Article pubs.acs.org/JPCA
Photoionization Cross Section of the Propargyl Radical and Some General Ideas for Estimating Radical Cross Sections Hong Xu and S. T. Pratt* Argonne National Laboratory, Argonne, Illinois 60439, United States S Supporting Information *
ABSTRACT: A combination of velocity map ion imaging, mass spectrometry, and a laser-based vacuum ultraviolet light source was used to perform a new measurement of the absolute photoionization cross section of the propargyl radical. The measurements are in good agreement with the recent determination of Savee et al. [J. Chem. Phys. 2012, 136, 134307], and significantly larger than an earlier determination. The results are discussed and rationalized in terms of some general ideas about absolute photoionization cross sections. The potential utility of these ideas is illustrated by using recent cross section measurements for a number of molecular radicals, including methyl, allyl and 2propenyl, phenyl, and vinyl.
the propargyl cross section was one of the first to be measured.18 The absolute photoionization cross section of the propargyl radical has been the target of two experimental studies. Robinson et al.18 performed the first measurements by using translational spectroscopy to study the photodissociation of propargyl chloride. In these experiments, the photofragments were ionized by using synchrotron light. By looking at momentum-matched propargyl radicals and chlorine atoms, Robinson et al.18 could use the 1:1 correspondence between the two species, along with the known absolute photoionization cross section of chlorine atoms, to determine the absolute photoionization cross section of propargyl. Two aspects of these experiments deserve mention. First, the experiments were performed in a collision-free environment, so that the considerable internal energy of the propargyl radicals produced in the photodissociation process was not dissipated before the photoionization event. Second, the relative photoionization cross section of propargyl was measured at a different photon energy from the chlorine atoms, so that the photon flux had to be characterized at the two energies. Robinson et al.18 determined the absolute photoionization cross section of propargyl to be 8.3 ± 1.6 Mb at 10 eV, and used this to scale their photoionization efficiency curve between 7.75 and 10.75 eV.
I. INTRODUCTION As one of the simplest resonance-stabilized hydrocarbon radicals, the propargyl radical plays an important role in the chemistry of interstellar space, planetary atmospheres, lowtemperature plasmas, and combustion.1−3 The propargyl concentration in combustion environments is particularly important because the recombination of two propargyl radicals can produce benzene directly,2,3 and this process is thought to be a key step in the formation of soot and particulate matter. For this reason, methods for the detection and quantification of propargyl radicals are highly desirable. In recent years, synchrotron-based, single-photon mass spectrometry has been demonstrated to be a powerful method for the analysis of samples extracted from a variety of reacting environments, including flames and flow tubes.4−8 While mass spectrometry provides a determination of the relative abundances of species with different masses, the ability to tune the energy of the photon can also allow the identification of specific isomers, as a result of their different ionization energies and photoionization efficiency curves.5,6 However, the use of this technique to determine absolute concentrations requires a knowledge of the absolute photoionization cross section of the species of interest. In the past, even the determination of absolute photoionization cross sections for stable species was difficult,9,11 but the use of synchrotron sources has allowed the accurate determination of a large number of these cross sections.12−14 The determination of absolute photoionization cross sections for radicals and other highly reactive species remains a significant challenge, but several techniques have been developed to address this difficulty.15−22 Absolute photoionization cross sections have now been determined for approximately a dozen radicals. Given the importance of the propargyl radical, it is not surprising that © 2012 American Chemical Society
Special Issue: Oka Festschrift: Celebrating 45 Years of Astrochemistry Received: October 5, 2012 Revised: November 20, 2012 Published: November 26, 2012 9331
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Recently, Savee et al.23 have reported a new determination of the photoionization cross section of propargyl. They photodissociated propargyl precursors in a flow reactor, and directly sampled and analyzed the reaction mixture by using a multiplexed mass spectrometer. In this measurement, the sample was also photoionized by using tunable synchrotron light, with considerably higher resolution than the earlier measurement. Both 1-butyne and 1,3-butadiene were used as precursors, and the cross section of propargyl was determined relative to the absolute photoionization cross section of the methyl radical cofragment. Several previous measurements of the latter cross section are in good agreement,20−22 and Savee et al. actually reported a new value for this cross section that is in good agreement with the previous values, but with considerably reduced error bars. By using the methyl radical as a reference, the relative cross sections of the two fragments could be determined at the same photon energy, eliminating a potential source of error. The time scale of the measurements was also such that the methyl and propargyl radicals were thermalized to 298 K, in contrast to the hot radicals of Robinson et al.18 Savee et al. reported four separate measurements of the propargyl cross sections, determined at two different energies with the two different precursors. These values correspond to 26.1 ± 4.2 Mb, and 23.6 ± 3.6 Mb at 10.213 eV, and 23.4 ± 3.2 Mb and 25.1 ± 3.5 Mb at 10.413 eV. These values were used to put their photoionization efficiency curve for propargyl on an absolute scale. While the resolution of this curve is higher than that of Robinson et al., the shapes are very similar if the resolutions are convoluted to match. However, the absolute magnitude of the cross section reported by Savee et al. is approximately three times greater than that reported by Robinson et al. at the same energy. Although the difficulty of the experiments of Robinson et al.18 and the improvements in the experiments of Savee et al.23 suggest that the more recent measurement is likely correct, the importance of the propargyl radical suggests that a new independent measurement might be useful. In this paper, we report a new measurement of the photoionization cross section of the propargyl radical. The measurements employ a different approach from the two previous studies, but have elements in common with both. Specifically, we use photodissociation of 2-butyne and 1,2butadiene to produce propargyl radicals in a 1:1 ratio with methyl radicals, and use laser-based vacuum ultraviolet (vuv) light to photoionize both species. A photoion imaging apparatus is used to ensure that the photofragments are momentum-matched, and time-of-flight mass spectrometry is used to characterize the relative photoionization efficiencies of the two species. The absolute photoionization cross section of the methyl radical is used to put the propargyl measurement on an absolute scale. As in the experiments of Robinson et al.,18 the measurements are made under collision-free conditions, so that the radicals retain the significant internal energy they obtain in the photodissociation process. The present propargyl cross section is slightly smaller than, but consistent with, the results of Savee et al.23 In what follows, the experimental approach is first described in more detail. Some background on the photodissociation dynamics of 2-butyne and 1,2-butadiene is then discussed, followed by a presentation of the experimental results and their analysis. Some general considerations about photoionization cross section are next presented and used to rationalize the observations for propargyl. The utility of these general
considerations is then examined by applying them to several other molecular radical systems for which photoionization cross section data have been reported.
II. EXPERIMENTAL SECTION The collinear ion-imaging apparatus used for the present work has been described thoroughly in previous publications,24−27 and is only briefly reviewed here. The main components of the apparatus are two differentially pumped vacuum chambers, corresponding to a source chamber and an interaction chamber, which are separated by a skimmer with an aperture diameter of 2 mm. The molecular beam was introduced into the source chamber by using a pulsed valve (General Valve, Series 9), and passes through the skimmer into the interaction region, where it is crossed by the laser beams. In the present experiments, the 2-butyne and 1,2-butadiene samples were seeded in He at a concentration of 5%, and the valve stagnation pressure was ∼1500 Torr. The standard velocity map imaging optics consist of a repeller plate, extractor plate, and ground plate. Ions produced in the interaction region fly down the time-of-flight axis to an 80 mm diameter, dual channelplate detector coupled to a phosphor screen. In ion-imaging mode, a standard video camera synched to the experiment was used to record images on a shot-to-shot basis, and the images were centroided on each shot. In the time-of-flight mass spectrometry mode, data were acquired by sending the signal from the channelplate directly to a digital oscilloscope. In the interaction region, the molecular beam is crossed by the 193 nm light from an ArF excimer laser, which propagated perpendicular to the molecular beam. For the imaging experiments, this light was vertically polarized parallel to the face of the detector by using a Rochon polarizer; for the mass spectra, the excimer laser was either polarized in the same manner or used unpolarized. After a short delay (typically ∼100 ns), the photofragments were ionized by vuv light propagating counter to the 193 nm beam. This vuv light was generated by two methods. In the first, two-photon resonant, difference frequency mixing in Kr was used to generate tunable vuv light at 2ω1 − ω2. A frequency-tripled, Nd:YAG-pumped dye laser operating at ω 1 = 202.315 nm was used to pump the twophoton transition to the (2P1/2)5p[1/2]0 level of Kr,28 and a second tunable Nd:YAG-pumped dye laser was used to provide ω2.The two beams were focused into a cell containing Kr, and the diverging vuv light generated by the process was refocused into the interaction region by using an off-axis LiF lens. In the second method, the 355 nm, third-harmonic light from a Nd:YAG laser was focused into the same cell containing Xe. The third-harmonic light at 118 nm was then refocused into the chamber as in the first method. The wavelengths of the light were determined by using a commercial wavemeter (Coherent Wavemaster). The synchronization of the lasers, valve, detection electronics, and imaging system was performed by using a series of digital delay generators referenced to the video camera trigger. Photoion images were recorded at energy 10.486 eV for both precursors. The images were obtained by gating the detector around the mass of interest and recording the image with all lasers present, with only the 193 nm present, and with only the VUV present. Typically, data from 30,000 laser shots were summed to produce each image. The sums of the two images taken with the 193 nm or VUV beam alone were subtracted from the image taken with all lasers present to produce the final image. The subtracted images were reconstructed using the 9332
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pBASEX program.29 The total translational energy distributions were determined by integrating the reconstructed distributions over all angles. The translational energy distributions were calibrated by using images from the photodissociation of CH3I at 193 nm under the same conditions. Depending on the particular experiment, mass spectra generated by the 193 nm alone, by the vuv light alone, and by the 202.315 nm beam alone produced some background signal that required subtraction from the 193 + vuv mass spectrum of interest. Thus, mass spectra were recorded with all beams present, with only the vuv present, with only the 193 nm beam present, with 202.315 and 193 nm beams present (no ω2), and with no lasers present. Traces from 1000 laser shots were averaged for each mass spectrum. For 2-butyne, the sum of the signals with only the vuv or 193 nm light present was subtracted from the signal with all of the lasers present to give the final mass spectrum. For 1,2-butadiene, the signal with the 202.315 and 193 nm light present was subtracted from the signal with all the lasers present to give the final spectrum. Channelplate detectors typically have higher gains for lighter ions than for heavier ions.30,31 To account for this behavior, we have used the results of Krems et al.31 to correct the channelplate response. These results yield a correction factor of 1.13 for the detection of CH3+/C3H3+, with an estimated uncertainty of ±0.05 derived from the comparison of their results with other measurements.30 Thus, the integrated ion intensity ratio (C3H3+/CH3+) used to determine the absolute photoionization cross section of C3H3+ has been corrected using 1.13 ± 0.05. Unrestricted Hartree−Fock calculations at 6-311G level were performed using the Gaussian09 Program Suite32 to allow the visualization of the structure of the molecular orbitals of the radicals. Analogous restricted Hartree−Fock calculations were also performed for the closed shell species of interest. The results were confirmed by comparing with experimental and theoretical data from NIST webbook.33 The symmetry and nodal structure of molecular orbitals were displayed by using GaussView 5.0.9.34
isomerization on the ground state surface competes with dissociation, so that the dominant product channels are not necessarily the ones that would be predicted from the simple structural formulas of the parent species. For 1,2 butadiene, the dominant dissociation channel is to C3H3 + CH3, with experimental and theoretical branching fractions of 0.96 and 0.879, respectively. The second most significant dissociation channel is to C4H5 + H, with branching fractions of 0.04 and 0.059, respectively.38 For 2-butyne, the dominant dissociation channel corresponds to C4H5 + H, with a theoretical branching fraction of 0.566.38 Dissociation to C3H3 + CH3 is the second most important channel, with a branching fraction of 0.238. Theoretical calculations and experimental studies indicate that the C3H3 species formed in the 193 nm photodissociation of 1,2-butadiene and 2-butyne is the propargyl radical.36−38 The following discussion focuses predominately on the C3H3 + CH3 product channel. The photon energy of the 193 dissociation laser is 6.424 ± 0.015 eV, which is considerably larger than the bond dissociation energy of the C4H6 samples. In particular, the dissociation energies to C3H3 + CH3 are 3.34 and 3.52 eV for 1,2-butadiene and 2-butyne, respectively,33 and the corresponding dissociation energies to C4H5 + H are 3.69 and 3.84 eV.38 The excess energy can be distributed as internal energy of the fragments or into their relative translational energy. For statistical dissociation processes, most of the excess energy is expected to go to internal energy of the fragments. The present experiments are performed in a collision-free environment, and if the primary fragments have sufficient internal energy, they can undergo secondary fragmentation. For example, the bond dissociation energy of C4H5 → C2H3 + C2H2 is 2.34 eV,33 so that secondary dissociation is possible in principle. The loss of H atoms from C4H5 is also possible. However, the lowest dissociation energy of the propargyl radical is to the cyclopropenylidene isomer of C3H2 + H at ∼3.71 eV,33,39 while the dissociation energy of CH3 to CH2 + H is 4.725 ± 0.009 eV.40 Thus, secondary decomposition will not occur for these species in the present experiments. The adiabatic ionization energies of C3H3 (propargyl) and CH3 are 8.6982 ± 0.0005 eV41 and 9.83891 ± 0.00002 eV,42 respectively. In the present experiments, measurements are made using vuv photon energies between 10.4 and 10.5 eV, well above these ionization energies. This choice of photon energy is important for two reasons: we must assess the Franck−Condon factor for ionization of propargyl and methyl radicals with potentially significant internal energy, and we must assess the potential for dissociative photoionization of C3H3 and CH3. The geometry of the electronic ground state of CH3+ is similar to that of the electronic ground state of CH3, and the origin band is by far the strongest band in the photoelectron spectrum.43 More generally, the diagonal photoionizing transition that preserves the vibrational quantum numbers of the ground state neutral is expected to be the strongest, and long vibrational progressions are not expected. Thus, photon energies 0.6 to 0.7 above the ionization threshold are expected to be above most, if not all, of the Franck−Condon envelope for nearly all of the vibrational levels populated in the photodissociation process. In this case, the photoionization cross section is not expected to depend too strongly on the initial vibrational level. Similarly, the geometries of the neutral and ionic ground states of propargyl are nearly the same, and the Franck−Condon factors are expected to be strongly peaked
III. CROSS SECTION DETERMINATION A. Background. The photodissociation of 1,2-butadiene, 2butyne, and other C4H6 isomers have been studied in some detail both experimentally and theoretically.35−38 There are five principal dissociation channels for these molecules, corresponding to C4 H6 → C4 H5 + H (1) C4 H6 → C4 H4 + H 2
(2)
C4 H6 → C3H3 + CH3
(3)
C4 H6 → 2C2H3
(4)
C4 H6 → C2H4 + C2H 2
(5)
Studies of the translational energy release and branching fractions for the different channels strongly suggest that the molecules excited at 193 nm undergo rapid internal conversion from the optically excited state to the surface of the electronic ground state, and that dissociation occurs on that surface.35−38 Detailed calculations of the ground state surfaces for these reactions have been performed, and provide information on the energetics of the barrier heights and dissociation pathways.38 Theoretical studies of the dissociation processes suggest that 9333
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for ionizing transitions that are diagonal in the vibrational quantum numbers.44 The present photon energies are 1.7−1.8 eV above the ionization threshold of propargyl, which should encompass most, if not all, of the Franck−Condon envelopes from the initial vibrational levels of the neutral. Thus, the photoionization cross section of propargyl at these photon energies is expected to depend only weakly on the initial vibrational level. Although the neutral C3H3 and CH3 produced in the photodissociation processes cannot have sufficient internal energy to undergo secondary dissociation, it is possible that, upon photoionization, the corresponding cations will have sufficient internal energy to dissociate, resulting in dissociative ionization. (Note that by dissociative ionization we include both direct excitation to a dissociative ionization continuum and the sequential process of photoionization producing the parent ion followed by unimolecular fragmentation of the parent.) The dissociation threshold for CH3+ → CH2+ + H is approximately 5.3 eV,33 so that even if all of the excess energy of the photodissociation went into the CH3 and all of the excess energy of the photoionization processes went into internal energy of the corresponding CH3+, the ion would still have insufficient energy to dissociate. In contrast, the lowest energy dissociation path of the propargyl cation is to cyclic C3H2+ + H, with a dissociation energy of 2.21 eV.33 In principle, some of the neutral C3H3 radicals produced by the photodissociation process could have at least this much internal energy. Thus, even if the ionization process only preserves the internal energy, some of the propargyl cations could dissociate. Such dissociation would lead to a loss in signal at the C3H3+ mass, distort the measurement of the relative yields of C3H3+ and CH3+, and thus result in a smaller than expected value for the C3H3 photoionization cross section. Thus, a measurement of the translational energy distributions of the C3H3 and CH3 is essential to ensure that the fragments are truly momentum matched, and that dissociative ionization is minimal. B. Determination of the Propargyl Cross Section. Figures 1 and 2 show the reconstructed velocity map images recorded following the photodissociation of 1,2-butadiene and 2-butyne, respectively, and monitoring the C3H3+ and CH3+ ion signals at a vuv photon energy of 10.486 eV. Also shown are the corresponding total translational energy distributions of the fragments; these distributions were extracted from the reconstructed images. For both precursors, the translational energy distributions extracted from the C3H3+ and CH3+ images are essentially identical. This observation strongly suggests that dissociative ionization of the C3H3 is not a significant process, as it would be expected to deplete the low translational energy (high internal energy) portion of the distribution determined from the C3H3+ image. This similarity of the distributions obtained from the two different ions also suggests that the internal energy of the radicals does not significantly affect the photoionization cross sections. As a result, the measurement of the relative ion signals in the mass spectrum should allow the determination of the relative photoionization cross sections of the propargyl and methyl. As discussed previously, the shapes of the translational energy distributions are also consistent with the unimolecular decomposition of the vibrationally hot C4H6 molecules on the potential surface of the electronic ground state. Typical mass spectra following the photodissociation of 1,2butadiene and 2-butyne at 193 nm and ionization of the products at 10.486 eV are shown in Figures 3 and 4,
Figure 1. Raw velocity map ion images of (a) the CH3+ ion signal, and (b) the C3H3+ ion signal following the photodissociation of 1,2butadiene at 193 nm and photoionization of the fragments at 10.486 eV. Frame (c) shows the total translational energy distributions extracted from the reconstructed images.
respectively. Mass spectra were recorded for a variety of acceleration conditions and detector voltages to check the consistency of the data. The vuv photon energy is above the ionization energy of both parent compounds, resulting in an extremely intense parent peak that is difficult to subtract effectively. As a result, the mass spectra in Figures 3 and 4 do not show the region near the parent mass. For the present purposes, the important feature of the spectra is the relative intensity of the C3H3+ (mass 39) and CH3+ (mass 15) peaks. Before addressing this, however, some other features of the mass spectra should first be mentioned. 9334
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Figure 3. Mass spectrum following the photodissociation of 1,2butadiene at 193 nm and photoionization of the fragments at 10.486 eV. The photon energy is above the ionization potential of the parent, and the region around the corresponding peak at mass 54 is not shown.
Figure 4. Mass spectrum following the photodissociation of 2-butyne at 193 nm and photoionization of the fragments at 10.486 eV. The photon energy is above the ionization potential of the parent, and the region around the corresponding peak at mass 54 is not shown.
produced C4H5+ would have significant internal energy. Additional experiments are necessary to determine which mechanism produces the C2H3+. Note, however, that the C2H3+ signal is far more intense in 2-butyne than in 1,2-butadiene, which is consistent with the much larger branching fraction for C4H6 → C4H5 + H in the former case.38 The intensities of the propargyl and methyl peaks were determined by integrating the mass spectra. Data from ∼20 separate mass spectra were averaged for each cross section determination. The propargyl to methyl intensity ratio was then corrected for the mass-dependent discrimination factor discussed above. Finally, the values of the absolute photoionization cross section of methyl of 6.10 ± 0.67 Mb at 10.413 eV and 5.68 ± 0.67 Mb at 10.486 eV were used from the most recent measurement of Savee et al.23 The former value was directly reported and the latter value was determined from Figure 2 of their paper. Multiplying these values by the corrected propargyl to methyl ratio yielded the absolute photoionization cross section for the propargyl radical. These values correspond to σpropargyl(10.413 eV) = 21.4 ± 2.7 Mb and σpropargyl(10.486 eV) = 19.0 ± 2.7 Mb from the 1,2-butadiene
Figure 2. Raw velocity map ion images of (a) the CH3+ ion signal, and (b) the C3H3+ ion signal following the photodissociation of 2-butyne at 193 nm and photoionization of the fragments at 10.486 eV. Frame (c) shows the total translational energy distributions extracted from the reconstructed images.
In particular, the peak at mass 27 in both Figures 3 and 4 corresponds to the vinyl radical, C2H3. This peak is actually quite intense in the mass spectrum from 2-butyne, and substantially weaker, but still present, in the spectrum from 1,2-butadiene. In both cases the predicted amount of C2H3 from the primary photodissociation process is very small (2.5% for 2-butyne and 0.47% from 1,2-butadiene),38 so it is unlikely to come from that process. More likely, the C2H3+ is produced by the secondary dissociation of C4H5 → C2H2 + C2H3, or by the dissociative ionization of C4H5 to C2H2 + C2H3+. This latter process would be enhanced because in the primary dissociation process C4H6 → C4H5 + H, all of the excess internal energy ends up in the C4H5, increasing the likelihood that the initially 9335
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measurements, and σpropargyl(10.486 eV) = 17.8 ± 2.7 Mb from the 2-butyne measurements. These values are also given in Table 1. The measurements with two different precursors are in
including alkanes, alkenes, alcohols, and ethers. He noted that while the energy dependence of absorption cross sections of the species in the same group were often very different, the ionization cross sections were generally quite similar. Koizumi48 concluded that, for many species, autoionization was not very important, and that the principal decay pathway for superexcited states was dissociation. In this situation, the ionization cross section is predominately determined by direct ionization alone. Thus, the photoionization cross section shows steps at the energy of each ionization threshold, with plateaus between the thresholds. Koizumi also modeled the energy dependence of the plateaus by using the energy dependence of the atomic hydrogen cross section. This approach works quite well, and Koizumi’s ideas and form for the photoionization cross section have been extremely useful for estimating ionization cross sections. The discussion that follows incorporates a number of ideas discussed by Koizumi, including the dominance of direct ionization in determining most photoionization cross sections. However, rather than trying to derive general formulas for the cross sections, we try instead to make use of the considerable amount of new information on photoabsorption and photoionization cross sections that has become available since the publication of Koizumi’s paper.48 While Bobeldijk et al. focused on bonded pairs of atoms,47 here we focus instead on the character of the atomic or molecular orbital from which the electron is ejected, as well as on the state (or states) of the ion that is (are) produced. For atoms, systematic studies of the photoionization cross sections of individual subshells have been carried out.49,50 For example, Yeh and Lindau50 have reported results of Hartree−Fock− Slater calculations based on a one-electron, central potential model in the dipole approximation. While these calculations ignore the atomic fine structure and many other details, they still provide a good overview of the systematic behavior of the cross sections. In this approximation, and after summing over final states and averaging over initial states, the photoionization cross section is given by50
Table 1. Photoionization Cross Sections for the Propargyl Radical precursor
photoionization energy (eV)
cross section (Mb)
2-butyne 1,2-butadiene 1,2-butadiene
10.486 10.413 10.486
17.8 ± 2.7 21.4 ± 2.7 19.0 ± 2.7
excellent agreement, and the values at 10.413 and 10.486 eV are very close to each other, which is consistent with the wavelength dependent cross section given by Savee et al.23 The value at 10.413 eV is slightly lower than the values reported by Savee et al. at that energy of σpropargyl(10.413 eV) = 23.4 ± 3.2 Mb and σpropargyl(10.413 eV) = 25.1 ± 3.5 Mb from the photolysis of 1-butyne and 1,3-butadiene, respectively, but considering the error bars, the agreement is actually quite good. Thus, it appears that the internal energy of the propargyl radical does not significantly affect the photoionization cross section of propargyl between 10.4 and 10.5 eV, and that internal energy of the radical cannot account for the difference between the results of Savee et al.,23 who had a thermalized sample, and the earlier results of Robinson et al.,18 who had internally hot C3H3 like that studied here.
IV. PHOTOIONIZATION CROSS SECTIONS OF RADICALS A. General Considerations. The propargyl cross section reported by Savee et al.23 was rationalized by comparison with the cross sections of allene and propyne, and was found to have a similar value to these closed-shell systems around 10.2−10.4 eV. Here we present some general ideas that may prove useful for estimating photoionization cross sections in radicals, along with a somewhat different perspective and rationalization of the propargyl cross section. A number of other recent measurements of absolute photoionization cross sections of radicals are also discussed in light of these considerations. The development of general rules for estimating absolute photoionization cross sections is fraught with potential pitfalls, especially close to the first ionization threshold, where autoionizing resonances, shape resonances, Cooper minima, multiple ionization thresholds, and other phenomena can dramatically affect the cross section.45 While some of these effects can be minimized by working well above threshold, working near threshold is highly desirable to make use of the “soft-ionization” capability of photoionization and minimize fragmentation.46 Perhaps the most successful general method for estimating absolute photoionization cross sections was developed by Bobeldijk et al.47 In their approach, the cross section is estimated by using the sum of the cross sections for all of the atom pairs in the molecule. Although not explicitly stated, their standard model is meant for closed-shell molecules. In addition, by providing an estimate of the cross section at a fixed energy, Bobeldijk et al.47 did not take account of potential variations in ionization energies and the relative positions of excited states of the ions. While Bobeldijk et al. were certainly aware of these limitations, the overall agreement of their model with experimental cross sections is actually quite reasonable. Koizumi48 has also discussed general aspects of the photoionization cross sections of a broad range of species
σn , l =
4πα0a02 Nn , l hν[lR n2, l − 1(εkin) 3 2l + 1 + (l + 1)R n2, l − 1(εkin)]
(6)
Here, σ is the cross section in cm2, α0 is the fine-structure constant, a0 is the Bohr radius, Nn,l is the number of electrons in the n,l subshell, the Rn,l±1 are the one-electron radial dipole matrix elements between the initial bound state and the continuum, and εkin is the electron kinetic energy given by the difference between the photon energy and the ionization energy of the given subshell.50 The expression is proportional to the number of electrons in the subshell of interest, Nn,l. This dependence is what gives rise to the rule of thumb in molecular photoelectron spectroscopy that, for spectra recorded at the magic angle, the integrated intensity of the photoelectron band (i.e., integrated over the full final-state vibrational distribution) is proportional to the number of electrons in the molecular orbital from which the electron is ejected.51,52 Of course, even in the central field model, this rule of thumb is complicated by many factors; for example, the radial matrix elements from different subshells (and at different εkin) can vary substantially, and effects such as interchannel coupling can cause significant deviations from the expected behavior. Nevertheless, it is a useful starting point for qualitative estimates of photoionization cross sections. 9336
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corresponds to a linear combination of the first components of the degenerate HOMOs of propyne and allene. In propargyl, a second orbital corresponding to the HOMO-1 is made from a linear combination of the second components of the degenerate HOMOs for the two closed-shell systems. This HOMO-1 orbital lies in the plane of the hydrogen atoms in propargyl and is only slightly more strongly bound than the HOMO. The importance of HOMO-1 in determining the photoionization cross section of propargyl is considered in more detail below. The photoelectron spectra of both allene and propyne are well-known.53 In allene, the photoelectron band corresponding to ionization out of the HOMO extends from the ionization threshold at 9.688 eV to ∼11.6 eV. The second photoelectron band begins at ∼14 eV. For comparison with propargyl, the cross section should be determined just above the first photoelectron band, that is, 11.7−12.0 eV. Examination of the photoionization cross section of allene shows it rises to a maximum at ∼11.6 eV, and then decreases gradually up to 12 eV, where it begins a second rise.6,54 Thus, electronic autoionization of Rydberg series converging to higher excited states of the allene cation do not appear to have a big effect on the absolute photoionization cross section up to ∼12 eV. Interestingly, the photoabsorption cross section does show an intense broad resonance between 10.7 and 12.2 eV,54 but this resonance appears to decay almost entirely through dissociation. (See the comparison of the photoabsorption, photoionization, and photodissociation cross sections of allene in Reference 54.) Between 11.7 and 12.0 eV, two measurements of the absolute photoionization cross section give values of 28− 31 Mb, which corresponds to the contribution from the fourelectron HOMO.6,54 Thus, the one-electron cross section from this orbital is expected to be 7−8 Mb. In propyne, the photoelectron band corresponding to ionization out of the HOMO extends from the ionization threshold55 at 10.367 eV to ∼11.4 eV, and the onset of the second photoelectron band occurs just below 14 eV.53 At moderate resolution, the photoionization cross section rises steeply at threshold to a plateau at ∼10.8 eV.56 Both the photoionization and photoabsorption cross sections are relatively flat between ∼10.8 and 11.7 eV, and thus Rydberg series converging to higher electronic states of the ion do not contribute substantially to the cross section in this region.6,10,56 The photoionization cross section between 10.8 and 11.7 eV takes on values of 41−44 Mb.6 As this cross section corresponds to the contribution from the 4-electron HOMO, the one electron cross section is expected to be 10−11 Mb. Taken together with the 7−8 Mb value for allene, this estimate suggests that photoionization out of the one-electron HOMO of the propargyl radical should have a cross section of ∼7−11 Mb. The photoionization cross section for the propargyl radical rises sharply at the threshold of 8.6982 eV,23,41,57 with evidence for some resonance structure, followed by a drop and then a sloping plateau with a cross section of 9−11 Mb between 8.8 and 8.9 eV. Calculations44 and threshold photoelectron spectroscopy41,58 show that the geometries of the neutral and ionic ground states are similar, and that photoionization from the ground vibrational levels is strongly peaked at the ground vibrational level of the ion. Thus, the cross section from 8.8 to 8.9 eV should reflect the full contribution of the one-electron HOMO. The cross section in this region reported by Savee et
In molecules, the photoionization cross section near threshold will depend on the photon energy relative to the Franck−Condon envelope for the ionizing transition. If a wavelength is chosen within this envelope, the photoionization cross section will not reflect the full contribution of the relevant molecular orbital of the neutral. Thus, rather than choosing a specific photon energy for the comparison of photoionization cross sections of similar species, it makes more sense to compare cross sections at photon energies above the full Franck−Condon envelope of the bands of interest in each molecule. Although this photon energy may be different for the molecules under comparison, by choosing photon energies above the Franck−Condon envelope, the chance that vibrational or rotational autoionization will skew the comparison can also be minimized. The estimation of the photoionization cross section can then be made in the following manner: (1) identify stable molecules with known cross sections and in which the molecular orbitals can be correlated with those of the radical of interest-typically this may involve both the highest occupied molecular orbital (HOMO) and other orbitals; (2) evaluate the cross section in the stable molecule at an energy above the full photoelectron band(s) relevant to the molecular orbital(s) of interest; (3) Scale the cross section by the ratio of occupancy numbers in the HOMO and other relevant orbitals; (4) use the scaled value for the unknown cross section at an energy above the corresponding photoelectron band of the molecule of interest. While there are likely many systems for which this approach will fail due to well-known effects, we can illustrate its potential by considering the results on the propargyl radical discussed above. B. Propargyl. Propargyl is a resonance stabilized radical with two structures, HCC−Ċ H2 and HĊ CCH2, that are analogous to propyne and allene, respectively. Figure 5
Figure 5. Molecular orbitals for the HOMO and β component of the HOMO-1 of propargyl, as well as for the two components of the degenerate HOMOs of propyne and allene.
shows the HOMO and HOMO-1 of propargyl along with the two components of the degenerate HOMOs of propyne and allene. The HOMOs of both allene and propyne are π orbitals containing four electrons, while the HOMO of propargyl contains only one electron. The HOMO for propargyl is perpendicular to the plane of the hydrogen atoms and roughly 9337
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al.23 is 9−11 Mb, in good agreement with the value of 7−11 Mb estimated from the allene and propyne cross sections. Above 8.9 eV, the propargyl cross section rises rapidly and displays a series of intense resonances that must converge to an electronically excited state of the propargyl cation. The lowest excited state of the cation corresponds to the a 3A′ electronic state, which was observed as a broad band centered at 10.4 eV in the propargyl photoelectron spectrum of Minsek and Chen.59 The next excited state of the cation corresponds to the A 1A′ state, which lies 4.63 eV above the ground state.44 Both possibilities for the series limit were tested by using the Rydberg formula En = E ip −
9 (n − μ)2
effectiveness of the present approach might be questioned. In particular, the HOMO in methyl is a nonbonding, out-of-plane pz orbital, while the HOMO in methane is a triply degenerate tg orbital. Images of these orbitals are shown in Figure S1 of the Supporting Information. Nevertheless, the three components of the tg orbital do have the same nodal structure as the pz orbital in methyl. The first three photoelectron bands in methane correspond to ionization out of the HOMO.53 The three bands are strongly overlapped, and the structure broadens with increasing energy. The fourth photoelectron band lies at significantly higher energy, so we consider the cross section just above the first three photoelectron bands, at ∼16 eV. Here, the total photoionization cross section is ∼45 Mb,61 although we note that at this energy there is some fragmentation of the parent CH4+ to CH3+ + H. Using the total photoionization cross section61 and dividing by 6, the occupancy of the tg HOMO, gives a photoionization cross section of ∼7.5 Mb/electron. The first excited state of the methyl cation lies well above the electronic ground state; in addition, below 11.5 eV the relative photoionization cross section of CH3 shows no significant structure from electronically autoionizing states.23,40 The cross section rises steeply at threshold and reaches a plateau at ∼10.5 eV. Because there is only one electron in the HOMO of CH3, the cross section at this energy is thus estimated to be ∼7.5 Mb. As discussed above, there have been several measurements of the cross section at this plateau, and all agree within the stated experimental uncertainties.20−23 The most recent value being 6.10 ± 0.67 Mb at 10.413 eV.23 The present estimate is somewhat greater than this value, but given the qualitative nature of the argument, the agreement must be considered good. D. 2-Propenyl and Allyl. Robinson et al.17 have reported absolute photoionization cross sections for both allyl and 2propenyl. The HOMOs and HOMO-1s of these radicals and propene are shown in Figure S2 of the Supporting Information. Allyl is a resonance stabilized radical, and its HOMO looks like a stretched, out-of plane, dπ orbital, which can be roughly reproduced by taking an out-of-phase linear combination of the propene HOMO and its mirror image. The HOMO of 2propenyl is similar to the HOMO-1 of propene, a relatively complex orbital with approximate fπ character. This orbital is stabilized in propene (relative to 2-propenyl) by the in-plane H atom on the central carbon atom. Both radicals have a single electron occupying the HOMO. The photoabsorption spectrum of propene rises gradually between 9.6 and 11.6 eV.11 The first photoelectron band shows a progression in the CC stretching vibration, extending from threshold to approximately 11 eV.53 This band is well-resolved from the second photoelectron band, which arises from ionization from the HOMO-1 and is diffuse. The photoionization cross section of propene rises fairly steeply at threshold,11 reflecting the Franck−Condon envelope of the first photoelectron band, reaching a plateau at 10.5 eV. Between 10.5 and 11.7 eV, the photoionization cross section rises slowly, with no evidence for resonant ionization processes. The absolute photoionization cross section in this region increases from 10.9 Mb to 13.4 Mb, yielding an average value of 12.2 Mb.11 The HOMO of propene contains two electrons, giving a cross section for the HOMO of 6.1 Mb/electron. The experimentally determined absolute photoionization cross section of allyl rises gradually from threshold to a plateau at approximately 9 eV, where it reaches a value of 5.9 Mb.17
(7)
where En is the level energy, Eip is the relevant ionization limit, 9 is the Rydberg constant for propargyl, n is the principal quantum number, and μ is the quantum defect. These considerations strongly suggest that the intense resonances correspond to states converging to the a 3A′ state. Indeed, the resonances are no longer resolved above ∼10.1 eV, and the cross section flattens out between 10.1 and 10.5 eV.23,57 Above both the a 3A′ and A 1A′ thresholds, the total cross section should reflect the contribution of both electrons of the HOMO-1. However, the 3A′ level lies somewhat below the 1A′ level, so that the relative contributions of the two ion states must be assessed. Cox and Orchard60 have discussed the related problem of the intensities of photoelectron bands in open-shell molecules and shown that for ionization out of a closed shell that lies below an open shell, the relative intensities are related to the statistical weights of the two ion states. Their arguments lead to a 3:1 intensity ratio for the 3A′ and 1A′ continua, respectively. A second argument leading to the same conclusion comes from consideration of the α and β orbitals. If the HOMO is an α orbital, ionization from the β component of the HOMO-1 leads to a pure triplet state of the cation. However, ionization from the α component of the HOMO-1 leads to a 50:50 mixture of triplet and singlet character. Again, the ratio of triplet to singlet character of the continuum is 3:1. The HOMO-1 of propargyl is very similar to the second component of the HOMOs of propyne and allene. Above the 3A′ and 1A′ thresholds, the two electrons in the HOMO-1 of propargyl are expected to contribute ∼14−22 Mb to the total cross section. Between the 3A′ and 1A′ thresholds, however, these arguments suggest that the contribution of the HOMO-1 will be 3/4 of this value, or 10.5−16.5 Mb. Adding the cross section for the HOMO then yields a value of 17.5−27.5 Mb for the total photoionization cross section of propargyl near 10.4 eV. Considering the nature of the estimate, this value is in reasonable agreement both with the results of Savee et al.,23 which give 22−24 Mb between 10.2 and 10.5 eV, and with the present measurements. Cross section measurements at higher energy would be interesting to assess the contribution of ionization to the A 1A′ state, but such measurements become difficult for experimental reasons due to dissociative ionization of the propargyl precursor. C. Methyl. The success of the present approach at rationalizing the propargyl cross sections suggests that the examination of other recent measurements from this perspective might prove informative. For the methyl radical, the closest closed-shell molecule corresponds to methane. The structure of the two species are substantially different, so the 9338
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The α component of the a1 HOMO and both the α and β components of the b1 HOMO-1 of phenyl look like slightly asymmetric versions of the two degenerate components of the e1g HOMO of benzene. The 1A1 ground state of the phenyl cation corresponds to the removal of the electron from the singly occupied a1 HOMO, whereas the 3B1 first excited state corresponds to removal of an electron from the HOMO-1. The geometry of the 3B1 state is closer to that of the neutral phenyl ground state, and as a result, the vertical ionization energy to the 1A1 state is calculated to lie only ∼0.35 eV below that of the 3 B1 state.64 Specifically, whereas the adiabatic ionization energies to the 1A1 and 3B1 states are 8.272 ± 0.01065 and 9.10 eV, respectively, the vertical ionization energies are calculated to be 9.13 and 9.48 eV, respectively.64 Above ∼9.5 eV, the cross section for ionization out of the HOMO is expected to be ∼6.25 Mb. Using the arguments discussed above for propargyl, the cross section for ionization out of the HOMO-1 to produce the 3B1 state is expected to be 3/4 × 2 × 6.25 Mb = 9.4 Mb. Thus, one expects the photoionization cross section to rise slowly from the adiabatic threshold and reach a value of ∼15.7 Mb at a little over 9.5 eV. However, the calculations on phenyl64 indicate that there are three more excited states of the phenyl cation whose vertical ionization energies lie within 0.6 eV of the vertical ionization energy to the 3 B1 state. One of these states corresponds to the 1B1 singlet component paired with the 3B1 state, with a vertical ionization energy of ∼10.1 eV. Above this energy, ionization to the 1B1 state is expected to add ∼1/4 × 2 × 6.25 Mb = 3.1 Mb to the cross section. The two other lower energy states of the phenyl cation correspond to the 3A2 and 1A2 states, with vertical ionization energies from the ground state neutral of ∼9.73 and 9.75 eV, respectively.64 Although the 1A1, 3B1, and 1B1 states of the phenyl radical are produced by the removal of electrons from orbitals analogous to the e1g HOMO of benzene, the 3A2 and 1 A2 states are produced by the removal of electrons from the a2 HOMO-2 of phenyl. The energy orderings of the α and β orbitals in phenyl are different: whereas the α orbital is related to the e2g HOMO-1 of benzene, the β orbital is similar to the e1g HOMO of benzene. (The β component of the HOMO of phenyl is thus correlated with the e2g HOMO-1 of benzene.) In principle, the photoionization cross section from the e2g orbital of benzene could be different from that from the e1g orbital, but the relative intensities of the e1g and e2g bands in the He I photoelectron spectrum of benzene are similar. Baltzer et al. have reported branching fractions for the different electronic states of the benzene cation near threshold.66 At ∼14.1 eV, which is above both the X̃ and à states of the benzene cation and the lowest energy, they reported branching fractions; the e2g branching fraction is ∼1.26 times greater than the e1g branching fraction.66 At energies above both the 3A2 and 1A2 thresholds, ionization out of the β component leads purely to the triplet state with a cross section of 1 × 6.25 Mb, whereas ionization out of the α component leads to a 50:50 mixture of 3 A2 and 1A2 with a cross section of 1 × 1.26 × 6.25 Mb. Thus, the total cross section for the HOMO-2 orbital above the 3A2 and 1A2 thresholds is 14.1 Mb, and the total photoionization cross section at ∼10.5 eV is estimated to be (6.25 + 9.4 + 3.1 + 14.1) Mb, or ∼32.8 Mb. The present estimate for the phenyl photoionization cross section is considerably larger than the value of ∼16.5 Mb reported by Sveum et al. at the same energy.19 The shape of the
This value is in reasonable agreement with the estimate of 6.1 Mb based on the propene cross section. The plateau in the relative photoionization cross sections of allyl extend to approximately 10.7 eV, and there is no evidence of secondary rises associated with excited states of the ions. To our knowledge, the excited states of the allyl cation are not well characterized. The lowest excited state is expected to be a triplet, and preliminary calculations on the allyl cation indicate that it lies approximately 2.4 eV above the ground state, which would be near the high energy end of the reported allyl spectrum. At higher energies, the allyl cross section is expected to undergo a second rise. Estimating the photoionization cross section of the 2propenyl radical is more difficult for several reasons. The absolute photoionization cross section of propene has not been reported above ∼11.8 eV.11 In principle, the relative intensities of the first two photoelectron bands in the He I photoelectron spectrum of propene could be used to scale the absolute cross section of the first band.53 Unfortunately, the second photoelectron band is overlapped by the third photoelectron band, making it difficult to determine the relative intensity compared to the first band. Nevertheless, a crude estimate of the two band intensities in the photoelectron spectrum, along with a correction for the different photoelectron angular distributions for the two bands,62 gives a cross section for the HOMO-1 of ∼1.9 times that of the HOMO, or 11.6 Mb/ electron. The experimental cross section for the 2-propenyl radical rises slowly from threshold to a plateau of ∼4.9 Mb between 9 and 10.5 eV. 17 The experimental value is considerably smaller than the present estimate. One possible explanation for this is that the photoelectron spectrum is measured well above the threshold of the two bands. Because the HOMO-1 has l = 3, or f character, the strongest transition will be to the l = 4 continuum, which may be weak very close to threshold, but significantly larger at 21.2 eV, the energy in the photoelectron spectrum. Note, however, that preliminary calculations indicate that the binding energies of the HOMO and HOMO-1 of the 2-propenyl radical are very similar, and thus at least two orbitals are expected to contribute to the photoionization cross section. If this is the case, the relatively small total photoionization cross section determined in the previous experiment17 is rather surprising. More detailed theoretical calculations, as well as additional experiments, would provide a better understanding of the source of this discrepancy. E. Phenyl. The structure of the molecular orbitals of the phenyl radical is similar to that of benzene orbitals. Images of these orbitals are shown in Figure S3 of the Supporting Information. In benzene, the HOMO is a doubly degenerate e1g π orbital involving p orbitals of the carbon ring.53 Ionization out of this orbital produces the first photoelectron band, which extends from threshold to approximately 10 eV. The geometries of the neutral and cation are similar, and the transition to the vibrationless ground state is the dominant feature in this band. The onset of the second photoelectron band is at over 11 eV, so the structure is well-resolved. The photoabsorption spectrum is relatively flat from threshold to ∼10.25 eV,63 and the photoionization cross section rises smoothly across the Franck−Condon envelope.63 No significant features from electronic autoionization are observed. The photoionization cross section at 10 eV is ∼25 Mb.63 Dividing by 4, the occupancy of the HOMO, gives a cross section of 6.25 Mb/ electron. 9339
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This comparison allows an estimate of the HOMO cross section for the vinyl cation, although it must be remembered that it is based on the cross section ratio for ethylene at 21.2 eV, and this ratio is almost certainly energy dependent. The relative cross sections of the HOMO and HOMO-1 could in principle also be estimated from the photoionization and photoabsorption spectra of ethylene, but contributions from unresolved autoionizing resonances based on higher excited states of the ion are difficult to assess. Nevertheless, near threshold, these ethylene spectra do suggest a larger photoionization cross section from the HOMO-1 than from the HOMO. Using the ratio of 1.9 determined from the photoelectron spectrum of ethylene, and the absolute cross section estimated for the HOMO, a value of ∼(4.5) × 1.9 = 8.6 Mb per electron is expected for ionization out of the HOMO-1 of ethylene, and for ionization out of the HOMO of vinyl. Thus, above the 1A′ Franck−Condon envelope of vinyl, the cross section is expected to be ∼8.6 Mb. The first ionization potential for vinyl has been reported as
