Dissociative electron attachments to ethanol and acetaldehyde: A combined experimental and simulation study Xu-Dong Wang, Chuan-Jin Xuan, Wen-Ling Feng, and Shan Xi Tian Citation: The Journal of Chemical Physics 142, 064316 (2015); doi: 10.1063/1.4907940 View online: http://dx.doi.org/10.1063/1.4907940 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/142/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Temperature dependence of the cross section for the fragmentation of thymine via dissociative electron attachment J. Chem. Phys. 142, 174303 (2015); 10.1063/1.4919638 Dissociative electron attachment studies on acetone J. Chem. Phys. 141, 164320 (2014); 10.1063/1.4898144 Dissociative electron attachment to pentaerythritol tetranitrate: Significant fragmentation near 0 eV J. Chem. Phys. 132, 134305 (2010); 10.1063/1.3386386 Dissociative electron attachment to gas phase valine: A combined experimental and theoretical study J. Chem. Phys. 125, 204301 (2006); 10.1063/1.2400236 High resolution dissociative electron attachment to gas phase adenine J. Chem. Phys. 125, 084304 (2006); 10.1063/1.2336775
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THE JOURNAL OF CHEMICAL PHYSICS 142, 064316 (2015)
Dissociative electron attachments to ethanol and acetaldehyde: A combined experimental and simulation study Xu-Dong Wang, Chuan-Jin Xuan, Wen-Ling Feng, and Shan Xi Tiana) Hefei National Laboratory for Physical Sciences at the Microscale, Center of Advanced Chemical Physics, and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
(Received 24 November 2014; accepted 30 January 2015; published online 13 February 2015) Dissociation dynamics of the temporary negative ions of ethanol and acetaldehyde formed by the lowenergy electron attachments is investigated by using the anion velocity map imaging technique and ab initio molecular dynamics simulations. The momentum images of the dominant fragments O−/OH− and CH3− are recorded, indicating the low kinetic energies of O−/OH− for ethanol while the low and high kinetic energy distributions of O− ions for acetaldehyde. The CH3− image for acetaldehyde also shows the low kinetic energy. With help of the dynamics simulations, the fragmentation processes are qualitatively clarified. A new cascade dissociation pathway to produce the slow O− ion via the dehydrogenated intermediate, CH3CHO− (acetaldehyde anion), is proposed for the dissociative electron attachment to ethanol. After the electron attachment to acetaldehyde molecule, the slow CH3− is produced quickly in the two-body dissociation with the internal energy redistributions in different aspects before bond cleavages. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4907940]
I. INTRODUCTION
Dissociative electron attachment (DEA) to molecule AB, e− + AB → (AB−)# → A + B−, is a key process in the radiation-induced chemistry, where the active neutral (A) and anionic (B−) radicals are produced, and the short-lived intermediate (AB−)# is usually called temporary negative ion (TNI).1 DEA can be generally classified into two types:2 one is one-particle process, namely, the incoming electron is captured into a virtual molecular orbital, and TNI is formed at a shape resonant state; the other is two- or multi-particle process. In the latter, during the electron capture, the electron(s) of molecular target could be excited simultaneously. The latter, core-excited resonant state, is quite complicated, and its identification needs the sophisticated theoretical analysis3 and the references of different spectroscopic studies.4,5 In addition, the molecular vibrations of the target may be excited when the electron is captured. As a doorway, this process may be more responsible for the chemical bond cleavages, in particular, at the low electron attachment energy. Since the DEAs to biomolecules are investigated extensively,1 hydrocarbons containing the amino- and hydroxyl groups, as the model molecules of biological compounds, also receive much attention.6–10 However, there are many challenges toward understanding of the DEA to polyatomic molecule, for examples, more resonant states of TNI in the narrow energy space; novel spatial effects on the electron attachment11,12 arising from the various conformers or isomers; and the internal energy redistributions in multiple freedoms before dissociations.
a)Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0021-9606/2015/142(6)/064316/8/$30.00
Here, we report a study of the DEAs to ethanol (CH3CH2OH) and acetaldehyde (CH3CHO), focusing on their dynamics features and differences. The previous studies indicate that the dominant anionic fragments are O− and OH− ions for ethanol8 while O− and CH3− ions for acetaldehyde.4,5,9,13 Some anionic dehydrogenated fragments were also found for ethanol.7 Interpretations to the O− production in the DEA to ethanol are still plausible, because the thermodynamic threshold (2.68 eV for the dissociation to CH3CH3 + O−) is much lower than the experimental appearance.8 The recent experimental study showed both fast and slow O− ions were produced in the DEA to acetaldehyde.9 It is still unclear about the kinetic energy distributions of O− and OH− ions for ethanol. The kinetic energy of CH3− produced in the DEA to acetaldehyde at 6.6 eV is near zero eV, while the thermodynamic threshold of its production is 3.66 eV.9 If the CH3− is a yield in the two-body fragmentation (accompanying the CHO radical), the excess energy about 1.9 eV9 should be shared between the internal modes of the negative ion CH3− and those of the radical CHO.4,5 On the other hand, it is still a challenge to simulate theoretically the multichannel dissociation pathways of the polyatomic molecule induced by the electron attachments at different energies. Quantum scattering theories, such as the complex Kohn variational, the Schwinger variational, and R-matrix methods, can treat strictly the vertical electron attachments to molecules,3,14 but are unfeasible to simulate the subsequent dissociation processes. Molecular dynamics simulations based on quantum chemistry methods are applicable and provide for some insights into the dissociation dynamics of the complicated polyatomic molecules.15,16 In this work, the DEAs to ethanol and acetaldehyde are investigated by both the state-of-the-art anion velocity map imaging (VMI)17,18 experiments and ab initio molecular dynamics simulations.
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© 2015 AIP Publishing LLC
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FIG. 1. Negative ion yields for ethanol (a) and acetaldehyde (b) as a function of electron energy. Ion intensity is normalized, respectively.
II. EXPERIMENTAL AND COMPUTATIONAL METHODS
Our home-made VMI apparatus for the DEA study was described in detail elsewhere.17,18 A brief introduction is given here. An effusive molecular beam of the sample was perpendicular to the pulsed electron beam (with a thermal energy spread of 0.5 eV) which was emitted from a homemade electron gun and collimated with the homogenous magnetic field (∼20 Gauss) produced by a pair of Helmholtz coils. The anionic fragments produced in the DEA were periodically pushed out of the reaction area and then passed through the time-of-flight tube. The anions produced in one electron pulse expanded and formed a Newton sphere by the space and velocity focusing. The three-dimensional momentum distribution of the anions of one certain type was detected with a set of microchannel plates (triple plates) and a phosphor screen, by applying a high-voltage pulse (width ∼80 ns) on the last microchannel plate. This high-voltage pulse acted as the time gate to identify different anions and to make a central slice of the Newton sphere of the selected anions. The timesliced image was directly recorded with a CCD camera. The time-of-flight mass spectrometer mode was operated when the DC high voltages were added on the microchannel plates. The weak current pulse on the DC high voltage could be produced by the anionic fragment impacts on the detector
FIG. 2. Momentum images of O−/OH− ions for ethanol recorded at 6.0 (a) and 9.0 eV (b). The electron incident direction is from left to right and through the image center. Ion intensity is normalized, respectively.
and directly decoupled from the circuit,19 then amplified with VT120 (ORTEC, Inc.). The time-of-flight signals were recorded with the 100-ps Time Digitizer/Multichannel Scaler 9353 (ORTEC, Inc.). The production efficiency curves of the anionic fragments were calibrated with the electron beam intensities. Liquid samples (Aladdin Industrial Inc., >99%) were commercial and used after several freeze-pump-thaw cycles. No contaminants were found by testing their electron-impact ionization mass spectra. The volatility of the sample placed in ice-water mixture was high enough to create a sufficient concentration of the target molecules in gas phase; the ambient pressure was controlled at ca. 2 × 10−4 Pa. We carried out the ab initio molecular dynamics simulations for the dissociation trajectories of the TNIs of ethanol and acetaldehyde by using the atom-centered density matrix propagation method20 [ADMP-B3LYP/6-31G(d)]. The structural propagation was initiated in the Franck-Condon region for the vertical attachment to the neutral target. Quasiclassical
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FIG. 3. Momentum images of O− ion for acetaldehyde recorded at 9.0 (a), 9.5 (b), 10.0 (c), 10.5 (d), 11.0 (e), and 11.3 eV (f). The electron incident direction is from left to right and through the image center. Ion intensity is normalized, respectively.
trajectories were sampled with the initial internal energies 3.0, 5.0, and 8.0 eV of the TNI of ethanol and 4.0, 7.0, and 10.0 eV of the TNI of acetaldehyde, which mimicked the DEA processes at different attachment energies. However, the different resonant states formed by the electron attachment were unable to be reproduced in above simulations. The start point of the trajectories was assumed to be the TNI at the lowest one-particle shape resonant state, namely, the excess electron occupied at the lowest virtual molecular orbital of the neutral target. Supposing the non-adiabatic transition between the different resonant states (e.g., π∗→ σ∗)7,21 was very fast, the following dynamic evolutions eventually occurred at the lowest resonant state of the TNI and led to the groundstate fragments.22 Here, different initial energies would be transferred to the internal modes of the TNI at the σ∗ resonant state (ethanol) or the π∗ resonant state (acetaldehyde). The time step was 0.1 or 0.2 (fs) and the time scale of simulations was
about 2 ps. All calculations were performed with GAUSSIAN program.23 III. RESULTS AND DISCUSSION
The production efficiency curves of the anion yields O−/OH− are shown in Fig. 1. Due to the low energy and mass resolutions of the VMI spectrometer, the O− and OH− ions for the DEA to ethanol cannot be identified directly with the time-of-flight mode. However, two peaks at 6.2 and 8.5 eV in the present yield curve (Fig. 1(a)) correspond to two bands of the O− and OH− curves recorded with the highresolution mass spectrometer,8 respectively. A peak at 6.35 eV of the [CH3CH2OH–H]− yield curve was also observed, which was attributed to a Feshbach resonance with a hole in the nO oxygen lone pair orbital.7 It is unknown whether there is some correlation between the O−/OH− products and this
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FIG. 4. The kinetic energy of O− ion [not those with the low kinetic energies observed in Figs. 3(c)-3(f)] for acetaldehyde as a function of electron energy. The black squares represent the data obtained in this work, while the red circles are cited from Ref. 9.
Feshbach resonance or its mixture with a σ∗ shape resonance.8 In Fig. 1(b), the O− yield curve for acetaldehyde shows the peak about 10.0 eV, as well as a small peak around 6.8 eV and a shoulder at 8.0 eV. The profile of this curve is generally in agreement with the previous measurements,5,9,13 but the lowenergy part was assigned as the OH− product.9,13 A 2(π, π∗2) core-excited shape resonance of the acetaldehyde TNI at 8 eV was proposed to play a role in the dissociations in this energy range.5,9 If the fragments in the dissociative asymptote are at the electronically ground states, the thermodynamic threshold for the cleavage of A–B bond, Ethreshold = DA–B − EAB, where DA–B is the bond energy, EAB is the electron affinity of B, and the fragments A and B− are at the ground states. The theoretical Ethreshold value can be compared with the appearance energy of the B− ion signals. In the DEA to polyatomic molecules, the
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appearance energy shifts to the higher value if the fragments A and B− have the high internal energies Eint, namely, the hot A or B− may be populated at the vibrationally or rotationally excited states. The VMI experiments can provide us with information about the dissociation dynamics, i.e., the kinetic energy and angular distributions of B−. According to the momentum and energy conservations, one can deduce the total kinetic energy of the fragments, Ek(tot) = Ek(B−)mAB−/mB−, where Ek(B−) is the measured kinetic energy of B− and m is the mass of AB− or B−, and then the appearance energy of B− equals [E − Ethreshold − Ek(tot) − Eint], where E is the electron attachment energy. However, it is still a challenge to measure Eint value due to the low energy resolution of the present anion VMI experiments; more awkwardly, Ethreshold and Ek(tot) will be uncertain when the many-body dissociation pathway cannot be confirmed.24 The momentum distributions of the O−/OH− ions produced in the DEA to ethanol at 6.0 and 9.0 eV are depicted in Fig. 2. According to the analysis of Fig. 1(a) and Ref. 8, the ions at 6.0 and 9.0 eV should correspond to two different products O− and OH−, respectively; all of them indicate the much low kinetic energy distributions. In the previous study,8 the Ethreshold values of the possible dissociation pathways are 2.4 eV and 3.82 eV for e− + CH3CH2OH → CH3CH2 + OH− and → C2H4 + H + OH−, respectively. For the low kinetic energy [Ek(tot) ∼ 0 eV], the total internal energy of CH3CH2 and OH− should be 6.6 eV at the electron energy of 9.0 eV. Consider the EAOH = 1.82 eV,25 one can further estimate that the internal energy of CH3CH2 reaches 4.78 eV at most. Obviously, this hot CH3CH2 radical is unstable in thermodynamics and potentially decomposes to C2H4 plus H. If the concerted three-body fragmentation (→ C2H4 + H + OH−) is predominant, the most of excess energy can be carried out by the light fragment H, leaving the much slower fragments C2H4 and OH−. Similarly, a three-body fragmentation to C2H5 + H + O− was proposed for the appearance of O−, but it was impossible due to
FIG. 5. Angular distributions (solid circles, experimental data; red lines, fittings) of the fast O− ions produced in the electron attachment to acetaldehyde at the energies 10.0 (a), 10.5 (b), 11.0 (c), and 11.3 eV (d). The ions are selected within the kinetic energy ranges 0.3-0.4 eV (a), 0.48-0.58 eV (b), 0.53-0.63 eV (c), and 0.56-0.66 eV (d).
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presented as red circles in Fig. 4. Some distinct differences between this work and the previous study9 should be addressed here. The discrepancies about the anisotropic distributions observed at 9.5, 10.0, 10.5, and 11.0 eV are notable. The forward distributions at 10 ∼ 11.3 eV in Figs. 3(c)-3(f) are much weaker than the backward, while their intensities are comparable in the study by Szyma´nska et al.9 We did not find the anisotropic outer ring in the image at 9.5 eV (Fig. 3(b)), but a weak anisotropy was shown in that study.9 Meanwhile, as shown in Fig. 4, the kinetic energies of O− ions measured here are generally larger than those reported previously.9 On the basis of the linear correlation between the kinetic energy and electron energy with an intercept at the electron energy of 9.25 eV, the authors suggested that the ions observed below 9.25 eV should be OH−, rather than of O−.9 Here, we find a nonlinear correlation between the kinetic energy and electron energy; thus, 9.25 eV may not be the production threshold of the OH− ions.13 On the other hand, the formation of OH− needs a hydrogen abstraction before fragmentation, while there are no proofs supporting the existence of hydrogen scrambling.4,5,9 Assuming the diffuse band in Fig. 1(b) is primarily attributed to O− ions, at the energies higher than 9.5 eV, there is an amount of excess energies to be transferred to the internal modes of the companying fragment CH3CH, because Ethreshold equals 3.45 eV for the two-body dissociation to CH3CH + O−.9 We speculate that the partition between the translational and internal energies may not obey the simple linear rule. The O− ions with the much low kinetic energies, observed as the central spots in the images at the higher electron energies, may be produced in the concerted threeor many-body dissociations. FIG. 6. (a) Production efficiency curve of CH3− for acetaldehyde. (b) The momentum image of CH3− recorded at the electron energy 6.0 eV, where the electron incident direction is from left to right and through the image center and the ion intensity is normalized.
the higher threshold 7.04 eV of this three-body process.8 A molecular rearrangement via the hydrogen transfer to α-carbon was possibly responsible for the O− production: → C2H6(ethane) + O−(Ethreshold = 2.68 eV).8 We will suggest that there is another pathway to the O− yield in the following text. In contrast to the momentum distributions of the O−/OH− yields for ethanol, as shown in Fig. 3, the momentum distributions of the O− ion for acetaldehyde show the remarkable changes with the increase of the electron energy. At the lower energies 9.0 and 9.5 eV, the O− images exhibit the nearly isotropic distributions, while become anisotropic at the electron energies higher than 10.0 eV. Moreover, with the increase of the electron energy (9.0, 9.5, 10.0, 10.3, 10.5, 10.8, 11.0, and 11.3 eV), the images (except for the central spots in the images at 10.0 ∼ 11.3 eV) appear to grow in size radially. In Fig. 4, the kinetic energies of O− ions observed in the outer rings of the images at 10.0 ∼ 11.3 eV, together with those in the central spots at the lower energies 9.0 and 9.5 eV, are plotted in terms of the electron energy. The kinetic energies of O− ions measured in the previous study9 are also
FIG. 7. (a) The lowest virtual molecular orbital of ethanol and (b) snapshots of the start (upper) and 20 fs-later (below) structures after the electron attachment. Red: oxygen; white: hydrogen; and brown: carbon.
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FIG. 8. (a) The lowest virtual molecular orbital of acetaldehyde; (b) snapshots of the start (0 fs) and 25 fslater structures after the electron attachment (red: oxygen; white: hydrogen; and brown: carbon); and (c) the variances of atom-atom distances and the Hβ–Cβ–Cα–O dihedral angle in terms of the simulation time.
Using the polynomial function, σDEA ∼ Σcn(cos θ)n (n = 0-7), proposed by Szyma´nska et al.,9 we have good fits to the angular distributions of the ions with the selected kinetic energies. As shown in Fig. 5, there are two maxima around 90◦ and 125◦ at 10.0 eV and these two maxima become indistinct at 10.5 eV; there are three maxima around 60◦, 100◦, and 125◦ at 11.0 eV and four maxima around 50◦, 90◦, 110◦, and 145◦ at 11.3 eV. This is in line with the common rule, i.e., with the increase of electron energy, the higher order partial waves (such as d- and f -partial waves) could play more important roles and provide the additional structures of the angular distribution. One can find some deviations between the fitting curves and experimental data in Figs. 5(c) and 5(d).
Therefore, to have the better fittings to the angular distributions at the higher electron energies, we should introduce more terms for the higher order partial waves into the polynomial function. The anisotropic angular distributions of the fast O− ions at the high electron energies imply that the TNI quickly dissociates, possibly to O− plus CH3CH. This could be further revealed by the electron scattering calculations within the molecular frame.26 Although there are anionic fragments other than O− and − CH3 observed for the DEA to acetaldehyde,9 here we only report the production efficiency curve and momentum image of CH3− (see Fig. 6) because of the previous arguments about its production dynamics in the DEA process.4,5 In the
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high-resolution production curves, two sharp peaks at 6.34 and 6.64 eV were observed and assigned to the vibrational Feshbach resonances.4,5 In our and the recent measurements, one diffuse band with the maximum at 6.6 eV (Ref. 9) or 6.0 eV (Fig. 6(a)) is observed. As shown in Fig. 6(b), the CH3− ions show the much low kinetic energy and isotropic distribution, in line with the observation of Szyma´nska et al.9 The thermodynamic threshold of two-body dissociation, e− + CH3CHO → (CH3CHO−)# → CHO + CH−3 , is about 3.66 eV,9 thereby, the total internal energy of CHO and CH3− should be 2.34 eV at the electron energy of 6.0 eV. The vibrations of CH3− , ν6 (CH bond) and ν7 (CH3 deformation), were found to be active; meanwhile, the vibrations of such hot CH3− also led to electron autodetachment due to the much smaller EA(CH3) value of 0.08 eV.4,5 Upon above studies, Szyma´nska et al. conjectured that the CH3− might be produced in the three-body dissociation.9 To have insights into the dissociation dynamics of these TNIs, ab initio molecular dynamics simulations with the ADMP method were performed. As mentioned above, the traditional quantum chemistry methods cannot strictly treat the TNI resonant states.1–3 However, with the chemical bond elongations, the coupling between the discrete states and electron continuum background becomes weak;3 thereby, the quantum chemistry methods are reasonable at least away from the Franck-Condon region and near the dissociation limit.22 In our ADMP calculations, no dissociation pathways were constrained, but all of the dissociations mentioned above cannot be presented in a finite number of trajectories. As shown in Fig. 7(a), the lowest virtual molecular orbital of ethanol shows the σ∗(OH, CH) anti-bond character; and thus ∗ the TNI of ethanol could be formed at the 2σ resonant state. Two hydrogen atoms are lost almost simultaneously at 20 fs after the electron attachment around 3.0 eV, in which one is from the hydroxyl group and the other is from the methylene (CH2). This is in good agreement with the previous findings about the excitations of O—H and C—H stretch vibrations by the low-energy electron collisions.7 It is noted that the Feshbach resonant state may be initially formed by the electron vertical attachment, then couples with this σ∗ shape resonance,8 while the dehydrogenations occur at the latter state. The residual moiety, acetaldehyde anion (CH3CHO−), was not observed,7 implying that this unstable intermediate should dissociate, possibly to CH3CH plus O−. This cascade process is different from that proposed by Ib˘anescu et al.,7 and may be another important pathway to the O− yields observed in Fig. 1(a). The fleeing hydrogen atoms carry out the most of the total kinetic energy; thus, the CH3CH and O− fragments are very slow. As last, the C–C bond cleavage in the DEA to acetaldehyde around 6.0 eV is simulated. The lowest virtual molecular orbital of acetaldehyde in Fig. 8(a) shows the typical π∗ (C==O) ∗ antibond character, corresponding to a 2π shape resonance ∗ of the TNI. The transition from π to σ∗ was frequently observed in the DEA to organic molecules,21 which also plays the important role in the present C—C bond cleavage. As mentioned above, even if the other resonances are formed in this energy range, the coupling between them and the lowest σ∗ shape resonant state eventually leads to the subsequent chemical-bond evolvements at the σ∗ resonant state. Two
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snapshots and the variances of some atom-atom distances and the Hβ–Cβ–Cα–O dihedral angle in terms of the flight time are depicted in Figs. 8(b) and 8(c). The fragmentation to CHO and CH3− could occur at 25 fs after the electron attachment, and the Cα–Cβ distance continuously increases. The Cβ–Hβ and Cα–O bond stretching motions are found, implying the existences of the excited vibrations of CHO and CH3− fragments. It is more interesting that the value of Hβ–Cβ–Cα–O dihedral angle oscillates remarkably. This indicates that during the C—C bond break, there is a torsional motion between CHO and CH3 groups. The rotations of CHO and CH3− cost some of the available energy, resulting in the much lower kinetic energies of these two fragments. The Cα–H bond length is about 3.37 Å at 175 fs, then Cα and H atoms are recombined. This implies that three fragments, CO, H, and CH3−, might be produced in the cascade process, rather than a concerted three-body dissociation.
IV. CONCLUSION
We have investigated the dynamics of DEAs to ethanol and acetaldehyde, using a combination of anion VMI experiments and ab initio molecular dynamics simulations. In contrast to the O− ions produced in the DEA to acetaldehyde, the O− and OH− ions of the DEA to ethanol show the very low kinetic energies. A cascade process to the O− yield of the DEA to ethanol is proposed, namely, it could be produced from the intermediate species [CH3CHO]− which is formed by the double dehydrogenations of the TNI. The anisotropic angular distributions of the fast O− ions of the DEA to acetaldehyde indicate that the higher order partial waves should play more important roles at the higher electron attachment energies. The CH3− ion is produced in the fast two-body dissociation of acetaldehyde TNI, and its low kinetic energy can be interpreted by the various partitions between the translation energy and the ro-vibrational energy of two fragments (CHO and CH3−). ACKNOWLEDGMENTS
This work is supported by NSFC (Grant No. 21273213), MOST (Grant No. 2013CB834602), and FRFCU (Grant No. WK2060030015). 1I.
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J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, GAUSSIAN 09, Revision D.01, Gaussian, Inc., Wallingford, CT, 2009. 24H.-K. Li, L. Xia, X.-J. Zeng, and S. X. Tian, J. Phys. Chem. A 117, 3176 (2013). 25See http://webbook.nist.gov/chemistry for NIST chemistry web-book. 26D. S. Slaughter, D. J. Haxon, H. Adaniya, T. Weber, T. N. Rescigno, C. W. McCurdy, and A. Belkacem, Phys. Rev. A 87, 052711 (2013).
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THE JOURNAL OF CHEMICAL PHYSICS 142, 064316 (2015)
Dissociative electron attachments to ethanol and acetaldehyde: A combined experimental and simulation study Xu-Dong Wang, Chuan-Jin Xuan, Wen-Ling Feng, and Shan Xi Tiana) Hefei National Laboratory for Physical Sciences at the Microscale, Center of Advanced Chemical Physics, and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
(Received 24 November 2014; accepted 30 January 2015; published online 13 February 2015) Dissociation dynamics of the temporary negative ions of ethanol and acetaldehyde formed by the lowenergy electron attachments is investigated by using the anion velocity map imaging technique and ab initio molecular dynamics simulations. The momentum images of the dominant fragments O−/OH− and CH3− are recorded, indicating the low kinetic energies of O−/OH− for ethanol while the low and high kinetic energy distributions of O− ions for acetaldehyde. The CH3− image for acetaldehyde also shows the low kinetic energy. With help of the dynamics simulations, the fragmentation processes are qualitatively clarified. A new cascade dissociation pathway to produce the slow O− ion via the dehydrogenated intermediate, CH3CHO− (acetaldehyde anion), is proposed for the dissociative electron attachment to ethanol. After the electron attachment to acetaldehyde molecule, the slow CH3− is produced quickly in the two-body dissociation with the internal energy redistributions in different aspects before bond cleavages. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4907940]
I. INTRODUCTION
Dissociative electron attachment (DEA) to molecule AB, e− + AB → (AB−)# → A + B−, is a key process in the radiation-induced chemistry, where the active neutral (A) and anionic (B−) radicals are produced, and the short-lived intermediate (AB−)# is usually called temporary negative ion (TNI).1 DEA can be generally classified into two types:2 one is one-particle process, namely, the incoming electron is captured into a virtual molecular orbital, and TNI is formed at a shape resonant state; the other is two- or multi-particle process. In the latter, during the electron capture, the electron(s) of molecular target could be excited simultaneously. The latter, core-excited resonant state, is quite complicated, and its identification needs the sophisticated theoretical analysis3 and the references of different spectroscopic studies.4,5 In addition, the molecular vibrations of the target may be excited when the electron is captured. As a doorway, this process may be more responsible for the chemical bond cleavages, in particular, at the low electron attachment energy. Since the DEAs to biomolecules are investigated extensively,1 hydrocarbons containing the amino- and hydroxyl groups, as the model molecules of biological compounds, also receive much attention.6–10 However, there are many challenges toward understanding of the DEA to polyatomic molecule, for examples, more resonant states of TNI in the narrow energy space; novel spatial effects on the electron attachment11,12 arising from the various conformers or isomers; and the internal energy redistributions in multiple freedoms before dissociations.
a)Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0021-9606/2015/142(6)/064316/8/$30.00
Here, we report a study of the DEAs to ethanol (CH3CH2OH) and acetaldehyde (CH3CHO), focusing on their dynamics features and differences. The previous studies indicate that the dominant anionic fragments are O− and OH− ions for ethanol8 while O− and CH3− ions for acetaldehyde.4,5,9,13 Some anionic dehydrogenated fragments were also found for ethanol.7 Interpretations to the O− production in the DEA to ethanol are still plausible, because the thermodynamic threshold (2.68 eV for the dissociation to CH3CH3 + O−) is much lower than the experimental appearance.8 The recent experimental study showed both fast and slow O− ions were produced in the DEA to acetaldehyde.9 It is still unclear about the kinetic energy distributions of O− and OH− ions for ethanol. The kinetic energy of CH3− produced in the DEA to acetaldehyde at 6.6 eV is near zero eV, while the thermodynamic threshold of its production is 3.66 eV.9 If the CH3− is a yield in the two-body fragmentation (accompanying the CHO radical), the excess energy about 1.9 eV9 should be shared between the internal modes of the negative ion CH3− and those of the radical CHO.4,5 On the other hand, it is still a challenge to simulate theoretically the multichannel dissociation pathways of the polyatomic molecule induced by the electron attachments at different energies. Quantum scattering theories, such as the complex Kohn variational, the Schwinger variational, and R-matrix methods, can treat strictly the vertical electron attachments to molecules,3,14 but are unfeasible to simulate the subsequent dissociation processes. Molecular dynamics simulations based on quantum chemistry methods are applicable and provide for some insights into the dissociation dynamics of the complicated polyatomic molecules.15,16 In this work, the DEAs to ethanol and acetaldehyde are investigated by both the state-of-the-art anion velocity map imaging (VMI)17,18 experiments and ab initio molecular dynamics simulations.
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© 2015 AIP Publishing LLC
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FIG. 1. Negative ion yields for ethanol (a) and acetaldehyde (b) as a function of electron energy. Ion intensity is normalized, respectively.
II. EXPERIMENTAL AND COMPUTATIONAL METHODS
Our home-made VMI apparatus for the DEA study was described in detail elsewhere.17,18 A brief introduction is given here. An effusive molecular beam of the sample was perpendicular to the pulsed electron beam (with a thermal energy spread of 0.5 eV) which was emitted from a homemade electron gun and collimated with the homogenous magnetic field (∼20 Gauss) produced by a pair of Helmholtz coils. The anionic fragments produced in the DEA were periodically pushed out of the reaction area and then passed through the time-of-flight tube. The anions produced in one electron pulse expanded and formed a Newton sphere by the space and velocity focusing. The three-dimensional momentum distribution of the anions of one certain type was detected with a set of microchannel plates (triple plates) and a phosphor screen, by applying a high-voltage pulse (width ∼80 ns) on the last microchannel plate. This high-voltage pulse acted as the time gate to identify different anions and to make a central slice of the Newton sphere of the selected anions. The timesliced image was directly recorded with a CCD camera. The time-of-flight mass spectrometer mode was operated when the DC high voltages were added on the microchannel plates. The weak current pulse on the DC high voltage could be produced by the anionic fragment impacts on the detector
FIG. 2. Momentum images of O−/OH− ions for ethanol recorded at 6.0 (a) and 9.0 eV (b). The electron incident direction is from left to right and through the image center. Ion intensity is normalized, respectively.
and directly decoupled from the circuit,19 then amplified with VT120 (ORTEC, Inc.). The time-of-flight signals were recorded with the 100-ps Time Digitizer/Multichannel Scaler 9353 (ORTEC, Inc.). The production efficiency curves of the anionic fragments were calibrated with the electron beam intensities. Liquid samples (Aladdin Industrial Inc., >99%) were commercial and used after several freeze-pump-thaw cycles. No contaminants were found by testing their electron-impact ionization mass spectra. The volatility of the sample placed in ice-water mixture was high enough to create a sufficient concentration of the target molecules in gas phase; the ambient pressure was controlled at ca. 2 × 10−4 Pa. We carried out the ab initio molecular dynamics simulations for the dissociation trajectories of the TNIs of ethanol and acetaldehyde by using the atom-centered density matrix propagation method20 [ADMP-B3LYP/6-31G(d)]. The structural propagation was initiated in the Franck-Condon region for the vertical attachment to the neutral target. Quasiclassical
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FIG. 3. Momentum images of O− ion for acetaldehyde recorded at 9.0 (a), 9.5 (b), 10.0 (c), 10.5 (d), 11.0 (e), and 11.3 eV (f). The electron incident direction is from left to right and through the image center. Ion intensity is normalized, respectively.
trajectories were sampled with the initial internal energies 3.0, 5.0, and 8.0 eV of the TNI of ethanol and 4.0, 7.0, and 10.0 eV of the TNI of acetaldehyde, which mimicked the DEA processes at different attachment energies. However, the different resonant states formed by the electron attachment were unable to be reproduced in above simulations. The start point of the trajectories was assumed to be the TNI at the lowest one-particle shape resonant state, namely, the excess electron occupied at the lowest virtual molecular orbital of the neutral target. Supposing the non-adiabatic transition between the different resonant states (e.g., π∗→ σ∗)7,21 was very fast, the following dynamic evolutions eventually occurred at the lowest resonant state of the TNI and led to the groundstate fragments.22 Here, different initial energies would be transferred to the internal modes of the TNI at the σ∗ resonant state (ethanol) or the π∗ resonant state (acetaldehyde). The time step was 0.1 or 0.2 (fs) and the time scale of simulations was
about 2 ps. All calculations were performed with GAUSSIAN program.23 III. RESULTS AND DISCUSSION
The production efficiency curves of the anion yields O−/OH− are shown in Fig. 1. Due to the low energy and mass resolutions of the VMI spectrometer, the O− and OH− ions for the DEA to ethanol cannot be identified directly with the time-of-flight mode. However, two peaks at 6.2 and 8.5 eV in the present yield curve (Fig. 1(a)) correspond to two bands of the O− and OH− curves recorded with the highresolution mass spectrometer,8 respectively. A peak at 6.35 eV of the [CH3CH2OH–H]− yield curve was also observed, which was attributed to a Feshbach resonance with a hole in the nO oxygen lone pair orbital.7 It is unknown whether there is some correlation between the O−/OH− products and this
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FIG. 4. The kinetic energy of O− ion [not those with the low kinetic energies observed in Figs. 3(c)-3(f)] for acetaldehyde as a function of electron energy. The black squares represent the data obtained in this work, while the red circles are cited from Ref. 9.
Feshbach resonance or its mixture with a σ∗ shape resonance.8 In Fig. 1(b), the O− yield curve for acetaldehyde shows the peak about 10.0 eV, as well as a small peak around 6.8 eV and a shoulder at 8.0 eV. The profile of this curve is generally in agreement with the previous measurements,5,9,13 but the lowenergy part was assigned as the OH− product.9,13 A 2(π, π∗2) core-excited shape resonance of the acetaldehyde TNI at 8 eV was proposed to play a role in the dissociations in this energy range.5,9 If the fragments in the dissociative asymptote are at the electronically ground states, the thermodynamic threshold for the cleavage of A–B bond, Ethreshold = DA–B − EAB, where DA–B is the bond energy, EAB is the electron affinity of B, and the fragments A and B− are at the ground states. The theoretical Ethreshold value can be compared with the appearance energy of the B− ion signals. In the DEA to polyatomic molecules, the
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appearance energy shifts to the higher value if the fragments A and B− have the high internal energies Eint, namely, the hot A or B− may be populated at the vibrationally or rotationally excited states. The VMI experiments can provide us with information about the dissociation dynamics, i.e., the kinetic energy and angular distributions of B−. According to the momentum and energy conservations, one can deduce the total kinetic energy of the fragments, Ek(tot) = Ek(B−)mAB−/mB−, where Ek(B−) is the measured kinetic energy of B− and m is the mass of AB− or B−, and then the appearance energy of B− equals [E − Ethreshold − Ek(tot) − Eint], where E is the electron attachment energy. However, it is still a challenge to measure Eint value due to the low energy resolution of the present anion VMI experiments; more awkwardly, Ethreshold and Ek(tot) will be uncertain when the many-body dissociation pathway cannot be confirmed.24 The momentum distributions of the O−/OH− ions produced in the DEA to ethanol at 6.0 and 9.0 eV are depicted in Fig. 2. According to the analysis of Fig. 1(a) and Ref. 8, the ions at 6.0 and 9.0 eV should correspond to two different products O− and OH−, respectively; all of them indicate the much low kinetic energy distributions. In the previous study,8 the Ethreshold values of the possible dissociation pathways are 2.4 eV and 3.82 eV for e− + CH3CH2OH → CH3CH2 + OH− and → C2H4 + H + OH−, respectively. For the low kinetic energy [Ek(tot) ∼ 0 eV], the total internal energy of CH3CH2 and OH− should be 6.6 eV at the electron energy of 9.0 eV. Consider the EAOH = 1.82 eV,25 one can further estimate that the internal energy of CH3CH2 reaches 4.78 eV at most. Obviously, this hot CH3CH2 radical is unstable in thermodynamics and potentially decomposes to C2H4 plus H. If the concerted three-body fragmentation (→ C2H4 + H + OH−) is predominant, the most of excess energy can be carried out by the light fragment H, leaving the much slower fragments C2H4 and OH−. Similarly, a three-body fragmentation to C2H5 + H + O− was proposed for the appearance of O−, but it was impossible due to
FIG. 5. Angular distributions (solid circles, experimental data; red lines, fittings) of the fast O− ions produced in the electron attachment to acetaldehyde at the energies 10.0 (a), 10.5 (b), 11.0 (c), and 11.3 eV (d). The ions are selected within the kinetic energy ranges 0.3-0.4 eV (a), 0.48-0.58 eV (b), 0.53-0.63 eV (c), and 0.56-0.66 eV (d).
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presented as red circles in Fig. 4. Some distinct differences between this work and the previous study9 should be addressed here. The discrepancies about the anisotropic distributions observed at 9.5, 10.0, 10.5, and 11.0 eV are notable. The forward distributions at 10 ∼ 11.3 eV in Figs. 3(c)-3(f) are much weaker than the backward, while their intensities are comparable in the study by Szyma´nska et al.9 We did not find the anisotropic outer ring in the image at 9.5 eV (Fig. 3(b)), but a weak anisotropy was shown in that study.9 Meanwhile, as shown in Fig. 4, the kinetic energies of O− ions measured here are generally larger than those reported previously.9 On the basis of the linear correlation between the kinetic energy and electron energy with an intercept at the electron energy of 9.25 eV, the authors suggested that the ions observed below 9.25 eV should be OH−, rather than of O−.9 Here, we find a nonlinear correlation between the kinetic energy and electron energy; thus, 9.25 eV may not be the production threshold of the OH− ions.13 On the other hand, the formation of OH− needs a hydrogen abstraction before fragmentation, while there are no proofs supporting the existence of hydrogen scrambling.4,5,9 Assuming the diffuse band in Fig. 1(b) is primarily attributed to O− ions, at the energies higher than 9.5 eV, there is an amount of excess energies to be transferred to the internal modes of the companying fragment CH3CH, because Ethreshold equals 3.45 eV for the two-body dissociation to CH3CH + O−.9 We speculate that the partition between the translational and internal energies may not obey the simple linear rule. The O− ions with the much low kinetic energies, observed as the central spots in the images at the higher electron energies, may be produced in the concerted threeor many-body dissociations. FIG. 6. (a) Production efficiency curve of CH3− for acetaldehyde. (b) The momentum image of CH3− recorded at the electron energy 6.0 eV, where the electron incident direction is from left to right and through the image center and the ion intensity is normalized.
the higher threshold 7.04 eV of this three-body process.8 A molecular rearrangement via the hydrogen transfer to α-carbon was possibly responsible for the O− production: → C2H6(ethane) + O−(Ethreshold = 2.68 eV).8 We will suggest that there is another pathway to the O− yield in the following text. In contrast to the momentum distributions of the O−/OH− yields for ethanol, as shown in Fig. 3, the momentum distributions of the O− ion for acetaldehyde show the remarkable changes with the increase of the electron energy. At the lower energies 9.0 and 9.5 eV, the O− images exhibit the nearly isotropic distributions, while become anisotropic at the electron energies higher than 10.0 eV. Moreover, with the increase of the electron energy (9.0, 9.5, 10.0, 10.3, 10.5, 10.8, 11.0, and 11.3 eV), the images (except for the central spots in the images at 10.0 ∼ 11.3 eV) appear to grow in size radially. In Fig. 4, the kinetic energies of O− ions observed in the outer rings of the images at 10.0 ∼ 11.3 eV, together with those in the central spots at the lower energies 9.0 and 9.5 eV, are plotted in terms of the electron energy. The kinetic energies of O− ions measured in the previous study9 are also
FIG. 7. (a) The lowest virtual molecular orbital of ethanol and (b) snapshots of the start (upper) and 20 fs-later (below) structures after the electron attachment. Red: oxygen; white: hydrogen; and brown: carbon.
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FIG. 8. (a) The lowest virtual molecular orbital of acetaldehyde; (b) snapshots of the start (0 fs) and 25 fslater structures after the electron attachment (red: oxygen; white: hydrogen; and brown: carbon); and (c) the variances of atom-atom distances and the Hβ–Cβ–Cα–O dihedral angle in terms of the simulation time.
Using the polynomial function, σDEA ∼ Σcn(cos θ)n (n = 0-7), proposed by Szyma´nska et al.,9 we have good fits to the angular distributions of the ions with the selected kinetic energies. As shown in Fig. 5, there are two maxima around 90◦ and 125◦ at 10.0 eV and these two maxima become indistinct at 10.5 eV; there are three maxima around 60◦, 100◦, and 125◦ at 11.0 eV and four maxima around 50◦, 90◦, 110◦, and 145◦ at 11.3 eV. This is in line with the common rule, i.e., with the increase of electron energy, the higher order partial waves (such as d- and f -partial waves) could play more important roles and provide the additional structures of the angular distribution. One can find some deviations between the fitting curves and experimental data in Figs. 5(c) and 5(d).
Therefore, to have the better fittings to the angular distributions at the higher electron energies, we should introduce more terms for the higher order partial waves into the polynomial function. The anisotropic angular distributions of the fast O− ions at the high electron energies imply that the TNI quickly dissociates, possibly to O− plus CH3CH. This could be further revealed by the electron scattering calculations within the molecular frame.26 Although there are anionic fragments other than O− and − CH3 observed for the DEA to acetaldehyde,9 here we only report the production efficiency curve and momentum image of CH3− (see Fig. 6) because of the previous arguments about its production dynamics in the DEA process.4,5 In the
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high-resolution production curves, two sharp peaks at 6.34 and 6.64 eV were observed and assigned to the vibrational Feshbach resonances.4,5 In our and the recent measurements, one diffuse band with the maximum at 6.6 eV (Ref. 9) or 6.0 eV (Fig. 6(a)) is observed. As shown in Fig. 6(b), the CH3− ions show the much low kinetic energy and isotropic distribution, in line with the observation of Szyma´nska et al.9 The thermodynamic threshold of two-body dissociation, e− + CH3CHO → (CH3CHO−)# → CHO + CH−3 , is about 3.66 eV,9 thereby, the total internal energy of CHO and CH3− should be 2.34 eV at the electron energy of 6.0 eV. The vibrations of CH3− , ν6 (CH bond) and ν7 (CH3 deformation), were found to be active; meanwhile, the vibrations of such hot CH3− also led to electron autodetachment due to the much smaller EA(CH3) value of 0.08 eV.4,5 Upon above studies, Szyma´nska et al. conjectured that the CH3− might be produced in the three-body dissociation.9 To have insights into the dissociation dynamics of these TNIs, ab initio molecular dynamics simulations with the ADMP method were performed. As mentioned above, the traditional quantum chemistry methods cannot strictly treat the TNI resonant states.1–3 However, with the chemical bond elongations, the coupling between the discrete states and electron continuum background becomes weak;3 thereby, the quantum chemistry methods are reasonable at least away from the Franck-Condon region and near the dissociation limit.22 In our ADMP calculations, no dissociation pathways were constrained, but all of the dissociations mentioned above cannot be presented in a finite number of trajectories. As shown in Fig. 7(a), the lowest virtual molecular orbital of ethanol shows the σ∗(OH, CH) anti-bond character; and thus ∗ the TNI of ethanol could be formed at the 2σ resonant state. Two hydrogen atoms are lost almost simultaneously at 20 fs after the electron attachment around 3.0 eV, in which one is from the hydroxyl group and the other is from the methylene (CH2). This is in good agreement with the previous findings about the excitations of O—H and C—H stretch vibrations by the low-energy electron collisions.7 It is noted that the Feshbach resonant state may be initially formed by the electron vertical attachment, then couples with this σ∗ shape resonance,8 while the dehydrogenations occur at the latter state. The residual moiety, acetaldehyde anion (CH3CHO−), was not observed,7 implying that this unstable intermediate should dissociate, possibly to CH3CH plus O−. This cascade process is different from that proposed by Ib˘anescu et al.,7 and may be another important pathway to the O− yields observed in Fig. 1(a). The fleeing hydrogen atoms carry out the most of the total kinetic energy; thus, the CH3CH and O− fragments are very slow. As last, the C–C bond cleavage in the DEA to acetaldehyde around 6.0 eV is simulated. The lowest virtual molecular orbital of acetaldehyde in Fig. 8(a) shows the typical π∗ (C==O) ∗ antibond character, corresponding to a 2π shape resonance ∗ of the TNI. The transition from π to σ∗ was frequently observed in the DEA to organic molecules,21 which also plays the important role in the present C—C bond cleavage. As mentioned above, even if the other resonances are formed in this energy range, the coupling between them and the lowest σ∗ shape resonant state eventually leads to the subsequent chemical-bond evolvements at the σ∗ resonant state. Two
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snapshots and the variances of some atom-atom distances and the Hβ–Cβ–Cα–O dihedral angle in terms of the flight time are depicted in Figs. 8(b) and 8(c). The fragmentation to CHO and CH3− could occur at 25 fs after the electron attachment, and the Cα–Cβ distance continuously increases. The Cβ–Hβ and Cα–O bond stretching motions are found, implying the existences of the excited vibrations of CHO and CH3− fragments. It is more interesting that the value of Hβ–Cβ–Cα–O dihedral angle oscillates remarkably. This indicates that during the C—C bond break, there is a torsional motion between CHO and CH3 groups. The rotations of CHO and CH3− cost some of the available energy, resulting in the much lower kinetic energies of these two fragments. The Cα–H bond length is about 3.37 Å at 175 fs, then Cα and H atoms are recombined. This implies that three fragments, CO, H, and CH3−, might be produced in the cascade process, rather than a concerted three-body dissociation.
IV. CONCLUSION
We have investigated the dynamics of DEAs to ethanol and acetaldehyde, using a combination of anion VMI experiments and ab initio molecular dynamics simulations. In contrast to the O− ions produced in the DEA to acetaldehyde, the O− and OH− ions of the DEA to ethanol show the very low kinetic energies. A cascade process to the O− yield of the DEA to ethanol is proposed, namely, it could be produced from the intermediate species [CH3CHO]− which is formed by the double dehydrogenations of the TNI. The anisotropic angular distributions of the fast O− ions of the DEA to acetaldehyde indicate that the higher order partial waves should play more important roles at the higher electron attachment energies. The CH3− ion is produced in the fast two-body dissociation of acetaldehyde TNI, and its low kinetic energy can be interpreted by the various partitions between the translation energy and the ro-vibrational energy of two fragments (CHO and CH3−). ACKNOWLEDGMENTS
This work is supported by NSFC (Grant No. 21273213), MOST (Grant No. 2013CB834602), and FRFCU (Grant No. WK2060030015). 1I.
Baccarelli, I. Bald, F. A. Gianturco, E. Illenberger, and J. Kopyra, Phys. Rep. 508, 1 (2011). 2L. G. Christophorou, D. L. McCorkle, and A. A. Christodoulides, in Electron-Molecule Interactions and their Applications, edited by L. G. Christophorou (Academic Press Inc., New York, 1984), Vol. 1. 3Y. -F. Wang and S. X. Tian, Phys. Rev. A 84, 022709 (2011). 4R. Dressler and M. Allan, Chem. Phys. Lett. 118, 93 (1985). 5R. Dressler and M. Allan, J. Electron Spectrosc. Relat. Phenom. 41, 275 (1986). 6I. Bald, J. Kopyra, and E. Illenberger, Angew. Chem., Int. Ed. 45, 4851 (2006). 7B. C. Ib˘ anescu, O. May, A. Monney, and M. Allan, Phys. Chem. Chem. Phys. 9, 3163 (2007). 8M. Orzol, I. Martin, J. Kocisek, I. Dabkowska, J. Langer, and E. Illenberger, Phys. Chem. Chem. Phys. 9, 3424 (2007). 9E. Szyma´ nska, V. S. Prabhudesai, N. J. Mason, and E. Krishnakumar, Phys. Chem. Chem. Phys. 15, 998 (2013). 10T. Skalick` yand M. Allan, J. Phys. B: At., Mol. Opt. Phys. 37, 4849 (2004). 11V. S. Prabhudesai, A. H. Kelkar, D. Nandi, and E. Krishnakumar, Phys. Rev. Lett. 95, 143202 (2003).
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