Experimental and Theoretical Studies of Roaming Dynamics in the Unimolecular Dissociation of CH 3 NO 2 to CH 3 O + NO

Z. Phys. Chem. 227 (2013) 1267–1280 / DOI 10.1524/zpch.2013.0409© by Oldenbourg Wissenschaftsverlag, München

Experimental and Theoretical Studies of RoamingDynamics in the Unimolecular Dissociation ofCH3NO2 to CH3O+++ NO

By Zahra Homayoon1, Joel M. Bowman1,∗, Arghya Dey2, Chamara Abeysekera2,Ravin Fernando2, and Arthur G. Suits2,∗1 Department of Chemistry and Cherry L Emerson Center for Scientific Computation, Emory University,

Atlanta, GA 30322, USA2 Department of Chemistry, Wayne State University, Detroit, MI 48202, USA

(Received March 5, 2013; accepted in revised form May 4, 2013)

(Published online July 8, 2013)

Roaming Reaction / Photochemistry / Theoretical Dynamics / TrajectoryCalculations / Potential Energy Surfaces / Isomerization

Characteristic signatures of roaming are seen in the translational energy distribution and rotationalenergy distributions in the products CH3O + NO from the unimolecular dissociation of nitromethanein both theory and experiment. Calculations on a new global potential energy surface revealthe detailed roaming-isomerization dynamics in this process, and these are supported by theexperimental observations. Calculations find a characteristic of roaming, namely production ofvibrationally excited CH3O, which is consistent with experiment. This continues to challengethe conventional idea in transition state theory of a localized transition state bottleneck that isa cornerstone of chemical reaction theory.

1. Introduction

Transition state theory (TST), which dates back to the 1930s [1,2], is the ubiquitoustheory of reaction rates. Its widespread use is overwhelmingly in the form given in theoriginal papers. The theory identifies the bottleneck to the reaction by locating a first-order saddle point separating reactants from products. The transition-state partitionfunction is obtained using a separable vibration-rotation analysis, i.e., by performinga normal mode analysis of the vibrations and a rigid-rotator analysis of the rotations atthe saddle point and evaluating the resulting partition function, denoted Q ′

TS, where theprime indicates that the energy zero is relative to the saddle point energy Vsp. Then interms of these quantities and the total partition function for the reactants, denoted Qreact,

* Corresponding authors. E-mail: [email protected]; [email protected]

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1268 Z. Homayoon et al.

the TST expression for the rate constant, k(T ) is [3]

k(T ) = kBT

h

Q ′TS

Qreact

exp(−Vsp/kBT) (1)

where kB is the Boltzmann constant and h is Planck’s constant, and where the referencegiven is a popular undergraduate textbook in physical chemistry.

Historically, the H + H2 reaction has played a major role in formulating and alsotesting the accuracy of TST. In considering both the significant barrier in this reaction,as well as the light mass of hydrogen, quantum mechanical tunneling clearly becamean issue to be addressed. This important effect is missing in Eq. (1) and formulatingcorrections due to tunneling to TST has arguably occupied more thinking and researchthan other corrections to TST. In general, the correction to TST is expressed by a simplemultiplicative factor, denoted κ(T), and often referred to as the transmission coefficient.Wigner derived a simple expression for κ(T), that elegantly made use of the informationcontained in the normal-mode analysis of the TS at the saddle point [2]. Going beyondthat simple theory has become a major research area and the literature on quantum me-chanical tunneling corrections to transition state theory is huge, and certainly beyondthe scope of this paper. Review articles by Miller [4], Truhlar [5], and others can be con-sulted for much more about this. However, it is worth noting that the majority of moresophisticated treatments of tunneling, e.g., the Eckart treatment, are one dimensionalin the kinetic energy operator and require information about the potential away fromthe saddle point, e.g., along the so-called reaction path connecting the saddle point tothe reactants and products [6–8]. This is a major departure from the theory representedby Eq. (1), which requires much less information about the potential. As correctionsto TST have become evermore sophisticated, including consideration of the local zero-point energy, more information about the potential energy surface (PES) is needed. Forexample, methods that utilize two mathematical degrees of freedom (dof) in the kineticenergy operator require information about PES in that 2 dof space. One of the most re-cent reviews of this so-called reduced dimensionality quantum approach is now morethan 10 years old [9]; however, the method is currently being used, with significantimprovements and success to polyatomic reactions [10]. Recent work on full dimen-sionality quantum and semi-classical approaches [11–14] that are still TST-oriented,require full-dimensional, if not global information about the PES.

To close this very brief review of the key ideas of conventional TST and modern ex-tensions of it, it is worth showing a figure of the potential along the reaction path froma very accurate H3 PES as well as the “zero-point corrected” energy along this path.These are shown in Fig. 1, but for the unusual variant of the H + H2 reaction, namelyMu + H2 → MuH + H, where Mu (muonium) is a light metastable analogue of H. Thisfigure shows the extreme effect of adding the local ZPE, which greatly affects the reac-tion dynamics and which has been beautifully analyzed in detail recently [15]. As seen,unlike V(s), the effective potential is not thermoneutral and it has a maximum not at thesaddle point on the potential. This simple reaction also illustrates several aspects of thewidespread quasiclassical trajectory (QCT) method. For a detailed discussion of thesespecifically for this reaction, see references [15,16]. However, one important point tonote in QCT is that the reactant is given zero-point energy and there has been muchdiscussion about subsequent “leakage” of this energy as the reaction proceeds, unlike



Roaming Dynamics in the Unimolecular Dissociation of CH3NO2 1269

Fig. 1. Reaction path potential, V(s), for the Mu + H reaction taken from an ab initio potential energy sur-face and also the effective potential including the local zero-point energy.

the assumption of no leakage in a quantum calculations. Clearly, the Mu + H2 reactionexhibits a large effect of this presumed conserved zero-point energy and indeed QCTcalculations do reflect this adiabaticity to a large extent [16] (as do exact quantum cal-culations) and thus the threshold for the reaction is in good accord with the maximumin the effective potential shown in the figure.

With the advent of QCT calculations on model, but full dimensional PESs foratom-diatom reactions in the 1970s, examples of reaction pathways that were “non-TST” were discovered. One striking example came from the Polanyi group, who hadmeasured a bimodal vibrational distribution in HCl from the reaction H + ICl in chemi-luminscence experiments [17]. Trajectories on a model PES revealed two microscopicmechanisms for formation of HCl; these were labeled “direct” and “migratory” [18].The direct mechanism was the usual TS one, that is, the H atom approaches ICl onthe Cl side passing over the saddle point and forms HCl, and with low vibrational ex-citation. A surprising, “migratory” mechanism has the H attacking the I side of ICl,followed by a rebound and then subsequent reaction via insertion into ICl. This pathwayresults in vibrationally excited HCl. Other examples of (high-energy) bimolecular re-actions that sample regions of configuration space far from the reaction path have beenreported in joint work by Zare, Schatz and Hase and reviewed recently [19,20].

In the case of unimolecular reactions, a striking example of a two-pathway mechan-ism was reported in 2004 for the highly-studied photodissociation of H2CO to molecu-lar products H2 + CO [21]. The first pathway is via the conventional, tight first-ordersaddle point. The second one, termed “roaming”, was a surprising one. In this pathway,H2CO begins to fragment in the direction of the radical products, H + HCO, but doesnot form them owing to insufficient relative translational energy. However, instead ofre-forming the H2CO complex, which does happen in many trajectories, the incipientradicals “self-react” at large HH separations to form H2, highly vibrationally excited,and CO. This second pathway thus deviates dramatically from the conventional tight TSpathway. Representations of this roaming pathway and detailed analysis of new experi-




ments have appeared in the literature along with reviews of this phenomenon [19–26].There are now numerous examples of roaming in unimolecular reactions. The follow-ing is a list of reactions where roaming has been identified as a reaction pathway anda partial list of references for each: H2CO [20–27], CH3CHO [28–31], (CH3)2CO [32]HOONO [33], various alkanes [34,35], C2H4OH [36], (CH3)2O [37] NO3 [38–41],CH3NH2 [42], C6H5NO2 [43], HCOOH [44], and CH3NO2 [45,46]. Roaming has alsobeen reported in bimolecular reactions, H + HCO [47] and in a quantum scattering cal-culation of the reaction MgH + H → Mg + H2 [48].

Finally, we direct the interested reader to recent reviews and perspectives of roam-ing [20,24–27].

The present paper focuses on the dynamics of the unimolecular dissociation ofCH3NO2, which as noted above does exhibit roaming dynamics. Nitromethane (NM)is a simple prototype energetic molecule, and its photodissociation dynamics havebeen studied for many years both in the ultraviolet and via infrared multiphoton dis-sociation (IRMPD) on the ground electronic state [49–55]. In the classic paper byWodtke, Lee and coworkers [55], the IRMPD studies documented two decompositionchannels:

CH3NO2 +nhv → CH3 +NO2 (R1)

CH3NO2 +nhv → CH3ONO∗ → CH3O+NO (R2)

with branching to R2 accounting for 40% of the dissociation events. This large per-centage implied efficient isomerization to the nitrite prior to dissociation. The en-ergy barrier for isomerization was estimated to be 55.5 kcal mol−1, based on theRRKM modeling with some assumptions about the isomerization TS properties [55].This is about 5 kcal mol−1 lower than the C-N bond fission threshold, therefore, ac-counting for the significant NO yield. Subsequent theoretical calculations from manygroups [56–58] failed to identify an isomerization TS at an energy consistent withthe substantial branching to R2. In 2009 Zhu and Lin [45] reexamined the theoret-ical calculations of CH3NO2 decomposition. They confirmed a loose transition state(TS1 in Fig. 2), reported by Mckee [59] and Saxon et al. [60] at a large C-N dis-tance just below the C-N dissociation threshold and suggested it could be analogousto the roaming behavior seen in formaldehyde, i.e., roaming isomerization for theCH3NO2 ↔ cis-CH3ONO reaction. They reproduced the experimental branching ratioof Ref. [55] by this pathway. The interesting background and unknown mechanismof NM decomposition encouraged us to do dynamical calculations based on a globalpotential energy surface (PES) and to undertake state-resolved imaging experimentsin parallel. Properties of the new fitted PES have been reported in our recent pa-per [46] and so only a brief description of the PES will be presented in the nextsection.

Using the PES, quasiclassical trajectory calculations (QCT) were performed toinvestigate the details of the roaming pathway and the branching ratio of the reac-tions R1, R2 and reaction R3, which is the lowest energy plausible product channel:

CH3NO2 → CH3ONO∗ → CH2O+HNO . (R3)




Fig. 2. Schematic of the fitted potential energy surfaces (with harmonic zero-point energy) of CH3NO2 in-dicating CH3 + NO2 and CH3O + NO products channels.

From analyzing the reactive trajectories to the CH3O + NO products, reaction R2,a roaming-isomerization pathway was found but the C-N distances for the isomer-ization step are at significantly larger distances than the loose saddle-point (Fig. 10Ref. [46]).

In the present work the translational energy distributions for reaction R2 are re-ported and compared to DC slice imaging [61] measurements of the 266 nm pho-todissociation of NM. Although we are here comparing ground state trajectory cal-culations with UV photodissociation results, we will argue below that it is likelythat the UV excitation leads ultimately to ground state dissociation following internalconversion.

The paper is organized as follows. Relevant details of the experiment and calcula-tions are presented, followed by results. We give theoretical results first along with theevidence of roaming mediated isomerization. The experimental results, which presentlyconsist of translational energy distributions for specific NO-rotational states, along withstate-selected angular distributions, are then given, followed by a brief discussion of thetwo sets of results. A brief summary and conclusions are given in the final section.

2. Details of the experiment and calculations

2.1 Experiment

A detailed description of the DC sliced imaging apparatus used in this experiment is de-scribed elsewhere [61,62]. A brief explanation of the current experimental conditions isreported here. The buffer gas helium having a backing pressure of 2 atm was bubbledthrough nitromethane maintained at 298 K. The molecular beam is generated by super-sonic expansion into the source chamber through a pulsed nozzle (General Valves series




9) of diameter 0.3 mm. The expanded beam passes into the detection chamber througha skimmer of 1 mm diameter and enters the DC sliced imaging ion optics assemblycomprising of four electrodes where it intersects with two counterpropagating laserbeams of 266 nm and ∼ 226 nm. The pressure of the source chamber and the detec-tion chamber was maintained at 1×10−5 Torr and 1×10−7 Torr respectively. The twolaser beams of 266 nm and 226 nm were generated from different sources. The 266 nmbeam was generated from the fourth harmonic of the fundamental of Nd : YAG laser andmaintained near 1 mJ pulse. The 266 nm beam was used both for dissociation and toionize the NO product following resonant excitation via the A state by the 226 nm beamin a 1 + 1′ scheme. The intensity of the 226 nm beam was attenuated to ∼ 50 μJ/pulseto eliminate any photodissociation signal arising from the probe. The 226 nm beamwas repetitively scanned across the Doppler profile of the transition while accumulatingeach image. Both the beams were aligned counterpropagating and focused loosely onthe molecular beam through a lens having focal length of 250 mm. The temporal over-lap between the two laser beams was controlled through a digital delay generator. Theions originating from the interaction of the laser beams with the molecular beam weredirected through the time-of-flight tube and detected by a 120 mm dual microchannelplate detector coupled with a P-47 phosphor screen. The ion image was captured usinga USB CCD camera (USB 2 uEye SE, IDS) and the acquisition was performed using theour own NuACQ program. The acquired image was then analyzed to obtain the trans-lational energy distributions for the various rotational levels. The distributions for Qand R branches from the same lower state were not independently normalized, so therelative intensities seen faithfully reflect the populations.

2.2 The global PES and QCT calculations

The calculations made use of the global potential energy surface for CH3NO2 decom-position [46]. The PES is a permutationally invariant representation of 114 000DFT/B3LYP energies describing isomerization and dissociation channels of NM. ThePES precisely reproduces the reaction paths, as described in Ref. [46]. Here we presentthe relevant channels of reaction 2 from the PES in Fig. 2. TS1 is the loose saddle point(SP) that connects CH3NO2 to cis-CH3ONO. Cis- and trans-CH3ONO isomerizationtakes place via TS2. Finally CH3O + NO products are from O-N bond dissociation ofCH3ONO. We also present the CH3 + NO2 products from C-N bond dissociation of NMthat is relevant to the roaming path.

The calculations are at three different energies, 54.9 (E1), 62.9 (E2) and 88.8(E3) kcal mol−1 above the harmonic zero point energy of the CH3NO2 global minimum(GM). 30 000 trajectories were run using the global PES with a maximum of 4 000 000steps (with 0.097 fs step-size) for 54.9 and 62.9 kcal mol−1 energies. The trajectorieswere initiated at the GM. As we discussed in our recent paper [46], the dominantchannel with increasing energy is R1. Therefore, at 88.8 kcal mol−1 energy 150 000 tra-jectories were run with 30 000 time steps. The trajectories were terminated when oneof the internuclear distances became larger than 20 bohr. To deal with the usual ZPE is-sues of QCT we adopt the “hard-constraint” in which trajectories are discarded if eitherfragments NO or CH3O is formed with less than the (harmonic) ZPE.




Fig. 3. Frames of a roaming trajectory forming CH3O + NO from GM. Time sequences proceed alphabeti-cally.

3. Results and discussion

Figure 3 shows frames of a sample roaming trajectory initiated at CH3NO2. global min-imum. The trajectory was run at 88.8 kcal mol−1 energy above the harmonic zero pointenergy of the GM. The energized CH3NO2 enters the incipient radical channel, CH3–NO2, but at large CN distances (around 4.7 Å) orients and enters the cis-CH3ONO wellat low relative kinetic energy. Finally, products form following N–O bond dissociation.We also examined the variation of all internuclear distances for several reactive trajecto-ries leading to CH3O + NO products. This is shown in Fig. 4 for the active internucleardistances for a reactive trajectory at 88.8 kcal mol−1 energy. As seen, for this sample tra-jectory C–N, C–O(1) and C–O(2) distances increase for the roaming step up to roughly4.5 Å. The O(2)-atom exchange occurs after several vibrations of the isomer complexand, as seen, the CO(2) bond is formed vibrationally excited. Clearly from this sampletrajectory the CH3ONO isomer configuration is very short-lived.

Translational energy distributions of products for three total energies are shown inFig. 5. The lowest energy, 54.9 kcal mol−1, is about 2 kcal mol−1 above the CH3 + NO2

asymptote. For this case there is 18.3 kcal mol−1 energy available for CH3O + NO prod-ucts (R2). The available energies increase with increasing the total energy up to 26.3and 52.2 kcal mol−1 for E2 and E3. As seen, the translational energy distributions are




Fig. 4. The variation of internuclear distances for a sample trajectory running from the CH3NO2 globalminimum leading to CH3O and NO at 88.8 kcal mol−1 energy (relative to the CH3NO2 zero-point energy).

quite “cold”, roughly 2.5, 5, and 9 kcal/mol average translational energy release for thethree energies. This is qualitatively the expected result from the barrierless dissocia-tion from the CH3ONO isomers. As seen, at the lowest total energy the P(ET) peaks at1 kcal mol−1. This is in good agreement with the experiment of Wodtke et al. [55]. forthe experiment near the threshold for formation of CH3O + NO. As the total energy in-creases, the P(ET) remains cold with the peak increasing by only a few kcal mol−1 evenat the highest energy, more than 30 kcal mol−1 higher than the threshold energy. TheNO rotational distributions have been calculated at these three total energies. The oneat the highest energy, E3, is shown in Fig. 6. As seen, the distribution is broad, witha maximum in the range J = 20–30. This corresponds to roughly 2.5 kcal mol−1 of rota-tional energy, and this, coupled with the calculated low degree of vibrational excitationin NO (roughly peaking at about 1 kcal mol−1) and the cold P(ET) distribution impliesthat the CH3O is highly internally excited, and this is indeed the case. At this levelof internal excitation, the methoxy radical product will ultimately undergo secondarydecomposition to CH2O + H or HCO + H2.

The experimental results are now presented and discussed in relation to the theor-etical observations. The DC sliced images of various rotational states of NO obtainedfrom the photodissociation of nitromethane at 266 nm are presented in Fig. 7. The totalcenter-of-mass translational energy distributions are also displayed alongside. In theimages, the brighter regions indicate higher intensity of the products and the distancefrom the center of the image is the measure of increasing velocity. The images recorded




Fig. 5. Translational energy distribution of the products of reaction (R2) at the indicated total energies.

Fig. 6. Calculated NO rotational distribution corresponding to a photolysis energy of 88.8 kcal mol−1.

for the different probed levels of Q- and R-branches of NO from nitromethane dissocia-tion are almost identical as seen from the overlapping translational energy distributions.This implies the absence of a lambda doublet propensity in the decomposition [63].




Fig. 7. Direct current sliced images of NO from the photodissociation of nitromethane by excitation at∼ 226 nm and dissociation at 266 nm. The images were recorded for the Q- and R-branches of various ro-tational levels. The total translational energy distributions obtained from the images for the Q- (blue) andR-branches (red) are also presented. A trace of residual signal from NO2 dissociation used for calibrationis visible in some images but makes no significant contribution to the product distributions.




Fig. 8. Angular distributions obtained from Fig. 7 for indicated rotational level and probe transition. Fittedanisotropy parameters are indicated in each plot.




The images of NO at all rotational levels consistently peak at total translational en-ergy release of 10–16 kcal mol−1 while extending to a limit of 40 kcal mol−1 or so.This is somewhat in excess of the QCT results at 88 kcal mol−1 but our energy isabout 107 kcal mol−1 above the GM, readily accounting for the difference. The trendsare the same. The images all show a similar average translational energy release of∼ 16 kcal/mol.

The images also show some anisotropy, which is quantified in Fig. 8. They are con-sistently modestly parallel dissociations with anisotropy parameters, β, ranging fromto 0.25 for low J up to β = 0.45 at the highest levels. This is an unexpected feature ofroaming dynamics implying a somewhat short lifetime for the excited molecule on theground state. Examination of several trajectories at the highest collision energy giveslifetimes on the order of a few picoseconds, which is below the rotational period, likelyon the order of 10–20 ps for the low rotational levels populated in the molecular beam.This, particularly in light of the higher energy of the experiment compared to the theory,is consistent with our observation of anisotropy in the images.

This raises the opportunity to discuss the nature of the electronic excitation andplausible decay pathways at this energy. There is a weak transition centered at 271 nmand a much stronger one centered at 180 nm relevant to the 193 nm dissociationstudies. The first band was long assigned to an n(O) →π∗(NO) transition based ona 1954 assignment [64]. Recent CASPT2 calculations have led to a reassignment asa σ(CN) →π∗(NO) transition [65]. This band was studied by Schoen et al. [66] andMialocq et al. [67] who both reported simple bond fission to CH3 and NO2 as the ma-jor channels. At slightly higher energies, formation of NO2 in the 2B2 excited state hasbeen reported, while at in the second band formation of NO2 in the second excited statedominates and multiphoton processes are invoked to account for the NO2 dissociation.In an infrared emission study, Wade and coworkers [68] reported a vanishing yield ofNO∗

2 at 266 nm, consistent with predominant formation of CH3 and ground state NO2 atthis energy. These observations further justify the comparison of our UV dissociationstudies with the ground electronic state dynamics. All of the excited states in this re-gion were found to have dissociation barriers on along the C-N coordinate [65]. Furtherconfirmation will come in planned IRMPD studies in the near future.

4. Summary and conclusions

Very low translational energy release and rotational excitation are observed in the NOproducts of nitromethane dissociation under collisionless conditions at 266 nm. Thisimplies both an efficient isomerization pathway, and one that gives rise to very high in-ternal excitation in the methoxy radical coproduct. Roaming-mediated isomerization,clearly seen in the trajectory calculations, is a likely means of accounting for these ob-servations. Calculations on a new global potential energy surface reveal the detailedroaming-isomerization dynamics in this process, and these are supported by the experi-mental observations. Calculations find a characteristic of roaming, namely productionof vibrationally excited CH3O, which is consistent with experiment. This continues tochallenge the conventional idea in transition state theory of a localized transition statebottleneck that is a cornerstone of chemical reaction theory.




Acknowledgement

J. M. B. thanks the Army Research Office (W911NF-11-1-0477) and A. G. S. acknowl-edges the ARO under award number 58245-CH-II for financial support. We thankB. Joalland for performing exploratory excited state calculations.

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Experimental and Theoretical Studies of Roaming Dynamics in the Unimolecular Dissociation of CH 3 NO 2 to CH 3 O + NO