Laser-assisted electron diffraction for femtosecond molecular imaging Yuya Morimoto, Reika Kanya, and Kaoru Yamanouchi Citation: The Journal of Chemical Physics 140, 064201 (2014); doi: 10.1063/1.4863985 View online: http://dx.doi.org/10.1063/1.4863985 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Intramolecular photoelectron diffraction in the gas phase J. Chem. Phys. 139, 124306 (2013); 10.1063/1.4820814 N2O ionization and dissociation dynamics in intense femtosecond laser radiation, probed by systematic pulse length variation from 7 to 500 fs J. Chem. Phys. 138, 204311 (2013); 10.1063/1.4804653 Imaging transient species in the femtosecond A -band photodissociation of CH 3 I J. Chem. Phys. 131, 134311 (2009); 10.1063/1.3236808 Dissociative ionization of ethanol by 400 nm femtosecond laser pulses J. Chem. Phys. 125, 184311 (2006); 10.1063/1.2387177 Electron rescattering and the dissociative ionization of alcohols in intense laser light J. Chem. Phys. 119, 12224 (2003); 10.1063/1.1625637
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THE JOURNAL OF CHEMICAL PHYSICS 140, 064201 (2014)
Laser-assisted electron diffraction for femtosecond molecular imaging Yuya Morimoto,1 Reika Kanya,1 and Kaoru Yamanouchi1,2,a) 1
Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 2 NANOQUINE, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
(Received 25 December 2013; accepted 21 January 2014; published online 11 February 2014) We report the observation of laser-assisted electron diffraction (LAED) through the collision of 1 keV electrons with gas-phase CCl4 molecules in a femtosecond near-infrared laser field. In the angular distribution of the scattered electrons with the energy shifts of ±¯ω, we observed clear diffraction patterns which reflect the geometrical structure of the molecules at the moment of laser irradiation. Our results demonstrate that ultrafast nuclear dynamics of molecules can be probed by LAED with the high temporal ( 0) and emission (n < 0) processes for a given |n| are nearly identical because of the formula J–n (x) = (–1)n Jn (x).30 The calculated An (θ ) is a slightly decreasing function when n = 0 within the angular range, while it is monotonically increasing function when n = ±1, ±2. In the calculations of the elastic DCS, dσ el /d, of gasphase electron diffraction, the independent atomic model (IAM)1, 2 has commonly been employed. In IAM, the total scattering amplitude is defined as the sum of the scattering amplitudes from the respective atoms in a molecule. For the randomly oriented CCl4 , the elastic DCS denoted by IIAM (s) is given by IIAM (s) = |fC (s)|2 + 4 |fCl (s)|2 + 8 |fC (s)| · |fCl (s)|
sin(srC−Cl ) − lC−Cl 2 s 2 e 2 srC−Cl
× cos (ηC (s) − ηCl (s)) + 12 |fCl (s)|2
sin(srCl−Cl ) − lCl−Cl 2 s 2 e 2 , srCl−Cl
(3)
where fC (s) and fCl (s) are the atomic scattering amplitudes of C and Cl atoms, ηC (s) and ηCl (s) are the phases associated with the respective scattering amplitudes, rC-Cl is the internuclear distance between C and Cl atoms, rCl-Cl is that between two Cl atoms, lC-Cl 2 and lCl-Cl 2 are the mean square amplitudes for the C-Cl and Cl-Cl distances, and s is the absolute value of s and simply written as FIG. 3. Spatio-temporally averaged squared Bessel functions. Red curves show the spatio-temporally averaged squared Bessel functions for n-photon absorption processes (n = 0 (a), ±1 (b), ±2 (c)).
dσ n /d is given by dσ |kf,n | 2 e dσ n el = , ε·s Jn |ki | d mω2 d
(1)
where ki and kf,n are initial and final electron wave vectors, Jn (x) is the nth order Bessel function of the first kind, e is the unit charge, ε is an electric field vector, m is the electron mass, ω is an angular frequency of the laser field, s is a scattering vector defined as ki – kf,n , and dσ el /d is the field-free elastic DCS. In the LAED experiment, the ki, kf,n , and ε are on the same plane (Fig. 2). The magnitude of s depends on the scattering angle θ . For the simulation of the observed LAES angular distributions In (θ ), we performed the spatiotemporal averaging of Eq. (1) by considering the overlap of the three beams, i.e., the electron beam, the laser beam, and the molecular beam. When we define An (θ ) as the spatiotemporal average of Jn2 (eε · s /mω2 ), In (θ ) can be written as In (θ ) =
|kf,n | dσ el . An (θ ) |ki | d
(2)
In Fig. 3, we show the simulated An (θ ) (n = 0, ±1, ±2) by considering the spatio-temporal averaging described above. Since we measure 1 keV electrons scattered by molecules in the 800 nm laser field (¯ω = 1.55 eV), the difference
θ , s = 2k sin 2 θ 4π sin , = λ 2
(4)
where k = |ki | = |kf,0 | and λ is the de Broglie wavelength of electrons. It has been known that IAM is a good model that could describe DCSs in the large scattering angle regions (s ≥ 10 Å−1 ). However, in the small scattering angle region of our measurement between θ = 2.5◦ (s = 0.7 Å−1 ) and θ = 12.5◦ (s = 3.5 Å−1 ), deviations from IAM are expected to appear because the electron density distribution ρ(r) within a molecule is affected by the chemical bonding effect.1, 31, 32 In addition to this chemical bonding effect, we should also consider the charge cloud polarization effect33 which could enhance the DCS in the small scattering angle region.34, 35 Therefore, the scattering potential in our model is represented as V (r) = VIAM (r) + V (r), (5) V (r) = VCBE (r) + VPOL (r) , where VIAM (r) is the sum of the atomic potentials. VCBE (r) is the additional potential originating from the chemical boding
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064201-4
Morimoto, Kanya, and Yamanouchi
J. Chem. Phys. 140, 064201 (2014)
FIG. 4. Elastic angular distribution of CCl4 . Red circles shows the experimental data. The error bars represent one standard deviation. Blue line is the calculated elastic angular distribution (Eq. (B5)).
effect defined as
VCBE (r) =
e2 ρ(r ) dr , |r − r |
(6)
where ρ(r) is the deviation of the electron density distribution induced by the chemical bonding effect. The detailed description on ρ(r) of CCl4 is given in Appendix B. VPOL (r) is the polarization potential and here we adopted the Buckingham-type polarization potential33 described by VPOL (r) = −
αe2 , 2(|r|2 + d 2 )2
(7)
where α is a static polarizability and d is a cutoff parameter. We assume that the origin of this potential is located at the C atom, and adopted α = 10.0 Å3 from Ref. 36, and d = 1.77 Å from Ref. 37. In order to evaluate the elastic DCS numerically, the atomic scattering factors, fC (s) and fCl (s) in Eq. (3), were obtained by the ELSEPA code28 and the first Born approximation was adopted for the evaluations of the scattering amplitudes from VCBE (r) and VPOL (r). We neglected the effect of the phase shift between the scattering at the C atom and that at the Cl atoms because this effect is negligibly small in the small scattering angle region. We adopted the structural parameters (rg ) of CCl4 at 295 K38 determined by the conventional GED. The calculated elastic angular distribution is plotted in Fig. 4 as a blue line. This distribution shows a good agreement with the experimental angular distribution shown in Fig. 4 as red circles. IV. RESULTS AND DISCUSSION
In Fig. 5(a), we show the kinetic energy spectrum of the scattered electrons recorded at the delay time t of the laser pulse with respect to the electron pulse is zero (t = 0), which was obtained by integrating the electron signals over the scattering angle θ in the entire recorded range (2.5o ≤ θ ≤ 12.5o ). For comparison, we show the kinetic energy spectra recorded at t = –70 ps and +70 ps in Figs. 5(b) and 5(c), respectively. In either case, there was almost no temporal overlap between the laser and electron pulses. The spectral intensities in Figs. 5(a)–5(c) are normalized by the intensity of the
FIG. 5. Kinetic energy spectra of scattered electrons at t = 0 (a), –70 ps (b), and +70 ps (c). The intensities are normalized by their peak intensity at E = 0. Only when the electron pulse and laser pulse are overlapped (t = 0), signals from laser-assisted scatterings arise at the energy shifts of onephoton and two-photons. Broken line in each figure shows the same spectrum multiplied by a factor of 1/1000.
peak appearing at the zero energy shift, E = 0 eV. Only when the laser and electron pulses are temporally overlapped (t = 0), the increases in the LAES signal intensities at the kinetic energy shifts of E = ±¯ω (±1.55 eV) and ±2¯ω (±3.10 eV) are recognized. The weak intensities of the LAES signals of the order of 10−3 reflect the fact that the duration of the laser pulses (520 fs) was significantly shorter than the time required for electrons to pass through the gas sample (∼70 ps). The observed angular distributions of the one-photon LAES signals (E = +¯ω and –¯ω) of CCl4 are shown in Fig. 6 with red circles. In both of the angular distributions, which are nearly identical to each other within the experimental uncertainties, we find a clear modulation with a minimum at around 5.5◦ and a maximum at around 9.0◦ . Since these modulation patterns were not identified in the angular distributions of the LAES signals of Xe atoms,20 the observed modulation characteristic of CCl4 is considered to be an electron diffraction pattern of CCl4 .
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064201-5
Morimoto, Kanya, and Yamanouchi
J. Chem. Phys. 140, 064201 (2014)
V. CONCLUSION
FIG. 6. Laser-assisted electron diffraction patterns of CCl4 . Red circles show the experimental LAED patterns at E = +¯ω (a) and E = –¯ω (b). These distributions are obtained by integrating the electron signals at t = 0 over 0.4 eV energy range centered at E = ±¯ω. Background signals obtained when t = ±70 ps are subtracted. The error bars represent one standard deviation. The blue solid lines are the simulated LAED patterns. The green broken lines show the simulated LAES angular distributions when the interference effects are neglected.
In Figs. 6(a) and 6(b), we show the simulated LAES (n = ±1) angular distributions of CCl4 as blue lines. These distributions reproduce the positions of the minima and maxima and agree quantitatively with the observed distributions. The green broken line in Figs. 6(a) and that in Fig. 6(b) are the LAES angular distributions calculated as a simple sum of the LAES angular distributions originating from one C atom and from four Cl atoms. The DCSs of field-free elastic scattering of electrons by C and Cl atoms were calculated by the ELSEPA code28 with the polarization effect (the polarizabilities of C and Cl atoms were taken from Ref. 39). The angular distributions look similar to those of Xe atoms,20 but do not exhibit the minima and maxima having appeared in the observed LAES signals of CCl4 . The numerical simulation confirms that the observed modulation patterns are the electron diffraction patterns of CCl4 reflecting its geometrical structure. We find that the visibility of the modulation in the LAED angular distributions of CCl4 is much higher than that in the conventional GED angular distribution obtained without a laser field (Fig. 4). This is because the intensity of the LAES signals is significantly small in the small scattering angle θ region (Fig. 3), which is an advantage of the LAED method in determining geometrical structure of molecules over the conventional GED method in which the huge signal intensity in the small θ region needs to be decreased by a rotating sector.1, 2
In conclusion, we recorded the LAED pattern of CCl4 as the angular distributions of the one-photon LAES signals (E = +¯ω and –¯ω). Through the comparison with the numerical simulations, we have confirmed that the observed diffraction patterns are reproduced by the field-free geometrical structure of CCl4 . It has been discussed in these years that geometrical structures of gas-phase molecules can be probed in real time by ultrafast X-ray diffraction using an X-ray free electron laser40, 41 as well as by photoelectron diffraction methods such as laser-induced electron diffraction.42, 43 Our present study shows that the LAED will also be a promising technique. If molecules are pumped by an ultrashort laser pulse and are probed by LAED, the temporal evolution of the geometrical structure of molecules, undergoing chemical bond breaking and rearrangement, can be determined as a series of snapshots of diffraction images with high precision (∼0.01 Å) as well as with high temporal resolution (
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THE JOURNAL OF CHEMICAL PHYSICS 140, 064201 (2014)
Laser-assisted electron diffraction for femtosecond molecular imaging Yuya Morimoto,1 Reika Kanya,1 and Kaoru Yamanouchi1,2,a) 1
Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 2 NANOQUINE, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
(Received 25 December 2013; accepted 21 January 2014; published online 11 February 2014) We report the observation of laser-assisted electron diffraction (LAED) through the collision of 1 keV electrons with gas-phase CCl4 molecules in a femtosecond near-infrared laser field. In the angular distribution of the scattered electrons with the energy shifts of ±¯ω, we observed clear diffraction patterns which reflect the geometrical structure of the molecules at the moment of laser irradiation. Our results demonstrate that ultrafast nuclear dynamics of molecules can be probed by LAED with the high temporal ( 0) and emission (n < 0) processes for a given |n| are nearly identical because of the formula J–n (x) = (–1)n Jn (x).30 The calculated An (θ ) is a slightly decreasing function when n = 0 within the angular range, while it is monotonically increasing function when n = ±1, ±2. In the calculations of the elastic DCS, dσ el /d, of gasphase electron diffraction, the independent atomic model (IAM)1, 2 has commonly been employed. In IAM, the total scattering amplitude is defined as the sum of the scattering amplitudes from the respective atoms in a molecule. For the randomly oriented CCl4 , the elastic DCS denoted by IIAM (s) is given by IIAM (s) = |fC (s)|2 + 4 |fCl (s)|2 + 8 |fC (s)| · |fCl (s)|
sin(srC−Cl ) − lC−Cl 2 s 2 e 2 srC−Cl
× cos (ηC (s) − ηCl (s)) + 12 |fCl (s)|2
sin(srCl−Cl ) − lCl−Cl 2 s 2 e 2 , srCl−Cl
(3)
where fC (s) and fCl (s) are the atomic scattering amplitudes of C and Cl atoms, ηC (s) and ηCl (s) are the phases associated with the respective scattering amplitudes, rC-Cl is the internuclear distance between C and Cl atoms, rCl-Cl is that between two Cl atoms, lC-Cl 2 and lCl-Cl 2 are the mean square amplitudes for the C-Cl and Cl-Cl distances, and s is the absolute value of s and simply written as FIG. 3. Spatio-temporally averaged squared Bessel functions. Red curves show the spatio-temporally averaged squared Bessel functions for n-photon absorption processes (n = 0 (a), ±1 (b), ±2 (c)).
dσ n /d is given by dσ |kf,n | 2 e dσ n el = , ε·s Jn |ki | d mω2 d
(1)
where ki and kf,n are initial and final electron wave vectors, Jn (x) is the nth order Bessel function of the first kind, e is the unit charge, ε is an electric field vector, m is the electron mass, ω is an angular frequency of the laser field, s is a scattering vector defined as ki – kf,n , and dσ el /d is the field-free elastic DCS. In the LAED experiment, the ki, kf,n , and ε are on the same plane (Fig. 2). The magnitude of s depends on the scattering angle θ . For the simulation of the observed LAES angular distributions In (θ ), we performed the spatiotemporal averaging of Eq. (1) by considering the overlap of the three beams, i.e., the electron beam, the laser beam, and the molecular beam. When we define An (θ ) as the spatiotemporal average of Jn2 (eε · s /mω2 ), In (θ ) can be written as In (θ ) =
|kf,n | dσ el . An (θ ) |ki | d
(2)
In Fig. 3, we show the simulated An (θ ) (n = 0, ±1, ±2) by considering the spatio-temporal averaging described above. Since we measure 1 keV electrons scattered by molecules in the 800 nm laser field (¯ω = 1.55 eV), the difference
θ , s = 2k sin 2 θ 4π sin , = λ 2
(4)
where k = |ki | = |kf,0 | and λ is the de Broglie wavelength of electrons. It has been known that IAM is a good model that could describe DCSs in the large scattering angle regions (s ≥ 10 Å−1 ). However, in the small scattering angle region of our measurement between θ = 2.5◦ (s = 0.7 Å−1 ) and θ = 12.5◦ (s = 3.5 Å−1 ), deviations from IAM are expected to appear because the electron density distribution ρ(r) within a molecule is affected by the chemical bonding effect.1, 31, 32 In addition to this chemical bonding effect, we should also consider the charge cloud polarization effect33 which could enhance the DCS in the small scattering angle region.34, 35 Therefore, the scattering potential in our model is represented as V (r) = VIAM (r) + V (r), (5) V (r) = VCBE (r) + VPOL (r) , where VIAM (r) is the sum of the atomic potentials. VCBE (r) is the additional potential originating from the chemical boding
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064201-4
Morimoto, Kanya, and Yamanouchi
J. Chem. Phys. 140, 064201 (2014)
FIG. 4. Elastic angular distribution of CCl4 . Red circles shows the experimental data. The error bars represent one standard deviation. Blue line is the calculated elastic angular distribution (Eq. (B5)).
effect defined as
VCBE (r) =
e2 ρ(r ) dr , |r − r |
(6)
where ρ(r) is the deviation of the electron density distribution induced by the chemical bonding effect. The detailed description on ρ(r) of CCl4 is given in Appendix B. VPOL (r) is the polarization potential and here we adopted the Buckingham-type polarization potential33 described by VPOL (r) = −
αe2 , 2(|r|2 + d 2 )2
(7)
where α is a static polarizability and d is a cutoff parameter. We assume that the origin of this potential is located at the C atom, and adopted α = 10.0 Å3 from Ref. 36, and d = 1.77 Å from Ref. 37. In order to evaluate the elastic DCS numerically, the atomic scattering factors, fC (s) and fCl (s) in Eq. (3), were obtained by the ELSEPA code28 and the first Born approximation was adopted for the evaluations of the scattering amplitudes from VCBE (r) and VPOL (r). We neglected the effect of the phase shift between the scattering at the C atom and that at the Cl atoms because this effect is negligibly small in the small scattering angle region. We adopted the structural parameters (rg ) of CCl4 at 295 K38 determined by the conventional GED. The calculated elastic angular distribution is plotted in Fig. 4 as a blue line. This distribution shows a good agreement with the experimental angular distribution shown in Fig. 4 as red circles. IV. RESULTS AND DISCUSSION
In Fig. 5(a), we show the kinetic energy spectrum of the scattered electrons recorded at the delay time t of the laser pulse with respect to the electron pulse is zero (t = 0), which was obtained by integrating the electron signals over the scattering angle θ in the entire recorded range (2.5o ≤ θ ≤ 12.5o ). For comparison, we show the kinetic energy spectra recorded at t = –70 ps and +70 ps in Figs. 5(b) and 5(c), respectively. In either case, there was almost no temporal overlap between the laser and electron pulses. The spectral intensities in Figs. 5(a)–5(c) are normalized by the intensity of the
FIG. 5. Kinetic energy spectra of scattered electrons at t = 0 (a), –70 ps (b), and +70 ps (c). The intensities are normalized by their peak intensity at E = 0. Only when the electron pulse and laser pulse are overlapped (t = 0), signals from laser-assisted scatterings arise at the energy shifts of onephoton and two-photons. Broken line in each figure shows the same spectrum multiplied by a factor of 1/1000.
peak appearing at the zero energy shift, E = 0 eV. Only when the laser and electron pulses are temporally overlapped (t = 0), the increases in the LAES signal intensities at the kinetic energy shifts of E = ±¯ω (±1.55 eV) and ±2¯ω (±3.10 eV) are recognized. The weak intensities of the LAES signals of the order of 10−3 reflect the fact that the duration of the laser pulses (520 fs) was significantly shorter than the time required for electrons to pass through the gas sample (∼70 ps). The observed angular distributions of the one-photon LAES signals (E = +¯ω and –¯ω) of CCl4 are shown in Fig. 6 with red circles. In both of the angular distributions, which are nearly identical to each other within the experimental uncertainties, we find a clear modulation with a minimum at around 5.5◦ and a maximum at around 9.0◦ . Since these modulation patterns were not identified in the angular distributions of the LAES signals of Xe atoms,20 the observed modulation characteristic of CCl4 is considered to be an electron diffraction pattern of CCl4 .
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 149.150.51.237 On: Sun, 29 Mar 2015 15:21:16
064201-5
Morimoto, Kanya, and Yamanouchi
J. Chem. Phys. 140, 064201 (2014)
V. CONCLUSION
FIG. 6. Laser-assisted electron diffraction patterns of CCl4 . Red circles show the experimental LAED patterns at E = +¯ω (a) and E = –¯ω (b). These distributions are obtained by integrating the electron signals at t = 0 over 0.4 eV energy range centered at E = ±¯ω. Background signals obtained when t = ±70 ps are subtracted. The error bars represent one standard deviation. The blue solid lines are the simulated LAED patterns. The green broken lines show the simulated LAES angular distributions when the interference effects are neglected.
In Figs. 6(a) and 6(b), we show the simulated LAES (n = ±1) angular distributions of CCl4 as blue lines. These distributions reproduce the positions of the minima and maxima and agree quantitatively with the observed distributions. The green broken line in Figs. 6(a) and that in Fig. 6(b) are the LAES angular distributions calculated as a simple sum of the LAES angular distributions originating from one C atom and from four Cl atoms. The DCSs of field-free elastic scattering of electrons by C and Cl atoms were calculated by the ELSEPA code28 with the polarization effect (the polarizabilities of C and Cl atoms were taken from Ref. 39). The angular distributions look similar to those of Xe atoms,20 but do not exhibit the minima and maxima having appeared in the observed LAES signals of CCl4 . The numerical simulation confirms that the observed modulation patterns are the electron diffraction patterns of CCl4 reflecting its geometrical structure. We find that the visibility of the modulation in the LAED angular distributions of CCl4 is much higher than that in the conventional GED angular distribution obtained without a laser field (Fig. 4). This is because the intensity of the LAES signals is significantly small in the small scattering angle θ region (Fig. 3), which is an advantage of the LAED method in determining geometrical structure of molecules over the conventional GED method in which the huge signal intensity in the small θ region needs to be decreased by a rotating sector.1, 2
In conclusion, we recorded the LAED pattern of CCl4 as the angular distributions of the one-photon LAES signals (E = +¯ω and –¯ω). Through the comparison with the numerical simulations, we have confirmed that the observed diffraction patterns are reproduced by the field-free geometrical structure of CCl4 . It has been discussed in these years that geometrical structures of gas-phase molecules can be probed in real time by ultrafast X-ray diffraction using an X-ray free electron laser40, 41 as well as by photoelectron diffraction methods such as laser-induced electron diffraction.42, 43 Our present study shows that the LAED will also be a promising technique. If molecules are pumped by an ultrashort laser pulse and are probed by LAED, the temporal evolution of the geometrical structure of molecules, undergoing chemical bond breaking and rearrangement, can be determined as a series of snapshots of diffraction images with high precision (∼0.01 Å) as well as with high temporal resolution (
