant. For comparison, in H2CO dissociation, the difference between radical (H ⫹ HCO) dissociation and the TS to H2 ⫹CO Heazlewood et al.
Conclusions In this article, we have presented experimental evidence that the CH4 product from 308-nm photodissociation of CH3CHO is formed with extremely high vibrational energy. The peak in the experimental CH4 vibrational energy distribution is at ⬇95% of the available energy. QCT calculations were used to interpret this distribution and reveal that the dominant mechanism for CH4 ⫹ CO production is a CH3 roaming mechanism. We have therefore demonstrated that roaming dynamics are not restricted to small molecules such as H2CO, nor are they limited to H atoms being the roaming fragment. The conventional TS and other roaming mechanisms were also observed but found to be minor. Comparison with direct-dynamics calculations initiated at the conventional TS allowed us to estimate that the roaming mechPNAS 兩 September 2, 2008 兩 vol. 105 兩 no. 35 兩 12723
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54 fs
is also ⬇8 kcal䡠mol⫺1, and H roaming was found to be the minor pathway to molecular products, similar to the H roaming pathway determined here for CH3CHO. Because the roaming pathways occur in regions of incipient radical formation, it seems reasonable that there is competition between the radical channel(s) and the molecular one via roaming. Radical products can only be formed if sufficient energy is in the appropriate degrees of freedom. As the sizes of the radical fragments increase, energy is more likely to be sequestered within the internal degrees of freedom, and it follows that roaming mechanisms may become more prevalent as the number of atoms in the system increases. Roaming mechanisms may therefore have a much broader impact in chemical reactions than previously anticipated. For example, in the combustion of fuels, roaming pathways would replace some free radicals with less reactive, closed-shell molecules, with ramifications in the delicate balance of chain propagation, branching, and termination. Because roaming pathways have only recently been reported in joint experiment/theoretical research, where experimental observables were correlated with dynamics via roaming pathways (9), it is not surprising that methods for incorporating roaming dynamics into predictive models of chemical systems have not yet been developed. In both H2CO and CH3CHO, roaming pathways to the molecular dissociation products involve internal abstraction within the radical dissociation channels. Harding et al. (26) have recently located what they refer to as ‘‘roaming transition states’’ for both H2CO and CH3CHO decomposition. These stationary points are very loose, first-order saddle points lying 0.1–1.0 kcal䡠mol⫺1 below the radical dissociation asymptotes. They are located in a very flat region of the PES within the broad region of roaming geometries seen in the QCT calculations. Harding et al. were correctly circumspect about their results and wrote, ‘‘Because this [roaming] pathway involves large amplitude, anharmonic motion, this saddle point (and the reaction path associated with it) should be regarded as only representative of the region of the potential surface controlling this process.’’ Using the standard harmonic-rigid rotor model, they obtained a flux through this roaming TS ⬇20 times that of the tight transition state and concluded that an ‘‘anharmonic treatment would likely give a much lower dissociation rate.’’ In CH3CHO, the roaming saddle point is nearly isoenergetic with the conventional TS and the relative flux through the roaming saddle point surface will be even higher than in H2CO. Thus, the roaming saddle point is most likely not the dynamical bottleneck in the CH3CHO reaction. The identification of these roaming saddle points is important, however, and their presence suggests that statistical approaches to calculating rates may yet be possible if appropriate dividing surfaces can be constructed with proper treatment of low-frequency vibrations. It will be important to have experimental data on roaming mechanisms in larger systems to compare with theory, although such experiments will also be challenging.
anism accounts for 84 ⫾ 10% of the total CH4 ⫹ CO flux. We conclude that the dominance of the CH3 roaming over both conventional TS dynamics and H roaming is due to the fact that the CH3 ⫹ HCO radical asymptote and the TS barrier to CH4 ⫹ CO are nearly isoenergetic. We predict, as a consequence, that such roaming mechanisms may be more widespread and important in other systems with these characteristics. Materials and Methods Liquid CH3CHO (Sigma–Aldrich; 99.5%) was degassed by bubbling helium through the sample. Approximately 31 standard cm3䡠min⫺1 (sccm) of neat CH3CHO (at 293 K) was subsequently delivered through a calibrated mass flow controller. Pressure in the cell was maintained at 137 mtorr by a computercontrolled valve throttling the vacuum pump. A schematic of the optical set-up is shown in Fig. S2. CH3CHO was excited by using an unfocused 308-nm excimer laser (30-Hz repetition rate). The resulting infrared emission was collected by Welsh-type multipass optics and focused into an evacuated FTIR spectrometer (Bruker IFS 66v/S) operated in step-scan mode. The FTIR spectrometer was operated under vacuum and was attached to a vibrationisolated table. A liquid-nitrogen-cooled InSb photodiode was used as a detector. The ac-coupled output was amplified and recorded every 1 s. A digital delay/pulse generator orchestrated timing and triggering, with data collection initiated 40 s before the laser fired. Electronic energies describing the stationary points and separated fragments on the CH3CHO potential energy surface were determined by using both the model G3 chemistry (27) and a coupled cluster composite approach (ref. 28 and reference therein). The latter method involved optimizing the geometries by using the CCSD(T)/aug-cc-pVTZ method and performing singlepoint energy calculations at CCSD(T)/cc-pVnZ (n ⫽ T, Q, 5) to extrapolate to the 1. Eyring H (1935) The activated complex in chemical reactions. J Chem Phys 3:107–115. 2. Manolopoulos DE, et al. (1993) The transition-state of the F⫹H2 reaction. Science 262:1852–1855. 3. Truhlar DG, Garrett BC, Klippenstein SJ (1996) Current status of transition-state theory. J Phys Chem 100:12771–12800. 4. Arakawa H, et al. (2001) Catalysis research of relevance to carbon management: Progress, challenges, and opportunities. Chem Rev 101:953–996. 5. Garcia-Viloca M, Gao J, Karplus M, Truhlar DG (2004) How enzymes work: Analysis by modern rate theory and computer simulations. Science 303:186 –195. 6. ter Horst M, Schatz GC, Harding LB (1996) Potential energy surface and quasiclassical trajectory studies of the CN⫹H2 reaction. J Chem Phys 105:558 –571. 7. Marcy TP, et al. (2001) Theoretical and experimental investigation of the dynamics of the production of CO from the CH3⫹O and CD3⫹O reactions. J Phys Chem A 105:8361– 8369. 8. Sun LP, Song KY, Hase WL (2002) A SN2 reaction that avoids its deep potential energy minimum. Science 296:875– 878. 9. Townsend D, et al. (2004) The roaming atom: Straying from the reaction path in formaldehyde decomposition. Science 306:1158 –1161. 10. Houston PL, Kable SH (2006) Photodissociation of acetaldehyde as a second example of the roaming mechanism. Proc Nat Acad Sci USA 103:16079 –16082. 11. Lopez JG, et al. (2007) A direct dynamics trajectory study of F⫺⫹CH3OOH reactive collisions reveals a major non-IRC reaction path. J Am Chem Soc 129:9976 –9985. 12. Rubio-Lago L, et al. (2007) Slice imaging of the photodissociation of acetaldehyde at 248 nm. Evidence of a roaming mechanism. Phys Chem Chem Phys 9:6123– 6127. 13. Mikosch J, et al. (2008) Imaging nucleophilic substitution dynamics. Science 319:183– 186. 14. Shepler BC, Braams BJ, Bowman JM (2007) Quasiclassical trajectory calculations of acetaldehyde dissociation on a global potential energy surface indicate significant non-transition state dynamics. J Phys Chem A 111:8282– 8285. 15. Thompson KC, Crittenden DL, Kable SH, Jordan MJT (2006) A classical trajectory study of the photodissociation of T1 acetaldehyde: The transition from impulsive to statistical dynamics. J Chem Phys 124:044302.
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complete basis set (CBS) limit. Core-valence (CV) corrections were calculated as the difference in energy between all-electron and valence-only correlation calculations; i.e., the difference between calculations at the CCSD(T)/aug-ccpwCVTZ and CCSD(T)/aug-cc-pVTZ levels of theory. Sixty-eight hundred and 4000 QCTs were run on each of the fifth- and sixth-order PESs, respectively, starting at the CH3CHO equilibrium geometry. Four hundred eighty-seven direct-dynamics trajectories calculated at the MP2/ cc-pVDZ level of theory and basis were started at the TS geometry for molecular products. In all cases, the total energy corresponded to photolysis at 308 nm; that is, 308-nm excitation plus the CH3CHO harmonic ZPE. For both the direct-dynamics TS and EQ trajectories, this energy was randomly distributed to the Cartesian momenta in all degrees of freedom by using microcanonical sampling, subject to the constraints of zero total angular and linear momentum (23). For the former set of trajectories, the phase space dividing surface that contains the conventional TS was sampled. The CH4 vibrational energy was determined for all trajectories yielding CH4 ⫹ CO by subtracting the ‘‘instantaneous’’ CH4 rotational energy from the total CH4 internal energy, as described in SI Text. The resulting CH4 vibrational distribution, averaged over the fifth- and sixth-order PESs, is given in Fig. 3. The CH4 vibrational energy distributions for each PES are shown separately in Fig. S3. ACKNOWLEDGMENTS. Mr. Howard Johnsen is gratefully acknowledged for excellent technical support. This work was supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the National Nuclear Security Administration under Contract DE-AC04-94-AL85000. J.M.B. and B.C.S. thank the Department of Energy (DE-FG02-97ER14782) and BJB thanks the Office of Naval Research (N00014-05-1-0460) for financial support. The Sydney group thanks the Australian Research Council (DP0772006) for financial support and an Australian Postgraduate Award (to B.R.H.).
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