Three-body fragmentation of CO2 driven by intense laser pulses , Chengyin Wu , Cong Wu, Yameng Fan, Xiguo Xie, Peng Wang, Yongkai Deng, Yunquan Liu, and Qihuang Gong
Citation: The Journal of Chemical Physics 142, 124303 (2015); doi: 10.1063/1.4916045 View online: http://dx.doi.org/10.1063/1.4916045 View Table of Contents: http://aip.scitation.org/toc/jcp/142/12 Published by the American Institute of Physics
THE JOURNAL OF CHEMICAL PHYSICS 142, 124303 (2015)
Three-body fragmentation of CO2 driven by intense laser pulses Chengyin Wu,1,2,a) Cong Wu,1 Yameng Fan,1 Xiguo Xie,1 Peng Wang,1 Yongkai Deng,1 Yunquan Liu,1,2 and Qihuang Gong1,2 1
State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, People’s Republic of China 2 Collaborative Innovation Center of Quantum Matter, Beijing 100871, People’s Republic of China
(Received 27 November 2014; accepted 11 March 2015; published online 24 March 2015) Dissociative ionization dynamics were studied experimentally for CO2 driven by intense laser pulses. Three-dimensional momentum vectors of correlated atomic ions were obtained for each three-body fragmentation event using triple ion coincidence measurement. Newton diagram demonstrated that three-body fragmentation of CO2n+ (n = 3-6) can occur through Coulomb explosion process and sequential fragmentation process depending on the fragmentation channels. The experimental data from these two processes were disentangled by using correlation diagram of correlated ions. Based on the accurate Coulomb explosion data, we reconstructed the bond angle distributions of CO2n+ at the moment of fragmentation, which are close to that of neutral CO2 before laser irradiation. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4916045]
I. INTRODUCTION
Studying many-body fragmentation of polyatomic molecules is a big challenge to both theory and experiment. Even in the simplest three-body fragmentation, its dynamics is also very complicated. It can occur through a concerted or a sequential fashion. In the case of concerted fragmentation process, the three products are generated simultaneously and all chemical bonds break in a single kinetic event. Instead, there exists an intermediate and the three products are generated in two independent dissociation steps for the sequential fragmentation process. Moreover, the time interval between the two dissociation steps is longer than the rotational period of the intermediate. Exploring three-body fragmentation dynamics has attracted much attention of both experimental and theory groups.1–5 In order to experimentally explore three-body fragmentation mechanism, various experimental techniques have been developed, such as photofragment translational spectroscopy,6,7 photoelectron-photoion coincidence approach,8,9 and momentum vectors imaging of correlated fragments.10,11 As a prototype system, three-body fragmentation of CO2 ions with various charge states has been extensively studied.12–24 The CO2 ions were generated by synchrotron radiation,12 collision of charged ions,13 electron impact,14 or intense laser pulses interaction with various laser parameters.15–21 The momentum vectors of fragmental ions were measured using the coincidence technology. Most of the studies assumed that the three atomic ions were generated through the concerted fragmentation process, i.e., Coulomb explosion process. The geometric structures prior to explosion were therefore reconstructed from the measured momentum vectors of three correlated atomic ions. The channel-dependent reconstructed structures indicated that the molecular structure was deformed during the process of multiple ionization.17,20,21 However, a)Email: [email protected]
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recent results demonstrated that the three-body fragmentation of CO2 ions does not always occur through the concerted process. Singh et al. studied fragmentation dynamics of CO23+ generated by photoionization of CO2 at 200 eV photon energy.22 They concluded that the fragmentation of CO23+ can occur either by simultaneous breaking of the two C==O bonds or by sequential fragmentation. Neumann et al. studied fragmentation dynamics of CO23+ generated by collision of CO2 with slow highly charged ions.23 They confirmed the existence of sequential fragmentation process by using Dalitz plots and Newton diagrams. Very recently, Wu et al. studied fragmentation dynamics of CO23+ by irradiation of CO2 with intense femtosecond laser pulses.24 They further disentangled the channels of the sequential fragmentation and the concerted fragmentation by developing correlation diagram of correlated ions and obtained the precise data of Coulomb explosion. The C==O bond length was therefore precisely reconstructed for CO23+ at the moment of fragmentation, which turns out to be close to the neutral CO2 before the laser irradiation. In this article, we experimentally studied three-body fragmentation of CO2n+ (n = 3-6) by irradiating CO2 with intense femtosecond laser pulses and clarified the mechanism for each threefragmentation channel.
II. EXPERIMENTAL METHODS
Figure 1 shows the sketch of the experimental platform. It consists of a femtosecond laser amplifier and a reaction microscope.25 The laser amplifier has a repetition rate of 3 kHz, a central wavelength of 800 nm, and a pulse duration of 24 fs. The reaction microscope has four chambers, which are the jet chamber, the expansion chamber, the collimation chamber, and the reaction chamber, respectively. These chambers are separated by a skimmer or an aperture with a diameter of 1 mm. In the jet chamber, the continuous CO2 molecular beam was generated through a 30 µm nozzle with a driving pressure of 2
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following three-body fragmentation channels. (1) Two oxygen ions and one carbon ion were detected in one laser pulse. (2) The sum-momentum of the three atomic ions was less than 10 atomic units to meet the momentum conservation of threebody fragmentation, + + + CO2 (1, 1, 1) : CO3+ 2 → O +C +O , + 2+ + CO2 (1, 2, 1) : CO4+ 2 → O +C +O , 2+ + 2+ CO2 (2, 1, 2) : CO5+ 2 → O +C +O , 2+ 2+ 2+ CO2 (2, 2, 2) : CO6+ 2 → O +C +O .
(1) (2) (3) (4)
FIG. 1. Sketch of the reaction microscope at Peking University. (a) Jet chamber, (b) expansion chamber, (c) collimation chamber, and (d) reaction chamber.
III. RESULTS AND DISCUSSION
bars. Then, the molecular beam passed through the expansion chamber and the collimation chamber. Finally, it arrived at the reaction chamber and interacted with the focused laser. All ions produced in the interaction zone were collected by a temporal and position-sensitive detector (RoentDek, Germany). By recording the position and the time of flight, the initial threedimensional momentum vectors of the ions were derived. In the experiment, we adjusted the reaction chamber pressure to ensure that there was much less than one ionization event in average within one laser pulse. There are many reaction channels for CO2 in intense laser fields. Dissociative ionization of CO2 is a tiny fraction among all ionization events. One of the advantages of the reaction microscope is that the data of all reaction channels can be recorded in one experiment. In the off-line analysis, these reaction channels can be disentangled by using the coincidence constraints to filter the experimental data. Here, we applied two constraints to filter the experimental data to select out the
Figure 2 shows the experimentally measured two-dimensional momentum distributions in the center-of-mass coordinate frame for the correlated atomic ions generated in dissociative ionization of CO2 by intense laser pulses. The linearly polarized laser pulses have a central wavelength of 800 nm, a pulse duration of 24 fs, and an intensity of around 1 × 1015 W/cm2. The laser polarization direction is defined as 2 z axis. The P ∥ (=Pz) and P⊥(= Px + P2y) represent the momentum vectors parallel and perpendicular to the laser polarization direction. The middle section with low momentum comes from carbon ions and the outside one with large momentum comes from oxygen ions. Three-body fragmentation of CO2n+ can take place through the Coulomb explosion process or the sequential fragmentation process.22–24 In the case of Coulomb explosion process, the two C==O bonds break simultaneously and the three atomic ions are generated at the same time. In the case of sequential process, the two C==O bonds break one after the other and there
FIG. 2. Two-dimensional momentum distribution of correlated atomic ions generated from the three-body fragmentation channels of CO2 driven by intense laser pulses. (a) O+ + C+ + O+, (b) O+ + C2+ + O+, (c) O2+ + C+ + O2+, and (d) O2+ + C2+ + O2+.
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exists an intermediate. The intermediate further dissociates into two atomic ions and the dissociation time is comparable to or longer than the rotational period of the intermediate. Newton diagram can visualize the momentum correlation of reaction products and is effective to identify the mechanisms of three-body fragmentation process. A circle structure will be exhibited in the Newton diagram because of the rotation of the intermediate if the sequential three-body fragmentation process exists.24 Therefore, we plotted the Newton diagrams with the experimental data, as shown in Figure 3. The momentum vector of the first oxygen ion is represented by an arrow fixed at one arbitrary unit. The momentum vectors of the carbon ion and the second oxygen ion are normalized to the amplitude of the first oxygen ion momentum vector and mapped in the left of the plot. It can be seen that different structures were observed in the Newton diagrams depending on the three-body fragmentation channels. A pair of crescent-like structures was exhibited for the channels of CO2 (1, 2, 1), CO2 (2, 1, 2), and CO2 (2, 2, 2). The lack of a circle structure demonstrated that the three-body fragmentation occurs only through Coulomb explosion process. While for the channel of CO2 (1, 1, 1), a circle structure was superimposed in the pair of crescent-like structure, which indicated that sequential fragmentation and Coulomb explosion coexist. We have demonstrated that kinetic energy correlation diagram of correlated atomic ions can separate the channels from the Coulomb explosion process and the sequential fragmentation process.24 In the case of Coulomb explosion process, the two C==O bonds break simultaneously and the three atomic ions are generated at the same time. The symmetry in the geometric space can be preserved in the momentum space if the identical components carry the same charge. As a result, the two oxygen ions carrying the same charge will have comparable kinetic energies. However, the symmetry will be destroyed because of the rotation of the intermediate when
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the sequential fragmentation process occurs. As a result, there is no obvious correlation for the kinetic energies of the two correlated oxygen ions. Figure 4 shows the kinetic energy correlation diagram of the two oxygen ions. It can be seen that the two identical oxygen ions have almost the same kinetic energy for the channels of CO2 (1, 2, 1), CO2 (2, 1, 2), and CO2 (2, 2, 2). This observation indicated that Coulomb explosion dominates for these three-body fragmentation channels, which agree with the conclusion based on the analysis of Newton diagram. However, two obvious structures were observed for the channel of CO2 (1, 1, 1), which was separated by a red circle with radius of about 10 eV. The two oxygen ions outside the circle have almost equal kinetic energies and should come from Coulomb explosion process. Instead, the two oxygen ions inside the circle should come from sequential fragmentation process because their kinetic energies have no obvious relationship. This separation was confirmed by their Newton diagrams. Thus, we obtained the momentum vectors of the atomic ions produced in the Coulomb explosion process. Based on these precise experimental data of all Coulomb explosion channels, we reconstructed the geometric structure of CO2n+ (n = 3-6) at the moment of fragmentation. Due to the lack of the accurate ab initio potential energy surface for three-body fragmentation of CO2n+ (n = 3-6), we assumed the nuclei moving in a Coulomb repulsive potential and simulated the explosion dynamics of CO2n+. The Hamilto3 p 1 ⃗ i2 with mi ,⃗r i , and nian was written by Hˆ = 21 m + r i −⃗ rj| i > j |⃗ i=1 i P⃗i = mi⃗r˙i (t) being the mass, position, and momentum of each ion in the center-of-mass coordinate system. The subscript 1 represents the first oxygen ion, 2 and 3 represent the carbon ion and the second oxygen ion. Thus, the lengths of the two −→ C==O bonds can be, respectively, expressed by r−→ 21 and r 23 with ⃗r i j = ⃗r i − ⃗r j and the bond angle θ OCO can be expressed −→ by the angle between vectors of r−→ 21 and r 23. Experimental data
FIG. 3. Newton diagram for correlated atomic ions generated from the threebody fragmentation channels of CO2 driven by intense laser pulses. (a) O+ + C+ + O+, (b) O+ + C2+ + O+, (c) O2+ + C+ + O2+, and (d) O2+ + C2+ + O2+.
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FIG. 4. Kinetic energy release (KER) correlation diagram for two correlated oxygen ions generated from the threebody fragmentation channels of CO2 driven by intense laser pulses. (a) O+ + C+ + O+, (b) O+ + C2+ + O+, (c) O2+ + C+ + O2+, and (d) O2+ + C2+ + O2+.
demonstrated that the two oxygen ions are generated at the same time and have almost equal kinetic energies. It is therefore reasonable to assume that the two C==O bonds were stretched equally before explosion. Thus, we set the mo −→ mentum of each ion as zero and r−→ 21 = r 23 at the beginning of explosion during the theoretical simulation. By solving the equation of nuclei motion numerically, the momentum vectors of the three atomic ions can be obtained for each explosion event. Figure 5 shows the calculated vector angle θ CM, which was defined as the angle between the momentum vectors of the two oxygen ions, as a function of the bond angle θ OCO and the bond length r CO. It can be seen that θ CM is mainly determined by θ OCO. The large variation of r CO has little effect on the relationship between θ CM and θ OCO. Thus, the bond angle θ OCO can be derived through the experimental measurement of θ CM for each explosion event. Through the statistical analysis of thousands of explosion events, we obtained the geometric structure distribution as a function of bond angle
FIG. 5. Calculated vector angle θ CM as a function of the bond angle θ OCO and the bond length r CO for the explosion channel of CO23+ → O+ + C+ + O+. θ CM is defined as the angle between the momentum vectors of the two oxygen ions produced in the explosion process.
θ OCO, which are shown in Figure 6. The results showed that the reconstructed bond angle have similar distributions. The most probable angle is about 169◦ regardless of the explosion channels. The similarity of the reconstructed bond angle distribution demonstrated that the derived structural parameters do not depend on the channel from which the molecular structure is reconstructed. The independence of the reconstructed structural parameters on the explosion channels indicated that the bond angle was kept unchanged during the multiple ionization under the present experimental condition.26 Then, why the reconstructed structure deviates from the well-known linear structure of neutral CO2 molecules? Tri-atomic molecules CO2 have three characteristic vibration frequencies, which correspond the symmetric stretching mode, the anti-symmetric stretching mode, and the bending mode. Among them, the bending mode is doubly degenerate
FIG. 6. Bond angle distribution of CO2n+ (n = 3-6) reconstructed from the momentum vectors of correlated atomic ions generated in the Coulomb explosion channel.
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and has the lowest vibrational frequency. For an ensemble of CO2 with all vibrational modes are in the ground states, the bond angle varies from 150◦ to 180◦ with the most probable bond angle of 172.5◦ according to the Monte Carlo simulation,27 in agreement with our experimental results. The agreement can be improved when the bending excitation is taken into account for CO2 molecules. It is known that the population at higher vibrational state cannot be neglected with the increase of the vibrational temperature. Even though supersonic molecular beam is applied in the present measurement, the supersonic expansion is not effective to cool the vibrational temperature of neutral CO2 molecules.28 Assuming the vibrational temperature was close to the room temperature, the population of higher vibration levels can reach 4% for the bending mode. As a result, the most probable bond angle becomes smaller than 172.5◦ and the agreement is improved. The agreement further supported our conclusion that the bond angle was kept unchanged during the multiple ionization and the reconstructed structural parameters for ions represented the structure of neutral one before laser irradiation. The present study, together with previous reports,29–33 demonstrated that Coulomb explosion is a promising approach for imaging geometric structures of polyatomic molecules. However, a closer inspection indicates that there are some discrepancies between the reconstructed structure of CO2n+ (n = 3-6) and the predicted structure of CO2 before laser irradiation. The main discrepancy is the probability of the bond angle at 180◦, which is near zero for CO2n+ and much lower than that of neutral CO2. We attributed this discrepancy to the assumptions during the process of structure reconstruction, in which we assumed that the two C==O bonds were equal and the momentum of each ion was zero before explosion. With these assumptions, only the zero kinetic energy of carbon ions can lead to the 180◦ of the bond angle. However, the momentum of carbon ions will not be zero because of the energy exchange between the carbon ion and the ionized electron during the process of ionization. Therefore, the probability will be underestimated for CO2n+ at the bond angle of 180◦ because of the assumptions in the process of structure reconstruction.
IV. CONCLUSION
In summary, we have measured three-dimensional momentum vectors of three correlated atomic ions and explored the three-body fragmentation dynamics of CO2n+ (n = 3-6). The results demonstrated that three-body fragmentation can occur through both Coulomb explosion process and sequential fragmentation process. By using correlation diagram of correlated ions, we separated these two processes and obtained accurate experimental data from Coulomb explosion process. Further, we simulated the explosion dynamics of CO2n+ based on Coulomb potential approximation. The relationship of the bond angle θ OCO was constructed as a function of the vector angle θ CM with θ CM representing the angle between the momentum vectors of the two oxygen ions. Based on the relationship, the bond angle θ OCO was derived through the measured θ CM for each explosion event. After the statistical analysis of thousands of explosion events, we obtained the bond angle
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distribution of CO2n+ at the moment of fragmentation. The most probable angle is about 169◦ regardless of the reconstructed channels, in agreement with the theoretical prediction for neutral CO2 molecules. This study demonstrates that the molecular structure can be imaged by Coulomb explosion technique. ACKNOWLEDGMENTS
This work is supported by the 973 Program under Grant No. 2013CB922403 and by the National Natural Science Foundation of China under Grant Nos. 61178019, 11474009, 11434002, and 11121091. 1C.
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Citation: The Journal of Chemical Physics 142, 124303 (2015); doi: 10.1063/1.4916045 View online: http://dx.doi.org/10.1063/1.4916045 View Table of Contents: http://aip.scitation.org/toc/jcp/142/12 Published by the American Institute of Physics
THE JOURNAL OF CHEMICAL PHYSICS 142, 124303 (2015)
Three-body fragmentation of CO2 driven by intense laser pulses Chengyin Wu,1,2,a) Cong Wu,1 Yameng Fan,1 Xiguo Xie,1 Peng Wang,1 Yongkai Deng,1 Yunquan Liu,1,2 and Qihuang Gong1,2 1
State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, People’s Republic of China 2 Collaborative Innovation Center of Quantum Matter, Beijing 100871, People’s Republic of China
(Received 27 November 2014; accepted 11 March 2015; published online 24 March 2015) Dissociative ionization dynamics were studied experimentally for CO2 driven by intense laser pulses. Three-dimensional momentum vectors of correlated atomic ions were obtained for each three-body fragmentation event using triple ion coincidence measurement. Newton diagram demonstrated that three-body fragmentation of CO2n+ (n = 3-6) can occur through Coulomb explosion process and sequential fragmentation process depending on the fragmentation channels. The experimental data from these two processes were disentangled by using correlation diagram of correlated ions. Based on the accurate Coulomb explosion data, we reconstructed the bond angle distributions of CO2n+ at the moment of fragmentation, which are close to that of neutral CO2 before laser irradiation. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4916045]
I. INTRODUCTION
Studying many-body fragmentation of polyatomic molecules is a big challenge to both theory and experiment. Even in the simplest three-body fragmentation, its dynamics is also very complicated. It can occur through a concerted or a sequential fashion. In the case of concerted fragmentation process, the three products are generated simultaneously and all chemical bonds break in a single kinetic event. Instead, there exists an intermediate and the three products are generated in two independent dissociation steps for the sequential fragmentation process. Moreover, the time interval between the two dissociation steps is longer than the rotational period of the intermediate. Exploring three-body fragmentation dynamics has attracted much attention of both experimental and theory groups.1–5 In order to experimentally explore three-body fragmentation mechanism, various experimental techniques have been developed, such as photofragment translational spectroscopy,6,7 photoelectron-photoion coincidence approach,8,9 and momentum vectors imaging of correlated fragments.10,11 As a prototype system, three-body fragmentation of CO2 ions with various charge states has been extensively studied.12–24 The CO2 ions were generated by synchrotron radiation,12 collision of charged ions,13 electron impact,14 or intense laser pulses interaction with various laser parameters.15–21 The momentum vectors of fragmental ions were measured using the coincidence technology. Most of the studies assumed that the three atomic ions were generated through the concerted fragmentation process, i.e., Coulomb explosion process. The geometric structures prior to explosion were therefore reconstructed from the measured momentum vectors of three correlated atomic ions. The channel-dependent reconstructed structures indicated that the molecular structure was deformed during the process of multiple ionization.17,20,21 However, a)Email: [email protected]
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recent results demonstrated that the three-body fragmentation of CO2 ions does not always occur through the concerted process. Singh et al. studied fragmentation dynamics of CO23+ generated by photoionization of CO2 at 200 eV photon energy.22 They concluded that the fragmentation of CO23+ can occur either by simultaneous breaking of the two C==O bonds or by sequential fragmentation. Neumann et al. studied fragmentation dynamics of CO23+ generated by collision of CO2 with slow highly charged ions.23 They confirmed the existence of sequential fragmentation process by using Dalitz plots and Newton diagrams. Very recently, Wu et al. studied fragmentation dynamics of CO23+ by irradiation of CO2 with intense femtosecond laser pulses.24 They further disentangled the channels of the sequential fragmentation and the concerted fragmentation by developing correlation diagram of correlated ions and obtained the precise data of Coulomb explosion. The C==O bond length was therefore precisely reconstructed for CO23+ at the moment of fragmentation, which turns out to be close to the neutral CO2 before the laser irradiation. In this article, we experimentally studied three-body fragmentation of CO2n+ (n = 3-6) by irradiating CO2 with intense femtosecond laser pulses and clarified the mechanism for each threefragmentation channel.
II. EXPERIMENTAL METHODS
Figure 1 shows the sketch of the experimental platform. It consists of a femtosecond laser amplifier and a reaction microscope.25 The laser amplifier has a repetition rate of 3 kHz, a central wavelength of 800 nm, and a pulse duration of 24 fs. The reaction microscope has four chambers, which are the jet chamber, the expansion chamber, the collimation chamber, and the reaction chamber, respectively. These chambers are separated by a skimmer or an aperture with a diameter of 1 mm. In the jet chamber, the continuous CO2 molecular beam was generated through a 30 µm nozzle with a driving pressure of 2
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following three-body fragmentation channels. (1) Two oxygen ions and one carbon ion were detected in one laser pulse. (2) The sum-momentum of the three atomic ions was less than 10 atomic units to meet the momentum conservation of threebody fragmentation, + + + CO2 (1, 1, 1) : CO3+ 2 → O +C +O , + 2+ + CO2 (1, 2, 1) : CO4+ 2 → O +C +O , 2+ + 2+ CO2 (2, 1, 2) : CO5+ 2 → O +C +O , 2+ 2+ 2+ CO2 (2, 2, 2) : CO6+ 2 → O +C +O .
(1) (2) (3) (4)
FIG. 1. Sketch of the reaction microscope at Peking University. (a) Jet chamber, (b) expansion chamber, (c) collimation chamber, and (d) reaction chamber.
III. RESULTS AND DISCUSSION
bars. Then, the molecular beam passed through the expansion chamber and the collimation chamber. Finally, it arrived at the reaction chamber and interacted with the focused laser. All ions produced in the interaction zone were collected by a temporal and position-sensitive detector (RoentDek, Germany). By recording the position and the time of flight, the initial threedimensional momentum vectors of the ions were derived. In the experiment, we adjusted the reaction chamber pressure to ensure that there was much less than one ionization event in average within one laser pulse. There are many reaction channels for CO2 in intense laser fields. Dissociative ionization of CO2 is a tiny fraction among all ionization events. One of the advantages of the reaction microscope is that the data of all reaction channels can be recorded in one experiment. In the off-line analysis, these reaction channels can be disentangled by using the coincidence constraints to filter the experimental data. Here, we applied two constraints to filter the experimental data to select out the
Figure 2 shows the experimentally measured two-dimensional momentum distributions in the center-of-mass coordinate frame for the correlated atomic ions generated in dissociative ionization of CO2 by intense laser pulses. The linearly polarized laser pulses have a central wavelength of 800 nm, a pulse duration of 24 fs, and an intensity of around 1 × 1015 W/cm2. The laser polarization direction is defined as 2 z axis. The P ∥ (=Pz) and P⊥(= Px + P2y) represent the momentum vectors parallel and perpendicular to the laser polarization direction. The middle section with low momentum comes from carbon ions and the outside one with large momentum comes from oxygen ions. Three-body fragmentation of CO2n+ can take place through the Coulomb explosion process or the sequential fragmentation process.22–24 In the case of Coulomb explosion process, the two C==O bonds break simultaneously and the three atomic ions are generated at the same time. In the case of sequential process, the two C==O bonds break one after the other and there
FIG. 2. Two-dimensional momentum distribution of correlated atomic ions generated from the three-body fragmentation channels of CO2 driven by intense laser pulses. (a) O+ + C+ + O+, (b) O+ + C2+ + O+, (c) O2+ + C+ + O2+, and (d) O2+ + C2+ + O2+.
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exists an intermediate. The intermediate further dissociates into two atomic ions and the dissociation time is comparable to or longer than the rotational period of the intermediate. Newton diagram can visualize the momentum correlation of reaction products and is effective to identify the mechanisms of three-body fragmentation process. A circle structure will be exhibited in the Newton diagram because of the rotation of the intermediate if the sequential three-body fragmentation process exists.24 Therefore, we plotted the Newton diagrams with the experimental data, as shown in Figure 3. The momentum vector of the first oxygen ion is represented by an arrow fixed at one arbitrary unit. The momentum vectors of the carbon ion and the second oxygen ion are normalized to the amplitude of the first oxygen ion momentum vector and mapped in the left of the plot. It can be seen that different structures were observed in the Newton diagrams depending on the three-body fragmentation channels. A pair of crescent-like structures was exhibited for the channels of CO2 (1, 2, 1), CO2 (2, 1, 2), and CO2 (2, 2, 2). The lack of a circle structure demonstrated that the three-body fragmentation occurs only through Coulomb explosion process. While for the channel of CO2 (1, 1, 1), a circle structure was superimposed in the pair of crescent-like structure, which indicated that sequential fragmentation and Coulomb explosion coexist. We have demonstrated that kinetic energy correlation diagram of correlated atomic ions can separate the channels from the Coulomb explosion process and the sequential fragmentation process.24 In the case of Coulomb explosion process, the two C==O bonds break simultaneously and the three atomic ions are generated at the same time. The symmetry in the geometric space can be preserved in the momentum space if the identical components carry the same charge. As a result, the two oxygen ions carrying the same charge will have comparable kinetic energies. However, the symmetry will be destroyed because of the rotation of the intermediate when
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the sequential fragmentation process occurs. As a result, there is no obvious correlation for the kinetic energies of the two correlated oxygen ions. Figure 4 shows the kinetic energy correlation diagram of the two oxygen ions. It can be seen that the two identical oxygen ions have almost the same kinetic energy for the channels of CO2 (1, 2, 1), CO2 (2, 1, 2), and CO2 (2, 2, 2). This observation indicated that Coulomb explosion dominates for these three-body fragmentation channels, which agree with the conclusion based on the analysis of Newton diagram. However, two obvious structures were observed for the channel of CO2 (1, 1, 1), which was separated by a red circle with radius of about 10 eV. The two oxygen ions outside the circle have almost equal kinetic energies and should come from Coulomb explosion process. Instead, the two oxygen ions inside the circle should come from sequential fragmentation process because their kinetic energies have no obvious relationship. This separation was confirmed by their Newton diagrams. Thus, we obtained the momentum vectors of the atomic ions produced in the Coulomb explosion process. Based on these precise experimental data of all Coulomb explosion channels, we reconstructed the geometric structure of CO2n+ (n = 3-6) at the moment of fragmentation. Due to the lack of the accurate ab initio potential energy surface for three-body fragmentation of CO2n+ (n = 3-6), we assumed the nuclei moving in a Coulomb repulsive potential and simulated the explosion dynamics of CO2n+. The Hamilto3 p 1 ⃗ i2 with mi ,⃗r i , and nian was written by Hˆ = 21 m + r i −⃗ rj| i > j |⃗ i=1 i P⃗i = mi⃗r˙i (t) being the mass, position, and momentum of each ion in the center-of-mass coordinate system. The subscript 1 represents the first oxygen ion, 2 and 3 represent the carbon ion and the second oxygen ion. Thus, the lengths of the two −→ C==O bonds can be, respectively, expressed by r−→ 21 and r 23 with ⃗r i j = ⃗r i − ⃗r j and the bond angle θ OCO can be expressed −→ by the angle between vectors of r−→ 21 and r 23. Experimental data
FIG. 3. Newton diagram for correlated atomic ions generated from the threebody fragmentation channels of CO2 driven by intense laser pulses. (a) O+ + C+ + O+, (b) O+ + C2+ + O+, (c) O2+ + C+ + O2+, and (d) O2+ + C2+ + O2+.
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FIG. 4. Kinetic energy release (KER) correlation diagram for two correlated oxygen ions generated from the threebody fragmentation channels of CO2 driven by intense laser pulses. (a) O+ + C+ + O+, (b) O+ + C2+ + O+, (c) O2+ + C+ + O2+, and (d) O2+ + C2+ + O2+.
demonstrated that the two oxygen ions are generated at the same time and have almost equal kinetic energies. It is therefore reasonable to assume that the two C==O bonds were stretched equally before explosion. Thus, we set the mo −→ mentum of each ion as zero and r−→ 21 = r 23 at the beginning of explosion during the theoretical simulation. By solving the equation of nuclei motion numerically, the momentum vectors of the three atomic ions can be obtained for each explosion event. Figure 5 shows the calculated vector angle θ CM, which was defined as the angle between the momentum vectors of the two oxygen ions, as a function of the bond angle θ OCO and the bond length r CO. It can be seen that θ CM is mainly determined by θ OCO. The large variation of r CO has little effect on the relationship between θ CM and θ OCO. Thus, the bond angle θ OCO can be derived through the experimental measurement of θ CM for each explosion event. Through the statistical analysis of thousands of explosion events, we obtained the geometric structure distribution as a function of bond angle
FIG. 5. Calculated vector angle θ CM as a function of the bond angle θ OCO and the bond length r CO for the explosion channel of CO23+ → O+ + C+ + O+. θ CM is defined as the angle between the momentum vectors of the two oxygen ions produced in the explosion process.
θ OCO, which are shown in Figure 6. The results showed that the reconstructed bond angle have similar distributions. The most probable angle is about 169◦ regardless of the explosion channels. The similarity of the reconstructed bond angle distribution demonstrated that the derived structural parameters do not depend on the channel from which the molecular structure is reconstructed. The independence of the reconstructed structural parameters on the explosion channels indicated that the bond angle was kept unchanged during the multiple ionization under the present experimental condition.26 Then, why the reconstructed structure deviates from the well-known linear structure of neutral CO2 molecules? Tri-atomic molecules CO2 have three characteristic vibration frequencies, which correspond the symmetric stretching mode, the anti-symmetric stretching mode, and the bending mode. Among them, the bending mode is doubly degenerate
FIG. 6. Bond angle distribution of CO2n+ (n = 3-6) reconstructed from the momentum vectors of correlated atomic ions generated in the Coulomb explosion channel.
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and has the lowest vibrational frequency. For an ensemble of CO2 with all vibrational modes are in the ground states, the bond angle varies from 150◦ to 180◦ with the most probable bond angle of 172.5◦ according to the Monte Carlo simulation,27 in agreement with our experimental results. The agreement can be improved when the bending excitation is taken into account for CO2 molecules. It is known that the population at higher vibrational state cannot be neglected with the increase of the vibrational temperature. Even though supersonic molecular beam is applied in the present measurement, the supersonic expansion is not effective to cool the vibrational temperature of neutral CO2 molecules.28 Assuming the vibrational temperature was close to the room temperature, the population of higher vibration levels can reach 4% for the bending mode. As a result, the most probable bond angle becomes smaller than 172.5◦ and the agreement is improved. The agreement further supported our conclusion that the bond angle was kept unchanged during the multiple ionization and the reconstructed structural parameters for ions represented the structure of neutral one before laser irradiation. The present study, together with previous reports,29–33 demonstrated that Coulomb explosion is a promising approach for imaging geometric structures of polyatomic molecules. However, a closer inspection indicates that there are some discrepancies between the reconstructed structure of CO2n+ (n = 3-6) and the predicted structure of CO2 before laser irradiation. The main discrepancy is the probability of the bond angle at 180◦, which is near zero for CO2n+ and much lower than that of neutral CO2. We attributed this discrepancy to the assumptions during the process of structure reconstruction, in which we assumed that the two C==O bonds were equal and the momentum of each ion was zero before explosion. With these assumptions, only the zero kinetic energy of carbon ions can lead to the 180◦ of the bond angle. However, the momentum of carbon ions will not be zero because of the energy exchange between the carbon ion and the ionized electron during the process of ionization. Therefore, the probability will be underestimated for CO2n+ at the bond angle of 180◦ because of the assumptions in the process of structure reconstruction.
IV. CONCLUSION
In summary, we have measured three-dimensional momentum vectors of three correlated atomic ions and explored the three-body fragmentation dynamics of CO2n+ (n = 3-6). The results demonstrated that three-body fragmentation can occur through both Coulomb explosion process and sequential fragmentation process. By using correlation diagram of correlated ions, we separated these two processes and obtained accurate experimental data from Coulomb explosion process. Further, we simulated the explosion dynamics of CO2n+ based on Coulomb potential approximation. The relationship of the bond angle θ OCO was constructed as a function of the vector angle θ CM with θ CM representing the angle between the momentum vectors of the two oxygen ions. Based on the relationship, the bond angle θ OCO was derived through the measured θ CM for each explosion event. After the statistical analysis of thousands of explosion events, we obtained the bond angle
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distribution of CO2n+ at the moment of fragmentation. The most probable angle is about 169◦ regardless of the reconstructed channels, in agreement with the theoretical prediction for neutral CO2 molecules. This study demonstrates that the molecular structure can be imaged by Coulomb explosion technique. ACKNOWLEDGMENTS
This work is supported by the 973 Program under Grant No. 2013CB922403 and by the National Natural Science Foundation of China under Grant Nos. 61178019, 11474009, 11434002, and 11121091. 1C.
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