Photodissociation resonances of jet-cooled NO2 at the dissociation threshold by CW-CRDS.

Photodissociation resonances of jet-cooled NO2 at the dissociation threshold by CW-CRDS Patrick Dupré Citation: The Journal of Chemical Physics 142, 174305 (2015); doi: 10.1063/1.4919093 View online: http://dx.doi.org/10.1063/1.4919093 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/142/17?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Dissociation dynamics of thiolactic acid at 193 nm: Detection of the nascent OH product by laser-induced fluorescence J. Chem. Phys. 120, 6964 (2004); 10.1063/1.1667878 Vibronic structure and photodissociation dynamics of the Ã state of jet-cooled ammonia J. Chem. Phys. 116, 9315 (2002); 10.1063/1.1471908 Specific rate constants k (E,J) for the dissociation of NO 2 . II. Linewidths of rotationally selected NO 2 near to the dissociation threshold J. Chem. Phys. 115, 6531 (2001); 10.1063/1.1398306 Emission spectroscopy of photodissociating N 2 O 4 excited near 200 nm to the π nb,O π NO 2 * /nσ N–N * avoided crossing J. Chem. Phys. 111, 8486 (1999); 10.1063/1.480189 Photofragment excitation spectrum for O(1D) from the photodissociation of jet-cooled ozone in the wavelength range 305–329 nm J. Chem. Phys. 106, 6390 (1997); 10.1063/1.473629

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THE JOURNAL OF CHEMICAL PHYSICS 142, 174305 (2015)

Photodissociation resonances of jet-cooled NO2 at the dissociation threshold by CW-CRDS Patrick Dupréa) Laboratoire de Physico-Chimie de l’Atmosphère, Université du Littoral Côte d’Opale, 189A Avenue Maurice Schumann, 59140 Dunkerque, France

(Received 28 July 2014; accepted 15 April 2015; published online 4 May 2015) Around 398 nm, the jet-cooled-spectrum of NO2 exhibits a well identified dissociation threshold (D0). Combining the continuous-wave absorption-based cavity ringdown spectroscopy technique and laser induced fluorescence detection, an energy range of ∼25 cm−1 is analyzed at high resolution around D0. In addition to the usual molecular transitions to long-lived energy levels, ∼115 wider resonances are observed. The position, amplitude, and width of these resonances are determined. The resonance width spreads from ∼0.006 cm−1 (i.e., ∼450 ps) to ∼0.7 cm−1 (∼4 ps) with large fluctuations. The identification of at least two ranges of resonance width versus the excess energy can be associated with the opening of the dissociation channels NO2 → NO X 2Π1/2, v = 0, J = 1/2 + O 3 P2 and NO2 → NO X 2Π1/2, v = 0, J = 3/2 + O 3 P2 . This analysis corroborates the existence of loose transition states close to the dissociation threshold as reported previously and in agreement with the phase space theory predictions as shown by Tsuchiya’s group [Miyawaki et al., J. Chem. Phys. 99, 254–264 (1993)]. The data are analyzed in the light of previously reported frequency- and time-resolved data to provide a robust determination of averaged unimolecular dissociation rate coefficients. The density of reactant levels deduced (ρreac ∼ 11 levels/cm−1) is discussed versus the density of transitions, the density of resonances, and the density of vibronic levels. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4919093]

I. INTRODUCTION

The study of highly excited (high-lying) vibrational and rovibrational molecular energy levels, i.e., for interatomic distances beyond the region of the potential energy surface (PES) minima, is of crucial interest to quantify the dissociation processes. Unfortunately, the experimental access of these levels is usually difficult by one-step absorption-based spectroscopic techniques. The main reason is the weakness of the vibrational overlap between initially populated and assignable lower levels, and the targeted single-state (if possible) upper levels. For a polyatomic molecule, this comes from the large dissemblance between the vibrational wavefunctions involved. Multi-step (or multi-photon, like double resonance) techniques may help to palliate such difficulties. However, albeit promising, these approaches make the analysis of quantities related to the wavefunction amplitude (like the line strength) arduous. The complexity of the spectra of polyatomic molecules obtained at room temperature may be a huge source of frustration, because the molecular recurrences may not be recognizable. For example, numerous levels may coincidentally absorb at the same wavelength yielding inextricable transition patterns. Hence, routinely under single-step energy level excitation, molecule cooling simplifies efficiently the absorption spectrum allowing unambiguous transition identification when molecular Hamiltonians are recognized.

a)[email protected]

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When approaching a dissociation threshold, the spectroscopic analysis of polyatomic molecules becomes usually entangled and statistical analysis may appear as a legitimate alternative (pre-dissociation processes are ignored). Above such thresholds, the molecular dynamics becomes prevailing. At the passage between spectroscopy studies and temporal analyses, theoretical models can help to bridge the gap between these two conjugate domains. Furthermore, in the presence of dissociation processes, the analysis of the reactant products is possible and can provide conclusive information about the reactant dissociation. Such energy regions are also fascinating, because of the recent discovering of roaming mechanism: a light fragment roaming around the remaining body of the molecule before dissociation.1–3 In addition, if scattering Feshbach resonances4,5 in molecules are well known for a while, their affiliation to photodissociation resonances remains to be established. The nitrogen dioxide radical (NO2) is considered as a prototype molecule to address the barrierless unimolecular reaction (bond fission) NO2 → NO X 2Π + O 3 P , because exhaustive spectroscopy data cover from the lowest energy level up to the first dissociation threshold (i.e., D0 ∼ 3.115 eV and De ∼ 3.23 eV6,7) and even beyond. NO2 has a long spectroscopic history for several specific reasons: (i) it absorbs from the near-infrared up to the near-ultraviolet ranges,8 (ii) it is a reactive atmospheric constituent,9 (iii) it exhibits a rich and complex spectroscopy, and (iv) it is a test molecule for benchmarking ab initio quantum chemistry calculations. After several decades of frustration,10 thanks to the advent of supersonic jet expansion pioneering initiated by

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Levy’s group,11,12 NO2 spectroscopy is now well understood, at least up to ∼10 000 cm−1. Above this energy, a conical intersection13,14 strongly perturbs the vibrational structure and, possibly, the rotational structure at higher energy.15,16 The vibronic level distribution up to the dissociation threshold has been statistically analyzed; it shows a level repulsion characterizing a chaotic behavior.15,17–23 Ab initio calculations showed that the X˜ and A˜ electronic states are strongly coupled through the asymmetric stretching mode (ν3), providing a nonadiabatic interaction (i.e., non-Born-Oppenheimer coupling).13,24–26 Hence, NO2 is a benchmarking molecule for ab initio calculations regarding specifically the conical interaction. It is also probably one of the rare molecular systems allowing experimental verification of the rapid increase of the unimolecular dissociation rate above the first dissociation threshold. Thus, understanding the photodissociation processes and the energy redistribution in the reaction products is not only of high spectroscopic interest but also of pivotal importance for atmospheric chemistry (photolysis27) and combustion processes.28 The study of species around the dissociation energy challenges several experimental techniques, because the dissociation of the reactant prohibits the observation of fluorescence (the fluorescence quantum yield approaching zero).29 Actually, the laser-induced fluorescence (LIF) is a fantastic spectroscopic technique for probing excited molecular levels, because of its high sensitivity: it is a background-free technique. However, this technique infers that the LIF collection is possible by an efficient photodetector such as a photomultiplier tube (PMT). In the absence of LIF, absorption-based techniques (i.e., based on the Beer-Lambert law) are remarkable alternatives. The sensitivity of absorption-based technique can efficiently be improved by increasing the equivalent absorption length (see Sec. III). The intensity fluctuations inherent to the light source can be fought by dual acquisition30 or by heterodyne detection.31,32 When the reactant dissociates, usually, at least one of the photofragments can be observed optically with a good efficiency giving potentially access to the same information as direct absorption. Compared with data obtained at room temperature, jetcooled NO2 spectra exhibit a spectacular extinction of the LIF around 398 nm which allows an accurate determination of the dissociation threshold (i.e., D0, the first dissociation energy for nonrotating vibrationless molecules) by high-resolution spectroscopy.22 Above the dissociation threshold, the reactant may remain bound or quasi-bound during a period of time long enough to give rise to detectable Lorentzian-shaped resonances (Siegert states33) as pioneering described by Rice.34 Hence, different spectroscopic techniques have been setup to quantitatively probe the metastable energy levels located above D0. Let us briefly mention among these techniques those based on pulsed sources: photofragment excitation,35,36 socalled PHOFEX,7,20,37,38 grating-PHOFEX,39 photofragment yield (PHOFRY, similar to PHOFEX),40,41 zero kinetics energy detection (ZEKE),42 REMPI/PHOMPI43 (a PHOFEX variant), and population depletion.44 Time-revolved fluorescence techniques (in a pump-probe scheme) have been implemented by Wittig’s group (using picosecond sources)45–47 and by Troe’s group (using sub-picosecond sources)48,49 to access directly to

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the photodissociation times. Recently, a femtosecond pumpprobe technique has been set up to probe the dissociation dynamics of the vibronic states imprinted in the transient gratings.50–52 High-resolution continuous-wave cavity ringdown spectroscopy (CW-CRDS) technique53 is a good alternative to the techniques mentioned previously for studying non-fluorescing but absorbing molecular systems. In the linear absorption limit, it offers the unique advantage of self-calibrated absorption. CW-CRDS is a technique relatively easy to set up even in the CW mode. It can be combined with LIF detection for simultaneous absorption/fluorescence acquisitions as well as with a supersonic slit jet expansion. Indeed, the absorption length is artificially increased by the finesse of an optical cavity: the equivalent absorption length can reach several tens of kilometers. Some NO2 studies questioning the reactant decomposition have been the object of controversies about the statistical7,40,54 (or nonstatistical7,36,37,54,55) character of the energy redistribution in the fragments. This may question the speed of the intramolecular vibrational redistribution (IVR) relatively to the dissociation process since the RRKM (Rice–Ramsperger– Kassel–Marcus) theory assumes the complete (i.e., fast) randomization of the initial energy (ergodicity) prior to dissociation.56 Another controversy concerns the interpretation of different experimental data sets.57–59 One argued point stated about the observation (or not) of the opening of specific dissociation channels, and of the existence of loose (freely rotating fragments) or tight (hindered rotation motion of the two fragments) transition states (TS) along the reaction coordinate. This controversy probably indicates that temporal and spectral experiments do not necessarily provide data that are easy to reconcile. This will be discussed throughout the paper: experimental and theoretical difficulties depict the laborious convergence towards definitive conclusions when molecule dissociation is concerned. Since the introduction of the Rice-Marcus version (i.e., emphasizing the specific role of the transition states) of the RRK theory60 during the 1950s,61–63 much more experimental and theoretical works have been reported to determine the unimolecular dissociation coefficients, i.e., to bridge the gap between spectroscopy and dynamics.64 Basically, the idea is to collapse the complexity of the dissociation processes to a unique and determinable dissociation rate: it can be classical, statistical, or quantal. Several models, complemented by numerous variants, have been suggested. The reader can refer to several reviews.56,65–70 To oversimplify, the reaction rate coefficient kuni E † can be deduced from the generic RRKM formula (see Sec. V B for the details) N † E† † , (1) k uni E = h ρ (E †) where N † E † is the number of states at the TS which is usually defined as a dividing (hyper)surface separating the phase space into reactant and fragments (reaction products) along a reaction path.71 Intuitively, when considering a barrierless reaction, the coordinate of the TS (R†) should match a large interfragment distance (loose states). Actually, the definition and then the calculation of this coordinate are a key point of all RRKM


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formalisms. Overall, it occurs that a variational treatment (VRRKM)72,73 is well appropriate to provide the value of the TS coordinate in the absence of barrier. For example, it seems accepted that R† decreases versus the excess energy (E †): a tightening of the TS of the species CH2OH and NCNO74–77 looks admitted from VRRKM calculations, while the same interpretation about NO278 remains controversial.57,58 Another very popular theory is the PST79–81 which arose derived approaches like Statistical Adiabatic Channel Model (SACM),82 PST-SACM,83 or PST/SSE.40,84 Actually, NO2 has been the first test molecules of the SACM theory82,85–90 (for a review, see Refs. 91 and 92). Albeit they proceed differently, the convergence of these approaches is expected at low excess † 93 energy, and for large values of R . Actually, the †calculation † † of N E in PST is very easy when considering R = ∞ (free rotation of the fragments), because it does not require knowledge of the PES. Furthermore, the rate constants computed within the variational RRKM and SACM theories using ab initio PESs are close to the statistical rate constants given by classical trajectory calculations.90 Such a simple formula as Eq. (1) is appealing from an experimental point of view, and the dependence of k uni E † with the excess energy has been reported for a multitude of molecules. However, under usual temperature conditions (i.e., room temperature), the canonical value k uni (T)69 is very difficult to interpret and actually only microcanonical behaviors can be deciphered to some extend. This requires typically running experiment at low temperature (using a supersonic jet expansion, for example) to selectively excite energy levels, allowing the excess energy E † to be probed (the RRKM theory assumes the complete loss of state selectivity before the decomposition processes94). From a theoretical point of view, the description of the dissociation is a severe challenge since different theories need to be accurately benchmarked. Indeed, the PESs require calculating from the fundamentals of quantum chemistry. Of course, approximations issued from empirical or semiempirical analytical potential shapes can be useful ersatz. From there, the determination of the TS can be obtained variationally for a range of energy and for a set of quantum numbers including a vibrational adiabatic passage to the PESs of the fragments.95 The statistical value of kuni E † can be obtained † † by determining N E and the density of reactant levels. If full quantum chemistry calculations are possible to determine the value of D0 (for NO2, see Refs. 96 and 97), it is preferable to consider the experimental value of D0 known with a very good accuracy. The density of reactant levels close to D0 requires special attention, because it is usually barely known from experiments, while it requires very accurate calculations from the PESs. For NO2, the ab initio calculations are complexified by the conical interaction (in addition to the Renner-Teller ef† fect). Nevertheless, a value reaction product of R ∼ 3 Å for the 2 3 NO X Π1/2 + O P2 has been estimated.78,98,99 Nowadays, fully quantum calculations can be performed to determine kuni E † by identifying the scattering-type resonances, i.e., the poles of the scattering matrix in the complex energy plane.48,100 This paper is mainly devoted to the analysis of resonance width observed around D0. These widths are direct measurements of the dissociation rate coefficients. The resonances

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reveal “long-lived-intermediate” (or metastable) upper energy levels, i.e., conventional TS (or activated complex) driven to chemical reaction. The width of quantal TS (in the language of resonance scattering theory) gives information about stateselective processes, and the resonance transmission coefficients give a measure of their contribution to the total reactivity.69 Both experimental38 and theoretical48 fluctuations of the resonance width have been previously reported. These fluctuations are clearly identified here and they are discussed. As mentioned earlier, the value of the density of reactant levels around the dissociation threshold is a key quantity. However, until now, this density has never been accurately measured above D0. This paper provides a good estimation of this density (or at least an upper limit). It is compared to other density values to which it is related to such as the density of observed transitions below D0. Since the energy progression of the vibronic levels is perfectly predictable almost up to D0, it is possible to calculate a density of vibronic levels at D0, either from a polynomial fit of experimental data: ρvib ≃ 0.65 levels/cm−1 (Ref. 90) or ρvib ≃ 0.754 levels/cm−1,101 or from a Dunham expansion: ρvib ≃ 0.94 levels/cm−1 (Refs. 89 and 102, see also Ref. 88), or even from ab initio calculations.89 These values can be compared with the vibronic density extrapolated from the density of transitions observed just below D0. Unfortunately, the correlation between these two densities (i.e., the density of transitions and the vibronic density) is far to be trivial: it depends upon the intramolecular coupling modeling. In addition, an “anomalous” increase of the density of observed transitions between D0 − 20 cm−1 and D0 has been stated previously and a density ρvib ≃ 2.7 levels/cm−1 has been deduced.103 This sudden increase of the density of observed transitions has been attributed to a rotational selection rule breakdown. Recently, Jost and co-authors have even proposed a larger density of vibronic levels ρvib = 5.8 ± 0.24 levels/cm−1 by comparing the densities of transitions of several jet-cooled NO2 isotopologues.23 In this paper, we analyze the NO2 absorption CW spectrum from 25 121 to 25 146 cm−1. If the spectral resolution does not reach the lowest value reported previously on LIF spectrum,101 it is almost one order of magnitude narrower [residual Doppler broadening: ∼130 MHz at half-width-athalf-maximum (HWHM)] than the absorption-based data reported previously. Hence, the spectrum presently shown exhibits differences with those precedently reported. We consider both regular transitions (i.e., excitation of long-lived energy levels) and resonances, i.e., excitation of metastable, quasibound states of a “molecular complex”64 (short-lived upper energy levels). We try to provide spectroscopic assignments based on the pairing of transitions and also on a few resonances. Despite spectral congestion and resonance width fluctuations, we report about the density of reactant levels around D0 (i.e., up to ∼D0 + 17 cm−1) and about the resonance width versus the excess energy. The narrowest observed resonance has a HWHM of 0.006 cm−1 (compared with ∼0.025 cm−1 reported by Abel and co-workers44), while the broadest ones approach ∼0.72 cm−1. Actually, the resonance widths spread over two orders of magnitude. We observed a resonance width stepwise at ∼D0 + 5 cm−1 displaying a relative step amplitude close to 3. We concluded


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that our data agree with those of Tsuchiya’s group38 and we mainly valid the PST approach,40,104 and the hypothesis of loosely bound transition states in the probed excess energy range despite the fact that we did not study the photofragments. This conclusion may disagree with time-resolved measurements,44,47,59 while the move of the transition states from loosely to tightly bounding has been suggested as a plausible way to reconcile the different experimental observations. However, the disparate spectral resolution associated with each experimental setup has to be considered. Resonance width fluctuations, over an energy range of ∼20 cm−1, are in agreement with the quantum mechanical calculations based on a 3D-PES of Schinke’s group44,48,59 and with PST. Despite these quantum fluctuations, we report on the unimolecular dissociation coefficients relatively to the opening of the two first dissociation 2 channels NO2 J ′ = 1/2, 3/2 → NO X Π1/2, v2 = 0, J = 1/2 3 ′ +O P 2 and NO 2 J = 1/2, 3/2 → NO X Π1/2, v = 0, J = 3/2 + O 3 P2 . This allows us to provide an effective (or reactant) level density ρreac ∼ 11 levels/cm−1. We ascribe this high density to a change of geometry of the molecule: one of the bonds becoming very large. The large amplitude motions are associated with lack of rigidity and “scrambling” as observed in CH+5 (lack of classical spectral structure).105,106 Singularly, we have identified one quasi-isolated resonance whose width could summarize the entire photodissociation dynamics at least in the probed energy range. Taking advantage of a CW source and of an absorptionbased technique, this study probably does not close previous controversies about the unimolecular dissociation rates of NO2. However, it provides informative and complementary data about the chemical bond breakdown around a dissociation threshold. II. EXPERIMENTAL SETUP

The experimental setup implements the usual CW-CRDS technique. Furthermore, the simultaneous acquisition of LIF is possible while a slit nozzle is set up at the center of the optical cavity to provide rotational cooling (see Fig. 1). The laser chain is based on a scanable, externally stabilized Ti:Sapphire (Ti:Sa) laser source (Coherent model 899-

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21) delivering up to 2.5 W in single longitudinal mode (stability: ∼0.5 MHz rms) when it is optically pumped by an Ar+ laser source (Spectra Physics, model 2045). Using a set of beam splitters (BS, actually uncoated BK7 plates set at 45◦in P-polarization), small fractions (∼1% per interface) of the outgoing laser beam are directed to (i) a Fabry-Perot solid étalon (Eksma, finesse ∼20) associated with a photodiode for spectral linearization purpose, (ii) a 1 m long iodine cell (made of silica/quartz at the University of Göttingen [B. Abel]) temperature controlled up to 450 ◦C (it is equipped with a cold finger to control the I2 vapor pressure) for spectral calibration purposes, and (iii) a home-made interferometric lambdameter107 for pre-selection of wavelength of interest (actually the reading of this lambdameter is possible through an asynchronous serial line). Blue wavelengths are obtained by using an external intracavity frequency doubling unit (ring-shaped) operating a LBO crystal (Wavetrain, Laser Analytical System) and generating up to I0 ∼ 350 mW. The frequency mode matching is provided by a Hänsch-Couillaud servo control.108 The high-finesse CRDS cavity is built around a homemade chamber (aggregating pieces of aluminum and stainless steel) supporting two high reflectance (R ∼ 0.999 962) superpolished plano-concave mirrors 0.35 m apart (radius of curvature [ROC] ∼1 m, diameter ∼7.75 mm) from Research Electro Optics. The “output” mirror sits on an annular cylindrical piezo-electric (PZT) actuator (Physik Instruments) allowing cavity length control. The incoming beam is “cleaned” by a spatial filter (association of the lens L1, the pinhole PH, the lens L2 and the diaphragm D). The spatial power distribution of the cropped central lobe of the diffracted beam is very close to the Gaussian profile of a pure TEM00 transverse mode. The adjustable position of the lens L2 complemented by the periscope (mirrors M1 and M2) provides a good impedance matching between the laser beam and one of the TEM00 modes of the evacuated cavity: a rejection rate of the non-TEM00 modes of 1:100 or less is routinely obtained. The transverse beam waist size at the center of the symmetric cavity is estimated at 220 µm109 (none significant diffraction loss is expected). The beam transmitted through the cavity is collected on a thermally controlled fast silicon avalanche photodiode (APD from

FIG. 1. Schematic of the experimental arrangement. Cavity length ∼0.35 m, ROC of the mirrors ∼1 m. Abbreviations are as following: FP is a FabryPerot étalon, PD are photodiodes, PH is a pinhole, AOM is an acousto-optics modulator, BS are beamsplitters, D are circular apertures, M are periscope mirrors, PZT is a piezoelectric actuator and L1, and L2 are two focusing lens.


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Hamamatsu, model S6045-04) feeding a home-made large bandwidth transimpedance amplifier (feedback resistor: RF = 10 kΩ). This photodetector is used for both cavity control and RD time acquisition. A PMT collects the LIF emitted by the molecules seeding the jet expansion perpendicularly to the optical axis. A collimating lens and a colored filter rejecting the scattering light complete the setup. A home-made control box allows tracking a narrow cavity mode (∼5 kHz, HWHM) of the high-finesse cavity (F ∼ 82 000 in the range of interest) compared with the “large” time-averaged laser spectral width (∼0.5 MHz): the laser source is not tightly locked against the optical cavity. The tracking mode is obtained by feeding back the high-voltage on the PZT actuator matching the cavity length by maximizing the transmission through the cavity in average. Giving more detail: the control box generates a low frequency (40–500 Hz) amplitude modulated high-voltage superimposed to a DC voltage (maintaining positive the resulting voltage), towards the PZT actuator through a current driver. It provides a cavity length modulation whose peak-topeak amplitude matches approximately four times the cavity bandwidth at resonance. When tracking operates (i.e., after the initial detection of a cavity mode), the correction signal tunes the DC component of the voltage to balance the modulated voltage against the cavity transmission.53,110 Thus, the maximum power trapped inside the cavity is determined by manually trimming a threshold voltage triggering the acquisition chain. The intracavity power build-up time is determined by the value of this threshold, the modulation amplitude, the impinging power, and the cavity finesse. However, the triggering threshold is adjusted to obtain a maximum intracavity power value estimated to ∼1 W, i.e., well below the theoretical maximum intracavity power: I0F/π (I0 is the impinging power). The trigger signal is used (i) to interrupt the cavity length modulation in preparation to the data acquisition, (ii) to “switch off” the laser beam through the current driven the acoustooptics modulator (AOM from AA Opto-Electronique), and (iii) to trigger (with a delay) the data acquisition chain. The AOM is activated by a RF current at 110 MHz (4 W) building an acoustic grating diffracting the impinging blue beam in the order −1 (the diffraction order zero is dumped). The switching time is estimated to less than 100 ns. The RF power rejection rate (between the off and on transmission modes) is higher than 70 dB, and it is obtained by a mini-circuits switch device. The entire setup is driven by a personal computer, the graphic-user-interface application (virtual instrument) was implemented by using Labview (National Instruments). It embeds a central processing unit (CPU)-optimized subroutine to determine the RD times. The application allows stepping the laser frequency and acquiring simultaneously both the RD decay and LIF signals by a 12-bit analog-to-digital converter (ADC) sampling up to 5 MHz (National Instruments acquisition card). Several RD decays can be summed up before the determination of the RD time values which can also be averaged over several acquisitions. At each wavenumber step, a few (1–4) RD time values are determined from the ac-

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quired data samples by running linear regressions on the (pretabulated) logarithm value of the offset-freed data and after correction of the nonlinearities of the ADC predetermined. This regression is carefully weighted to take into account a constant technical noise (1–2 mV), since the intensity of the collected signal (a few hundreds of µW) provides a negligible photon-shot-noise in comparison with the electronics noise sources. In addition, the acquisition algorithm has the capability of self-rejecting spurious decays, i.e., exhibiting RD time values out of a range determined by the previous acquisitions (this mechanism rejects possible non-TEM00 mode tracked by error and exhibiting shorter decay time). The linearity of the absorbance versus the intensity of the trapped EM field has been checked up to intracavity power of 5 W by comparing the value of the different RD time determinations calculated on a same decay.111 This linearity check has demonstrated that the value of the power threshold was not important for the present study. The proportionality factor between the acquired voltage and the value of the intracavity power can be established after evaluating the mirror transmission and the responsivity of the photodetector. The time-resolved LIF signal exhibits non-analytical shape. For a given molecular transition, it results from several factors such as the RD decay, the spontaneous emission rate of the transition, and the molecule flow provided by the slit jet expansion. The temporal sampling of LIF signal is identical to that of the RD decay, but only the summed data samples (providing the LIF temporal integral) are saved. Unfortunately, the absence of saturation of the PMT gain and of the associated ADC amplifier has not been checked over the strongest NO2 transitions. The cavity is evacuated by a dual root blowers (250 m3/h + 500 m3/h). The (continuous) slit-shaped jet expansion (∼45 µm × 7 mm) is located in the middle of the high-finesse cavity. A pre-mixed (0.1%) NO2/He gas is carried to the nozzle and it is monitored by a crude pressure indicator (stagnation pressure: ∼1.5 atm). Scans of the Ti:Sa laser are externally controlled by the home-made application previously described through a 16bit digital-to-analog-converter (DAC) controlling the external input of the laser control box. Each wavenumber scan (8196 steps) is usually of the order of 2.2 cm−1 (after frequency doubling). The effective mean acquisition rate is of the order of 50 Hz. The resulting √ rms noise equivalent absorption (NEA) is ∼5.7 × 10−9 cm−1/ Hz (empty cavity). III. PRINCIPLES OF THE CRDS

Several review papers53,112–119 have been devoted to the CRDS technique and only the general principles will be reminded here. First, it is useful to note that the well established Beer-Lambert law can be very simply adapted to an optical cavity of finesse F by replacing the absorption length by an equivalent absorption length L eq = f occ 2F π L cav in the optically thin medium approximation (L cav is the length of the cavity and f occ is the cavity occupancy factor). When running straight absorption technique, the absorption coefficient α (ω) is deduced from the absorbance measurement and from the


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absorption length L abs I0 − I (ω) = α (ω) L abs, (2) I0 where I0 is the intensity of the non absorbing reference beam and I (ω) is the intensity of the beam imprinted by the molecular absorption signature at the angular frequency ω. The sensitivity of the technique is directly controlled by the signalto-noise altering I0 and I (ω). On the other hand, the CRDS technique gives direct access to the coefficient α (ω) (in the linear absorption limit) from A (ω) =

1 1 = + c α(ω), τRD(ω) τe

(3)

where τRD (ω) is the measured RD time in the presence of the absorber and τe is the RD time obtained when the cavity is empty (here, τe ∼ 30 µs). The characteristic time is generically deduced from the fit of formula (see Sec. II for more details) −τ

I(t,ω) = I0 e

t R D(ω)

+ Ioff .

(4)

The sensitivity (or limit of detection, LOD) of crude absorption measurements is basically provided by the noise amplitude stirring the source, while the limit of sensitivity of the CRDS technique is provided by the inaccuracy on the cavity characteristic time [∆τRD (ω)], which is intrinsically immune to the source intensity fluctuations. When setting up a crude absorption experiment, it is important to deal with the source intensity fluctuations, either by using a normalization technique (dual-beam)30 or by employing a modulation technique.120 In any case, different techniques can only be compared after analyzing the Allan variance.121 The CW-CRDS remains 1 to 2 orders of magnitude away from best phase modulation technique using an optical cavity allowing the photon-shot-noise limit to be approached.122,123 The CRDS is penalized by a discontinuous temporal acquisition. However, when considering intracavity absorption, the financial cost effectiveness remains greatly in favor of the CRDS technique. In CRDS, the determination of the absorption coefficient is based on a time decay rate [see Eq. (4)], which can be eventually spread over a large voltage range [V (t,ω) = RF η I (t,ω), where η is the responsivity of the detector]. Thus, it is relevant to check the linearity of the detection chain over the acquisition voltage range. For the present study, we have checked over numerous decays and concluded that they are almost pure exponential decays over more than three orders of magnitude. However, the average of numerous temporal decays reveals small distortions; this is due to residual unidentified nonlinearities. This is one of the limiting factors of the CW-CRDS technique. IV. DATA SHAPING AND FITTING

The data files generated by the Labview application accommodate the RD time values τRD (ω) (indeed, possibly several values obtained at the same value of ω, see Sec. II), the LIF integral, the solid étalon interference fringes, and the iodine cell absorption. Each scan can reach a maximum

“spectral length” of 2.2 cm−1 (so-called segment) potentially without laser mode hop. The data were first processed by using a home-made application so-called “analysis.” The acquisition of the étalon fringes allowed prior checking over the free mode hop during data collection. Then, the application was able to linearize the full set of samples by using an automatic detection of the étalon transmission maxima (∼17 per scan), followed by a rescaling based on a polynomial regression. During the following step, the linearized spectra (LIF and CRDS absorption) were frequency calibrated by matching the acquired iodine lines with those provided by the iodine atlas.124 Long range spectra were obtained by patching spectrum pieces and by taking advantage of the partial piece overlaps. Usually each segment was recorded at least two times in order to obtain a good monitoring of the acquisitions. An improvement of the signal-to-noise ratio was obtained by averaging multiple data acquisitions (typically two) weighted according to the estimated residual noise. As explained in more detail in Sec. VI, to be able to analyze the transitions and the resonances, we run a home-made application so-called “multiline”: a graphical-user-interfacebased application, written in C++, capable of fitting multiple Gaussian, Lorentzian, and Voigt125 profiles. Position, amplitude, and width(s) of the singular lines were fitted (global envelop fit) with the option of constraining if necessary, some parameters. The graphics and fit subroutines belong to the root library (CERN).126 Actually, the fitting routines were parts of the package minuit2.127,128 Multiline offers several options, the basic one is an automatic line recognition which is only used in the preliminary steps of the analysis when the lines are unambiguous, typically to analyze the transitions. Then, the analysis of the data is a step-by-step process consisting of “manually” adding new lines (either one by one or by group) and of running a fitting process. The line type, initial position, amplitude, and width are chosen at each step. These parameters can be individually kept fixed or freed before fitting (the parameters fitted previously can either be kept fixed, or partially freed according to the estimated correlations between the prior and new lines). Usually, when fitting new resonances, the amplitude, then the width, and finally the position are freed in that order. At the end of each fitting process (whatever the convergence status provided by Minuit is), the experimental and fitted spectra are visually inspected and the mean-square-error χ2 coefficient is considered. In case of unsatisfactory fit, multiline allows step backing. Obviously, the convergence of this fitting process is faster in the lowest energy part of the spectrum. When the resonance shape was ambiguous (typically in the high energy part of the spectrum), several Lorentzian profiles are required to obtain a correct simulation. The final goal was to free all the parameters simultaneously; however, this was not necessarily possible, because of the large CPU time required when more than 200 parameters are included in the fit. In that situation, parameters were alternatively freed and constrained by step. The more arbitrary decision throughout this process concerns the choice of the ending step. Actually, the noise level is considered while the number of profiles is slightly arbitrary, because at one point, the canceling or the adding of a couple of lines barely alters the shape of the fitted spectrum.


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Standard deviations were also provided by the minimization routine. Nevertheless, a final careful inspection of the standard deviations was necessary to determine relevant error bars: insecure lines grab large error bars on 1, 2, or 3 parameters of the profile.

V. BACKGROUND A. Spectroscopy

The energy level structure of NO2 (asymmetric rotor exhibiting a weak asymmetry factor129) is complex except for the lowest energy levels. This complexity is attributed to a conical intersection between the ground ( X˜ 2 A1) and the first ( A˜ 2 B2) electronic states ∼9737 cm−1 apart.102 The possible contributions due to the B˜ state are ignored.19,130 In the symmetric top wavefunction basis (N is the rotational angular momentum), it results from the high symmetry (orthorhombic) of the molecule (group C2v ) and from the two equivalent spinless oxygen atoms that only the rotational levels with even values of Ka + Kc (Ka and Kc are the projections of the rotational angular momentum N on the two principal axes of inertia a and c, respectively)131 are allowed for ground vibronic levels with symmetry A1. Only rotational transitions with odd values of Ka + Kc are allowed for vibronic levels of symmetry B2. Accordingly, the value of the nuclear spin of the nitrogen atom (I = 1 for 14N) rules the nuclear spin statistic gns equals either 3 or zero. The full vibrational assignment is only possible below ∼10 000 cm−1. Above this energy, only rotational assignments can be obtained; nevertheless, these assignments can still be ambiguous even by using a supersonic jet expansion, typically when the rovibronic “chaos” starts to develop.15,16 However, due to the Fermi resonances, polyads can be identified and assigned, thanks to ab initio calculations.132,133 NO2 is an open-shell molecular system, i.e., it is addicted to spin-rotation and hyperfine couplings (Fermi-contact and spin-electronic-spin nuclear dipole). Except for the lowest energy levels, the strength of these couplings is irregular and the lines may be difficult to assign.134,135 The scheme of coupling needs to be worked out. If F is the total angular momentum, a G-scheme of coupling F = G + N with G = I + S (S = 1/2 is the electronic spin)136,137 is preferable when the spin-rotation Hamiltonian tensorial components are weaker than those of hyperfine Hamiltonians,138 while a J-scheme of coupling (F = J + I with J = N + S) is more appropriate when the spinrotation coupling components are larger than the hyperfine ones. Both schemes of couplings can be preferred in the energy range located between 11 000 and 14 000 cm−1 where the spin-electronic-spin-nuclear dipole coupling remains weak (usually smaller than 20 MHz111,139–141). Above 11 000 cm−1, the measured Fermi-contact term strongly fluctuates; nevertheless, it tends to gradually decrease by one order of magnitude (∼130 to ∼15 MHz),139,142,143 while it is equal to 147.263 ± 0.012 MHz for the vibrationless X˜ 2 A1 state.138 For convenience, we will use the assignment relative to the J-scheme since it is well appropriate for the lowest energy levels, while close to the dissociation energy, the hyperfine structure seems weak whereas the values of the spin-rotation coupling components remain difficult to appreciate (vide infra).

J. Chem. Phys. 142, 174305 (2015)

The barely resolved hyperfine structures in electronic and vibrational spectroscopy (as opposed to the microwave spectroscopy) and the weak rotor asymmetry have inclined some authors to use a simplified notation as R(0) and then to only provide J ′ assignment (for the upper level), since the spinrotation Hamiltonian constants of the upper level cannot be ignored usually. Instead, the modified Mulliken notation144–147 as Q21(0.5) and R11(0.5) for the rotational transition 101 ← 000 [q R0(0)] is preferable (see Fig. 2). Here, both notations are used, but we think that they can easily be distinguished without possible confusion. Around the dissociation energy, the spectroscopic extrapolations from the lower energy level analyses may not be valid while the scheme of coupling is key input to associate the density of transitions observed with a density of vibronic levels: a crucial quantity for arguing about unimolecular reaction rate. The low “rotational” temperature reached inside a jet slit expansion and the relatively large value of the rotational constant A′′ (∼8 cm−1 [Refs. 138 and 148]) allow mainly observing q R0(0), q P0(2), and q R0(2) transitions of a-type (as observed below the dissociation energy). The transitions q Q0 are forbidden for a symmetric top. If the vibrationless ground state is well documented since the 1960s, thanks to the microwave studies,138,149–152 the spectroscopic “constants” suffer from large fluctuations in the energy range considered here. In the Doppler broadening limit, the spectral shape of the transitions differs according to their assignment, because of the value of the fine and hyperfine structures (see Fig. 2). Hence, we can use the transition spectral shape to help performing the line assignments. For this purpose, transition simulations have been obtained by using the application so-called “Stepram” previously reported.111 B. Microcanonical unimolecular dissociation rate

The standard RRKM formalism provides statistical dissociation rate coefficients kuni based on the microcanonical tran-

FIG. 2. Fine structure components of the transitions q R 0 (0) and q P0 (2) (J -scheme of coupling) providing parity146 and using the modified Mulliken notation (the hyperfine splittings are given on the left side of the diagram).


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sition state theory (TST). The expression of kuni (in s−1) for a total energy E ≥ D0 (i.e., for the excess energy E ‡ = E − D0) is given by68 N ‡ E‡ , (5) kuni E ‡ = c 2π ρreac (E ‡) where ρreac E ‡ is the density of reactant levels (in level/cm−1) and N ‡ E ‡ is the number of energetically accessible levels (quantum states including the level degeneracy) at the transition state (c is the speed of light in cm/s). The exact definition of the reaction coordinate R†56,65,153 differs according to the TST considered68,70,154 and, accordingly, the definition and the calculation of the quantity N ‡ E ‡ may be argued. We emphasize that the accurate evaluation of the density of reactants ρreac E ‡ (in first approximation a rovibronic density of levels) is far too trivial either. Theoretically, quantum chemistry ab initio calculations of the nonadiabatic PESs in complex geometries are required. For uncoupled PESs, analytical semiempirical PES can be used while the equivalent to the classical saddle point remains to be evaluated variationally for each quantum number set (i.e., for each reaction controlled by vibrational adiabatic motions). In addition, the spin-orbit, spin-rotation, and hyperfine couplings should be considered in a region of the phase space where we have only little consistent experimental information. From a strict experimental point of view, these calculations can first be ‡ ignored since the value from of ρreac E will‡ be ‡determined ‡ the values of kuni E after evaluating N E . The PST155 is a version of the RRKM theory that focuses on the energetics of the separated fragments at a loose TS (the relative motions of the fragments are completely unhindered).69 PST is based on locating the TS at the centrifugal barrier for long range spherical interaction due to an attractive potential in −C6 r −6 (Lennard-Jones parameter, dispersion term). PST assumes the conservation of the total energy and of the total angular momentum (but not of the projection of the total angular momentum). Hence, the non-conservation of this projection as well as the freely rotation at the TS may overestimate the number of accessible levels. In any case, despite these weaknesses, at low excess energy, the TS calculated by PST are assumed to converge towards those determined by more sophisticated theories, for example, assuming adiabatic reactions.78 Here, we assume that the Λ-doublet (∼355 MHz for JNO = 1/2 and ∼710 MHz for JNO = 3/2156) and the hyperfine structures (lesser than the Λ-doublet separations) of the radical NO can be ignored. This approximation is reasonable because of the average value and the fluctuations of the resonance

width almost hide the details associated with the opening of the dissociation channels under concern. Equation (5) suggests a progression of k uni versus E ‡ and ′ implicitly versus JNO which takes half integer values. We ′ 2 is the total angular momentum (i.e., assume here that JNO 2 it is a good quantum number) excluding the nuclear spin in the upper level (see Sec. V A); the role of the respective hyperfine couplings will be discussed later. By extrapolating the observations just below D0 to the energy range of interest, ′ only two values of JNO need to be independently considered of 2 ‡ E . According to the usual angular momentum coupling rules, ′ several values of JNO can be associated with one value of JNO 2 (depending on the angular momentum of the relative rotation ′ of the fragments L): JNO = JNO + JO + L. Hence, a stepwise 2 of k uni can be expected for each channel openings associated with JNO. The quantity NJ‡NO E ‡ has to be calculated in this context. The accounting for the channel opening can be obtained for the three lowest energy levels of NO by following Refs. 38, 104, and 153 and assuming an isotropic space distribution of the reaction products (see Table I). Accordingly, N ‡ E ‡ can be deduced for each opening channel from JNO   NJ‡NO E ‡ = N ‡ E ‡, JNO2 J ′ × w JNO , 2

NO

′ =1/2 J JNO NO2

(6)

where J +JNO

′ +J JNO O

N E , JNO2 ‡

‡

′ JNO

2



=

1,

(7)

′ −J J = JNO O L= J −JNO2

|

|

and where w JNO set for the weighting of the density of levels 2 ′ JNO observed for the long-lived levels (i.e., w1/2 = 1/3, w3/2 2 = 2/3, see Sec. VI A). The energy of the corresponding opening channel is given by EJNO = BNO JNO (JNO + 1) and JO = 2 (BNO is the rotational constant of NO). In PST, constrains on the energy conservation versus E ‡ can be considered by limiting the value of L to L max which is determined by the value of C6. However, the experimental data do not show any evidence that we should consider this constrain in the energy range under study: no identifiable change of the resonance width inside the stepwises, i.e., for JNO constant, has been stated. However, a careful inspection of Fig. 5 between 25 134 and 25 142 cm−1 may slightly invalidate this statement if attention is paid on the width fluctuation: the range 25 134–25 139 cm−1 exhibiting less fluctuations than the range 25 139–25 142 cm−1. The upper limits of

TABLE I. Number of accessible levels for each reaction channel in PST according to formula (7) (following Refs. 38, 104, and 153). Number of accessible levels: N ‡ E ‡, JNO2

Reaction channels (J ′ = 1/2) →

NO2 NO2 (J ′ = 3/2) → NO2 (J ′ = 1/2) → NO2 (J ′ = 3/2) → NO2 (J ′ = 1/2) → NO2 (J ′ = 3/2) →

NO NO NO NO NO NO

X 1/2, v = 0, X 2Π1/2, v = 0, X 2Π1/2, v = 0, X 2Π1/2, v = 0, X 2Π1/2, v = 0, X 2Π1/2, v = 0, 2Π

J = 1/2 + O J = 1/2 + O J = 3/2 + O J = 3/2 + O J = 5/2 + O J = 5/2 + O

3P

2 3P 2 3P 2 3P 2 3P 2 3P 2

N‡

E ‡,

N‡ N‡ N‡ N‡ N‡

E ‡, E ‡, E ‡, E ‡, E ‡,

JNO

J ′ = 1/2

=4 1/2 J ′ = 3/2 1/2 = 8 J ′ = 1/2 3/2 = 8 ′ J = 3/2 3/2 = 14 ′ J = 1/2 5/2 = 10 J ′ = 3/2 5/2 = 18


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N ‡ E ‡, JNO2 J for JNO2 = 1/2 and 3/2 are provided in Table I: NO we assume that resonances involving higher values of JNO2 marginally fall in the energy range considered. The spin-orbit interaction between the states X˜ and A˜ at the dissociation energy99 is ignored here. VI. TRANSITION AND RESONANCE

While the LIF and the CRDS spectra were simultaneously acquired, we only show absorption-based spectra here. As previously mentioned, there is no LIF cold spectrum above 25 128.56 cm−1 (i.e., above the lowest energy level considered here: 00 0, J ′′ = 1/2). Below 25 128.56 cm−1, the shape of the LIF transitions is very similar to that of the absorption transitions (ignoring the dissociation resonances) at the exception of a few of them exhibiting slightly larger amplitude. The present residual Doppler broadening is slightly larger than that reported on the previous data (by a factor 2), while the rotational temperature is also slightly higher. The less efficient jet-cooling results from the use of a CW slit jet expansion compared with a CW pinhole expansion complemented by an observation slit.102,135 Hence, we will refer to LIF spectra reported previously when it is necessary. In any case, this slightly larger residual Doppler broadening has only a little impact on the resonance analysis. When inspecting visually the absorption spectrum, reader attention (see Fig. 3) is caught by the broad structures (resonances) absent in the LIF spectra: resonances are visible between 25 126 and 25 130 cm−1 and more clearly above 25 127 cm−1. The dissociation threshold D0 is indicated by vertical dashed lines in the different figures. The absence of transition above D0 contrasts with the existence of resonances slightly below D0. In addition, a slight increase of the absorption background appears above ∼25 126 cm−1, i.e., above D0 − 2.53 cm−1, while the density of transitions is larger below this latter energy than above. Above D0, the CRDS spectrum (see Fig. 4) exhibits clear similarities with spectra previously published by different

J. Chem. Phys. 142, 174305 (2015)

groups, if we kindly appreciate the disparities of the experimental spectral resolutions (e.g., see Fig. 1 of Ref. 7, Fig. 1 of Ref. 37, Fig. 3 of Ref. 38, Fig. 3 of Ref. 157, or Figs. 6 and 8 of Ref. 39). These jet-cooled spectra obtained with a pulsed nozzle exhibit spectral resolutions 1 to 2 orders of magnitude broader than that of this work, but slightly better rotational cooling. Before analyzing the resonances minutely (see Sec. VI B), it is worthwhile first analyzing the transitions (see Sec. VI A) to establish a bridge between both line types. The simultaneous acquisition of the LIF and absorption spectrum prevents from possible confusions between transitions and narrow resonances, which are both observable below D0. To determine the position and amplitude of the transitions as well as the amplitude, position, and width of the resonances, the entire absorption spectrum (piecewise displayed) is fitted (see Sec. IV). A Gaussian profile is associated with each identified transition while a Lorentzian or a Voigt profile is associated with each resonance. The spectral broadening of the long-lived energy levels is neglected (lifetime > 20 µs158). Actually, a Gaussian profile imperfectly matches the transition shapes, because of the hyperfine at least of the lower level, and possibly spin-rotation structures of the upper energy level. However, to avoid fitting multiple transition widths, a unique linewidth is set for all transitions. An overall width of ∼0.0063 cm−1 (HWHM) is obtained from the process while the residual Doppler broadening is ∼0.004 cm−1 (HWHM). Fortunately, this approximation (single profile) has only minor disturbances on the complete fitting process. The analysis is based on the uncorrelation of the resonance width and position. Ignoring possible interference between resonances is not considered as a severe approximation for NO2.159,160 A. Analysis of the transitions

In the energy range framed by D0 − 2.53 cm−1 and D0, it seems established that only transitions R(0) are observed by

FIG. 3. Absorption spectrum around the dissociation energy. Two dissociation thresholds NO2 → NO X 2Π1/2 + O 3P2 are indicated by vertical dashed lines −1 138 ¯ ¯ in green, corresponding to D0 − 6 B and D 0 ( B ≃ 0.422 cm is the lower level rotational constant ). The identified paired transitions are indicated by arrows of the same color (the continuous and dashed line show the R(0) and P(2) line components, respectively): the arrow pointing towards the bottom indicated secure pairing, the arrow pointing towards the top indicated pairing with relative amplitude of the components off the 1:2 expected ratio by less than a factor 2 (i.e., ratio in the range 1:1 or 1:4). The lines without arrow indicate that the ratio between the component amplitude is outside the fork values mentioned previously. Experimental spectral resolution: ∼130 MHz (HWHM).


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LIF.22,101 They are also well identified here: barely resolved doublets with 1:2 component amplitude. The robustness of the shape of these 41 doublets is quite surprising and it has been emphasized anteriorly. It raises the question of the assignment of the fine structure components [i.e., Q21 (0.5) or R11 (0.5), see Fig. 2]. These 1:2 doublets must result from the hyperfine structure of the lower level J ′′ = 1/2 with two components F ′′ = 1/2 and 3/2 split by ∼221 MHz, and from the absence or quasi-absence of structure of the upper level (i.e., assuming the degeneracy of the upper hyperfine structure); the fine structure component Q21(0.5) results from two doublets overlapping (F ′ = 1/2 ← F ′′ = 1/2, F ′ = 1/2 ← F ′′ = 3/2) and (F ′ = 3/2 ← F ′′ = 1/2, F ′ = 3/2 ← F ′′ = 3/2); the fine structure component R11(0.5) results from the overlapping of the two similar doublets (F ′ = 1/2 ← F ′′ = 1/2, F ′ = 1/2 ← F ′′ = 3/2) and (F ′ = 3/2 ← F ′′ = 1/2, F ′ = 3/2 ← F ′′ = 3/2) with the single hyperfine transition F ′ = 5/2 ← F ′′ = 3/2. This systematic lack of upper degeneracy lift differs from behaviors reported at lower energy by four different groups (sparse data): the Fermi-contact coupling (the Fermi-contact coupling dominates the spin-electronic-spin-nuclear dipole coupling by one order of magnitude) spreading almost randomly, but trendily from 130 to 15 MHz between 11 200 and ∼21 500 cm−1.111,139–141,143,161 However, our observations are in agreement with the hyperfine structures reported around D0 by Xin and Reid who established that these structures are five times weaker than those below 22 000 cm−1.162 In 2002, they reported on 20 components located between D0 − 15 cm−1 and D0 with 2 ≤ aFC ≤ 17 MHz.163 The behavior of the hyperfine couplings with the excitation energy requires attention because the character of the state X˜ in the hybrid levels observed should increase when approaching D0 (the Fermi-contact value of the state A˜ being negligible142). Correlations with the line intensity (also imprinted by the state mixing) has been sought139,140,143 but not demonstrated. The more serious hypothesis is a variation of the Fermicontact interaction with the nuclear coordinates.143 Under the assumption of a negligible upper level hyperfine structure, the relative amplitude of the fine structure components Q21(0.5) to R11(0.5) must be 2:1 whatever the spinrotation constants are. These doublets should be sought between D0 − 2.53 cm−1 and D0. However, if the value of the ′ ′ is weak, the two spin-rotation tensor component ϵ bb + ϵ cc fine structure components Q21(0.5) and R11(0.5) overlap as well as the fine structure components Q12 (1.5) and P22 (1.5). In this energy range, Reid and co-worker analyzed six162 and latter eight163 of these fine structure components by using a quantum beat technique. They identified mainly R11(0.5) transitions. Theoretically, the spectral analysis of the fluorescence emitted by the individual upper levels (i.e., by dispersed LIF) should be a decisive technique to help assigning the transition components.102,164 Two alternative approaches have been proposed to identify the transition components Q21(0.5) and R11(0.5): they are based on the line pairing. A component Q21(0.5) should be paired with a component P22(1.5) located ∼2.53 cm−1 (i.e., 6 B¯ ′′) below and two times weaker, while a transition component R11(0.5) should be paired with a component P11(2.5) also ∼2.53 cm−1 below and also two

J. Chem. Phys. 142, 174305 (2015)

times weaker. The pairing of components R11(0.5) with transition components Q12(1.5) is not considered because these latter transitions are weak compared with components P11(2.5) which are in addition far by only ∼120 MHz. Thus, the components Q12(1.5) are indeed not observable. If the spin-rotation coupling is weak in the upper level, both pairs merge in a single one, forming single pairs [R(0), P(2)]. The shape of components P22(1.5) differs from the shape of component P11(2.5), because of the value of the hyperfine splittings of the lower level: a quasi single line versus a doublet whose component amplitudes are almost identical, respectively. The component (or transition) pairing can be conducted by transition shape recognition as shown above but also by varying the temperature of the jet expansion which induces a change of the amplitude of the components P11 (2.5) relatively to that of the components R11 (0.5), and of the components P22 (1.5) relatively to the components Q21 (0.5).101 This temperature-based recognition is not considered here. The component pairing of the transitions R(0), located between D0 − 2.53 cm−1 and D0 with their sister components of the transitions P(2) located in the range D0 − 5.06 cm−1— D0 − 2.53 cm−1, has unfortunately not been achieved for all the candidate transitions. We only paired 26 components (or transitions, see above) of the 36 transitions observed, over a total of 41 transitions previously reported22,101 (see Table II and Fig. 3). Five transitions in the highest energy part of the absorption spectrum are not observed, because of a weaker signalto-noise ratio compared with the LIF data; it is worth pointing that the amplitude of the transitions decreases very close to the dissociation threshold. Among the 26 pairs, the assignment of J ′ is retrieved for only 19 pairs. The 7 pairs remaining exhibit profiles barely identifiable, they could be superimposition of fine components Q21(0.5) or R11(0.5). Table II reports also about the mismatching to the theoretical amplitude ratio 1:2 of the paired components. Some of the pairs involving a component of the transition R(0) located between D0 − 2.53 cm−1 and D0 have been reported in a previous work (see Fig. 1 of Ref. 101) allowing double checking. However, the present assignment shows two mismatches with that proposed by Xin and Reid.162 It is worth noting that in this latter study, several beating frequencies associated with the sum frequency are missing. This provides insecure assignments of the energy levels J ′ = 3/2. Considering the energy range D0 − 5.06 cm−1—D0 − 2.53 cm−1, we do expect not only components of the transitions P(2) (see above) but also a substantial number of components of the transitions R(0) (a total of 89 transitions are observed) whose again sister components of the transitions P(2) must be sought in the D0 − 7.59 cm−1—D0 − 5.06 cm−1 energy range. The higher density of transitions in these two energy ranges makes the search more difficult than in the higher energy range. Furthermore, components of the transitions R(2) have been identified below D0 − 2.53 cm−1 previously.101 The identification of pairs [R(0), P(2)] has been assisted by these anterior assignments. The concatenated data are provided by Table II. A total of 49 pairs have been identified between 25 120.8 and 25 128.4 cm−1, 28 of them have been assigned. Some energy


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TABLE II. Transition pairing. When it is possible, the J ′ values are deduced from the profile shape of the fine structure components of the transitions P(2). Parity assignments can be obtained from Fig. 2. The wavenumber of the transitions q R 0(0) corresponds to the energy of the upper level (the energy of the lower level being taken as the energy reference) and can straightly be compared to D0. For the transitions q P0 (2), the energy of the lower level is ∼2.53 cm−1. Line component centers cm−1

qP

0(2)

qR

J′

0(0)

25 123.524 25 123.744 25 123.825 25 124.048 25 124.229 25 124.310 25 124.512 25 124.578 25 124.648 25 124.722 25 124.845 25 124.951 25 125.006 25 125.045 25 125.078 25 125.106 25 125.116 25 125.363 25 125.533 25 125.655 25 125.738 25 125.964 25 126.103 25 126.205 25 126.223 25 126.306 25 126.351 25 126.412 25 126.654 25 126.736 25 126.834 25 126.909 25 126.929 25 126.986 25 127.079 25 217.079 25 127.184 25 127.369 25 127.616 25 127.782 25 127.860 25 127.904 25 127.934 25 128.000 25 128.085 25 128.147 25 128.190 25 128.348 25 128.379

This work

Reference 162

Comments Reference 163

Reference 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

25 120.995 25 121.216 25 121.298 25 121.520 25 121.695 25 121.773 25 121.981 25 122.044 25 122.117 25 122.188 25 122.312 25 122.421 25 122.470 25 122.510 25 122.544 25 122.577 25 122.588 25 122.831 25 123.002 25 123.114a 25 123.212 25 123.432 25 123.570 25 123.673 25 123.691 25 123.774 25 123.815 25 123.876 25 124.110a 25 124.202 25 124.309 25 124.378 25 124.395 25 124.453 25 124.451a 25 124.541a 25 124.646a 25 124.832 25 125.077a 25 125.250 25 125.324a 25 125.363 25 125.400 25 125.464 25 125.555 25 125.625a 25 125.655 25 125.825a 25 125.848

a Indicates

that the energy gap between the two components of the [ P(2), R(0)] pairs is slightly higher than the expected value (nevertheless, by less than 0.015 cm−1).

3/2 3/2

3/2

3/2

3/2

3/2

3/2 3/2

3/2 1/2 3/2

3/2

3/2

3/2

3/2

3/2 3/2 1/2

3/2

3/2

3/2 1/2

3/2

1/2 3/2 3/2

Wrong relative amplitude Wrong relative amplitude Wrong relative amplitude, overlap Relative amplitude almost correct Wrong relative amplitude Wrong relative amplitude Wrong relative amplitude, overlap Wrong relative amplitude, overlap Relative amplitude almost correct, shape not OK Wrong relative amplitude, overlap Relative amplitude almost correct Wrong relative amplitude, overlap Relative amplitude almost correct Wrong relative amplitude, overlap Wrong relative amplitude, overlap Wrong relative amplitude, overlap Relative amplitude almost correct Relative amplitude not correct Relative amplitude almost correct, overlap Relative amplitude not correct Relative amplitude almost correct, overlap

Relative amplitude not correct Relative amplitude not correct Relative amplitude not correct Relative amplitude not correct

Relative amplitude not correct 3/2 3/2 1/2 1/2 1/2 3/2 3/2 1/2 1/2

Relative amplitude not correct 3/2

3/2

3/2 3/2 1/2 3/2

¯ between paired components [R(0), P(2)] are differences (6 B) slightly higher than expected and they are indicated by an asterisk. This concerns almost all the pairs [Q21(0.5), P22(1.5)]. On the other hand, all the energy differences of the pairs

Relative amplitude not correct, Relative amplitude not correct, Overlap Relative amplitude not correct Relative amplitude almost correct Relative amplitude not correct Relative amplitude not correct Relative amplitude not correct, overlap

3/2 3/2

3/2

3/2 3/2 3/2 3/2

Weak Weak, relative amplitude not correct Relative amplitude not correct Relative amplitude not correct

[R11(0.5), P11(2.5)] are usually larger than expected (i.e., increased by 0.01–0.015 cm−1). This may be attributed to transition approximated by a single Gaussian profile, while they are actually doublets (due to the hyperfine splitting of


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the lower energy level): the fitted positions are slightly incorrect. The difficulty to identify transition pairs usually results from transition overlapping, but not necessarily. Sometimes there is just no transition to associate with. The J ′ assignments resulting from the analysis of the fine component shape of the transition P(2) are reported only if they are unambiguous. We reported “wrong relative amplitude” when the expected amplitude ratio 1:2 between the R(0) and P(2) components is off by more than a factor two (one way or the other). When this ratio is off by less than a factor two, we only reported “relative amplitude almost correct.” These three classes of assignments are also indicated in Fig. 3 by using specific coding. Each transition component of an identified pair is shown with the same color (see figure caption). It is worth observing that two times more energy levels J ′ = 3/2 than J ′ = 1/2 have been reported. This is in agreement with the previous observations reported by the Grenoble group.15,103 Let us note that a Porter-Thomas amplitude distribution of the transitions P(0) between D0 − 2.53 cm−1 and D0 has been previously stated.22 B. Analysis of the resonances

In addition to the usual transitions reported in Sec. VI A, Fig. 3 shows broader Lorentzian-shape resonances. For example, at 25 127.23 cm−1, a clear and remarkable resonance is identifiable. Four enlargements of the analyzed energy range are shown in Figures 4(a)–4(d). A narrow range, from 25 130 to 25 130.8 cm−1, is missing, because the laser system was unable of scanning this energy range without manageable mode hop. The absorption spectrum exhibits a continuum background αoff ≃ 1.5 × 10−5/cm which seems to decrease only above 25 145 cm−1. Its origin remains unclear, but it does not appear to be strictly associated with the resonance patterns. One may speculate about the formation of N2O4 dimer165 in the jet-expansion since the LIF spectrum does not show such a background.7,139 A similar background has also been observed on PHOFEX spectrum when the fragment NO is detected.38 Another hypothesis could be the role of fast nonradiative processes like IVR.48,166 We did not consider the existence of Fano profiles. The quantitative analysis of the resonances is not an easy task, because only a small number of them are isolated. Actually, even massive overlapping is observable as in the highest energy part of our spectrum. We opted for the individual parametrization of the resonances by performing a fit program extracting the position, amplitude, and width of the individual resonances (see Sec. IV). Although the entire spectrum has been divided into three parts to reduce the number of parameters to simultaneously incorporate in the fit process, more than 215 parameters are still required for fitting the most complex part of the spectrum. As pointed out previously, below D0, resonances and transitions compete. Hence, it was necessary to fit this part of the spectrum by a manifold of Gaussian and Lorentzian profiles. In addition, few Voigt profiles have been incorporated to fit the narrowest resonances and accounting for the residual Doppler broadening. Possible sub-structures

J. Chem. Phys. 142, 174305 (2015)

altering the resonance shape were ignored, because the resonances are assumed broader than any fine or hyperfine structures (see Sec. VI A). Indeed, if a “sub-structure” was suspected, an additional Lorentzian profile was added to the line manifold. The imperfect simulation of the transitions fitted by unique-width Gaussian profiles (mentioned in Sec. VI A) provides additional contributions to the χ2 coefficient (see Sec. IV). These contributions might prevent fitting process rapidly converging. Below D0, the resonances do not usually overlap, if they do, there are only partial overlaps making the fit convergence readily achieved. However, above D0, resonance overlaps are more a rule than an exception. Accordingly, it is almost impossible to provide accurate determination of the parameters of the broadest resonances. Likewise, the cross-correlation coefficients between the resonance parameters may be strong, which then requires special attention for obtaining satisfactory fit convergences. Large parameter uncertainties (either derived from the standard deviation of the fit or from a visual analysis of the resonances) reflect these glitches. Actually, the total number of resonances extracted from the experimental data should not be considered as absolute: it is probably reasonable to consider than some resonances may have been missed. The final determination of 115 resonances covering the range 25 125.167–25 145.429 cm−1 is summarized in Table III. The resonance integrals and the derived unimolecular dissociation time are also provided. In addition, the three fitted pieces of the experimental spectrum are shown in the different subfigures of Fig. 4. It seems clear that above 25 131 cm−1, the broadest resonances contribute to the quasi-continuum background of the absorption spectrum (Lorentzian tails). The resonance pairing similar to the transition pairing discussed in Sec. VI A has been considered. However, the absence of resonance assignment based on the resonance shape makes this task very insecure. We report 8 possible pairs [R(0), P(2)] in Table III. To correlate two resonances, two criteria have been used: (i) the energy difference (i.e., 2.53 ± 0.015 cm−1) and (ii) the resonance amplitude (amplitude ratio between the two resonances should be less than a factor two). Based on these two criteria, it appears that the relative widths of paired resonances can reach one order of magnitude (two pairs reported). Of course, the relevance of this pairing is not entirely established, because no double checking is presently possible. The value of the resonance strength  S= N −1 α (ω) dω = π N −1 α0 Γ, (8) where N is the radical number density, α0 is the absorption coefficient at the resonance center, and Γ is the HWHM of the resonance. N is not provided, because the number density of radicals is barely known. No direct measurement is possible (even based on the transition amplitude) and only approximate values can be afforded. From the usual hydrodynamic modeling,167,168 a number density of 6 × 1012 molecules/cm3 5 mm downstream of the jet-expansion, and a limit temperature of 4.15 K can be estimated for the present experimental slit expansion conditions (an effective rotational temperature Trot of 10-15 K is speculated).


174305-13

Patrick Dupré

J. Chem. Phys. 142, 174305 (2015)

FIG. 4. Enlargements of the absorption spectrum around the dissociation energy. The experimental spectra are plotted in dark blue while the fitted spectrum is plotted in red. The center and the amplitude of the resonances are indicated by cyan sticks. The dissociation threshold D0 is indicated by a vertical green dashed line. An isolated Lorentzian profile is emphasized in sub-figure (a) (it is associated with a unimolecular dissociation time of ∼50 ps). (a) Analysis of 24 resonances located just below the dissociation energy. (b) Analysis of 19 resonances located just above the dissociation energy. (c) Lower part of the analysis of 70 resonances covering ∼14.5 cm−1 above the dissociation energy. (d) Upper part of the analysis of 70 resonances covering ∼14.5 cm−1 above the dissociation energy.

VII. DISCUSSION

A. Dissociation channel opening

The value of the width (i.e., Γ) of the 115 resonances observed is plotted versus their position (or wavenumber); the analyzed resonances cover a range of ∼20 cm−1 (see Fig. 5). A dual y-scale allows associating the dissociation times with the resonance widths. They spread over two orders of magnitude (approximately from ∼0.006 to ∼0.72 cm−1 or from ∼4 to ∼450 ps). The broadest resonances are small and suffer from large uncertainty (see Table III). For example, the two broadest ones (Γ > 0.5 cm−1, #53 and #111) are not reported in any other work and they may be questioned; Tsuchiya’s group38 only reported resonances with Γ < 0.36 cm−1. On the other hand, it is worth pointing out that the narrowest resonances (i.e., Γ < 0.025 cm−1) have never been reported previously neither. They are observable in this work, thanks to the use of a CW laser source.

Figure 5 clearly shows that despite the use of logarithmic scales attenuating visually the amplitude changes, an alteration of the dissociation time is observable around D0 + 5 cm−1. Actually, Fig. 5 should be compared to Fig. 5 of Ref. 38, which has been obtained with an experimental resolution of only ∼0.05 cm−1: the width of the 55 resonances reported spreads from ∼0.025 to ∼0.35 cm−1 (HWHM) over an energy range of 13 cm−1. The one-to-one association of the resonances of the two sets of data is partially possible. Indeed, 19 resonances match with a good agreement, 13 can be matched by relaxing one of the matching criteria: either the position or the width, while 20 resonances cannot be matched (the three remaining ones fall outside our scanned energy range). The 19 resonances matched are identified in Table III with the assignments provided by Miyawaki and co-workers.38 Numerous


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Patrick Dupré

J. Chem. Phys. 142, 174305 (2015)

FIG. 5. Synthesized summary of the resonance width distribution. The fitted values are given in Table III. The deduced photodissociation times are obtained from 1/(4 π c Γ) where Γ is the fitted resonance width (HWHM). The bottom blue area indicates the limit of the narrowest widths observable by the experimental setup (residual Doppler broadening). The dissociation threshold (D0) associated with the transitions issued from the ground 00 0 (J ′′ = 1/2) energy level is indicated by a dashed green line (the hyperfine structure of the lower energy level is ignored, see Fig. 2). The thinner dashed line indicates the dissociation threshold shifted down by 2.53 cm−1 associated with transitions issued from the ground rotational level 20 2. The green-olive dashed lines indicate the shifted energy thresholds: D 0 + 5 cm−1 and D0 + 13.57 cm−1. The two horizontal dashed lines indicate the unimolecular dissociation rates k uni1/2 and k uni3/2 associated with the channel opening (see text). The yellow area indicates a small energy range not scanned.

resonances reported in this work have not been observed by PHOFEX experiment; while that is perfectly understandable when the resolution is considered, surprisingly, a few resonances observed by PHOFEX experiment are not observed in this work. It is noteworthy that the PHOFEX spectra differ slightly according to the photofragment monitored (NO or O). The same energy range has also been analyzed in the following Refs. 44, 47, 59, and 169, but they do not dispense additional information. Regardless to the large resonance width fluctuations, a clear stepwise appears at ∼25 133.6 cm−1 (i.e., approximately at D0 + 5.01 cm−1). Thus, we are inclined to attribute the change of the unimolecular dissociation rate to the opening of a new dissociation channel located 3BNO170 above the lowest energy dissociation channel NO X 2Π1/2, v = 0 + O 3 P2 as suggested previously by Miyawaki and co-workers38 (see Sec. V B), and ignoring the Λ-doubling and hyperfine splittings (see Sec. V B). Provided this point is valid, the next dissociation channel should open at D0 + 13.57 cm−1 (i.e., 8BNO above the lowest energy decomposition channel) with a stepwise amplitude of 2 according to PST (see Table I). Figure 5 seems to indicate that it is a plausible option (the energies of the channel opening are indicated in the figure by vertical green-olive dashed lines) while only seven (broad) resonances are reported above D0 + 13.57 cm−1: resonances broader than 0.5 cm−1 are either not detectable or barely detectable while they are presumed. Accordingly, three energy ranges can be considered for analyzing our data against the PST (see Sec. V B); however, only the two lowest energy ranges can reliably be acknowledged. We wish to emphasize that the association of the 3 channel openings, NO2 → NO X 2Π1/2, J = 1/2 + O 3 P2 , NO2

→ NO X 2Π1/2, J = 3/2 + O 3 P2 , and NO2 → NO X 2Π1/2, J = 5/2 + O 3 P2 , with the energy ranges E < D0 + 5 cm−1, D0 + 5 cm−1 ≤ E < D0 + 13.57 cm−1, and E ≥ D0 + 13.57 cm−1, respectively, is arguable, because of the excitation of some “hot” resonances. Indeed, some are clearly observable ¯ below D0: the energy range D0 − 6 B—D 0 is probably dominated by resonances of type q P0(2) while only two candidates have been identified below D0. Similar “hot” resonances have already been reported by Wittig and co-authors by using a colder expansion.104 These “hot” resonances could theoretically mix up the energy thresholds associated with the channel opening. However, the possible bias associated is actually not detectable on the figure, because of the direction that the stepwises rise up (vide infra). Finally, 73 resonances are attributed to the first channel opening and 35 to the second channel opening. Despite the fact that probably some of the highest energy resonances (and also likely the broadest ones) among the 73 resonances (associated with the first channel opening) are due to the second channel opening. This is not identifiable in Fig. 5, because these resonances mix up with the resonances located below D0 + 5 cm−1. This assumption does not deeply skew the shape and the position of the identified stepwises. Provided this point is correct, the unimolecular dissociation coefficients provided in Table IV may suffer from a slight overestimation difficult to evaluate. B. Dissociation rate coefficients and density of reactant levels

The large fluctuations of the width and amplitude of the resonances have already been reported, they are indisputable when examining the present data. Large fluctuations of the


174305-15

Patrick Dupré

J. Chem. Phys. 142, 174305 (2015)

TABLE III. Resonance list. Overlapping between resonances is indicated (parentheses indicate partial overlap). The JNO assignments according to Ref. 38 are given when the resonance parameters match well. The possible pairing of resonances [R(0), P(2)] is given. The energy of the resonance cannot be referenced to the lowest energy level (while D0 is) except when they are assigned as P (0). Assignments

1 2

Resonance center cm−1

Resonance HWHM cm−1

Absorption coefficient at center (α 0) cm−1

Resonance integral  α (ω) dω 10−6 cm−2

Dissociation time (ps)

25 125.1678 (18) 25 125.1820 (16)

0.0179 (25) 0.0160 (24)

4.88 (80) 6.91 (99)

0.27 (8) 0.35 (10)

148 (21) 166 (25)

0.28 (6) 1.06 (19) 0.63 (9) 0.023 (34) 2.5 (3.0) 0.16 (15) 0.57 (49) 0.30 (8) 0.76 (89) 4.7 (4.2) 0.05 (3) 1.9 (7) 4.42 (17) 0.40 (10) 2.1 (4) 0.034 (32) 0.65 (50) 0.20 (20) 0.17 (17) 0.14 (11) 0.7 (8) 0.2 (2) 1.6 (1.7) 0.04 (6)

263 (26) 86.5 (8.4) 163 (10) 440 (295) 12 (8) 95 (34) 31 (19) 90.0 (3.3) 40 (19) 7.6 (3.2) 390 (92) 52 (10) 50.2 (9) 119 (16) 26.8 (1.9) 442 (221) 126 (60) 51 (18) 115 (40) 177 (47) 19 (15) 52 (36) 24 (17) 204 (157)

Comments

Overlap Overlap

D 0 − 2.53 cm−1 3a 4 5a 6 7 8 9 10 11 12b 13a 14 15c 16 17 18 19 20 21 22 23 24 25 26

25 126.0601 (34) 25 126.0970 (39) 25 126.1484 (15) 25 126.1825 (150) 25 126.3219 (900) 25 126.3793 (260) 25 126.3900 (546) 25 126.5547 (60) 25 126.6412 (280) 25 126.6732 (360) 25 126.8870 (250) 25 127.0742 (70) 25 127.2347 (14) 25 127.4064 (40) 25 127.4674 (50) 25 127.4750 (39) 25 127.4880 (150) 25 127.6450 (250) 25 127.6550 (100) 25 127.6780 (50) 25 127.9168 (900) 25 127.9730 (400) 25 128.1142 (800) 25 128.4180 (100)

0.0101 (10) 0.0307 (30) 0.0162 (10) 0.006 (4) 0.22 (15) 0.028 (10) 0.087 (9) 0.0295 (11) 0.067 (32) 0.35 (15) 0.0068 (16) 0.051 (10) 0.0529 (10) 0.0223 (30) 0.099 (7) 0.006 (3) 0.021 (10) 0.052 (18) 0.023 (8) 0.015 (4) 0.14 (11) 0.051 (35) 0.11 (8) 0.013 (10)

8.82 (96) 11.0 (9) 12.3 (1.0) 1.2 (1.0) 3.6 (2.0) 1.8 (1.1) 2.1 (1.6) 3.2 (7) 3.6 (2.5) 4.6 (2.0) 2.34 (97) 11.8 (2.0) 26.6 (5) 5.7 (7) 6.8 (9) 1.8 (8) 9.8 (2.9) 1.2 (8) 2.3 (1.5) 2.9 (1.6) 1.6 (1.1) 1.2 (1.0) 4.5 (2.9) 0.9 (8)

Overlap Overlap Overlap Overlap Overlap Overlap Overlap Possibly P(2) (#38), (overlap) Overlap (Overlap) (Overlap) Overlap Overlap Overlap Overlap Overlap Overlap Overlap Possibly P(2) (#49), overlap

D0 27 28 29 30 31 32 33b 34 35 36 37 38

25 128.5711 (100) 25 128.6641 (31) 25 128.7806 (18) 25 128.7972 (42) 25 128.8644 (9) 25 129.0056 (6) 25 129.0120 (41) 25 129.0737 (25) 25 129.2182 (14) 25 129.2238 (40) 25 129.3282 (26) 25 129.4148 (29)

0.0182 (25) 0.0302 (11) 0.0379 (16) 0.0108 (9) 0.0255 (14) 0.0699 (36) 0.371 (49) 0.0465 (30) 0.0571 (22) 0.0108 (20) 0.0644 (35) 0.0268 (12)

7.74 (98) 2.52 (86) 7.6 (1.6) 2.9 (2.1) 6.51 (82) 9.96 (50) 2.96 (21) 2.32 (54) 9.1 (1.1) 2.1 (1.6) 3.00 (54) 3.14 (96)

0.44 (12) 0.24 (9) 0.90 (22) 0.10 (8) 0.52 (9) 2.19 (22) 3.4 (7) 0.34 (10) 1.63 (26) 0.07 (7) 0.61 (14) 0.26 (9)

146 (20) 87.9 (3.2) 70.0 (3.0) 246 (20) 104.1 (5.7) 38.0 (2.0) 7.15 (9) 57.1 (3.7) 46.5 (1.8) 246 (46) 41.2 (2.2) 99 .0 (4.4)

39 40 41 42 43 44 45

25 129.4971 (92) 25 129.5348 (279) 25 129.6465 (93) 25 129.6916 (79) 25 129.7306 (52) 25 129.8397 (33) 25 129.9755 (24)

0.0464 (29) 0.0089 (62) 0.0266 (20) 0.0317 (26) 0.0506 (18) 0.0629 (50) 0.101 (84)

1.5 (1.1) 3.5 (2.6) 2.1 (1.9) 2.9 (2.6) 4.2 (2.1) 1.71 (49) 3.21 (46)

0.22 (17) 0.10 (11) 0.18 (17) 0.29 (28) 0.67 (36) 0.34 (12) 1.0 (9)

57.2 (3.6) 298 (208) 99.8 (7.5) 84 (7) 52.5 (1.9) 42.2 (3.4) 26 (22)

JNO = 1/2, A′′ Possibly P(2) (#55), (overlap) (Overlap) (Overlap) (Overlap) Possibly P(2) (#57), (overlap) (Overlap) JNO = 1/2, A′′ (overlap) (Overlap) Overlap Possibly R(0) (#13), JNO = 1/2, A′′, over. JNO = 1/2, A′, overlap Overlap Overlap Overlap Overlap Overlap JNO = 1/2, A′′, overlap

46 25 130.6800 (100) 0.024 (6) 0.8 (3) 0.060 (37) 111 (28) Overlap 47 25 130.8778 (310) 0.013 (4) 1.6 (7) 0.065 (49) 204 (62) Overlap 48 25 130.8925 (400) 0.062 (20) 2.3 (1.0) 0.44 (34) 43 (13) Overlap 49 25 130.9481 (200) 0.020 (15) 0.34 (30) 0.021 (20) 133 (99) Possibly R(0) (#26), overlap 50 25 130.9910 (50) 0.008 (5) 0.54 (40) 0.014 (14) 322 (207) Overlap 51 25 131.0186 (50) 0.011 (3) 0.89 (25) 0.031 (17) 241 (66) Overlap 52 25 131.0840 (100) 0.026 (3) 2.04 (40) 0.17 (5) 102 (12) Possibly P(2) (#74), overlap This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

131.170.6.51 On: Wed, 19 Aug 2015 11:14:17

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J. Chem. Phys. 142, 174305 (2015)

TABLE III. (Continued.) Assignments






Comments

53b 54 55 56 57 58

25 131.2589 (670) 25 131.2931 (800) 25 131.3158 (102) 25 131.4713 (300) 25 131.5430 (120) 25 131.7140 (900)

0.72 (7) 0.14 (10) 0.023 (8) 0.034 (30) 0.036 (23) 0.094 (88)

0.96 (9) 5.0 (2.0) 5.9 (2.0) 0.21 (16) 0.52 (35) 0.66 (60)

2.2 (2.1) 2.2 (2.1) 0.43 (29) 0.022 (21) 0.059 (59) 0.19 (30)

3.7 (3.0) 19 (13) 115 (40) 78 (68) 74 (47) 28 (27)

59 60 61 62 63 64 65 66 67 68 69 70 71 72 73

25 131.8019 (950) 25 131.9107 (980) 25 132.1481 (90) 25 132.1649 (70) 25 132.4680 (200) 25 132.5398 (400) 25 132.7034 (105) 25 132.7965 (247) 25 132.9043 (120) 25 132.9609 (150) 25 133.0556 (296) 25 133.2275 (50) 25 133.2857 (50) 25 133.3776 (100) 25 133.4634 (100)

0.16 (14) 0.16 (15) 0.029 (9) 0.016 (7) 0.022 (20) 0.11 (5) 0.104 (7) 0.133 (8) 0.015 (12) 0.026 (15) 0.066 (50) 0.038 (5) 0.045 (5) 0.013 (10) 0.015 (10)

2.7 (1.9) 0.77 (7) 1.6 (8) 1.5 (8) 0.59 (49) 3.7 (1.9) 2.6 (6) 1.82 (45) 0.69 (59) 4.6 (2.5) 1.2 (9) 1.3 (4) 1.3 (4) 0.54 (50) 0.60 (55)

1.4 (1.5) 0.39 (55) 0.15 (11) 0.075 (70) 0.04 (5) 1.3 (1.1) 0.85 (25) 0.75 (23) 0.033 (40) 0.38 (37) 0.24 (26) 0.16 (7) 0.18 (8) 0.022 (21) 0.028 (31)

17 (14) 17 (15) 92 (28) 166 (72) 121 (109) 24 (11) 25.5 (1.7) 20.0 (1.2) 177 (140) 102 (59) 40 (30) 69 (9) 59 (7) 204 (157) 177 (118)

Overlap Overlap Possibly R(0) (#29), overlap Overlap Possibly R(0) (#33), overlap Possibly P(2) (#74), JNO = 1/2, A′′, overlap Overlap JNO = 1/2, A′, overlap JNO = 1/2, A′′, overlap Overlap Overlap JNO = 1/2, A′, overlap Overlap Overlap Overlap JNO = 1/2, A′, overlap Overlap JNO = 1/2, A′, overlap Overlap Overlap Overlap

2.9 (3.3) 0.29 (26) 0.56 (35) 0.32 (19) 2.8 (1.5) 3.0 (1.8) 1.52 (44) 4.5 (2.3) 0.26 (22) 1.22 (26) 0.11 (10) 2.43 (45) 1.10 (73) 0.68 (40) 2.5 (8) 0.69 (39) 0.64 (36) 0.20 (12) 0.23 (15) 0.79 (43) 0.66 (31) 0.20 (30) 0.26 (12) 1.6 (1.5) 1.6 (1.9) 0.58 (35) 2.8 (3.9) 1.49 (48) 0.22 (24) 0.37 (20) 3.1 (3.5) 0.47 (65) 0.14 (11) 0.07 (6) 4.84 (22)

9.5 (8.1) 34 (16) 19.5 (2.9) 23.1 (3.8) 12.9 (2.3) 12.6 (2.1) 12.5 (1.8) 11 (2) 38 (16) 18.1 (2.4) 38 (27) 14.7 (4.1) 7.0 (1.1) 20 (8) 12.8 (2.2) 12.1 (2.7) 12.6 (2.9) 48 (9) 25 (6) 24 (6) 24 (6) 33 (24) 50 (7) 11.5 (6.0) 11.5 (9) 20.4 (3.9) 7.4 (6) 13.3 (6.6) 20 (15) 31 (7) 9.2 (6.3) 18 (11) 51 (14) 92 (34 11.5 (3.0)

Possibly R(0) (#52), overlap JNO = 1/2, A′, overlap Possibly R(0) (#58), overlap Overlap JNO = 1/2, A′, overlap Overlap Overlap Overlap Overlap Possibly P(2) (#94), overlap Overlap Possibly P(2) (#96), overlap Overlap Overlap JNO = 1/2, A′, overlap JNO = 3/2, A′′, overlap Overlap Overlap Overlap Overlap Possibly R(0) (#83), overlap JNO = 3/2, A′, overlap Possibly R(0) (#85), overlap Overlap Overlap JNO = 3/2, A′′, overlap Overlap Overlap JNO = 3/2, A′′, overlap JNO = 1/2, A′′, overlap Overlap Overlap Overlap Overlap Overlap

D 0 + 5.01cm−1 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100b 101 102 103 104 105 106 107 108

25 133.6181 (999) 25 133.7722 (300) 25 134.2466 (250) 25 134.4560 (222) 25 135.0476 (300) 25 135.3054 (300) 25 135.7329 (261) 25 136.2297 (430) 25 136.3453 (300) 25 136.6209 (200) 25 136.6690 (500) 25 136.8542 (500) 25 137.1678 (600) 25 137.3664 (502) 25 137.6818 (290) 25 138.0713 (413) 25 138.3437 (400) 25 138.6696 (100) 25 138.7948 (280) 25 138.9294 (200) 25 139.1495 (200) 25 139.2765 (600) 25 139.3864 (100) 25 139.6193 (980) 25 139.8487 (990) 25 140.1772 (220) 25 140.4606 (300) 25 140.8400 (950) 25 141.0497 (1500) 25 141.1818 (200) 25 141.4306 (1400) 25 141.7623 (888) 25 141.8102 (150) 25 141.9134 (122) 25 142.0699 (600)

0.28 (25) 0.078 (37) 0.136 (20) 0.115 (20) 0.205 (36) 0.21 (4) 0.212 (31) 0.240 (44) 0.07 (3) 0.147 (20) 0.07 (5) 0.18 (5) 0.38 (6) 0.130 (46) 0.207 (35) 0.219 (49) 0.207 (48) 0.055 (10) 0.105 (24) 0.110 (29) 0.110 (29) 0.08 (6) 0.053 (8) 0.23 (12) 0.23 (18) 0.13 (10) 0.36 (32) 0.20 (10) 0.13 (10) 0.085 (19) 0.29 (20) 0.15 (10) 0.052 (15) 0.029 (11) 0.23 (6)

3.6 (2.0) 1.20 (52) 1.31 (65) 0.88 (42) 4.4 (2.0) 4.6 (2.0) 2.28 (33) 6.0 (2.0) 1.2 (5) 2.5 (5) 0.48 (30) 4.6 (6) 0.92 (47) 1.66 (52) 3.84 (54) 1.00 (35) 0.98 (35) 1.15 (50) 0.70 (32) 2.3 (6) 1.9 (4) 0.8 (7) 1.54 (51) 2.2 (1) 2.2 (1) 1.42 (60) 2.5 (1.5) 2.5 (1.2) 0.55 (49) 1.4 (49) 3.4 (2.1) 1.0 (9) 0.87 (80) 0.8 (4) 6.7 (1.3)


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J. Chem. Phys. 142, 174305 (2015)

TABLE III. (Continued.) Assignments






Comments

D0 + 13.57 cm−1 109b 110 111b 112b 113 114 115

25 142.4060 (1550) 25 142.8908 (770) 25 143.5586 (1500) 25 144.1428 (888) 25 144.5413 (525) 25 145.0671 (975) 25 145.4292 (680)

0.35 (29) 0.27 (8) 0.69 (28) 0.32 (15) 0.25 (6) 0.24 (10) 0.15 (8)

1.2 (1.0) 2.4 (7) 2.2 (1.0) 1.1 (0.5) 3.4 (1.0) 0.32 (30) 0.58 (35)

1.3 (1.9) 2.0 (1.1) 4.7 (4.0) 1.11 (1.0) 2.6 (1.4) 0.24 (32) 0.27 (27)

7.6 (6) 9.8 (2.9) 3.8 (1.6) 8.3 (3.8) 10.6 (2.6) 11.3 (4.7) 18 (9)

Overlap Overlap Overlap Overlap Overlap Overlap Overlap

a Indicates

a fit by a Voigt profile. large resonance. c Indicates the broadest amplitude resonance. b Indicates

unimolecular dissociation coefficient are also predicted by the SACM theory when considering scattering matrix theory48 and reveal the quantum character of the short-lived levels coupled to a continuum. They are reported on formaldehyde at the dissociation threshold while the resonances are two orders of magnitude narrower than those observed on NO2.171 The averaged experimental unimolecular dissociation rates can be inquired in the framework of the present RRKM models, and special attention is required when calculating these values. We have considered three types of data weighting (w denotes the weight): uniform weighting (w = C te), weighting by the error bar on the resonance width [w ∝ 1/(∆Γ)2], and weighting by the resonance strength [w ∝ S/(∆Γ)2, see Table III and Eq. (8)]. Actually, this latter data weighting is the most relevant one for evaluating the effective (mean) unimolecular dissociation rates kuni. As shown in Table IV, under this weighting condition, the values of kuni fall between the values provided by the two other weighting methods. The usual standard deviations (σkuni) are also determined. Below D0 + 5.01 cm−1, a weighted mean dissociation coefficient k uni1/2 ∼ 0.016 ps−1 (∼61 ps) is obtained compared with kuni3/2 ∼ 0.054 ps−1 (∼18 ps) above this energy threshold. Surprisingly, the value of k uni1/2 is very close to the smallest dissociation rates previously reported (∼0.01 − 0.02 ps−1)38,44,47,104 despite the large fluctuations of the resonance width. It is also a factor 2 less than the averaged value proposed by Wittig and Ionov57 commenting Miyawaki and co-authors analysis based on ρreac = 4.1 levels/cm−1. The ratio k uni3/2/kuni1/2 is close to 3 whatever the weighting method used (2.8 is the predicted value by PST, see Sec. V B). A density of reactant levels can be determined by applying the formalism introduced in Sec. V B to both values of kuni and by considering that two times more resonances J ′ = 3/2 (w JNO = 2/3) than J ′ = 1/2 (w JNO = 1/3) are observed. 2 2 Without constraining the value of L, it becomes ρreac ∼ 11.2 levels/cm−1. We think that this determination is reliable because it is not deduced from the density of resonances but from two weighted mean dissociation rates. It is worth noting that the value of the product ρres · ⟨Γ⟩ ∼ 0.41 below D0 + 5.01 cm−1 clearly hints partial resonance overlapping. ρres ∼ 9.5/cm−1 is the density of resonances in this energy range. The value of this product and the large fluc-

tuations of the resonance width have already received attention specifically with regards to the temporal determinations of the dissociation rate coefficient. For example, it has been concluded that the temporal decays might remain exponential (statistical)159,172 or not.48 The fluctuations of the dissociation rate have been intensively studied by NO photofragment LIF yield in the context of resonance overlapping.7,173,174 An accurate statistical analysis of these fluctuations would be very helpful. However, the small number of consistent resonance widths available (73 and 35) as well as the associated error bars do not allow substantial investigations. Under these circumstances, statistical theories suggest to deduce the number of degrees of freedom of the system from the variance95 ndof = 2

⟨Γ⟩2 . σΓ2

(9)

We have deduced (from the values provided in Table IV) two values of ndof : approximately 12.5 and 8.3 for both energy ranges of interest. These two values suggest a reduction of the number of degrees of freedom and of the resonance width fluctuations when a new dissociation channel opens. Nonetheless, our analysis has been based on the absence of interference between the resonances whereas one moves from ρres · ⟨Γ⟩ < 1 below D0, to ρres · ⟨Γ⟩ ∼ 1 between D0 and D0 + 5 cm−1, and to ρres · ⟨Γ⟩ > 1 above D0 + 5 cm−1. Furthermore, the determination of kuni from ⟨Γ⟩ relatively to the highest energy range is irrelevant, because of the too few number of data.159 In addition, the density of resonances becoming the leading term, Ericson fluctuations175–178 can be expected when ρ. ⟨Γ⟩ approaches unity. Nevertheless, the value 12.5, corresponding to the effective number of independent decay channels, is almost equal to the value deduced from the PST below D0 + 5 cm−1 (see Table I). Resonance width fluctuations confirm the belief that the RRKM rate applies to statistical system exhibiting a complete loss of state selectivity in the decomposition processes (ergodicity) and the energy redistribution among the various degrees of freedom: the amplitude of the fluctuations (two orders of magnitude) depends markedly on the coupling between the intramolecular vibrational modes which is irregular (or chaotic).179,180 Albeit different regimes of resonance overlapping can be recovered, the decrease of the


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J. Chem. Phys. 142, 174305 (2015)

TABLE IV. Unimolecular dissociation rate coefficients. All values are given in ps−1. The unimolecular dissociation rates k uni and the associated standard deviations σ k uni have been calculated for three types of weightings. The resonance strength weighting encompasses the error bar on the resonance width. Uniform weighting

E < D 0 + 5.01 D 0 + 5.01 cm−1 ≤ E < D0 + 13.57 cm−1

cm−1

Standard error weighting

Resonance strength weighting

k uni

σ k uni

k uni

σ k uni

k uni

σ k uni

n dof

0.025

0.038

0.010

0.064

0.016

0.0066

12.5

0.061

0.033

0.031

0.021

0.054

0.027

8.3

fluctuation amplitude versus the opening of new channels is anticipated.70 The IVR processes between the A˜ and X˜ states are assumed to be very fast (less than 1 ps), i.e., shorter than the dissociation time in the energy range of interest (i.e., close to D0). IVR rate has been estimated from ab initio quantum chemistry calculations: an internal conversion time of ∼120 fs has been deduced by the wave packet dynamics166 while the Lyapunov exponent has been estimated.48 This conversion time is compatible with the recent photoelectron observations.52 Resonance spectra have been synthesized by Someda’s group (Feshbach theory of resonance scattering)181 for the three regimes of overlapping. The RRKM regime is identified to the regime of the partial (or critical) overlapping resonances which is visually comparable to our resonance spectrum whereas the amplitude of the background contribution may be argued.94,177 C. Comparison of the densities

The experimental density of reactant levels (ρreac ∼ 11.2 levels/cm−1) can be compared to several densities, the first one is the density of observed resonances: ρres ∼ 9.5/cm−1. These two densities (ρreac and ρres) are very close especially if we take into account the presupposed uncertainties attached to both values. Let us note that a density of resonances of 3.4 peaks/cm−1 has been reported by the PHOFEX experiment.38 This lower value is coherent with the resonance matching process discussed above: numerous resonances have not been observed by PHOFEX. Both density values can also be compared with the density of transitions R(0) observed between D0 − 2.53 cm−1 and D0 from LIF spectra. The last reported value is ρtrans = 16.6/cm−1 whose vibronic level density ρvib = 5.8 ± 0.24 levels/cm−1 has been derived (the largest vibronic level density never reported).23 According to these values, the density of reactant levels is approximately twice larger than the density of vibronic levels. The interpretation of this factor is beyond the scope of this work in the absence of a relevant spin-rotation coupling scheme under vibronic interactions at dissociation threshold. The relatively close values of ρres ∼ 9.5/cm−1 and ρtrans ∼ 16.6/cm−1 can be questioned: the absence of failure in these two densities (assuming the conservation of the selection rules relative to the angular momenta) is usually postulated in the RRKM theories when the dissociation threshold matters. Unfortunately, we cannot turn out the strict identity of these two quantities.

The density of vibronic levels observed just below D0 (i.e., between D0 − 20 cm−1 and D0) has been qualified of “anomalously” large previously.103 The value ρvib = 5.8 ± 0.24/cm−1 (Ref. 23) reflects this statement. It is almost an order of magnitude higher than the density extrapolated from a Dunham expansion or estimated from lower energy ranges [ρvib = 0.65 − 0.94/cm−1 (Refs. 88–90, 101, and 102)]. It sounds clear that the energy levels around D0 do not follow a conventional behavior. We hypothesize that the large amplitude of the vibrational motions breaks, at least, the common separation between the rotational and vibrational internal degrees of freedom. The floppy frame of the molecule, well beyond the current anharmonicities, distortions, rotational Ka -mixing,182 ro-vibrational couplings, and BornOppenheimer approximation183 remains to be depicted. Actually, this picture prevents us from using the usual spectroscopic assignments since only the total angular momentum (F), the full parity, and the Cs geometry representations with unequal bond lengths99 are conserved quantities. The loose character of the transition states around D0 and their location at 2 − 3 Å78,97 from the stable geometry seems compatible with such a hypothesis. The shape of the long range PESs coupled by nonadiabatic interactions is probably key parameters. D. Questioning PST model

Regardless to the large fluctuations of the resonance width, the observation of a stepwise around D0 + 5 cm−1, revealing the opening of the second dissociation channel, is not disputable. The opening of the third dissociation channel is possibly observed around D0 + 13.6 cm−1. Unfortunately, the location of this third channel would have help to validate the PST versus the SCAM predictions: different stepwise lengths are expected.70 Let us note that the experimental data do not show a change of the resonance width over the energy range matching the interval between each channel opening, only unexplained slight changes in the error bars of the resonance widths could be noticed around 25 130 and 25 139 cm−1. Albeit the distribution of reaction products has not been analyzed here, we think that our overall analysis markedly indicates that the PST is valid around D0. Nevertheless, if this result agrees with Miyawaki and co-authors conclusions, it does not match the conclusions of Abel’s group.59 On the other hand, the energy distribution in the fragment NO (v = 1), i.e., from dissociation energies well above D0 shows imperfect agreement with PST.40 This latter group reported on dissociation rates kuni(E ‡) based on quantum mechanical calculations up to D0 + 1000 cm−1, and he has claimed that he


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could not rule out a contribution of long-range interactions to the dissociation rates at threshold (“they only play a minor role”). He concluded that “the measured dependence of k(E ‡) is most likely due to the energy dependence of the resonance structure and not of the opening of individual channels.” On the other hand, the same simulated data clearly show a span over two orders of magnitude of the dissociation rate kuni(E ‡) just above D0. This is exactly what is observed in the present study (but not in experimental data obtained at too poor spectral resolution). The other experimental data which must be contemplated against ours are issued from time-resolved measurements of the decomposition rate. Unfortunately, the number of unimolecular dissociation coefficients reported in the energy range of interest is low. The stepwise at D0 + 5 cm−1 is not viewed47,104 while only smooth stepwises are observable [i.e., no abrupt rise of kuni (E)] at higher energies, e.g., at ∼25 142 cm−1. This stepwise could be attributed to the opening of the third dissociation channel (i.e., JNO = 5/2). This behavior results probably from a lack of spectral resolution. The application of a well chosen convolution function to our data could probably reproduce the data set obtained with a spectral resolution of the order of 2 cm−1 (laser pulse duration: 30 ps). This latter set of data has been compared to PST calculations of the rate coefficient by using a density of 2.7 levels/cm−1 and by considering only levels J ′ = 1/2. The proposed analysis only matches qualitatively (i.e., not quantitatively) our analysis. The same kind of data has been reported later again by the same group by using an improved laser source (10 ps resolution, spectral broadening ∼3 cm−1)47 and only marginal changes have been shown. We emphasize that we report on resonance widths as narrow as ∼0.006 cm−1 (HWHM) compared with the lowest value ∼0.046 cm−1 (FWHM) obtained by using a 0.05 cm−1 “broad” pulsed laser source.38 Both values differ by a factor five. E. Few perspectives

As it has been shown, the broad width of the NO2 resonances above D0 + 5 cm−1 prevented us from using the full capabilities of high spectral resolution of the CW-CRDS technique. The association of the CW-CRDS with an analysis of the photofragment distributions may help to make progress in the characterization of the dissociation resonances. However, the possibility of breaking the space anisotropy by strong electromagnetic field (e.g., by using an optical cavity) as well as the transfer of the molecular anisotropy towards the fragments should be considered in the perspective to better characterize the NO2 photodissociation process. Lowering the rotational temperature should also probably simplify the absorption spectrum allowing more accurate determinations of the resonance-densities and -widths and accordingly of the channel opening thresholds. The energy level degeneracy due to the nuclear spin near the dissociation energy has been mainly ignored. Nevertheless, the density of rovibronic levels is identical for the two isotopologues 14NO2 and 15NO2,23 while they exhibit a different value of the nuclear spin. The comparison of both absorption spectra

J. Chem. Phys. 142, 174305 (2015)

above the dissociation threshold should be of acute interest to determine the possible role of the nuclear spin, for example. Time resolved measurements are crucial data. However, they do not necessary provide information readily reconcilable with pure spectroscopy data. In addition, the change of status of the transition states when moving from energy just above the dissociation threshold to higher energy requires further works for unifying the RRKM predictions. Beyond the relevance of the theoretical models relatively to the probed excess energy, the understanding of statistical quantum dissociation is of pivotal interest for the chemical physics. Since its discovery, the roaming mechanism has been drawing attention as a third dissociation way. It has been first observed on formaldehyde by analyzing the reactant products CO and H2, which exhibit cold rotational and high vibrational temperatures, respectively, compared with the conventional decomposition.184,185 It conveniently deciphers the bimodal rotation distribution reported by Moore’s group in the 1990s.186 Questioning the existence of a similar mechanism in NO2 as possibly contributing to the complexity of the resonance spectrum and about the high level density just D0 seems relevant. However, the absence of calculation providing measurable temporal behaviors preserves a highly speculative character to this conjecture whereas correlations between overlapping resonances and oscillations of the NO rotational distribution174 have suggested the existence of roaming states in NO2.187 Roaming based on PST has been recently proposed and can give some directions to identified these states for a barrierless radical like NO2: it requires identifying ∆roam and kroam.188 The observation of roaming quantum states by a standard spectroscopic technique raises now intriguing questions linked to the photodissociation resonances.189 VIII. CONCLUSIONS

The present analysis of jet-cooled radical NO2 around its lowest dissociation energy is primary based on the experimental absorption spectrum obtained by the combination of the CW-CRDS and LIF techniques, and of a CW supersonic slit expansion. From an energy range spanning over 25 cm−1, we were able to discuss two kinds of lines: (i) the transitions to long-lived energy levels which can be observed easily by the LIF technique, because none decomposition process follows the excitation step and (ii) the photodissociation “resonances” associated with the decomposition of NO2 in NO + O, which are not observable by detecting the NO2 fluorescence. These two types of lines are easily distinguishable, because their spectral shape and fluorescence yield are very different. The NO2 LIF spectrum is renowned for its complexity which even increases when approaching the dissociation energy. This complexity is usually ascribed to the strong mixing of the two electronic states X˜ and A˜ above 10 000 cm−1. The level mixing appears even strongly emphasized ∼20 cm−1 below the dissociation energy. On the other hand, the LIF spectrum (as well as the absorption spectrum if the resonances are ignored) reveals an apparent spectral simplification in the range D0 − 2.53 cm−1—D0: the density of observed transitions decreases markedly; astonishingly, the transitions exhibit all the same profile in this energy range. The LIF spectrum


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between D0 − 7.2 cm−1 and D0 has been reanalyzed to valid the acquisition technique by pairing the transitions R(0) and P(2) sharing the same upper level. Nevertheless, this pairing remains incomplete while the weakness of the hyperfine structures in the upper has been noted. The main analysis deals with the resonances observed at high resolution. All the structures have been fitted to obtain their energy position, width, and amplitude. 115 resonances are compared with the Miyawaki and co-authors data (55 resonances were observed). Only 17 of them have been perfectly well matched while the density of resonances differs by a factor ∼3. We were able to pair a ten of resonances by using an approach slightly different than that utilized for the transition pairing. The synthetic plot of the resonances evidently displays large amplitude fluctuations of the resonance widths (spanning over two orders of magnitude). This behavior well characterizes the RRKM regime, it cannot be observed when laser sources suffering from inadequate spectral resolution are used. The central discussion of this paper is about the interpretation of the two stepwises identified around D0, D0 + 5 cm−1 and probably around D0 + 13.6 cm−1 in the plot of the resonance width versus their energy position. The rise of the first stepwise reaches almost a factor 3 which can be qualified of “abrupt” increase despite the large fluctuations carried by the resonance widths. A similar behavior has been reported and commented on previously. It had been associated with the opening of a new dissociation channel correlated to the increase of the quantized rotation energy of the fragment NO. Associated with the analysis of the photofragment energy distribution, this observation had been a pivotal criterion to valid the PST while time-resolved data obtained over a larger excess energy range are in better agreement with variational RRKM theory. Despite the partial failure of the resonance pairing, the predictions of PST have been applied to the calculation of the dissociation rate coefficients. Assuming that only J ′ = 1/2 and 3/2 upper energy levels are excited (and not mixed) in the ratio 1:2 and applying relevant weighting to the resonance widths, two values of the unimolecular dissociation rate coefficients (k uni) have been deduced for the channel opening associated with the two lowest dissociation energies. Regardless to possible interference of “hot” resonances, we believe that these two values are relevant, because they are not derived from densities of resonances. Accordingly, a density of reactant levels (ρreac ∼ 11.2 levels/cm−1) has been determined. Actually, this value is markedly close to that of the density of resonances observed just above D0. Both densities are compared with the densities of rovibronic and of vibronic levels previously reported. An almost isolated resonance located at ∼25 127.23 cm−1 (τdiss ∼ 50 ps) seems to be a good nugget of the unimolecular reaction such as analyzed here since it nearly provides the averaged dissociation rate coefficient kuni ∼ 0.016 ps−1 at D0. Our analysis emphasizes the existence of loose transition states at the dissociation threshold while time-resolved direct measurements of the unimolecular dissociation coefficient emphasize tight transition states. Accounting for the lack of spectral resolution inherent to the time-resolved experiment when probing high excess energy resonances (i.e., at excess

J. Chem. Phys. 142, 174305 (2015)

energy > 100 cm−1) allows reconciling spectrally and temporally resolved data if one accepts that the transition states move to shorter reaction distances when the excess energy increases as suggested by the VRRKM theory. However, ab initio quantum chemistry calculations run by Abel’s group seem to fail to entirely valid this hypothesis, as well as they fail to reproduce the resonance width stepwise at low excess energy. Nevertheless, the amplitude of the unimolecular dissociation rate fluctuations predicted by these calculations (scattering matrix) seems to be in good agreement with our experimental observations at low excess energy. Although the characterization of the NO2 potential energy surfaces at very long distance is probably a key data to predict the dissociation processes and the related quantities, our experimental approach seems touching its own limits. For example, high-resolution spectroscopy yields decisive information below the dissociation energy and slightly above, but its capabilities become rapidly pointless when the product ρres · ⟨Γ⟩ passes 1, i.e., already a few cm−1 above D0. Above this energy range, femtosecond time-revolved experiments take over to provide direct measurements of the unimolecular dissociation rate. This gives hope for future significant improvements although we think that very low temperatures (

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