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Dependence of the distributions of kinetic energies of products on photoionization energy in the photodissociation of ethene at 157 nm
Chemical Physics Letters 419 (2006) 158–163 www.elsevier.com/locate/cplett
Dependence of the distributions of kinetic energies of products on photoionization energy in the photodissociation of ethene at 157 nm Shih-Huang Lee a
a,*
, Yuan T. Lee
b
National Synchrotron Radiation Research Center, Research Division, 101 Hsin-Ann Road, Hsinchu Science Park, Hsinchu 30076, Taiwan b Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei 106, Taiwan Received 22 September 2005 Available online 15 December 2005
Abstract The dependence of distributions of kinetic energies of H2 and C2H2 products on energy of photoionization is investigated upon photodissociation of ethene at 157 nm. The average kinetic energy of each product decreases with decreasing energy of photoionization, but more markedly for H2 than for C2H2. The dissociation of CH2CD2 into C2H2 + D2 and C2HD + HD differentiates 1,1- from 1,2-elimination of molecular hydrogen. With increasing photon energy, the ratio of HD to D2 decreases and of C2HD to C2H2 increases in both kinetic energy and intensity of product signals. The internal energies of products are roughly estimated. 2005 Elsevier B.V. All rights reserved.
1. Introduction Much experimental [1–7] and theoretical work [8–15] has been directed to the photolysis of ethene (CH2CH2). Ethene dissociates on the ground electronic surface via a non-adiabatic transition [16–19] following optical excitation in the vacuum ultraviolet (VUV) region; four dissociation channels – into CH2CH + H, CHCH + 2H, CHCH + H2, and CH2C +H2 – are identified. Ethyne (CHCH) and vinylidene (CH2C ) are formed following elimination of 1,2- and 1,1H2 through four- and three-center mechanisms, respectively. Vinylidene has electronic energy 43 kcal mol1 larger than ethyne and the barrier height for isomerization from vinylidene to ethyne is only 1.4 kcal mol1 [15]. The distributions of kinetic energy P(Et) and branching ratios in the photolysis of ethene and its isotopic variants at 193 nm were investigated with a molecular-beam apparatus [2,3]. The distributions of rotational and vibrational states of H2 from photolysis of ethene at 193 nm were investigated using 1+1 resonance-enhanced multiphoton ionization [4]; a Boltzmann-like distribution was observed in the populations of *
Corresponding author. Fax: +886 3 578 3813. E-mail address: [email protected] (S.-H. Lee).
0009-2614/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.11.044
vibrational and rotational states for 0 6 v00 6 3 of H2. The dependence of kinetic energy of H2 on its internal energy exhibits a linear decay with a slope 0.213 and an extrapolated value 22.6 kcal mol1 at zero internal energy. The branching ratios and distributions of kinetic energy of fragments from the photolysis of ethene and its isotopic variants at 157 nm were investigated using electron-impact [5,6] and photoionization [7]. Using synchrotron radiation for ionization, the fragments H, H2, C2H2, C2H3 and their isotopic variants are all detectable. Site and isotopic effects on the branching ratios and distributions of kinetic energy were unraveled. A theoretical calculation [15] based on Rice–Ramsperger–Kassel–Marcus (RRKM) theory cannot satisfactorily explain these experimental results, indicating that processes following the photolysis of ethene are not fully statistical. Angular anisotropy parameters b of fragments have been investigated in our laboratory. Site and isotopic effects on the angular anisotropies of products were observed upon photolysis of ethene in three dideuterated isotopic variants. For instance, H2, HD and D2 from photolysis of CH2CD2 have negative, near-zero, and positive b values, respectively. Many experimental techniques have been used to explore the distributions of states of products. In this work
S.-H. Lee, Y.T. Lee / Chemical Physics Letters 419 (2006) 158–163
IE
hν
e d
Eint
c b
hνc
a Fig. 1. Schematic representation of selective photoionization of a species with a wide distribution of internal energy. Species with enough internal energy, i.e., Eint P IE hm, can be ionized with ionizing photons at energy hm. The internal energy of the species is divided into five intervals a–e from small to large energy.
we attempted to derive some information about the internal energies of C2H2 and H2 products after photolysis of ethene through measurements of their time-of-flight (TOF) spectra using varied photoionization energies. Fig. 1 depicts the relationship between the distribution of internal energy of a product and the employed photon energy, which indicates that only products with sufficient internal energy can be ionized when the photon energy is less than the ionization energy (IE) of a product. 2. Experiments We investigated the photodissociation of ethene using a molecular-beam apparatus that has been described in detail elsewhere [7,20,21]. The molecular-beam apparatus comprises two source chambers, a reaction chamber and a detection chamber. The detection chamber contains ion optics, a quadrupole mass filter and an ion detector of Daly type. A solenoid valve located in a source chamber served to expand neat h4-ethene (CH2CH2) and 1,1-d2-ethene (CH2CD2) into the reaction chamber. No clustering occurs at a backing pressure 300 Torr. The source-chamber assembly is rotatable relative to the ion detector. A F2 excimer laser served to generate photolysis light at 157 nm that intercepted the molecular beam perpendicularly in the reaction chamber. The photon flux of the photolysis beam was set about 10 mJ pulse1 cm2 in the reaction region to avoid multiphoton absorption. Photofragments flew along a path of length 100 mm to the ionization region in which fragments were ionized with radiation from an undulator in a synchrotron. The radiation from an undulator has a harmonic structure in photon energy. A windowless gas filter filled with noble gas served to absorb harmonic photons because only the fundamental frequency was desired in the present work. A MgF2 window (thickness 2 mm) absorbed residual photons at high harmonics when the desired pho-
159
ton energy was less than 10 eV. A cryogenic system comprising a liquid-nitrogen trap and a He refrigerator, in addition to turbo-molecular pumps, served to evacuate the ionization region to 5 · 1012 Torr. After ionization, ion optics extracted and focused ions into the quadrupole mass filter through which only species with a selected ratio of mass to charge (m/z) passed. Subsequently, the ion detector counted ions and transferred signals to a multichannel scaler for data acquisition. The background, if not negligibly small, had to be recorded and subtracted from a raw TOF spectrum. After subtraction of a flight interval of ions from the total flight duration, a TOF spectrum of a photofragment was derived. 3. Results and discussion TOF spectra of H2, C2H2, and their isotopic variants upon photolysis of CH2CH2 and CH2CD2 were recorded at a laboratory angle 30 using ionizing photons at several energies. Photolysis of CH2CD2 serves to differentiate 1,1from 1,2-elimination of molecular hydrogen. We measured no TOF spectrum of H2 and its cofragment C2D2 because þ þ D+ and C2 DHþ 2 interfere with H2 and C2 D2 , respectively, in the mass spectrometer. Ion signals of the products decrease rapidly when the photon energy is smaller than ionization energies of the products. The ionization energies of H2 and C2H2 are 15.4 and 11.4 eV, respectively [22]. The TOF spectra of products recorded with a photon energy larger than their IE have been reported in [7]. The TOF spectrum of C2H2 has two components; the rapid and slow components are due to elimination of H2 and of two H-atoms [7], and are thus designated binary and ternary components, respectively. The ternary component of C2H2 disappeared in the TOF spectra when the employed photon energy was less than 10 eV. With decreasing photoionization energy, the TOF distributions of H2 and of the binary component of C2H2 became slow and broad; H2 has a larger variation than C2H2. With a simulation program (PHOTRAN) we fitted the TOF spectra of products with a trial distribution of kinetic energy P(Et) based on a forward convolution technique. Et is the center-of-mass kinetic energy of products including the detected fragment and its cofragment. After iterative convolution, we obtained a satisfactory fit. Figs. 2a,b show the distributions of kinetic energy derived from H2 and the binary component of C2H2, respectively, after photolysis of CH2CH2. Figs. 2c–f show the distributions of kinetic energy derived from HD, C2HD, D2 and C2H2, respectively, after photolysis of CH2CD2. All P(Et) distributions are normalized to unity, although they correspond to separate ensembles. The maximum probability of kinetic energy shifts to the large-energy part with increasing photon energy. The distribution of kinetic energy remains the same when the photon energy is greater than 17.1 eV for H2/HD/D2 and 12.8 eV for C2H2/C2HD. That these two values are larger than the IE of H2 and C2H2, respectively, we attribute to a difference in relative ionization efficiencies
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S.-H. Lee, Y.T. Lee / Chemical Physics Letters 419 (2006) 158–163 0.05
45
0.03 0.02
b
HD 12.8 eV 13.8 14.8 15.9 17.1
d
D2 13.8 eV 14.8 15.9 17.1
f
C2H2 8.6 eV 9.5 10.3 11.1 11.9
0.01 0.00
c
P(Et)
0.04 0.03 0.02
C2HD 9.5 eV 10.3 11.1 11.9 12.8
40 -1
0.04
H2 12.8 eV 13.8 14.8 15.9 17.1
/ kcal mol
a
35 30 25
C2H2 ; C2HD ; C2H2 ;
20
0.01
e
0.03 0.02
C2H2 9.5 eV 10.3 11.1 11.9 12.8
0.01 0.00
0
20
40
60
80
0
20
Et / kcal mol
40
60
80 100
-1
Ratio of
0.00 0.04
H2 HD D2
15 1.3 1.2
HD / D2 C2HD / C2H2
1.1 1.0 8
10
12
14
16
18
Photon energy / eV
Fig. 2. Distributions of kinetic energy derived from TOF spectra of products from photolysis of CH2CH2 (a–b) and CH2CD2 (c–f). Products and employed photoionization energies are shown in the panels. Panels (b), (d) and (f) show P(Et) of the binary component of product ethyne (or vinylidene). The area of each curve is normalized to unity.
Fig. 3. Relationships of product kinetic energy ÆEtæ vs. photon energy (upper panel) and kinetic-energy ratio vs. photon energy (lower panel). Circles, squares, and triangles are experimental data for dissociation of C2H2 + H2, C2HD + HD, and C2H2 + D2, respectively. Solid lines serve as visual guides. The dotted line in the lower panel indicates a value 1.19.
among quantum states of a product when the photon energy is not much larger than the IE. The upper panel of Fig. 3 shows the relationship between average kinetic energy ÆEtæ and photoionization energy for dissociation into C2H2 + H2, C2HD + HD, and C2H2 + D2. ÆEtæ is calculated with P(Et) dependent on photon energy as a weighting factor and has the same value for two momentum-matched products at large photon energies. Dissociations into C2H2 + H2, C2HD + HD and C2H2 + D2 have maximal ÆEtæ equal to 40.1, 40.4 and 34.1 kcal mol1, respectively. The value of ÆEtæ decreases with decreasing photon energy. C2H2 has a smaller slope than H2 in the photolysis of CH2CH2; C2HD and C2H2 have likewise smaller slopes than HD and D2 in the photolysis of CH2CD2, reflecting that ethyne (or vinylidene) has more internal energy than its cofragment, molecular hydrogen. The dependence of ÆEtæ on photon energy pertains to a distribution of internal energy of a product, state-specific ionization cross-sections of a product, and the distributions of kinetic energy of products at a specific internal energy. ÆEtæ for the C2HD + HD channel is nearer that of the C2H2 + H2 dissociation than of the C2H2 + D2 channel, because the HD-elimination channel has twice the branching ratio of the D2-elimination channel [7]. The lower panel of Fig. 3 indicates that in the photolysis of CH2CD2 the ratio of HD to D2 in ÆEtæ decreases whereas the ratio of C2HD to C2H2 increases with increasing photon energy; both ratios converge to the same value, 1.19, at large photon energies. These two opposite trends reflect
that HD has more internal energy than D2 whereas C2HD has less internal energy than C2H2, which is confirmed in Fig. 4. Fig. 4a shows the dependence of a ratio of ternary to binary components of ethyne (or vinylidene) on photoionization energy. The ratios of C2H2 + 2H to C2H2 + H2, C2HD + H + D to C2HD + HD, and C2H2 + 2D to C2H2 + D2 increase from zero to 1.13, 1.96 and 0.33, respectively, with increasing photon energy; these three values are the relative branching ratios of the channel for elimination of two hydrogen atoms to the channel for elimination into molecular hydrogen. For a clear comparison of the dependence of the ratios on photoionization energy, the ratios shown in Fig. 4a are normalized to nearly unity at photon energy 13 eV. The dissociation into C2H2 + H2 has available energy (Eava) as large as 140 kcal mol1 whereas the dissociation into C2H2 + 2H has only 35 kcal mol1. The binary component of ethyne (or vinylidene) has more internal energy than the ternary component thereof, such that only the binary component is still observable when the photoionization energy is less than 10 eV. The dissociation CH2CD2 ! CH2C + 2D is energetically forbidden with 157-nm excitation. Isomerization from CH2CD to CHCHD needs at least 47 kcal mol1 [23], which is above the barrier, 39 kcal mol1 [15], for dissociation of CH2CD into CHCD + H. In addition, the barriers of isomerization for CH2CD2 ! CHCHD2 and CHCHD2 ! CHDCHD are 75 and 1.2 kcal mol1, respectively; those values are smaller than the bond energy
S.-H. Lee, Y.T. Lee / Chemical Physics Letters 419 (2006) 158–163
a
1.0 0.02
a 0.6 0.4
0.01
b
C2H2+2H / C2H2+H2 C2HD+H+D / C2HD+HD C2H2+2D / C2H2+D2
0.2 0.0 10.5
11.0
11.5
12.0
12.5
c
13.0
P(Et)
Ternary / binary
0.8
b
161
e
0.00
d
a b c d e
0.04
4
0.03
Signal ratio
3
0.02
HD / D2 0.01
2
0.00
C2HD / C2H2
0
1 10
12
14
16
18
20
Photon energy / eV Fig. 4. (a) Relationship of the signal ratio of ternary to binary component of product ethyne (or vinylidene) vs. photoionization energy. For a clear comparison, the ratios are normalized to nearly unity at 13 eV. Sigmoidal curves serve as visual guides. (b) Dependence of signal ratios of HD to D2 and of C2HD to C2H2 on photoionization energy. Exponential curves serve as visual guides. The dotted line indicates a value 1.83.
110 kcal mol1 of CH2CD–D [15]. We propose that CH2CD2 isomerizes to CHDCHD first on the ground electronic surface before elimination of 2D; thus, the internal energy of the CHCH product due to elimination of two D-atoms is presumably near that of the CHCD product due to elimination of H and D atoms. Accordingly, C2HD increases more rapidly than C2H2 in the ratio of ternary to binary component, indicating that the binary component of C2HD has less internal energy than that of C2H2. That C2H2 has more internal energy than C2HD in the binary component is also observable for signal ratios of C2HD to C2H2 and of HD to D2 as shown in Fig. 4b. The signal ratio of C2HD to C2H2 increases but that of HD to D2 decreases with increasing photon energy; the two ratios converge to the same value, 1.83, that is the relative branching ratio of the C2HD + HD channel to the C2H2 + D2 channel. The signal ratio of C2HD to C2H2 decreases at small photon energies, indicating that C2H2 has more internal energy than C2HD. In contrast, the signal ratio of HD to D2 increases at small photon energies, indicating that D2 has less internal energy than HD. To estimate internal energies of H2 and C2H2 produced on photolysis of CH2CH2, we rearranged P(Et) of C2H2
20
40
60
Et / kcal mol
80
100
-1
Fig. 5. Distributions of kinetic energy of product derived from TOF spectra of H2. The upper panel shows the same P(Et) as shown in the upper left panel of Fig. 2 except for a rearrangement; see text. The area of the solid P(Et) is normalized to unity. The lower panel shows P(Et) of H2 in intervals a–e.
and H2 as shown in the upper panel of Fig. 5 based on a concept that P(Et) at small photon energy is smaller than that at a large photon energy over all kinetic energies. The difference between two adjacent P(Et) must be nonnegative because a negative value has no physical meaning. Because P(Et) remains constant when the photoionization energy is greater than 17.1 eV for H2 and 11.9 eV for C2H2, areas of P(Et) of H2 at 17.1 eV and of C2H2 at 11.9 eV are normalized to unity. We made an assumption that the area between two adjacent P(Et) curves is the probability of species within a corresponding interval of internal energy. The internal energies of H2 and C2H2 are divided into five intervals a–e from small to large energy using ionizing photons at 12.8, 13.8, 14.8, 15.9 and 17.1 eV for H2 and 8.6, 9.5, 10.3, 11.1 and 11.9 eV for C2H2. Accordingly, intervals a–e have internal energies 0–27, 27–52, 52–75, 75–97 and 97–D0 kcal mol1, respectively, for H2, and 0–19, 19–38, 38–57, 57–76 and 76– D0 kcal mol1, respectively, for C2H2. D0 is the bond strength 104 kcal mol1 for H–H and 133 kcal mol1 for H–CCH [22]. Thus, the average internal energies ÆEintæ in intervals a–e of H2 are estimated to be 13.5, 39.5, 63.5, 86.0 and 100.5 kcal mol1 and of C2H2 are estimated to be 9.5, 28.5, 47.5, 66.5 and 104.5 kcal mol1. In the present work, the stated kinetic energy of a product includes the
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kinetic energies of a detected fragment and its cofragment whereas the internal energy of a product is specified only for the detected fragment. Based on the arrangement of P(Et) shown in the upper panel of Fig. 5, the probabilities of H2 lying in intervals a–e are 0.51, 0.32, 0.10, 0.05 and 0.02. In the same manner, we obtained 0.14, 0.13, 0.11, 0.24 and 0.38 for intervals a–e of C2H2. The probability in greater energy intervals, particularly interval e, might be overestimated because of the bandwidth (DE/E 3%) of ionizing photon energy. We evaluate the average internal energy ÆEintæ of H2 and C2H2 in a whole ensemble to be 33 and 66 kcal mol1, respectively. During data analysis, we took into account the total average internal energy 99 kcal mol1, a difference between available energy 139 kcal mol1 and total average kinetic energy 40 kcal mol1. The fractions of available energy deposited in internal degrees of freedom of H2 and C2H2 are roughly estimated to be 24% and 47%, respectively. Fig. 3 indicates that C2H2 and H2 have nearly linear relationships between ÆEtæ and photon energy when the photon energy is less than 12 and 16 eV, respectively. The slope of ÆEtæ vs. photon energy is fitted to be 3.5 kcal mol1 eV1 for C2H2 and 6.0 kcal mol1 eV1 for H2. We find that the ratio 6.0/3.5 is near the ratio 66/33 of estimated internal energy of C2H2 to that of H2. The lower panel of Fig. 5 shows P(Et) of H2 within intervals a–e; for a clear comparison the areas of these five P(Et) are normalized to unity. The H2 products lying in an interval of smaller internal energy has a P(Et) distribution towards larger kinetic energy. H2 in internal-energy intervals a–e has an average kinetic energy, ÆEtæ, 47.6, 39.7, 34.9, 26.1 and 18.2 kcal mol1 with its cofragment C2H2. In the same manner, C2H2 in its internal-energy intervals a–e has an average kinetic energy 59.6, 51.9, 46.1, 37.9 and 28.6 kcal mol1 with its cofragment H2. These average kinetic energies show a linear decay as a function of average internal energy: ÆEtæ = 53 0.32 · ÆEintæ for H2 and ÆEtæ = 62 0.33 · ÆEintæ for C2H2; both ÆEtæ and ÆEintæ are expressed in unit kcal mol1. Cromwell et al. [4] took only the kinetic energy of H2 into account in their report on the photolysis of ethene at 193 nm. For comparison with the present result, the kinetic energy of C2H2 momentummatched with H2 is included; thus, the extrapolated value and slope become 24.3 and 0.23, respectively. The extrapolated value and slope at 157 nm are greater than those at 193 nm, which we attribute mainly to a large release of kinetic energy in the former. According to a similar analysis, the average internal energies of C2HD, HD, C2H2 and D2 products from photolysis of CH2CD2 at 157 nm are roughly estimated to be 63, 36, 74 and 31 kcal mol1, respectively. The theoretical result of Chang et al. [15] indicates that the H–H bond ˚ in a transition structure of CH2CH2 for length 0.908 A elimination of 1,2-H2 is greater than the H–H bond length ˚ in another transition structure for elimination of 0.838 A 1,1-H2 from CH2CH2. A longer H–H bond in a transition structure correlates with occupancy of higher vibrational
levels of the H2 product, which accounts for the present result of HD having more internal energy than D2. Vinylidene and ethyne are initial products after elimination of D2 and HD, respectively, which is consistent with the interpretation of the result of C2H2 having more internal energy than C2HD. Although a substitution of deuterium atoms might influence the vibrational frequencies and state-tostate cross-sections for ionization of a product, the results shown in Figs. 3 and 4 still indicate that HD and C2H2 have greater internal energy than D2 and C2HD, respectively. Moreover, the distribution of internal energy of the C2H3 product is derivable from the kinetic-energy distribution P(Et) of the C2H3 + H channel [7] based on Eint = Eava Et; Eava = 70.1 kcal mol1. The P(Et) has zero probability at a kinetic energy larger than 65 kcal mol1 and a maximum probability at 35 kcal mol1, below which the probability becomes zero due to dissociation. As atomic H(2S) carries no internal energy, the C2H3 product has an inverse population in its internal energy – a zero probability at zero-point energy, a maximum probability near the dissociation threshold 36 kcal mol1, and an average internal energy 29 kcal mol1. The C2H3 fragments with internal energy larger than 36 kcal mol1 further decompose to C2H2 + H. The average internal energy of the C2H2 product due to loss of two H atoms is 14 kcal mol1, which we evaluate from the available energy, 35 kcal mol1, and the total release of kinetic energy, 21 kcal mol1 [7]. 4. Conclusion This work has provided insight into the internal energies of H2 and C2H2 through measurements of their kineticenergy distributions using varied photoionization energies. The kinetic energy of products including a detected fragment in a sub-ensemble and its cofragment decreases with decreasing photon energy. H2 has a greater slope than C2H2 in the relationship of ÆEtæ vs. photon energy, which reflects that C2H2 acquires more internal energy than H2. Molecular hydrogen due to 1,2-elimination has greater internal energy than that due to 1,1-elimination, but is the reverse for their cofragments; evidence for this condition comprises observations of products HD, D2, C2H2, and C2HD upon photolysis of CH2CD2. First, the ÆEtæ ratio of HD to D2 decreases but that of their cofragments C2HD to C2H2 increases to the same value 1.19 with increasing photon energy. Second, the signal ratio of HD to D2 decreases but hat of C2HD to C2H2 increases to the same value 1.83 with increasing photon energy. Third, in the ratio of ternary to binary component of ethyne (or vinylidene), the ratio of C2HD increases more rapidly than that of C2H2 with increasing photon energy. The present work provides a semi-quantitative approach to reveal the internal energy of a large polyatomic product that is difficult to determine using quantum-state-resolved spectroscopy.
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Acknowledgements We thank the National Synchrotron Radiation Research Center, Academia Sinica and the National Science Council of Taiwan (Grant NSC93-2113-M-213-001) for support. References [1] S. Satyapal, G.W. Johnston, R. Bersohn, I. Oref, J. Chem. Phys. 93 (1990) 6398. [2] B.A. Balko, J. Zhang, Y.T. Lee, J. Chem. Phys. 97 (1992) 935. [3] A. Stolow, B.A. Balko, E.F. Cromwell, J. Zhang, Y.T. Lee, J. Photochem. Photobiol. A 62 (1992) 285. [4] E.F. Cromwell, A. Stolow, M.J.J. Vrakking, Y.T. Lee, J. Chem. Phys. 97 (1992) 4029. [5] J.J. Lin, D.W. Hwang, S. Harich, Y.T. Lee, X. Yang, J. Chem. Phys. 109 (1998) 2979. [6] J.J. Lin, C.C. Wang, Y.T. Lee, X. Yang, J. Chem. Phys. 113 (2000) 9668. [7] S.-H. Lee, Y.T. Lee, X. Yang, J. Chem. Phys. 120 (2004) 10983. [8] E.M. Evleth, A. Sevin, J. Am. Chem. Soc. 103 (1981) 7414.
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[9] K. Raghavachari, M.J. Frisch, J.A. Pople, P.v.R. Schleyer, Chem. Phys. Lett. 79 (1981) 408. [10] K. Raghavachari, M.J. Frisch, J.A. Pople, P.v.R. Schleyer, Chem. Phys. Lett. 85 (1982) 145. [11] J.H. Hensen, K. Morokuma, M.S. Gordon, J. Chem. Phys. 100 (1994) 1981. [12] G.J. Collin, Adv. Photochem. 14 (1988) 135. [13] J.D. Goddard, Chem. Phys. Lett. 83 (1981) 312. [14] A.H.H. Chang, A.M. Mebel, X. Yang, S.H. Lin, Y.T. Lee, Chem. Phys. Lett. 287 (1998) 301. [15] A.H.H. Chang, A.M. Mebel, X. Yang, S.H. Lin, Y.T. Lee, J. Chem. Phys. 109 (1998) 2748. [16] M. Persico, V. Bonacic-Koutecky, J. Chem. Phys. 76 (1982) 6018. [17] I. Ohmine, J. Chem. Phys. 83 (1985) 2348. [18] L. Freund, M. Klessinger, Int. J. Quantum Chem. 70 (1998) 1023. [19] M. Ben-Nun, T.J. Martinez, Chem. Phys. Lett. 298 (1998) 57. [20] C.C. Wang, Y.T. Lee, J.J. Lin, J. Shu, Y.-Y. Lee, X. Yang, J. Chem. Phys. 117 (2002) 153. [21] S.-H. Lee, Y.-Y. Lee, Y.T. Lee, X. Yang, J. Chem. Phys. 119 (2003) 827. [22] D.R. Lide, Handbook of Chemistry and Physics, 78th edn., CRC, Boca Raton, FL, 1997. [23] J.-H. Wang, H.-C. Chang, Y.-T. Chen, Chem. Phys. 206 (1996) 43.
Dependence of the distributions of kinetic energies of products on photoionization energy in the photodissociation of ethene at 157 nm Shih-Huang Lee a
a,*
, Yuan T. Lee
b
National Synchrotron Radiation Research Center, Research Division, 101 Hsin-Ann Road, Hsinchu Science Park, Hsinchu 30076, Taiwan b Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei 106, Taiwan Received 22 September 2005 Available online 15 December 2005
Abstract The dependence of distributions of kinetic energies of H2 and C2H2 products on energy of photoionization is investigated upon photodissociation of ethene at 157 nm. The average kinetic energy of each product decreases with decreasing energy of photoionization, but more markedly for H2 than for C2H2. The dissociation of CH2CD2 into C2H2 + D2 and C2HD + HD differentiates 1,1- from 1,2-elimination of molecular hydrogen. With increasing photon energy, the ratio of HD to D2 decreases and of C2HD to C2H2 increases in both kinetic energy and intensity of product signals. The internal energies of products are roughly estimated. 2005 Elsevier B.V. All rights reserved.
1. Introduction Much experimental [1–7] and theoretical work [8–15] has been directed to the photolysis of ethene (CH2CH2). Ethene dissociates on the ground electronic surface via a non-adiabatic transition [16–19] following optical excitation in the vacuum ultraviolet (VUV) region; four dissociation channels – into CH2CH + H, CHCH + 2H, CHCH + H2, and CH2C +H2 – are identified. Ethyne (CHCH) and vinylidene (CH2C ) are formed following elimination of 1,2- and 1,1H2 through four- and three-center mechanisms, respectively. Vinylidene has electronic energy 43 kcal mol1 larger than ethyne and the barrier height for isomerization from vinylidene to ethyne is only 1.4 kcal mol1 [15]. The distributions of kinetic energy P(Et) and branching ratios in the photolysis of ethene and its isotopic variants at 193 nm were investigated with a molecular-beam apparatus [2,3]. The distributions of rotational and vibrational states of H2 from photolysis of ethene at 193 nm were investigated using 1+1 resonance-enhanced multiphoton ionization [4]; a Boltzmann-like distribution was observed in the populations of *
Corresponding author. Fax: +886 3 578 3813. E-mail address: [email protected] (S.-H. Lee).
0009-2614/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.11.044
vibrational and rotational states for 0 6 v00 6 3 of H2. The dependence of kinetic energy of H2 on its internal energy exhibits a linear decay with a slope 0.213 and an extrapolated value 22.6 kcal mol1 at zero internal energy. The branching ratios and distributions of kinetic energy of fragments from the photolysis of ethene and its isotopic variants at 157 nm were investigated using electron-impact [5,6] and photoionization [7]. Using synchrotron radiation for ionization, the fragments H, H2, C2H2, C2H3 and their isotopic variants are all detectable. Site and isotopic effects on the branching ratios and distributions of kinetic energy were unraveled. A theoretical calculation [15] based on Rice–Ramsperger–Kassel–Marcus (RRKM) theory cannot satisfactorily explain these experimental results, indicating that processes following the photolysis of ethene are not fully statistical. Angular anisotropy parameters b of fragments have been investigated in our laboratory. Site and isotopic effects on the angular anisotropies of products were observed upon photolysis of ethene in three dideuterated isotopic variants. For instance, H2, HD and D2 from photolysis of CH2CD2 have negative, near-zero, and positive b values, respectively. Many experimental techniques have been used to explore the distributions of states of products. In this work
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IE
hν
e d
Eint
c b
hνc
a Fig. 1. Schematic representation of selective photoionization of a species with a wide distribution of internal energy. Species with enough internal energy, i.e., Eint P IE hm, can be ionized with ionizing photons at energy hm. The internal energy of the species is divided into five intervals a–e from small to large energy.
we attempted to derive some information about the internal energies of C2H2 and H2 products after photolysis of ethene through measurements of their time-of-flight (TOF) spectra using varied photoionization energies. Fig. 1 depicts the relationship between the distribution of internal energy of a product and the employed photon energy, which indicates that only products with sufficient internal energy can be ionized when the photon energy is less than the ionization energy (IE) of a product. 2. Experiments We investigated the photodissociation of ethene using a molecular-beam apparatus that has been described in detail elsewhere [7,20,21]. The molecular-beam apparatus comprises two source chambers, a reaction chamber and a detection chamber. The detection chamber contains ion optics, a quadrupole mass filter and an ion detector of Daly type. A solenoid valve located in a source chamber served to expand neat h4-ethene (CH2CH2) and 1,1-d2-ethene (CH2CD2) into the reaction chamber. No clustering occurs at a backing pressure 300 Torr. The source-chamber assembly is rotatable relative to the ion detector. A F2 excimer laser served to generate photolysis light at 157 nm that intercepted the molecular beam perpendicularly in the reaction chamber. The photon flux of the photolysis beam was set about 10 mJ pulse1 cm2 in the reaction region to avoid multiphoton absorption. Photofragments flew along a path of length 100 mm to the ionization region in which fragments were ionized with radiation from an undulator in a synchrotron. The radiation from an undulator has a harmonic structure in photon energy. A windowless gas filter filled with noble gas served to absorb harmonic photons because only the fundamental frequency was desired in the present work. A MgF2 window (thickness 2 mm) absorbed residual photons at high harmonics when the desired pho-
159
ton energy was less than 10 eV. A cryogenic system comprising a liquid-nitrogen trap and a He refrigerator, in addition to turbo-molecular pumps, served to evacuate the ionization region to 5 · 1012 Torr. After ionization, ion optics extracted and focused ions into the quadrupole mass filter through which only species with a selected ratio of mass to charge (m/z) passed. Subsequently, the ion detector counted ions and transferred signals to a multichannel scaler for data acquisition. The background, if not negligibly small, had to be recorded and subtracted from a raw TOF spectrum. After subtraction of a flight interval of ions from the total flight duration, a TOF spectrum of a photofragment was derived. 3. Results and discussion TOF spectra of H2, C2H2, and their isotopic variants upon photolysis of CH2CH2 and CH2CD2 were recorded at a laboratory angle 30 using ionizing photons at several energies. Photolysis of CH2CD2 serves to differentiate 1,1from 1,2-elimination of molecular hydrogen. We measured no TOF spectrum of H2 and its cofragment C2D2 because þ þ D+ and C2 DHþ 2 interfere with H2 and C2 D2 , respectively, in the mass spectrometer. Ion signals of the products decrease rapidly when the photon energy is smaller than ionization energies of the products. The ionization energies of H2 and C2H2 are 15.4 and 11.4 eV, respectively [22]. The TOF spectra of products recorded with a photon energy larger than their IE have been reported in [7]. The TOF spectrum of C2H2 has two components; the rapid and slow components are due to elimination of H2 and of two H-atoms [7], and are thus designated binary and ternary components, respectively. The ternary component of C2H2 disappeared in the TOF spectra when the employed photon energy was less than 10 eV. With decreasing photoionization energy, the TOF distributions of H2 and of the binary component of C2H2 became slow and broad; H2 has a larger variation than C2H2. With a simulation program (PHOTRAN) we fitted the TOF spectra of products with a trial distribution of kinetic energy P(Et) based on a forward convolution technique. Et is the center-of-mass kinetic energy of products including the detected fragment and its cofragment. After iterative convolution, we obtained a satisfactory fit. Figs. 2a,b show the distributions of kinetic energy derived from H2 and the binary component of C2H2, respectively, after photolysis of CH2CH2. Figs. 2c–f show the distributions of kinetic energy derived from HD, C2HD, D2 and C2H2, respectively, after photolysis of CH2CD2. All P(Et) distributions are normalized to unity, although they correspond to separate ensembles. The maximum probability of kinetic energy shifts to the large-energy part with increasing photon energy. The distribution of kinetic energy remains the same when the photon energy is greater than 17.1 eV for H2/HD/D2 and 12.8 eV for C2H2/C2HD. That these two values are larger than the IE of H2 and C2H2, respectively, we attribute to a difference in relative ionization efficiencies
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45
0.03 0.02
b
HD 12.8 eV 13.8 14.8 15.9 17.1
d
D2 13.8 eV 14.8 15.9 17.1
f
C2H2 8.6 eV 9.5 10.3 11.1 11.9
0.01 0.00
c
P(Et)
0.04 0.03 0.02
C2HD 9.5 eV 10.3 11.1 11.9 12.8
40 -1
0.04
H2 12.8 eV 13.8 14.8 15.9 17.1
a
35 30 25
C2H2 ; C2HD ; C2H2 ;
20
0.01
e
0.03 0.02
C2H2 9.5 eV 10.3 11.1 11.9 12.8
0.01 0.00
0
20
40
60
80
0
20
Et / kcal mol
40
60
80 100
-1
Ratio of
0.00 0.04
H2 HD D2
15 1.3 1.2
HD / D2 C2HD / C2H2
1.1 1.0 8
10
12
14
16
18
Photon energy / eV
Fig. 2. Distributions of kinetic energy derived from TOF spectra of products from photolysis of CH2CH2 (a–b) and CH2CD2 (c–f). Products and employed photoionization energies are shown in the panels. Panels (b), (d) and (f) show P(Et) of the binary component of product ethyne (or vinylidene). The area of each curve is normalized to unity.
Fig. 3. Relationships of product kinetic energy ÆEtæ vs. photon energy (upper panel) and kinetic-energy ratio vs. photon energy (lower panel). Circles, squares, and triangles are experimental data for dissociation of C2H2 + H2, C2HD + HD, and C2H2 + D2, respectively. Solid lines serve as visual guides. The dotted line in the lower panel indicates a value 1.19.
among quantum states of a product when the photon energy is not much larger than the IE. The upper panel of Fig. 3 shows the relationship between average kinetic energy ÆEtæ and photoionization energy for dissociation into C2H2 + H2, C2HD + HD, and C2H2 + D2. ÆEtæ is calculated with P(Et) dependent on photon energy as a weighting factor and has the same value for two momentum-matched products at large photon energies. Dissociations into C2H2 + H2, C2HD + HD and C2H2 + D2 have maximal ÆEtæ equal to 40.1, 40.4 and 34.1 kcal mol1, respectively. The value of ÆEtæ decreases with decreasing photon energy. C2H2 has a smaller slope than H2 in the photolysis of CH2CH2; C2HD and C2H2 have likewise smaller slopes than HD and D2 in the photolysis of CH2CD2, reflecting that ethyne (or vinylidene) has more internal energy than its cofragment, molecular hydrogen. The dependence of ÆEtæ on photon energy pertains to a distribution of internal energy of a product, state-specific ionization cross-sections of a product, and the distributions of kinetic energy of products at a specific internal energy. ÆEtæ for the C2HD + HD channel is nearer that of the C2H2 + H2 dissociation than of the C2H2 + D2 channel, because the HD-elimination channel has twice the branching ratio of the D2-elimination channel [7]. The lower panel of Fig. 3 indicates that in the photolysis of CH2CD2 the ratio of HD to D2 in ÆEtæ decreases whereas the ratio of C2HD to C2H2 increases with increasing photon energy; both ratios converge to the same value, 1.19, at large photon energies. These two opposite trends reflect
that HD has more internal energy than D2 whereas C2HD has less internal energy than C2H2, which is confirmed in Fig. 4. Fig. 4a shows the dependence of a ratio of ternary to binary components of ethyne (or vinylidene) on photoionization energy. The ratios of C2H2 + 2H to C2H2 + H2, C2HD + H + D to C2HD + HD, and C2H2 + 2D to C2H2 + D2 increase from zero to 1.13, 1.96 and 0.33, respectively, with increasing photon energy; these three values are the relative branching ratios of the channel for elimination of two hydrogen atoms to the channel for elimination into molecular hydrogen. For a clear comparison of the dependence of the ratios on photoionization energy, the ratios shown in Fig. 4a are normalized to nearly unity at photon energy 13 eV. The dissociation into C2H2 + H2 has available energy (Eava) as large as 140 kcal mol1 whereas the dissociation into C2H2 + 2H has only 35 kcal mol1. The binary component of ethyne (or vinylidene) has more internal energy than the ternary component thereof, such that only the binary component is still observable when the photoionization energy is less than 10 eV. The dissociation CH2CD2 ! CH2C + 2D is energetically forbidden with 157-nm excitation. Isomerization from CH2CD to CHCHD needs at least 47 kcal mol1 [23], which is above the barrier, 39 kcal mol1 [15], for dissociation of CH2CD into CHCD + H. In addition, the barriers of isomerization for CH2CD2 ! CHCHD2 and CHCHD2 ! CHDCHD are 75 and 1.2 kcal mol1, respectively; those values are smaller than the bond energy
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a
1.0 0.02
a 0.6 0.4
0.01
b
C2H2+2H / C2H2+H2 C2HD+H+D / C2HD+HD C2H2+2D / C2H2+D2
0.2 0.0 10.5
11.0
11.5
12.0
12.5
c
13.0
P(Et)
Ternary / binary
0.8
b
161
e
0.00
d
a b c d e
0.04
4
0.03
Signal ratio
3
0.02
HD / D2 0.01
2
0.00
C2HD / C2H2
0
1 10
12
14
16
18
20
Photon energy / eV Fig. 4. (a) Relationship of the signal ratio of ternary to binary component of product ethyne (or vinylidene) vs. photoionization energy. For a clear comparison, the ratios are normalized to nearly unity at 13 eV. Sigmoidal curves serve as visual guides. (b) Dependence of signal ratios of HD to D2 and of C2HD to C2H2 on photoionization energy. Exponential curves serve as visual guides. The dotted line indicates a value 1.83.
110 kcal mol1 of CH2CD–D [15]. We propose that CH2CD2 isomerizes to CHDCHD first on the ground electronic surface before elimination of 2D; thus, the internal energy of the CHCH product due to elimination of two D-atoms is presumably near that of the CHCD product due to elimination of H and D atoms. Accordingly, C2HD increases more rapidly than C2H2 in the ratio of ternary to binary component, indicating that the binary component of C2HD has less internal energy than that of C2H2. That C2H2 has more internal energy than C2HD in the binary component is also observable for signal ratios of C2HD to C2H2 and of HD to D2 as shown in Fig. 4b. The signal ratio of C2HD to C2H2 increases but that of HD to D2 decreases with increasing photon energy; the two ratios converge to the same value, 1.83, that is the relative branching ratio of the C2HD + HD channel to the C2H2 + D2 channel. The signal ratio of C2HD to C2H2 decreases at small photon energies, indicating that C2H2 has more internal energy than C2HD. In contrast, the signal ratio of HD to D2 increases at small photon energies, indicating that D2 has less internal energy than HD. To estimate internal energies of H2 and C2H2 produced on photolysis of CH2CH2, we rearranged P(Et) of C2H2
20
40
60
Et / kcal mol
80
100
-1
Fig. 5. Distributions of kinetic energy of product derived from TOF spectra of H2. The upper panel shows the same P(Et) as shown in the upper left panel of Fig. 2 except for a rearrangement; see text. The area of the solid P(Et) is normalized to unity. The lower panel shows P(Et) of H2 in intervals a–e.
and H2 as shown in the upper panel of Fig. 5 based on a concept that P(Et) at small photon energy is smaller than that at a large photon energy over all kinetic energies. The difference between two adjacent P(Et) must be nonnegative because a negative value has no physical meaning. Because P(Et) remains constant when the photoionization energy is greater than 17.1 eV for H2 and 11.9 eV for C2H2, areas of P(Et) of H2 at 17.1 eV and of C2H2 at 11.9 eV are normalized to unity. We made an assumption that the area between two adjacent P(Et) curves is the probability of species within a corresponding interval of internal energy. The internal energies of H2 and C2H2 are divided into five intervals a–e from small to large energy using ionizing photons at 12.8, 13.8, 14.8, 15.9 and 17.1 eV for H2 and 8.6, 9.5, 10.3, 11.1 and 11.9 eV for C2H2. Accordingly, intervals a–e have internal energies 0–27, 27–52, 52–75, 75–97 and 97–D0 kcal mol1, respectively, for H2, and 0–19, 19–38, 38–57, 57–76 and 76– D0 kcal mol1, respectively, for C2H2. D0 is the bond strength 104 kcal mol1 for H–H and 133 kcal mol1 for H–CCH [22]. Thus, the average internal energies ÆEintæ in intervals a–e of H2 are estimated to be 13.5, 39.5, 63.5, 86.0 and 100.5 kcal mol1 and of C2H2 are estimated to be 9.5, 28.5, 47.5, 66.5 and 104.5 kcal mol1. In the present work, the stated kinetic energy of a product includes the
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kinetic energies of a detected fragment and its cofragment whereas the internal energy of a product is specified only for the detected fragment. Based on the arrangement of P(Et) shown in the upper panel of Fig. 5, the probabilities of H2 lying in intervals a–e are 0.51, 0.32, 0.10, 0.05 and 0.02. In the same manner, we obtained 0.14, 0.13, 0.11, 0.24 and 0.38 for intervals a–e of C2H2. The probability in greater energy intervals, particularly interval e, might be overestimated because of the bandwidth (DE/E 3%) of ionizing photon energy. We evaluate the average internal energy ÆEintæ of H2 and C2H2 in a whole ensemble to be 33 and 66 kcal mol1, respectively. During data analysis, we took into account the total average internal energy 99 kcal mol1, a difference between available energy 139 kcal mol1 and total average kinetic energy 40 kcal mol1. The fractions of available energy deposited in internal degrees of freedom of H2 and C2H2 are roughly estimated to be 24% and 47%, respectively. Fig. 3 indicates that C2H2 and H2 have nearly linear relationships between ÆEtæ and photon energy when the photon energy is less than 12 and 16 eV, respectively. The slope of ÆEtæ vs. photon energy is fitted to be 3.5 kcal mol1 eV1 for C2H2 and 6.0 kcal mol1 eV1 for H2. We find that the ratio 6.0/3.5 is near the ratio 66/33 of estimated internal energy of C2H2 to that of H2. The lower panel of Fig. 5 shows P(Et) of H2 within intervals a–e; for a clear comparison the areas of these five P(Et) are normalized to unity. The H2 products lying in an interval of smaller internal energy has a P(Et) distribution towards larger kinetic energy. H2 in internal-energy intervals a–e has an average kinetic energy, ÆEtæ, 47.6, 39.7, 34.9, 26.1 and 18.2 kcal mol1 with its cofragment C2H2. In the same manner, C2H2 in its internal-energy intervals a–e has an average kinetic energy 59.6, 51.9, 46.1, 37.9 and 28.6 kcal mol1 with its cofragment H2. These average kinetic energies show a linear decay as a function of average internal energy: ÆEtæ = 53 0.32 · ÆEintæ for H2 and ÆEtæ = 62 0.33 · ÆEintæ for C2H2; both ÆEtæ and ÆEintæ are expressed in unit kcal mol1. Cromwell et al. [4] took only the kinetic energy of H2 into account in their report on the photolysis of ethene at 193 nm. For comparison with the present result, the kinetic energy of C2H2 momentummatched with H2 is included; thus, the extrapolated value and slope become 24.3 and 0.23, respectively. The extrapolated value and slope at 157 nm are greater than those at 193 nm, which we attribute mainly to a large release of kinetic energy in the former. According to a similar analysis, the average internal energies of C2HD, HD, C2H2 and D2 products from photolysis of CH2CD2 at 157 nm are roughly estimated to be 63, 36, 74 and 31 kcal mol1, respectively. The theoretical result of Chang et al. [15] indicates that the H–H bond ˚ in a transition structure of CH2CH2 for length 0.908 A elimination of 1,2-H2 is greater than the H–H bond length ˚ in another transition structure for elimination of 0.838 A 1,1-H2 from CH2CH2. A longer H–H bond in a transition structure correlates with occupancy of higher vibrational
levels of the H2 product, which accounts for the present result of HD having more internal energy than D2. Vinylidene and ethyne are initial products after elimination of D2 and HD, respectively, which is consistent with the interpretation of the result of C2H2 having more internal energy than C2HD. Although a substitution of deuterium atoms might influence the vibrational frequencies and state-tostate cross-sections for ionization of a product, the results shown in Figs. 3 and 4 still indicate that HD and C2H2 have greater internal energy than D2 and C2HD, respectively. Moreover, the distribution of internal energy of the C2H3 product is derivable from the kinetic-energy distribution P(Et) of the C2H3 + H channel [7] based on Eint = Eava Et; Eava = 70.1 kcal mol1. The P(Et) has zero probability at a kinetic energy larger than 65 kcal mol1 and a maximum probability at 35 kcal mol1, below which the probability becomes zero due to dissociation. As atomic H(2S) carries no internal energy, the C2H3 product has an inverse population in its internal energy – a zero probability at zero-point energy, a maximum probability near the dissociation threshold 36 kcal mol1, and an average internal energy 29 kcal mol1. The C2H3 fragments with internal energy larger than 36 kcal mol1 further decompose to C2H2 + H. The average internal energy of the C2H2 product due to loss of two H atoms is 14 kcal mol1, which we evaluate from the available energy, 35 kcal mol1, and the total release of kinetic energy, 21 kcal mol1 [7]. 4. Conclusion This work has provided insight into the internal energies of H2 and C2H2 through measurements of their kineticenergy distributions using varied photoionization energies. The kinetic energy of products including a detected fragment in a sub-ensemble and its cofragment decreases with decreasing photon energy. H2 has a greater slope than C2H2 in the relationship of ÆEtæ vs. photon energy, which reflects that C2H2 acquires more internal energy than H2. Molecular hydrogen due to 1,2-elimination has greater internal energy than that due to 1,1-elimination, but is the reverse for their cofragments; evidence for this condition comprises observations of products HD, D2, C2H2, and C2HD upon photolysis of CH2CD2. First, the ÆEtæ ratio of HD to D2 decreases but that of their cofragments C2HD to C2H2 increases to the same value 1.19 with increasing photon energy. Second, the signal ratio of HD to D2 decreases but hat of C2HD to C2H2 increases to the same value 1.83 with increasing photon energy. Third, in the ratio of ternary to binary component of ethyne (or vinylidene), the ratio of C2HD increases more rapidly than that of C2H2 with increasing photon energy. The present work provides a semi-quantitative approach to reveal the internal energy of a large polyatomic product that is difficult to determine using quantum-state-resolved spectroscopy.
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Acknowledgements We thank the National Synchrotron Radiation Research Center, Academia Sinica and the National Science Council of Taiwan (Grant NSC93-2113-M-213-001) for support. References [1] S. Satyapal, G.W. Johnston, R. Bersohn, I. Oref, J. Chem. Phys. 93 (1990) 6398. [2] B.A. Balko, J. Zhang, Y.T. Lee, J. Chem. Phys. 97 (1992) 935. [3] A. Stolow, B.A. Balko, E.F. Cromwell, J. Zhang, Y.T. Lee, J. Photochem. Photobiol. A 62 (1992) 285. [4] E.F. Cromwell, A. Stolow, M.J.J. Vrakking, Y.T. Lee, J. Chem. Phys. 97 (1992) 4029. [5] J.J. Lin, D.W. Hwang, S. Harich, Y.T. Lee, X. Yang, J. Chem. Phys. 109 (1998) 2979. [6] J.J. Lin, C.C. Wang, Y.T. Lee, X. Yang, J. Chem. Phys. 113 (2000) 9668. [7] S.-H. Lee, Y.T. Lee, X. Yang, J. Chem. Phys. 120 (2004) 10983. [8] E.M. Evleth, A. Sevin, J. Am. Chem. Soc. 103 (1981) 7414.
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