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Ultrafast hydrogen migration in allene in intense laser fields: Evidence of two-body Coulomb explosion
Chemical Physics Letters 469 (2009) 255–260
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Ultrafast hydrogen migration in allene in intense laser fields: Evidence of two-body Coulomb explosion Huailiang Xu, Tomoya Okino, Kaoru Yamanouchi * Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
a r t i c l e
i n f o
Article history: Received 4 December 2008 In final form 30 December 2008 Available online 4 January 2009
a b s t r a c t Two-body Coulomb explosion of allene induced by an ultrashort (40 fs) intense laser field is investigated by the coincidence momentum imaging (CMI) method. From the CMI maps, two types of two-body þ þ 2þ þ þ Coulomb explosion pathways, C3 H2þ 4 ! CHm þ C2 H4m (m = 1–3) and C3 H4 ! C3 H4n þ Hn (n = 1–3), are þ þ , C H , and H shows that the chemical bond rearrangement securely identified. The formation of CHþ 2 3 3 3 associated with the ultrafast hydrogen migration occurs prior to the ionization into C3 H2þ 4 and that the extent of the hydrogen migration determines either one of the two initially identical C@C chemical bonds is broken. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The interaction of molecules with ultrashort intense laser fields has been an attractive research subject in these years both experimentally and theoretically [1]. In an intense laser field, the geometrical structure of molecules is strongly deformed, and molecules exhibit a variety of characteristic dynamical processes, such as laser-induced rearrangement of chemical bonds and Coulomb explosion [2–5]. In 2001, a method called coincidence momentum imaging (CMI) was introduced for studying the decomposition processes of molecules in intense laser fields [6]. By the CMI method, in which fragment ions originated from the Coulomb explosion of a single parent ion are detected in coincidence, the decomposition pathways can be identified definitively. For example, doubly charged methanol ions (CH3OH2+) formed in intense laser fields were shown to dissociate via two types of two-body Coulomb explosion pathways, CH3 OH2þ ! CHþ ð3nÞ þ 2þ þ ! Hþ OHþ m þ CHð3mÞ OH (m = 1–3) [7]. ð1þnÞ (n = 0–2) and CH3 OH It was also shown for a variety of hydrocarbon molecules that ultrafast hydrogen atom migration proceeds by ultrashort intense laser fields within a molecule [7–14]. Since such hydrogen migration is expected to induce further deformation of molecular structure and rearrangement of chemical bonds, the investigation of the ultrafast hydrogen migration will afford us a new strategy of controlling chemical-bond breaking and chemical-bond formation processes in intense laser fields through controlling the ultrafast migration of hydrogen atoms or protons within a molecule. In this Letter, we study for the first time the two-body Coulomb explosion processes of allene (CH2@C@CH2) in an ultrafast intense laser field (40 fs, 2 1013 W/cm2) using the CMI method. From the
* Corresponding author. Fax: +81 3 5689 7347. E-mail address: [email protected] (K. Yamanouchi). 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.12.097
CMI maps, two types of two-body Coulomb explosion pathways from doubly charged parent ion, C3 H2þ 4 , are securely identified, that is, the fragmentation pathways in which one of the two C–C bonds is broken, þ þ C3 H2þ 4 ! CHm þ C2 H4m
ðm ¼ 1—3Þ
and the fragmentation pathways in which
C3 H2þ 4
!
Hþn
þ
C3 Hþ4n
ðn ¼ 1—3Þ:
CHþ 3
ð1Þ Hþ n
is ejected,
ð2Þ
C2 Hþ 3
The formation of and in Eq. (1) and the formation of in Eq. (2) can be regarded as direct evidence that the hydrogen Hþ 3 atom migration proceeds prior to the Coulomb explosion. On the basis of the experimental evidence, we will show that the hydrogen migration proceeds within the period of an ultrashort laser pulse (40 fs) and that the extents of the hydrogen migration determines either one of the two initially equivalent C@C chemical bonds is broken. 2. Experimental The light source used in the experiments was a Ti:Sapphire femtosecond laser system (Pulsar 5000, Amplitude Technologies). The output pulses from a Ti:Sapphire oscillator (Femtosource S20, Femtolasers) were positively chirped to 100 ps in an aberration-free stretcher, and then, passed through an acousto-optic programmable dispersive filter (Dazzler, Fastlite), which controlled simultaneously the spectral phase and amplitude of the pulses. The stretched pulses were then regeneratively amplified in a regenerative amplifier with a repetition-rate at 5 kHz, and further amplified in a two-pass preamplifier and a cryogenically cooled four-pass amplifier. Finally, the amplified pulses were compressed by a two-grating compressor to 40 fs, which was measured by a SPIDER. The ultrashort laser pulses, whose pulse energy was
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Intensity (arb. units)
1
3
Hi+
C3Hm+
2+
C3H k
12
0
plates, and the surface of the detector were all set to be parallel to the plane formed by the molecular beam and laser beam axes. The spatial and temporal resolutions of the PSD were 0.255 mm and 0.5 ns, respectively. The details of the coincidence measurement are described in Ref. [6]. Briefly, the three-dimensional momentum vectors of ith fragment ions were determined by their positions (xi, yi) and arrival time (ti) on the detector plane. False coincidence events originating from the fragment ions generated from two or more parent ions in the interaction region were excluded by imposing the momentum P P conservation condition, j i P i j 6 ð ðdP 2x þ dP 2y þ dP2z ÞÞ1=2 B dP, where the momentum uncertainty dP was determined to be 1.4 104 u m s1 from the three-dimensional momentum distribution of singly-charged parent ions C3 Hþ 4 . In order to secure the coincidence conditions, the number of events of the generation of ionic species per laser shot was kept to be 0.55 events/pulse by lowering the pressure in the sample chamber to be 2.6 105 Pa during the experiment, so that the pressure in the main chamber became 1 107 Pa.
4
0 4
8
+
+
CH j 0
4
C2 Hl 3
0
3
0 0
10
20
30
40
m/z Fig. 1. Time-of-flight mass spectrum of allene in an intense laser field (40 fs, 2 1013 W/cm2).
adjusted to be 40 lJ by a half-wave plate and a polarizer, were introduced into an ultrahigh-vacuum chamber through a quartz lens (f = 15 cm) to achieve the laser field intensity of 2 1013 W/cm2 at the focal spot, which was estimated from the pulse duration (40 fs) and the radius (40 lm) of the focal spot measured by a CCD camera. The sample gas, allene (CH2@C@CH2) (98% purity, Matheson), was introduced into the sample vacuum chamber through a micro-syringe (0.51 mm/), and skimmed by a skimmer (0.48 mm/) to form a molecular beam on the side of the main ultrahigh vacuum chamber pumped differentially, whose base pressure was 1 108 Pa. The molecular beam and the laser beam crossed at right angles, and the ions generated at the laser focal spot in the molecular beam were projected onto a position-sensitive detector (PSD) with delay-line anodes readout (RoentDek DLD 80) by three equally spaced parallel-plate electrodes in the velocity mapping configuration [15]. The laser polarization direction, electrode
+
u m s-1
(a) CH (
3. Results and discussion 3.1. Coincidence ion images Fig. 1 shows the recorded time-of-flight (TOF) mass spectrum of the ionic species generated from C3H4 in the intense laser field. As þ 2þ þ assigned in Fig. 1, Hþ i (i = 1–3), CHj (j = 0–3), C3 Hk (k = 0–4), C2 Hl þ (l = 0–3), and C3 Hm (m = 0–4) are observed. Among the fragment þ þ ions, Hþ 3 , CH3 , and C2 H3 are noteworthy. These ions can only be generated after at least one hydrogen atom (or a proton) migrates from one end towards the other. In this study, we focus our attention to the CMI maps of the two-body Coulomb explosion processes of C3 H2þ 4 . The momentum imaging maps of CHþ m (m = 1–3) appearing in coincidence with C2 Hþ 4m are shown in Fig. 2a–c, which represent the two-body Cou-
+
= 1)
(b) CH2 (
+
(c) CH3 (
= 2)
100
100
0
0
0
-100
-100
-100
y /10
3
100
-100
0
-100
100
0
-100
100
0
= 3)
100
Signal Intensity
3 -1 x /10 u m s + 1.0 (d) CH
+ 1.0 (e) CH2
+ 1.0 (f) CH3
0.5
0.5
0.5
0.0 -90
-45
0
45
0.0 90 -90
-45
0
45
90
0.0 -90
-45
0
45
90
/deg þ 2þ Fig. 2. Observed two-dimensional coincidence momentum maps of (a) CH+, (b) CHþ 2 , (c) CH3 produced through the two-body Coulomb explosion processes of C3 H4 , and þ their angular distributions (d) CH+, (e) CHþ 2 , and (f) CH3 . The solid lines are the least-squares fits of the angular distribution to Eq. (7). The laser polarization direction (e) is set to be parallel with the py axis, as indicated by the arrow.
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+
u m s-1 3
y /10
+
+
(a) H ( = 1)
(c) H3 ( = 3)
(b) H2 ( = 2)
100
100
100
0
0
0
-100
-100
-100
-100
0
-100
100
0
-100
100
0
100
Signal Intensity
3 -1 x /10 u m s
(e) H2+
(d) H+
(f) H3+
1.0
1.0
1.0
0.5
0.5
0.5
0.0 -90
-45
0
45
0.0 90 -90
-45
0
0.0 90 -90
45
-45
0
45
90
/deg þ 2þ Fig. 3. Observed two-dimensional coincidence momentum maps of (a) H+, (b) Hþ 2 , and (c) H3 produced through the two-body Coulomb explosion processes of C3 H4 and their þ angular distributions (d) H+, (e) Hþ 2 , and (f) H3 . The solid lines are the least-squares fits of the angular distribution to Eq. (14).
hcos2 hi ¼
R
IðhÞ cos2 h sin hdh R IðhÞ sin hdh
ð3Þ
þ is calculated. For the C–C bond breaking pathways, CHþ m þ C 2 H4m (m = 1–3), hcos2hi = 0.41 (m = 1), 0.54 (m = 2) and 0.49 (m = 3) are þ obtained, and for the C–H bond breaking pathways, Hþ n þ C3 H4n , (n = 1–3), hcos2hi = 0.37 (n = 1), 0.38 (n = 2) and 0.39 (n = 3) are obtained, as listed in Table 1 and plotted in Fig. 5. The relatively large hcos2hi values for the C–C bond breaking pathways, representing the relatively short dissociation lifetime, þ may indicate that the precursor species CHþ m C2 H4m (m = 1–3)
+
4- m
(aa m= (a) =1 b m= m= 2 (b) (b (c m= (c) =3 +
+
Hn + C H -n 3 4
(d) n = 1 (e) n= =2 (f) n = 3
3.2. Fragment anisotropy The angular distributions, I(h), of the fragment ions CH+, CHþ 2, þ þ + and CHþ 3 are shown in Fig. 2d–f, and those of H , H2 , and H3 are shown in Fig. 3d–f, where h is the ejection angle of the fragment ions with respect to the laser polarization direction. For evaluation of the extent of anisotropy in the explosion process, the expectation value of the squared cosine defined as [7]
+
CHm + C2H
Signal Intensity /a.u.
lomb explosion pathways Eq. (1) through the C–C bond breaking. For m = 2 and 3, the CMI maps exhibit a pair of clear crescent-like patterns, while the extent of the anisotropy for m = 1 is less pronounced. In Fig. 3a–c, the CMI maps of Hþ n (n = 1–3) appearing in coincidence with C3 Hþ 4n are shown, representing the two-body Coulomb explosion pathways Eq. (2) through the C–H bond breaking. The signals appearing in the central part of Fig. 3a and b are the accidental false coincidence events from residual H2O in the vacuum chamber. For all the three pathways (n = 1–3), the extent of the anisotropy is found to be much lower than the m = 2 and 3 channels of the C–C bond breaking. From the three-dimensional momentum distributions of the fragment ions, the distributions of the released kinetic energy Ekin for the six explosion pathways shown in Fig. 4 are obtained, where Ekin is the sum of the kinetic energy released from a pair of the fragment ions. It can be seen that the kinetic energy distributions are peaked at 6.2 eV for the C–C bond breaking pathways, and at 4.6 eV for the C–H bond breaking pathways. Under the assumption that the potential curve along the dissociation coordinate of the two-body Coulomb explosion is expressed as a repulsive Coulombic potential between two charge centers separated by the length R, the released kinetic energy Ekin can be written as Ekin = q1q2/(4pe0R) where q1 and q2 are the charges of the two fragment moieties. For the C–C bond breaking, þ CHþ m C2 H4m (m = 1–3), R = 2.3 Å is obtained from Ekin = 6.2 eV, þ and for the C–H bond breaking, Hþ n C3 H4n (n = 1–3), R = 3.1 Å is obtained from Ekin = 4.6 eV.
2
4
6 Ekin / eV
8
10
Fig. 4. Kinetic energy distributions of the fragment ion pairs (a) CHþ þ C2 Hþ 3 , (b) þ þ þ þ þ þ þ þ þ CHþ 2 þ C2 H2 , (c) CH3 þ C2 H , (d) H þ C3 H3 , (e) H2 þ C3 H2 , and (f) H3 þ C3 H .
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Table 1 The hcos2hi values and yields of the fragment ions, ejected through the two-body Coulomb explosion of C3 H2þ 4 , and the parameters obtained by least-squares fits. 2
Explosion pathways
a2
a4
a6
Yields
hcos hi
(a) C–C bond breakinga CHþ þ C2 Hþ 3 ðm ¼ 1Þ þ CHþ 2 þ C2 H2 ðm ¼ 2Þ þ CH3 þ C2 Hþ ðm ¼ 3Þ
0.60(5) 1.61(9) 1.24(14)
0.55(6) 1.42(9) 1.05(15)
0.10(6) 0.94(8) 0.33(12)
0.08 1 0.03
0.41 0.54 0.49
Explosion pathways
h0m =deg
sx
s/ps
Yields
hcos2hi
(b) C–H bond breakingb þ C3 Hþ 3 þ H ðn ¼ 1Þ þ C3 Hþ 2 þ H2 ðn ¼ 2Þ C3 Hþ þ Hþ 3 ðn ¼ 3Þ
31(2) 23(2) 12(4)
>5.0 >5.0 3.2(1.1)
>1.9 >1.9 1.2(4)
1 0.03 0.08
0.37 0.38 0.39
a b
Fits to Eq. (7). Fits to Eq. (14).
are prepared on the mostly repulsive Coulombic potential energy surfaces and dissociate immediately. On the other hand, the relatively small hcos2hi values for the C–H bond breaking pathways, representing a relatively long dissociation lifetime, may indicate þ that the precursor species Hþ n C3 H4n (n = 1–3) are trapped in the metastable quasi-bound well of the potential energy surfaces, in a similar manner to that in the C–H bond breaking pathways of methanol in intense laser fields [7]. þ The conjecture that the precursor species, CHþ m C2 H4m þ (m = 1–3) and Hþ C H (n = 1–3), are prepared on the potential 3 4n n energy surfaces having totally different shapes is also supported by the distributions of the kinetic energy release of the fragments produced after the C–C and C–H bond breaking processes shown in Fig. 4. The kinetic energy releases peaked at 6.2 eV for the C–C bond breaking, representing a relatively short distance between two moieties (R 2.3 Å) from which the Coulomb explosion proceeds, indicate the precursor states are prepared on the steep slope of the Coulombic repulsive wall of the potential energy surface, and the C–C bond breaking proceeds immediately. On the other hand, the kinetic energy releases peaked at 4.6 eV for the C–H bond breaking processes indicate that the distance between the two moieties at the top of the barrier of the quasi-bound well is relatively long (R 3.1 Å). In the following sections, we will separately discuss the two types of the decomposition pathways, i.e., those of the C–C and C–H bond breaking processes. 3.3. Decomposition pathways 3.3.1. C–C bond breaking Among the fragment ions originating from the C–C bond breakþ ing, the CHþ 2 signals in Fig. 2b detected in coincidence with C2 H2 can unambiguously be assigned to the decomposition process,
+
CHm
2
< cos >
0.5
0.4 +
Hn
þ þ CH2 CCH2þ 2 ! CH2 þ C2 H2
ðm ¼ 2Þ:
As shown in Fig. 2c, it is also confirmed that coincidence with C2 Hþ as þ þ CH2 CCH2þ 2 ! CH3 þ C2 H
CHþ 3
ðm ¼ 3Þ:
ð4Þ CHþ 3
is produced in
ð5Þ
+
The formation of and C2H shows clearly that the migration of one hydrogen atom (or a proton) proceeds from one of the two methylene group to the other within an allene molecule to form C2 Hþ CHþ 3 , and then, the C C bond is broken. The third C–C bond breaking pathway, þ þ CH2 CCH2þ 2 ! CH þ C2 H3
ðm ¼ 1Þ
ð6Þ
is confirmed by the coincident formation of CH+ and C2 Hþ 3 shown in Fig. 2a. In this pathway, a hydrogen atom (or a proton) in one of the two methylene groups migrates to form CHþ C2 Hþ 3 , and then, the C C bond is broken. The relatively large hcos2hi values shown in Fig. 5 for the C–C bond breaking pathway without hydrogen atom migration (m = 2) and that with the migration of one hydrogen atom to the other end (m = 3) indicate that, for these channels, the allene molecules whose C@C@C skeletal axis is directed along the laser polarization direction are doubly ionized efficiently, and that the þ þ þ are prepared on precursor species CHþ 2 C2 H2 and CH3 C2 H the repulsive Coulombic potential energy surfaces so that the two-body Coulomb explosion proceeds more rapidly than the þ overall molecular rotation. After the formation of CHþ 3 C2 H within the intense laser field, the probability that a hydrogen atom jumps between the two distant moieties, CH3+ and C2H+, may be significantly small. This means that the hydrogen migration is expected to stop prior to the CC bond breaking. Since the doubly þ charged precursor species, CHþ m C2 H4m , are considered to be produced in the intense laser field, the hydrogen migration processes are expected to proceed within the period of the ultrafast laser pulse (40 fs). This is consistent with our previous conjecture that the hydrogen migration processes in methanol in intense laser fields take place within the laser pulse duration (60 fs) prior to the C–O bond breaking [7]. As shown in Fig. 5, the hcos2hi value for the C–C bond breaking pathway of m = 1 is smaller than that for the pathways of m = 2 and þ m = 3. Since all the three precursor species CHþ m C2 H4m (m = 1– 3) are prepared on the Coulombic repulsive potential after the interaction with the ultrashort intense laser field, they are expected to dissociate immediately into two fragment ions. Therefore, the difference among the hcos2hi values may not be ascribed to the difference in the lifetimes of these precursor species, but rather reflect the geometrical structures of the precursor species. is exThe migration of the hydrogen atom (or proton) in C3 H2þ 4 pected to induce the structural deformation of the C–C–C skeleton, leading to the deflection of the ejection direction of CH+ and CHþ 3 with respect to the laser polarization. The smaller hcos2hi value for the m = 1 pathway, in which CH+ is ejected, may reflect the larger bending angle, \C–C–C, in the precursor species CHþ C2 Hþ 3 þ than in CHþ 3 C2 H . This deformation of the skeletal structure can be described as that induced by the rehybridization of chemical bonds associated with the hydrogen migration in intense laser fields. The observed angular distributions shown in Fig. 2d–f can be fitted to the Legendre expansion [5],
IðhÞ ¼ 1 þ
X
aL PL ðcos hÞ ðL ¼ 2; 4; 6Þ;
ð7Þ
L
0.3 1
2 Number of hydrogen atoms
3
þ Fig. 5. Schematic diagram for the hcos2hi values of the fragment ions, CHþ m and Hn .
where PL denotes the Legendre polynomial and aL is the expansion coefficient. The aL values (L = 2, 4, 6) for the three explosion pathways through the C–C bond breaking are determined as listed in
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Table 1, and the best fit distributions are drawn by the solid curves in Fig. 2d–f. þ Table 1 shows that the relative yields of CHþ m C2 H4m for the m = 1 and 3 pathways with respect to the m = 2 pathway are 0.08 and 0.03, respectively. The differences in the relative yields of CH+ and CHþ 3 may reflect the chemical-bond rearranging dynamics associated with the ultrafast hydrogen atom migration in allene. To form the precursor species CHþ C2 Hþ 3 , the hydrogen atom migrating from one of the two methylene groups would be trapped in a specific area around the central carbon site of the allene molþ ecule. In the formation of CHþ 3 C2 H , however, the hydrogen atom migrating towards the other end is expected to pass through + the central carbon area. The lower yield of CHþ 3 than CH is consistent with this picture that a hydrogen atom (or a proton) migrates first into the central carbon area, and then, proceeds to reach the other end. 3.3.2. C–H bond breaking pathways From the CMI measurement, the existence of the following three types of decomposition pathways is securely identified: þ þ CH2 CCH2þ 2 ! H þ C3 H3
ðn ¼ 1Þ;
ð8Þ
þ þ CH2 CCH2þ 2 ! H2 þ C3 H2
ðn ¼ 2Þ;
ð9Þ
CH2 CCH2þ 2
ðn ¼ 3Þ:
ð10Þ
!
Hþ3
þ
þ C3 H
Hþ n
C3 Hþ 4n
The relative yields of for n = 2 and 3 pathways with respect to the n = 1 pathway are 0.03 and 0.08, respectively. The ejection of Hþ 3 indicates that the migration of one hydrogen atom proceeds from one methylene group to the other within the allene molecule prior to the formation of Hþ 3. As shown in Fig. 5, the hcos2hi values for the three C–H bond breaking pathways in the range of 0.37–0.39 show that the angular distributions are more isotropic than the C–C bond breaking. This þ suggests that the precursor species Hþ n C3 H4n (n = 1–3) from þ which Hn is ejected are prepared in the metastable quasi-bound area of the potential energy surfaces, and that their dissociation lifetimes are comparable with the rotational period of the parent allene molecule. Since the bond breaking proceeds long after the period of the interaction with the intense laser field, it can be regarded as a unimolecular decomposition process. When diatomic or linear triatomic molecules rotate freely in space, the rotational period of the overall molecular rotation, srot, can be written as [16]
srot
sffiffiffiffiffiffiffiffiffiffiffi 2 4ph ¼ ¼ ; x kTB0 2p
ð11Þ
where T is the temperature and B0 is the rotational constant. When the rotational motion of allene is approximated as that of linear polyatomic molecules, the rotational period of allene is estimated to be srot = 2.4 ps using the rotational constant B0 = 0.296 cm1 of allene [17] and T = 300 K, showing that the dissociation lifetimes þ of the precursor states Hþ n C3 H4n may roughly be 2–3 ps. It should be noted that the angular distributions for the C–H bond breaking pathways could also be influenced by the ejection direction of Hþ n with respect to the molecular principal axis. Since the C–H bond breaking processes can be regarded as unimolecular dissociation proceeding long after the interaction with the intense laser field, the coefficients aL in Eq. (7) can be expressed as [8,16]
aL ¼ bL cL PL ðcos h0m Þ ðL ¼ 2; 4; 6Þ;
ð12Þ
where bL reflects the angular distribution of the molecular principal axis of the parent molecules with respect to the laser polarization direction, h0m is the ejection angle of the fragment ions with respect to the molecular principal axis of the parent ion, and cL [8,16],
cL ¼
L=2 Y ð1=sxÞ2 þ ð2k 1Þ2 k¼1
ð1=sxÞ2 þ ð2kÞ2
;
ð13Þ
represents the effect of the molecular rotation, where s denotes the dissociation lifetime of the precursor species. Thus, Eq. (7) can be expressed as
IðhÞ ¼ 1 þ
X
bL cL PL ðcos h0m ÞPL ðcos hÞ ðL ¼ 2; 4; 6Þ:
ð14Þ
L
If it is assumed that the molecular principal axis of the precurþ sor species Hþ n C3 H4n (n = 1–3) is aligned along the same direction as that of the parent ion CH2 C2 H2þ 2 (m = 2 pathway) from which the dissociation proceeds immediately, and that the ejection 2þ direction of CHþ 2 from CH2 C2 H2 is along the molecular axis, the aL coefficients determined for the m = 2 pathway can be adopted as the bL values. This is because the expression of Eq. (14) becomes identical to Eq. (7) (i.e., aL = bL), when both h0m and s are set to be zero. The observed angular distributions of the fragment ions Hþ n (n = 1–3) through the C–H bond breaking pathways are fitted to Eq. (14) by the least-squares analysis. The best-fit distributions are shown in Fig. 3d–f with the solid lines and the optimized parameters, h0m and sx, are determined as listed in Table 1, even though these two fitting parameters are strongly correlated with each other for the n = 3 pathway. From the determined sx values, þ the dissociation lifetimes of the precursor species, Hþ n C3 H4n (n = 1–3) are determined to be s (n = 1) > 1.9 ps, s (n = 2) > 1.9 ps, and s (n = 3) = 1.2 (4) ps. These values, comparable to the rotational lifetimes (srot = 2.4 ps) of parent allene molecules, are consistent þ with our predictions that the precursor species, Hþ n C3 H4n (n = 1–3) are prepared in the metastable states. The small ejection 0 angle of the fragment ions Hþ 3 , hm ¼ 12ð4Þ , indicates that the fragtends to be ejected along the molecular principal axis, ment ion Hþ 3 whereas the relatively large ejection angles, h0m ¼ 31ð2Þ for the H+ ejection and h0m ¼ 23ð2Þ for the Hþ 2 ejection indicate that their ejection directions with respect to the molecular principal axis are more deflected than the Hþ 3 case. In view of the local geometrical structure of the terminal methylene (CH2) part of allene, the large ejection angle obtained for H+ is understandable if the C–H is considered to be stretched along its chemical bond. On the other hand, if the two hydrogen atoms in the terminal CH2 are assumed to be stretched simultaneously þ along the C–C–C direction to form Hþ 2 C3 H2 , the ejection angle 0 is expected to be h 0 , which is inconsistent with the of Hþ m 2 present results, h0m 23ð2Þ . Therefore, the relatively large deflecþ tion angle of Hþ 2 indicates that H2 is formed after the migration of H from the other terminal CH2 or after one of the two hydrogen atoms in the terminal CH2 moves towards the original position of the other hydrogen atom in the same CH2 group.
4. Summary The two-body Coulomb explosion of allene induced by an ultrafast intense laser field has been investigated by using the coincidence momentum imaging method. Two types of the fragmentation pathways through the C–C bond breaking, þ þ C3 H2þ 4 ! CHm þ C2 H4m (m = 1–3), and the C–H bond breaking, þ þ ! H þ C H (n = 1–3), have been identified C3 H2þ 3 4n 4 n unambiguously. þ þ It is shown from the ejection of Hþ 3 , CH3 , and C2 H3 that the hydrogen migration proceeds prior to the Coulomb explosion. In addition, the differences in the hcos2hi values between the C–C and C–H bond breaking processes suggest that the precursor speþ cies CHþ m C2 H4m (m = 1–3) are prepared on the mostly repulsive Coulombic potential energy surfaces, and that the precursor
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þ species C3 Hþ 4n Hn (n = 1–3) tend to be trapped in the metastable quasi-bound well of the potential energy surfaces. It is also inferred for the C–C bond breaking pathways that the hydrogen migration proceeds within the period of the ultrafast laser pulse, and that the extent of the hydrogen migration determines either one of the two initially equivalent C@C chemical bonds is broken within the allene molecule. This finding provides a new strategy for the breaking and/or generation of specific chemical bonds via controlling the hydrogen migration within a hydrocarbon molecule by a suitable designing of ultrashort intense laser pulses.
Acknowledgements The present research was supported by the following two grants from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan: the Grant-in-Aid for Specially Promoted Research on Ultrafast Hydrogen Migration (#19002006), and the Grant-in-Aid for Global COE Program for Chemistry Innovation.
References [1] K. Yamanouchi, S.L. Chin, P. Agostini, G. Ferrante (Eds.), Progress in Ultrafast Intense Laser Science III, Springer, Berlin, Heidelberg, 2008. [2] K. Yamanouchi, Science 295 (2002) 1659. [3] A.D. Bandrauk, E.S. Sedik, C.F. Matta, J. Chem. Phys. 121 (2004) 7764. [4] A.N. Markevitch, D.A. Romanov, S.M. Smith, R.J. Levis, Phys. Rev. Lett. 96 (2006) 163002. [5] A. Assion, T. Baumert, U. Weichmann, G. Gerber, Phys. Rev. Lett. 86 (2001) 5695. [6] H. Hasegawa, A. Hishikawa, K. Yamanouchi, Chem. Phys. Lett. 349 (2001) 57. [7] T. Okino et al., Chem. Phys. Lett. 419 (2006) 223. [8] A. Hishikawa, H. Hasegawa, K. Yamanouchi, J. Electron Spectrosc. Relat. Phenom. 141 (2004) 195. [9] T. Okino et al., Chem. Phys. Lett. 423 (2006) 220. [10] T. Okino et al., J. Phys. B 39 (2006) S515. [11] A.S. Alnaser et al., J. Phys. B 39 (2006) S485. [12] R. Itakura, P. Liu, Y. Furukawa, T. Okino, K. Yamanouchi, J. Chem. Phys. 127 (2007) 104306. [13] A. Hishikawa, A. Matsuda, E.J. Takahashi, M. Fushitani, J. Chem. Phys. 128 (2008) 084302. [14] K. Hoshina, Y. Furukawa, T. Okino, K. Yamanouchi, J. Chem. Phys. 129 (2008) 104302. [15] A.T.J.B. Eppink, D.H. Parker, Rev. Sci. Instrum. 68 (1997) 3477. [16] G.E. Busch, K.R. Wilson, J. Chem. Phys. 56 (1972) 3638. [17] A.A. Auer, J. Gauss, Phys. Chem. Chem. Phys. 3 (2001) 3001.
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Ultrafast hydrogen migration in allene in intense laser fields: Evidence of two-body Coulomb explosion Huailiang Xu, Tomoya Okino, Kaoru Yamanouchi * Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
a r t i c l e
i n f o
Article history: Received 4 December 2008 In final form 30 December 2008 Available online 4 January 2009
a b s t r a c t Two-body Coulomb explosion of allene induced by an ultrashort (40 fs) intense laser field is investigated by the coincidence momentum imaging (CMI) method. From the CMI maps, two types of two-body þ þ 2þ þ þ Coulomb explosion pathways, C3 H2þ 4 ! CHm þ C2 H4m (m = 1–3) and C3 H4 ! C3 H4n þ Hn (n = 1–3), are þ þ , C H , and H shows that the chemical bond rearrangement securely identified. The formation of CHþ 2 3 3 3 associated with the ultrafast hydrogen migration occurs prior to the ionization into C3 H2þ 4 and that the extent of the hydrogen migration determines either one of the two initially identical C@C chemical bonds is broken. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The interaction of molecules with ultrashort intense laser fields has been an attractive research subject in these years both experimentally and theoretically [1]. In an intense laser field, the geometrical structure of molecules is strongly deformed, and molecules exhibit a variety of characteristic dynamical processes, such as laser-induced rearrangement of chemical bonds and Coulomb explosion [2–5]. In 2001, a method called coincidence momentum imaging (CMI) was introduced for studying the decomposition processes of molecules in intense laser fields [6]. By the CMI method, in which fragment ions originated from the Coulomb explosion of a single parent ion are detected in coincidence, the decomposition pathways can be identified definitively. For example, doubly charged methanol ions (CH3OH2+) formed in intense laser fields were shown to dissociate via two types of two-body Coulomb explosion pathways, CH3 OH2þ ! CHþ ð3nÞ þ 2þ þ ! Hþ OHþ m þ CHð3mÞ OH (m = 1–3) [7]. ð1þnÞ (n = 0–2) and CH3 OH It was also shown for a variety of hydrocarbon molecules that ultrafast hydrogen atom migration proceeds by ultrashort intense laser fields within a molecule [7–14]. Since such hydrogen migration is expected to induce further deformation of molecular structure and rearrangement of chemical bonds, the investigation of the ultrafast hydrogen migration will afford us a new strategy of controlling chemical-bond breaking and chemical-bond formation processes in intense laser fields through controlling the ultrafast migration of hydrogen atoms or protons within a molecule. In this Letter, we study for the first time the two-body Coulomb explosion processes of allene (CH2@C@CH2) in an ultrafast intense laser field (40 fs, 2 1013 W/cm2) using the CMI method. From the
* Corresponding author. Fax: +81 3 5689 7347. E-mail address: [email protected] (K. Yamanouchi). 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.12.097
CMI maps, two types of two-body Coulomb explosion pathways from doubly charged parent ion, C3 H2þ 4 , are securely identified, that is, the fragmentation pathways in which one of the two C–C bonds is broken, þ þ C3 H2þ 4 ! CHm þ C2 H4m
ðm ¼ 1—3Þ
and the fragmentation pathways in which
C3 H2þ 4
!
Hþn
þ
C3 Hþ4n
ðn ¼ 1—3Þ:
CHþ 3
ð1Þ Hþ n
is ejected,
ð2Þ
C2 Hþ 3
The formation of and in Eq. (1) and the formation of in Eq. (2) can be regarded as direct evidence that the hydrogen Hþ 3 atom migration proceeds prior to the Coulomb explosion. On the basis of the experimental evidence, we will show that the hydrogen migration proceeds within the period of an ultrashort laser pulse (40 fs) and that the extents of the hydrogen migration determines either one of the two initially equivalent C@C chemical bonds is broken. 2. Experimental The light source used in the experiments was a Ti:Sapphire femtosecond laser system (Pulsar 5000, Amplitude Technologies). The output pulses from a Ti:Sapphire oscillator (Femtosource S20, Femtolasers) were positively chirped to 100 ps in an aberration-free stretcher, and then, passed through an acousto-optic programmable dispersive filter (Dazzler, Fastlite), which controlled simultaneously the spectral phase and amplitude of the pulses. The stretched pulses were then regeneratively amplified in a regenerative amplifier with a repetition-rate at 5 kHz, and further amplified in a two-pass preamplifier and a cryogenically cooled four-pass amplifier. Finally, the amplified pulses were compressed by a two-grating compressor to 40 fs, which was measured by a SPIDER. The ultrashort laser pulses, whose pulse energy was
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Intensity (arb. units)
1
3
Hi+
C3Hm+
2+
C3H k
12
0
plates, and the surface of the detector were all set to be parallel to the plane formed by the molecular beam and laser beam axes. The spatial and temporal resolutions of the PSD were 0.255 mm and 0.5 ns, respectively. The details of the coincidence measurement are described in Ref. [6]. Briefly, the three-dimensional momentum vectors of ith fragment ions were determined by their positions (xi, yi) and arrival time (ti) on the detector plane. False coincidence events originating from the fragment ions generated from two or more parent ions in the interaction region were excluded by imposing the momentum P P conservation condition, j i P i j 6 ð ðdP 2x þ dP 2y þ dP2z ÞÞ1=2 B dP, where the momentum uncertainty dP was determined to be 1.4 104 u m s1 from the three-dimensional momentum distribution of singly-charged parent ions C3 Hþ 4 . In order to secure the coincidence conditions, the number of events of the generation of ionic species per laser shot was kept to be 0.55 events/pulse by lowering the pressure in the sample chamber to be 2.6 105 Pa during the experiment, so that the pressure in the main chamber became 1 107 Pa.
4
0 4
8
+
+
CH j 0
4
C2 Hl 3
0
3
0 0
10
20
30
40
m/z Fig. 1. Time-of-flight mass spectrum of allene in an intense laser field (40 fs, 2 1013 W/cm2).
adjusted to be 40 lJ by a half-wave plate and a polarizer, were introduced into an ultrahigh-vacuum chamber through a quartz lens (f = 15 cm) to achieve the laser field intensity of 2 1013 W/cm2 at the focal spot, which was estimated from the pulse duration (40 fs) and the radius (40 lm) of the focal spot measured by a CCD camera. The sample gas, allene (CH2@C@CH2) (98% purity, Matheson), was introduced into the sample vacuum chamber through a micro-syringe (0.51 mm/), and skimmed by a skimmer (0.48 mm/) to form a molecular beam on the side of the main ultrahigh vacuum chamber pumped differentially, whose base pressure was 1 108 Pa. The molecular beam and the laser beam crossed at right angles, and the ions generated at the laser focal spot in the molecular beam were projected onto a position-sensitive detector (PSD) with delay-line anodes readout (RoentDek DLD 80) by three equally spaced parallel-plate electrodes in the velocity mapping configuration [15]. The laser polarization direction, electrode
+
u m s-1
(a) CH (
3. Results and discussion 3.1. Coincidence ion images Fig. 1 shows the recorded time-of-flight (TOF) mass spectrum of the ionic species generated from C3H4 in the intense laser field. As þ 2þ þ assigned in Fig. 1, Hþ i (i = 1–3), CHj (j = 0–3), C3 Hk (k = 0–4), C2 Hl þ (l = 0–3), and C3 Hm (m = 0–4) are observed. Among the fragment þ þ ions, Hþ 3 , CH3 , and C2 H3 are noteworthy. These ions can only be generated after at least one hydrogen atom (or a proton) migrates from one end towards the other. In this study, we focus our attention to the CMI maps of the two-body Coulomb explosion processes of C3 H2þ 4 . The momentum imaging maps of CHþ m (m = 1–3) appearing in coincidence with C2 Hþ 4m are shown in Fig. 2a–c, which represent the two-body Cou-
+
= 1)
(b) CH2 (
+
(c) CH3 (
= 2)
100
100
0
0
0
-100
-100
-100
y /10
3
100
-100
0
-100
100
0
-100
100
0
= 3)
100
Signal Intensity
3 -1 x /10 u m s + 1.0 (d) CH
+ 1.0 (e) CH2
+ 1.0 (f) CH3
0.5
0.5
0.5
0.0 -90
-45
0
45
0.0 90 -90
-45
0
45
90
0.0 -90
-45
0
45
90
/deg þ 2þ Fig. 2. Observed two-dimensional coincidence momentum maps of (a) CH+, (b) CHþ 2 , (c) CH3 produced through the two-body Coulomb explosion processes of C3 H4 , and þ their angular distributions (d) CH+, (e) CHþ 2 , and (f) CH3 . The solid lines are the least-squares fits of the angular distribution to Eq. (7). The laser polarization direction (e) is set to be parallel with the py axis, as indicated by the arrow.
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H. Xu et al. / Chemical Physics Letters 469 (2009) 255–260
+
u m s-1 3
y /10
+
+
(a) H ( = 1)
(c) H3 ( = 3)
(b) H2 ( = 2)
100
100
100
0
0
0
-100
-100
-100
-100
0
-100
100
0
-100
100
0
100
Signal Intensity
3 -1 x /10 u m s
(e) H2+
(d) H+
(f) H3+
1.0
1.0
1.0
0.5
0.5
0.5
0.0 -90
-45
0
45
0.0 90 -90
-45
0
0.0 90 -90
45
-45
0
45
90
/deg þ 2þ Fig. 3. Observed two-dimensional coincidence momentum maps of (a) H+, (b) Hþ 2 , and (c) H3 produced through the two-body Coulomb explosion processes of C3 H4 and their þ angular distributions (d) H+, (e) Hþ 2 , and (f) H3 . The solid lines are the least-squares fits of the angular distribution to Eq. (14).
hcos2 hi ¼
R
IðhÞ cos2 h sin hdh R IðhÞ sin hdh
ð3Þ
þ is calculated. For the C–C bond breaking pathways, CHþ m þ C 2 H4m (m = 1–3), hcos2hi = 0.41 (m = 1), 0.54 (m = 2) and 0.49 (m = 3) are þ obtained, and for the C–H bond breaking pathways, Hþ n þ C3 H4n , (n = 1–3), hcos2hi = 0.37 (n = 1), 0.38 (n = 2) and 0.39 (n = 3) are obtained, as listed in Table 1 and plotted in Fig. 5. The relatively large hcos2hi values for the C–C bond breaking pathways, representing the relatively short dissociation lifetime, þ may indicate that the precursor species CHþ m C2 H4m (m = 1–3)
+
4- m
(aa m= (a) =1 b m= m= 2 (b) (b (c m= (c) =3 +
+
Hn + C H -n 3 4
(d) n = 1 (e) n= =2 (f) n = 3
3.2. Fragment anisotropy The angular distributions, I(h), of the fragment ions CH+, CHþ 2, þ þ + and CHþ 3 are shown in Fig. 2d–f, and those of H , H2 , and H3 are shown in Fig. 3d–f, where h is the ejection angle of the fragment ions with respect to the laser polarization direction. For evaluation of the extent of anisotropy in the explosion process, the expectation value of the squared cosine defined as [7]
+
CHm + C2H
Signal Intensity /a.u.
lomb explosion pathways Eq. (1) through the C–C bond breaking. For m = 2 and 3, the CMI maps exhibit a pair of clear crescent-like patterns, while the extent of the anisotropy for m = 1 is less pronounced. In Fig. 3a–c, the CMI maps of Hþ n (n = 1–3) appearing in coincidence with C3 Hþ 4n are shown, representing the two-body Coulomb explosion pathways Eq. (2) through the C–H bond breaking. The signals appearing in the central part of Fig. 3a and b are the accidental false coincidence events from residual H2O in the vacuum chamber. For all the three pathways (n = 1–3), the extent of the anisotropy is found to be much lower than the m = 2 and 3 channels of the C–C bond breaking. From the three-dimensional momentum distributions of the fragment ions, the distributions of the released kinetic energy Ekin for the six explosion pathways shown in Fig. 4 are obtained, where Ekin is the sum of the kinetic energy released from a pair of the fragment ions. It can be seen that the kinetic energy distributions are peaked at 6.2 eV for the C–C bond breaking pathways, and at 4.6 eV for the C–H bond breaking pathways. Under the assumption that the potential curve along the dissociation coordinate of the two-body Coulomb explosion is expressed as a repulsive Coulombic potential between two charge centers separated by the length R, the released kinetic energy Ekin can be written as Ekin = q1q2/(4pe0R) where q1 and q2 are the charges of the two fragment moieties. For the C–C bond breaking, þ CHþ m C2 H4m (m = 1–3), R = 2.3 Å is obtained from Ekin = 6.2 eV, þ and for the C–H bond breaking, Hþ n C3 H4n (n = 1–3), R = 3.1 Å is obtained from Ekin = 4.6 eV.
2
4
6 Ekin / eV
8
10
Fig. 4. Kinetic energy distributions of the fragment ion pairs (a) CHþ þ C2 Hþ 3 , (b) þ þ þ þ þ þ þ þ þ CHþ 2 þ C2 H2 , (c) CH3 þ C2 H , (d) H þ C3 H3 , (e) H2 þ C3 H2 , and (f) H3 þ C3 H .
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Table 1 The hcos2hi values and yields of the fragment ions, ejected through the two-body Coulomb explosion of C3 H2þ 4 , and the parameters obtained by least-squares fits. 2
Explosion pathways
a2
a4
a6
Yields
hcos hi
(a) C–C bond breakinga CHþ þ C2 Hþ 3 ðm ¼ 1Þ þ CHþ 2 þ C2 H2 ðm ¼ 2Þ þ CH3 þ C2 Hþ ðm ¼ 3Þ
0.60(5) 1.61(9) 1.24(14)
0.55(6) 1.42(9) 1.05(15)
0.10(6) 0.94(8) 0.33(12)
0.08 1 0.03
0.41 0.54 0.49
Explosion pathways
h0m =deg
sx
s/ps
Yields
hcos2hi
(b) C–H bond breakingb þ C3 Hþ 3 þ H ðn ¼ 1Þ þ C3 Hþ 2 þ H2 ðn ¼ 2Þ C3 Hþ þ Hþ 3 ðn ¼ 3Þ
31(2) 23(2) 12(4)
>5.0 >5.0 3.2(1.1)
>1.9 >1.9 1.2(4)
1 0.03 0.08
0.37 0.38 0.39
a b
Fits to Eq. (7). Fits to Eq. (14).
are prepared on the mostly repulsive Coulombic potential energy surfaces and dissociate immediately. On the other hand, the relatively small hcos2hi values for the C–H bond breaking pathways, representing a relatively long dissociation lifetime, may indicate þ that the precursor species Hþ n C3 H4n (n = 1–3) are trapped in the metastable quasi-bound well of the potential energy surfaces, in a similar manner to that in the C–H bond breaking pathways of methanol in intense laser fields [7]. þ The conjecture that the precursor species, CHþ m C2 H4m þ (m = 1–3) and Hþ C H (n = 1–3), are prepared on the potential 3 4n n energy surfaces having totally different shapes is also supported by the distributions of the kinetic energy release of the fragments produced after the C–C and C–H bond breaking processes shown in Fig. 4. The kinetic energy releases peaked at 6.2 eV for the C–C bond breaking, representing a relatively short distance between two moieties (R 2.3 Å) from which the Coulomb explosion proceeds, indicate the precursor states are prepared on the steep slope of the Coulombic repulsive wall of the potential energy surface, and the C–C bond breaking proceeds immediately. On the other hand, the kinetic energy releases peaked at 4.6 eV for the C–H bond breaking processes indicate that the distance between the two moieties at the top of the barrier of the quasi-bound well is relatively long (R 3.1 Å). In the following sections, we will separately discuss the two types of the decomposition pathways, i.e., those of the C–C and C–H bond breaking processes. 3.3. Decomposition pathways 3.3.1. C–C bond breaking Among the fragment ions originating from the C–C bond breakþ ing, the CHþ 2 signals in Fig. 2b detected in coincidence with C2 H2 can unambiguously be assigned to the decomposition process,
+
CHm
2
< cos >
0.5
0.4 +
Hn
þ þ CH2 CCH2þ 2 ! CH2 þ C2 H2
ðm ¼ 2Þ:
As shown in Fig. 2c, it is also confirmed that coincidence with C2 Hþ as þ þ CH2 CCH2þ 2 ! CH3 þ C2 H
CHþ 3
ðm ¼ 3Þ:
ð4Þ CHþ 3
is produced in
ð5Þ
+
The formation of and C2H shows clearly that the migration of one hydrogen atom (or a proton) proceeds from one of the two methylene group to the other within an allene molecule to form C2 Hþ CHþ 3 , and then, the C C bond is broken. The third C–C bond breaking pathway, þ þ CH2 CCH2þ 2 ! CH þ C2 H3
ðm ¼ 1Þ
ð6Þ
is confirmed by the coincident formation of CH+ and C2 Hþ 3 shown in Fig. 2a. In this pathway, a hydrogen atom (or a proton) in one of the two methylene groups migrates to form CHþ C2 Hþ 3 , and then, the C C bond is broken. The relatively large hcos2hi values shown in Fig. 5 for the C–C bond breaking pathway without hydrogen atom migration (m = 2) and that with the migration of one hydrogen atom to the other end (m = 3) indicate that, for these channels, the allene molecules whose C@C@C skeletal axis is directed along the laser polarization direction are doubly ionized efficiently, and that the þ þ þ are prepared on precursor species CHþ 2 C2 H2 and CH3 C2 H the repulsive Coulombic potential energy surfaces so that the two-body Coulomb explosion proceeds more rapidly than the þ overall molecular rotation. After the formation of CHþ 3 C2 H within the intense laser field, the probability that a hydrogen atom jumps between the two distant moieties, CH3+ and C2H+, may be significantly small. This means that the hydrogen migration is expected to stop prior to the CC bond breaking. Since the doubly þ charged precursor species, CHþ m C2 H4m , are considered to be produced in the intense laser field, the hydrogen migration processes are expected to proceed within the period of the ultrafast laser pulse (40 fs). This is consistent with our previous conjecture that the hydrogen migration processes in methanol in intense laser fields take place within the laser pulse duration (60 fs) prior to the C–O bond breaking [7]. As shown in Fig. 5, the hcos2hi value for the C–C bond breaking pathway of m = 1 is smaller than that for the pathways of m = 2 and þ m = 3. Since all the three precursor species CHþ m C2 H4m (m = 1– 3) are prepared on the Coulombic repulsive potential after the interaction with the ultrashort intense laser field, they are expected to dissociate immediately into two fragment ions. Therefore, the difference among the hcos2hi values may not be ascribed to the difference in the lifetimes of these precursor species, but rather reflect the geometrical structures of the precursor species. is exThe migration of the hydrogen atom (or proton) in C3 H2þ 4 pected to induce the structural deformation of the C–C–C skeleton, leading to the deflection of the ejection direction of CH+ and CHþ 3 with respect to the laser polarization. The smaller hcos2hi value for the m = 1 pathway, in which CH+ is ejected, may reflect the larger bending angle, \C–C–C, in the precursor species CHþ C2 Hþ 3 þ than in CHþ 3 C2 H . This deformation of the skeletal structure can be described as that induced by the rehybridization of chemical bonds associated with the hydrogen migration in intense laser fields. The observed angular distributions shown in Fig. 2d–f can be fitted to the Legendre expansion [5],
IðhÞ ¼ 1 þ
X
aL PL ðcos hÞ ðL ¼ 2; 4; 6Þ;
ð7Þ
L
0.3 1
2 Number of hydrogen atoms
3
þ Fig. 5. Schematic diagram for the hcos2hi values of the fragment ions, CHþ m and Hn .
where PL denotes the Legendre polynomial and aL is the expansion coefficient. The aL values (L = 2, 4, 6) for the three explosion pathways through the C–C bond breaking are determined as listed in
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H. Xu et al. / Chemical Physics Letters 469 (2009) 255–260
Table 1, and the best fit distributions are drawn by the solid curves in Fig. 2d–f. þ Table 1 shows that the relative yields of CHþ m C2 H4m for the m = 1 and 3 pathways with respect to the m = 2 pathway are 0.08 and 0.03, respectively. The differences in the relative yields of CH+ and CHþ 3 may reflect the chemical-bond rearranging dynamics associated with the ultrafast hydrogen atom migration in allene. To form the precursor species CHþ C2 Hþ 3 , the hydrogen atom migrating from one of the two methylene groups would be trapped in a specific area around the central carbon site of the allene molþ ecule. In the formation of CHþ 3 C2 H , however, the hydrogen atom migrating towards the other end is expected to pass through + the central carbon area. The lower yield of CHþ 3 than CH is consistent with this picture that a hydrogen atom (or a proton) migrates first into the central carbon area, and then, proceeds to reach the other end. 3.3.2. C–H bond breaking pathways From the CMI measurement, the existence of the following three types of decomposition pathways is securely identified: þ þ CH2 CCH2þ 2 ! H þ C3 H3
ðn ¼ 1Þ;
ð8Þ
þ þ CH2 CCH2þ 2 ! H2 þ C3 H2
ðn ¼ 2Þ;
ð9Þ
CH2 CCH2þ 2
ðn ¼ 3Þ:
ð10Þ
!
Hþ3
þ
þ C3 H
Hþ n
C3 Hþ 4n
The relative yields of for n = 2 and 3 pathways with respect to the n = 1 pathway are 0.03 and 0.08, respectively. The ejection of Hþ 3 indicates that the migration of one hydrogen atom proceeds from one methylene group to the other within the allene molecule prior to the formation of Hþ 3. As shown in Fig. 5, the hcos2hi values for the three C–H bond breaking pathways in the range of 0.37–0.39 show that the angular distributions are more isotropic than the C–C bond breaking. This þ suggests that the precursor species Hþ n C3 H4n (n = 1–3) from þ which Hn is ejected are prepared in the metastable quasi-bound area of the potential energy surfaces, and that their dissociation lifetimes are comparable with the rotational period of the parent allene molecule. Since the bond breaking proceeds long after the period of the interaction with the intense laser field, it can be regarded as a unimolecular decomposition process. When diatomic or linear triatomic molecules rotate freely in space, the rotational period of the overall molecular rotation, srot, can be written as [16]
srot
sffiffiffiffiffiffiffiffiffiffiffi 2 4ph ¼ ¼ ; x kTB0 2p
ð11Þ
where T is the temperature and B0 is the rotational constant. When the rotational motion of allene is approximated as that of linear polyatomic molecules, the rotational period of allene is estimated to be srot = 2.4 ps using the rotational constant B0 = 0.296 cm1 of allene [17] and T = 300 K, showing that the dissociation lifetimes þ of the precursor states Hþ n C3 H4n may roughly be 2–3 ps. It should be noted that the angular distributions for the C–H bond breaking pathways could also be influenced by the ejection direction of Hþ n with respect to the molecular principal axis. Since the C–H bond breaking processes can be regarded as unimolecular dissociation proceeding long after the interaction with the intense laser field, the coefficients aL in Eq. (7) can be expressed as [8,16]
aL ¼ bL cL PL ðcos h0m Þ ðL ¼ 2; 4; 6Þ;
ð12Þ
where bL reflects the angular distribution of the molecular principal axis of the parent molecules with respect to the laser polarization direction, h0m is the ejection angle of the fragment ions with respect to the molecular principal axis of the parent ion, and cL [8,16],
cL ¼
L=2 Y ð1=sxÞ2 þ ð2k 1Þ2 k¼1
ð1=sxÞ2 þ ð2kÞ2
;
ð13Þ
represents the effect of the molecular rotation, where s denotes the dissociation lifetime of the precursor species. Thus, Eq. (7) can be expressed as
IðhÞ ¼ 1 þ
X
bL cL PL ðcos h0m ÞPL ðcos hÞ ðL ¼ 2; 4; 6Þ:
ð14Þ
L
If it is assumed that the molecular principal axis of the precurþ sor species Hþ n C3 H4n (n = 1–3) is aligned along the same direction as that of the parent ion CH2 C2 H2þ 2 (m = 2 pathway) from which the dissociation proceeds immediately, and that the ejection 2þ direction of CHþ 2 from CH2 C2 H2 is along the molecular axis, the aL coefficients determined for the m = 2 pathway can be adopted as the bL values. This is because the expression of Eq. (14) becomes identical to Eq. (7) (i.e., aL = bL), when both h0m and s are set to be zero. The observed angular distributions of the fragment ions Hþ n (n = 1–3) through the C–H bond breaking pathways are fitted to Eq. (14) by the least-squares analysis. The best-fit distributions are shown in Fig. 3d–f with the solid lines and the optimized parameters, h0m and sx, are determined as listed in Table 1, even though these two fitting parameters are strongly correlated with each other for the n = 3 pathway. From the determined sx values, þ the dissociation lifetimes of the precursor species, Hþ n C3 H4n (n = 1–3) are determined to be s (n = 1) > 1.9 ps, s (n = 2) > 1.9 ps, and s (n = 3) = 1.2 (4) ps. These values, comparable to the rotational lifetimes (srot = 2.4 ps) of parent allene molecules, are consistent þ with our predictions that the precursor species, Hþ n C3 H4n (n = 1–3) are prepared in the metastable states. The small ejection 0 angle of the fragment ions Hþ 3 , hm ¼ 12ð4Þ , indicates that the fragtends to be ejected along the molecular principal axis, ment ion Hþ 3 whereas the relatively large ejection angles, h0m ¼ 31ð2Þ for the H+ ejection and h0m ¼ 23ð2Þ for the Hþ 2 ejection indicate that their ejection directions with respect to the molecular principal axis are more deflected than the Hþ 3 case. In view of the local geometrical structure of the terminal methylene (CH2) part of allene, the large ejection angle obtained for H+ is understandable if the C–H is considered to be stretched along its chemical bond. On the other hand, if the two hydrogen atoms in the terminal CH2 are assumed to be stretched simultaneously þ along the C–C–C direction to form Hþ 2 C3 H2 , the ejection angle 0 is expected to be h 0 , which is inconsistent with the of Hþ m 2 present results, h0m 23ð2Þ . Therefore, the relatively large deflecþ tion angle of Hþ 2 indicates that H2 is formed after the migration of H from the other terminal CH2 or after one of the two hydrogen atoms in the terminal CH2 moves towards the original position of the other hydrogen atom in the same CH2 group.
4. Summary The two-body Coulomb explosion of allene induced by an ultrafast intense laser field has been investigated by using the coincidence momentum imaging method. Two types of the fragmentation pathways through the C–C bond breaking, þ þ C3 H2þ 4 ! CHm þ C2 H4m (m = 1–3), and the C–H bond breaking, þ þ ! H þ C H (n = 1–3), have been identified C3 H2þ 3 4n 4 n unambiguously. þ þ It is shown from the ejection of Hþ 3 , CH3 , and C2 H3 that the hydrogen migration proceeds prior to the Coulomb explosion. In addition, the differences in the hcos2hi values between the C–C and C–H bond breaking processes suggest that the precursor speþ cies CHþ m C2 H4m (m = 1–3) are prepared on the mostly repulsive Coulombic potential energy surfaces, and that the precursor
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þ species C3 Hþ 4n Hn (n = 1–3) tend to be trapped in the metastable quasi-bound well of the potential energy surfaces. It is also inferred for the C–C bond breaking pathways that the hydrogen migration proceeds within the period of the ultrafast laser pulse, and that the extent of the hydrogen migration determines either one of the two initially equivalent C@C chemical bonds is broken within the allene molecule. This finding provides a new strategy for the breaking and/or generation of specific chemical bonds via controlling the hydrogen migration within a hydrocarbon molecule by a suitable designing of ultrashort intense laser pulses.
Acknowledgements The present research was supported by the following two grants from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan: the Grant-in-Aid for Specially Promoted Research on Ultrafast Hydrogen Migration (#19002006), and the Grant-in-Aid for Global COE Program for Chemistry Innovation.
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