Spectral dependence of photoemission in multiphoton ionization of NO2 by femtosecond pulses in the 375–430 nm range

S. Marggi Poullain *ab, R. Cireasa a, C. Cornaggia c, M. Simon d, T. Marin d, R. Guillemin d, J. C. Houver a, R. R. Lucchese e and D. Dowek a
aInstitut des Sciences Moléculaires d'Orsay (ISMO), CNRS, Université Paris-Sud, Université Paris-Saclay, F-91405 Orsay, France
bDepartamento de Química Física I, Facultad de Ciencias Químicas, Universidad Complutense de Madrid (Unidad Asociada I + D + i CSIC), 28040 Madrid, Spain. E-mail: smarggi@ucm.es
cLIDYL, CEA, CNRS, UMR 9222, Université Paris-Saclay CEA Saclay, bât. 522, F-91191 Gif-sur-Yvette, France
dLaboratoire de Chimie Physique Matière et Rayonnement, Université Pierre et Marie Curie et CNRS, 75005 Paris, France
eDepartment of Chemistry, Texas A&M University, College Station, TX 77840, USA

Received 30th March 2017 , Accepted 12th July 2017

First published on 27th July 2017

We investigate the multiphoton ionization of NO2 using tunable (430–375 nm) femtosecond pulses and photoelectron–photoion coincidence momentum spectroscopy. In order to understand the complex electronic and nuclear photodynamics at play following absorption of three to five photons, we also report extended photoionization calculations using correlated targets and coupled channels. Exploring the multiphoton dissociative ionization (MPDI) and multiphoton ionization (MPI) processes over such a broad energy range enables us to lend further support to our work carried out around 400 nm of a femtosecond laser [S. Marggi Poullain et al., J. Phys. B: At., Mol. Opt. Phys., 2014, 47, 124024]. Two excitation energy regions are identified and discussed in terms of the proposed reaction pathways, highlighting the significant role of Rydberg states, such as the [R*(6a1)−1, 3pσ] Rydberg state, in the NO2 multiphoton excitation and photoionization. These new results support our previous assumption that different bent and linear geometries of the NO2+(X1Σg) ionic state contribute to the MPDI and MPI, consistent with the reported calculations which reveal an important vibronic coupling characterizing the photoemission. Remarkably, the strong anisotropy of the recoil frame photoelectron angular distribution (RFPAD) previously observed at 400 nm appears as a fingerprint across the whole explored photon energy range.

1. Introduction

Molecular dynamics in the nitrogen dioxide molecule has attracted much interest in recent years. Despite its apparent simplicity as a triatomic molecule, this non-linear molecule of C2v geometry in its (4b2)2(1a2)2(6a1)1 open-shell ground state presents a very rich photochemistry governed by ultrafast non-adiabatic couplings involving different electronic states, such as vibronic couplings favoured at conical intersections. We refer to the comprehensive review1 by Wilkinson and Whitaker for the vast literature dedicated to the spectroscopy and photodynamics of NO2 for excitation energies up to 20 eV, and in particular the extensive work addressing multiphoton photodissociation and photoionization processes in the 400 nm region relevant for the present work. NO2 is an interesting prototype molecular system to investigate to which extent methodological approaches such as modelling the recoil frame photoemission in small polyatomic molecules can probe ultrafast molecular dynamics in multiphoton induced photoionization reactions.

In a previous paper2 referred to as paper I, we reported the experimental results for multiphoton dissociative ionization (MPDI) and non-dissociative multiphoton ionization (MPI) of NO2 induced by 400 nm femtosecond pulses, obtained using coincident electron–ion momentum spectroscopy, also referred to as the vector correlation (VC) method.3,4 The key observations for the two dominant MPDI and MPI processes, derived from the complete energy and angular analysis of the coincident events involving the (NO+, e) fragment and (NO2+, e) parent channels, respectively, were the following: (i) a quite similar photoelectron energy, but (ii) different asymmetry parameters describing the photoemission in the laboratory frame, (iii) a significant ro-vibrational excitation of the NO+ fragment, (iv) a strong alignment of the NO+ recoil direction parallel to the laser polarization axis and (v) a remarkable anisotropy of the recoil frame photoelectron emission in the recoil direction of the NO+ fragment. To facilitate the interpretation of the RFPAD, T(n,RF)fi(θe, ϕe, χ), where χ is the polar angle of the fragment ion recoil direction relative to the light polarization axis and θe and ϕe are the polar and azimuthal angles defining the electron emission direction in the recoil frame,2,5 a formalism was developed to describe a n-photon MPDI process (n = 5), involving (n − 1)-photon bound-to-bound transitions and one-photon ionization of a molecular excited state of C2v symmetry. It was further extended to enable the most tractable comparison with the one-channel and two-channel photoionization calculations also reported in paper I.

Combining the MPDI and MPI results at 400 nm with those obtained for single-photon ionization (SPI)6 and single-photon dissociative ionization (SPDI)2 using synchrotron radiation of comparable total excitation energy, a reaction pathway for the dominant MPDI and MPI processes was tentatively proposed2 as shown schematically in Fig. 1. This figure includes a simplified diagram of the NO2 energy levels, at the equilibrium geometry: the NO2(X2A1) (bent) ground state, the NO2+(X1Σg) (linear) and the NO2+(a3B2) (bent) lowest ionic states, and the corresponding Rydberg series [R*(6a1)−1] and [R*(4b2)−1], as well as the lowest dissociation limits for dissociative ionization (NO+(X2Π),O(3P)) and ion-pair formation (NO+(X2Π),O(2P)). In the proposed reaction pathway, the first four-photon step consists of three bound-to-bound transitions exciting the molecule into a valence state strongly coupled with the [R*(6a1)−1 3pσ2B2, v] Rydberg states, with the latter being subsequently ionized into the NO2+(X1Σ+g, ν) manifold while preserving their initial vibrational quantum number labelled ν (representing the set of three quantum numbers ν1, ν2, and ν3). For the dominant MPDI reaction, an additional (fifth) photon is absorbed leading to the dissociation of the vibrationally excited molecular ion. Due to the Franck–Condon (FC) overlap, this process is expected to be strongly dependent on the ion bending angle.

image file: c7cp02057k-f1.tif
Fig. 1 Energy levels of the NO2 ground state and NO2+(X1Σ+g), (a3B2) and (B1B2) states. [R*(6a1)−1] and [R*(4b2)−1] Rydberg series converging to NO2+(X1Σ+g) and NO2+(a3B2) states, respectively, are represented. The reaction mechanism proposed for A and D processes is schematized here, red arrows represent one-photon absorption. The first (NO+ + O) and (NO+ + O) dissociation limits are also indicated. The lowest neutral dissociation channels NO(12Σ+) + O(3P2) and NO(22Π1/2) + O(3P2) lie at 8.596 and 8.757 eV (ref. 1), respectively, which is quasi-resonant with 3-photon excitation at 429 nm and with the [R*(6a1)−1] 3pσ2B2 Rydberg state in the FC region. The {NO(32Π1/2) + O(3P2)} dissociation limit (ref. 7) lies at 9.61 eV, which is quasi resonant with 3-photon excitation at 375 nm.

However, a number of questions remained opened in this study. In particular, the remarkable forward–backward (FW–BW) emission anisotropy observed in the experimental RFPAD – the electron is ejected close to the ion recoil direction – was not well reproduced by the calculations describing the photoionization of the Rydberg [R*(6a1)−1 3pσ2B2, ν] series. As pointed out in paper I, a similar anisotropy was observed in electron–ion femtosecond time-resolved coincidence studies of dissociative multiphoton ionization.7,8 Namely, it was reported at a wavelength of 375 nm7 for a zero delay between the pump and probe beams, and qualitatively attributed to the photoionization of the nascent NO(C2Π1/2) fragment in early stages of the photodissociation,9 as well as at zero time delay in two-colour experiments employing 400–266 nm8 for the major MPDI process attributed to the absorption of three 400 nm and one 266 nm photons leading to ionization into the NO2+(a3B2) dissociative state.

The main goal of the present work is therefore to explore the validity and range of applicability of the reaction pathways we proposed in paper I for the multiphoton ionization of NO2 around 400 nm. For this purpose, we have improved the femtosecond laser system in order to obtain an extended tunability between 375 nm and 430 nm wavelengths, shorter pulses and an increase of the repetition rate from 1 kHz to 3 kHz. The new experiments performed using the VC method enable us to observe the evolution of the different dissociative and non-dissociative ionization processes as a function of the excitation wavelength and indeed to identify two different regions in terms of excitation energy corresponding to different reaction pathways. Furthermore, new calculations have been carried out to extend the work published in paper I by including correlated targets and up to five coupled channels to describe the photoionization step.

Finally, we note that (NO+,O) ion pair formation has also been recorded in the explored photon excitation energy range and confirmed to be a remarkable channel resulting from 4-photon absorption:10 these results will be reported separately.

The paper is organized as follows. In Section 2, the experimental setup and the computational method are briefly described. In Section 3, we report the measured (NO+, e) kinetic energy correlation diagrams (KECDs) and photoelectron spectra for MPDI and MPI, respectively, as well as the ion and electron angular distributions in the laboratory frame, as a function of the photon excitation energy. The measured recoil frame photoelectron angular distributions (RFPADs) for the dominant MPDI process are also reported and analysed based on the methodology developed in paper I. In Section 4, the computed photoelectron asymmetry parameters βe and the molecular and recoil frame photoelectron angular distributions (MFPAD and RFPAD) are discussed. In Section 5, we conclude with a comparison and discussion of the experimental results against the reported calculations. An extended discussion of the theoretical results and their comparison with the measured RFPADs is the subject of a forthcoming paper [under preparation].

2. Methods

2.a. Experimental

The experiments were carried out at the SOFOCKLE laser facility (LIDYL) which is based on a titanium–sapphire system delivering pulses of 1 mJ at 800 nm, with a 3 kHz repetition rate. A hollow fiber filled with argon was used to obtain a spectral broadening between 700 nm and 900 nm, based on the self-phase modulation. The output pulses around 800 nm were recompressed to 10 fs with a series of chirped mirrors. The use of a type I BBO crystal of 300 μm thickness for frequency doubling yielded wavelengths between 375 and 430 nm by varying the phase matching angle. Final pulses were characterized by a spectral width varying between 5 and 12 nm and by a duration of 50 fs (±5 fs) for 385–415 nm wavelengths and of 80 fs (±10 fs) for 375–385 and 415–430 nm wavelengths estimated by autocorrelation measurements as well as by self-referenced spectral interferometry measurements.11 The laser beam is focused at the center of the VC electron–ion double momentum spectrometer by a fused silica lens of f = 44 cm focal length. The intensity of the laser in the interaction region was estimated to vary between ∼4.5 × 1011 W cm−2 and ∼ 9 × 1011 W cm−2, considered here as corresponding to weak field conditions.

These measurements were performed using the CELIMENE set-up described in detail previously.12 CELIMENE, equipped with a supersonic molecular expansion (nozzle ϕ = 70 μm and skimmer ϕ = 1 mm), hosts a VC electron–ion double momentum spectrometer3,4 based on two time and position sensitive detectors (PSDs)13 of ϕ = 80 mm diameter. The NO2 molecular beam was produced by expanding 1.5 bar of a gas mixture (5% NO2 in He). The nozzle was continuously heated at 120 degrees to suppress the N2O4 present at room temperature in the gas mixture. NO2+ and NO+ photoions (i) and photoelectrons (e) were extracted from the interaction region by a dc uniform electric field fixed between 15 and 30 V cm−1 such that a 4π collection of electrons and ions guided towards their respective PSD13 was achieved. For each (i, e) coincident event, the three components of the emission (Vi, Ve) velocity vectors were derived from the measured time of flight (TOF) and impact position of the particle on the PSD.

During the VC experiments, the signal rate was controlled and the mean number of events was kept in the order of 100 coincidences per second, corresponding to 0.03 events per pulse, in order to ensure a true coincidence acquisition mode.

2.b. Theoretical

The calculations reported here for bound and scattering target states were performed using the one-electron basis set described in paper I2 which was based on the standard augmented correlation-consistent polarized valence triple zeta aug-cc-pVTZ basis set14,15 that was then augmented by diffuse functions. In all calculations, the bond length was held constant at its experimental equilibrium16 value R(NO) = 1.1945 Å with a range of ∠ONO angles also being considered. Note that the equilibrium structure of NO2 in its ground state has ∠ONO = 133.85°.

The transition dipole moments for photoionization were computed using correlated target wave functions and included one, two, and five coupled electronic channels. These calculations are extensions of the results reported earlier2 where here we have included the full one-electron basis set described above, extended the calculations to include five coupled channels, and also considered one-channel calculations with a correlated target state. They were performed using the complex Kohn method.17,18

The orbitals used to represent the bound molecular orbitals were obtained from a state-averaged multi-configuration self-consistent field (SA-MCSCF) calculation19,20 which is the same as performed previously, using however the improved one-electron basis set. For calculations for ionization from the [R*(6a1)−1] 3pσ2B2 state, an additional 5b2 orbital was computed by adding a b2 orbital to the active orbital set and three 2B2 states to the state average, but freezing the 14 orbitals obtained in the first SA-MCSCF calculation.

In the scattering calculations, one-channel calculations included only the X1A1 state of the ion, two-channel calculations added the a3B2 ion state, and five-channel calculations included three additional low lying NO2+ ion states (b3A2, A1A2, and B1B2).

Here, we are modelling the dominant MPDI and non-dissociative MPI processes for which the observed photoelectron energy is near 0.5 eV. Thus, in the present calculations we considered mainly photoionization from excited Rydberg states of NO2 which have an IP of ∼2.6 eV relative to the X1A1 state of NO2+: one ∼400 nm photon, with an energy of ∼ 3.1 eV, then results in a photoelectron with a kinetic energy of ∼0.5 eV, when vibrational energy is conserved.

To compare efficiently the computed and measured RFPADs, we exploit the method presented in paper I. We consider the principal component analysis of the recoil-frame azimuthal harmonics (PCA-RFAH) of the total RFPAD intensity using the form (see eqn (16) of paper I2):

image file: c7cp02057k-t1.tif(1)
We have computed the PCA-RFAH expansion for five-photon MPDI for the scheme described in paper I, which is equivalent to a [2,2,2,2] bound-to-bound excitation scheme with a fifth photon leading to ionization. The [2,2,2,2] pathway refers to four type 2 transitions associated with a transition dipole parallel to the O–O axis, which corresponds to transitions between states of symmetry A1 and B2. For simplicity, we assume that the MPDI process can be characterized by two ∠ONO angles. The first is the ∠ONO angle at the time of photoionization, θP, and second angle, θR, gives the structure of the molecule when it fragments, and thus defines the recoil direction. Calculations performed as a function of these angles show that the dynamical parameters characterizing the one-photon ionization of the [R*(6a1)−1] Rydberg states vary strongly with θP. Therefore, both θP and θR influence the resulting RFPADs. In the present study, we focus on the results for the [R*(6a1)−1 3pσ2B2] Rydberg state and θP = 134° and θR = 150°. Other results will be reported and discussed in a forthcoming publication.

3. Experimental results

3.a. Electron–ion kinetic energy correlation

The electron–ion kinetic energy correlation diagrams (KECDs) for the (NO+, e) coincident events corresponding to the dissociative photoionization (MPDI) of NO2 are presented in Fig. 2 at several wavelengths in the 430–375 nm range. The dissociation limits deduced from eqn (2) by energy conservation are also shown in the KECDs:
nhνE(L)D = EKER + Ee(2)
where n is the number of absorbed photons and E(L)D represents the dissociation energy for an asymptotic limit (L).

image file: c7cp02057k-f2.tif
Fig. 2 Kinetic energy correlation diagrams (KECDs) for coincident events (NO+, e) from MPDI at 429 nm (a), 416 nm (b), 400 nm (c), 393 nm (d), 386 nm (e), 383 nm (f), 380 nm (g) and 375 nm (h) wavelengths using a 30 V cm−1 (a–d and f), 40 V cm−1 (e), 20 V cm−1 (g) or 15 V cm−1 (h) extraction field and linearly polarized light along the x axis. The ordinate axis represents the Ee photoelectron (PE) energy, while the abscissa axis is EKER, the total kinetic energy release (KER) of the fragments (KER = ENO+ + EO). The L1[5] and L2[5] black continuous lines represent the ground state and first excited state dissociation limits assuming a five-photon absorption and the L1[4] green continuous line represents the ground state dissociation limit assuming a four-photon absorption. The black dashed lines correspond to the position of the L1[5] dissociation limit when the NO+ fragment is vibrationally excited (v = 2, 4 and 6). The inset in (b) represents a zoom of the A process from MPDI at 416 nm using linearly polarized light along the z axis.

When five photons are absorbed in the 430–375 nm range, two series of dissociative ionization limits can be populated, labelled as L1[5] and L2[5], corresponding to O(3P) + NO+(X1Σ+, v) (E(1)D = 12.38 eV, for v = 0) and O(1D) + NO+(X1Σ+, v) (E(2)D = 14.35 eV) where the vibrational spacing of NO+(X1Σ+, v) is ΔEv ≈ 290 meV. For a four-photon process, the lowest dissociation limit, labelled as L1[4], opens up at wavelengths shorter than 400.5 nm.

The wavelength dependence of the KECDs reveals the existence of two excitation regions: region I (λ ≥ 400.5 nm) and region II (λ ≤ 400.5 nm).

For λ ≥ 400.5 nm (region I), only two broad structures are observed and attributed to MPDI processes due to five-photon absorption to reach L1[5], labelled as A and B, following the notation introduced in paper I, with a major contribution of peak A (Fig. 2(a) and (b)). Their main characteristics, a rather well-defined photoelectron energy for each process, varying between 0.2 and 0.8 eV with a maximum around 0.2–0.4 eV (A), and 1.3–1.5 eV (B), are quite similar to those reported previously2 around 400 nm. The elongation of the A and B structures along the total KER axis shows that the NO+(X1Σ+, v) fragment is produced with an extended ro-vibrational energy distribution. For process A, the peak of the vibrational distribution of the NO+(X1Σ+, v) fragment shifts from v = 2 at 429 nm to v = 6 at higher excitation energies.

The detailed analysis of process A reveals indeed a correlation between the vibrational excitation of the NO+(X1Σ+, v) fragment ion and the one of the NO2+(X1Σg, ν1, ν2, ν3) parent ion produced prior photodissociation-reflected in the Ee energy distribution. This correlation evolves with the excitation wavelength (see insets Fig. 2(b) and (c) for examples). Although neither the NO+(X1Σ+, v) vibrational spacing in the KER distribution (∼290 meV) nor those of the NO2+(X1Σg, ν1, ν2, ν3) state (175 meV, ∼77 meV, and 296 meV, respectively) in the Ee distribution are well resolved, a filtering of events enabling better electron energy resolution shows that ionization takes place into the NO2+(X1Σg) molecular ion, where different vibrationally excited levels in the bending mode and/or in the stretching modes are correlated to a different NO+ vibrational excitation.

At λ = 400 nm, the four-photon excitation energy becomes enough to reach the first dissociation limit L1[4] and a new process (D) appears in the KECD. This process may be interpreted as an ionisation into vibrationally excited NO2+(X1Σg, ν1, ν2, ν3) followed by quasi-resonant dissociation with no excess of energy to the ground state limit L1 (NO+(X2Π), O(3P)). We note that such a reaction necessarily involves an intersystem crossing mechanism. Large spin–orbit coupling values are indeed found in the CASPT2 calculations21 in particular between the NO2+(X1A1) and (a3B2) ionic states.

Process D is observed over the whole 375–400 nm range (region II) and becomes dominant for λ ≤ 380 nm with a significant increase of the total MPDI probability, from ∼65% in the 430–400 nm range up to ∼90% of the total PI probability at λ = 375 nm (see the ESI). At λ ≈ 375 nm, a small amount of excess energy is released into the translational energy of the fragments (KER ≤ 0.3 eV).

3.b. Photoelectron energy spectra

Fig. 3 displays the PE spectra for the MPDI channel compared to those measured for non-dissociative MPI at the same wavelengths and attributed to PI into the NO2+(X1Σg) ionic state. The amplitudes of peaks A (MPDI) and α (MPI) are adjusted to facilitate the comparison of their energy profile. In region I (430 ≤ λ ≤ 400 nm, Fig. 3(a)–(c)), both PE spectra show a dominant structure corresponding to processes A for MPDI and α for MPI, observed at similar values of the photoelectron energy Ee but with a different energy width, and a second peak attributed to process B for MPDI and process β for non-dissociative MPI. These remarkable similarities throughout the explored energy range support a common interpretation of the PI reactions, as proposed in paper I. Three-photon absorption to an excited valence state strongly mixed with a [R*(6a1)−1] Rydberg state followed by one-photon ionization to the NO2+(X1Σg, ν1, ν2, ν3) state leads to processes α and β, while subsequent dissociation after absorption of a fifth photon leads to processes A and B.
image file: c7cp02057k-f3.tif
Fig. 3 Photoelectron energy spectra for (NO+, e) MPDI events corresponding to the KECDs displayed in Fig. 1 (blue line) and (NO2+, e) MPI events (red line) at the same wavelengths. The maxima of peaks A (MPDI) and α (MPI) are adjusted to favour the detailed comparison of their energy profile. The branching ratio between MPDI and MPI is of the order of 60% for longer wavelengths λ > 400 nm and increases up to 90% when λ varies between 400 and 375 nm (see text). The two structures labelled as γ and δ are assigned to ν1 symmetric stretching vibrational excitation.

The widths associated with processes A (350 meV FWHM) and α (150 meV FWHM) reflect a different vibrational distribution, although centred around a similar Ee value, of the NO2+(X1Σg, ν1, ν2, ν3) ion responsible of the MPDI and MPI, respectively. Process α appears to be more selective in terms of internal excitation than process A (MPDI).

In region II (375 ≤ λ ≤ 400 nm, Fig. 3(d)–(f)), two trends can be identified in the photoelectron spectra characterized by the position of the E(4)B binding energy with respect to the E(1)D dissociation limit, where the binding energy is defined as the difference between the excitation energy (with n = 4 here) and the photoelectron energy: E(n)B = nhνEe. For 383 ≤ λ ≤ 400 nm, processes A and α are still observed at a similar Ee position as illustrated in Fig. 3(d), and they correspond to E(4)B < E(1)D, while process D assigned to four-photon MPDI corresponds to E(4)BE(1)D. In contrast, for 375 ≤ λ ≤ 383 nm, the condition E(4)BE(1)D is true for all the identified processes. Process D which becomes the dominant structure in the PE spectrum, corresponds now to a Ee value close to that of process α, while process A vanishes (see the ESI). At the highest photon energy, λ = 375 nm (Fig. 3(h)), the relative contribution of (NO2+, e) MPI is strongly reduced (10%) and it includes a new contribution through a second resolved peak, assigned to the excitation of the ν3 asymmetric stretching vibrational mode.

The contribution of processes β and B amounts to ∼15–20% of the MPI and MPDI channels, respectively, for λ values around 383–400 nm and vanishes for λ ≤ 380 nm.

Fig. 4 presents the dependence on the photon energy (eV) of the peak position in the PE spectrum for processes A, D and α as well as the corresponding fit by linear regression. It shows that for the MPDI process A and MPI process α, in the whole explored λ range the peak shift is well described by a straight line of slope close to 1, i.e. it varies as the energy of one absorbed photon, with the excess energy being therefore transferred into internal energy of the ionic state. This behaviour is the signature of a reaction pathway involving the PI of a Rydberg state converging to the NO2+(X1Σg) state,2 which preserves the Evib internal excitation of the molecule.22 For process D, the results are shown for 375 ≤ λ ≤ 383 nm, where the energy shift is also close to the energy of one photon absorbed.

image file: c7cp02057k-f4.tif
Fig. 4 Position of the intensity maxima in the PE spectra as a function of the one-photon excitation energy for (NO+, e) MPDI process A (blue), process D (purple) and (NO2+, e) MPI process α (red). The experimental data are represented by circles (A, α) or triangles (D) and the results of a linear fitting procedure by continuous lines (slope ≈ 1.2; r = 0.997 for A and α and 0.937 for D).

3.c. Laboratory frame angular distributions

The laboratory frame angular distribution of both ion fragments and photoelectrons emitted in a n-photon MPDI process can be expanded as:
image file: c7cp02057k-t2.tif(3)
where β2k are the asymmetry parameters and P2k (cos[thin space (1/6-em)]χ) the Legendre polynomials.

The measured β2k,NO+ asymmetry parameters for process A are reported in Table 1 at different wavelengths in the explored range. The NO+ ion fragment angular distributions are characterized by two or three asymmetry parameters, consistent with the absorption of at least three photons prior to the dissociation step. The positive and significant values of β2k,NO+ parameters reflect the strong alignment of the NO+ recoil direction along the polarization axis, remaining quite stable as a function of the excitation wavelength.

Table 1 β 2k asymmetry parameters (±0.1) characterizing the angular distribution in the laboratory frame for ions fragments resulting from the A MPDI process, for measurements performed using H linearly polarized light. The decrease in β2k observed at λ = 393 nm may be due to the presence of a resonance inducing a depolarization of the fragment photoemission
  λ (nm)
429 416 405 393 383 380
β 2 2.4 2.42 2.35 1.80 2.36 2.01
β 4 1.2 1.15 1.10 0.50 1.08 0.90
β 6 0.2 0.28 0.20 −0.08 0.20 −0.03

Referring to the reaction pathway proposed in paper I, the ion fragment angular distribution in the n-photon MPDI process results from the (n − 1) one-photon bound-to-bound transitions between near resonant states, plus the one-photon ionization step. Using here a similar representation for the bound-to-bound transitions depending on the orientation of the transition dipole moments,2,10 A process can be described by a reaction scheme labelled as [2,2,2,2] which involves four bound-to-bound transitions of type-2 with the molecule at a geometry close to equilibrium.

Extraction of the NO+ angular distribution for process D is subject to larger uncertainties due to the small emission velocities of the ion fragments, which results in a narrow position and TOF distributions using the extraction fields required for a complete collection of all processes. The NO+ angular distribution is there characterized by two asymmetry parameters varying around β2 ≈ 1.5 and β4 ≈ 0.5, rather consistent with a three-photon absorption pathway labelled as [2,2,2].

For the A (MPDI) and α (MPI) processes, the photoelectron angular distributions are mainly characterized by a single β2k,e asymmetry parameter, which supports the description of a reaction pathway involving the ionization of a Rydberg state.2Fig. 5 displays the evolution of β2,e as a function of the excitation wavelength for these two processes which reveals two distinct behaviours. For E(4)BE(1)D, processes A and α are characterized by quite different β2,e values, around 0.9 for the A process and around 0.4 for the α process, which remain rather constant as a function of the excitation wavelength (for λ ≥ 385 nm). This difference in β2,e values between A and α for a PI reaction involving the same electronic state can be interpreted as the reflection of the contribution of two geometries in the ionization reaction (as shown later in Section 4) and thus in the populated NO2+(X1Σg, ν1, ν2, ν3) manifold, leading either to MPDI (bent case) after absorption of the fifth photon or to MPI (linear case).

image file: c7cp02057k-f5.tif
Fig. 5 Asymmetry parameter β2,e characterizing the photoelectron angular distribution in the laboratory frame as a function of the excitation wavelength for MPDI process A (blue), process D (purple) and MPI process α (red). Statistical error bars are about ±0.1.

For E(4)BE(1)D, the β2,e values for A, D and α processes are now similar and increase from ∼0.6 up to ∼0.9 with the excitation energy (for λ ≤ 385 nm). We note that at the shorter wavelengths, the β4,e parameter amounts to −0.2 for processes D and α. At λ = 375 nm, the second peak resolved in the MPI photoelectron spectrum (Fig. 3h) and assigned to the excitation of the ν3 asymmetric stretching vibrational mode corresponds to larger β2,e parameters (∼1.2 for ν3 = 1 vs. 0.7 for ν3 = 0).

3.d. Recoil frame angular distributions

Fig. 6(a–e) presents the RFPADs measured for MPDI process A at several excitation wavelengths, selecting only the dominant parallel orientation. For the whole range of wavelengths, RFPADs for a perpendicular orientation have an almost zero intensity, consistent with the [2,2,2,2] “parallel” reaction pathway. The remarkable FW–BW asymmetry reflecting the favoured photoelectron emission in a direction around the NO+ ion recoil axis is shown to be a striking robust feature in the whole explored range of excitation energies. Some differences are nevertheless observed in the shape of the RFPAD: the “conical” angle which characterizes the photoemission lobe of the emitted electron is found to increase from θe ∼ 10° to about 35° when the wavelength decreases from 429 nm to 380 nm. We note that two lobes around θe = 30° are observed at 400 nm and lower wavelengths, similar to the results reported in paper I at 397 nm.
image file: c7cp02057k-f6.tif
Fig. 6 RFPADs measured (in arb. units) for MPDI process A (a–e) and process D (f and g) at different excitation wavelengths using linearly polarized light and for an orientation of the NO+ fragment recoil axis parallel to the polarization axis (χ = 0°).

The RFPADs for process D at λ = 380 nm and 375 nm are also reported in Fig. 6(f and g). The FW–BW asymmetry is recovered, even though the asymmetry is stronger at higher photon energies. At 375 nm, two lobes for θe emission angles around 40° are observed in fair agreement with previous RFPADs measured by Davies and co-workers.7 We note that for this process, the perpendicular component amounts to about 20% contrary to the findings for process A, thus RFPADs for other orientations than the parallel one also contain information on the PI process.

In paper I, we have introduced the method of the principal component analysis (PCA) based on RFPAD development in terms of RK(χ, θe) recoil frame azimuthal harmonics (RFAHs). The PCA allows us to extract the fingerprints for each RFAH of order K in the RFPAD expansion in ϕe. Therefore, it permits an efficient quantitative comparison of the experimental results with the calculations as well as, comparisons between different experiments or calculations. We report in Fig. 7, the experimental results for three selected reactions: process A at 416 nm and 383 nm, and process D at 380 nm, focusing on the lowest K orders i.e., on the RK=0(χ, θe) and RK=1(χ, θe) RFAHs. Here, we display the J(K)uλ(χ) and G(K)uλ(θe) angular expansions based on the unitary eigenvectors of the covariance matrix, ordered and weighted by the Λλ eigenvalues, limited to the first and second orders (λ = 1, 2). In the following sections, we omit the u index for sake of simplicity. In this description, the first order J(K)λ=1(χ) functions describe the main features of the reaction pathway for the most effective θe MF angular profile, while the G(K)λ=1(θe) functions account for those of the MF emission profile, for the most effective χ recoil angle distribution.

image file: c7cp02057k-f7.tif
Fig. 7 PCA-RFAH J(0)λ=1,λ=2(χ) (a), J(1)λ=1,λ=2(χ) (b), G(0)λ=1,λ=2(θe) (c) and G(1)λ=1,λ=2(θe) (d) resulting from the analysis of the R0(χ, θe) (a–c) and R1(χ, θe) (b–d) RFAHs corresponding to process A at λ = 416 nm (solid line) and λ = 383 nm (dashed line), and to process D at λ = 380 nm (dotted line), compared to those from the one-channel calculation for the R*[(6a1)−1] 3pσ2B2 Rydberg state with correlated targets considering the [2,2,2,2] reaction pathway and the chosen (θP = 134°, θR = 150°) angles (dash-dotted line).

Fig. 7(a and c) show that RK=0(χ, θe) is indeed mainly characterized by the first order J(0)λ=1(χ) and G(0)λ=1(θe) functions. J(0)λ=1(χ) has a similar shape for both processes A and D in the whole range of energies, close to the measured photoion angular distribution in the laboratory frame, consistent with a [2,2,2,2] or [2,2,2] reaction pathway, respectively. The G(0)λ=1(θe) function reflects the strong FW–BW asymmetry observed. For process A, a single maximum at 0° is observed, reflecting the FW peaked shape of the RFPAD for a parallel orientation. For process D, the FW–BW asymmetry is structured differently, with a relative maximum at 30° reflecting the two observed lobes in the corresponding RFPAD. For RK=1(χ, θe), J(1)λ=1(χ), antisymmetric relative to 90°, remains stable as a function of the process or the excitation energy. G(1)λ=1(θe) also displays a similar shape observed for both A and D processes in the whole range of excitation energies, however the intensity of the maximum at 45° varies, as well as the observed minimum around 15°.

4. Theoretical results

Theoretical results are presented in terms of the β2k,e asymmetry parameters and RFPAD observables for five-photon MPDI, in order to probe the proposed reaction scheme. The angular distribution of the ion fragments is interpreted as a signature of the orientation of the transition moment for the three or four-photon bound-to-bound excitation pathway plus the photoionization step, as discussed earlier.

PI calculations have been performed considering different parameters: (i) the single-configuration or correlated description of the NO2+ target (ii) the number of channels implied in the scattering process (iii) the electronic character of the ionized [R*(6a1)−1] 3pπ2B1, [R*(6a1)−1] 3pπ2A1 and the [R*(6a1)−1] 3pσ2B2 Rydberg states, as well as (iv) a set of (θP) and (θR) ∠ONO PI and recoil angles, which all influence the photoelectron angular distributions. Here, we consider the PI of the [R*(6a1)−1] 3pσ2B2 Rydberg state, and focus on the effect of electronic correlation in the ground state of NO2+ which is dominant, and it is found to be more important than the dynamical electronic correlation included when the calculation is extended from one-channel to five-channel – involved in the scattering process – [see e.g. discussion in ref. 23], except in the vicinity of autoionizing resonances. Thus, one-channel calculations with correlated targets are a good representation of the photoionization step and will be the primary type of calculation considered here.

The β2,e photoelectron asymmetry parameters computed for the one-photon PI of this 3pσ Rydberg state as well as taking into account the previous three-photon absorption considering a [2,2,2] pathway are reported in Fig. 8 as a function of the θP angle, selecting here the condition θP = θR. A strong dependence of β2,e on θP the angle is observed, with values varying from 1.2 at smaller θP angles to about 0 or slightly negative values near 180°, comparable to the difference in β2,e observed for the α MPI and A MPDI processes, assigned to quasi-linear or bent geometries of the NO2+ molecular ion in the proposed reaction scheme, respectively. This significant dependence indeed features the role of vibronic coupling in the NO2+(X1A1, ν1, ν2, ν3) ionic state i.e., a coupling between electronic and nuclear vibrational motion. This occurrence when ascribed to an intrachannel effect is referred to as “type (a)” vibronic interaction by Herzberg24,25 of Herzberg–Teller vibronic coupling.26 We remark that β4,e and β6,e computed values (not shown here) are almost zero at the ∠ONO angles considered here in agreement with the photoelectron angular distributions measured for the α and A processes mostly characterized by a single β2,e.

image file: c7cp02057k-f8.tif
Fig. 8 Photoelectron β2,e asymmetry parameter as a function of the ONO bending angle at the time of ionization (θP) for the selected R*[(6a1)−1] 3pσ2B2 Rydberg state in the Hartree–Fock calculation as well as in the one-channel and two-channel calculations with correlated targets considering the [2,2,2] reaction pathway prior to photoionization.

Fig. 8 also illustrates the key feature of the PI calculations mentioned above, i.e., the fact that the one-channel βe computed using Hartree–Fock type wave functions are significantly different from all results obtained using correlated targets,2 whether the latter correspond to one-channel or few-channel scattering calculations. The most important source of the observed qualitative differences among computed observables is the fact that the Hartree–Fock wave function and the configuration interaction (CI) wave function for the NO2+ ground state correspond to significantly different electronic density distributions. This will be discussed in more detail in the forthcoming publication.

image file: c7cp02057k-f9.tif
Fig. 9 One-channel correlated computed MFPADs (in Mb sr−1) for one-photon PI of NO2 3pσ2B2 [R(6a1)−1] Rydberg states (θP = 134°) for three main orientations of the polarization axis as shown (see text) (a–c) and the corresponding χ = 0° RFPAD for a recoil angle θR = 150° (d).

In Fig. 9, we display the computed MFPADs for the three most relevant transitions (type 3 (zMF, (a)), type 2 (yMF, (b)) and type 4 (parallel to an NO bond, (c))) in one-photon PI of this [R(6a1)−1] 3pσ2B2 state, computed for θP ≈ 134° (a–c) (one-channel correlated calculation), as well as the RFPAD corresponding to a polarization axis parallel to the recoil direction (χ = 0°), for a recoil angle θR ≈ 150° (d). The RFPAD is obtained after integration over the γR Euler angle of the MFPAD expressed in the R-MF reference frame, whose z axis is parallel to the NO+ ion fragment recoil velocity [see paper I]. Fig. 9, compared with Fig. 11 of paper I, illustrates the major differences at the level of MFPADs between the HF and the correlated one-channel PI calculations for the θP ≈ 134° PI angle, which lead in particular to a different interpretation of the observed FW–BW recoil frame photoemission anisotropy. In the correlated calculation, PI is strongly favoured for the 3pσb2 → kb2 type 3 transition which corresponds to a well-structured MFPAD, while the 3pσb2 → ka1 type 2 transition, which is dominant in the HF calculation, is here significantly reduced and displays a blurred structure MFPAD. In the present case, the RFPAD asymmetry displayed in Fig. 9(d) originates mostly from the contribution of the dominant type 3 transition to the MFPAD associated with a type 4 transition, where the transition moment is parallel to the NO breaking bond. Combined with a [2,2,2,2] pathway, a similar FW–BW anisotropy is nevertheless preserved in the RFPAD.

5. Discussion and conclusion

We focus the discussion of the reported results on the main processes, A and D (MPDI) and α (MPI) observed following excitation at wavelengths between 430 and 375 nm, which reveal two different excitation regions. In region (I), 430 ≤ λ ≤ 400 nm, a progressive evolution of the A and α processes attributed to different components of the PI to the NO2+ (X1Σg) state is observed. For wavelengths between 375 ≤ λ ≤ 400 nm (region (II)), a new four-photon process D is observed in which the branching ratio increases when the wavelength decreases becoming dominant for wavelengths λ ≤ 386 nm.

The measured RFPADs for A and then D processes show that the remarkable electron emission anisotropy, strongly favouring photoemission in the NO+ recoil direction, parallel to the polarization axis, or at small θe emission angles (θe ≤ 30°), is a fingerprint of MPDI in the whole explored wavelength range. The comparison between experimental and theoretical RFPADs leads us to the conclusion that, in the major part of the explored energy range, the [R*(6a1)−1, 3pσb2] Rydberg state is the most likely populated excited state after three-photon absorption, with preferred geometries around (θP = 134°, θR = 150°) at the moment of PI and dissociation, respectively. Furthermore, this comparison emphasizes the importance of electronic correlation of the NO2+(X1Σg) ground state, which plays a major role in the description of the PI process. The calculation for the PI of the [R*(6a1)−1, 3pσb2] Rydberg state reproduces the values of the β2,e asymmetry parameters measured for MPDI and MPI processes, if the α MPI process is assigned to the PI of the 3pσb2 Rydberg state, at a geometry closer to the linear conformation θP ≈ 180°.

The different reaction mechanisms proposed in paper I2 are shown in Fig. 1 and discussed below in the light of the new experimental and theoretical results presented herein.

In region (I), the results obtained for the whole explored range of wavelengths are quite robust and support the validity of the reaction pathway proposed for the excitation with λ ≈ 400 nm2. In this scheme, the three-photon absorption excites the molecule to a valence state strongly coupled to the [R*(6a1)−1] Rydberg series, favouring the [R*(6a1)−1] 3pσ2B2 state in an excited vibrational state with a large degree of bending mode excitation. The absorption of a fourth photon by these Rydberg states bringing the molecule to the ionization continua between 11.5 and 12.4 eV results in photoionization into the NO2+(X1Σg, v1, v2, v3) manifold. The potential surfaces of the [R*(6a1)−1] Rydberg states closely resemble that of the ionic state NO2+(X1Σg), to which these states converge leading to the conservation of the vibrational quantum numbers during ionization, a fingerprint of the PI of Rydberg states.22 This mechanism is supported by the single-photon dependence of the peak energies in the photoelectron spectrum associated with A and α processes, as a function of the excitation wavelength (Fig. 3).

This complex ionization mechanism involving an important vibronic coupling, consistent with the reported calculations, may create a bimodal distribution in the NO2+(X1Σg, v1, v2, v3) population, associated with two dominant geometries of the molecule: linear and bent, characterized by different values of the photoelectron asymmetry parameter β2,e. In this scheme, the selective photodissociation of preferably bent NO2+(X1Σg, v1, v2, v3) molecular ions, by the fifth photon absorption leads to the population of dissociative excited states of NO2+, such as the NO2+(A1A1 or B1B2) states, while the population associated with a linear geometry remains in the NO2+ ground state. It thereby acts thus as a sorting between these two populations. The dissociation of the A1A1 or B1B2 excited state to the L1 limit, for which the system is in a triplet spin state, necessarily occurs through intersystem crossing mechanism,21 which is expected to occur on a time scale shorter than the molecular rotation or bending, preserving thus the validity of the axial recoil approximation usually demanded by the VC method. The stability of the two β2,e values characterizing the MPDI and non-dissociative MPI in the entire region (I) supports this proposed reaction mechanism for the whole excitation energy range. For the A MPDI process, the translational versus internal energy sharing of the fragments, leading to an extended v = 0–6 vibrational distribution of the NO+1X) molecular ion is then attributed to the photodissociation step induced by the fifth photon absorption.

In region (II), λ < 400 nm, the total excitation energy corresponding to a four-photon absorption is higher than the adiabatic MPDI threshold, located at 12.38 eV (L1). The reaction mechanism involving the ionization of the [R*(6a1)−1, 3pσb2] Rydberg state to the NO2+(X1Σg), preserving the Evib internal excitation, i.e. the vibrational quantum number in the ionization step, can also be proposed to interpret the MPDI process A and MPI process α. For the four-photon MPDI process D, a similar scheme applies for wavelengths λ ≤ 383 nm, where conservation of vibrational excitation of the [R*(6a1)−1, 3pσb2] Rydberg state in the ionization step leads to the population of the NO2+(X1Σg, v1, v2, v3) manifold around the NO+1X) + O(3P) dissociation threshold, or directly into the dissociative continuum, at shorter λ values. The probability for the A process becomes negligible for an E(4)B energy above the E(1)D dissociation energy. The characteristics of the MPI process α, similar to those of the MPDI process A for E(4)BE(1)D, become very similar to those of process D for E(4)BE(1)D.

A remarkably similar value of the β2,e asymmetry parameter (β2,e ∼ 0.9) characterizes the three processes A, α and D in region (II). This suggests that both the non-dissociative and dissociative ionization reactions now involve the same population in terms of vibrational states of the NO2+ (X1Σg, v1, v2, v3) ion. This may then correspond either to a single geometry of the molecule, or to a composite population involving a few geometries, but no longer discriminated in the photodissociation step.

At shorter wavelengths, in particular at λ = 375 nm, other Rydberg states such as [R*(6a1)−1] 3pπ2A1, may be involved in the PI step associated with process D as will be discussed in the forthcoming publication. Moreover, we remark that the reaction pathway proposed here at λ = 375 nm does not contradict the interpretation by Davies et al.7 in their time-resolved study. In such a scheme, at Δt = 0 the dominant contribution would be the ionization of the invoked Rydberg state (including possibly a nascent dissociation of the NO2 excited state), while at longer pump–probe delays dissociation of the Rydberg state leading to the production of the NO(C2Π1/2) fragment occurs prior to the second pulse, which will then act as a probe of the dissociation process via ionization of the NO fragment.7,9 Their determined dissociation time9 around 500 fs is indeed coherent with the lifetimes around 600 fs for [R*(6a1)−1] Rydberg states lying around 9.3 eV previously reported by both López-Martens et al.27 and Cireasa et al.28 Such lifetimes support our proposed reaction pathways: photodissociation after three-photon absorption within the shorter duration of our laser pulse is indeed not possible.

Complementary theoretical results will be reported in a forthcoming publication, which will also address the influence of the stretching vibrational excitation in the photoionization of NO2 Rydberg states. Further investigation of the proposed reaction scheme would also benefit from femtosecond pump–probe experiments at a shorter time scale, where one VUV photon excites the [R*(6a1)−1] NO2 Rydberg states around 9.3 eV, whose relaxation can be probed by a delayed 400 nm femtosecond laser pulse.


The authors gratefully acknowledge K. Veyrinas, N. Saquet, L. Journel and O. Gobert for their contribution to experiments and S. Lupone from ISMO for his technical support. This work was supported by the “Fondation de cooperation scientifique Digitéo-Triangle de la physique” (project: 2010-078T-High Rep Image) and by a public grant from the “Laboratoire d'Excellence Physics Atoms Light Matter” (LabEx PALM) overseen by the French National Research Agency (ANR) as part of the “Investissements d'Avenir” program (reference: ANR-10-LABX-0039-PALM). The work at Texas A&M University was supported by the United States Department of Energy, Office of Science, Basic Energy Science, Geoscience, and Biological Divisions, under Award No. DE-SC0012198. The support of the Robert A. Welch Foundation (Houston, Texas) under Grant No. A-1020 is also acknowledged.

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Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp02057k
These authors have equally contributed to the work.

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