Visualizing rotational wave functions of electronically excited nitric oxide molecules by using an ion imaging technique

Kenta Mizuse *a, Nao Chizuwa b, Dai Ikeda a, Takashi Imajo b and Yasuhiro Ohshima *ac
aDepartment of Chemistry, Tokyo Institute of Technology, 2-12-1-W4-9 Ookayama, Meguro, Tokyo 152-8550, Japan. E-mail:;
bDepartment of Chemical and Biological Sciences, Japan Women's University, 2-8-1 Mejirodai, Bunkyo, Tokyo 112-8681, Japan
cInstitute for Molecular Science, 38 Nishi-Gonaka, Myodaiji, Okazaki, Aichi 444-8585, Japan

Received 15th September 2017 , Accepted 8th November 2017

First published on 8th November 2017

Here we report the dissociative ionization imaging of electronically excited nitric oxide (NO) molecules to visualize rotational wave functions in the electronic excited state (A 2Σ+). The NO molecules were excited to a single rotational energy eigenstate in the first electronic excited state by a resonant nanosecond ultraviolet pulse. The molecules were then irradiated by a strong, circularly polarized femtosecond imaging pulse. Spatial distribution of the ejected N+ and O+ fragment ions from the dissociative NO2+ was recorded as a direct measure of the molecular axis distribution using a high-resolution slice ion imaging apparatus. The circularly polarized probe pulse realizes the isotropic ionization and thus undistorted shapes of the functions can be visualized. Due to the higher ionization efficiency of the excited molecules relative to the ground state ones, signals from the excited NO were enhanced. We can, therefore, extract shapes of the square of rotational wave functions in the electronic excited state although the unexcited ground state molecules are the majority in an ensemble. The observed images show s-function-like and p-function-like shapes depending on the excitation wavelengths. These shapes well reflect the rotational (angular momentum) character of the prepared states. The present approach directly leads to the evaluation method of the molecular axis alignment in photo-excited ensembles, and it could also lead to a visualization method for excited state molecular dynamics.

1 Introduction

Deeper understanding and effective utilization of molecular motions are important subjects in various fields of molecular science, e.g., fundamental reaction dynamics research, fabrications of molecular machines,1,2 and development of quantum molecular computing based on the wave nature of rotational/vibrational eigenstates.3,4 Because motions of molecules (molecular rotation and vibration) are described by wave functions, it is of great importance to experimentally characterize wave functions.

Recent advances in charged particle imaging5–10 and diffraction-based imaging11–14 techniques for gas-phase molecular systems offer ways to directly visualize (the square of) rotational and vibrational wave functions, and their ultrafast wave packet dynamics.8,9,12–21 A simple but powerful imaging method is Coulomb explosion or dissociative ionization imaging of the rotational wave packet of linear molecules.8,9,15–18 In such an experiment, a molecular ensemble in a specific rotational state is irradiated by a strong, ultrashort imaging pulse, and multiply ionized. Upon rapid dissociation or Coulomb explosion, atomic fragment ions are ejected along the molecular axis direction. The spatial distribution of the ejected ions is a direct measure of the molecular axis distribution, i.e. the square of a rotational wave function, at the imaging pulse irradiation. With regard to the position sensitive detection of the fragment ions, 2D velocity map imaging or 3D imaging experiments have been frequently carried out since the pioneering imaging study on rotational wave packet (molecular axis alignment) dynamics.15,17,21 In a conventional 2D velocity map imaging, however, a polarization condition of the imaging pulse is generally limited to the linear polarization,10 and therefore full characterization of wave functions in the detector plane was not realized. This is because a linearly polarized imaging pulse preferentially explodes the molecules whose axis is parallel to the polarization axis. Although more versatile 3D imaging techniques have successfully been applied for such a system,17 a 2D detector has many advantages over a 3D detector: higher multi-hit capability (higher measurement efficiency), lower cost, simpler setup, and higher image resolution. Recently, we developed a conceptually new 2D imaging setup, in which the polarization plane of an incident laser pulse is automatically parallel to the detector even when a circularly polarized pulse is used.8,9 Ion imaging with a circularly polarized pulse enables the isotropic probe, and then undistorted molecular axis distributions can be measured. By using the new apparatus, we carried out high-resolution Coulomb explosion imaging of a well-controlled rotational wave packet, and succeeded in visualizing the wave nature of dynamics, including complicated nodal structures in the angular distributions.8,9 Our previous studies opened a new avenue of high-resolution imaging of rotational wave functions.

Including rotational wave packet imaging mentioned above, most of the wave function imaging studies were limited to electronic ground state molecules. Characterization of wave functions in neutral electronic excited states is also desired to deepen our understanding of photochemistry and molecular dynamics in excited states. For tracking of excited state molecular dynamics, ultrafast spectroscopy including the pioneering real-time study of the photodissociation dynamics22 has been a powerful approach. Real space information is, however, limited because spectroscopy generally provides indirect structural information. Direct imaging experiments for spatial information of the excited state molecules are therefore desired.

Practically, one of the experimental difficulties in excited state imaging is low yields of excited state molecules upon photoexcitation. Because only a few percent of molecules are typically excited, signals from the excited state molecules tend to be buried with those from unexcited ground state ones. Such a difficulty can be overcome by a selective imaging technique for excited state molecules.

Here, we apply our high-resolution rotational wave function imaging to electronically excited molecules. Dissociative ionization imaging of electronically excited nitric oxide (NO) molecules was carried out to visualize the square of rotational wave functions in the first electronic excited state (A 2Σ+ state). Since the ionization energy (efficiency) of an excited state is lower than that of a ground state, ion signals from an excited state are expected to be enhanced in a strong-field ionization imaging experiment. Fig. 1a shows an excitation scheme. A rotational energy eigenstate in the excited state is prepared with a resonant nanosecond ultraviolet (UV) pulse, and then, molecular axis distribution of the ensemble is measured with a femtosecond laser pulse-based strong-field ionization and high-resolution spatial-slice ion imaging apparatus.

image file: c7cp06347d-f1.tif
Fig. 1 (a) Excitation scheme of dissociative ionization imaging for electronic excited state NO molecules. (b) Schematic of experimental setup and the present coordinate system. The UV pump was linearly polarized along the Z-axis, while the polarization plane of the femtosecond probe pulse was in the XZ-plane.

Recently, Yang et al. reported diffractive imaging of vibrational wave packet dynamics in electronically excited iodine molecules using an ultrashort relativistic electron pulse.14 Their study offers a new experimental technique for excited state imaging. Their research target was, however, limited to a heavy atom system, in which high diffraction efficiency was expected, and time resolution was a few hundred femtoseconds. For studies of photochemical reactions and excited state dynamics of fundamental organic molecules, ultrafast motions of light atoms should be tracked. In this context, our present approach is complementary to the diffractive imaging: The detection efficiency of ion imaging is not lowered for light atom systems, and femtosecond laser-based imaging offers better time resolution.

2 Experimental

A gaseous mixture of nitric oxide and helium (1% NO, 3 MPa total pressure) was expanded into a vacuum chamber through a pulsed valve (Even–Lavie valve23,24). Thus, adiabatically cooled molecules were introduced to the interaction region of the imaging apparatus (Fig. 1b) through two molecular beam skimmers. The molecules in the ground state (X 2Π1/2) were then irradiated with a linearly polarized (along the Z-axis in Fig. 2b) nanosecond UV pump pulse (∼226 nm), which excites the molecules to a rotational energy eigenstate in the first electronic excited state (A 2Σ+ state). After a 50 ns delay from the UV pulse, a femtosecond non-resonant probe pulse (820 nm, 40 fs, circularly polarized in the XZ-plane) was introduced. Within such a relatively long pump–probe delay, ions formed in the one-color resonant ionization process escape from the interaction region of the probe pulse due to the electric field of the ion optics. We can, therefore, safely ignore the contribution of the NO+ species to the observed images. We also carried out a shorter (∼5 ns) pump–probe delay experiment. The results are shown in the ESI. In the observed distribution, similar trends to those of the longer delay experiments were identified, and no remarkable delay time dependence was characterized.
image file: c7cp06347d-f2.tif
Fig. 2 (a) One-color resonant two-photon ionization spectrum of NO. The three lines are labelled with the assignments, shown with standard notations. (b) A schematic diagram of the relevant energy levels and observed transitions are indicated by arrows. J: total angular momentum, M: projection of J onto the space-fixed axis (Z-axis here), N: total angular momentum excluding electron spin, S: electronic spin angular momentum, Ω: projection of Λ + Σ on the molecular axis, where Λ and Σ are the projection of orbital and electronic spin angular momenta on the molecular axis, respectively.

Before the UV wavelength was set to a rotational line, a one-color resonant two-photon ionization spectrum was also measured by scanning the dye laser wavelength while monitoring the intensity of the NO+ signal. Fig. 2 shows the observed spectrum and a relevant energy level scheme.25–27 The observed three strong lines correspond to the transitions from the rotational ground state, and their assignments are also shown by standard labels.25 Other lines, i.e., transitions from rotational excited states, were almost negligible in the spectrum, indicating most of the molecules lie in the rotational ground state. Rotational temperature is, thus, estimated to be below 2 K. Among the three prominent lines, we used only Q11(1/2) and R12(1/2) lines to prepare a rotational energy eigenstate. Although the angular distribution depends on J and M (see Appendix), because of the initial rotational level J = 1/2, |M| = 1/2, and the selection rule of ΔM = 0, only the |M| = 1/2 final state is accessible. In this study, we therefore probe the shape of the function of the J = 1/2, |M| = 1/2 state through the Q11(1/2) transition, and J = 3/2, |M| = 1/2 state through the R12(1/2) transition. The middle line at ∼44[thin space (1/6-em)]203 cm−1 is a convolution of the two transitions, and is difficult to resolve in the present setup.

The nanosecond tunable UV light pulse (∼226 nm) was obtained as the second harmonic of a dye laser output (Allegro, Sirah; with a Coumarin 450 dye) pumped by the third harmonic of a Nd:YLF laser (INNOSLAB IS6III-E, Edgewave; 500 Hz repetition rate, 1.6 mJ @ 349 nm). A zeroth order half waveplate and a brewster window were used to rotate the polarization plane and to evaluate and improve the polarization quality, respectively. In the imaging measurement, pulse intensity was tuned to the highest intensity in which no significant resonant two-photon ionization signal was observed. Typically, ion signal from the MCP stack was less than 1 mV (after amplification, obtained with 50 Ω termination), while higher UV intensity led to more than 1.2 V. Assuming that 100% of molecules are ionized in the high UV intensity, this implies the ionization yield upon weak UV irradiation was less than 0.1%. Because the cross sections of the A–X transition and that of the A state to the ionization continuum are almost the same order of magnitude,28–30 0.1% in one-color ionization yield implies the A state yield can be estimated to be ∼3% (0.032∼0.001). We also note that the A state population is much smaller at the probe irradiation due to the 50 ns pump–probe delay. According to the reported A state lifetime (200 ns),31 ∼20% of the optically excited molecules relax to the ground state.

The femtosecond imaging pulse was a fundamental output of a Ti:Sapphire amplifier (Odin-II HE, Quantronix: 820 nm, 500 Hz repetition rate, <2 mJ per pulse, 35 fs FWHM at Fourier limit). An achromatic quarter waveplate was used to create a circularly polarized light pulse. Thus, the obtained pulse was focused onto the molecular beam from the opposite direction to the UV pulse. The peak intensity and time width (FWHM) in the interaction region were estimated to be ∼200 TW cm−2 and 50 fs, respectively. The intensity used here was chosen according to the balance between the excited state selectivity and signal to noise ratio. A much stronger pulse ionized both the ground and excited state molecules without significant selectivity. The use of a weaker pulse would lead to the selective (double) ionization from the excited state molecules due to their lower ionization energy, however, a weaker pulse also leads to lower signal counts.

Upon femtosecond probe pulse irradiation, NO molecules were multiply ionized and then exploded into atomic ions. The ejected angle is parallel to the molecular orientation angle at the probe irradiation. The spatial distributions of N+ and O+ were measured by a 2D spatial-slice imaging apparatus, as shown in Fig. 1b. Details of the imaging procedures have been reported in the previous papers on rotational wave packet imaging,8,9 therefore, only brief descriptions are given here. Fragment ions were accelerated to the +X direction by ion lens optics. Ion distribution was expanded three-dimensionally during the flight, and the ion cloud thus created was sliced by a 1 mm width mechanical slit. After the slit, a 1 mm ion sheet was projected onto a 2D position sensitive detector (microchannel plates/phosphor screen/camera) by applying a high voltage pulse (∼4 kV cm−1, ∼30 ns rise time) to the pulsed repeller. The timing of the high voltage pulse was adjusted so that the ions of interest hit the detector. In the present setup, ions were accelerated to ∼1200 eV, and distance of flight from the laser-interaction region to the detector was ∼350 mm, therefore, the pulse timing for N+ imaging was ∼3000 ns after the laser irradiation, as estimated by a time of flight calculation. The ions repelled hit the detector within or just after the high voltage pulse (typical time of flight after the pulse was a few tens of ns). The finite size of the detector works as a mass gate. In the present measurements, only ions in the mass to charge ratio of 14 to 16 have been imaged simultaneously. Here, the detector surface is parallel to the cutting-plane of the ion sheet. In the pump process, the axial symmetry is conserved along the UV pump polarization (Z-axis), and images taken with the present setup are direct slices including the symmetry axis, offering the full 3D spatial information (due to the lack of ϕ-dependence of the excited ensembles). This Z-axis symmetry was used to redress a certain region of the detector in which unwanted signals overlap, as mentioned later. To obtain undistorted angular functions, the position-dependent sensitivity of the detector and effect of the small ellipticity of the probe were calibrated. This was done by measuring the experimental “isotropic” ion image while scanning the polarization angle of the UV pulse in the XZ-plane from 0 to 2π. All the experimentally observed angular distributions reported in this study were normalized by the angular distribution of the isotropic image thus obtained.

3 Results and discussion

Dissociative ion imaging of NO with the slice imaging apparatus

Fig. 3a shows an observed 2D image of ions in the mass to charge ratio of 14 to 16. Both the UV pump and femtosecond probe were irradiated. In this mass to charge ratio region, N+, NO2+, and O+ were observed. Two bright double-wall ellipses correspond to N+ and O+. In the middle of these two, the signature of NO2+ was observed. A weak ellipse of NO2+ (from (NO)2) partially overlaps with those of N+ and O+. Each ellipse has a defect in the bottom. Although the origin of this effect was not fully understood, several groups have observed similar forward/backward asymmetry of N+/O+ in time of flight mass spectra.32–35 The plausible origins are the detector inhomogeneity/angular dependence of the detection efficiency, unwanted ion–ion lens interactions, or ion–neutral beam interactions. The overlapped regions and the defect regions were compensated by the above-mentioned usage of the symmetry. The observed elliptical shapes are due to the ion acceleration.8,9 To obtain the angular distribution, they can be transformed to circles just by multiplying a factor with the X coordinate (Fig. 3b and c). In Fig. 3b and c, both the N+ and O+ images show a concentric outer ring with an inner circle signature. According to the previously reported femtosecond laser ionization studies,32–36 the observed signature was assigned as shown in Fig. 3b and c: The inner circles (kinetic energy was < ∼3 eV) correspond to the fragments from the dissociative NO+, while the outer rings come from the charge-symmetric dissociation of NO2+. The thickness of the outer ellipse is much narrower than that of the inner one. This implies a steeper dissociative potential, and then, faster dissociation of NO2+.
image file: c7cp06347d-f3.tif
Fig. 3 (a) The observed image of N+, O+, and NO2+ taken with the spatial-slice imaging apparatus. Both the UV pump and femtosecond probe were irradiated, and the UV photon energy was set to 44[thin space (1/6-em)]210 cm−1 (R12 transition). (b) The shape-corrected image of N+ obtained from (a). (c) The shape-corrected image of O+ obtained from (a).

For the angular distribution measurements, we used the outer ring of N+ (from NO2+; kinetic energy is around >5 eV). This is because faster fragmentation is desired in terms of the axial recoil approximation. Furthermore, the spatial resolution of the inner circles was limited and also interfered with by unwanted dark regions. It is expected that the outer ring of the O+ distribution also gives similar information to the N+ counterpart. Both the upper and lower part of the O+ distribution were, however, interfered with by NO2+ and fragments from the residual H2O/O2. In the case of N+, the upper region of the image was not disturbed. We, therefore, focus on the N+ images hereafter.

Angular distributions in the electronic excited state

Fig. 4a shows the N+ image taken with the 44[thin space (1/6-em)]211 cm−1 UV pump, which stimulates the R12(1/2) transition. With this UV irradiation, the |N S J |M|〉 = |2 1/2 3/2 1/2〉 rotational energy eigenstate was prepared. (The detail of the A state rotational energy eigenstate is described in the Appendix section. Simply, angular distribution is a function of J and M.) The observed image also contains the contribution from the unexcited ground state molecules. To account for this background, we also measured a probe-only image (Fig. 4b). Brightness (signal counts) in Fig. 4b is much smaller than in Fig. 4a, although only a few percent of the molecules are excited in the case of Fig. 4a. This implies a much higher detection efficiency of the electronically excited molecules in the present scheme. From the brightness of the image and the excited state population (see Experimental section), we estimated the detection efficiency of the excited molecules is at least 10 times higher than that of the ground state molecules. This would relate to the ionization process of the excited state molecules, however, such a topic is beyond the scope of this paper. Here, we just used the present process as a suitable detection method of excited molecules. Fig. 4c is the background-subtracted image of N+ (difference image between Fig. 4a and c). Because the probe-only image Fig. 4b shows an isotropic distribution, this subtraction enhances the anisotropic signature. In the outer ring of Fig. 4c, clear anisotropy was observed, i.e., signals are concentrated along the laser polarization direction (horizontal axis of the image) and intensity minima (the narrow part of the function) were found in the top and bottom region. Here, we carried out a simple subtraction neglecting the ground state depletion upon UV irradiation. This is based on our estimation that the excitation efficiency is only a few percent. We also tried the subtraction by varying the relative ratio of the ground state from 1 to 0.9, e.g. (Fig. 4a–0.95 × Fig. 4b), however, no significant change in the angular distribution was seen. This is because the signal count in Fig. 4b (ground state background) is much lower than Fig. 4a (excited state + ground state).
image file: c7cp06347d-f4.tif
Fig. 4 Dissociative ionization imaging of NO with a 44[thin space (1/6-em)]211 cm−1 UV pump (R12(1/2) transition). (a) N+ ion image taken with a UV pump. (b) Probe-only N+ ion image. (c) Difference image between the pump + probe image (a) and the probe-only image (b). (d) Brightness-amplified image of (c). Only N+ ions from NO2+ are highlighted. (e) Polar plot of the angular distribution obtained from (d). (f) Calculated distribution function of |N S J |M|〉 = |2 1/2 3/2 1/2〉 state.

The outer ring signature in Fig. 4c was intensity-amplified and is highlighted in Fig. 4d. Larger signals are observed along the polarization direction leading to an anisotropic angular distribution. In Fig. 4d, there is small left–right asymmetry due to the inhomogeneity of the detector. To calibrate this effect, we normalize the angular distribution by the “isotropic” image as taken with the procedure described in the Experimental section. The thus obtained distribution is displayed in the polar plot (Fig. 4e). In Fig. 4e, a gourd-shaped function elongated in the polarization axis was clearly identified. The thus obtained angular distribution directly shows the shape of the square of the rotational wave function. For comparison, the calculated angular distribution of the |N S J |M|〉 = |2 1/2 3/2 1/2〉 state is plotted in Fig. 4f. This angular distribution was obtained according to the relations shown in the Appendix and literature. Both the experimental and calculated distributions show a p-orbital-like gourd shape elongated in the polarization (Z) axis. The finite width of the narrow part at around Z = 0 was also reproduced. This waist is a characteristic of the present state, compared to the p-function having a nodal plane at Z = 0. The measured distribution in Fig. 4e is in good agreement with the calculated one, including the signature of the waist at around Z = 0, which is a characteristic of this state in contrast to the p-function.

For further demonstration of the present imaging approach, a different final state was also probed. Fig. 5 shows the results obtained with the 44[thin space (1/6-em)]199 cm−1 UV wavenumber, which is resonant to the Q11(1/2) transition. The similar measurement and analyses as in Fig. 4 were carried out. In Fig. 5d and e, the isotropic distribution can clearly be seen. No remarkable intensity maxima/minima were found, in contrast to the J = 3/2 case in Fig. 4. This is also in agreement with the calculated distribution of the |N S J |M|〉 = |0 1/2 1/2 1/2〉 state.

image file: c7cp06347d-f5.tif
Fig. 5 Dissociative ionization imaging of NO with a 44[thin space (1/6-em)]199 cm−1 UV pump (Q11(1/2) transition). (a) N+ ion image taken with a UV pump. (b) Probe-only N+ ion image. (c) Difference image between the pump + probe image (a) and the probe-only image (b). (d) Brightness-amplified image of (c). Only N+ ions from NO2+ are highlighted. (e) Polar plot of the angular distribution obtained from (d). (f) Calculated distribution function of |N S J |M|〉 = |0 1/2 1/2 1/2〉 state.

The observed wavelength dependence of the images and agreement with the theoretical distribution show the validity of the present approach as an excited state-selective ion imaging technique, opening a new way to probe the photochemistry. The present results are also important as experimental images of the square of the rotational energy eigenstates of a doublet molecule. Recently, rotational wavepacket imaging has been frequently carried out,8,9,12–21 however, imaging of the rotational eigenstate is still rare. This is mainly due to the difficulty in creating a pure ensemble of a specific rotational state and in measuring undistorted angular distribution by a typical imaging setup. In this study, the rotational state-selective excitation and the spatial-slice imaging based on a circularly polarized pulse were employed to overcome such difficulties. Furthermore, to the best of our knowledge, rotational wave functions (eigenstates) of doublet molecules had never been visualized although their shapes have been theoretically assumed and used for the analyses of various experiments on NO including strong-field induced rotational dynamics and holography/rescattering.21,37,38 The observed wavelength-dependent (J-dependent) angular distributions of NO (2Σ) are analogous to standard rotational wave functions of a singlet molecule, spherical harmonics. The J = 1/2 state is the lowest total angular momentum state, and the corresponding angular distribution is isotropic (Fig. 5), the same as the s-function (J = 0 function). On the other hand, J = 3/2 is the second lowest total angular momentum state, and its shape (Fig. 4) is close to that of the p-function (J = 1 function). The difference between the doublet NO and singlet molecules is attributed to the spin angular momentum and its couplings.

4 Conclusions

We report the femtosecond dissociative ionization imaging of a rotational energy eigenstate in the first electronic excited state (A 2Σ+ state) of NO molecules. Due to the higher ionization efficiency of the excited state molecules, excited state-selective imaging was achieved. The observed angular distributions show s-function-like and p-function-like shapes, reflecting the characters of the excited rotational states. The results were reproduced well by the square of the theoretical rotational wave functions, indicating the validity and accuracy of the present approach as a new imaging method. The present approach can be almost directly applied to the evaluation of the molecular axis alignment in photo-excited ensembles. We also hope it will lead to a visualization method for molecular dynamics in excited states for example by utilizing multi-particle imaging.

Conflicts of interest

There are no conflicts to declare.


Theoretical angular distributions of NO in the A 2Σ+ state

The rotational states in the A 2Σ+ state are generally expressed in terms of Hund's case (b). We numerically calculate the angular distributions by using the relationship between the function of case (a) and case (b).27 The case (b) wave function, |N S J |M|〉 as shown in Fig. 2b, is an equally weighted summation of the case (a) wave functions |J ± Ω |M|〉, leading to
image file: c7cp06347d-t1.tif
where the selection of the sign reflects the parity. We note the optically prepared states in the present study are the single parity case. Here, the case (a) function is written as
image file: c7cp06347d-t2.tif
where image file: c7cp06347d-t3.tif is the rotational matrix.27 In the present observation, this corresponds to the θ-dependence of the square of |N S J |M|〉. Due to the axial symmetry, no ϕ-dependence exists.


This work was supported in part by grants-in-aid KAKENHI from JSPS/MEXT (#JP15H03766, #JP15KT0060, #JP16H00826, and #JP16K13927), the grant for Basic Science Research Projects from the Sumitomo Foundation, Konica Minolta Science and Technology Foundation and Consortium for Photon Science and Technology (CPhoST).


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Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp06347d

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