Fragmentation pathways for selected electronic states of the acetylene dication

T Osipov¹, T N Rescigno¹, T Weber¹, S Miyabe², T Jahnke³, A S Alnaser^4,5, M P Hertlein¹, O Jagutzki³, L Ph H Schmidt³, M Schöffler³, L Foucar³, S Schössler³, T Havermeier³, M Odenweller³, S Voss³, B Feinberg¹, A L Landers⁶, M H Prior¹, R Dörner³, C L Cocke⁴ and A Belkacem¹

¹ Lawrence Berkeley National Laboratory, Chemical Sciences, Berkeley, CA 94720, USA
² Department of Chemistry, University of California, Davis, CA 9566, USA
³ Institut für Kernphysik J W Goethe-Universität Frankfurt am Main, Max-von-Laue-Str. 1, D-60438 Frankfurt, Germany
⁴ Department of Physics, Kansas State University, Manhattan, KS 66506, USA
⁵ Physics Department, American University of Sharjah, Sharjah, UAE
⁶ Department of Physics, Auburn University, AL 36849, USA

E-mail: TYOsipov@lbl.gov

Received 24 March 2008, in final form 25 March 2008
Published 23 April 2008

Nature's smallest stable hydrocarbon, the symmetric linear acetylene molecule, C₂H₂, is an important polyatomic system for the study of photo-initiated processes. Important features of the intramolecular dynamics in neutral acetylene have been revealed over many years through numerous spectroscopic studies. More recently, the availability of synchrotron radiation and intense laser sources has led to intriguing studies of the ionization, isomerization and breakup dynamics of acetylene ions. Fragmentation of the dication, C₂H ^+  + ₂, formed by direct UV photo-double ionization, was first studied by Thissen et al [1] who measured yields into different channels and proposed structural configurations through which the fragmentation occurred. Of particular interest are the yields into the symmetric (A, CH ⁺ /CH ⁺ ), deprotonation (P, HCC ⁺ /H ⁺ ) and quasi-symmetric (V, HHC ⁺ /C ⁺ ) channels, the latter involving isomerization from the neutral acetylene structure into the vinylidene configuration prior to breakup. One expects that the products of dissociation, their kinetic energy releases (KER) and the isomerization times will depend on the particular initial electronic states of the dication involved, but such detailed information has heretofore not been available. In this work, the dication of acetylene is prepared by Auger decay following core-level x-ray photoionization. The basic technique of Auger electron–ion fragment coincidence was pioneered by Eberhardt and coworkers with their study on N₂ [2]. In our work, the energy and the angular distribution of the Auger electron is measured in coincidence with the kinetic energy of the fragments. We show that this experimental approach, in combination with ab initio quantum-mechanical calculations, can yield a comprehensive map of the two-body dissociation pathways including transition through different electronic energy surfaces, barriers to direct dissociation and the associated rearrangement channels as well as information on core–hole localization at one of the carbon atoms.

While the fragmentation and isomerization of the acetylene dication have been studied for a number of years, the only experimental information previously available on the energetic pathways are measurements of appearance energies reported by Thissen et al [1] and some information on the KER in the symmetric breakup channels [3, 4]. Osipov et al [3] reported an upper limit of 60 fs for the isomerization time when the dication is formed by K-shell photoionization followed by Auger decay, but did not control the electronic state from which the isomerization occurred. Adachi et al [5] have recently reported coincident measurements of K-shell photoelectron angular distributions with A, P and V breakup channels, but like earlier investigators, did not attempt to identify specific parent electronic states.

We produce the dication by using 310 eV photons to remove one of the carbon K-shell electrons; the system then promptly (6 fs) Auger decays to the dication [6]. The process is C₂H₂  +  hν→ C₂H ⁺ *₂  +  e^–(~ 20 eV) → C₂H ^+  + ₂  +  2e^– (Auger ~ 250 eV). The Auger decay can leave the dication in any of a number of electronic states. If such a state has sufficient energy, through either vibrational or electronic energy or both, to dissociate into two charged fragments, we measure the momenta of the positively charged ions in coincidence with the Auger electrons. A related experiment was performed by Osipov et al [3]; however here we do not measure the photoelectron but instead measure the Auger electron with sufficient energy resolution to determine the electronic state of the dication which is fed. We can thus determine the fragmentation pattern for different electronic states of the dication and determine which ones fragment into the symmetric channel (acetylene, A, C₂H ^+  + ₂→ CH ⁺   +  CH ⁺ ), which to the quasi-symmetric channel (vinylidene, V, C₂H ^+  + ₂→ CH ⁺ ₂  +  C ⁺  ) and which by ejection of a single proton (deprotonation, P, C₂H ^+  + ₂→ C₂H ⁺   +  H ⁺ ). (We consider only these fully kinematically determined two-body channels.)

The experimental details are similar to those described in [7–9]. A jet of acetylene gas was photoionized by a beam of circularly polarized photons from the LBNL advanced light source. A COLTRIMS (cold target recoil ion momentum spectroscopy) spectrometer [7] was used to extract positively charged ions to one side of the spectrometer and electrons to the other. RoentDek position-sensitive delay line detectors [10] were placed at both ends of the spectrometer for measuring the position and the time-of-flight (TOF) of the charged particles. By using a weak magnetic field (~10 gauss) collinear with the spectrometer extraction field, we were able to collect all Auger electrons emitted within 15° of the spectrometer axis (transverse to the photon beam) while all positive ions were measured with 4π solid angle efficiency. For each ionization event the vector momenta of both ion fragments and the Auger electron were determined by the times and positions of arrival of the particles on the detectors. From these the ion species, the Auger energies and the kinetic energy release were calculated for whichever channel (A,V or P) was populated in the event.

K-shell photoionization of C₂H₂ creates an energetic, singly-charged, quasi-degenerate state(s) of the core-ionized molecule, 1σ^–1_g,u(²Σ ⁺ _g,u) 291.1 eV above the neutral, which then decays by filling the core vacancy and ejecting a fast electron. The Auger energy measurement determines the electronic state of the dication C₂H ^+  + ₂ from which the dissociation starts. The KER is a measure of the energy difference between the starting point of the dissociation and the final state of the fragments. In figure 1 we display a density plot of Auger energy versus KER for the symmetric and quasi-symmetric channels A and V (figure 1(a)) and the deprotonation channels (figure 1(b)). The g/u splitting of the initial state(s) is ~100 meV [11], smaller than the Auger energy resolution of our apparatus (~0.5 eV) and of the same order of magnitude as the natural linewidths of the states (~90 meV), thus they can barely be resolved in principle. The sum of the KER and the Auger energy is the difference in energy between the initial core–hole state(s) and the final state of the fragments. This is shown as the x-axis intercepts of the solid lines in figure 1. Each intercept represents a different asymptotic state of the fragments.

Turning to figure 1(a), we see two intense spots at Auger energies of 255.5 and 250 eV. Since the sum momentum of the fragment ions must be approximately zero (the photoelectron energy and photon momenta are much smaller) we were able to determine that the 255.5 eV peak corresponds almost exclusively to V fragmentation (with possibly small contributions from A fragmentation), while the 250 eV peak corresponds exclusively to A fragmentation. The details of this separation are similar to those discussed in [3, 12]. Figure 1(b) exhibits two intense spots labelled P1 and P2 which were determined to correlate with the deprotonation channel.

We extracted the relevant energetics information associated with the A, V, P1 and P2 dissociation channels from figure 1. This information is summarized in table 1. To assist in the interpretation of these measured data, we carried out configuration-interaction calculations on the electronic states of the dication. The calculations included all single and double excitations from a ten-orbital complete active space, with the restriction that the carbon 1s core-orbitals remain doubly occupied. Our computed adiabatic double ionization energies are close to recent experimental determinations [13]. Figure 2 shows two cuts in linear geometry through the potential surfaces of the states relevant to this study, corresponding to symmetric breakup and deprotonation, respectively. Note that the bond distances other than that being plotted are fixed at the equilibrium geometry of neutral acetylene.

It is well known that Auger decays from closed-shell molecules populate triplet states only weakly. In the simplest spin-restricted theory, the Auger decay probability is determined by a two-electron Coulomb integral involving a core orbital, a continuum orbital and two valence orbitals. For triplet states, where the two valence orbitals must necessarily be different, the transition matrix element involves the antisymmetric combination of two spatial integrals, which tend to cancel for high-energy continuum orbitals [14]. This feature of Auger spectra for similar molecules is well established [15] and leads us to eliminate triplet states from consideration.

The experiment and theory show that the A (acetylene) and P2 (deprotonation) channels originate from higher excited states of the dication. We find that the fragmentation of the A channel occurs along the 1π^–1_u2σ^–1_u, ¹Π_g state, which was seen in the Auger spectrum of Kivimaki et al [16], but was not considered in earlier theoretical studies [1, 17, 18]. Figure 2 shows that this state intersects the Franck–Condon (FC) distance of 1.2 Å near an energy of 41 eV and dissociates to CH ⁺ (¹Σ)  +  CH ⁺ *(¹Π) near 34.5 eV, which is consistent with the observed data. Although figure 2(a) shows a barrier to dissociation when the CH distances are constrained to their initial values, optimization of these distances (shown as the `relaxed' curve in figure 2(a)) reveals that dissociation is possible with essentially no barrier.

Turning next to the P2 deprotonation channel in figure 1(b), close examination shows that the Auger energy, at 252 eV, is slightly higher than the 250 eV Auger energy in the A channel of figure 1(a). Kivimaki et al [16] also saw two peaks in this region, and that at 252 eV is interpreted as 1π^–1_u3σ^–1_g, ¹Π_u. On energetic grounds, the ¹Π_u assignment is consistent with our calculations as well as the other theoretical studies [1, 17, 18] and, as shown in figure 2(b), there is no barrier to dissociation in this channel. It is also noteworthy that the observed KER of 5.3 eV for this channel indicates that C₂H ⁺  is evidently formed in its ¹Δ or ¹Σ ⁺  excited state.

We have measured the Auger angular distributions for each of the features discussed above. These distributions are shown in figure 3. If the axial recoil approximation is valid, i.e. if the axis along which the departing fragments fly is approximately that of the original acetylene molecule, then these molecular frame angular distributions can provide a valuable consistency check on the deduced state identifications and, as we show below, give additional insight into the dissociation dynamics. K-shell photoionization will eject electrons from either the 1σ_g or 1σ_u orbitals. Whether Auger decay populates the even parity 1π^–1_u2σ^–1_u, ¹Π_g final state at 250 eV or the odd parity 1π^–1_u3σ^–1_g, ¹Π_u state at 252 eV, the Auger electrons would be ejected into kπ_g or kπ_u continua, so we would expect a node in the Auger angular distribution along the axis of the molecule. The Auger angular distributions for the A and P2 channels shown in figures 3(a) and (d), respectively, clearly support this expectation. The distributions associated with the P1 and V channels are more difficult to interpret and will be discussed further below.

Experiment and theory show that the P1(256 eV) and V(255.5 eV) channels originate from lower states of the dication. Peaks at these energies appear in the non-coincident Auger spectra of Kivimaki et al [16] and were identified as 1π^–2_u states, where the vacuum state is neutral acetylene with configuration 1σ²_g, 1σ²_u, 2σ²_g, 2σ²_u, 3σ²_g, 1π⁴_u. Removal of two π_u electrons from this configuration gives the lowest three electronic states of the double cation, ³Σ^–_g, ¹Δ_g and ¹Σ ⁺ _g [1]. As mentioned above, the triplet state is not (or only weakly) fed by the Auger process. Moreover, these states are not expected to be major gateways into the A channel because the barrier along the CC bond, seen in figure 2(a), is too high. We note that the location of this barrier has been the subject of considerable controversy [17, 18], since it does not seem to be consistent with the low appearance energy for the A channel seen by Thissen et al [1]. Indeed, we cannot rule out the possibility, based on the examination of the Auger angular distributions, that some contribution to symmetric breakup originates from the ¹Δ_g state. We argue below, however, that both the V and P1 channels originate from the ¹Σ ⁺ _g dication state.

The equilibrium separation of the C atoms in the neutral, 1.2 Å, allows the ¹Σ ⁺ _g state to be fed with only about 2 eV of vibrational energy in an FC process, which is insufficient to overcome the barriers seen in figure 2(a). However, previous theoretical calculations [17, 18] show that dissociation to the V or P1 configuration is expected to pass through much lower barriers, low enough that even an FC process could supply the required vibrational energy. The Auger intensity plots in figure 1 show that the P1 and V KERs are clipped from below, indicating that the intensities are determined by energy barriers, which can be deduced from the measured data. The KER values and corresponding Auger energies where the intensities are clipped indicate that the barriers for the P1 and V channels lie at 34.85 and 35.35 eV, respectively, as shown by the flat portion of the broken lines in figure 2. Excitation energies between 34.85 and 35.35 eV lead to the deprotonation P1. For energies above 35.35 eV, where the KER intensity for P1 is again clipped, the V channel opens up and overtakes deprotonation. Although the ¹Δ_g and ¹Σ ⁺ _g states are both FC allowed, previous theory [18] finds that the V barrier is lower than the P barrier on the ¹Δ_g surface. Since we observe the opposite order, we are led to believe that both the P1 and V channels are fed by the ¹Σ ⁺ _g state. For the P1 channel, the measured KER indicates that C₂H ⁺  ion is produced in its ground ³Π state. As the potential curves in figure 2(b) show, the dissociation may begin with the ¹Σ ⁺ _g state, but the excited 1π^–1_u3σ^–1_g, ³Π_u state, which crosses the ¹Σ ⁺ _g state and correlates with the observed products, is evidently involved in the dissociation dynamics of P1. We must also point out that the 35.35 eV barrier position we deduce for V formation on the ¹Σ ⁺ _g surface is very close to the barrier for A formation on the ¹Δ_g surface calculated by Zyubina et al [18]. Since the ground-state asymptotes for the V and A channels only differ by a fraction of an eV, we must consider the possibility that, in addition to quasi-symmetric (V) breakup via the ¹Σ ⁺ _g state, symmetric breakup via the ¹Δ_g state also contributes to the fragmentation in the 255.5 eV channel. This hypothesis is supported by the Auger angular distributions for this channel (figure 3(b)).

Returning to a discussion of the Auger angular distributions, we see that the distribution shown in figure 3(d), which is associated with the P2 deprotonation channel, shows a clear left/right asymmetry, which we believe to be evidence of a localized core–hole in the initial ionized state. Such a localized hole could impart different initial momenta to the two H atoms and break the g/u symmetry of the ion in the ~6 fs before the hole is filled. In this way, the memory of the initial core–hole is reflected in the dissociation dynamics following Auger decay, leading in turn to the observed left/right asymmetry. This explanation is also consistent with the recent work of Adachi et al [5], who observed asymmetry in the photoelectron angular distributions associated with deprotonation, and leads us to believe that we are seeing an indication of proton dynamics induced by core–hole creation [19]. Note that, in contrast to the P2 angular distribution, the Auger angular distribution associated with the lower P1 deprotonation channel (figure 3(c)) is essentially isotropic, indicating that there is substantial rearrangement of the molecule prior to dissociation in this channel. This rearrangement also washes out any left/right asymmetry in the Auger angular distributions for this channel. Turning finally to the distribution in figure 3(b), we again find some left/right asymmetry, consistent with hole localization in the quasi-symmetric V breakup channel. But the elongated shape of the distribution relative to the molecular axis is what one would expect from Auger decay into the ¹Δ_g dication state, so we believe that the measured Auger distribution for this channel contains a superposition of Auger electrons corresponding to two different parent states.

In conclusion, we have measured the fragmentation patterns of the acetylene dication prepared in different electronic states. The identification of these states is consistent with the measured Auger angular distributions and is supported by our theoretical calculations. The states were prepared by identifying the Auger decay channels fed by a K core–hole created through photoionization. The vinylidene-like fragmentation is found to proceed mainly through the ¹Σ ⁺ _g(1π^–2_u) dication state while symmetric fragmentation occurs when the system is prepared in the excited 1π^–1_u2σ^–1_u, ¹Π_g state. We find two deprotonation channels, one through the ¹Σ ⁺ _g state and the other through the 1π^–1_u3σ^–1_g, ¹Π_u state. For the latter, the Auger angular distribution shows an asymmetry that gives clear evidence of hole localization in the initial core-ionized state. There is also evidence of hole localization in the quasi-symmetric V break-up channel, which is partially obscured by a competing symmetric break-up channel into ground-state CH ⁺   +  CH ⁺  products. It is noteworthy that only in the A channel does the dissociation lead directly to the expected correlated products. In all other channels, the fragmentation appears to involve curve crossings and/or conical intersections.

Acknowledgments

This work was supported by the USDOE Office of Basic Energy Sciences, Division of Chemical Science, by the Deutsche Forschungsgemeinschaft and DAAD.

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