Photofragment spin–orbit fine-structure branching ratios have long been predicted to depend on the rotational quantum number J′ by theory near the dissociation thresholds of several diatomic molecules, while this has rarely been observed in any photodissociation experiments yet. Here, we measured the fine-structure branching ratios N(2D5/2)/N(2D3/2) produced in the N(2D5/2,3/2) + N(2D5/2,3/2) channel at the b1Σu+(v = 20) state of 14N2 by using our vacuum ultraviolet (VUV)-pump–VUV-probe time-sliced velocity-mapped ion imaging setup. It is found that 14N2 almost exclusively dissociates into the spin–orbit channel N(2D5/2) + N(2D3/2) at low rotational levels and gradually approaches the statistical or diabatic limit by distributing all possible spin–orbit channels at higher rotational levels. The strongly rotationally dependent fine-structure branching ratios should be due to the increasing strength of nonadiabatic Coriolis interaction among various dissociative states in the so-called “recoupling zone” as J′ increases. They are supposed to provide unprecedented information on the near threshold photodissociation dynamics of 14N2.

Interesting quantum dynamical effects are frequently observed near the photodissociation thresholds, mainly due to the strong nonadiabatic interactions among the nearly degenerate molecular states correlating to the same dissociation limit.1,2 Photodissociation study near the threshold has been an important methodology for investigating chemical reaction dynamics in cold and ultracold regimes.3–6 If one or both of the two photofragments are open-shell atomic species and in quantum states with non-zero total angular momentums, there will be several different electronic states correlating with the same atomic dissociation limit. For molecules dissociating from the Franck–Condon (FC) region to the asymptotic limit, there is an intermediate region called the “recoupling zone,” where the spin–orbit and nonadiabatic interactions (e.g., Coriolis interactions) are comparable to the energy gaps among different Born–Oppenheimer electronic states. The spin–orbit and nonadiabatic interactions in the recoupling zone could exert profound effects on the final outputs of the photodissociation process, for example, the angular anisotropic distributions and spin–orbit fine-structure branching ratios of the atomic photofragments.7–10 Particularly, the atomic fine-structure branching ratios have long been predicted to be sensitive to the Coriolis interactions in the recoupling zone for several diatomic molecules, such as NaH and OH near the dissociation thresholds.8–10 As the Coriolis interaction becomes stronger as the molecular rotational quantum number J′ increases, the atomic fine-structure branching ratios are thus also dependent on J′.8–10 

Besides the spin–orbit and nonadiabatic interactions in the recoupling zone, the atomic fine-structure branching ratios are also influenced by those interactions in the FC and asymptotic regions along the dissociation coordinate. This makes the measurement of atomic fine-structure branching ratios an extremely sensitive probe to the molecular photodissociation dynamics. Numerous experiments have been performed to measure the atomic fine-structure branching ratios generated from state-selected molecular photodissociation processes, for example, OH,11,12 O2,13 ClO,14,15 CO,1614N2,17 D2,18 and so on. In these experiments, the atomic fine-structure branching ratios were found to strongly depend on the electronic characteristics and vibrational levels of the directly photoexcited states, as these determined the types and strengths of spin–orbit and nonadiabatic interactions in the FC region and also those in the asymptotic limit. However, none of the experimental measurements reported thus far have noticed any profound rotational effects, despite the facts that theoretical calculations have long predicted strong rotational dependence of the atomic fine-structure branching ratios,8–10 and many of the above experiments have devoted great efforts to search for such rotational effects. There are two reasons why such rotational effects were elusive in previous experiments. First, the small energy gaps among different rotational levels cannot significantly affect the spin–orbit and nonadiabatic interactions in the FC region; second, all the previous experiments were performed at energy levels highly above the studied photodissociation thresholds; thus, the atomic fragments traverse the recoupling zone fast enough that the rotationally dependent Coriolis interactions have negligible effects on the final outputs of the photodissociation process (the so-called “diabatic recoil limit”). Thus, experimental measurements aimed for elucidating the rotationally dependent photodissociation mechanisms need to be done in energy regimes near the dissociation thresholds, where Coriolis interactions in the recoupling zone could play an important role in determining the final outputs of the photodissociation process.8–10 

The valence b1Σu+(v = 20) state is the first vibronic level above the spin-allowed channel N(2D5/2,3/2) + N(2D5/2,3/2) of 14N2. Our recent state-to-state photodissociation study showed that 14N2 in b1Σu+(v = 20) predominantly dissociates into the N(2D5/2,3/2) + N(2D5/2,3/2) channel, particularly at high J′ levels.19 The N(2D5/2,3/2) atomic products have two different spin–orbit fine-structure levels N(2D5/2) and N(2D3/2), and N(2D3/2) is 8.713 cm−1 higher in energy than N(2D5/2). Thus, the N(2D5/2,3/2) + N(2D5/2,3/2) channel can be further divided into the following three correlated spin–orbit fine-structure channels,

(1)
(2)
(3)

where the N(2D5/2) + N(2D5/2) channel is the lowest one in energy and the N(2D5/2) + N(2D3/2) and N(2D3/2) + N(2D3/2) channels are 8.713 and 17.426 cm−1 higher than the lowest channel, respectively. The bond dissociation energy (BDE) of 14N2 for dissociating into the lowest correlated spin–orbit fine-structure channel N(2D5/2) + N(2D5/2) was recently measured to be ∼117 137 cm−1.20 The spectroscopic term energies (ET) of the upper rotational levels of 14N2 in the b1Σu+(v = 20) state and their energy differences with respect to the dissociation limit N(2D5/2) + N(2D5/2) are provided in Table S1 in the supplementary material. It can be seen that the lowest rotational level is only 67.9 cm−1 above the dissociation limit N(2D5/2) + N(2D5/2); thus, photodissociation of 14N2 in the b1Σu+(v = 20) state could be a good candidate system for observing the rotational dependence of spin–orbit fine-structure branching ratios. In this study, we systematically measured the spin–orbit fine-structure branching ratios N(2D5/2)/N(2D3/2) corresponding to the N(2D5/2,3/2) + N(2D5/2,3/2) channel at different J′ levels in the b1Σu+(v = 20) state of 14N2 by using the same method recently used by Chang et al.17 Strongly rotational dependence of the fine-structure branching ratios N(2D5/2)/N(2D3/2) was confirmed for the first time, which should provide detailed information on the nonadiabatic interactions in the recoupling zone of 14N2 photodissociation into the N(2D5/2,3/2) + N(2D5/2,3/2) channel.

The measurement was performed on our recently constructed vacuum ultraviolet (VUV)-pump–VUV-probe time-sliced velocity-mapped ion imaging (VUV–VUV-TS-VMI) setup.19,21,22 Detailed procedures of the experimental measurements are provided in the supplementary material. Briefly, 14N2 molecules in a pulsed supersonic molecular beam were first excited to a specific rotational J′ level in the b1Σu+(v = 20) state in the photodissociation and photoionization (PD/PI) region of the setup by absorbing a single VUV photon from the pump VUV beam; after a delay of about 10 ns, the probe VUV beam arrived and excited the atomic products N(2D5/2) and N(2D3/2) to the common autoionization level 2s22p2(1D)4s2D3/2,5/2 at 119 210.0 cm−1.17 The intensity of the formed N+ ions were measured by the TS-VMI mass spectrometer. The photofragment excitation (PHOFEX) spectra obtained in this way were presented in Fig. S1 in the supplementary material. Then, the pump VUV was fixed to each of the rotational peaks in the PHOFEX spectra, and the probe VUV was scanned through the two N atomic transitions from 2D5/2 and 2D3/2 to 2s22p2(1D)4s2D3/2,5/2, and the atomic excitation spectra were obtained.

To eliminate the possible contributions from the lower dissociation channel N(4S) + N(2D5/2,3/2),19 an electrically grounded stainless-steel plate with central opening was put in front of the MCP detector. The N atoms generated in the channel N(4S) + N(2D5/2,3/2) have much higher speeds than those from the channel N(2D5/2,3/2) + N(2D5/2,3/2). Thus, the Newton sphere corresponding to the channel N(2D5/2,3/2) + N(2D5/2,3/2) is much smaller and can pass through the central hole of the plate to reach the detector, while that of the channel N(4S) + N(2D5/2,3/2) is almost completely blocked by the plate. Two typical atomic excitation spectra are presented in Fig. 1. They were collected under the same experimental conditions, except that the top spectrum is for J′ = 0 [the pump VUV was at the P(1) transition] and the bottom one is for J′ = 10 [the pump VUV was at the P(11) transition] rotational levels of the b1Σu+(v = 20) state. It is immediately seen from Fig. 1 that the relative intensity ratios of the two peaks corresponding to N(2D5/2) and N(2D3/2) in the two atomic excitation spectra are different from each other, implying obvious rotational dependence of the fine-structure branching ratio N(2D5/2)/N(2D3/2).

FIG. 1.

Atomic excitation spectra of N(2D5/2) and N(2D3/2) produced from the dissociation channel N(2D5/2,3/2) + N(2D5/2,3/2) of 14N2 in the b1Σu+(v = 20) state by tuning the pump VUV to the P(1) (top spectrum) and P(11) (bottom spectrum) rotational transitions. The probe VUV was scanned through the transitions from 2D5/2 and 2D3/2 to the common autoionization level 2s22p2(1D)4s2D3/2,5/2 of N at 119 210.0 cm−1.

FIG. 1.

Atomic excitation spectra of N(2D5/2) and N(2D3/2) produced from the dissociation channel N(2D5/2,3/2) + N(2D5/2,3/2) of 14N2 in the b1Σu+(v = 20) state by tuning the pump VUV to the P(1) (top spectrum) and P(11) (bottom spectrum) rotational transitions. The probe VUV was scanned through the transitions from 2D5/2 and 2D3/2 to the common autoionization level 2s22p2(1D)4s2D3/2,5/2 of N at 119 210.0 cm−1.

Close modal

To obtain the fine-structure branching ratios, the areas under the corresponding peaks in the atomic excitation spectra are integrated and calibrated with the probe VUV intensities and the respective atomic transition probabilities, as done in the same way by Chang et al.17 (see the supplementary material). Measurements were performed at each of the rotational transitions in both R- and P-branches for 3–6 individual trials, and the averaged results are presented in Fig. S2 in the supplementary material as a function of the rotational quantum number J′ for both R- and P-branches. The rotational transitions of R(J′ − 1) and P(J′ + 1) have the same upper rotational level J′; they should have the same value of N(2D5/2)/N(2D3/2). We, thus, further averaged the results from R- and P-branches, and the obtained fine-structure branching ratio N(2D5/2)/N(2D3/2) vs the rotational quantum number J′ of the upper level is plotted in Fig. 2. The ratio of N(2D5/2)/N(2D3/2) is close to 1 at J′ = 0, gradually increases to ∼1.35 at intermediate J′ levels of 6–12, and then slowly decreases to 1 again at higher J′ levels at ∼19. Such complicated dependence of the fine-structure branching ratio on the rotational quantum number should reveal the detailed nonadiabatic interactions in the predissociation process of 14N2 near the threshold N(2D5/2,3/2)+N(2D5/2,3/2).

FIG. 2.

Spin–orbit fine-structure branching ratios N(2D5/2)/N(2D3/2) as a function of the rotational quantum number J′ for the b1Σu+(v = 20) state of 14N2. The uncertainties are due to the standard deviations of 6–12 individual measurements.

FIG. 2.

Spin–orbit fine-structure branching ratios N(2D5/2)/N(2D3/2) as a function of the rotational quantum number J′ for the b1Σu+(v = 20) state of 14N2. The uncertainties are due to the standard deviations of 6–12 individual measurements.

Close modal

As discussed above, there are three correlated fine-structure dissociation channels (1)–(3) separated only by 8.713 cm−1 from each other at the asymptotic limit. To gain further information on the relative ratios of the three channels, we collected the TS-VMI images of the N(2D5/2,3/2) + N(2D5/2,3/2) channel by state-selectively photoionizing N(2D5/2) and N(2D3/2) at each of the rotational transition lines. Typical images collected at P(1), P(2), R(3), and R(4) transitions are presented in Fig. 3. In each image, the right half was collected when N(2D5/2) was state-selectively photoionized, and the left half was collected when N(2D3/2) was state-selectively photoionized. Other than the slightly different wavelengths of the probe VUV for state-selectively photoionizing N(2D5/2) and N(2D3/2), all the experimental conditions were kept the same for the two halves in each image. It can be seen that the velocity resolution of our TS-VMI setup is not high enough to resolve the three correlated fine-structure channels. However, interesting size differences between the right and left half images can be noticed, which could provide useful hints for the relative ratios of the three correlated channels. For images of P(1) and P(2) [Figs. 3(a) and 3(b)], the diameters of the right halves match perfectly with those of the left halves, implying that the correlated fine-structure channel with the highest available kinetic energy probed in the two measurements should be the same, irrespectively whether N(2D5/2) or N(2D3/2) was selectively photoionized. This observation points to the only possibility that N(2D5/2) + N(2D3/2) is the channel with the highest available kinetic energy formed in the photodissociation of rotational states with J′ = 0 and 1, and the lowest channel N(2D5/2) + N(2D5/2) is not accessed. For images of R(3) and R(4) [Figs. 3(c) and 3(d)], the diameters of the right halves are slightly larger than those of the left halves, which are quite different with the images of P(1) and P(2), as discussed above. This observation provides clear evidence that the lowest channel N(2D5/2) + N(2D5/2) is formed in the photodissociation of rotational states with J′ = 4 and 5. Clearly, the TS-VMI measurements also prove that the correlated fine-structure branching ratios strongly depend on the rotational quantum number J′.

FIG. 3.

Raw TS-VMI images collected at the rotational transitions of (a) P(1), (b) P(2), (c) R(3), and (d) R(4) in the absorption band b1Σu+(v = 20) of 14N2. The right half of each image was collected when N(2D5/2) was state-selectively photoionized, and the left half was collected when N(2D3/2) was state-selectively photoionized.

FIG. 3.

Raw TS-VMI images collected at the rotational transitions of (a) P(1), (b) P(2), (c) R(3), and (d) R(4) in the absorption band b1Σu+(v = 20) of 14N2. The right half of each image was collected when N(2D5/2) was state-selectively photoionized, and the left half was collected when N(2D3/2) was state-selectively photoionized.

Close modal

The measurements by the atomic excitation spectroscopic method (Fig. 2) show that the spin–orbit fine-structure branching ratio N(2D5/2)/N(2D3/2) at low J′ levels, particularly for J′ = 0, is close to 1, and the TS-VMI measurements show that the lowest channel N(2D5/2) + N(2D5/2) is not formed for rotational levels of J′ = 0 and 1. Since the single correlated channel N(2D5/2) + N(2D3/2) produces N(2D5/2)/N(2D3/2) ratio of exactly 1, the combination of the above two measurements can lead to the conclusion that 14N2 excited to rotational levels of J′ = 0 and 1 in the b1Σu+(v = 20) state almost exclusively dissociates into the correlated fine-structure channel N(2D5/2) + N(2D3/2), and the lowest channel N(2D5/2) + N(2D5/2) and probably also the highest channel N(2D3/2) + N(2D3/2) only start to be populated at higher J′ levels.

There are three models, namely, the adiabatic correlation, diabatic, and statistical models, which are often used to predict the atomic spin–orbit fine-structure branching ratios in molecular photodissociation processes.7–10 In the adiabatic correlation model, the fragments depart from each other infinitely slow along a single Born–Oppenheimer potential energy curve, and this usually results in the dissociation into a single correlated channel. In the diabatic model (or in the “diabatic recoil limit”), the fragments move infinitely fast and traverse through the recoupling zone with no time. In this case, the spin–orbit fine-structure branching ratio is determined by the interactions among different electronic states in the FC region, and the interference effects between multiple dissociative states in the asymptotic region could also influence the outcomes significantly, while the spin–orbit and nonadiabatic interactions (e.g., Coriolis) in the recoupling zone have negligible effects. Molecular photodissociation close to the diabatic model has been observed in many previous experiments.11–18 Calculating the N(2D5/2)/N(2D3/2) ratio under the diabatic limit is not feasible at the current stage, since the repulsive states responsible for predissociation in the FC region and their interference effects are not known for 14N2 in the studied energy region.10,11,19,23 In the statistical model, strong spin–orbit and nonadiabatic interactions exist among different electronic states near the dissociation limit so that the spin–orbit components are distributed according to their degeneracies. This gives the statistical spin–orbit fine-structure branching ratio of 1.5 for N(2D5/2)/N(2D3/2). According to the above discussions, we tentatively conclude that the photodissociation of the low J′ levels (J′ = 0, 1) into the N(2D5/2,3/2) + N(2D5/2,3/2) channel may follow the adiabatic limit that only a single correlated fine-structure channel is exclusively populated; as the rotational excitation increases, the Coriolis interaction in the recoupling zone becomes stronger and the fragment recoil velocity also increases; these two effects together make the photodissociation process evolve gradually from the adiabatic limit to the diabatic or statistical limit that other spin–orbit fine-structure channels are also populated significantly.

Previous theoretical calculations showed that the fine-structure branching ratio Na(2P3/2)/Na(2P1/2) in the photodissociation of NaH approaches the diabatic limit when the excess kinetic energy is more than an order of magnitude larger than the atomic spin–orbit splitting,8 while the diabatic limit for the OH predissociation is reached much slower than NaH.9 The term energy of the J′ = 0 level in the b1Σu+(v = 20) state of 14N2 is about 67.9 cm−1 above the lowest dissociation limit N(2D5/2) + N(2D5/2), which is less than an order of magnitude of the spin–orbit splitting of 8.713 cm−1 for N(2D5/2,3/2). Compared to NaH and OH, the reduced mass of 14N2 is much larger; thus, the corresponding recoil velocity should be much smaller, which makes the near threshold photodissociation of 14N2 here closer to the adiabatic limit.7 Another important reason for the occurrence of almost pure adiabatic photodissociation at the J′ = 0 level is that the nonadiabatic Coriolis interaction is zero for J′ = 0 in the recoupling zone. Besides Coriolis interaction, the spin–orbit interaction could also strongly mix the dissociative states populated in the FC region with other “dark” states in the recoupling zone, which could significantly alter the spin–orbit fine-structure branching ratios.8–10 The observation of pure adiabatic photodissociation at J′ = 0 level indicates that the spin–orbit interactions in the recoupling zone may play a negligible role for determining the fine-structure branching ratios, as the spin–orbit interaction is independent of J′.

The fine-structure branching ratio reaches a maximum value of ∼1.35, which is slightly below the statistical limit of 1.5, when J′ = 6, and stays unchanged until J′ = 12. This could be caused by the stronger Coriolis interaction in the recoupling zone as J′ increases and makes it approach the statistical limit. Another possibility for this change could be due to the involvement of other dissociative states crossing with the b1Σu+(v = 20) state in the FC region that populate the other two correlated spin–orbit fine-structure channels as J′ increases. Our recent study on the multi-channel photodissociation dynamics of the b1Σu+(v = 20) state showed that several different dissociative electronic states should be responsible for its dissociation into the channel N(2D5/2,3/2) + N(2D5/2,3/2) when J′ > 0.19 At rotational levels J′ > 12, the ratio starts to decrease again. Here, the only possible explanation could be that new dissociative states start to contribute to the dissociation process in the FC region, as predicted in OH,9–12 considering the fact that the rotational term energy increases as a function of J′(J′ + 1), and it could become significant enough that the crossings with higher lying dissociative states start to contribute to the dissociation process at high J′ levels (e.g., the J′ = 13 level is ∼193 cm−1 higher than the J′ = 0 level; see Table S1 in the supplementary material). The photodissociation dynamics of the b1Σu+(v = 20) state of 14N2 has been proved to be complicated in the FC region and strongly rotationally dependent;19,23 theoretical calculation revealed high density of potential energy curves correlating to the N(2D5/2,3/2) + N(2D5/2,3/2) limit, and sophisticated spin–orbit interactions exist among them.24 Thus, quantitative understanding of the rotational dependence of the fine-structure branching ratio, as shown in Fig. 2, is not feasible at the current stage, which requires detailed information on the potential energy curves near the dissociation limit and all the spin–orbit and nonadiabatic interactions among them from the FC to the asymptotic regions.8–10 

In summary, rotationally dependent spin–orbit fine-structure branching ratios N(2D5/2)/N(2D3/2) and also the branching ratios into the three correlated fine-structure channels at the dissociation limit of N(2D5/2,3/2) + N(2D5/2,3/2) for 14N2 have been observed for the first time. The current study shows that 14N2 in low rotational levels (J′ = 0 or 1) of the b1Σu+(v = 20) state dissociates almost adiabatically along a single Born–Oppenheimer electronic potential energy curve and exclusively ends at the correlated fine-structure channel N(2D5/2) + N(2D3/2). Other correlated fine-structure channels start to be populated rapidly as J′ increases due to the stronger Coriolis interaction in the recoupling zone and the participation of other dissociative states at higher J′ levels. To our best knowledge, such transition from a nearly pure adiabatic process to the statistical or diabatic limit in photodissociation near the threshold as rotational excitation increases has never been observed in any experiments before. Besides photodissociation, the current experiment near the threshold should also provide critical information on the cold collision dynamics between two N(2D5/2,3/2) atoms, as photodissociation can be treated as a “half-collision” process.3–6 This will be discussed in the future.

The supplementary material contains the experimental details, Figs. S1 and S2, and Table S1.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 21973100 and 22103090), the Program for Young Outstanding Scientists of Institute of Chemistry, Chinese Academy of Science (ICCAS), and the Beijing National Laboratory for Molecular Sciences (BNLMS). Hong Gao was also supported by the K. C. Wong Education Foundation. Pan Jiang was supported by the China Postdoctoral Science Foundation Grant No. 2020TQ0324.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Supplementary Material