Conical Intersection Dynamics in NO2 Probed by Homodyne High-Harmonic Spectroscopy

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Science  14 Oct 2011:
Vol. 334, Issue 6053, pp. 208-212
DOI: 10.1126/science.1208664


Conical intersections play a crucial role in the chemistry of most polyatomic molecules, ranging from the simplest bimolecular reactions to the photostability of DNA. The real-time study of the associated electronic dynamics poses a major challenge to the latest techniques of ultrafast measurement. We show that high-harmonic spectroscopy reveals oscillations in the electronic character that occur in nitrogen dioxide when a photoexcited wave packet crosses a conical intersection. At longer delays, we observe the onset of statistical dissociation dynamics. The present results demonstrate that high-harmonic spectroscopy could become a powerful tool to highlight electronic dynamics occurring along nonadiabatic chemical reaction pathways.

The outcome of chemical reactions is determined by the valence electronic structure of molecules. Therefore, the elucidation of elementary reaction mechanisms requires an understanding of the valence electron dynamics. Recently developed techniques that are efficient in probing valence electron dynamics include attosecond transient absorption (1), extreme ultraviolet photoelectron spectroscopy (XUV-PES) (2), high-order harmonic spectroscopy (HHS) (35) and strong-field ionization (6). Both time-resolved PES (7) and time-resolved HHS are sensitive to valence electron dynamics through the molecular photoionization matrix elements.

Electronic dynamics in molecules are particularly challenging to observe when they are strongly coupled to nuclear dynamics. Such situations often arise in polyatomic molecules where conical intersections between the potential energy surfaces induce very rapid radiationless transitions at particular nuclear configurations (see inset of Fig. 1) (8, 9). These features channel electronic excitation into atomic motion in such diverse contexts as the primary steps of vision (10) and the dynamics underlying electron transfer and the photostability of DNA bases (11).

Fig. 1

Schematic representation of the potential energy surfaces of the ground Embedded Image 2A1 and excited Embedded Image 2B2 electronic states of NO2. The dominant electronic configuration in the two highest-lying molecular orbitals is shown for each state on the left. The orbitals are represented by isoamplitude surfaces of the wave function with color-coding of the sign. After excitation by a 400-nm pump pulse (blue arrow), the wave packet initially moves along the bending coordinate, crosses the conical intersection (shown in the top left inset) several times during the first 100 fs, and spreads along the asymmetric-stretch coordinate. Wave-packet population that has returned to the ground electronic state and possesses an energy above 3.1155 eV (green dashed line) dissociates on the picosecond time scale (dashed arrow).

Here, we show that high-harmonic spectroscopy reveals the variations in electronic character during the conical intersection dynamics and the subsequent dissociation of nitrogen dioxide (NO2). We chose NO2, a radical, because of its model status for theories of unimolecular dissociation (1214) and conical intersection dynamics (1519). Our results translate the previously recognized sensitivity of HHS to electronic structure into a tool for elucidating chemical reaction dynamics.

High-harmonic spectroscopy can be factored into three steps: removal of an electron by an intense femtosecond laser field, acceleration of the electron in the laser field, and photorecombination (20, 21). Each step contributes an amplitude and a phase to the emitted XUV radiation (2224, 20, 25). The measurement relies on a coherent detection scheme in a transient grating geometry, using unexcited molecules as a local oscillator (4, 5). It is thus sensitive to both amplitude and phase of the photorecombination matrix elements, a quantity that has recently attracted a lot of interest (26, 27). Time-resolved HHS is thus related to time-resolved PES but differs in its sensitivity to the continua associated with different ionic states. PES projects the molecular wave packet onto a set of ionic states, influenced by resonances, Franck-Condon factors, and dissociative ionization. HHS involves recombination from an energetic continuum electron with one or a few of the lowest ionic states that were selected by tunneling ionization.

A schematic representation of the potential energy surfaces of NO2 is shown in Fig. 1. In the X˜ 2A1 electronic ground state, NO2 possesses a bent equilibrium geometry and the dominant electronic configuration in the two highest occupied orbitals is (b2)2(a1)1. Single-photon absorption at 400 nm excites the molecule to the A˜ 2B2 state of dominant configuration (b2)1(a1)2. The A˜ 2B2 excited state forms a conical intersection with the ground state (see inset of Fig. 1). Wave-packet calculations have shown that within the first femtoseconds after excitation, the nuclear wave packet moves along the bending coordinate toward the conical intersection, where it can either cross the intersection and remain on the same diabatic surface or else stay in the upper cone of the intersection and thus change the diabatic surface (gray arrows in Fig. 1) (1518). After a few hundred femtoseconds, the nuclear wave packet returns to the electronic ground state through internal conversion. If the energy of the absorbed photon lies above the first dissociation limit at 3.1155 eV (397.95 nm) (all quoted wavelengths are vacuum values), the molecule dissociates into NO (X 2ΠΩ) and O (3PJ) on the picosecond time scale (dotted arrow in Fig. 1). Previous studies using laser-induced fluorescence have characterized the picosecond dissociation in detail (14, 28). However, the femtosecond conical intersection dynamics has been largely obscured by competing multiphoton processes (19), requiring elaborate coincidence detection methods (29).

The experimental setup is illustrated in Fig. 2. We excite NO2 in a transient grating formed from two synchronized 400-nm laser pulses and probe its dynamics by high-harmonic generation from an 800-nm, 32-fs laser pulse (4, 30). The excitation pulses are generated either in a 2-mm-thick β-barium borate (BBO) crystal, providing 160-fs pulses of 1-nm spectral width tunable from 395 to 407 or in a 100-μm-thick BBO crystal, giving 40-fs pulses of 5-nm spectral width. The combination of the transient grating with an XUV monochromator allows us to spectrally resolve the high harmonics (H11 to H21 in this experiment) and to measure both the undiffracted (m = 0) and diffracted (m = ±1) components of each harmonic order. The signal observed in m = 0 is equivalent to a measurement done in a collinear pump-probe geometry, whereas the diffracted signal results from an interference between equal populations of excited and unexcited molecules (4).

Fig. 2

Experimental setup for high-harmonic transient grating spectroscopy as first described in (4). The transient grating creates a spatially modulated population of excited molecules accompanied by a depletion of the unexcited molecules. The periodic structure results in a modulation of amplitude and phase of the XUV emission in the near field that leads to first-order diffraction in the far field. An XUV grating disperses the radiation in one dimension while the beam freely diverges in the other dimension. With r(cos(kx) + 1) being the spatially modulated excitation fraction, the signal in m = 0 is given by Embedded Image and that in m = ± 1 by Embedded Image, where the symbols are defined in the text relating to Eq. 1.

We first discuss the picosecond photodissociation dynamics, which show that our measurement is dominated by single-photon absorption. The measurements were done with the 160-fs pulses, but we have obtained fully consistent results with the 40-fs pulses. The dynamics observed after excitation by pump pulses centered at 407 nm or 397.2 nm are shown in Fig. 3, A and C, respectively. Figure 3A shows a step-like decrease of the undiffracted XUV radiation and a corresponding increase of the diffracted intensity. The total ion yield, measured simultaneously and shown in Fig. 3B, increases, whereas the high-order harmonic signal decreases; this indicates a destructive interference between harmonics emitted by the ground state and those emitted by the excited state (4, 5). In this scan, performed with a 200-fs delay step, there is no signature of any regular dynamics. Figure 3, C and D, however, show exponential growth or decay on the picosecond time scale, following the step-like variations.

Fig. 3

High-harmonic and ion yields as a function of delay between two synchronized near-UV pump pulses setting up a transient grating and an 800-nm probe pulse generating high harmonics in the excited sample. (A) The yield of diffracted (red dots) and undiffracted (blue dots) high-harmonic signals, normalized to the undiffracted signal at negative pump-probe delays, for excitation by 407-nm pump pulses. The full lines represent the results of the theoretical model described in the text. (B) H13, m = 0, and m = 1 from (A) together with the total ion yield measured in parallel to the experiment (green dots) and the theoretical model (green line). (C and D) The same observables as (A and B), but for a pump pulse centered at 397.2 nm. Polarization of pump and probe are parallel. The typical pump energy is 10 μJ to minimize multiphoton processes.

The combined information from Fig. 3 shows that the step-like response to excitation below threshold characterizes electronic excitation without dissociation (Fig. 3, A and B), whereas the exponential variation of the signal in Fig. 3, C and D shows the unimolecular decomposition of NO2. To quantify these observations, we introduce a simple model. When excitation takes place below threshold, the radiated XUV field can be described as in Eq. 1EXUV(Ω)=(1r)dgeiϕg+rdeeiϕe(1)where r is the spatially modulated fraction of excited molecules, and dg, de and ϕg, ϕe are the high-harmonic amplitudes and phases of the ground or excited molecular states, respectively. When the excitation frequency exceeds threshold, the excited molecules can undergo dissociation into NO(2Π)+O(3P) that, together, emit harmonics with a resultant amplitude df and phase ϕf. The radiated XUV field is then given by Eq. 2EXUV(Ω,t)=(1r)dgeiϕg+ret/τdeeiϕe+r(1et/τ)dfeiϕf(2)where t is the time elapsed since excitation and τ is the time constant of the unimolecular dissociation.

To extract the relevant parameters from the measurement, both the diffracted and undiffracted high-harmonic signals are normalized by the signal measured in the absence of excitation (namely, |dg|2). We calculate the excited state fraction from the measured pulse energy, focal spot size, and the known absorption cross section of NO2 and determine the unknown parameters in a global nonlinear least-squares fit. The determined parameters are given in Table 1, and the corresponding fit is shown as full lines in Fig. 3, A to D. The total ion yield is represented by equations similar to Eqs. 1 and 2 but with phases set to zero.

Table 1

Molecular parameters for strong-field ionization and high-harmonic generation, determined by fitting Eqs. 1 and 2 to the experimental data shown in Fig. 3, A to D. The excitation fraction r has been determined from the experimental parameters as described in the text.

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The global fit to all high-harmonic orders and ion signals in Fig. 3, B and D, provides a time constant τ = 2.71 ± 0.15 ps, in agreement with the 2.78 ps measured previously at room temperature (14). The deep modulation of the signals demonstrates that the probed dynamics are dominated by one-photon absorption, which is in general difficult to achieve in femtosecond time-resolved measurements on molecules because of multiphoton processes (19). The strong-field ionization probability of vibrationally excited NO2 molecules in the electronic ground state is larger than that of unexcited molecules [vertical ionization potential (Ip) = 11.2 eV] by a factor of (iig)4.5. The ionization rate of NO + O (dominated by NO because the vertical Ip values are 9.2 and 13.8 eV, respectively) exceeds that of the unexcited molecules by a factor of ≈ 2.3. The relative high-harmonic amplitudes are larger for the excited molecules than for the unexcited molecules, especially for low harmonic orders, and the phase shift is substantial, as expected from the observed destructive interference. The relative amplitudes for the NO + O pair decrease particularly fast with increasing harmonic order, as expected from the lower cutoff of the harmonic emission from NO. We thus conclude that the observed high-harmonic signal is dominated by single-photon excitation, in contrast to previous femtosecond time-resolved measurements that reported oscillatory components of periods in the range of 500 to 850 fs (3133). The latter were indeed attributed to multiphoton excitations to higher-lying electronic states that would not emit high harmonics owing to their low binding energies.

In the following, we exploit this property to investigate the hitherto unobserved femtosecond dynamics of NO2 in the A˜ 2B2 state. These measurements were done with 40-fs excitation pulses centered at 401 nm. The experimental results measured with cross-polarized laser pulses are shown in Fig. 4, A and B. Fig. 4A shows the undiffracted and diffracted signals measured in harmonics 11 through 17 (blue and red dots, respectively), and Fig. 4B shows the same quantities for H15 and H16 (green line). The latter allows an accurate determination of the zero time delay and the cross-correlation function (34). Whereas the m = 0 order decreases smoothly over the duration of the cross correlation, the diffracted order (m = 1) increases and reaches a maximum at a pump-probe delay of 35 fs. The diffracted signal subsequently decreases and reaches a minimum around 70 fs, followed by another maximum at 130 fs. Further modulations with decreasing contrast are observed at longer pump-probe delays. As we show and discuss in fig. S2 and the accompanying text, no modulations are observed in parallel polarization.

Fig. 4

(A) The high-harmonic yields after excitation by a pair of 10-μJ, 401-nm laser pulses in the undiffracted (blue) and diffracted orders (red) of the odd harmonics (H11 to H17). Experimental data points appear as dots and a three-point-smoothed version as lines. (B) The undiffracted (blue) and diffracted orders of H15 (red) and H16 (green line). (C) The diabatic excited state population from (17) convoluted with a 50-fs Gaussian cross-correlation function. (D) Illustration of how high-harmonic transient-grating spectroscopy probes the electronic character of the molecule during the conical intersection dynamics. The top illustrates the spatial intensity structure of the transient grating. The bottom shows schematically the lowest two potential energy surfaces of NO2. When the molecule is in the excited diabatic state (represented as a blue wave packet), the high-harmonic emission differs significantly from the unexcited (2A1) molecules, leading to a large variation of high-harmonic amplitude and phase across the transient grating and thus to strong diffraction. When population is transferred into the ground diabatic state (red wave packet), the modulation depth of high-harmonic amplitude and phase across the transient grating, and therefore the diffracted intensity, decreases.

These oscillations, observed in the diffracted XUV radiation, are a fingerprint of the electronic dynamics of the molecule taking place around the conical intersection, as illustrated schematically in Fig. 4D. In the bright zones of the transient grating, the electronic character of the excited molecules oscillates between X˜ 2A1 and A˜ 2B2. When the molecule is in the X˜ 2A1 state, the near-field variation of the high-harmonic emission is much smaller for most molecular geometries than when it is in the A˜ 2B2 state, which we detect as a variation of the intensity of diffracted radiation [see section VI of the supporting online material (SOM)].

To rationalize these observations, we introduce a simple model based on diabatic electronic states and coordinate-independent transition moments (more detailed calculations are given in the SOM). The total radiated XUV field is the coherent sum of contributions from the unexcited molecules (subscript g) and excited molecules in the two diabatic A˜ 2B2 and X˜ 2A1 states (Eq. 3)EXUV(Ω,t)=[1r(t)]dgeiϕg+rA˜(t)dA˜eiϕA˜+rX˜(t)dX˜eiϕX˜(3)where r(t)=rA˜(t)+rX˜(t) is the total fraction of excited molecules before dissociation takes place. The intensity of the diffracted light is thus given by Eq. 4 (4)Im=1(Ω,t)=14|rA˜(t)(dA˜eiϕA˜dgeiϕg)+rX˜(t)(dX˜eiϕX˜dgeiϕg)|2(4)The high-harmonic amplitude is determined by the probabilities of ionization and recombination. The phase is determined by the phase accumulated by the bound state (Ip τ), and the recombination phase (24), where τ stands for the transit time of the electron in the continuum (~1 to 1.7 fs). To the first order, ionization from either A˜ 2B2 or X˜ 2A1 involves the removal and recombination of an a1 electron in the cross-polarized case (Fig. 1). The main difference is due to the Ip τ phase. The ground-state channel 1A12A1 has an Ip of 11.2 eV, whereas the main excited-state ionization channel 3B22B2 has an Ip that varies between 9.8 eV and 13.2 eV as a function of the bending coordinate. The relative phase difference ∆Ip τ stays close to zero for the X˜ 2A1 state, whereas it is significantly larger (between 1 and 3 radians) for most geometries of the A˜ 2B2 state. Hence, in Eq. 4, |dA˜eiϕA˜dgeiϕg||dX˜eiϕX˜dgeiϕg| and the time dependence of the diffracted signal will be dominated by HHG emission from the A˜ 2B2 state. It is thus sensitive to the temporal variation of the population in the A˜ 2B2 state, as illustrated in Fig. 4D. This conclusion is also supported by the detailed calculations described in the SOM.

The observed polarization dependence of the oscillations is a consequence of the electronic symmetries. Photoexcited molecules have their y axis (O-O axis) parallel to the polarization of the exciting field (Fig. 1). In the cross-polarized experiment, the emission from excited molecules is thus dominated by those probed along their z axis (C2 axis). The same orientation also dominates the emission from the unexcited molecules, resulting in a sensitivity to the diabatic electronic state of the excited molecule (2B2 versus 2A1). In the case of parallel polarizations, the photoexcited molecules are being probed along their y axis, whereas the unexcited molecules are probed along their z axis. Therefore, the emission from excited molecules in both diabatic states differs significantly from that of the unexcited molecules, and the amount of diffracted light is sensitive only to the total population of excited molecules.

Because the electronic dynamics between X˜ 2A1 and A˜ 2B2 have not been observed experimentally before, we compare the measurements to recent quantum dynamical calculations on NO2 (17, 18). These three-dimensional wave packet calculations have predicted characteristic oscillations in the diabatic populations over the first few hundred femtoseconds. The diabatic A˜ 2B2 population rA˜(t), convoluted with a 50-fs Gaussian cross-correlation function, is shown in Fig. 4C. Both the overall behavior and the distinct features observed in the diffracted high-harmonic signal are present in the calculated diabatic state population. The first maximum occurs at a delay of 26 fs, the first minimum at 68 fs, and the second maximum at 106 fs. The modulations in the diffracted signal thus reflect the diabatic state population dynamics. Considering the complexity of the problem and the simplicity of our model, the agreement is remarkable. To exclude the possibility that the observed modulations result from a change of the strong-field-ionization rate of the molecule as a function of the nuclear coordinates, we have also measured the total ion yield in parallel to the high-harmonic yield and have not observed any modulation on top of the smooth increase (see fig. S3 and accompanying text).

Comparing the experimental and theoretical results, we can draw a qualitative picture of the evolution of the electronic structure of the molecule as it crosses the conical intersection. Photoexcitation prepares the wave packet on the upper diabatic state as shown in Fig. 4D. When it first approaches the conical intersection, it has little expansion along the asymmetric stretch coordinate (the b2 mode responsible for vibronic coupling), and thus most of the amplitude traverses the intersection and remains on the same diabatic state [80% according to the wave packet calculation (17)]. This fraction, the diabatic wave packet, returns to the conical intersection with a significant spread along the bond-stretching coordinate, resulting in a strong transfer to the ground diabatic state. This leads to the first minimum in the diabatic state population around 60 fs. After two or three periods of motion along the bending coordinate, wave packet components from diabatic and adiabatic traversals interfere with each other and extend so significantly along the symmetric and asymmetric stretch coordinates that no appreciable motion of the wave packet average position can be defined for times longer than 200 fs (15, 17).

High-harmonic spectroscopy is a powerful probe of electronic dynamics in nonadiabatic processes. The homodyne interference of species in different electronic states has enabled us to distinguish multiple photochemical pathways—electronic excitation to bound states versus excitation followed by dissociation. The coherence of the high-harmonic emission also enabled us to extract amplitudes and phases of the various species occurring in the photochemical transformation and to learn how to interpret them. Temporal variations in the dominant electronic configuration of the photoexcited wave packet are manifested in a polarization dependence of the pump-probe signal, which is expected to be a powerful property in future studies of electronic dynamics.

We have thus demonstrated how to use high-harmonic spectroscopy to elucidate a complex photochemical process from the first femtoseconds that are governed by a conical intersection to the picosecond time scale where dissociation proceeds statistically. Our results on the femtosecond dynamics may be used in the future to check high-level quantum dynamical calculations. We anticipate that this property will be of great value to femtochemistry and ultrafast imaging.

Supporting Online Material

Materials and Methods

Figs. S1 to S5

Tables S1 to S6

References (3543)

References and Notes

  1. Acknowledgments: We thank A. Stolow for fruitful discussions and B. Whitaker and K. Takatsuka for permission to use information underlying Figs. 1 and 4C. We acknowledge financial support from the Swiss National Science Foundation (PP00P2_128274), Agence Nationale de la Recherche (ANR-08-JCJC-0029 HarmoDyn), Centre National de la Recherche Scientifique (PICS: Imagerie moléculaire par impulsions attosecondes), National Sciences and Engineering Research Council of Canada, Canadian Institute for Photonic Innovations, and Air Force Office of Scientific Research.
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