Femtosecond isomerization dynamics in the ethylene cation measured in an EUV-pump NIR-probe configuration

J van Tilborg¹, T K Allison^1,2, T W Wright¹, M P Hertlein¹, R W Falcone^1,2, Y Liu¹, H Merdji³ and A Belkacem¹

¹ Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
² University of California at Berkeley, Berkeley, CA 94720, USA
³ Service des Photons, Atomes et Molécules, CEA-Saclay, 91191 Gif-sur-Yvette, France

E-mail: JvanTilborg@lbl.gov

Received 10 March 2009
Published 6 April 2009

Photochemical reactions can be described in terms of photoinduced vibrational wave packets evolving on one or several adiabatic potential energy surfaces (PES). Quantum-mechanical studies have established that numerous ultrafast reactions are intimately connected with the internal conversion of electronic energy to nuclear motion via so-called conical intersections (CI) [1]. In this highly non-adiabatic region, electronic and molecular dynamics are strongly coupled. Even if the dynamics of large systems such as proteins and chromophores are quite complicated, the initial steps of internal conversion can often be traced back to the excitation of a specific small hydrocarbon unit. For example, the photoisomerization of retinal in rhodopsin can be effectively modelled using the reduced reaction coordinate set of the twist and stretch of the C₁₁  =  C₁₂ double bond [2].

The simplest molecule containing a carbon double bond is ethylene (C₂H₄, also referred to as ethene), which has been a model molecule for theoretical and experimental studies for decades. Theoretical insight into ethylene has improved over the years due to the availability of more advanced tools. These studies [3–9] have shown that in neutral ethylene excited to the V-state (ππ* state), twisting and pyramidalization, hydrogen migration, and isomerization to ethylidene (HC–CH₃) are important configurations that connect the excited state to a vibrationally hot ground state. Experimental efforts have been largely limited to time-independent studies; following absorption of photons over a wide range of energies, groups have studied the yield of ion fragments [10, 11], photo-electrons [12, 13] and fluorescence photons [14] (see also references therein). Time-dependent work was performed only on excitations in the neutral state through pumping with 6–8 eV photons and probing with a near infrared (NIR) laser [15–17].

Here we apply a pump pulse at extreme ultraviolet (EUV) photon energies, several eV above the ethylene ionization potential. Theory predicts [3, 4] that several CIs will be crossed after population of the excited cationic states (A ²B_3g, B ²A_g, C ²B_2u, D ²B_1u and E ²A_g, see energy diagram in figure 1). The isomerization sequence [4, 17] is depicted as a cartoon on the right of figure 1. Just as for excited neutral ethylene [5–9], and references therein, the isomerization to ethylidene in the cation is found to play a major role in photodissociation and -excitation dynamics. Therefore, the ethylidene configuration was chosen as the focus of our study. The EUV-induced isomerization to (HC–CH₃) ⁺  can be directly observed through probing by an NIR pulse intense enough to break the C–C bond, leaving the fragments CH ⁺  and CH ⁺ ₃ to be detected. The fs EUV source has to be intense enough to pump a substantial fraction of the C₂H₄ target to the excited states of the cation.

We report here on a direct measurement of ethylidene isomerization, which, as we found, develops in a transient matter several tens of femtoseconds after pumping. To achieve this measurement, we developed a unique intense synchronized EUV-pump NIR-probe source. Our results, and the applicability of our setup in general, provide new insight and demonstrate experimental opportunity in the timescales involved in isomerization and electronic relaxation in ethylene and other model molecules.

We have constructed an intense high-harmonic generation (HHG) system delivering per shot both an NIR probe laser and ~10⁹ EUV pump photons (20–25 eV range) on an ethylene gas target. The experimental setup used for our studies, constructed at the Lawrence Berkeley National Laboratory (LBNL) in Berkeley, CA, is depicted in figure 2. The setup (similar to [18]) is based on a home-built 10 Hz laser system delivering 25 mJ 35 fs laser pulses at 800 nm central wavelength. After the pulse compressor, a 90/10 beam splitter (see figure 2) delivers 10% of the energy to a laser probe arm, with the remaining 90% used for the production of higher order harmonics. The HHG production beam enters the vacuum system, is incident on the curved mirror CM1 (focal length of 4.5 m) and focuses onto a 5 cm long gas cell (laser-drilled entrance holes) filled with xenon (Xe) gas. The gas cell position, gas pressure and laser focal parameters were varied to yield optimum phase matching and HHG yield. Both the HHG beam (also labelled as EUV pump beam) and remnant NIR laser light exit the cell. Two silicon (Si) plates (rotated to the laser's Brewster angle) reflect only the EUV pulse (efficiency ~60% per plate). The EUV pulse is then propagated through a 45° mirror with a 2 mm diameter hole in the middle (located 4 m from the gas cell). A curved mirror (labelled CM2) with a focal length of 10 cm was coated with a multi-layer to reflect EUV radiation with energies around 20–25 eV. The coating was performed by the Center for X-Ray Optics (CXRO) at LBNL. CM2 was slightly tilted to guarantee that the focus did not overlap with the incoming EUV beam.

The transmitted beam through the 90/10 beam splitter (see figure 2) was propagated through a delay stage, a half-wave plate and polarizer combination (used for intensity control), another half-wave plate (for polarization control), window W2 and onto the mirror-with-hole. The effects of the optical components were calculated to have stretched the pulse to 100 fs (full width at half-maximum, FWHM) inside the vacuum chamber. A large fraction of the beam was reflected (with the central part missing due to the hole) and co-propagated with the EUV beam. The curved mirror CM2 has a non-zero reflectivity for low energy photons in the 1–10 eV range due to metallic elements in the multi-layer coating. Therefore, both NIR and EUV beams were reflected and focused onto the same focal volume. A supersonic gas flow of ethylene molecules was directed to overlap at focus (background pressure in the chamber, mainly water, was ≊4 × 10^–8 mbar). Ions produced in the focal region were selected by a 2 mm aperture and directed to a time-of-flight mass spectrometer.

The red curve in the inset of figure 2 shows the EUV spectrum incident on CM2, measured by removing it and allowing the beam to be incident on a Rowland circle monochromator (Acton GIMS-551.5-M). The monochromator was calibrated to give absolute photon numbers. The blue area curve in the inset of figure 2 shows the expected spectrum after reflection off CM2 (the mirror reflectivity was modelled and measured by CXRO). One can see that the reflected spectrum mainly consists of the 13th and 15th harmonics (20–25 eV photons), with close to 10⁹ photons per harmonic. Note that the insertion of the mirror-with-hole (see figure 2) further reduces the EUV flux by about a factor of 2–3.

At each temporal delay between the EUV pump and NIR probe pulses (same polarization) we collected ions during 800 laser shots (two identical scans of 400 shots in opposite direction), yielding an average count rate. The error bars are derived from the square root of the total ion count, assuming Poisson statistics. The laser intensity was estimated to be 8 × 10¹³ W cm^–2 based on observing the ratio of Ar^2 +  to Ar ⁺  produced at focus with only the NIR beam [19]. For determination of time zero t₀ (the delay at which both beams are overlapped in time) we followed two approaches: (1) by leaking laser light of opposite polarization in the EUV arm, we performed an NIR-pump NIR-probe scan observing C₂H ⁺ ₄ through multi-photon ionization. Also (2) the EUV-pump NIR-probe dataset already includes a transient ion yield peaked at t₀, namely H₂O ⁺  (from chamber background), see figure 3(a). As was extensively studied, the two methods agreed on the t₀ timing. The t₀ curve was fitted with a Gaussian profile (see black curve). The fit provided us with the value of σ  =  105 fs (FWHM) for the Gaussian instrument response function (the temporal convolution of pump and probe pulses), see figure 4.

The ion yields for CH ⁺ ₃ and CH ⁺ , reflecting the break-up of the transient ethylidene configuration (HC–CH₃) ⁺  by the NIR probe, are plotted in figure 3(b). While both CH ⁺ ₃ and CH ⁺  yields have a strong transient component, the CH ⁺  curve does have a more prominent background. In this work we will focus our analysis on the transient profile that we consistently measure, which peaks at τ ≊ 80 fs for both CH ⁺ ₃ and CH ⁺ . The measurement is consistent with the NIR probe breaking the C–C bond of the ethylidene cation. The NIR beam is sufficiently intense to remove a second electron. We have verified that the results are not related to multi-photon ionization with remnant lower orders (photons <10 eV) in the pump beam since insertion of a MgF₂ window [20] (transmission <10 eV) did not show any contribution to ion transient signals reported here.

In order to get a better understanding of the isomerization dynamics, we fit the data with a model (see also figure 4), which is based on an extension of the simple single- or double-decay model [15, 17]. After EUV excitation to the excited cationic states, the molecule will undergo nuclear rearrangement. As the nuclear wave packet spreads over the PES, a specific region L with a unique probe channel (such as the ethylidene configuration) is reached after time t_isom. The population probability N(t) in L has a decay rate of 1/τ₁. The modelled probe signal S(τ), see the blue dashed curve in figure 4, is constructed by convolving N(t) with the instrument response function. Note that the maximum for S(τ) does occur at a time later than t_isom, which is due to the convolution of the Gaussian instrument response function with the asymmetric exponential function N(t). The background to the data (see black dotted curves in figures 3(b)and (c)) was modelled based on a secondary weaker probe channel with slower decay rate. Also, for CH ⁺  in figure 3(b), we found a nonzero background contribution at negative delays based on an NIR-pump EUV-probe time ordering. Note that the background was found to have negligible impact on the analysis of the stronger transient signals. Also, we checked that the temporal location of the transients was not affected by an increase of NIR probe energy.

The transient yields for CH ⁺  and CH ⁺ ₃ are both best modelled based on the parameters t_isom  =  50 ± 25 fs and τ₁ < σ (transient limit). The confidence interval for t_isom. is based on variation of χ² by 68%, with t_isom and τ₁ as free fitting parameters while keeping the background curves constant. The transient curves are plotted as blue curves in figure 3(b), using τ₁  =  50 fs, while the full fits (including background) are the solid black curves. Based on the data, and within the framework of our proposed model, we can therefore state that upon EUV excitation it takes about 50 fs for the molecule to undergo isomerization to the ethylidene configuration. Whether the molecule undergoes electronic relaxation (through a CI) or further isomerization along the same PES is beyond the scope of our analysis. However, as noted in several publications (for example [4, 17]) the ethylidene configuration is potentially followed up by an H₂ stretch leading to H₂ elimination, see cartoon on the left of figure 3(c). It is therefore conceivable that at a specific H₂ distance the NIR probe is able to isolate and ionize H₂. The data for H ⁺ ₂ are plotted in figure 3(c). The strong transient signal is consistent with the interpretation that the H ⁺ ₂-yielding configuration is populated at the same rate (1/τ₁) that the ethylidene configuration is depleting. The solid black curve in figure 3(c) reflects this match, with model parameters of t_isom  =  50 fs and τ₁  =  50 fs for ethylidene, and a transient lifetime (τ₂ < σ) for the H ⁺ ₂-yielding configuration. Note that for the H ⁺ ₂ fit we had to use a shorter instrument response function (70 fs FWHM), which could be due to a higher degree of nonlinearity for the probe beam.

It is important to note that most pump–probe models are fully based on decay rates [15, 17], and do not include a delay term such as t_isom. However, application of such a simple model to our data (having strong transient features for CH ⁺ ₃ and CH ⁺  around τ  =  80 fs and for H ⁺ ₂ around τ  =  110 fs) failed to yield agreement. It is not our goal to provide a detailed and comprehensive pump–probe model for molecules undergoing isomerization, but we do want to point out that the simplest modification of the decay model (inclusion of the constant t_isom) already provides a robust match to the data. Note that our method is a direct measurement of the isomerization time scale, in contrast to more indirect methods such as photo-electron analysis performed on hydrogen migration in C₂H₂ (acetylene) [21, 22].

In summary, we have studied the dynamics in the EUV-pumped excited ethylene cation (C₂H ⁺ ₄), leading to formation of the transient ethylidene configuration (HC–CH₃) ⁺ . Application of an NIR probe resulted in ethylidene fragmentation to CH ⁺ ₃ and CH ⁺ , which occurred favourably at a 80 fs probe delay. A model was proposed to match the data, and within the framework of this model we found an isomerization time of 50 ± 25 fs. The fragment H ⁺ ₂ was measured predominantly at a 110 fs probe delay, consistent with the concept of the ethylidene population decaying into the H ⁺ ₂-yielding configuration. A simple rate-based model had to be expanded through inclusion of an isomerization time in order to match the data, mainly due to the measured presence of strong transient signals at positive probe delays.

Acknowledgments

We thank T Osipov F Salmassi and A Aquila for their assistance. This work was performed under the auspices of the US Department of Energy and was supported by the DOE Office of Basic Energy Sciences, Chemical Sciences Division under contract no. DE-AC02-05CH11231. T K Allison was supported by the DOE SSAA under grant no. DE-FG52-06NA26212. We also acknowledge financial support from UC Berkeley's France–Berkeley fund.

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