Research Article

Time-Resolved Dynamics in N2O4 Probed Using High Harmonic Generation

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Science  21 Nov 2008:
Vol. 322, Issue 5905, pp. 1207-1211
DOI: 10.1126/science.1163077


The attosecond time-scale electron-recollision process that underlies high harmonic generation has uncovered extremely rapid electronic dynamics in atoms and diatomics. We showed that high harmonic generation can reveal coupled electronic and nuclear dynamics in polyatomic molecules. By exciting large amplitude vibrations in dinitrogen tetraoxide, we showed that tunnel ionization accesses the ground state of the ion at the outer turning point of the vibration but populates the first excited state at the inner turning point. This state-switching mechanism is manifested as bursts of high harmonic light that is emitted mostly at the outer turning point. Theoretical calculations attribute the large modulation to suppressed emission from the first excited state of the ion. More broadly, these results show that high harmonic generation and strong-field ionization in polyatomic molecules undergoing bonding or configurational changes involve the participation of multiple molecular orbitals.

In polyatomic molecules, electronic and vibrational excitations can couple and rapidly redistribute both energy and charge during dynamic processes. Because of the importance of these dynamics in chemical and biological systems, the ability to probe dynamics in larger polyatomic molecules ultimately is a requirement for any broadly useful spectroscopy or dynamical imaging technique. As an example, time-resolved photoelectron spectroscopy (TRPES) is a weak-field perturbative method that can probe these dynamics (13). In TRPES, the molecule is first excited by a pump pulse. A time-delayed probe pulse then projects the complex evolving wave packet onto the molecular ionization continuum, and the outgoing electron is analyzed as a function of pump-probe delay. The cation electronic states, their associated electronic continua, and the vibrational structure of the ionization continuum are used as “templates” for projecting out the electronic and vibrational components of the complex wave packet. This evolving projection onto multiple electronic continua permits the disentangling of electronic and vibrational dynamics during nonadiabatic processes in polyatomic molecules (4).

High harmonic generation (HHG) is a strong-field nonperturbative process (5, 6) that is closely related to photoelectron spectroscopy, occurring at laser intensities of >1013 W cm–2. In atoms, HHG is successfully described by an adiabatic single active electron (SAE) model involving three steps: strong-field tunnel ionization, propagation of the continuum electron in response to the laser field, and finally, recombination of the electron with its parent ion, which results in the emission of a high-energy photon (710). However, in the case of HHG from a polyatomic molecule, the physics is more complex because of the many-body electronic structure of polyatomic molecules and the existence of rovibrational and nonadiabatic dynamics. The recombination matrix element for the HHG process and the photoionization matrix element of the photoabsorption process are the same because these steps are the inverse of each other. Therefore, the multiple electronic continua relevant to probing complex polyatomic dynamics via TRPES must also play a role when HHG is used to probe these dynamics. The use of HHG as a probe has two potential advantages over TRPES: the ability to access attosecond–time-scale processes and the ability of HHG to simultaneously probe with many photon energies. However, until recently (11, 12), only the highest occupied molecular orbital (HOMO) has usually been considered to explain both strong-field ionization and high harmonic emission. This simplification comes from the adiabatic and SAE approximations that underlie theories of tunnel ionization in atoms and molecules [Ammosov-Delone-Krainov (ADK) and molecular ADK (13, 14) models] and are integral to the three-step model of HHG (79). In polyatomic molecules, however, both approximations can fail dramatically, particularly so when the molecule is dynamically evolving, as we show here. Strong-field ionization can become nonadiabatic and involve multielectron excitations (15, 16). Theoretical efforts to relax the SAE approximation are being attempted in order to address these issues by introducing multielectron effects in the recombination step of HHG (11, 12, 17, 18).

Prior investigations showed that HHG from rotational axis–aligned molecules is a potential probe of static molecular structure (19, 20) because the emission strength depends on the molecular orbital nature of the ground electronic state and its alignment with respect to the laser field. Recent related work used the photoelectrons released and rescattered during the strong-field ionization process to recover the static orbital structure of simple diatomic molecules (21). HHG was also used as a probe of simple dynamics in molecules in which, for example, the molecular structure varied slightly without any bond reorganization. Past work showed that the HHG process is sensitive to simple vibrational dynamics in a molecule, even to modes that cannot readily be optically probed (22, 23). The rearrangement of atoms within a molecule during the HHG process can also be inferred by comparing HHG spectra of isotope-substituted molecules (24). Chemical dynamics, however, involve large-amplitude motions. HHG experiments have yet to succeed in observing and understanding large-amplitude structural rearrangements within a polyatomic molecule, in which the simple assumptions are unlikely to remain valid because of dramatic and evolving changes in the ionization/recombination dynamics.

We successfully applied HHG as a time-resolved probe of chemical dynamics in a polyatomic molecule. By exciting a large-amplitude vibrational wave-packet motion in the ground state of a dinitrogen tetraoxide (N2O4) molecule, we observed large modulations in harmonic yield. We discovered that at the outer turning point of the vibration, tunnel ionization populates the ground state of the ion (HOMO+ Ag continuum), which has a large recombination dipole and therefore a high probability for harmonic emission. In contrast, at the inner turning point, the first excited state of the ion is populated by tunnel ionization [that is, the (HOMO-1)+ B2g continuum]. This channel has a reduced recombination cross-section and thus suppresses the harmonic emission.

HHG probing of N2O4dynamics. N2O4 is a dimer of NO2, with a dissociation energy of ∼0.65 eV. N2O4 can be present in dominant quantities (80%) even at room temperature. The molecule has D2h symmetry and six Raman-active vibrational modes, the strongest being the low-frequency N-N symmetric stretch (265 cm–1, 0.03 eV). By nonresonantly exciting this mode via impulsive stimulated Raman scattering (ISRS), we were able to generate a large-amplitude ground-state vibrational wave packet along the N-N coordinate. This large-amplitude motion correlates upon ionization with a broad range of ionic configurations, leading to the participation of more than one molecular ionization continuum in the HHG process (Fig. 1).

Fig. 1.

(A) Experimental setup. N2O4 molecules from an effusive nozzle are excited and probed using ultrafast 800-nm laser pulses. The pump-pulse intensity and duration are chosen to impulsively excite, but not ionize or dissociate, N2O4. A more intense collinear probe pulse generates harmonics from the vibrationally excited dimer. (B) Schematic of the experiment.

In our experiment, ultrashort laser pulses from a Ti:sapphire laser system (800 nm, ∼30 fs, 4 mJ, and 1 kHz) were split into pump and probe pulses. The pump pulse was focused on to a N2O4 gas jet (backing pressure ∼700 torr) at an incident intensity of ∼2 × 1013 W cm–2 to impulsively excite ground-state vibrations in the molecule. The time-delayed probe pulse was focused to an intensity of ∼2 × 1014 W cm–2 to generate high harmonics from the vibrationally excited molecules. The relative polarizations of the pump and the probe pulses were controlled using a half-wave plate in the pump-beam path. The generated harmonics were then spectrally separated using an extreme ultraviolet (EUV) spectrometer and imaged onto an EUV-sensitive charge-coupled device camera (Andor Technology, South Windsor, CT). The ion signal could also be collected using a mass spectrometer.

In Fig. 2A, we show the experimentally observed high harmonics, from orders 15 to 23, as a function of pump-probe time delay. Lower-order harmonics were not observed because of absorption by the 0.2-μm-thick aluminum filter that was used to reject the pump laser light. Even in the raw data, a time-dependent oscillation of the harmonic yield is apparent. For all the harmonic orders observed, the time dependence of the HHG emission (Fig. 2C) shows several common characteristics: a sudden drop in HHG yield when the sample is initially excited at time-zero followed by strong oscillations in the HHG yield imposed on a slowly rising baseline. The strong suppression of harmonic generation at time zero is a result of coherent effects due to the overlap of the pump and probe. Strong oscillations in the harmonic yield are present for both parallel and perpendicular polarizations of the pump and probe (Fig. 2).

Fig. 2.

Harmonic yield as a function of delay between the alignment and HHG pulses using (A) parallel (∥) and (B) perpendicular (⊥) pump and probe polarizations. The harmonic yield is normalized to the harmonic emission at negative pump-probe delays. Time dependence of the 17th harmonic yield for (C) parallel and (D) perpendicular polarizations. The insets in (C) and (D) show the Fourier transform, dominated by the N-N stretch mode at 255 cm–1.

Harmonic modulation by the N-N stretch. The origin of the strong oscillations in the harmonic yield becomes apparent if we apply a discrete Fourier transform to these data. A single peak at 255 ± 10 cm–1 appears in the transform spectra (Fig. 2, C and D, insets). This frequency corresponds unambiguously to the Raman active 265 cm–1 N-N stretch mode of N2O4. Given the ISRS pump mechanism employed here, the initial motion of the vibrational wave packet will be repulsive, with the outer turning point occurring one quarter period after the pump pulse. To verify the exact timing of the emission, we used argon gas in the same setup because HHG from argon exhibits a transient only at time zero because of coherent effects. We thus verified that in N2O4, a large peak in HHG yield appears at 170 ± 10 fs in very good agreement with the expected value of T + T/4 where T = 130 fs, which is the vibration period of the N-N stretch mode of N2O4. This timing clearly indicates that harmonic yield maximizes at the outer turning point of the N-N stretch vibration. The first peak in emission at T/4 (∼35 fs) is less discernible in the data, probably because of a pump-probe overlap that suppresses the signal.

Only those N2O4 molecules for which the N-N bond axis is closely aligned with the pump-beam polarization are vibrationally excited. This same population of molecules is probed by the HHG probe beam, and exhibit oscillations in high harmonic yield corresponding to the N-N stretch as discussed above. In Fig. 2, the amplitude of the harmonic oscillations diminishes as a function of time following the pump pulse, on a time scale consistent with rotational/vibrational dephasing.

We also measured the ionization yield as a function of pump-probe delay (fig. S1). The yield of N2O +4 is approximately the same at the inner and outer turning points. This finding shows that at the inner turning point, the molecule is ionized but harmonic emission is suppressed. Hence, ionization alone (modulation of the ionization potential or rate due to the vibrational motion) cannot account for the observed large modulation in HHG yield.

The other possibility for the suppression of HHG at the inner turning point of the vibration is a contribution from a different electronic continuum, one that has smaller recombination amplitudes for HHG. We have evidence that this is the case. In Fig. 3, we plot the measured intensity dependence of the HHG peak-to-peak modulation depth of different harmonic orders. The modulation depth increases with increasing laser intensity and decreases with increasing harmonic order. If only a single continuum transition is involved in harmonic emission, then at the relatively high laser intensities that were used in these experiments, ionization will be more saturated at the outer turning point because of the lower ionization potential at this position relative to the inner turning point. This should lead to a reduced intensity ratio between harmonics emitted at the outer and inner points of the vibration with increasing laser intensity. In contrast, the observed modulation depth increases with increasing laser intensity.

Fig. 3.

Laser intensity–dependence of the vibrational modulation depth for different harmonic orders, showing an increasing modulation depth with increasing laser intensity.

Ionization of the (HOMO-1) orbital. To understand the effect of a large excursion on the HHG process, we performed ab initio calculations of the structure of both the N2O4 neutral and cation states (25). For N2O4 molecules, ISRS in the strongly anharmonic ground-state potential results in large vibrational amplitudes of up to 0.6 Å (from ∼1.6 to 2.2 Å). The calculated potential energy curves for the ground state of neutral N2O4, the ground state of the cation N2O4+ (Ag), and the first excited state of the cation (B2g) are shown in Fig. 4A. The equilibrium bond length of the Ag cation has a substantially elongated N-N bond (2.21 Å vertical, elongating to 2.25 Å upon complete optimization). This bond lengthening is a consequence of HOMO ionization to the cation ground electronic state, removing a bonding electron. In contrast, ionization of the (HOMO-1) to the B2g excited state of the cation leaves the N-N bond relatively unchanged (1.75 Å vertical, increasing to 1.80 Å upon relaxation). This picture is confirmed by the previously reported He(I) photoelectron spectra of N2O4, which show a delayed onset and long progression to the cation ground electronic state as compared with sharp lines and very limited progression to the cation first excited state (26).

Fig. 4.

(A) Calculated second-order multiconfigurational quasidegenerate perturbation theory/complete active space self-consistent field method potential energy curves for neutral N2O4 (bottom) and the first two cation states (top). (B) Structural factors for ionization calculated at different bond lengths. At the short bond length, ionization favors the first excited state of the ion (B2g continuum), whereas the ground Ag continuum dominates at long bond lengths

The significant difference in bond length for the ground and excited states of the cation implies a strong bond-length dependence of the structural (Franck-Condon) factors for tunnel ionization: The Ag ground state is expected to be favored at longer N-N distances, whereas the B2g excited channel benefits when the N-N bond is compressed. To quantify this argument, we performed a model calculation of the energy-dependent contribution to the structural ionization factors using the potential energy surfaces shown in Fig. 4A [supporting online material (SOM) text]. The results (Fig. 4B) show that for N-N bond lengths (rN-N) below 1.7 Å, structural factors favor ionization to the B2g excited state. At longer bond lengths, ionization to the Ag ground state of the cation is favored, with the corresponding structural factor increasing up to rN-N = 2.3 Å. Thus, because of the contribution of two ionization channels, the ion yield of N2O +4 is not expected to change significantly during the vibration, which is consistent with our experimental findings (fig. S1).

At the relatively high laser intensity used here, saturation due to the depletion of the neutral N2O4 population may become an important factor. In this regime, the total number of emitters of each type is determined by the ratio of the ionization rates for each species, rather than by the individual rates. The calculated ratio of the Ag/B2g structural factors in N2O4 increases monotonically with rN-N, with the B2g state as the preferred channel at short bond lengths, whereas the Ag state dominates when the bond is elongated. Thus, the relative importance of the two channels remains the same, even in the presence of saturation. This result is supported by the observed intensity dependence of the HHG modulation depth (Fig. 3), which increases with increasing laser intensity. As discussed earlier, a decreasing modulation depth with laser intensity is expected if only one electronic continuum is contributing to the harmonic signal.

Origins of HHG suppression at the inner turning point. For the propagation of the liberated electron in the continuum, the long-range part of the molecular potential is not substantially influenced by intramolecular vibrations, and no additional modulation of the HHG signal is expected. Therefore, we now consider the electron recombination step. To this end, we calculated the overlap between the N-electron wave function of the neutral species and the (N-1)–electron wave function of the ion, the Dyson orbital. This calculation captures the change in the electronic structure of the molecule upon electron removal or recombination. Dyson orbitals for the two main ionization channels, calculated at the equilibrium geometry of the neutral species, are shown in Fig. 5A. The final recombination dipoles for the Ag channel as a function of both their N-N bond separations and harmonic order are shown in Fig. 5B. As a result of the presence of nodal planes along all principal directions, the excited ion-state channel (B2g) is suppressed. Nodal planes both decrease recombination matrix elements and reduce the recollision probability (11, 12).

Fig. 5.

(A) Dyson orbitals corresponding to ionizing to the Ag cation state and the B2g cation state. The calculated equilibrium bond lengths for the neutral, Ag, and B2g cation states are 1.808 Å [close to the experimental value of 1.756 Å (27)], 2.248 Å, and 1.8 Å, respectively. (B) Recombination dipoles of harmonics for continuum at different bond lengths for parallel (red, ∥) and perpendicular (blue, ⊥) pump-probe polarization.

The radial dependence of the calculated recombination dipoles Math is sensitive to the harmonic order. At low harmonic orders (H17 to H21), the matrix elements for the parallel pump-probe orientation increase with the N-N bond length, leading to a doubling in harmonic radiation intensity at Math as compared with Math. At higher orders (H27, H29), the variation of Math with the bond length does not exceed 15%. This behavior is consistent with the observed decrease in the modulation of harmonic intensity for higher harmonic orders (Fig. 2A). The lower modulation depth observed for perpendicular polarization of the pump and probe pulse is also consistent with the overall ≈60% decrease of the recombination matrix elements for this geometry. For both geometries, the modulation remains in phase for all harmonics, indicating that the observed dependences cannot be explained by the structural dependence of the recombination matrix elements.

Even though the cation excited state (here B2g) does not substantially contribute to HHG emission in N2O4, in other molecules emission from different ionization continua will add coherently; thus, observables such as the ellipticity and phase shift of the HHG emission emerge as sensitive diagnostics of dynamics in polyatomic molecules.

Ruling out NO2participation. Because a small portion (<20%) of NO2 coexists with N2O4 in our sample, we had to eliminate the possibility that heterodyne mixing of harmonic emission from N2O4 and NO2 contributed to the observed modulation. If the phase of harmonics emitted from N2O4 at the inner turning and outer turning points were different, interference between emissions from NO2 and N2O4 could contribute to the modulation observed. Such phase variations could arise from intrinsic phase changes because of the differing ionization potentials at the inner and outer turning points of the vibration or from different generating ion states; that is, Ag and B2g. Only the latter is consistent with our proposed mechanism. Using an interferometry technique demonstrated recently (20), we monitored the fringe pattern generated by interfering HHG from vibrationally excited and unexcited N2O4 molecules (SOM text and fig. S2). No phase change in HHG emission was observed during the vibration within the sensitivity limit of our measurements. This null result is a clear indication that heterodyne mixing does not substantially contribute to our signal.

Outlook. This discovery brings both challenges and opportunities to the application of strong-field ionization and HHG to the study of polyatomic structure and dynamics. Although a simple adiabatic picture involving only a single HOMO orbital may be sufficient for some diatomic molecules, generalization to larger molecules undergoing structural changes (for example, chemical reaction) will require consideration of both many-body and nonadiabatic electronic dynamics (11, 12). However, the sensitivity of strong-field ionization and HHG to the different ionization continua promises that techniques monitoring tunnel ionization, TRPES, and HHG will uncover detailed information on electronic and nuclear structure and dynamics in polyatomic molecules.

Supporting Online Material

SOM Text

Figs. S1 and S2


References and Notes

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