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}
^{a}Institut des Sciences Moléculaires d'Orsay (ISMO), CNRS, Université Paris-Sud, Université Paris-Saclay, F-91405 Orsay, France
^{b}Departamento 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
^{c}LIDYL, CEA, CNRS, UMR 9222, Université Paris-Saclay CEA Saclay, bât. 522, F-91191 Gif-sur-Yvette, France
^{d}Laboratoire de Chimie Physique Matière et Rayonnement, Université Pierre et Marie Curie et CNRS, 75005 Paris, France
^{e}Department of Chemistry, Texas A&M University, College Station, TX 77840, USA
First published on 27th July 2017
We investigate the multiphoton ionization of NO_{2} 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*(6a_{1})^{−1}, 3pσ] Rydberg state, in the NO_{2} multiphoton excitation and photoionization. These new results support our previous assumption that different bent and linear geometries of the NO_{2}^{+}(X^{1}Σ_{g}) 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.
In a previous paper^{2} referred to as paper I, we reported the experimental results for multiphoton dissociative ionization (MPDI) and non-dissociative multiphoton ionization (MPI) of NO_{2} 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 (NO_{2}^{+}, 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}(θ_{e}, ϕ_{e}, χ), where χ is the polar angle of the fragment ion recoil direction relative to the light polarization axis and θ_{e} and ϕ_{e} 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 C_{2v} 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 proposed^{2} as shown schematically in Fig. 1. This figure includes a simplified diagram of the NO_{2} energy levels, at the equilibrium geometry: the NO_{2}(X^{2}A_{1}) (bent) ground state, the NO_{2}^{+}(X^{1}Σ_{g}) (linear) and the NO_{2}^{+}(a^{3}B_{2}) (bent) lowest ionic states, and the corresponding Rydberg series [R*(6a_{1})^{−1}] and [R*(4b_{2})^{−1}], as well as the lowest dissociation limits for dissociative ionization (NO^{+}(X^{2}Π),O(^{3}P)) and ion-pair formation (NO^{+}(X^{2}Π),O^{−}(^{2}P)). 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*(6a_{1})^{−1} 3pσ^{2}B_{2}, v] Rydberg states, with the latter being subsequently ionized into the NO_{2}^{+}(X^{1}Σ^{+}_{g}, ν) manifold while preserving their initial vibrational quantum number labelled ν (representing the set of three quantum numbers ν_{1}, ν_{2}, and ν_{3}). 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.
Fig. 1 Energy levels of the NO_{2} ground state and NO_{2}^{+}(X^{1}Σ^{+}_{g}), (a^{3}B_{2}) and (B^{1}B_{2}) states. [R*(6a_{1})^{−1}] and [R*(4b_{2})^{−1}] Rydberg series converging to NO_{2}^{+}(X^{1}Σ^{+}_{g}) and NO_{2}^{+}(a^{3}B_{2}) 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(1^{2}Σ^{+}) + O(^{3}P_{2}) and NO(2^{2}Π_{1/2}) + O(^{3}P_{2}) 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*(6a_{1})^{−1}] 3pσ^{2}B_{2} Rydberg state in the FC region. The {NO(3^{2}Π_{1/2}) + O(^{3}P_{2})} 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*(6a_{1})^{−1} 3pσ^{2}B_{2}, 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 nm^{7} for a zero delay between the pump and probe beams, and qualitatively attributed to the photoionization of the nascent NO(C^{2}Π_{1/2}) fragment in early stages of the photodissociation,^{9} as well as at zero time delay in two-colour experiments employing 400–266 nm^{8} for the major MPDI process attributed to the absorption of three 400 nm and one 266 nm photons leading to ionization into the NO_{2}^{+}(a^{3}B_{2}) 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 NO_{2} 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 β_{e} 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].
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 spectrometer^{3,4} based on two time and position sensitive detectors (PSDs)^{13} of ϕ = 80 mm diameter. The NO_{2} molecular beam was produced by expanding 1.5 bar of a gas mixture (5% NO_{2} in He). The nozzle was continuously heated at 120 degrees to suppress the N_{2}O_{4} present at room temperature in the gas mixture. NO_{2}^{+} 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 PSD^{13} was achieved. For each (i, e) coincident event, the three components of the emission (V_{i}, V_{e}) 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.
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 earlier^{2} 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) calculation^{19,20} which is the same as performed previously, using however the improved one-electron basis set. For calculations for ionization from the [R*(6a_{1})^{−1}] 3pσ^{2}B_{2} state, an additional 5b_{2} orbital was computed by adding a b_{2} orbital to the active orbital set and three ^{2}B_{2} 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 X^{1}A_{1} state of the ion, two-channel calculations added the a^{3}B_{2} ion state, and five-channel calculations included three additional low lying NO_{2}^{+} ion states (b^{3}A_{2}, A^{1}A_{2}, and B^{1}B_{2}).
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 NO_{2} which have an IP of ∼2.6 eV relative to the X^{1}A_{1} state of NO_{2}^{+}: one ∼400 nm photon, with an energy of hν ∼ 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 I^{2}):
(1) |
nhν − E^{(L)}_{D} = E_{KER} + E_{e} | (2) |
When five photons are absorbed in the 430–375 nm range, two series of dissociative ionization limits can be populated, labelled as L_{1}[5] and L_{2}[5], corresponding to O(^{3}P) + NO^{+}(X^{1}Σ^{+}, v) (E^{(1)}_{D} = 12.38 eV, for v = 0) and O(^{1}D) + NO^{+}(X^{1}Σ^{+}, v) (E^{(2)}_{D} = 14.35 eV) where the vibrational spacing of NO^{+}(X^{1}Σ^{+}, v) is ΔE_{v} ≈ 290 meV. For a four-photon process, the lowest dissociation limit, labelled as L_{1}[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 L_{1}[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 previously^{2} around 400 nm. The elongation of the A and B structures along the total KER axis shows that the NO^{+}(X^{1}Σ^{+}, v) fragment is produced with an extended ro-vibrational energy distribution. For process A, the peak of the vibrational distribution of the NO^{+}(X^{1}Σ^{+}, 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^{+}(X^{1}Σ^{+}, v) fragment ion and the one of the NO_{2}^{+}(X^{1}Σ_{g}, ν_{1}, ν_{2}, ν_{3}) parent ion produced prior photodissociation-reflected in the E_{e} energy distribution. This correlation evolves with the excitation wavelength (see insets Fig. 2(b) and (c) for examples). Although neither the NO^{+}(X^{1}Σ^{+}, v) vibrational spacing in the KER distribution (∼290 meV) nor those of the NO_{2}^{+}(X^{1}Σ_{g}, ν_{1}, ν_{2}, ν_{3}) state (175 meV, ∼77 meV, and 296 meV, respectively) in the E_{e} distribution are well resolved, a filtering of events enabling better electron energy resolution shows that ionization takes place into the NO_{2}^{+}(X^{1}Σ_{g}) 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 L_{1}[4] and a new process (D) appears in the KECD. This process may be interpreted as an ionisation into vibrationally excited NO_{2}^{+}(X^{1}Σ_{g}, ν_{1}, ν_{2}, ν_{3}) followed by quasi-resonant dissociation with no excess of energy to the ground state limit L_{1} (NO^{+}(X^{2}Π), O(^{3}P)). We note that such a reaction necessarily involves an intersystem crossing mechanism. Large spin–orbit coupling values are indeed found in the CASPT2 calculations^{21} in particular between the NO_{2}^{+}(X^{1}A_{1}) and (a^{3}B_{2}) 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).
Fig. 3 Photoelectron energy spectra for (NO^{+}, e) MPDI events corresponding to the KECDs displayed in Fig. 1 (blue line) and (NO_{2}^{+}, 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 ν_{1} 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 E_{e} value, of the NO_{2}^{+}(X^{1}Σ_{g}, ν_{1}, ν_{2}, ν_{3}) 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} = nhν − E_{e}. For 383 ≤ λ ≤ 400 nm, processes A and α are still observed at a similar E_{e} 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)}_{B} ≈ E^{(1)}_{D}. In contrast, for 375 ≤ λ ≤ 383 nm, the condition E^{(4)}_{B} ≥ E^{(1)}_{D} is true for all the identified processes. Process D which becomes the dominant structure in the PE spectrum, corresponds now to a E_{e} 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 (NO_{2}^{+}, e) MPI is strongly reduced (10%) and it includes a new contribution through a second resolved peak, assigned to the excitation of the ν_{3} 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 NO_{2}^{+}(X^{1}Σ_{g}) state,^{2} which preserves the E_{vib} 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.
(3) |
The measured β_{2k,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 β_{2k,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.
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 β_{2} ≈ 1.5 and β_{4} ≈ 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 β_{2k,e} asymmetry parameter, which supports the description of a reaction pathway involving the ionization of a Rydberg state.^{2}Fig. 5 displays the evolution of β_{2,e} as a function of the excitation wavelength for these two processes which reveals two distinct behaviours. For E^{(4)}_{B} ≤ E^{(1)}_{D}, processes A and α are characterized by quite different β_{2,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 β_{2,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 NO_{2}^{+}(X^{1}Σ_{g}, ν_{1}, ν_{2}, ν_{3}) manifold, leading either to MPDI (bent case) after absorption of the fifth photon or to MPI (linear case).
For E^{(4)}_{B} ≥ E^{(1)}_{D}, the β_{2,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 β_{4,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 ν_{3} asymmetric stretching vibrational mode corresponds to larger β_{2,e} parameters (∼1.2 for ν_{3} = 1 vs. 0.7 for ν_{3} = 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 θ_{e} 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 R_{K}(χ, θ_{e}) recoil frame azimuthal harmonics (RFAHs). The PCA allows us to extract the fingerprints for each RFAH of order K in the RFPAD expansion in ϕ_{e}. 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 R_{K=0}(χ, θ_{e}) and R_{K=1}(χ, θ_{e}) RFAHs. Here, we display the J^{(K)}_{u−λ}(χ) and G^{(K)}_{u−λ}(θ_{e}) angular expansions based on the unitary eigenvectors of the covariance matrix, ordered and weighted by the Λ_{λ} 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 θ_{e} MF angular profile, while the G^{(K)}_{λ=1}(θ_{e}) functions account for those of the MF emission profile, for the most effective χ recoil angle distribution.
Fig. 7(a and c) show that R_{K=0}(χ, θ_{e}) is indeed mainly characterized by the first order J^{(0)}_{λ=1}(χ) and G^{(0)}_{λ=1}(θ_{e}) 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}(θ_{e}) 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 R_{K=1}(χ, θ_{e}), 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}(θ_{e}) 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°.
PI calculations have been performed considering different parameters: (i) the single-configuration or correlated description of the NO_{2}^{+} target (ii) the number of channels implied in the scattering process (iii) the electronic character of the ionized [R*(6a_{1})^{−1}] 3pπ^{2}B_{1}, [R*(6a_{1})^{−1}] 3pπ^{2}A_{1} and the [R*(6a_{1})^{−1}] 3pσ^{2}B_{2} Rydberg states, as well as (iv) a set of (θ_{P}) and (θ_{R}) ∠ONO PI and recoil angles, which all influence the photoelectron angular distributions. Here, we consider the PI of the [R*(6a_{1})^{−1}] 3pσ^{2}B_{2} Rydberg state, and focus on the effect of electronic correlation in the ground state of NO_{2}^{+} 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 β_{2,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 θ_{P} angle, selecting here the condition θ_{P} = θ_{R}. A strong dependence of β_{2,e} on θ_{P} the angle is observed, with values varying from 1.2 at smaller θ_{P} angles to about 0 or slightly negative values near 180°, comparable to the difference in β_{2,e} observed for the α MPI and A MPDI processes, assigned to quasi-linear or bent geometries of the NO_{2}^{+} molecular ion in the proposed reaction scheme, respectively. This significant dependence indeed features the role of vibronic coupling in the NO_{2}^{+}(X^{1}A_{1}, ν_{1}, ν_{2}, ν_{3}) 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 Herzberg^{24,25} of Herzberg–Teller vibronic coupling.^{26} We remark that β_{4,e} and β_{6,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 β_{2,e}.
Fig. 8 also illustrates the key feature of the PI calculations mentioned above, i.e., the fact that the one-channel β_{e} 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 NO_{2}^{+} ground state correspond to significantly different electronic density distributions. This will be discussed in more detail in the forthcoming publication.
In Fig. 9, we display the computed MFPADs for the three most relevant transitions (type 3 (z_{MF}, (a)), type 2 (y_{MF}, (b)) and type 4 (parallel to an NO bond, (c))) in one-photon PI of this [R(6a_{1})^{−1}] 3pσ^{2}B_{2} state, computed for θ_{P} ≈ 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 θ_{R} ≈ 150° (d). The RFPAD is obtained after integration over the γ_{R} 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 θ_{P} ≈ 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 3pσb_{2} → kb_{2} type 3 transition which corresponds to a well-structured MFPAD, while the 3pσb_{2} → ka_{1} 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.
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 θ_{e} emission angles (θ_{e} ≤ 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*(6a_{1})^{−1}, 3pσb_{2}] Rydberg state is the most likely populated excited state after three-photon absorption, with preferred geometries around (θ_{P} = 134°, θ_{R} = 150°) at the moment of PI and dissociation, respectively. Furthermore, this comparison emphasizes the importance of electronic correlation of the NO_{2}^{+}(X^{1}Σ_{g}) ground state, which plays a major role in the description of the PI process. The calculation for the PI of the [R*(6a_{1})^{−1}, 3pσb_{2}] Rydberg state reproduces the values of the β_{2,e} asymmetry parameters measured for MPDI and MPI processes, if the α MPI process is assigned to the PI of the 3pσb_{2} Rydberg state, at a geometry closer to the linear conformation θ_{P} ≈ 180°.
The different reaction mechanisms proposed in paper I^{2} 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 nm^{2}. In this scheme, the three-photon absorption excites the molecule to a valence state strongly coupled to the [R*(6a_{1})^{−1}] Rydberg series, favouring the [R*(6a_{1})^{−1}] 3pσ^{2}B_{2} 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 NO_{2}^{+}(X^{1}Σ_{g}, v_{1}, v_{2}, v_{3}) manifold. The potential surfaces of the [R*(6a_{1})^{−1}] Rydberg states closely resemble that of the ionic state NO_{2}^{+}(X^{1}Σ_{g}), 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 NO_{2}^{+}(X^{1}Σ_{g}, v_{1}, v_{2}, v_{3}) population, associated with two dominant geometries of the molecule: linear and bent, characterized by different values of the photoelectron asymmetry parameter β_{2,e}. In this scheme, the selective photodissociation of preferably bent NO_{2}^{+}(X^{1}Σ_{g}, v_{1}, v_{2}, v_{3}) molecular ions, by the fifth photon absorption leads to the population of dissociative excited states of NO_{2}^{+}, such as the NO_{2}^{+}(A^{1}A_{1} or B^{1}B_{2}) states, while the population associated with a linear geometry remains in the NO_{2}^{+} ground state. It thereby acts thus as a sorting between these two populations. The dissociation of the A^{1}A_{1} or B^{1}B_{2} excited state to the L_{1} 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 β_{2,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^{+}(Σ^{1}X) 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 (L_{1}). The reaction mechanism involving the ionization of the [R*(6a_{1})^{−1}, 3pσb_{2}] Rydberg state to the NO_{2}^{+}(X^{1}Σ_{g}), preserving the E_{vib} 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*(6a_{1})^{−1}, 3pσb_{2}] Rydberg state in the ionization step leads to the population of the NO_{2}^{+}(X^{1}Σ_{g}, v_{1}, v_{2}, v_{3}) manifold around the NO^{+}(Σ^{1}X) + O(^{3}P) 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)}_{B} ≤ E^{(1)}_{D}, become very similar to those of process D for E^{(4)}_{B} ≥ E^{(1)}_{D}.
A remarkably similar value of the β_{2,e} asymmetry parameter (β_{2,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 NO_{2}^{+} (X^{1}Σ_{g}, v_{1}, v_{2}, v_{3}) 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*(6a_{1})^{−1}] 3pπ^{2}A_{1}, 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 NO_{2} excited state), while at longer pump–probe delays dissociation of the Rydberg state leading to the production of the NO(C^{2}Π_{1/2}) 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 time^{9} around 500 fs is indeed coherent with the lifetimes around 600 fs for [R*(6a_{1})^{−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 NO_{2} 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*(6a_{1})^{−1}] NO_{2} Rydberg states around 9.3 eV, whose relaxation can be probed by a delayed 400 nm femtosecond laser pulse.
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp02057k |
‡ These authors have equally contributed to the work. |
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