Letter pubs.acs.org/JPCL
Ultrafast Relaxation Dynamics in trans-1,3-Butadiene Studied by Time-Resolved Photoelectron Spectroscopy with High Harmonic Pulses Ayumu Makida,† Hironori Igarashi,† Takehisa Fujiwara,† Taro Sekikawa,*,† Yu Harabuchi,‡ and Tetsuya Taketsugu‡ †
Department of Applied Physics, Faculty of Engineering, Hokkaido University, Kita 13 Nishi 8, Kita-ku, Sapporo 060-8628, Japan Department of Chemistry, Faculty of Science, Hokkaido University, Kita 10 Nishi 8, Kita-ku, Sapporo 060-0810, Japan
‡
S Supporting Information *
ABSTRACT: In trans-1,3-butadiene, the ultrafast relaxation from the doubly excited state 21Ag and the corresponding recovery of the ground state 11Ag were observed simultaneously for the first time by time-resolved photoelectron spectroscopy (TRPES) using 29.5 eV high harmonic pulses. The fast recovery of 11Ag shows that the following dissociation upon photoexcitation takes place after returning to the ground state. At 427 fs after photoexcitation, only the ionization energy from the CC σ bond was found to remain shifted. Accompanying theoretical calculations with an assumption of Koopmans’ theorem show that the ionization energy of the CC σ bond is modulated by vibrational excitation of the antisymmetric CC stretching mode. TRPES by high harmonics can probe the changes in the molecular structure sensitively. SECTION: Spectroscopy, Photochemistry, and Excited States
C
in the 21Ag state, leading to the CI with the ground state.10 However, ionization spectroscopy provides only the lifetimes of the excited states. In addition, there still remains a question whether the excited molecules return to the original structure in the ground state or transform directly into other photoproducts, because trans-1,3-butadiene is known to dissociate into some fragments through several pathways upon photoexcitation.7 To gain insight into the relaxation dynamics of the trans-1,3butadiene molecule, we applied time-resolved photoelectron spectroscopy (TRPES) using high harmonic pulses to gaseous trans-1,3-butadiene. TRPES by high harmonic pulses is advantageous in that both excited states and the ground state can be observed simultaneously. In this work, the observed photoelectron bands were characterized by quantum chemical calculations based on Koopmans’ theorem. Reference13 shows that the calculated orbital energies and experimental ionization energies are consistent in trans-1,3-butadiene. Very recently, it was reported that orbital energies calculated by long-range corrected density functional theory (LC-DFT) reproduce the ionization energy very well.14,15 Hence, in this work, the observed spectra were characterized and discussed by LC-DFT calculations based on Koopmans’ theorem. Experimentally, trans-1,3-butadiene was pumped directly to the optically dark 21Ag state by two-photon excitation with 400 nm photons (= 3.10 eV) and was probed by the 19th harmonic
hromophores in molecules function as photodetecting antennas, effecting conformational changes upon photoexcitation during biological processes, such as photosynthesis, visual perception, and bioluminescence.1 The polyene structural moiety, a conjugated system consisting of alternating single and double bonds between carbon atoms, constitutes one of the fundamental chromophores. For example, the polyene all-trans-retinal is an essential component of bacteriorhodopsin in the visual cycle.1 Among the polyenes, trans-1,3-butadiene is the simplest conjugated diene. It has been investigated both experimentally and theoretically to understand energy relaxation processes in polyene chromophores in a simplified manner.2−12 In gaseous trans-1,3-butadiene, the lowest optical excitation corresponds to the π → π* transition, the 11Ag → 11Bu band, with a peak of around 207 nm (= 5.99 eV). The lifetime of 11Bu was found to be less than 50 fs by time-resolved ionization spectroscopy using ultraviolet and infrared pulses, owing to the coupling between the 11Bu state and the nearly degenerate optically forbidden 21Ag state.5,6 The nonfluorescent nature of trans-1,3butadiene is attributed to this fast relaxation, which is dominated by at least two conical intersections (CIs): the first between 11Bu and 21Ag that causes rapid decay of the 11Bu state to an optically dark state 21Ag and the second between 21Ag and 11Ag. Although time-resolved ionization spectroscopy revealed various relaxation processes of the excited states,6 ionization spectroscopy does not directly provide the energy levels and the molecular structures during and after the relaxations. For example, a theoretical work predicts that the molecule is twisted © 2014 American Chemical Society
Received: February 18, 2014 Accepted: May 2, 2014 Published: May 2, 2014 1760
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(= 42 nm) of a Ti:sapphire laser. The correlation function between them had a temporal width of 90 ± 5 fs. The high harmonics of ultrashort pulse lasers are promising for TRPES16−20 because the photon energy of a high harmonic is high enough to access electrons in the low-lying molecular orbitals (MOs). This can be the advantage of a high harmonic light over the visible and ultraviolet lights accessing only the electrons in excited states.12,21−24 In fact, the ionization from the low-lying MOs has never been accessed even in the very recent TRPES of trans-1,3-butadiene using ultraviolet lights.12 Another advantage is the time resolution reaching to the attosecond regime.25−28 Figure 1a and b show the photoelectron spectrogram and the photoelectron spectra, respectively, at delay times of −293, 40, and 427 fs after excitation. The negative delay means that the pump pulse comes after the probe pulse. The MOs at −293 fs were almost identical to the spectrum measured by a He lamp.13 The theoretical calculation based on Koopmans’ theorem reproduces the photoelectron peaks and shows that the MOs have the characters tabulated in Table 1. For example, the electrons in the highest occupied MO (HOMO) (1bg) mainly come from the π− orbital of the CC bond where the “+” or “−” label indicates the symmetric or antisymmetric MO with respect to the center of inversion. Here, we propose to assign 6ag and 5ag to σCC+ and πCH2−, respectively, which are assigned vice versa in ref 13. In the Supporting Information, the MOs obtained in this work are shown to rationalize the assignment. In the time-resolved photoelectron spectra shown in Figure 1, we found the following three features: (1) In Figure 1a, a short-lived state was found at around 7 eV and at a delay time of 0 fs. Figure 1c shows the integrated photoelectron spectra between −293 and −200 fs and those between −53 and 40 fs. The sideband is not due to the nonresonant two-photon transition by the pump and probe, because the energy separation from HOMO was 2.4 eV, which is smaller than 3.1 eV (= 400 nm). Therefore, these signals should come from an excited state. (2) The ultrafast recovery of HOMO within 427 fs was observed for the first time (Figure 1b). (3) On the other hand, only the band at around 15 eV consisting of πCH2− and σCC− was slightly shifted to the larger ionization energy after 427 fs, whereas the peak shift of the HOMO was much smaller. First, let us discuss the ultrafast decay of the band around 7 eV and the recovery of HOMO. Figure 2a shows the temporal evolution of the photoelectron count between 6.4 and 7.6 eV. The dynamics is reproduced by the fitting function describing the pump process expressed by the Gaussian correlation function with a time width of 90 fs and the exponential decay process (see Experimental Methods). The fitting result is shown by the solid line with a decay time constant of 55 ± 8 fs, corresponding to the lifetime of the excited state. This value is consistent with the lifetimes obtained by ionization spectroscopy5,6 and TRPES using ultraviolet light.12 To see the corresponding recovery dynamics of the HOMO band in detail, the time dependences between 9.35 and 9.40 eV (b), between 9.50 and 9.55 eV (c), between 9.65 and 9.70 eV (d), and between 9.75 and 9.8 (e) are shown in Figure 2b−e, respectively. The recovery time becomes faster with a decrease in the ionization energy, although a slight increase in the photoelectron intensity was observed in the negative temporal region in Figure 2b and c. When the fitting function is assumed
Figure 1. (a) Photoelectron spectrogram of trans-1,3-butadiene. The intensity for ionization energy less than 8.1 eV is magnified by 130. (b) Time-resolved photoelectron spectra of trans-1,3-butadiene at delay times of −293 (red solid line), 40 (green dotted line), and 427 fs (blue dashed-dotted line) and the assignment of the peaks by Table 1. The vertical lines indicate the theoretical ionization energies calculated in this work. (c) Photoelectron spectra integrated between −293 and −200 fs (red solid line) and between −53 and 40 fs (green dotted line). The magnified spectra below 8.8 eV are also shown.
to be the sum of the exponential recovery convoluted with the correlation function and the instantaneous response proportional to the Gaussian correlation function, the experimental data are well reproduced and the fitting results are shown by the solid lines (see Experimental Methods). We suspect that the instantaneous response to the correlation function is (1) due to the nonresonant two-photon transition of the electrons in πCC+ or σCC located about 3 eV below the HOMO band, absorbing the pump and probe photons simultaneously or (2) due to the resonance enhancement of photoemission by the ponderomotive shifts.29,30 In Figure 2f, the recovery time obtained by the fitting analysis is summarized as a function of ionization energy. The recovery time ranges from 22 to 132 fs, which are different from the lifetime of the excited state 55 ± 8 1761
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fs. The difference comes from the spectral interval of integration: Figure 2a was obtained by integrating the spectra between 6.4 and 7.6 eV because the signals within a 0.05 eV window were too weak to warrant the analysis. To compare with the decay times under the similar condition, the HOMO band between 9.0 and 10.0 eV was integrated and then the recovery time was obtained to be 70 ± 8 fs, which is almost identical to the decay time. This agreement confirms that the excited state relaxes to the ground state 11Ag through a CI. Now, we would like to discuss the ionization-energy dependence of the recovery time. The returning molecule to 11Ag through a CI further relaxes to the bottom of the potential energy surface of 11Ag by releasing the excess energy among many vibrational modes through intramolecular vibrational energy redistribution (IVR). The distribution among vibrational modes changes with IVR, that is, with time. The shape of a photoelectron spectrum depends on the Franck−Condon factor between the vibrational state of the neutral molecule and that of the ionized molecule. Because the vibrational state of a neutral molecule changes with IVR upon photoexcitation, the photoelectron spectrum is expected to change with time. The ionization-energy dependence of the recovery time corresponds to the spectral change during IVR. Figure 1c shows that the averaged spectrum between −53 and 40 fs had a slightly different spectrum from that before pump. The slower recovery of the larger ionization-energy side of the HOMO band corresponds to the spectral change during IVR. Then, what excited state was observed in the time-resolved photoelectron spectra? To gain insight into the short-lived state, the relaxation pathway starting from the Franck−Condon structure in the 21Ag state was calculated by the multistate complete-active-space second-order perturbation theory (MSCASPT2) method. Variations of the potential energy along the pathway are shown in Figure 3. In the Franck−Condon
Table 1. Character and Ionization Energy of Each MO of trans-1,3-Butadiene molecular orbital
charactera −
theoretical ionization energy (eV)b
1bg 1au 7ag 6bu
πCC πCC+ σC−C πCH2+
8.87 11.72 11.82 12.98
6ag 5ag
σCC+ πCH2−
13.25 15.26
5bu
σCC−
15.35
The “+” or “−” label indicates that a MO is symmetric or antisymmetric, respectively, to inversion through the center of the molecule. bThis work.
a
Figure 3. Potential energy curve describing the relaxation processes in trans-1,3-butadiene along the reaction coordinate. The red, blue, and black lines are the curves for doubly excited state, ππ* state, and the ground state, respectively. The insets are the molecular structures with bond length in Å at (S0)min, (S1/S0)CI, (S1)Cs‑min, and (S1)C1 min. The CI between S2 and S1 is indicated by (S2/S1)CI.
structure, the doubly excited π2π*2 state (21Ag) is located slightly higher than the ππ* state (11Bu). After the two-photon excitation to 21Ag, the molecule is relaxed rapidly to a region of the planar minimum energy structure, (S1)Cs‑min, after passing through the CI between S2 and S1, (S2/S1)CI. Around (S1)Cs‑min, the potential energy surface shows a very flat nature as shown in Figure 3. In the π2π*2 excitation, the CC bond becomes weak and lengthens to 1.5 Å, which is almost equivalent to the CC single bond. Then, the planarity and the inversion symmetry of the molecule are broken by the twist of one
Figure 2. (a) Time dependence of the photoelectron count of the sideband between 6.30 and 7.60 eV. Time dependence of the photoelectron count (b) between 9.35 and 9.40 eV, (c) between 9.50 and 9.55 eV, (d) between 9.65 and 9.70 eV, and (e) between 9.75 and 9.8 in the HOMO band. The solid lines are fitting results. (f) Recovery time of the HOMO band as a function of ionization energy.
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static planar symmetrical structure because of the inertia of the twisted structure and the asymmetrical bond stretching in the excited state. We suspect the return to the planar symmetrical structure from the twisted structure stimulates the antisymmetric CC stretching mode with a frequency of 1694 cm−1. With this expectation, we calculated the orbital energies of all MOs as a function of the normal coordinate for the antisymmetric CC stretching mode. Under the Koopmans’ theorem, the orbital energy can be regarded as approximation to the ionization energy from each orbital. The results are shown in Figure 4. The absolute orbital energies of σCC+ and
terminal CC bond. There is no barrier from (S1)Cs‑min to (S1)C1 min or from (S1)C1 min to the CI between S1 and S0, (S1/ S0)CI, indicating that the molecule easily goes back to the ground state through these key structures. The ionization energies in the 11Ag and 21Ag states were calculated as energy differences between the neutral and the corresponding cationic states at the MS-CASPT2 level. In the ground state, the lowest ionization energy was calculated to be 8.9 eV, which is consistent with the LC-DFT result (8.87 eV) based on Koopmans’ theorem. For the 21Ag excited state, the ionization energy was calculated to be 7.0 eV at the Franck− Condon structure and 7.4 eV at the (S1)Cs‑min structure, as the energy difference between the 21Ag state of neutral species and the excited state of cationic species with electronic configuration of (nHOMO, nLUMO) = (0, 1). The decrease in the ionization energy due to photoexcitation (8.9 → 7.0 eV) is consistent with the experimentally observed signal at around 7 eV (Figure 1c). To observe a characteristic behavior of other low-lying MOs, the photoelectron count was integrated and the time dependence was analyzed in the same way. The time dependence for each of the MOs was similar to that of the HOMO: The recovery times of πCC+, σCC, πCH2+ and πCC+, and σCH2− and σCC− were 47 ± 7, 63 ± 6, 52 ± 4, and 49 ± 7 fs, respectively. Because these values including the recovery time of πCC− were very close, the mechanism of the photoinduced changes in the spectrum was the same. When only the variation of the HOMO band is observed, the depletion of electrons in HOMO by pump pulses is one possible mechanism to explain the decrease in the photoelectron intensity. However, because the time dependence of the other orbitals related to πCH2 and σCC, which are less sensitive to pump depletion, were similar to that of the HOMO, it would be more appropriate to attribute the decrease in the photoelectron intensity to the variation of the ionization cross section induced by a structural deformation in the excited states. Then, the low-lying MOs also responded to the optical excitation on the same time scale. Concerning the second finding, the recovery to the original photoelectron spectrum at 427 fs indicates that the electronic state of a molecule almost returns to the ground state. Therefore, the photodissociation takes place not directly from the excited states but from the ground state. The same conclusion was reached by the analysis of the translational energy distributions in photofragment translational spectroscopy.7 The molecules after relaxation have an excess energy of nearly 6.2 eV, which is redistributed among the vibrational modes. These high vibrational states should provide the driving force of the isomerization or dissociation of the molecule. Now, we discuss the third finding. Figure 1b shows that the peak of the σCH2− and σCC− bands remained shifted by 0.1 eV larger, although the level shifts of HOMO and the others were smaller by 1 order of magnitude. The nonradiative relaxation upon photoexcitation indicates that the large amount of excess energy was redistributed among the vibrational modes. Because the orbital energies of a molecule is sensitive to the molecular structure, some vibrational modes should modulate the orbital energies of σCH2− and σCC−. The theoretical work shown in Figure 3 predicts that the molecule is deformed asymmetrically in the excited state. Even after returning to the ground state, the molecule does not immediately (within 427 fs) return to the
Figure 4. Orbital energies of molecular orbitals as a function of the displacement along the antisymmetric CC stretching normal mode with a frequency of 1694 cm−1.
σCC− are shifted larger by about 0.1 eV, which is larger than those of the other MOs. Therefore, the observed peak shift of the σCH2− and σCC− bands is attributable to the energy modulation by vibrational excitation of the antisymmetric C C stretching mode. In the case of the σCH2+ and σCC+ bands observed around 13.5 eV, the directions of the shifts are opposite and, therefore, the spectral shift canceled each other out. Other many-vibrational modes should also be excited after the relaxation to the ground state. However, our theoretical calculation predicts that the energy shifts of σCC− by the other vibrational modes are much smaller than that by the antisymmetric CC stretching mode because the CC antisymmetrical stretching mode changes the orbital energy significantly by modulating the overlap of the σ bonding. Finally, we would like to emphasize that the complete separation of a single high harmonic order from the others by a time-delay compensated monochromator (TDCM)31−35 enabled us to observe MOs with an ionization energy that is larger by 6 eV than HOMO. The observation over a large spectral region makes it possible to detect the deformation of the molecular structure upon photoexcitation. This is the advantage of the usage of a single harmonic order over the visible and ultraviolet lights used so far. The application of a new optical technology in combination with theoretical calculations provides us unique opportunities to gain insight into new 1763
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energies of the molecular orbitals are also shown. The electron distribution in the MOs suggest 6ag and 5ag are attributable to σCC+ and πCH2−, respectively, in contrast with ref 13. This material is available free of charge via the Internet at http:// pubs.acs.org
aspects of chemical reactions, which have been rarely investigated so far.
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EXPERIMENTAL METHODS TRPES Technique. We used a Ti:sapphire laser system delivering 1.1 mJ, 30 fs pulses at a repetition rate of 1 kHz. After the second harmonic generation by a LiB3O5 (LBO) crystal (500-μm thickness) for the pump pulses with a pulse energy of 15 μJ, the remaining fundamental pulses were focused into a Kr pulse gas jet for high harmonic generation. The 19th harmonic for the probe was selected among many harmonics by a TDCM, enabling the single harmonic selection with the time duration preserved.31−35 The shortest pulse duration achieved in our system was 11 fs.34 Both the pump and probe pulses were focused into the continuously flowing sample gas located at the entrance of a magnetic bottle photoelectron spectrometer with a polarization angle of 55° to avoid the time dependence induced by molecular rotation. The transient photoelectron spectra were recorded by changing the optical delay between the pump and probe pulses. The temporal response function of the system was determined by the temporal evolution of the photoelectrons ejected by the twophoton ionization of Kr gas by pump and probe pulses.33,34 The response function had a width τfwhm of 90 fs, limited by the pump pulse duration. Fitting Procedure. The decay or recovery time τ of the photoelectron intensity was obtained by the least-squares fitting of the data to the exponential function I(t) = exp(−t/τ) convoluted with the correlation function R(t) = exp{−4 ln2 (t/ τfwhm)2}, where t is time. For Figure 2a, the fitting function f(t) is expressed as
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*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS T.S. was supported by KAKENHI (23340116 and 23654140) and the Research Foundation for Opto-Science and Technology. Y.H. thanks a support from the Japan Society for the Promotion of Science for Research Fellowships for Young Scientist. Part of the calculations was performed on supercomputers at Research Center for Computational Science, Okazaki, Japan.
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∫−∞ R(t′)I(t − t′)dt′
where A is the amplitude. For Figure 2b−e, taking account of the instantaneous responses due to the nonresonant twophoton transition or the ponderomotive shifts, the fitting function g(t) is expressed as g (t ) = N0 − f (t ) + BR(t )
where N0 and B are the initial value and the amplitude of R(t), respectively. Theoretical Calculation. The steepest decent path from the Franck−Condon region to the planar minimum in the 21Ag state and the interpolated path from the planar minimum to the minimum energy CI (MECI) point between 21Ag and 11Ag states were determined by MS-CASPT2 with cc-pVDZ basis sets using MOLPRO2012.36 The MECI was optimized by GRRM11-package.37 The MECI between S0 and S1 states for butadiene was thoroughly investigated with GRRM approach very recently.38 The ionization energies in the 21Ag state were calculated as an energy difference between the neutral and cationic species along the relaxation pathway at the MSCASPT2 level. Under the Koopmans’ theorem, the ionization energies in the 11Ag state were also calculated from orbital energies by the density functional theory (DFT) with LCBOP/cc-pVDZ using the GAMESS-package.15,39
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AUTHOR INFORMATION
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ASSOCIATED CONTENT
S Supporting Information *
Molecular orbitals of trans-1,3-butadiene calculated at DFT(LC-BOP)/cc-pVDZ are presented. Characters and ionization 1764
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