Ion Pair Formation in Multiphoton Excitation of NO2 Using Linearly

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Ion Pair Formation in Multiphoton Excitation of NO2 Using Linearly and Circularly Polarized Femtosecond Light Pulses: Kinetic Energy Distribution and Fragment Recoil Anisotropy† C. Elkharrat,‡ Y. J. Picard,‡ P. Billaud,‡ C. Cornaggia,§ D. Garzella,§ M. Perdrix,§ J. C. Houver,‡ R. R. Lucchese,⊥ and D. Dowek*,‡ Institut des Sciences Molećulaires d’Orsay, UMR8214 UniV Paris-Sud et CNRS, Bat. 350, F-91405 Orsay Cedex, France, SerVice Photons Atomes & Molećules, CEA IRAMIS, SerVice des Photons, Atomes et Molécules, Saclay, Bat. 522, F-91191 Gif-sur-YVette, France, and Department of Chemistry, Texas A&M UniVersity, College Station, Texas 77843-3255 ReceiVed: April 23, 2010; ReVised Manuscript ReceiVed: June 30, 2010

The NO2 ion pair photodissociation dynamics leading to NO+(X1Σ+,V) + O-(2P3/2 or 2P1/2), induced by a 1 kHz femtosecond laser with wavelengths near 400 nm, has been characterized using the coincidence vector correlation method. The ion pair production after four-photon absorption reaches more than 15% of the primary ionization. The kinetic energy release of the fragments demonstrates a significant vibrational excitation of the NO+(X1Σ+,V) molecular fragment. Recoil ion fragment emission is strongly aligned along the polarization axis of linearly polarized light or preferentially emitted in the plane perpendicular to the propagation axis of circularly polarized light. The formalism describing the recoil anisotropy for bound-to-bound n-photon transition inducing prompt axial recoil dissociation of a nonlinear molecule has been developed to interpret the measured anisotropies in terms of excitation pathways via near-resonant intermediate states of specific symmetries. Possible reaction pathways are discussed that are consistent with the data and supported by calculations of potential energy surfaces and transition moments. I. Introduction 2

The NO2(X A1) molecule has a bent equilibrium geometry with C2V symmetry in its open-shell ground electronic state. The corresponding valence-shell electronic structure is (4a1)2(3b2)2(1b1)2(5a1)2(1a2)2(4b2)2(6a1)2. NO2 is of fundamental importance in chemistry, and the properties of its neutral and ionic states have attracted much interest. Despite its apparent simplicity as a triatomic molecule, NO2 has varied and complex behavior involving unimolecular reaction dynamics, intramolecular vibrational redistribution, vibronic coupling, and short-time nuclear and electronic dynamics. Consequentially, NO2 has been the subject of many experimental and theoretical studies in recent years that have investigated the photodissociation and photoionization reactions of NO2 in a wide variety excitation schemes (see, e.g., refs 1–22 and 23 for a recent review). The literature is too vast to be reviewed extensively, and in the following, we will only give references to papers directly relevant to the processes considered here. In this work, we focus on the new information which can be gained by combining the use of ultrashort light sources with coincident three-dimensional (3D) imaging techniques providing direct measurements of differential energetic and angular observables. In the course of a recent study of one-color multiphoton ionization of NO2 initiated by the absorption of 405-396 nm photons delivered by a femtosecond laser source, we have observed significant production of the NO+-O- ion pair. This †

Part of the “Reinhard Schinke Festschrift”. * To whom correspondence should be addressed. Tel: 33 (0)1 6915 7672. Fax: 33 (0)1 6915 5811. E-mail: [email protected]. ‡ Universite´ Paris-Sud. § CEA IRAMIS. ⊥ Texas A&M University.

paper is dedicated to the discussion of the ion pair formation results, obtained using the electron-ion velocity vector correlation method,22,24 which is focused here on the (VNO+,VO-,eˆ) vector correlation, where the polarization vector eˆ represents the polarization axis of linearly polarized light, P, or the propagation axis of circularly polarized light, k. The results for dissociative and nondissociative photoionization will be reported in another publication.25 To the best of our knowledge, this is the first observation of the NO+-O- ion pair in multiphoton excitation of the NO2 molecule. The thermochemical threshold of the NO+-O- ion pair process lies at 10.918 eV; then, using 405-396 nm photons, its formation requires the absorption of at least four photons. The explored range corresponds to an excitation energy ranging between 12.24 and 12.52 eV, which includes the threshold for the NO+(X1Σ+,V ) 0) + O(3P2) dissociative ionization channel at 12.37 eV. In the experimental conditions considered in this study, the NO+-O- ion pair is observed with an abundance larger than 15% relative to the total photoionization (PI) yield induced by linearly polarized light. This value is significantly larger than the value of ∼5 × 10-3 relative to the primary ionization found in a study of the O- ion yield in one-photon photoexcitation of NO226 using photoion mass spectrometry,27 which demonstrates that this dissociation channel plays a significant role among the multiphoton excitation schemes and may therefore be an important intermediate state in the pathways of other reaction channels. Since the ion pair threshold lies 1.3 eV above the adiabatic PI threshold of the NO2+(X1Σg+) ground-state parent molecular cation at 9.6 eV, this channel corresponds to a superexcited state of NO2, embedded in the ionization continuum; apart from neutral dissociation, other channels to be

10.1021/jp103672h  2010 American Chemical Society Published on Web 08/12/2010

Ion Pair Formation in Multiphoton Excitation of NO2 considered may then involve direct ionization, autoionization, and possibly dissociative ionization. Ion pair formation is most often associated with the photoexcitation of Rydberg states that have been identified as doorway states for such reactions (refs 26 and 28 and references therein). The role of specific Rydberg series in NO+-O- ion pair formation initiated by a direct one-photon VUV transition from the ground state was determined by the detection of the Onegative ion spectrum.26 This O- spectrum displays a weak sloping onset at the (NO+ + O-) thermochemical threshold of 10.918 eV, which could be assigned to a direct population of the ion pair state in the Franck-Condon region. However, the most prominent features appear as resolved narrow peaks in the 11.5-11.7 and 12.3-12.5 eV regions, assigned to the population of ν2 vibrationally resolved Rydberg states labeled as R*[(4b2)-1] converging to the NO2+(a3B2) first electronically excited state of NO2+.16–18 Such neutral excited states may then encounter curve crossings and interact with the ion pair potential curves above the dissociation limit, giving rise to indirect ion pair formation. They are also embedded in the ionization continuum of the NO2+(X1Σg+) ground state of the linear equilibrium geometry, where the R*[(6a1)-1] Rydberg series converging to vibrationally excited states of the NO2+(X1Σg+) ground state have been thoroughly studied in double- and tripleresonance spectroscopy (ref 20 and references therein). These states are known to decay via vibrational autoionization.20,21,29,30 In this paper, we report the energetic and angular characteristics of the NO+-O- ion pair dissociation channels, populated after absorption of four photons delivered by a 1 kHz linearly and circularly polarized femtosecond laser source of 70 fs pulse duration, at the 405, 397, and 396 nm photon wavelengths, obtained by using the vector correlation method previously developed for the study of valence-shell photoionization of molecules.22,24,31,32 The observables are two-fold, the kinetic energy release (KER) of the ion fragments and their angular distribution with respect to the light polarization axis, which constitute powerful means to characterize the photodissociation dynamics.33 Selected studies reporting kinetic energy and angular distributions for ion pair production in the photoexcitation of small polyatomic molecules have been reviewed by Suits and Hepburn.28 Kinetic energy and angular distributions were first derived using time-of-flight (TOF) techniques, as illustrated by the ion pair photodissociation of CH3Cl and CH3Br,34 followed by the implementation of ion fragment imaging techniques35,36 and velocity map imaging (VMI) for ion pair imaging spectroscopy (IPIS).37–40 Most of these works investigate a singlephoton excitation scheme and consider both spectroscopic information on the cation fragment38 and dynamics of the dissociation process.35,36,39,40 In particular, the angular distribution of the fragments characterized by the β asymmetry parameter (-1 e β e 2) is linked to the well-defined symmetry of the superexcited states excited by VUV synchrotron radiation or a tunable XUV laser irradiation, where the excited states correspond to the ion pair electronic state or, more commonly, Rydberg states which couple to the ion pair channel. The velocity imaging photoionization coincidence (VIPCO) technique was also applied to the study of ion pair dissociation of small polyatomic molecules, where three-body fragmentation mechanims could be identified in one-photon-induced dissociation of, for example, CH3F and SO2.41 Multiphoton excitation of ion pair Rydberg states has been reported in the study of threshold ion pair production spectroscopy (TIPPS),42 which has been used to characterize the long-

J. Phys. Chem. A, Vol. 114, No. 36, 2010 9903 range weakly bound ion pair states in high vibrational levels.43 The n-photon excitation mode is convenient for both widening the Franck-Condon window from the ground state and giving access to a wider range of doorway states to the final ion pair state. It also enables the study of directional dynamics of the photodissociation process33 since the molecule angular momentum is polarized in the laboratory frame by absorption of the n - 1 photons through intermediate states of defined symmetry.44,45 The dynamics of the ion pair dissociation can also be probed in the time domain; most recently, a pump-probe scheme with femtosecond time resolution was combined with VMI to gain insight into the pathways for optical excitation of ion pair states of the O2 molecule46 considered as a benchmark system in the study of ion pair production.47 The recoil anisotropy of the photofragments was interpreted as a direct three-photon excitation of the ion pair state via near-resonant intermediate states of Σ symmetry, following the formalism of Dixon for multiphoton dissociation of linear molecules.45 The paper is organized as follows. In section II, we give a brief description of the experimental setup, which includes the double velocity spectrometer allowing for the (VNO+,VO-,eˆ) vector correlation study of the NO+-O- ion pairs and the use of two types of light sources, 1 kHz femtosecond laser facilities provided by the Saclay Laser-matter Interaction Center (SLIC) and VUV synchrotron radiation at SOLEIL. In section III, we report the kinetic energy released to the NO+-O- ion pair state (KER) measured at the 405, 397, and 396 nm wavelengths, which demonstrates a significant vibrational excitation of the NO+ molecular fragment. In section IV, a formalism describing the fragment recoil anisotropy for photodissociation of a nonlinear molecule induced by multiphoton excitation via quasiresonant intermediate states is presented and applied to the fourphoton photodissociation of NO2. The measured angular distributions of the NO+-O- ionic fragments with respect to the linear and circular polarization of the exciting light are reported in section V and analyzed according to the formalism given in section IV. Prior to the discussion of the multiphoton ion pair results in terms of reaction pathways involving intermediate states of the NO2 molecule of different symmetries, based on recent calculations of potential energy surfaces and transition moments for the photoexcitation steps considered in this work (section VII), we report in section VI the results of a first vector correlation study of NO+-O- ion pair formation induced by one VUV photon absorption at the synchrotron radiation (SR) SOLEIL at hν ) 12.45 eV. This complementary experiment was performed in order to disentangle the characteristics of the ion pair formation attributed to the resonant excitation of the continuum in the 12.45 eV region, which corresponds to a four 400 nm photon total excitation energy, from those that might be assigned to nuclear or vibronic dynamics of the intermediate states. Indeed, although the laser pulse duration presently used is on the order of 70-100 fs, ultrafast dynamical effects may also occur at each step of the multiphoton absorption reaction, depending on the intermediate state potential curves, inducing internal excitation of the parent molecule. This has been discussed, for example, after absorption of one 400 nm photon, which populates a region characterized by dissociation dynamics taking place within a few femtoseconds, setting the scene for competing reaction pathways to up-pumping excitation and dissociation.13,14 Our conclusions in terms of reaction pathways leading to the ion pair channel are presented in section VIII, together with an overview of related issues of interest for the multiphoton photoionization channels, to be reported separately.

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Figure 1. Scheme of the velocity spectrometer and acquisition setup. Positively and negatively charged particles are extracted from the interaction volume at the crossing of the molecular beam and the light beam by a dc uniform electric field. Electrostatic lenses Λ+ and Λlocated outside of the extraction region focus the particle trajectories onto the position-sensitive detectors (PSD). For each particle, the measured time of flight T and the position (x,y) on the PSD enable determination of the three components of the emission velocity vector.

II. Experimental Method The (NO+,O-) coincidence events are recorded using the vector correlation (VC) method;24,31 however, the timing of the event acquisition has been modified, as detailed below. A schematic of the double velocity spectrometer described in detail previously is shown in Figure 1. The interaction region located at the center of the spectrometer is defined as the intersection of the supersonic molecular jet of NO2 (5% seeded in He) and the light beam. The experiments were carried out using two femtosecond lasers (SOFOCKLE and PLFA) of the Saclay Laser-matter Interaction Center (SLIC) facility of the Commissariat a` l’Energie Atomique. These are chirped pulse amplification titanium-sapphire (Ti:Sa) laser systems delivering few mJ pulses at a carrier frequency corresponding to λIR ≈ 800 nm with a 1 kHz repetition rate. The second harmonic pulses (λair ≈ 400 nm) are obtained by type-I frequency doubling in a BBO crystal (θc ) 29.2°; thickness of 200 or 250 µm). The pulse duration is on the order of 70 fs, and the spectral bandwidth is 6 nm full width at half-maximum (fwhm). The 6 nm width corresponds to an energy spread of about 46 meV per photon, involving a spread of ∼90 meV for four-photon absorption. The wavelength tunability between 395 and 405 nm was achieved by slightly tilting the doubling crystal, and the central wavelength was controlled to better than 0.3 nm using a spectrometer (B&W Tek, BRC112E). This technique for wavelength tuning leads to both a decrease of the doubled pulse spectral width (down to 2 nm fwhm), leading to an increase of their duration to about 120 fs, and a decrease of frequency doubling efficiency. The resulting energy spread for four-photon absorption is then on the order of 30 meV: in the forthcoming discussion the energy spread of 90 meV will be taken as an overall upperlimit. The variable energy per pulse, sufficient for these experiments, was adjusted between 5 and 20 µJ per pulse. The 1 cm diameter laser beam was focused by a fused silica lens of focal length f ) 1 m and entered into the vacuum chamber via a fused silica window. For production of circularly polarized light, a quarter wave plate at 400 nm was inserted before the focusing lens. Passing through these optical elements did not

Elkharrat et al. significantly modify the pulse characteristics. With a beam quality factor of M2 ) 2, the beam waist was ω0 ) 50 µm, and the Rayleigh length was ZR ) 1 cm. These two parameters determine the dimensions of the interaction zone, together with those of the molecular beam. Assuming a Gaussian beam profile, the fwhm of the intensity radial distribution was Dfwhm ) 60 µm. The order of magnitude of the irradiance at the waist was of few 1012 W cm-2. The VC spectrometer24 was installed either in the SAPHIRS setup,48 producing a molecular supersonic expansion (70 µm continuous nozzle and 1 mm diameter skimmer), or mounted onto the CIEL2 ultrahigh vacuum (UHV) chamber, working at a standing pressure of 10-9 mbar, equipped with a 50 µm continuous nozzle shaped by two skimmers.49 The continuous molecular beam (5% NO2 in He; backing pressure of 1.5 bar) corresponds to a beam diameter at the interaction center on the order of 2-3 mm on the SAPHIRS setup; it was reduced to 1 mm using the CIEL2 supersonic expansion. In both cases, heating up the nozzle to about 120 °C enabled us to suppress the N2O4 dimer component formed in the molecular expansion. Before heating, the presence of the N2O4 dimer can be clearly identified as a pedestal contribution to the NO2+ TOF peak, revealing fragmentation of the N2O4+ ion; the contribution of these NO2+ fragment ions amounts to about one-third of the total NO2+ signal at room temperature. A second series of measurements was performed on the VUV DESIRS beamline50 at the synchrotron radiation (SR) facility SOLEIL operated in the eight-bunch mode (period 147 ns; pulse time width 50 ps) for single-photon excitation, using the SAPHIRS setup. The dimensions of the light beam at the focus point are on the order of 100 µm in the horizontal direction and limited by the monochromator slit opening (typically between 10 and 100 µm) in the vertical direction. Positively and negatively charged particles are extracted from the interaction region by a dc uniform electric field of a few tens of V/cm and guided to two time- and position-sensitive delay line anode detectors (PSDs)51 through an intermediate region where two focusing electrostatic lens sets (Λ+ and Λ-) are applied. The efficiency of the detectors for these measurements was estimated to about 35% for positive ions, 20% for O- ions, and 50% for electrons in the current conditions. The time signals from the ends of the delay lines are encoded as stop signals in an eight channel time-to-digital converter (CTNTDC)52 with a large multihit capability and an encoding resolution of 250 ps, where four channels are dedicated to the positive ion detector and four to that of the negatively charged particles (electrons and negative ions). In the laser photoinduced experiment, we use a logical signal synchronous with the 1 kHz laser pulse as the common start for the eight channels of the TDC, which are stopped by the delay line signals; therefore, the TDC outgoing signals provide the ion position and TOF for each of the NO+ and O- coincident partners, enabling us to record the three components of the VNO+ and VO- ion emission velocity vectors for each particle. For the chosen extraction field on the order of 30 V/cm, a 4π collection of both ion fragments is achieved. The light signal also acts as a start for a time-toamplitude converter (TAC). At SOLEIL, the shorter period between two light pulses did not allow for the same procedure; therefore, we alternatively used the signal detected on the front microchannel plate of the negatively charged particle detector as a common start for the CTN-TDC and the TAC, as it is usually performed in the VC method. The electronic signal synchronous with the SOLEIL light pulse arriving after detection of an O- ion serves as the stop for the TAC, providing the O-

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TOF distribution with a coding resolution of 50 ps on the 200 ns scale, which leads to an excellent time resolution. However, the 147 ns period of the SR beam necessitated the use of an extraction field of 100 V/cm in order to collect all of the Oions produced within the same time interval between two successive pulses; this implies rather small impact positions which restricted the overall resolution of the VNO+ and VOvectors as compared to the wider range of impact radii obtained when the laser source is used. Further experiments are to be performed at SOLEIL using a single-bunch mode. The 1 µs bunching period will enable us to improve the resolution. Performing coincidence measurements requires the occurrence of a maximum of one event per pulse, which imposes the constraint that, on average, the count rate per pulse must be on the order of a few percent.5,9,53 When a SR light source is used, the few MHz repetition rate enables coincidence measurements with adequate acquisition statistics to be obtained when the number of events per pulse is on the order of ∼10-3. Using laser sources with a repetition rate of 1 kHz in the present working conditions, we determined that an acquisition rate of a maximum of 50 c/s (0.05 events/pulse) ensures a true coincidence acquisition mode. The data analysis providing the (Vx,Vy,Vz) velocity components from the positions and TOFs for each particle of the (NO+,O-) coincident events in the presence of focusing lenses is similar to the one described earlier for dissociative photoionization.24 Furthermore, for ion pair formation, the measured (VNO+,VO-) vector correlation enables us to control momentum conservation in the dissociation process and to determine the intrinsic fragmentation velocity vectors VNO+ and VO- by correcting, for each event, the measured velocities for the finite size of the interaction region and the parent molecule velocity in the supersonic expansion. This correction significantly improves the resolution of the velocity vector measurement. III. NO+-O- Ion Pair Formation Induced by Multiphoton Absorption: Kinetic Energy Distribution The NO+-O- ion pair formation, unambiguously identified among the ionization and dissociation events recorded in the study of multiphoton excitation of NO2 in the region of 400 nm, corresponds to the channel

NO2 + 4hν(∼400 nm) f NO+(X1Σ+, V) + O-(2P3/2 or 2P1/2)

(1)

where the NO+(X1Σ+,V ) 0) + O-(2P3/2) dissociation limit is at 10.915 eV with respect to the ground state of the neutral NO2 molecule. The two spin-orbit states O-(2P3/2) and O-(2P1/2) are separated by 22 meV.54,55 The thresholds for higher electronic ion pair channels such as NO+(a2Σ+,V ) 0) + O-(2P3/2) at 17.35 eV are at significantly higher energies. Taking into account the detector efficiencies for O- ions and electrons, the relative probability for this channel using linearly polarized light amounts to about 16-18% at λ ) 405 and 397 nm with respect to all of the other identified ionic channels corresponding to dissociative and nondissociative photoionization.25 This value is remarkably high compared to the relative value on the order of 5 × 10-3 of primary ionization reported in one-photon photoexcitation of NO2.26 The (VNO+,VO-) vector correlation provides the positive ion-negative ion kinetic energy correlation diagram (KECD), that is, the (ENO+, EO-) bidimensional histogram of the coincident events. It displays a sharp diagonal structure when the correction

Figure 2. (ENO+,EO-) kinetic energy correlation diagram (KECD) of the (NO+,O-) coincident events for a wavelength of λ ) 405 nm and an extraction field of 30 V/cm. The intensity scale runs from white (lowest intensity) to black (highest intensity) in linear scale, as shown; the contour lines are spaced by 10% of the maximum value.

procedure based on momentum conservation is applied, as shown in Figure 2 for a photon wavelength of 405 nm and an extraction field of 30 V/cm. The observed probability islands demonstrate the excitation of resolved vibrational levels of the NO+(X1Σ+,V) molecular fragment. The corresponding onedimensional ion pair KER distributions are displayed in Figure 3 for the 405 and 397 nm wavelengths using linearly polarized laser light and the 405 and 396 nm wavelengths using circularly polarized light. Although similar information might be obtained from the measured momentum of either the NO+ or the O- ion fragment, the KER of the dissociation channel is here directly determined as the sum of the kinetic energies of both fragments, thereby removing much of the instrumental uncertainty. For the kinetic energy determination, using this procedure is equivalent to applying the velocity correction described in section II. Population of the ion pair channel requires that the four photons be absorbed while the system remains quasi-molecular, that is, prior to any significant dissociation of a NO2 intermediate state that would prevent charge transfer between the two fragments from occurring. The fact that four photons are absorbed is confirmed by the maximum value of the measured KER value of about 1.5 eV, which is the excess energy obtained as the difference between the photon excitation energy and the ion pair ground-state dissociation limit. For the studied wavelengths corresponding to central excitation energies of 12.242, 12.489, and 12.520 eV, respectively, the population of the NO+(X1Σ+,V ) 0) ground state leads to maximum KERmax(V ) 0) values for the corresponding structure of 1.324, 1.571, and 1.602 eV. Since the 22 meV spacing of the two spin-orbit states O-(2P3/2) and O-(2P1/2) would not be resolved in the KER distribution, we label the O- state as O-(2P) in the discussion, although the numerical energies given correspond to excitation of O-(2P3/2). For the 405 nm wavelength in Figure 3a, the KER distribution displays resolved peaks which are the signature of the rovibrational excitation of the NO+(X1Σ+,V) molecular fragment, with a vibrational spacing of ∆Evib ≈ 0.29 eV. It illustrates the increasing excitation probability of the V ) 0, 1, 2, 3, and 4 levels with a remarkable maximum for V ) 4, corresponding to a low translational energy of the fragments. This preferred transfer of excess energy into the internal degrees of freedom of the system rather than translational energy is a common feature of the four spectra reported in Figure 3, and it has been found to characterize other ion pair processes previously.28 Although the five peaks are well-resolved, the widths of the peaks as well as the shoulders observed indicate that the underlying distribution may be more complex, as discussed

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Figure 3. Kinetic energy release (KER) distribution of the NO+ and O- ion fragments for the 405 and 397 nm wavelengths using linearly polarized laser light (a, b) and the 405 and 396 nm wavelengths using circularly polarized light (c, d). The spectra are fitted (red line) by a single series of Gaussians of common width, centered at the energies of the NO+(X1Σ+,V) vibrational levels. The arrows indicate position of the maximum KERmax(V ) 0) value for each central excitation energy (see text).

below. When the four-photon energy is increased by 0.247 eV, which corresponds to the change in total energy when going from 405 to 397 nm, the KER distribution keeps a similar general shape and leads to the excitation of one additional vibrational level of the NO+(X1Σ+,V) fragment. However, a remarkable increase of the relative population of the V ) 2 level is found for a wavelength of 397 nm instead of the V ) 4 dominance at 405 nm. A noticeable modification of the relative importance of the peaks is also observed when changing from linearly (a,b) to circularly polarized light (c,d). At 405 nm, the most significant change is observed for the V ) 3 peak, while at 396 nm, the relative maximum observed for V ) 2 with linearly polarized light is attenuated, and the V ) 5 level favored for circular polarization (although, in this case, the slightly modified energy might also be invoked). Comparing Figure 3a-d, one also notes that the width of the resolved peaks is narrower for the 405 nm wavelength than that for λ ) 397-396 nm, where, in particular, the shape of the V ) 0,1 and V ) 3,4 levels suggests a double-peak structure. The width of the peaks, ∆KER g 200 meV (fwhm), is significantly larger than the convolution of the photon bandwidth of about 90 meV and the resolution of the spectrometer for the extraction field used, the latter being on the order of a few meV when the KER is determined as the sum of the ENO+ and EO- kinetic energies. In the one-photon O- yield spectrum reported previously,26 the 12.24-12.5 eV region is structured with resolved peaks separated by about 80 meV. They are assigned to the ν2 bending modes of the Rydberg members arising from the excitation of

the 4b2 molecular orbital in the NO2(X2A1) ground state, converging to the NO2+(a3B2) first electronically excited state of NO2+.16–18 In this region, excitation of the R*[(4b2)-1] series from the NO2(X2A1) ground state, which has a bent geometry, is favored by Franck-Condon factors. The one-photon Ospectrum displays a sharp maximum characterized by a strong increase of the intensity for resonant excitation of two Rydberg states of this series at 12.4 and 12.47 eV, assigned to 4d (ν2 ) 5,6) or 5d (ν2 ) 1,2) Rydberg states,26 in a region where the ionization cross section is slowly varying with energy.56 The four-photon KER distributions reported in Figure 3 correspond to excitation energies just below (405 nm), on top of (397 nm), or just above (396 nm) this doublet; the sensitivity to the wavelength of the observed relative population of the NO+(X1Σ+,V) vibrational levels suggests that resonant excitation of Rydberg states of NO2 also plays a role in the multiphoton ion pair reaction studied here, possibly superimposed upon the excitation of a repulsive neutral state. For the two lowest energies studied with linear polarization, the relative branching ratio (BR) of ion pair formation with respect to photoionization is fairly constant and is on the order of 16-18%. It is smaller for circular polarization with values ranging from 12% for 405 nm to 8% for the third wavelength (396 nm). On the basis of the assignment of resolved R*[(4b2)-1] Rydberg series in the 12-13 eV energy range of absorption spectra (see e.g. Figure 5 and Table 5 of refs 17 and 26), one may tentatively go one step further in the description of the KER spectra, taking into account that, due to the rather broad



TABLE 1: Relative Amplitudes for the Population of the NO+(X1Σ+,W) Vibrational States, Normalized with the W ) 4 Amplitude Equal to 1, Obtained by a Fit Analysis of the KER Distributions in Figure 3a-da Λ 405 397 405 396

nm, nm, nm, nm,

lin lin cir cir

V)0

V)1

V)2

V)3

V)4

0.13 0.145 0.13 0.2

0.37 0.31 0.37 0.425

0.52 0.77 0.55 0.925

0.55 0.58 0.67 0.975

1 1 1 1

V)5 1.17 1.6

The peaks of common width are centered at the V (J ) 0) positions of the vibrational levels, assuming a single series of translational energies; the fit is optimized by slightly varying the position of the comb. a

photon bandwidth (δEph e 90 meV), the excitation process might populate neighboring Rydberg states coherently. Considering first the 12.242 eV energy (405 nm), the central excitation energy is quasi-resonant with a 4b2 f 4d(ν2 ) 3) state, which would correspond to a KERmax(V ) 0) ≈ 1.324 eV. One notices that the detailed structure of the KER spectrum in Figure 3a is rather consistent with the excitation of the 5s(ν2 ) 2) (or the degenerate 5p(ν2 ) 1)) state at 12.203 eV, which is the dominant accessible state in this region of the photoabsorption spectrum, leading to a KERmax(V ) 0) ≈ 1.285 eV. Excitation of the 5s(ν2 ) 3) (or the degenerate 5p(ν2 ) 2)) state at 12.279 eV corresponding to a KERmax(V ) 0) ≈ 1.361 eV might also contribute. Resonant excitation of these two states within the same photon bandwidth would contribute as two NO+(X1Σ+,V) + O-(2P) series of translational energy separated by 80 meV, consistent with the shoulders observed in the KER spectrum. The 12.488 eV energy (397 nm) is quasi-resonant with a 4b2 f 6s (ν2 ) 2) (or 7s (ν2 ) 0)) state,17 corresponding to a KERmax(V ) 0) ≈ 1.577 eV. The broadened shape of the peaks assigned to NO+(V ) 0,1 and V ) 3,4) is consistent with the simultaneous excitation of the 4d(ν2 ) 5,6) (or resonant 5d(ν2 ) 1,2) states. The 12.52 eV (396 nm), quasi-resonant with the position of the 6p(ν2 ) 2) state at 12.534 eV, lies at a minimum between the two resolved 5d(ν2 ) 2,3) Rydberg states observed in the photoabsorption spectrum.17 The measured KERmax(V ) 0) ≈ 1.61 eV and the position of structures in the peaks assigned to the NO+(X1Σ+,V ) 0-5) vibrational levels are consistent with the excitation of the 6p(ν2 ) 2) state. Varying the photon wavelength on the 405-396 nm limited range might then induce excitation of R*[(4b2)-1] Rydberg states of different C2V symmetry; ns molecular orbitals (MO) have the a1 symmetry character, np and nd MOs may involve all four a1,2 and b1,2 characters, although, for example, the nd MOs in the studied region had been assigned to an a2 symmetry.26 The width of the peaks in the KER spectra results from the convolution of the photon bandwidth with the intrinsic width of the NO2 Rydberg states shown, for example, in the photoabsorption spectrum,17 the unresolved contribution of neighboring Rydberg states, as well as from rotational excitation of the NO+ fragment in the dissociation. Although the detailed structure analysis of the KER spectra suggests the role of different contributions, the spectra have been fitted by a single series of Gaussians in order to provide an overall quantitative estimate of the relative weight of the NO+(X1Σ+,V) vibrational components. The results are reported in Table 1. The most prominent characteristic of the KER distributions in Figure 3 is the preferred transfer of excess energy into the internal degrees of freedom of the system rather than translational energy. This characteristic may be attributed to different possible origins. In the assumption of a direct ion pair excitation,

it may be induced by a rapid dissociation of the NO2 molecule and a significant geometry change from the bent molecule to a linear geometry. If optical excitation of R*[(4b2)-1] superexcited Rydberg states is favored in the FC region as considered above, the vibrational excitation of the NO+(X,V) fragment can be due to that of the resonantly excited Rydberg state. It may also be assigned to the internal conversion of primarily excited R*[(4b2)-1] states into quasi-resonant R*[(6a1)-1] Rydberg states converging to highly vibrationally excited levels of the NO2+(X 1 + Σg ) ionic state, with prompt dissociation of these states via coupling to the ion pair potential surfaces, as suggested, for example, for ion pair dissociation of CH3F.28 A second characteristic of the KER spectra is the significant variation of the amplitude of the V ) 2 and 4 or 5 levels of the NO+(X) fragment induced by the variation of the photon excitation energy of a few tens of meV, revealing a high sensitivity of the dissociation dynamics to the excitation energy and, to some extent, to the polarization of the light for a given photon energy. More insight about the dissociation dynamics may be gained from (i) the angular analysis of the ion fragments presented in sections IV and V for the three studied wavelengths, (ii) the presentation in section VI of the first results of a vector correlation study of NO+-O- ion pair formation induced by one VUV photon absorption at the SR SOLEIL at 12.45 eV, and (iii) the computed potential energy surface transition moments reported in section VII. IV. Recoil Anisotropy for Multiphoton Dissociation of Nonlinear Molecules A. Dissociation Pathway Involving One-Photon Transitions via near-Resonant Intermediate States. In this section, we establish the general form for the field dependence of the photofragment angular distribution in a bound-to-bound nphoton transition inducing dissociation of a nonlinear molecule, assuming prompt axial recoil. The observable is the recoil fragment distribution in the laboratory frame, that is, the field frame (FF), where xˆFF and yˆFF are two unit vectors perpendicular to the direction of propagation of the light, zˆFF. Following the work of Dixon and others,45,57–60 the n-photon absorption amplitude in the lowest order of perturbation theory and within the rotating wave approximation (RWA)61 has the form Jfi(n) ) n-1

∑ ∑··· ∑ k1

k2

kn-1

〈Ψf | b r ·b A*|ψn-1〉{

∏ 〈ψ |br · bA*|ψ kj

b

r · A*|Ψi〉 kj-1〉}〈ψk1 | b

j)2

n-1

∏ (∆E

kji

- jhν + iΓkj)

j)1

(2) where the intermediate states ψk have energy Ek so that they have an energy above the initial state of ∆Eki ) Ek - Ei and have a homogeneous half-width of Γk. In eq 2, the field is assumed to have the form62

1 b b E(t) ) {A exp(iωt) + b A* exp(-iωt)} 2

(3)

where the vector b A can be parametrized for elliptically polarized light using

9908


b A ) xˆFF cos λ + yˆFF sin λ exp(iδ)

Elkharrat et al.

(4)

In general, such a transition can have a very complicated angular dependence if many different pathways contribute to the transition. In order to simplify the discussion, we will assume that there is a single set of real states, Ψ1, Ψ2, ..., Ψn, that are nearly resonant in the n-photon process, and then, the transition amplitude in eq 2 reduces to

Jfi(n)

∏

〈ψk | b r ·b A*|ψk-1〉}〈ψ1 | b r ·b A*|Ψi〉

k)2

)

ˆtjk ) sin θjk cos(φjk + R)xˆRF + sin θjk sin(φjk + R)yˆRF + cos θjkzˆRF (10) Then, we define the Euler angles (γ,χ,β) to be the angles that rotate the RF into the FF,63 so that each transition probability can be written as

n-1

r ·b A*|ψn-1〉{ 〈Ψf | b

Then, the orientation of the transition dipole moment moves with the rotation of the molecule about the recoil direction by the angle R, thus giving the φjk + R dependence on the azimuthal angle in the expression of ˆtjk in the recoil frame (RF)

n-1

∏ (∆E

ki

- khν + iΓk)

Tjk ) IjkIjk*

k)1

(5) The excitation probability is then given by the absolute square (n) (n) of this amplitude R(n) fi ) Jfi [Jfi ]*. The numerator in eq 5 controls the angular dependence of the excitation process. Thus, the angular dependence can be written in terms of the square of the matrix element Ifi(n) defined as

2 ) cos λ{sin θjk cos χ cos β cos(φjk + R - γ) +

sin θjk sin β sin(φjk + R - γ) - cos θjk sin χ cos β}2 + sin2 λ{-sin θjk cos χ sin β cos(φjk + R - γ) + sin θjk cos β sin(φjk + R - γ) + cos θjk sin χ sin β}2 + 2 cos δ cos λ sin λ{sin θjk cos χ cos β cos(φjk + R - γ) + sin θjk sin β sin(φjk + R - γ) - cos θjk sin χ cos β} ×

n-1

∏ 〈ψk|br · bA*|ψk-1〉}〈ψ1|br · bA*|Ψi〉

r ·b A*|ψn-1〉{ 〈Ψf | b

k)2

Ifi(n) )

{-sin θjk cos χ sin β cos(φjk + R - γ) + sin θjk cos β sin(φjk + R - γ) + cos θjk sin χ sin β}

(11)

n-1

tf,n-1(

∏ tk,k-1)t1,i k)2

(6) where the transition moments of each transition are parametrized using

btjk ) 〈Ψj |x|Ψk〉xˆ + 〈Ψj |y|Ψk〉yˆ + 〈Ψj |z|Ψk〉zˆ

(7)

For circularly polarized (CP) light with λ ) π/4 and δ ) -π/ 2, where the upper sign is for left circularly polarized (LCP) and the lower sign is for right circularly polarized (RCP), eq 11 reduces to

1 Tjk(CP) ) {[sin θjk sin(φjk + R - γ)]2 + 2 [sin θjk cos χ cos(φjk + R - γ) - cos θjk sin χ]2}

(12)

and where btjk ) tjkˆtjk. Then, eq 6 becomes

Ifi(n) ) ˆtf,n-1 · b A*{

n-1

∏ ˆtk,k-1 · bA*}tˆ1,i · bA*

(8)

For linearly polarized light, where (χLP,γLP) gives the direction of polarization, by taking χ ) π/2, γ ) γLP - π/2, β ) π χLP, δ ) 0, and λ ) 0, eq 11 reduces to

k)2

Within the single excitation pathway approximation, the angular dependence of an n-photon bound-to-bound transition is given by to the absolute square of eq 8. Thus, we have

Tfi(n)

)

cos θjk cos χLP]2 (13)

Finally, the n-photon angular distribution, H(n), is obtained by averaging over the angle R using

Ifi(n)[Ifi(n)]*

A*| 2{ ) |tˆf,n-1 · b

T(LP) jk (χLP, γLP - R) ) [sin θjk sin χLP cos(γLP - φjk - R) +

n-1

∏ |tˆk,k-1 · bA*|2}|tˆ1,i · bA |2 k)2

Hfi(n) )

(9)

n-1

) Tf,n-1{

∏ Tk,k-1}T1,i k)2

To compute this probability, each transition dipole direction ˆtjk must be expressed in the field frame. It can first be written in terms of a spherical polar vector with angles (θjk,φjk) in the molecular frame (MF) in which the recoil axis is the zˆMF axis. When only two fragments are produced in the dissociative process, one can measure only the recoil frame distribution. This combined with the axial recoil approximation leads to averaging the molecular frame about the recoil direction with zˆMF ≡ zˆRF.

1 2π

∫02π Tfi(n) dR

(14)

B. Dissociation Pathway Involving Nonsequential Multiphoton Steps. We can also combine nonsequential multiphoton steps in a single pathway with nearly resonant steps. In analogy to eq 10, the contribution to the transition probability from a nonsequential multiphoton excitation step has the form

Tfi(n) )

|

3

3

3

∑ ∑ ··· ∑

k1)1 k2)1

kn)1

{ ( )}| n

tk(if) 1,k2, ...,kn

∏ Ak j)1

2

i

(15)


J. Phys. Chem. A, Vol. 114, No. 36, 2010 9909 Hfi(4,LP)[4, 4, 4, 4] ) cos8(χ)

where the transition tensor is defined as

Hfi(4,LP)[2, 2, 2, 4] ) -0.1077 cos8(χ) + 0.6040 cos6(χ) + n

tk(if) ) 〈Ψi | 1,k2, ...,kn

∏ rk |Ψf〉 j)1

j

(16)

0.1089 cos4(χ) + 0.0011 cos2(χ) Hfi(4,LP)[2, 2, 2, 2]

) -0.3737 cos8(χ) + 0.4964 cos6(χ) +

0.3641 cos4(χ) + 0.0262 cos2(χ) + 0.00015

C. Recoil Anisotropy for Four-Photon Dissociation of the NO2 Molecule. We now apply the expressions discussed in sections A and B to the four-photon-induced dissociation of NO2 leading to the NO+(X1Σ+) + O-(2P) ion pair. As discussed above, we will assume that there is only one excitation pathway populating the upper state reached by four-photon absorption. In addition, we will assume that the recoil axis lies along the direction of a NO bond, obeying the axial recoil approximation. The NO2 ground-state geometry has an apex angle of ∠O-N-O ) 133.85° with R(N-O) ) 1.19455 Å.64 The MF is defined with the zˆMF axis as the recoil axis, and the molecule is in the xˆMF-zˆMF plane, as illustrated in Figure 4. To give explicit expressions, we will consider four different possible directions, labeled 1, 2, 3, or 4, for the transition moments ˆtjk in the molecular frame (θjk,φjk), as shown in Figure 4. Directions 1, 2, and 3 correspond to the symmetry axes of the C2V NO2 molecule, where direction 1 is perpendicular to the plane of NO2, that is, θjk ) π/2 and φjk ) π/2; direction 2 is parallel to the line connecting the two O atoms and nearly aligned with the NO bonds with θjk ) 23.07° ) 0.4027 radians and φjk ) π; direction 3 corresponds to the C2V symmetry axis in the plane of the molecule and nearly perpendicular to the NO bonds with θjk ) 66.93° ) 1.1681 radians and φjk ) 0; and direction 4 corresponds to the recoil direction, that is, zˆMF ≡ zˆRF, and is aligned with one of the NO bonds with θjk ) 0 and φjk ) 0. Examples of type-1, type-2, and type-3 transitions between states of C2V symmetry correspond to, for example, A1 f B1, A1 f B2, and B2 f B2, respectively. A type-4 transition implies a transition between two states where either the molecule is linear or the states involved are localized on the dissociating bond. Considering selected examples among all possible four-photon pathways, with all transitions successively quasi-parallel to the NO bonds, that is, to the recoil axis (type-2 or -4, eq 17), pathways including one transition quasi-perpendicular to the recoil axis (type1, eq 18, or type-3, eq 19), independent of the order of the transitions, with a specific expression for Hfin,λ,δ for LP light are

(17)

Hfi(4,LP)[1, 4, 4, 4] ) sin2(χ){0.5 cos6(χ)} Hfi(4,LP)[1, 2, 2, 4] ) sin2(χ){0.2622 cos6(χ) + 0.0945 cos4(χ) + 0.0015 cos2(χ)} Hfi(4,LP)[1, 2, 2, 2]

(18)

) sin (χ){0.1154 cos (χ) + 2

6

0.1693 cos (χ) + 0.0183 cos2(χ) + 0.00014} 4

Hfi(4,LP)[3, 2, 2, 4] ) 0.3699 cos8(χ) - 0.4364 cos6(χ) + 0.1703 cos4(χ) + 0.0062 cos2(χ) ) 0.4891 cos8(χ) - 0.5503 cos6(χ) +

Hfi(4,LP)[3, 2, 2, 2]

0.0889 cos4(χ) + 0.0645 cos2(χ) + 0.0008

(19)

The corresponding expressions for CP light are Hfi(4,CP)[4, 4, 4, 4] ) (1/16) sin8(χ) Hfi(4,CP)[2, 2, 2, 4] ) (1/16) sin2(χ){0.1077 cos6(χ) + 0.4015 cos4(χ) - 1.3007 cos2(χ) + 0.7950} Hfi(4,CP)[2, 2, 2, 2] ) (1/16){-0.37371 cos8(χ) + 0.9275 cos6(χ) 0.0409 cos4(χ) - 1.2538 cos2(χ) + 0.7415}

(20)

Hfi(4,CP)[1, 4, 4, 4] ) (1/16) sin6(χ){0.5 cos2(χ) + 0.5} Hfi(4,CP)[1, 2, 2, 4] ) (1/16) sin2(χ){0.2622 cos6(χ) 0.6404 cos4(χ) + 0.0097 cos2(χ) + 0.3922} Hfi(4,CP)[1, 2, 2, 2]

) (1/16){-0.1154 cos8(χ) + 0.8403 cos6(χ) -

1.1622 cos4(χ) + 0.0926 cos2(χ) + 0.3483}

(21)

Hfi(4,CP)[3, 2, 2, 4] ) (1/16) sin2(χ){-0.3699 cos6(χ) + 0.9092 cos4(χ) - 1.0426 cos2(χ) + 0.5233} Hfi(4,CP)[3, 2, 2, 2]

) (1/16){0.4891 cos8(χ) - 1.5523 cos6(χ) +

2.0062 cos4(χ) - 1.4401 cos2(χ) + 0.5002}

Figure 4. Scheme of the molecular frame and transition-moment directions; the zˆMF axis is the recoil axis (along one of the NO bonds), and the molecule is in the xˆMF-zˆMF plane. The four directions considered for the transitions moments, labeled 1, 2, 3, or 4, correspond to the symmetry axes of the C2V NO2 molecule; directions 1, 2, and 3 are perpendicular to the NO2 plane, parallel to the line connecting the two O atoms, and along the C2V symmetry axis in the plane of the molecule, respectively; direction 4 is parallel to the recoil direction. Corresponding (θjk,φjk) angles for the transition moments in the MF frame are given in the text.

(22)

The analytical form of the recoil fragment angular distribution for other types of four-transition pathways can be derived using the general expression in eq 11. In Figure 5, we present selected H(χ) angular profiles relevant for the forthcoming discussion of the results. In Figure 5a-c and d-f corresponding to linearly and circularly polarized light, respectively, we give examples of pathways involving only (type-2 and type-4) transitions considered as parallel transitions in the frame of the present work and one transition of type-1 or type-3, acting as perpendicular transitions. They display characteristic shapes, in particular, when linear polarization is used.

9910


Elkharrat et al.

Figure 5. H(χ) model recoil fragment angular distributions for rapid dissociation induced by four selected one-photon transition excitation pathways (see legend) for a molecule of C2V symmetry at the NO2 equilibrium geometry according to eqs 17-19 for linearly polarized light (a-c) and eqs 20-22 for circularly polarized light (d-f); (a,d) parallel transitions (b,e) and (c,f) including one type-1 or type-3 perpendicular transition, respectively; (a) and (d) also include the four-photon three-transition [2,2,2p-5] model discussed in the text (long dashed line). The different models are normalized to the maximum of the angular profile equal to 1 for enlightening the characteristics of the shape.

A convenient way to characterize the angular distributions is to expand the above distributions in Legendre polynomials following the general expression

with, for example, two type-2 transitions leads to the following [2,2,2p-5] four-photon Hfi function for linearly polarized light

Hfi(4,LP)[2, 2, 2p-5] ) -0.7491 cos8(χ) + N

H(χ) ∝ 1 +

∑ β2kP2k(cos χ)

(23)

k)1

where N is the number of photons absorbed. Table 2 displays the (β2, β4, β6, β8) asymmetry parameters corresponding to selected reaction pathways and related expansions for four-photon absorption by the NO2 molecule of C2V symmetry, according to eqs 17-19 and 20-22 for linearly and circularly polarized light, respectively. We point out that different pathways can be clearly identified through the set of assigned asymmetry parameters, although some transitions such as the [2,2,2,4] and [2,3,4,4] cases, lead to comparable parameters. In the excitation of NO2, we have also examined threetransition pathways involving a B2 f B2 two-photon (2p) transition. This step corresponds to the excitation of the first excited state NO2(A2B2) (2A′ in the Cs symmetry) to the 4A′ or 5A′ state (A1 and B2 states in C2V geometries near the original equilibrium geometry, respectively), which occurs at ∼6.1 eV above the 2A′ state near ∠O-N-O ) 120° with R(N-O) ) 1.1 Å. These transitions are labeled as 2p-4 or 2p-5, as discussed in section VII. The two-photon transition moments were computed using MOLPRO65 using a five-state SA-CASSCF calculation at the geometry ∠O-N-O ) 120° with R(N-O1) ) R(N-O2) ) 1.19455 Å in the (tˆ1,tˆ2,tˆ3) coordinate system as defined in Figure 4. The basis set was the aug-cc-pVTZ basis set.66–68 The values of the transition moments in atomic units were t1,1 ) -0.0379, t2,2 ) 0.9015, and t3,3 ) -0.4299 for the 2p-5 transition. Combining this computed transition moment

0.97505 cos6(χ) + 0.1363 cos4(χ) - 0.01466 cos2(χ) + 0.00034 (24) and

Hfi(4,CP)[2, 2, 2p-5] ) (1/16){-0.7491 cos8(χ) + 1.67458 cos6(χ)-0.07238 cos4(χ) - 1.88120 cos2(χ) + 1.02890} (25) for circularly polarized light. The [2,2,2p-5] H(χ) model angular profiles described by eqs 24 and 25 are plotted in Figure 5a and d, respectively, and the corresponding asymmetry parameters are listed in Table 2. A [2,2,2p-5] pathway is found to give a distribution very close to that of a [2,2,2,2] pathway, in particular, for the β2 and β4 asymmetry parameters. The [2,2,2p-4] model angular profiles are identical to those obtained for a [2,2,2,3] pathway. We also include in Table 2 the β2-β8 asymmetry parameters for the [2,4,2p-4] (equivalent to [2,4,2,3]) and the [2,4,2p-5] model pathways, where the two-photon transition are combined with one type-2 and one type-4 transition. V. NO+-O- Ion Pair Formation Induced by Multiphoton Absorption: Angular Distribution Figure 6 presents the Vx-Vy and Vy-Vz projections of the O- velocity distribution measured for linearly polarized light at λ ) 397 nm, as well as the Vy-Vz projection of the Ovelocity distribution for circularly polarized light at λ ) 396



TABLE 2: β2-β8 Asymmetry Parameters for the Legendre Polynomial Expansion Characterizing the H(χ) Recoil Fragment Angular Distributions for Selected Model Pathways Assigned to Four-Photon Excitation of a Molecule of C2W Symmetry Taken at the NO2 Equilibrium Geometry Described by (a) Equations 17-19 for Linearly Polarized Light and (b) Equations 20-22 for Circularly Polarized Lighta β2

β4

β6

β8

(a) Four-Photon Transition, Linear [4,4,4,4] 3.64 3.02 [2,2,2,4] 3.18 1.83 [2,2,2,2] 2.8 1.012 [1,4,4,4] 2.27 -0.76 [2,1,4,4] 2.22 -0.81 [1,2,2,2] 1.64 -1.32 [3,4,4,4] 3.04 1.36 [2,3,4,4] 3.21 1.99 [3,2,2,2] 1.85 0.82 [2,2,2p-4] 1.85 0.82 [2,2,2p-5] 2.92 1.06 [2,4,2p-4] 2.89 1.82 [2,4,2p-5] 3.22 1.82

1.16 0.29 -0.13 -1.89 -1.84 -1.18 -0.18 0.51 1.58 1.58 -0.37 1.18 0.13

0.18 -0.02 -0.07 -0.63 -0.63 -0.14 -0.18 0.07 0.61 0.61 -0.19 0.49 -0.12

(b) Four-Photon [4,4,4,4] [2,2,2,4] [2,2,2,2] [1,4,4,4] [2,1,4,4] [1,2,2,2] [3,4,4,4] [2,3,4,4] [3,2,2,2] [2,2,2p-4] [2,2,2p-5] [2,4,2p-4] [2,4,2p-5]

-0.36 -0.09 0.04 0.02 0.05 0.17 -0.07 -0.13 -0.17 -0.17 0.04 -0.16 -0.08

0.05 -0.01 -0.02 -0.04 -0.03 -0.01 -0.02 0.01 0.04 0.04 -0.03 0.03 -0.02

Transition, Circular -1.82 1.13 -1.59 0.68 -1.4 0.38 -1.55 0.57 -1.48 0.46 -0.98 -0.17 -1.61 0.69 -1.62 0.75 -1.40 0.55 -1.40 0.55 -1.47 0.47 -1.55 0.69 -1.6 0.70

a The β2-β8 parameters for the [2,2(4),2p-4] and [2,2(4),2p-5] three-transition excitation pathways are also included (see text).

nm. These patterns show that the ion fragment emission is highly anisotropic, with a preferred recoil along the xˆFF polarization axis for linearly polarized light and in the (xˆFF-yˆFF) polarization plane for circularly polarized light propagating along the zˆFF axis. Such anisotropies may be taken as a first indication that the NO2 excited states involved in the process dissociate rapidly on the time scale of molecular rotation. In Figure 7, we report the H(χ) angular distributions measured at the 405, 397, and 396 nm wavelengths for linearly and circularly polarized light. The displayed distributions correspond either to the complete KER distribution (Figure 7a-d) or a selection of a given NO+(X1Σ+,V) vibrational level (V ) 2, Figure 7 e), according to the identification discussed in section III. These plots confirm the strong propensity for fragment emission parallel to the polarization axis of linearly polarized light or perpendicular to the propagation axis of circularly polarized light. Comparing the H(χ) measured anisotropy with the four-photon transition models described in section IV, after normalization to the measured integral intensity, the experimental result for linearly polarized light unambiguously excludes a four-transition pathway involving one (or more) type-1 perpendicular transition, that is a A1-B1 or B2-A2 (A′-A′′) transition. It excludes as well a four-transition pathway involving one type-3 transition, that is, a B2-B2 or A1-A1 (A′-A′), that would not be “balanced” when combined with two type-4 parallel transitions as is the case of [2,3,4,4]; such a scheme would imply a significant elongation of the molecule after

absorption of two photons and is not likely to play a major role in the present conditions, as discussed later. The closest models consistent with the measured distribution are of the type [2,2,2,2] and [2,2,2,4] (and [2,3,4,4]) for four-transition pathways and [2,2,2p-5] or [2,4,2p-5] for a three-transition pathway involving a B2 f B2 two-photon transition. When the sum over all KERs is considered, the measured distribution lies between the [2,2,2,2] or [2,2,2p-5] model profiles and the [2,2,2,4] or [2,4,2p-5] ones. The analysis based on the selection of events corresponding to different NO+(X1Σ+, V) vibrational levels is somewhat limited by the available energy resolution. However, it supports the existence of two angular regimes; the tendency for the highest levels V ) 2, 3, 4 at 405 nm and V ) 4, 5 at 397 nm is to favor the [2,2,2,2] (or [2,2,2p5]) angular profile, whereas the lowest vibrational levels V ) 0, 1 at 405 nm and V ) 0, 1, 2, 3 at 397 nm display an angular profile close to the [2,2,2,4] (or [2,4,2p-5]) one, as illustrated, for example, by Figure 7e. In Table 3, we report for linearly (a) and circularly (b) polarized light the β2, β4, and β6 asymmetry parameters assigned to the best Legendre polynomial fit of the distribution for each wavelength which quantify the H(χ) measured angular distributions. The β8 parameter, being on the order of the standard deviation, is not reported. We consider the angular distribution summed over all KERs, as well as the ones for selected vibrational levels of the NO+(X1Σ+) molecular fragment. Table 3 also includes the R coefficient, which measures the deviation between the fit of the experimental data and each of the transition models (square root of the quadratic mean of the deviations between the fit and model distributions, normalized to the mean of the measured H(χ)); the smallest R coefficient identifies the dominant transition type contributing to the measured angular profile. On the basis of the results shown in Figure 7, we restrict the comparison with the [2,2,2,2], [2,2,2,4], [2,3,4,4], [2,2,2p-5], and [2,4,2p-5] pathways, whose profiles are comparable with the measured recoil anisotropy. Although these five schemes correspond to the same general angular shape, they show differences in terms of asymmetry parameters (Table 2). The [2,3,2,2] pathway is also included for circular polarization. For the V ) 2, 3, and 4 levels at 405 nm, the angular analysis gives comparable results; the β2 and β4 asymmetry parameters favor the assignment of a [2,2,2,2] and then that of a [2,2,2p-5] pathway, the β6 value obtained being rather small. On the other hand, the V ) 0 and 1 level anisotropy is better described by a [2,2,2,4] or [2,4,2p-5] excitation scheme which involves larger β2 and β4 asymmetry parameters and a positive β6 value. At 397 nm, the V ) 4 and 5 levels show the same characteristics as those for 405 nm, favoring a [2,2,2,2] scheme and then a [2,2,2p-5] scheme. However, the remarkable V ) 2 vibrational level population and, to some extent, the V ) 3 population are now well-described by a [2,2,2,4] or [2,4,2p-5] angular profile, providing very similar characteristics with those of the V ) 0 and 1 level anisotropies. These results do not show evidence for four-photon primary excitation of R*[(4b2)-1] Rydberg states of different a1, b2, or a2 symmetry, which would significantly modify the parallel or perpendicular character of the fourth transition when varying the photon energy. The [2,2,2,2] pathway corresponds to dissociation of a NO2 superexcited state populated after four parallel transitions of type-2, close to the bent C2V geometry of the ground state. The type-4 character in, for example, the [2,2,2,4] angular profile may be considered as

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Elkharrat et al.

Figure 6. (a) Vx-Vy and (b) Vy-Vz projections of the O- velocity distribution measured for linearly polarized light P parallel to the xˆFF axis, as shown, at λ ) 397 nm. (c) Vy-Vz projection of the O- velocity distribution for circularly polarized light k propagating parallel to the zˆFF axis at λ ) 396 nm.

Figure 7. H(χ) recoil fragment distributions at 405 and 397/396 nm integrated over all KERs for (a,c) linearly polarized light (χ referred to the polarization axis) and (b,d) circularly polarized light (χ referred to the propagation axis) and (e) H(χ) for a selection of the NO+(X1Σ+,V ) 2) vibrational level at 397 nm (linearly polarized light); exp. (dots and fit black line), model angular distributions for selected four-photon excitation pathways, as indicated in the legend and according to the text (full and dashed lines). The measured and model angular profiles in arbitrary units are normalized such that their total cross sections are identical.

a fingerprint of nuclear dynamics leading to a significant increase of the ∠O-N-O apex angle or a significant elongation of a N-O bond. Similar trends are found for the reactions induced by circularly polarized light, as shown in Table 3b, although the sensitivity of the analysis is lower than that relying on the angular distributions induced by linearly polarized light due to the weaker laboratory frame scattering anisotropies. The [2,3,2,2] pathway, which is not consistent with the recoil anisotropy measured for linearly polarized light, is also included for circularly polarized light since it provides a good level of agreement with the measured angular distribution. Indeed, the relative population of excitation pathways involving intermediate states of different symmetries might be significantly modified when changing from linearly to circularly polarized light, as illustrated in Table 4. A more detailed investigation relying upon an accurate control of the laser intensity at the interaction region when changing from linearly to circularly polarized light will be performed in forthcoming experiments. Previous studies have shown that the first absorption band in the 400 nm wavelength range is dominated by the NO2(X2A1f

A2B2) transition, which carries most of the oscillator strength;23 therefore, the first step in the four-photon excitation pathway is most likely a type-2 transition. The other steps of the reaction pathways consistent with the angular anisotropies measured for the NO+(X1Σ+,V)-O-(2P) ion pair channels are discussed in section VII, based on computed potentials and transition moments involving NO2 excited states. VI. NO+-O- Ion Pair Formation Induced by One-Photon Absorption We have also studied the NO+-O- ion pair dissociation channel induced by a single-photon excitation at hν ) 12.45 eV energy at the SOLEIL synchrotron radiation facility. As discussed in section II, the time structure of the light source, even in the eight-bunch mode used for the VC experiments, does not allow for an acquisition where the light pulse is used as a common start for the CTN-TDC channels. The best acquisition scheme in such conditions required the use of the signal detected on the front microchannel plate of the negatively charged particle detector as a common start for the CTN-TDC



TABLE 3: β2, β4, and β6 Asymmetry Parameters and Standard Deviations Measured for (a) Linearly and (b) Circularly Polarized Lighta (a) Process Linear P

405 nm V)4 V)3 V)2 V ) 0,1 397 nm V)5 V)4 V)3 V)2 V ) 0, 1

β2

β4

β6

R for [2,2,2,2]-[2,2,2,4][2,3,4,4]-[2,2,2p-5]

2.83(0.03) 2.67(0.05) 2.81(0.06) 2.87(0.08) 3.14(0.07) 2.86(0.03) 2.56(0.07) 2.75(0.06) 2.91(0.09) 3.11(0.08) 3.05(0.07)

1.37(0.02) 1.19(0.04) 1.23(0.06) 1.32(0.07) 1.89(0.07) 1.47(0.04) 1.11(0.06) 1.23(0.06) 1.53(0.08) 1.87(0.07) 1.79(0.06)

0.17(0.04) 0.17(0.05) 0.06(0.07) 0.08(0.08) 0.34(0.07) 0.25(0.03) 0.16(0.07) 0.04(0.06) 0.42(0.09) 0.43(0.08) 0.39(0.07)

14-22-28-18.5 12-32-37-19 9-27-33-14 12-23-30-15 35-4-7.5-35 18-19-24.5-22 14-37-42-22 9-29-35-16 24-17-21-28 35-6-6.5-36 31-7-10.5-32

(b) Process Circular P

β2 405 nm V)4 V)3 V)2 V ) 0,1 396 nm V)5 V)4 V)3 V)2 V ) 0,1

-1.41(0.03) -1.34(0.06) -1.35(0.08) -1.44(0.08) -1.6(0.11) -1.38(0.04) -1.29(0.07) -1.32(0.09) -1.43(0.07) -1.46(0.09) -1.53(0.13)

β4

β6

R for [2,2,2,2]-[2,2,2,4][2,3,4,4]-[2,3,2,2][2,2,2p-5]

0.54(0.04) 0.46(0.07) 0.44(0.09) 0.56(0.09) 0.81(0.13) 0.51(0.04) 0.41(0.08) 0.42(0.10) 0.55(0.08) 0.57(0.10) 0.80(0.15)

-0.14(0.05) -0.19(0.08) -0.07(0.11) -0.12(0.10) -0.19(0.15) -0.07(0.05) -0.13(0.10) -0.11(0.12) -0.02(0.10) 0.05(0.12) -0.19(0.17)

8-9.5-12-1-6.5 8-14-16-4-9 5-14-16-5-7 8-8-10-4-5.5 18-5-3-12-14 5.5-11-13-3-5 8-16.5-19-7-10 6-15-17-6-8 6-8-11-5-4 7-8-11-8-4 16-6-5-10-13

a β8 values on the order of the standard deviation are not included. For each wavelength (405, 397, and 396 nm), the anisotropy parameters are reported for the complete KER distribution (first line) and for selected NO+(X1Σ+,V) vibrational levels. The R coefficient characterizes the deviation between the fit of the experimental data and the [2,2,2,2], [2,2,2,4], [2,3,4,4], [2,3,2,2], and [2,2,2p-5] transition models (see text).

TABLE 4: Relative Total Cross Sections for Four-Photon Bound-to-Bound Transitions Corresponding to the Discussed Excitation Pathways, Using Linearly and Circularly Polarized Light at a Comparable Laser Intensity, Normalized with the [2,2,2,2] Cross Section for Linearly Polarized Light Equal To 1 pathway

[2,2,2,2]

[2,2,2,4]

[2,3,4,4]

[2,3,2,2]

[2,2,2p-5]

LIN CIRC

1 0.014

0.87 0.135

0.17 0.144

0.14 0.144

0.71 0.018

and the TAC, as usually performed in the vector correlation method, and to work with a 100 V/cm extraction field in order to record the complete O- TOF spectrum. This constrained the resolution achieved for the momentum determination as compared with that of the measurements performed with the femtosecond laser source. Detailed results will be reported separately for measurements to be performed at a higher resolution using the single-bunch mode at SOLEIL. However, the preliminary results obtained in the present conditions show that the measured KER distribution at 12.45 eV displayed in Figure 8 is similar to the general shape of the KER spectra reported in Figure 5 and favors population of the NO+(X1Σ+,V ) 5) molecular fragment, that is, low translational energies. This character is therefore to be attributed to the excitation of NO2 electronic states in the 12.45 eV binding energy region and coupling to the ion pair dissociative state, rather than to nuclear dynamics that might be induced at an intermediate step of the multiphoton excitation

Figure 8. Kinetic energy release (KER) distribution of the NO+ and O- ion fragments measured at hν ) 12.45 eV using linearly polarized synchrotron radiation.

scheme. The NO+(X1Σ+,V) vibrational levels are not resolved, although the photon energy resolution is on the order of a few meV. The relative contribution of ion pair production on the order of 1.5% with respect to photoionization into the NO2+(X1Σg+) ionic state, which is the only ionization channel observed at the hν ) 12.45 eV photon excitation energy, is comparable with that reported in ref 26. Furthermore, the recoil fragment asymmetry parameter for the one-photon ion pair channel is negative, βO- ≈ -0.3 ( 0.1; this indicates a dominant perpendicular transition that should be assigned to a 4b2 f npb2 or ndb2 transition if excitation of a Rydberg state is considered or excitation of a continuum dissociative state of A1 (A′) symmetry otherwise. The expected values for the βO- asymmetry parameter corresponding to a one-photon-induced dissociation at a fixed ground-state equilibrium geometry are β ) 1.54 for a type-2 parallel transition and β ) -0.5 and -1 for a type-3 or type-1 perpendicular transitions, respectively. We note that, as far as symmetry is concerned, similar NO2 superexcited states might be involved in the one-photon and the four-photon pathways since they could correspond to a perpendicular transition in the one-photon case and to a parallel transition in the four-photon case. VII. Computed Potential Energy Surfaces and Transition Moments Potential energy surfaces for the ground and selected A′ excited state of NO2 were computed using an augmented correlation-consistent polarized valence triple-ζ (aug-cc-pVTZ) basis set66,67 and internally contracted multireference configuration interaction plus a Davidson correction (icMRCI+Q). The reference wave function for the icMRCI+Q calculation was obtained from a state-averaged valence complete active space self-consistent field (SA-VCASSCF) calculation, where the lowest five states of A′ symmetry were included in the calculation. All calculations were performed using the MOLPRO program.65 The R(N-O1) bond length was frozen at the initial state equilibrium value of 1.19455 Å,69 and the R(N-O2) bond length and bond angle ∠O-N-O were varied. The resulting potentials are very similar in quality to those obtained by Schinke in his study of NO2.70 In a dressed state and surface hopping picture,71,72 a multiphoton dissociation system can be thought of as proceeding along trajectories on the potential energy surface of a given electronic state until it reaches an intersection between the current dressed state potential, that is, the potential energy

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surface shifted up an integer times the photon energy, and a higher surface. The system then has a probability for absorbing a photon and making the transition to the excited state. Thus, in the dressed state surface hopping picture, the transitions between electronic states occur along the intersection seams between the lower dressed state and higher excited states. The probability of making the transition will depend on the oscillator strength for the transition at the geometry of the intersection as well as the field strength. To apply this idea to the angular distribution of the photofragments in the multiphoton excitation processes in NO2, we will consider both the regions of maximum oscillator strength and the direction of the polarization of the transition moment along the dressed state-excited state intersection seams. In Figure 9a, we consider the intensity of the transition from the ground state 1A′ to the first excited state of A′ symmetry 2A′. In this figure, the left panel shows the square of the dipole matrix element as a function of the R(N-O2) and ∠O-N-O coordinates. The right panel shows the value of 〈cos2 θjk〉 for the one-photon transition moment, where the angle is relative to the orientation of the direction of the N-O2 elongating bond. Using the notation introduced in the description of the angular distributions (section IV), a type-1 transition would have 〈cos2 θjk〉 ) 0, a type-2 transition would have 〈cos2 θjk〉 ) 0.85, a type-3 transition would have 〈cos2 θjk〉 ) 0.15, and a type-4 transition would have 〈cos2 θjk〉 ) 1. Superimposed on top of these two contour plots are three lines. The first two lines show the range of geometries that are accessible to the system in the ground state in a classical mechanical model with 0.5 and 3.1 eV of vibrational energy, and the third line shows the seam of the intersection of the excited-state potential surface and groundstate potential energy surface dressed with one photon of energy at 3.1 eV. The value of 0.5 eV was chosen to approximate the range of the ground-state vibrational probability density. The value of 3.1 eV shows the range of the probability on the lowest surface with 3.1 eV on the internal energy, which is possible if the system has already absorbed one photon and relaxed to the ground state through a radiationless nonadiabatic transition which is enhanced by the conical intersection between the ground and first excited states of A′ symmetry. This figure indicates that first, the excitation will primarily occur for R(N-O2) near 1.2 Å with a corresponding value of 〈cos2 θjk〉 at around 0.9, indicating a type-2 transition. In the symmetric C2V geometry, this transition corresponds to the X2A1 to A2B2 transition that has been considered in many previous studies.14 We also note that other geometries, which should be sampled in a few femtoseconds, might also favor electronic transition to the A 2B2 state (e.g., R(N-O2) near 1.15 Å and ∠O-N-O ≈ 90°); this would correspond to a different transition moment orientation (here, 〈cos2 θjk〉 ≈ 0.4) which is not observed presently. In Figure 9b, we consider possible excitation pathways out of the 2A′ state induced by a second 3.1 eV photon. We show here the intensities and transition moment orientations for transitions to the 3A′, 4A′, and 5A′ states (A1 and B2 states in C2V geometries near the original equilibrium geometry, respectively). In all of the panels of this figure, we indicate the range of classically accessible geometries in the 2A′ state for a total energy of 3.1 eV above the minimum in the ground-state potential. This range starts at R(N-O2) ) 1.1 Å and extends to 1.8 Å. The corresponding range for ∠O-N-O goes from 90 to 140°. The transition probability to the 3A′ state along the intersection seam is quite weak. We note that we also found a weak probability for the transition from the 1A′ state, which

Elkharrat et al. could be populated by nonadiabatic relaxation from the 2A′ state13,14 to the 3A′ state. In the case of excitation out of the 2A′ state to the 4A′ state, the most intense part of the seam occurs at R(N-O2) ) 1.6 Å, which corresponds to a significant elongation of the R(N-O2) bond, and for the 5A′ state, the seam is at slightly larger values. In addition, the orientation of the transition moment along both of these seams corresponds to 〈cos2 θjk〉 ≈ 0.9. This indicates that the orientation of the transition moment for the second absorbed photon will also correspond to a type-2 or type-4 transition. This strong propensity for the first two transition moments to be nearly aligned with the breaking N-O bond will lead to a strong alignment of the system with the N-O bond in the direction of the polarization for linearly polarized light. This will enhance the probability that subsequent transitions will also be along the N-O bond leading to transition patterns which do not include type-1 or type-3 transitions, consistent with the experimental results reported in section V. A second possible excitation is also considered in Figure 9b, where we plot the intersection of the 2A′ potential dressed by two photons and the 4A′ and 5A′ potentials. These intersections are indicated by the 6.2 eV short-dashed contour. In both cases, this intersection occurs inside of the 3.1 eV range of the vibrational state and for geometries with ∠O-N-O ) 110° and R(N-O2) ) 1.1 Å, close to the ground-state geometry. This observation is the basis for considering excitation schemes including one two-photon step, that is, the 2p-4 and 2p-5 transitions discussed in section IV. The computed potentials shown in Figure 9 do not include Rydberg type orbitals in the valence active space used in the SA-VCASSCF calculation. However, the 4A′ and 5A′ states are at energies where one expects low-lying Rydberg states to occur. We have investigated how these valence states would mix with Rydberg states by computing, at two geometries, extended state-averaged multiconfigurational self-consistent field (SA-MCSCF) calculations where we have included seven additional active orbitals of A′ symmetry but only allowed configurations with at most one electron total in this additional set of orbitals. In addition, we have extended the aug-cc-pVTZ basis set with additional diffuse basis functions73 (additional d functions on the O atom with exponent 0.0594, additional f functions on the O atoms with exponent 0.147, additional s functions on the N atom with exponents 0.01141, 0.00589, 0.00209, and 0.000387, additional p functions on the N atom with exponents 0.0167, 0.00813, 0.00273, 0.00106, and 0.00031, additional d functions on the N atom with exponents 0.0419, 0.0289, and 0.00846, and additional f functions on the N atom with exponents 0.107, 0.0315, and 0.00926). Using this approach, we have performed state-averaged calculations including the 10 lowest A′ states with the equilibrium bond length and ∠O-N-O ) 134 and 175°. Examining the resulting wave functions for ∠O-N-O ) 134°, we find that the 4A′ state strongly mixes with the 6a1 f 3pπ(A1) Rydberg state and that the 5A′ state strongly mixes with the 6a1 f 3pσ(B2) state. In each case, the purely valence state becomes part of two states formed by configuration mixing with the Rydberg state. The 6a1 f 4sσ(A1) Rydberg state appears at an energy below these states. Two of the states formed from the valence 4A′ and 5A′ states connect in a diabatic representation with the corresponding Rydberg states in the linear geometry, that is, they connect to the 6a1 f 3pπ(A1) and 6a1 f 3pσ(B2) states. However, in an adiabatic representation, the four states connect to the 6a1 f 3dπ(B2) and 6a1 f 3dδ(A1) states, and two states formed from



Figure 9. Two-dimensional contour plots displaying the intensity and orientation of the transition dipole moment as a function of the R(N-O2) and ∠O-N-O coordinates for the transition (a) from the ground state 1A′ to the first excited state 2A′ and (b) from the first excited state 2A′ to the 3A′, 4A′, and 5A′ higher excited states of A′ symmetry. The left panels show the square of the dipole matrix element, and the right panels show the value of 〈cos2 θjk〉 for the one-photon transition moment (see text). The lines superimposed on top of the contour plots represent the range of geometries that are accessible to the system in the ground state in a classical mechanical model with 0.5 or 3.1 eV of vibrational energy (long-short dashed lines with 0.5 or 3.1 label, blue) and the seam of the intersection of the higher-state potential surface and lower-state potential surface dressed with one photon of energy of 3.1 eV or two photons of energy of 6.2 eV (regular dashed lines with 3.1 or 6.2 label, red and green).

the mixing of the 6a1 f 3dσ(A1) Rydberg state and a valence 6a1 f σ*(A1) state.

Absorption of the fourth photon from one of the four states formed by the configuration interaction of the valence 4A′ and

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5A′ states and nearby Rydberg states will populate a region of high density of superexcited states of NO2, which include the R*[(4b2)-1] Rydberg states, converging to the NO2+(a3B2) first electronically excited state of NO2+.16–18 As discussed in section III, excitation of the (4b2)-1 series from the NO2(X2A1) ground state, which has a bent equilibrium geometry, is favored by Franck-Condon factors, and discrete states assigned to the ν2 bending modes of the Rydberg members have been identified previously in one-photon absorption spectra. Ion pair states typically have minima at relatively large intermolecular geometries compared to valence states;74 therefore, we expect that near the FC region, the two A′ and A′′ states, which correlate with the NO+(X1Σ+,V) + O-(2P3/2 or 2P1/2) ion pair channels, will have a strong repulsive character in the FC region. Such dissociative excited states may either be directly accessed by the fourth photon absorption or give rise to curve crossings and coupling with the R*[(4b2)-1] series, inducing their predissociation. Assuming a type-2 transition (or a type-4 transition) for the fourth photon absorption, the β2-β8 asymmetry parameters assigned to the Legendre polynomial fit of the ion-fragment angular distribution corresponding to [2,2(4),2p-4] and [2,2(4),2p5] transitions have been reported in Table 2. As discussed in section V, the [2,2(4),2p-5] pathways involving excitation of the 5A′ state (B2 symmetry in C2V) are quite consistent with the experimental results. The fourth photon type-2 and/or type-4 transitions are compatible with different combinations of initial and final states, among those listed above. As mentioned in section IV.C, the type-4 character implies that nuclear dynamics occurs, inducing an increase of the ∠O-N-O bond angle or a significant elongation of a N-O bond. This could take place after absorption of three photons due to the strong mixing between the.5A′ bent valence excited state and R*[(6a1)-1] Rydberg states (6a1 f 3pσ(B2) and the states formed from the mixing of the 6a1 f 3dσ(A1), 6a1 f σ*(A1) states), for example, converging to the NO2+(X1A1) state of linear equilibrium geometry. The conditions may then be met for both a type-2 transition close to the C2V initial geometry [2,2,2,2] or [2,2,2p-5] and for a [2,2,2,4] or [2,4,2p-5] type-4 transition. We also stress that a [2,2,2,2] reaction pathway in a C2V geometry corresponding to an increased ∠O-N-O apex angle, here, from 134 to 146°, may lead to a fragment anisotropy identical to that of the [2,2,2,4] pathway described above. A comparable dynamical effect could also be induced by an internal conversion of R*[(4b2)-1] Rydberg states populated in a [2,2,2,2] or [2,2,2p-5] transition into R*[(6a1)-1] Rydberg states. The forthcoming report of recoil frame photoelectron angular distributions (RFPADs) measured in dissociative photoionization of NO2 studied in identical experimental conditions, which likely involve similar intermediate states, will provide a stringent probe of these reaction pathways. VIII. Discussion and Conclusions In the present study, we have shown that the NO+(X1Σ+,V) + O-(2P3/2 or 2P1/2) ion pair channel is one of the major reactions induced by four-photon excitation using femtosecond laser light at a wavelength close to 400 nm. Although its threshold lies higher than the NO2+(X) adiabatic ionization potential, the ion pair branching ratio with respect to the total ion production (ion pair and photoionization) amounts to 15-20%, that is, one order of magnitude larger than the 1% value measured for one-photon ion pair production at a comparable photon excitation energy of hν ≈ 12.45 eV. The thorough analysis of the measured energetic and angular differential observables derived from the

Elkharrat et al. (VNO+,VO-,eˆ) vector correlation, supported by the presented bound-to-bound n-photon formalism describing the angular distributions and new calculations of potential energy surfaces and transition moments, enables us to identify excitation pathways for the reaction above. The KER distribution of the ion fragments displays resolved peaks which are the signature of the rovibrational excitation of the NO+(X1Σ+,V) molecular fragment. The excitation probability increases strongly as a function of the vibrational level, from V ) 0 to 4 or 5. It corresponds to a preferred transfer of excess energy to the internal degrees of freedom of the system rather than to translational energy, favoring the population of channels quasi-resonant with the photon excitation energy. This tendency has been observed for other ion pair processes previously,28 and it is also found here for the one-photon NO+(X1Σ+,V) + O-(2P3/ 2,1/2) ion pair channel. Superimposed with this behavior, the reported results show that the NO+(X1Σ+,V) vibrational excitation dynamics is very sensitive to the photon wavelength and the light polarization in the four-photon femtosecond absorption process, with, for example, a significant increase of the NO+(X1Σ+,V ) 2) at λ ) 397 nm. The measured fragment recoil anisotropy for the multiphoton ion pair channel (eq 1) reveals a prompt dissociation of the NO2 molecule, with a preferred emission along the polarization axis of linearly polarized light characterized by (β2, β4, β6, β8) asymmetry parameters, suggesting two types of excitation pathways. The angular distributions measured with circularly polarized light are consistent with those obtained with linearly polarized light, with a favored emission in the plane perpendicular to the propagation axis. The formalism describing a bound-to-bound n-photon transition inducing dissociation of a nonlinear molecule, applied to the four-photon dissociation of NO2 close to the ground-state geometry, enables us to identify model excitation pathways consistent with the experimental data; they involve parallel transitions via two or three intermediate states, labeled [2,2, 2p-5] or [2,2,2,2] and [2,4,2p-5] or [2,2,2,4]. The reported MRCI calculations of potential energy surfaces and transition moments emphasize some of the most probable state-to-state transitions. Although other possibilities might be found compatible with the experimental findings and the calculations, we select, for the discussion, pathways maintaining a geometry of NO2 close to that of the ground state for absorption of the first three photons, owing to the femtosecond character of the excitation. In such a scheme, the first photon absorption, assigned to the X2A1 to A2B2 type-2 transition, is followed by one two-photon absorption transition populating, for example, the 5A′ state. Near the ground-state geometry of NO2, the dominant electronic structure of the 5A′ state is strongly mixed with the 3pσ(B2) lowest member of the R*[(6a1)-1] Rydberg series, converging to the NO2+(X1A1) ground state of NO2, as described in section VII. Other R*[(6a1)-1] states of A′ symmetry and similar energy might also be involved as intermediate states. Absorption of the fourth photon populates a superexcited state of NO2, and the measured recoil anisotropy supports the conclusion that this transition-inducing dissociation is either a type-2 or type-4 transition. The type-2 transition implies excitation of a R*[(4b2)-1] state of A1 symmetry or that of a repulsive state of A′ symmetry correlated to the ion pair dissociation limit. In addition, the dynamics of the ion pair production induced after absorption of the four photons should account for the remarkable vibrational distribution of the NO+(X,V) fragment.

Ion Pair Formation in Multiphoton Excitation of NO2 As discussed in sections III and VII, the R*[(4b2)-1] Rydberg states may then undergo dissociation via a direct coupling to the ion pair surfaces, the vibrational excitation of the NO+(X,V) fragment resulting from that of the resonantly excited Rydberg state. The dissociation dynamics may also involve internal conversion of the R*[(4b2)-1] to highly vibrationally excited levels of the R*[(6a1)-1] Rydberg states converging to the NO2+(X1A1,V) ground-state levels of the parent ion prior to their dissociation via coupling to the ion pair state. Since the R*[(6a1)-1] Rydberg states have an equilibrium linear geometry, this process could account for the [2,2p-5,4] (or [2,2,2,4] for four one-photon transitions) excitation pathways observed for the lowest NO+(X1Σ+,V) vibrational states. As pointed out in section VI, the characteristics of ion pair production obtained in a preliminary study of one-photon excitation at hν ) 12.45 eV display similarities and differences with the four-photon results. The similarity in the KER distribution favoring a large energy transfer into the vibrational and rotational excitation of the molecular fragment confirms that this behavior should be assigned to the dissociation dynamics taking place in the 12.24-12.55 eV energy region. On the other hand, the branching ratio relative to ionization is much smaller in the one-photon case, and the fragment recoil anisotropy favors a perpendicular transition. The differences may reflect the different FC factors for the one-photon and the fourphoton reactions, even if we have considered here excitation pathways that involve geometries close to the ground-state equilibrium geometry due to the broader laser bandwidth at each step of the excitation pathway compared with the narrow band of the single XUV photon. The strong parallel transition found in the four-photon case is consistent with the excitation of superexcited states of the same C2V symmetry as that observed in the one-photon excitation scheme, which we assign at the level of the preliminarily reported study as a R*[(4b2)-1] Rydberg state of A1 symmetry, implying excitation of a npb2 or ndb2 MO. A definite interpretation would require complementary theoretical investigations of the dynamics of the dissociation ending in the ion pair channel. In both cases, the ion pair channels compete with other reactions such as neutral dissociation and ionization, which includes direct ionization to the NO2+(X1A1) ground state, autoionization, and dissociative ionization corresponding almost exclusively to a five-photon process. The results obtained for dissociative and nondissociative ionization of NO2 induced in the same experimental conditions as those described in the present work, together with the formalism for recoil frame photoelectron angular distributions (RFPADs) following multiphoton ionization and photoionization calculations, will be reported in a forthcoming paper. As it will be shown, the ion fragment angular distributions resulting from dissociative ionization display strong similarities with those reported here for the ion pair dissociation channel. Therefore, we expect that the presently discussed reaction pathways will provide clues for the interpretation of the dissociative ionization channels. On the other hand, the determination of the RFPADs will likely provide a means to characterize intermediate ionizing states and assist in the definite identification of the excitation pathways leading to ion pair dissociation. A third report will be dedicated to ion pair formation and ionization to the NO2+(X1A1) state induced by synchrotron radiation, performed using the singlebunch mode at SOLEIL and taking advantage of the tunability between the ion pair threshold at 10.918 eV and that of the first electronic excited state of NO2+ in the FC region at 12.75 eV. This study will also include the results for dissociative and

J. Phys. Chem. A, Vol. 114, No. 36, 2010 9917 nondissociative ionization of NO2 at the photon excitation energy of hν ) 15.69 eV, which corresponds to the absorption of five 400 nm photons. Finally, future experiments will benefit from foreseen improvements in the performance of the laser sources in terms of wavelength tunability at fixed pulse duration in the few femtosecond regime, increase of the repetition rate from 1 to a few kHz, a combination of two-color femtosecond linearly and circularly polarized laser pulses with accurate control of the laser intensity at the interaction region, as well as facilities for time-resolved investigations of the ion pair dissociation. Acknowledgment. The authors gratefully acknowledge O. Gobert, J. F. Hergott, D. Jourdain, and F. Lepetit for operating the PLFA facility at the Saclay Laser-matter Interaction Centre (SLIC) and B. Carre´ and P. Breger from the Attophysics group at SPAM (CEA, Saclay) for helpful discussions, A. Huetz for providing the CIEL2 UHV setup and helpful support, L. Nahon, DESIRS beamline director, G. Garcia, DESIRS beamline scientist (SOLEIL), and the machine department staff for operating SOLEIL, and E. Bouisset, S. Damoy (ISMO), and J. F. Gil (SOLEIL) for their technical support. D.D. and C.E. are very grateful to B. Soep and V. Blanchet for enlightening discussions about the multiphoton photodynamics of NO2. The SOFOCKLE femtosecond laser system is supported by ANR (Agence Nationale de la Recherche, Projet Image Femto, dećision d′aide No. ANR-07-BLAN-0162-01). D.D. acknowledges the support of the Triangle de la Physique (DYNELEC No. 2008-046T). R.R.L. acknowledges the support of the Robert A. Welch Foundation (Houston, TX) under Grant A-1020. The computational studies were performed at the Texas A&M University Supercomputing Facility and on facilities supported by the National Science Foundation (Grant No. CHE-0541587). References and Notes (1) Baltzer, P.; Karlsson, L.; Wannberg, B.; Holland, D. M. P.; MacDonald, M. A.; Hayes, M. A.; Eland, J. H. D. Chem. Phys. 1998, 237, 451. (2) Eland, J. H. D.; Karlsson, L. Chem. Phys. 1998, 237, 139. (3) Singhal, R. P.; Kilic, H. S.; Ledingham, K. W. D.; Kosmidis, C.; McCanny, T.; Langley, A. J.; Shaikh, W. Chem. Phys. Lett. 1996, 253, 81–86. (4) Vijayalakshmi, K.; Safvan, C. P.; Ravindra Kumar, G.; Mathur, D. Chem. Phys. Lett. 1997, 270, 37. (5) Davies, J. A.; Continetti, R. E.; Chandler, D. W.; Hayden, C. C. Phys. ReV. Lett. 2000, 84, 5983. (6) Schmidt, T. W.; Lopez-Martens, R. B.; Roberts, G. J. Chem. Phys. 2004, 121, 4133. (7) Form, N. T.; Whitaker, B. J.; Poisson, L.; Soep, B. Phys. Chem. Chem. Phys. 2006, 8, 2925–2932. (8) Coroiu, A. M.; Parker, D. H.; Gronenboom, G. C.; Barr, J.; Novalbos, I. T.; Whitaker, B. J. Eur. Phys. J. D 2006, 38, 151. (9) Vredenborg, A.; Roeterdink, W. G.; Janssen, M. H. M. J. Chem. Phys. 2008, 128, 204311. (10) Wilkinson, I.; Whitaker, B. J. J. Chem. Phys. 2008, 129, 154312– 154315. (11) Hamard, J. B.; Cireasa, R.; Chatel, B.; Blanchet, V.; Whitaker, B. J. J. Phys. Chem. A 2010, 114, 3167–3175. (12) Schinke, R.; Grebenshchikov, S. Y.; Zhu, H. Chem. Phys. 2008, 346, 99. (13) Sanrey, M.; Joyeux, M. J. Chem. Phys. 2007, 126, 07430/1–07430/ 8. (14) Arasaki, Y.; Takatsuka, K. Chem. Phys. 2007, 338, 175. (15) Hirst, D. M. J. Chem. Phys. 2001, 115, 9320. (16) Edqvist, O.; Lindholm, E.; Selin, L. E.; Asbrink, L.; Kuyatt, C. E.; Mielczarek, S. R.; Simpson, J. A.; Fischer-Hjalmars, I. Phys. Scr. 1970, 1, 172. (17) Morioka, Y.; Masuko, H.; Nakamura, M.; Sasanuma, M.; Ishiguro, E. Can. J. Phys. 1978, 56, 962. (18) Au, J. W.; Brion, C. E. Chem. Phys. 1997, 218, 109. (19) Jarvis, G. K.; Song, Y.; Ng., C. Y.; Grant, E. R. J. Chem. Phys. 1999, 111, 9568.

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Ion Pair Formation in Multiphoton Excitation of NO2 Using Linearly

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