Nanosecond time-resolved IR emission from

THE JOURNAL OF CHEMICAL PHYSICS 123, 154306 共2005兲

Nanosecond time-resolved IR emission from molecules excited in a supersonic jet: Intramolecular dynamics of NO2 near dissociation Jianqiang Ma, Peng Liu,a兲 Min Zhang, and Hai-Lung Daib兲 Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-632

共Received 9 May 2005; accepted 10 August 2005; published online 19 October 2005兲 IR emission from NO2 cooled in a supersonic jet and excited to a single, ˜B 2B1 state rovibronic level at 22 994.92 cm−1 above the ground-state zero point was detected with 10−8-s time resolution. The IR emission together with the laser-induced fluorescence decay measurement allows the deduction of the relaxation dynamics near the dissociation of NO2. Following the excitation this single rovibronic ˜B 2B1 level decays on 1.0-s time scale primarily through electronic radiation. Collisions induce internal conversion with a rate constant of 3.0⫻ 107 Torr−1 s−1 to the mixed Ã / ˜X states. Collisions further induce internal conversion of the Ã / ˜X mixed states into highly vibrationally excited levels in the ˜X states with a rate constant at least one order of magnitude slower. This mechanism results in the observation of a double-exponential decay in the laser-induced fluorescence and a rise in the IR emission intensity corresponding to the fast decay in the fluorescence intensity. The IR emission rate of the highly vibrationally excited ˜X-state levels is estimated to be about one order of magnitude larger than the isoenergetic Ã / ˜X mixed states and much larger than the ˜B 2B1 level, both with much less vibrational excitation. © 2005 American Institute of Physics. 关DOI: 10.1063/1.2049271兴 I. INTRODUCTION

An effective way of characterizing the dynamics of an excited molecule is to detect the photons emitted from this molecule with time and frequency resolutions. Photons detected in the visible and ultraviolet regions in the form of laser-induced and dispersed fluorescences indicate the nature of the emitting states and have been highly informative of the intramolecular dynamics following the excitation. As the excitation and the ensuing dynamics begin to involve vibrational degrees of freedom, IR emission from the excited molecules should be equally useful. Previously, IR emission has been valuable in revealing the dissociation dynamics of small molecules1 and intramolecular dynamics of low vibrational levels of medium size molecules.2,3 Time-resolved IR emission spectra have allowed the deduction of photodissociation4–6 and energy-transfer dynamics of highly vibrationally excited molecules.7 In general, since the IR emission lifetimes are much longer than those of UV and visible fluorescences, the detection of IR photons is much more of an experimental challenge. This is particularly the case when it is desirable to detect IR emission from molecules excited in a supersonic jet where the molecular density is low. Detecting IR emission from a supersonic jet is desirable because of the possibility that a single rovibronic state can be excited and that collisionless conditions are achieved. In this report, we show that time-resolved IR emisa兲

Present address: Department of Chemistry, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. b兲 Author to whom correspondence should be addressed. Electronic mail: [email protected] 0021-9606/2005/123共15兲/154306/7/$22.50

sion can be detected from supersonic expansion cooled NO2, excited to a single rovibronic state, to reveal its intramolecular dynamics near the dissociation limit. In recent years, many spectroscopic techniques are widely used in both atmospheric chemistry and combustion chemistry.8–11 As an important pollutant molecule in the atmosphere and a stable free radical, NO2 has been intensively studied through many spectroscopic methods.12,13 NO2 is one small molecule that has displayed complex spectroscopic patterns and rich dynamic behavior. The spectroscopy and intra- and intermolecular dynamics of NO2 near the origins of the low-lying electronic states have been well characterized.13 On the other hand, in the energy region near the dissociation limit of 25 000 cm−1, due to the high level densities and vibronic couplings among the multiple electronic states, the energy-level structure as well as the intraand intermolecular dynamics are much more complex to be characterized. The fluorescence decay following the pulsed laser excitation of NO2 has been studied for more than three decades. Donnelly and Kaufman first reported the observation of double-exponential decay with abnormally long lifetimes following excitation with wavelengths between 600 and 530 nm.14 The fast decay lifetimes are about 50 ␮s and the slow ones around 200 ␮s. Transitions in this wavelength range are from the ˜X 2A1 ground state to the Ã 2B2 state, which is strongly coupled with the ground state through the Renner-Teller effect.15 Spectral “chaos” appears in the energy range above 15 000 cm−1,13 where the molecular eigenstates have both Ã 2B2 and ˜X 2A1 characters. The ˜X 2A1 character in the molecular eigenstates is responsible for the

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abnormally long lifetimes in visible fluorescence decay. The double-exponential decay has been attributed to two sets of differently mixed states, with one of them mainly of the Ã 2B character while the other mainly ˜X 2A . This proposal, 2 1 however, remains to be tested. On top of the double-exponential components of the laser-induced fluorescence 共LIF兲 decay, a very fast decay on the order of 1 ␮s or shorter was observed by Sackett and Yardley for the 450– 460-nm excitation range.16 They assigned this fast decay to the depopulation of the second excited ˜B 2B1 state. Stevens et al. found that there are ˜X 2A1 to ˜B 2B transitions observed in the 593.4– 594-nm and shorter 1 wavelength ranges.17 In the excitation range near 480 nm, Paech et al. found that a double exponential still dominates the fluorescence decay behavior but a very fast decay component begins to appear.18 They have proposed a kinetic model based on the radiationless transition theory of intermediate cases19 to explain this multiple-exponential decay. A theoretical calculation of level density at that energy range showed, however, that the level density is too low for NO2 to be considered as an intermediate case.19 More recently, Sivakumaran et al. examined the fluorescence decay at several excitation wavelengths near the dissociation limit.20 They reported, though without explanation, fast decay lifetimes on the order of a microsecond. In the energy range just below the dissociation limit in which the intramolecular dynamics are considered “chaotic,”13 apparently due to the complexity of the energy levels, the observed transitions are usually difficult to assign. Only recently, Jost and co-workers were able to partially vibrationally assign and rotationally analyze the peaks in the 18 000– 23 000-cm−1 range by using a combination of laserinduced fluorescence and dispersed fluorescence methods.21,22 To study intramolecular energy-transfer dynamics near the dissociation limit of NO2, time- and frequency-resolved IR emission from the excited molecules should provide valuable information. IR emission spectra are particularly desirable in situations where highly vibrationally excited levels are involved in the dynamics following initial electronic excitation. This is exactly the case for NO2 in the energy region below dissociation where highly vibrationally excited levels of the low electronic states are strongly coupled to the excited electronic states. For characterizing dynamics in energy regions where level densities are high, it is preferable that measurements be conducted in a low-temperature environment, such as in a supersonic expansion, to reduce the contribution to spectroscopic congestion by rotational transitions. A supersonic molecular beam has the further advantage of near collisionless conditions for characterizing intramolecular dynamics. However, the IR emission signal would be very weak and hard to detect from molecules seeded in a supersonic expansion. The recently available fast IR detectors afford the possibility for detecting IR emission from a supersonic molecular beam with fast time resolution. In this paper, we report for the first time the detection of time-resolved IR emission from molecules excited in a supersonic beam. The analysis of the IR

emission confirms that the model17,18 proposed for lowerenergy regions of NO2 is effective in describing the intramolecular dynamics near the dissociation limit. II. EXPERIMENT

The experimental setup for the detection of IR emission from pulsed-laser-excited molecules in a supersonic molecular beam is described here. A Nd:YAG 共yttrium aluminum garnet兲共Spectra Physics Quanta-Ray Pro-Series, 30 Hz, 355 nm兲 pumped dye laser 共Lambda Physik Scanmate 2兲 provides the laser pulses tunable around 440 nm. The output of the dye laser was several mJ/pulse in a 2-mm-diam spot size with a 10-ns pulse duration and a 0.02-cm−1 bandwidth 关full width at half maximum 共FWHM兲兴. In the experiment, the laser-pulse energy was set lower than 0.1 mJ/pulse when collecting the LIF signal, but the highest pulse energy was used when collecting the IR signal. A 0.5% mixture of NO2 共Matheson Gas, C.P. 99.5%兲 seeded in Ar 关Spectra Gases, ultrahigh purity 共uhp兲 99.999%兴 was used for the supersonic expansion with the stagnation pressure adjusted between 10 and 100 psi into a background pressure of 5 ⫻ 10−6 Torr. The laser pulse intersected the supersonic beam 5 mm downstream from the 0.5-mm-diam orifice. The formation of NO2 dimer is negligible in this experiment because of the very low NO2 concentration.23 Laser-induced fluorescence and IR emission were concomitantly detected perpendicular to the laser and molecular beams. The fluorescence signal was collected by two 75-mm focal length lenses and detected by a photomultiplier tube 共Hamamatsu, rise time 2 ns兲 powered at usually 900 V. A broadband long-pass filter 共cut off at 440 nm兲 blocked the scattered laser light. The scanning of the fluorescence excitation spectrum was performed with 0.0002-nm step size. The IR signal was collected, collimated, and refocused by using two NaCl lenses and one silver concave reflector for detection by a liquid-N2-cooled, fast mercury cadmium telluride 共MCT兲 detector 共Kolmar, rise time 20 ns兲 with a spectral range of 2 – 12 ␮m. No band-pass filter was used. The emission from all three vibrations of NO2 falls within the detector spectral range with ⬎50% efficiency.24 The IR detection part is shielded from other sources of light. A Welsh cell setup with four gold mirrors was used to enhance the IR signal collection.25 A 500-MHz digital oscilloscope was used to monitor and record the time profiles of the fluorescence and the IR emission, and a boxcar 共SRS兲 interfaced with a microcomputer was used to process the fluorescence spectra. Since the emission photons are detected perpendicular to the molecule beam and because the radiative lifetimes of the electronic excited states of NO2 are known to be long 共several tens of microseconds usually兲, the effect of excited molecules moving out of the observation zone on emission signal decay is expected and will be discussed later in Sec. III. III. RESULTS

The LIF spectrum in the excitation range of 435.0– 434.75 nm of NO2 seeded in the supersonic jet with 40-psi stagnation pressure is shown in Fig. 1. The rotational temperature of NO2 has been estimated to be 10 K by using

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Dynamics of NO2 near dissociation

FIG. 1. The fluorescence excitation spectrum from 434.75 to 435.00 nm of NO2 seeded in a supersonic jet with 40-psi stagnation pressure. The arrow indicates the peak at 434.879 nm.

a free jet expansion theory calculation.26 In this wavelength range, at least three excited electronic states are involved in the spectrum: Ã 2B2 共with origin at 9000 cm−1兲, ˜B 2B1 共start˜ 2A 共from 14 000 cm−1兲. The ing from 13 000 cm−1兲, and C 2 Ã 2A ← ˜X 2A and ˜B 2B ← ˜X 2A bands are the strongest for 2 1 1 1 excitation. These excited electronic states, however, are strongly coupled with each other. The peak at 434.879 nm, assigned by Jost and co-workers as a single rovibrionic transition of ˜B 2B1兩N = 1 , K = 0 , J = 3 / 2典 ← ˜X 2A1兩N = 0 , K = 0 , J = 1 / 2典 21,22 was chosen as the excitation line for this study. The vibrational quantum numbers of the excited level were not assigned because of the mixing of vibrational modes. In the theoretical calculations and spectroscopic characterization by Jost and co-workers,21,22 a vibronic level density of 0.1 cm−1 was estimated for this energy range, indicating that the transitions in the detected region are the rotational transitions associated with one or two vibrational bands. Although the laser-pulse bandwidth is 0.02 cm−1, the spectral resolution is ⬃0.1 cm−1 because of Doppler broadening in the jet. The narrow bandwidth laser excited predominantly 共⬎99% 兲 one single rovibronic level of the ˜B 2B1 state initially. Both the visible fluorescence and IR emission decays, recorded concomitantly, for the supersonic jet with a stagnation pressure of 80 psi are displayed in Fig. 2. The LIF signal is strong and signal-to-noise 共S/N兲 ratio was more than 400 after a 256-pulse average by the oscilloscope. The IR signal is very weak with a S/N ratio of about 3 even after a 256pulse average. The fluorescence decay can be best fitted with a biexponential decay, Fig. 2共a兲, with the fast decay component as 0.364 ␮s and the slow component 4.0 ␮s in this case. The infrared emission displays a complex but different behavior in time. In the case of Fig. 2共b兲, following the laser pulse at t = 0, the IR intensity rises to a maximum at around 1.7 ␮s. This rise is followed by a decay with a time constant of 23 ␮s. The rise, slower than the LIF, can be interpreted and understood as resulting from intramolecular relaxation from the initially excited, poor-IR-emitting states to strongIR-emitting states. The even slower decay reflects both the final-state population decay and the effect of the excited molecules moving out of the observation zone. These observations are surprising in light of the fact that

FIG. 2. 共a兲 Fluorescence decay of NO2 in the supersonic jet with 80-psi stagnation pressure, following excitation of the 434.879-nm transition. The lower curve is the experimental observation decay and the dotted line is the fit with double exponential with a fast decay component of 364 ns and a slow component of 4.0 ␮s. The upper trace 共Diff.兲 is the residual between fitted and experimental data. 共b兲 IR emission signal detected under similar conditions as stated in 共a兲. The solid line represents the fitted curve with 兩A3兩 : 兩A4兩 : 兩A5兩 = 0.3: 1.3: 1.8 and K5 = 23 ␮s. The upper trace 共Diff.兲 is the residual between fitted and experimental data.

one single rovibronic molecular eigenstate is excited. Under supersonic beam conditions, one would expect only singleexponential decay in both LIF spectra and IR emission. It is reasonable to expect that collisions do happen in the supersonic jet and that collisions affect the intramolecular relaxation dynamics. Different stagnation pressures, from 12 to 100 psi, have been used to reveal if there is any effect due to local collisions in the observation region of the supersonic jet. Experimental results show that the stagnation pressure does affect the decay behavior. In LIF, the two decay rates become faster with the increase in the stagnation pressure. The IR emission displays similar dependences. Both the rise and decay rates become faster with increasing stagnation pressure. The decay time constant from the 40-psi experiment almost reduces to half at 100 psi. The change of the decay constants in the LIF as a function of pressure is registered in the Stern-Volmer plot in Fig. 3. For the fast decay component, the SternVolmer plot gives a slope of 3 ⫻ 107 Torr−1 s−1 and an intercept of 1.0⫻ 106 s−1, while for the slow decay component, the slope is 2.0⫻ 106 Torr−1 s−1 and the intercept is 1.33⫻ 105 s−1. The meaning of these fitting results will be discussed in Sec. IV. IV. ANALYSIS A. Kinetic model for collision-induced relaxation dynamics near the dissociation limit

Brucat and Zare have proposed a kinetic model to explain collisional quenching of the Ã 2B2 state fluorescence in

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FIG. 4. Model proposed for the inter- and intramolecular relaxation dynamics following the excitation of a single rovibronic level of the ˜B 2B1 state near the ˜X-state dissociation limit of NO2.

FIG. 3. Stern-Volmer plots of the decay rate constants of the fluorescence decay vs pressure in the observation zone of the supersonic jet. Black dots are experimental data. The solid lines are the fits with a linear equation. 共a兲 The fast decay rate constant. The slop is determined as 3.0⫻ 107 Torr−1 s−1 while the intercept is 1.0⫻ 106 s−1. 共b兲 The slow decay rate constant. The slop is determined as 2.0⫻ 106 Torr−1 s−1 while the intercept is 1.3⫻ 105 s−1.

their Zeeman quantum beat spectroscopy study of NO2.12 Previously, Paech et al. have proposed a multistep kinetic model to account for their collision-free fluorescence decay results.18 We combine and modify these two models on intramolecular and intermolecular relaxation to account for the fluorescence and IR emission observations made for this high-energy 共⬃23 000 cm−1兲 region. Of the three excited electronic states, the Ã 2B2, ˜B 2B1, ˜ 2A , in this energy region, the C ˜ 2A state is not inand C 2 2 cluded in our model. There is little initial population in the ˜ 2A state because the C ˜ 2A ← ˜X 2A transition is optically C 2 2 1 ˜ 2A state is not strongly forbidden. Furthermore, the C 2 coupled with any of the ˜X 2A1, Ã 2B2, and ˜B 2B1 states due to symmetry restrictions. Among the other three electronic states, the Ã 2B2 and ˜X 2A1 states are strongly coupled through the Renner-Teller effect and form mixed molecular eigenstates.13,15 Symmetry selection rules also allow vibronic coupling between the ˜B 2B1 and ˜X 2A1 electronic states through the antisymmetric stretching, B1-symmetry vibration mode of NO2 in both states. Based on all this information and the assignment of the excitation transition, we propose the excitation and relaxation schemes shown in Fig. 4, based on models proposed previously to account for the observed fluorescence and IR emission time dependences. The laser pulse excites the NO2 molecule into a single rovibrational level in the ˜B 2B1 electronic state. This level can emit both visible and IR photons. The initial decay of the single ˜B 2B1 rovibrational level is depicted by the rate constant k1⬘ which consists of contributions from both electronic

radiative decay and intramolecular relaxation. The IR emission from this level is defined by the radiative rate constant k1⬙, although the lifetime of the IR emission from this level will be determined by the total decay constant dominated by k1⬘. The ˜B 2B1 level is subjected to several relaxation pathways. The vibronic coupling between ˜B 2B1 and ˜X 2A1 and the Renner-Teller coupling between Ã 2B2 and ˜X 2A1 contribute to intramolecular relaxations.15 Collisionless intramolecular relaxation, however, is not considered a dominant effect here in comparison with collision-induced relaxation processes because of the relatively small coupling matrix elements between ˜B 2B1 and ˜X 2A1.17 According to previous studies and the observed pressure dependence in our experiment,7,12 collision-induced internal conversion 共CIIC兲 may occur. CIIC brings the population in the rovibronic ˜B 2B level to a group of mixed Ã 2B and ˜X 2A levels 1 2 1 through the Renner-Teller effect with a pressure-dependent relaxation rate constant k1共p兲. The mixed states with both Ã 2B and ˜X 2A characters can emit visible photons through 2 1 an average electronic radiative rate constant k2⬘ and IR photons through an average IR emission rate constant k2⬙. As the Ã 2B and ˜X 2A states have much lower origins in their elec2 1 tronic energies, the vibrational energy content here is much higher and the IR emission is expected to be more intense. It is expected that the Ã 2B2 character will continue to be diluted through the CIIC process as the number of isoenergetic levels in the ˜X 2A1 is much higher than the Ã 2B2 state.7 The highly vibrationally excited ˜X 2A1 levels would emit IR photons with an average IR emission rate constant k3⬙. In this model, there are two contributions to the LIF double-exponential decay. One is from the single rovibronic state in the ˜B 2B1 state and the other from the mixed Ã 2B2 and ˜X 2A1 states. For IR emission, there are three different sources: the initial ˜B 2B1 level, the mixed Ã 2B2, and the highly vibrationally excited ˜X 2A1 bath states. The effect of excited molecules moving out of the observation zones on the detected fluorescence and IR emission decays need to be considered. Estimation based on free jet expansion models gives an approximately 1000-m / s speed for molecules in the supersonic beam in the observation

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region.26 The effective observation zone lengths for the photomultiplier tube 共PMT兲 and MCT detectors in our setup are 10 and 25 mm, respectively, which correspond to the observation times of about 10 and 25 ␮s, respectively. This effect is depicted by the constants kd and kd⬘ in the fluorescence and IR emission decays, respectively, by considering this effect as a first-order kinetic process with rate constants of kd and kd⬘. According to the model laid out in Fig. 4, the intensity of the fluorescence ILIF and the intensity of the IR emission IIR can be related to the state of the excited molecules as ˜ 2B 兴共t兲 + k⬘关A ˜ 2B /X ˜ 2A 兴共t兲, ILIF ⬀ k1⬘关B 1 2 2 1 ˜ 2B 兴共t兲 + k⬙关A ˜ 2B /X ˜ 2A 兴共t兲 + k⬙关X ˜ 2A 兴共t兲. IIR ⬀ k1⬙关B 1 2 2 1 3 1 共1兲 The time evolution of the population of each set of states, marked as 关states兴 can be expressed as ˜ 2B 兴共t兲 d关B 1 ˜ 2B 兴共t兲, = − 共k1⬘ + k1⬙ + k1共p兲p兲关B 1 dt

molecules in the observation zone. In the LIF experiment, the lifetime of this process is estimated around 10 ␮s. From the literature,13,18 we found that the electronic radiative rate of the Ã 2B2 state is about 30– 100 ␮s, which is already slower than the decay lifetime related to excited molecules moving out of the observation zone. Similarly, the lifetime of this process for consideration in IR emission is 25 ␮s while the radiative rate of highly vibrationally excited ˜X 2A1 levels is expected to be on the order of milliseconds. These considerations result in k3⬙ Ⰶ kd⬙. In other words, we expect that the effect of the translational motion of the excited molecules is the leading cause for the decay of fluorescence and IR emission from the Ã 2B2 / ˜X 2A1 mixed states and ˜X 2A1 states. Based on these assumptions, we solved the three differ˜ 2B 兴共t兲, 关A ˜ 2B / ˜X 2A 兴共t兲, and ential equations for 关B 1 2 1 2 ˜ A 兴共t兲, respectively. Subsequently I and I of Eq. 共1兲关X LIF IR 1 can be expressed as ILIF ⬀ A1e−K1t + A2e−K2t , IIR ⬀ A3e−K3t + A4e−K4t + A5e−K5t .

共2兲

The coefficients are defined as ˜ 2B /X ˜ 2A 兴共t兲 d关A 2 1 ˜ 2B 兴共t兲 − 共k⬘ + k⬙ + k 共p兲p = k1共p兲p关B 2 1 2 2 dt ˜ 2B /X ˜ 2A 兴共t兲, + kd兲关A 2 1 ˜ 2A 兴 d关X 1 ˜ 2B /X ˜ 2A 兴共t兲 − 共k⬙ + k⬙兲关X ˜ 2A 兴共t兲, = k2共p兲p关A 2 1 3 1 d dt where p denotes the pressure at the observation region of the supersonic jet. To solve these coupled differential equations, several assumptions were made based on physical considerations. First we assume that k1⬘ , k2⬘ Ⰷ k1⬙ , k2⬙, i.e., the electronic radiative rate constants are much larger than the IR emission rate constants. Usually the former process corresponds to nanoseconds to microseconds range while the latter one is at the fastest in the range of milliseconds.6,4,9 With this assumption, k1⬙ and k2⬙ are negligible in comparison with k1⬘ and k2⬘ in the differential equations. The second assumption we made was on the relative magnitude of the IR emission rate constants, i.e., k1⬙ is much smaller than k2⬙ and k3⬙. There are two reasons for this assumption: First, at the excitation energy the vibrational level energy in the ˜B 2B1 state is smaller than the vibrational energy of the isoenergetic Ã 2B2 and ˜X 2A1 levels. Furthermore, according to theoretical calculations,15 the Frank-Condon factor of the ˜X 2A1 to ˜B 2B1 transition is preferred to occur by the bending mode, whose collisionless vibrational relaxation rate is at least one order of magnitude smaller than that of the corresponding stretching modes.15 This allowed us to neglect the first term, the ˜B 2B1 contribution, in the expression of IIR. A self-consistency check confirms the validity of this assumption as we found that with the term added into the equation after solving the equations for fitting the data, the result remains almost the same. The third assumption we made is on the motion of the excited

A1 = k1⬘ − k2⬘

k1共p兲p , k1共p兲p − 共k2共p兲p + kd兲

A2 = k2⬘

k1共p兲p , k1共p兲p − 共k2共p兲p + kd兲

A3 = k3⬙

k2共p兲 − k2⬙ , k1共p兲

A4 = k2⬙ − k3⬙ , A5 = k3⬙ , K1 = K3 = k1共p兲p + k1⬘ , K2 = k2共p兲p + kd , K4 = k2共p兲p + kd⬘ , K5 = kd⬘ .

共3兲

From this model, the double-exponential decay in the fluorescence 关ILIF in Eq. 共2兲兴 is clearly shown. The fast decay is the depopulation of the initially excited ˜B 2B1 state 关K1 = k1共p兲p + k1⬘兴 and the longer decay is influenced by both CIIC depopulation in the Ã 2B2 / ˜X 2A1 mixed states and the moving of molecules out of the observation zone 关K2 = k2共p兲p + kd兴. For the IR emission part 关IIR in Eq. 共2兲兴, we found that A4 is expected to be negative which corresponds to a rise in the emission intensity. A3 can be negative or positive depending on the relative magnitude of k3⬙共k2共p兲 / k1共p兲兲 and k2⬙. The long IR decay can be attributed to excited molecules moving out of the observation zone because kd⬘ Ⰷ k3⬙. The fitting of the IR signal will be discussed further in the following.

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B. Determination of the rate constants

The fluorescence decays are fitted with the doubleexponential decay of ILIF in Eq. 共2兲 for the determination of K1 and K2. A typical nonlinear least-squares-fitting result is shown in Fig. 2共a兲. Both K1 and K2 are pressure dependent. The K1 and K2 measured with the stagnation pressures between 12 and 100 psi are displayed as Stern-Volmer plots in Fig. 3. The pressures in the Stern-Volmer plots were calculated by using the free jet expansion model.26 The free jet model is validated in another study where the calculated local translational T is in good agreement with the local rotational temperature determined for SO2 seeded in He or Ar expansion.27 The values of k1共p兲 and k2共p兲 were determined as the slopes and the k1⬘ and kd values as the intercepts, respectively. A least-squares fitting gives k1共p兲 = 3.0 ⫻ 107 Torr−1 s−1 and k2共p兲 = 2.0⫻ 106 Torr−1 s−1. These constants 关k1共p兲 and k2共p兲兴 correspond to a 1.0 ␮s radiative lifetime for the single, excited rovibronic ˜B 2B1 level and a 7.5 ␮s lifetime in moving out the fluorescence observation zone. For model fitting of the IR emission traces IIR, we have set the constants K3共=K1兲 and k2共p兲 fixed at the values determined from the fluorescence decay fitting since the LIF intensity S/N ratio is much higher than the IR measurement. Figure 2共b兲 shows the nonlinear least-squares-fitting result of the IR signal. The initial rise in the IR signal corresponds to the K1 exponential component in the LIF fitting. The IR fitting gives the ratio of the preexponential factors: 兩A3兩 : 兩A4兩 : 兩A5兩 = 0.3: 1.3: 1.8 with less than 10% variation for different stagnation pressures. The translational motion related lifetime in the IR signal 共kd⬘兲 is determined to be 23 ␮s from the fitted K5 value. The nonlinear least-squares fitting of the experimental data was done by using the Igor data fitting program. The uncertainty of the fitted LIF decay constants 共K1 and K2兲 is smaller than 1%. The fitted preexponential factors 共A3, A4, and A5兲 have an uncertainty of 10%–20% and the uncertainty of the rate constant related to excited molecules moving out of the observation zone is about 20%. The uncertainty associated with the IR signal is large 共S/N ratio= 3兲 and has resulted in large uncertainties of 20% for kd⬘ and about 100% for preexponential factors. V. DISCUSSION A. Radiative lifetimes

In the kinetic model, the collisionless relaxation rate constant k1⬘ includes contributions from both electronic radiative decay and nonradiative relaxation of the single rovibronic ˜B 2B1 level. According to previous studies,16,18,20 the radiative decay should be the main contribution. The radiative lifetime of the ˜B 2B1 state can be obtained through either the absorption spectrum or radiative decay rate measurements in energy regions where nonradiative decay is not expected to contribute. As mentioned in the introduction, the fast electronic relaxation of the ˜B 2B1 state has been reported by several studies before. Our measurement shows good agreement with these studies within the uncertainty. The

relatively fast 1.0 s radiative decay time of this particular ˜B 2B level arises mainly from the strong Franck-Condon 1 overlap between the ˜B 2B1 excited state and the ˜X 2A1 ground state. This large Franck-Condon 共FC兲 factor is caused by a large shift of the equilibrium bond angle of the ˜B 2B1 state 共180°兲 from that of the ˜X 2A1 state 共134°兲. The doubleexponential decay behavior observed here also supports the observations made in former studies,16,18 though the longer lifetimes are not well determined in our case due to the effect of the translational motion of the excited molecules. B. Collision-induced internal conversion

The Stern-Volmer plot gives the k1共p兲 value, the CIIC rate constant from the ˜B 2B1 state to the mixed Ã 2B2 / ˜X 2A1 states, as 3.0⫻ 107 Torr−1 s−1. This value agrees well with the 2.2⫻ 107-Torr−1 s−1 value determined for the excitation wavelength of 436.7 nm by Sugimoto et al.28 It needs to be pointed out, however, that in Ref. 17 in which the experiment was conducted with a gas cell, the radiative lifetime of the ˜B 2B state was reported to be on the order of tens of micro1 seconds and the fast decay component was not observed, likely due to simultaneous excitation of many transitions of a thermal population. The k2共p兲 constant measured here is a convolution of an average of the collisional energy-transfer rate constants from the mixed Ã 2B2 / ˜X 2A1 states to the bath ˜X 2A1 states and the effect of excited molecules moving out of the observation zone. Thus, the k2共p兲 value sets an upper limit of 2.0⫻ 106 Torr−1 s−1 for this CIIC process. The fact that k1共p兲 is more than one order of magnitude larger than k2共p兲 implies that the vibronic coupling between the ˜B 2B1 state and the mixed Ã / ˜X states is much stronger than the coupling between the Ã / ˜X mixed states and the background ˜X levels. According to the symmetry, the zeroth-order ˜X 2A1 states need to have odd quantum numbers in the antisymmetric stretch B1 mode to couple with isoenergetic Ã 2B2 vibronic levels through the Renner-Teller effect, while such a symmetry restriction does not exist for the vibronic coupling between the ˜B 2B1 and Ã / ˜X mixed states.15 The very fast CIIC processes at this energy range shows that even in the supersonic expansion conditions, collisioninduced intramolecular relaxation is still observable. Based on the hard-sphere collision model and the free jet expansion theory, the NO2 - Ar collision frequency in our case is estimated to be about 107 Hz. This means that for every excited NO2 molecule there would be about ten collisions with Ar during 1 ␮s in the observation zone. C. IR emission

This is the first report of the direct detection of the IR emission of molecules cooled in supersonic jet conditions. Although IR emission from pulsed-laser-excited NO2 in a supersonic jet is very weak, the unique time behavior of the IR intensity provides new information for characterizing the intramolecular relaxation and collision-induced processes. Both the rise and decay rates in the IR emission intensity are

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very well understood with respect to the kinetic model presented here. The A factors obtained from the model analyses, which are the relative intensities of individual decay components, also contain useful information. From the kinetic model, i.e., Eq. 共3兲, A3, A4, and A5 are combinations of k2⬙, k3⬙, k1共p兲, and k2共p兲. From the LIF result, we have already determined an approximate 1:10 ratio for k2共p兲 : k1共p兲. Using this relationship, we can quantitatively determine that k2⬙ is about one order of magnitude smaller than k3⬙ according to the ratio of 兩A3兩 : 兩A4兩 : 兩A5兩. Here in the model, k2⬙ is the IR emission rate constant of the mixed Ã / ˜X states and k3⬙ is the average rate constant of the background ˜X 2A1 states. This result indicates that the highly vibrationally excited ˜X 2A1 states have a much larger IR emission rate than the electronically excited but less vibrationally excited states. This deduced result is expected since the high vibrational levels have much higher vibrational quantum numbers. It also agrees with observations made in our previous study on the energy transfer of vibrational relaxation of highly vibrationally excited states of NO2,7 in which IR emission following the initial electronic excitation of NO2 in a gas cell was recorded with time and frequency resolutions. VI. CONCLUSION

The detection of IR emission from molecules excited in a supersonic expansion allows the examination of intramolecular dynamics in the energy range where substantial vibrational excitation is present. For NO2 excited with energy near the dissociation limit, the combination of visible fluorescence and IR emission provides information for the elucidation of the complex intramolecular relaxation dynamics. Following the excitation of a single rovibronic ˜B 2B1 level, it decays on a 1.0-␮s time scale primarily through electronic radiation with perhaps minor contribution from the intramolecular relaxation to isoenergetic mixed Ã / ˜X states. Collisions also induce internal conversion of this level with a rate constant of 3.0⫻ 107 Torr−1 s−1 to the mixed Ã / ˜X states. Collisions further induce internal conversion of the Ã / ˜X mixed states into highly vibrationally excited ˜X-state levels with a rate constant at least one order of magnitude slower. The second collision-induced internal conversion process is relatively slower than the first because of the difference in the interelectronic state coupling strength due to symmetry restrictions.

This mechanism results in the observation of a doubleexponential decay in the laser-induced fluorescence and a rise in the IR emission intensity corresponding to the fast decay in the LIF. The IR emission rate of the highly vibrationally excited ˜X-state levels is estimated to be about one order of magnitude larger than the isoenergetic Ã / ˜X mixed states and much larger than the ˜B 2B1 level at 23 000 cm−1, both with much less vibrational excitation. ACKNOWLEDGMENT

This work is supported by NSF through Grant No. CHE0111520. 1

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