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CH branching ratio
Chemical Physics 237 Ž1998. 195–204
Reactions of Cž 1 D/ with H 2 , HD and D 2 : kinetic isotope effect and the CDrCH branching ratio Kei Sato, Naomi Ishida, Tsuyoshi Kurakata, Azusa Iwasaki, Shigeru Tsunashima Department of Applied Physics, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152, Japan Received 15 April 1998
Abstract Electronically excited carbon atom CŽ1 D. was produced by the 308 nm two-photon dissociation of C 3 O 2 . CH and CD radicals produced by the reactions of CŽ1 D. q H 2 , HD and D 2 were probed by laser-induced fluorescence. The nascent rotational state distributions of CHŽ Õ s 0. and CDŽ Õ s 0. were measured under single collision conditions. The distributions measured in the present study were close to those obtained in the previous studies using the 157 nm photodissociation. The rate constants at the room temperature were measured to be Ž2.0 " 0.6. = 10y10 , Ž1.7 " 0.4. = 10y10 and Ž1.4 " 0.3. = 10y10 cm3 moleculey1 sy1 for the reactions with H 2 , HD and D 2 , respectively. The CDrCH branching ratio in the CŽ1 D. q HD reaction was determined to be 1.6 " 0.1. The preference of the CD production suggests that this reaction proceeds mainly via the HCD intermediate complex. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction Atomic carbon is one of the most important species in combustion and hydrocarbon synthesis. Especially, the reaction of electronically excited carbon atom CŽ1 D. with H 2 ; k1
C Ž 1 D . q H 2 ™ CH q H,
Ž 1.
has been of interest in the field of physical chemistry. The central interest is to elucidate whether the reaction is abstractive or insertive in comparison with the OŽ1 D. q H 2 reaction. Reaction Ž1. proceeds with the comparable gas-kinetic rate constant, between 4.15 = 10 y 11 and 3.7 = 10 y 10 cm 3 moleculey1 sy1 w1–3x. Because of the small exoergicity, 25.0 kJ moly1 , the CH product is expected to be dominantly populated in the vibrational ground state. The rotational state distribution of CHŽ Õ s 0. was measured by several groups w3–8x. Jursich and
Wiesenfeld reported that the rotational state distribution matches well a prior distribution w4,5x. They considered that the reaction proceeds via the CH 2 intermediate complex. This mechanism is similar to that of OŽ1 D. q H 2 . On the other hand, Fisher et al. concluded that the abstractive mechanism is also important because the rotational energy fraction is lower than that for the OŽ1 D. q H 2 reaction. The reaction mechanism has not been completely established. Reaction Ž1. has also been studied from the theoretical side w9–13x. The reaction proceeds via the 1AX potential energy surface of CH 2 if the reaction is adiabatic. Blint and Newton calculated the 1AX surface employing a configuration-interaction model combined with a minimum basis set w9x. They reported that the barrier height is approximately zero for the perpendicular approach. This result was supported by the later studies at the higher levels of
0301-0104r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 1 8 3 - 9
K. Sato et al.r Chemical Physics 237 (1998) 195–204
196
theory w11–13x. For the collinear abstraction, Blint and Newton reported that the barrier height is 63 kJ moly1 . Their result suggested a preference of the perpendicular attack of carbon atom. No later workers has studied on the barrier height for the collinear abstraction. A study on the reactions of isotopomers; k 2a
C Ž 1 D . q HD ™ CD q H, k 2b
™ CH q D, k3
C Ž 1 D . q D 2 ™ CD q D,
Ž 2a . Ž 2b . Ž 3.
may provide more detailed information on the reaction dynamics. Especially, the CDrCH branching ratio for reaction Ž2. can be considered to be sensitive probe for the potential energy surface in comparison with the OŽ1 D. q HD reaction w14–25x. However, the isotope effect for reaction Ž1. has not been studied sufficiently. To our knowledge, only one experimental study of the isotope effect was performed by Fisher et al. w3x. They measured the CDrCH branching ratio to be 1.69 and roughly estimated the thermal rate constants for reactions Ž1. and Ž3.. Prior to the experimental study, Whitelock et al. predicted the CDrCH branching ratio to be 2.25 from trajectory calculations on the VB-DIM surface w26x. Their result was considerably larger than the experimental one. In order to obtain the detailed information on the potential energy surface, further studies on the isotope effect are necessary. This study presents laser-induced fluorescence ŽLIF. measurements of the kinetic isotope effect and the CDrCH branching ratio at the room temperature. The reactant CŽ1 D. atom was produced by the 308 nm two-photon dissociation of C 3 O 2 . In order to determine the accurate CDrCH ratio, the effect of possible exchange reactions between CD and CH is discussed in detail.
laser w28x. The product CH or CD was probed through LIF of the A2D § X 2 P transition. The nascent rotational state distributions of CHŽ Õ s 0. and CDŽ Õ s 0. were measured under single collision conditions. A XeCl excimer laser ŽLambda Physik, EMG50. was used as a pump laser. Laser beam of the pump laser was focused by a quartz lens Ž f s 60 cm.. A dye laser ŽLaser Photonics, DL14. pumped by a nitrogen laser ŽLaser Photonics, UV14. was used as a probe laser. CH was probed using the R branch of the Ž0,0. band in the 423–431 nm region. The LIF signals were processed by a digital boxcar integrator ŽNF Circuit Design, BX-531rBP10. and a personal computer ŽEPSON, PC286.. The two lasers and the detection system were synchronized by using a pulserdelay generator ŽStanford Research Systems, DG535.. The typical delay time between pump and probe pulses was 150 ns. The total pressure in the reaction vessel was 90 Pa, while the partial pressure of hydrogen molecule was 45 Pa. The rate constants and the CDrCH branching ratio were measured under rotationally relaxed conditions. Time-resolved measurements of the LIF signal were performed in the presence of 4–79 kPa of He. The pump-probe delay time was changed between 60 ns and 10 ms. For C 3 O 2rH 2rD 2 and C 3 O 2rHD systems, the R lines for CH significantly overlapped with those for CD. However, the Q lines of CH and CD did not overlap each other under rotationally relaxed conditions and could be recorded by a single scan in the 430.4–431.4 nm region. The relative CH andror CD concentrations were measured from the integrated intensity of the Q branch. Carbon suboxide was prepared by the dehydration of malonic acid with phosphorus pentoxide at 400– 420 K w29x. Purification from the main impurity, CO 2 , was achieved by careful pumping on the sample at ; 150 K. H 2 ŽTakachiho Kako., HD ŽMSD Isotopes 98.6%., D 2 ŽShowa Denko. and He ŽNihon Sanso. were used without further purification.
2. Experimental 3. Results A standard pump-and-probe technique was employed. The experimental apparatus was similar to that employed elsewhere w27x. C 3 O 2 was photolyzed to CŽ1 D. q 2CO by focused beam of a XeCl excimer
In the present study, the CH signal was measured by irradiating focused 308 nm light to C 3 O 2rH 2 mixture. In the absence of the focusing lens, no CH
K. Sato et al.r Chemical Physics 237 (1998) 195–204
Fig. 1. Log-log plot of pump-laser power versus the LIF signal. The slope of the solid line is 1.88"0.08.
signal could be measured. This suggests that the CH formation is due to a multiphoton dissociation of C 3 O 2 . Fig. 1 shows the signal-intensity dependence of the pump-laser pulse energy. A slope of a log-log plot of the intensity versus the pulse energy was determined to be 1.88 " 0.08 from Fig. 1. It was concluded that a photofragment of the two-photon dissociation is the source of the CH radical. Fig. 2 shows rotationally resolved spectra of the Ž0,0. band of CH measured under the single collision condition. No rotational lines of the Ž1,1. band was observed. The relative vibrational population of Õ s 1 to Õ s 0 was estimated to be less than 0.03. The relative rotational populations for Õ s 0 were calculated from the peak areas of the rotational lines of the Ž0,0. band. For the A2D § X 2 P transition, RŽ N . rotational line splits into two spin-orbit lines, R 1Ž N . and R 2 Ž N . w30–32x. The spin-orbit lines could be resolved at lower N, but could not be resolved at higher N as shown in Fig. 2. The resolved spin-orbit lines were treated as unresolved line by summing peak areas of the two lines. The Honl-London factors ¨ calculated by the method of Jursich and Wiesenfeld w4x were employed in the population calculation. The relative rotational state distributions of CH and CD are shown in Fig. 3. Fig. 3Ža. compares the CH distribution for reactions Ž1. and Ž2b., while Fig. 3Žb. compares the CD distributions for reactions Ž2a. and Ž3.. For reaction Ž2., overlap of the CH and CD rotational lines were significant. Thus, all the rotational populations could not be derived. There is no
197
Fig. 2. LIF spectrum of CH produced by reaction Ž1. measured at the total pressure of 92 Pa and the pump-probe delay time of 150 ns.
great difference in the CH distribution between reactions Ž1. and Ž2b. and in the CD distribution between reactions Ž2a. and Ž3.. Fig. 4 shows the time variation of the CH signal in the C 3 O 2rH 2 system. A similar plot was also
Fig. 3. Nascent rotational state distributions. Ža. CH distributions for reaction Ž1. Žopen circle. and reaction Ž2b. Žclosed square.. The solid line is the RRHO prior distribution for reaction Ž1. at 300 K Žsee text.. Žb. CD distributions for reaction Ž3. Žopen circle. and reaction Ž2a. Žclosed square.. The solid line is the RRHO prior distribution for reaction Ž3. at 300 K Žsee text..
198
K. Sato et al.r Chemical Physics 237 (1998) 195–204
Fig. 4. Time variation of the CH signal obtained for reaction Ž1.. The total pressure was 40 kPa, while the partial pressures of gases are 40 Pa for H 2 and 130 Pa for C 3 O 2 .
obtained for the C 3 O 2rD 2 system. In the C 3 O 2rHD system, both CH and CD are produced by reaction Ž2.. Fig. 5 shows results obtained at the HD partial pressures of 52, 169 and 367 Pa. The relative intensities of CH and CD signals were plotted as were
Fig. 5. Time variations of the LIF signal for reaction Ž2. obtained at the total pressure of 17 kPa. The partial pressure of HD were 52 Pa Ža., 169 Pa Žb. and 367 Pa Žc.. The open and closed circles represent the results of CH produced by reaction Ž2a. and CD produced by reaction Ž2b., respectively. The solid lines represent curves obtained from the simulations in which the rate constants listed in Table 3 ware used.
Fig. 6. Plot of a parameter Žsee text. versus the partial pressure of H 2 . The partial pressure of C 3 O 2 was 130 Pa. The open circles, the closed circles and the squares represent the results obtained at the total pressures of 4, 16 and 79 kPa, respectively.
measured. All the time-resolved data were fitted by the following double-exponential function; I Ž CH . A eya t y eyb t ,
Ž I.
where a and b are fitting parameters. The a and b parameters were obtained for various experimental conditions. Fig. 6 presents a plot of the a parameter versus the partial pressure of H 2 . The results obtained at various total pressures could be fitted by a single straight line. The similar trends were also observed for the case of D 2 . Fig. 7 shows the similar plot for the reaction of HD. The results for CH and
Fig. 7. Plot of a parameter Žsee text. versus the partial pressure of HD obtained at the total pressure of 17 kPa. The partial pressure of C 3 O 2 was 130 Pa. The open and closed circles represent the results for CH produced by reaction Ž2a. and CD produced by reaction Ž2b., respectively.
K. Sato et al.r Chemical Physics 237 (1998) 195–204
Fig. 8. Plot of b parameter Žsee text. versus the partial pressure of H 2 . The partial pressure of C 3 O 2 was 130 Pa. The open circles, the closed circles and the squares represent the results obtained at the total pressures of 4, 16 and 79 kPa, respectively.
CD could be fitted by a single straight line. Fig. 8 shows a plot for the b parameter versus the partial pressure of H 2 . As shown in Fig. 8, the slope of the fitted line depended on the total pressure. The partial C 3 O 2 pressure dependences of the a and b parameters were also measured at a constant partial pressure of H 2 . The linear dependence upon the pressure of C 3 O 2 was found. In order to obtain the CDrCH branching ratio for reaction Ž2., the relative LIF sensitivities of CD and CH are necessary. The relative sensitivities were obtained from the nascent signal intensities of CH and CD produced by the reaction of CŽ1 D. with an equi-molar mixture of H 2 and D 2 . By using these results and rate constants, k 1 and k 3 , the sensitivity ratio of CD to CH was determined to be 1.4 " 0.1. This result is close to that estimated from spectrum w33x and Flanck– simulations using Honl–London ¨ Condon w34x factors, i.e., 1.3. This means that the experimental result of the sensitivity ratio does not include a significant systematic error.
4. Discussion 4.1. Rotational state distribution The photodissociation of C 3 O 2 has been studied at various wavelengths w35–43x. The mechanism of the two-photon dissociation has not been known.
199
Considerable amount of CH radical was produced by the 308 nm two-photon dissociation of C 3 O 2rH 2 mixture. The energetically possible decomposition ˜ 3 Sq . and products may be CŽ 3 P., CŽ1 D., C 2 OŽX 1 3 C 2 O Ža˜ D .. However, C Ž P . q H 2 ™ CH q H, ˜ 3 Sq . q H 2 ™ CH q HCO and C 2 OŽa˜ 1D. C 2 OŽX qH 2 ™ CH q HCO are energetically inaccessible even though the translational energies of the photofragments are taken into account w44–46x. Thus, CH is produced by the reaction of CŽ1 D. with H 2 under the present experimental condition. The rotational state distribution of CHŽ Õ s 0. has been measured by the previous workers using the 157 nm and 248 nm two-photon dissociations of C 3 O 2 w3–8x. The present result obtained by using the 308 nm two-photon dissociation could be compared with the previous ones. As shown in Fig. 2, the CH signals for N F 13 were measured in the present study. Jursich and Wiesenfeld reported that maximal observable N is 14 for the 157 nm photodissociation w4,5x. Their result is very similar to the present result. This is reasonable because the excitation energy of C 3 O 2 is comparable between the 157 nm and 308 nm two-photon dissociations. On the other hand, Fisher et al. reported that CH for N s 13,14 was not measured though they also employed the 157 nm photodissociation w3x. They suggested that this is because the different LIF transitions were used between two 157 nm studies. They used the B § X transition, while Jursich and Wiesenfeld used the A § X transition. The LIF sensitivity for the B § X transition may be lower than that for the A § X transition. Scott et al. used the 248 nm two-photon dissociation and measured CH for N F 15 w6x. In this case, the translational energy of CŽ1 D. should be higher than that for the present study. Therefore, the maximal N is larger than that observed in the present study. The present results was very similar to the results of the 157 nm photodissociations. CH radical detected in the present study must be produced by reaction Ž1.. Under the single collision conditions, the collision energy between CŽ1 D. and H 2 is not relaxed. However, the maximal N observed for CH, 13, was the same as maximal accessible N expected for the total available energy of 300 K, yD H0 q 52 kT. This may be caused by the small reduced mass of the CŽ1 D.rH 2 system as discussed in the previous 157
K. Sato et al.r Chemical Physics 237 (1998) 195–204
200
nm study w3x. The mean collision energy should be close to that of 300 K. A solid curves in Figs. 3Ža. and 3Žb. are RRHO prior distributions w47x at 300 K for reactions Ž1. and Ž3., respectively. The prior distribution and experimental data were normalized at N s 7. The rotational state distributions matched well the RRHO prior distributions as shown in Fig. 3. This strongly suggests that the reaction proceeds via the long-lived intermediate complex. The adiabatic potential energy surface of the reaction has a deep potential well corresponding to CH 2 Ž1A1 .. The vibrationally excited CH 2 Ž1A 1 . intermediate complex should be produced in the reaction. The lifetime of the CH 2 intermediate may be long compared to the time for the intramolecular vibrational energy redistribution ŽIVR. because the well depth is much larger than the exoergicity, 25.0 kJ moly1 . In such a case, the vibrational energy of the intermediate complex is statistically partitioned into all the degrees of freedom prior to the decomposition. Therefore, the rotational state distribution of the product is close to that predicted from the statistical model. The OŽ1 D. q H 2 reaction is also considered to proceed via the deep potential well of H 2 O. However, it is known that the rotational state distribution of OH is much hotter than the statistical one w16x. Because of its large exoergicity, 182 kJ moly1 , the lifetime of the H 2 O may be short compared to the time for IVR. 4.2. Reaction mechanism and rate constants In order to explain the results such as shown in Figs. 6–8, the following mechanism was considered for the C 3 O 2rH 2 system:
k1
k4
C Ž 1 D . q C 3 O 2 ™ product, k5
CH q H 2 ™ product, k6
CH q C 3 O 2 ™ product.
a s k 1 wH 2 x q k 4 wC 3 O2 x , b s k 5 wH 2 x q k 6 wC 3 O2 x . k 1 could be obtained from the slope of Fig. 6 and the intercept of the plot of the a parameter versus wC 3 O 2 x under a constant H 2 partial pressure. The results obtained from two plots were consistent each other. k 2 and k 3 were obtained by the similar procedure for HD and D 2 , respectively. The results of k 1 –k 3 were listed in Table 1 with error of 95% confidence limit. The results of k 4 obtained from the intercept of Fig. 6 and the slope of the plot versus wC 3 O 2 x were also self consistent. Table 1 compares the present results with the previous ones. Braun et al. measured k 1 monitoring decay curves of CŽ1 D. through the resonance absorption method combined with the photograph technique and reported k 1 to be 4.15 = 10y1 1 cm3 moleculey1 sy1 w1x. This value is much smaller than the present one, 2.0 = 10y1 0 cm3 moleculey1 sy1 . Their results for the reactions, CŽ1 D. q NO, CH 4 and O 2 , are also greatly under-estimated compared to the results of other workers w2x. Husain and Kirsch also used the resonance absorption method but recorded the decay curves through a oscilloscope w2x. Their result, 2.7 = 10y1 0 cm3 moleculey1 sy1 , is close to the present result. By using LIF method, Fisher et al. roughly estimated k 1 and k 3 to be 3.7 = 10y1 0 cm3 moleculey1 sy1 w3x, which is also close to the present result.
Table 1 Rate constants for the CŽ1 D.qH 2 , D 2 and HD at the room temperature
C 3 O 2 q 2 hn ™ C Ž 1 D . q 2CO, C Ž 1 D . q H 2 ™ CH q H,
ŽI.. The fitting parameters in equation ŽI. are represented as functions of wH 2 x and wC 3 O 2 x:
Ž 1. Ž 4.
Reaction CŽ1 D.qH 2
Ž 5. Ž 6.
Assuming the initial concentration of CŽ1 D. to be much smaller than those of H 2 and C 3 O 2 , the time variation of the CH signal is represented by equation
CŽ1 D.qHD CŽ1 D.qD 2 a b
CŽ1 D. Source
Rate constant
C 3 O 2 rFP b C 3 O 2 rFP b C 3 O 2 r157 nm C 3 O 2 r308 nm C 3 O 2 r308 nm C 3 O 2 r157 nm C 3 O 2 r308 nm
0.415 2.6"0.3 3.7"0.2 2.0"0.6 1.7"0.4 3.7"0.4 1.4"0.3
In units of 10y10 cm3 moleculey1 sy1 . Vacuum ultra violet flash photolysis.
Ref. a
w1x w2x w3x this work this work w3x this work
K. Sato et al.r Chemical Physics 237 (1998) 195–204 Table 2 Rate constants for CHqH 2 and CDqD 2 at the room temperature Reaction
pŽkPa.ŽM.
Rate constant
CHqH 2
3.3ŽAr. 3.5ŽHe. 4.0ŽHe. 4.1ŽAr. 4.3ŽAr. 13ŽAr. 13ŽAr. 13ŽAr. 13ŽAr. 13ŽHe. 13ŽAr. 16ŽHe. 17ŽAr. 67ŽHe. 79ŽAr. 80ŽAr. 80ŽHe. 4.0ŽHe. 13ŽAr. 13ŽAr. 17ŽHe.
0.79"0.22 0.400"0.040 0.70"0.14 0.564"0.033 0.545"0.120 1.74"0.20 2.6"0.5 1.40"0.10 1.53"0.04 1.02"0.10 1.35"0.07 1.7"0.1 1.548"0.362 2.53"0.25 4.542"0.600 4.5"0.4 3.2"0.2 0.84"0.32 2.05"0.16 1.63"0.15 2.7"0.4
CDqD 2
a
a
Ref. w48x w55x this work w50x w49x w51x w52x w48x w53x w55x w50x this work w49x w55x w49x w48x this work this work w48x w55x this work
201
rable with the sum of the rotational radius of H 2 and ˚ This suggests that the the C–H bond length, 1.4 A. steric factor is close to unity for this reaction. The rate constant, k 5 , was obtained from the slope of Fig. 8, i.e., the plot of the b parameter versus wH 2 x. The results were summarized in Table 2 along with the previous ones w48–55x. As discussed in the previous studies, k 5 depended on the total pressure. This has been consistently explained by a model in which reaction Ž5. proceeds through formation of vibrationally excited CH 3 w48–55x. The excited CH 3 radicals decompose to products or undergoes vibrational relaxation through the collisions with the third body. Because of the collisional stabilization channel, k 5 depends on the total pressure. As shown in Table 2, the present result at each pressure shows good agreements with the previous ones. The similar trend was observed for the case of D 2 as shown in Table 2. In the C 3 O 2rHD system, the exchange reactions of CH and CD may take place:
In units of 10y11 cm3 moleculey1 sy1 . k7
CH q HD ™ CD q H 2 , As shown in Table 1, the larger the reduced mass of the reactant is, the overall rate constant is smaller, i.e. k 1 ) k 2 ) k 3 . The cross section of reactions Ž1., ˚ 2, Ž2. and Ž3. are evaluated to be 10, 10 and 9.6 A respectively. Though the rate constants are different, the cross sections were close each others for three ˚ deterisotopic reactions. The collision radius, 1.7 A, mined from the result of the cross section is compa-
Ž 7.
k8
CD q HD ™ CH q D 2 .
Ž 8.
In order to study influence of reactions Ž7. and Ž8. on the present result of k 2 , the time variation of the signals were numerically simulated taking into account these reactions. The reactions considered in the simulation were listed in Table 3. The CHrCD sensitivity ratio measured in the C 3 O 2rH 2rD 2 sys-
Table 3 Reactions and rate constants employed in the simulations of the CH and CD signals in the C 3 O 2 rHD system Reaction 1
CŽ D. q HD ™ CH q D CŽ1 D. q HD ™ CD q H CŽ1 D. q C 3 O 2 ™ product CH q HD ™ CD q H 2 CH q HD ™ other product CD q HD ™ CH q D 2 CD q HD ™ other product CH q C 3 O 2 ™ product CD q C 3 O 2 ™ product a b c
Rate constant Ž2a. Ž2b. Ž4. Ž7. Ž8. Ž6.
In units of 10y11 cm3 moleculey1 sy1 . Rate constants treated as the fitting parameter with the estimated fitting errors. Rate constants estimated from the results of the C 3 O 2 rH 2 and C 3 O 2 rD 2 systems.
b
7.0 " 3.0 12.0 " 5.0 b 3.0 c 1.0 " 0.5 b 2.0 " 0.5 b 1.0 " 0.5 b 2.0 " 0.5 b 1.0 c 1.0 c
a
202
K. Sato et al.r Chemical Physics 237 (1998) 195–204
be obtained. The result of the branching ratio, 1.6 " 0.1, is listed in Table 4 along with the previous results. Fisher et al. reported that the CDrCH branching ratio is 1.69 in the non-thermal condition w3x. Their result is close to the present result. Whitelock et al. studied the CDrCH branching ratio using the quasi-classical trajectory ŽQCT. calculations on a VB-DIM surface and evaluated the branching ratio to be 2.25 w26x. The result of the QCT calculation is larger than experimental results. The VB-DIM surface may not well represent the global potential
Table 4 XDrXH isotope branching ratio for the XqHD reactions X
D H0
a
a
Method
Ecoll
XDrXH
Ref.
expt. expt.
- 4.2 1.69"0.07 w3x 3.7 1.6"0.1 this work 12 2.25"0.15 w26x
XDqH XHqD CŽ1 D. y25.8 Fig. 9. Time variations of the CDrCH signal ratio obtained at the total pressure of 17 kPa. The partial pressures of HD were 52 Pa Ža., 169 Pa Žb. and 367 Pa Žc.. The solid and dotted lines are the curve simulated by using k 7 and k 8 listed in Table 3 and that simulated by setting k 7 and k 8 to be zero, respectively Žsee text..
tem was used in the simulation. The best-fitted curves were obtained from comparisons with 15 different time-resolved results. The rate constants deconvoluted from the simulations were listed in Table 3. Fig. 9 shows the time variations of the CDrCH signal ratio. The solid and dotted lines represent the curve simulated by using k 7 and k 8 listed in Table 3 and that simulated by setting k 7 and k 8 to be zero, respectively. The CDrCH signal ratio is sensitive to k 7 and k 8 . However, the time variations of the CH and CD signals, shown in Fig. 5, were not sensitive to these rate constants. In addition, the deconvoluted result of k 2a q k 2b , 1.9 " 0.6, is consistent with k 2 obtained from Fig. 7, 1.7 " 0.4. The influence of reactions Ž7. and Ž8. can be ignored on the estimation of k 2 .
OŽ1 D. y184
FŽ2 P. y137
4.3. Isotope branching ratio As shown in Fig. 9, the CDrCH signal ratio did not greatly change in the 0.06–0.1 ms region. By correcting the signal ratio in this region with the sensitivity ratio, the CDrCH branching ratio could
a b c d
y21.4
y178
y131
QCTr DIM expt. b expt. expt. expt. b expt. c expt. QCTr DIM QCTr MC QCTr SL1 QCTr MCMG expt. expt. expt. QCTr 6SCE QCTr T5A QCTr M5 QCTr SW IOSA d r TS
w18x w20x w14x w18x w18x w23x w26x
13 13 10 10 10 3.7 8.4
1.35"0.20 1.3"0.2 1.13"0.08 1.5"0.2 1.3"0.1 1.33"0.07 5.60"0.27
21
1.09"0.06 w15x
21
1.43"0.18 w15x
24
1.77"0.25 w17x
3.7 ;11 3.7
0.69 0.70 0.66 0.79
w56x w57,58x w14x w59x
3.7
0.95
w59x
3.7
1.03
w59x
3.7
0.79
w60x
8.3
2.18
w61x
In units of kJ moly1 . The multiphoton ionization measurement. The vacuum-ultra-violet LIF measurement. Infinite-order-sudden approximation.
K. Sato et al.r Chemical Physics 237 (1998) 195–204
energy surface. For the reaction of CŽ1 D., QCT calculations on ab initio surfaces have not been performed. In order to obtain detailed information on the potential energy surface, such a study is necessary. The XDrXH branching ratio for the X q HD reaction have been studied for the various reaction systems as shown in Table 4. The isotope branching ratio for the reaction of FŽ2 P. is smaller than unity, 0.7 w56–61x. This reaction is known to proceed via direct abstraction. Since the cross section of H atom is larger than that of D atom due to the rotation of HD, the HF becomes a dominant product in this reaction. On the other hand, the isotope branching ratios are larger than unity for the reactions of CŽ1 D. and OŽ1 D.. These reactions are considered to proceed via the deep potential well. In this case, the XDrXH branching ratio may be determined by the rate constants of unimolecular decomposition of the HXD intermediate complex. The XDrXH branching ratio, G , was evaluated from the following equation which was based on the Kassel equation;
Gs
ka kb
s
Aa Ab
Ea‡
ž / E b‡
2
,
where A is vibrational frequency for the dissociating bond of HXD, E ‡ is the total available energy of the product and subscripts ‘a’ and ‘b’ represent the HXD ™ H q XD and HXD ™ HX q D reactions, respectively. The results were 1.4 and 1.8 for OŽ1 D. and CŽ1 D., respectively. The XD diatomic product is dominantly produced because the elimination of light H atom is faster than that of heavy D atom. The lifetime of the H 2 O intermediate is considered to be short compared to the time for IVR w14–25x. If this is the case, the above treatment is not applicable to the OŽ1 D. q HD reaction. However, the result for OŽ1 D. qualitatively explains the experimental result, 1.13–1.5. The experimental results for the CŽ1 D., 1.6–1.69, is well explained by the above treatment. This result also suggests that the reaction of CŽ1 D. proceeds via the CH 2 intermediate complex. 5. Conclusion The reactions of CŽ1 D. with H 2 , HD and D 2 were investigated using the 308 nm two-photon dissocia-
203
tion of C 3 O 2 . The rate constants for the reactions of three isotopomers were simultaneously measured at the first time. Although the rate constants for three reactions are different, the reaction cross sections were the same. The obtained cross section was 10 ˚ 2 . The reaction proceeds with the rate constant A comparable with the gas-kinetic one. The CDrCH branching ratio and the rotational state distributions were also measured. The CDrCH branching ratio was well explained by the model based on the Kassel equation for the the unimolecular decomposition of HCD. The rotational state distribution matched well the RRHO prior distribution. These results strongly suggests that the long-lived intermediate complex is produced in the reaction. In order to obtain more detailed information on the reaction dynamics, the QCT calculations on the ab initio surface are necessary.
Acknowledgements The authors wish to thank Professor Okitsugu Kajimoto of Kyoto University and Professor Kenji Honma of Himeji Institute of Technology for a technical advice on the 308 nm photodissociation of C 3 O2 .
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Reactions of Cž 1 D/ with H 2 , HD and D 2 : kinetic isotope effect and the CDrCH branching ratio Kei Sato, Naomi Ishida, Tsuyoshi Kurakata, Azusa Iwasaki, Shigeru Tsunashima Department of Applied Physics, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152, Japan Received 15 April 1998
Abstract Electronically excited carbon atom CŽ1 D. was produced by the 308 nm two-photon dissociation of C 3 O 2 . CH and CD radicals produced by the reactions of CŽ1 D. q H 2 , HD and D 2 were probed by laser-induced fluorescence. The nascent rotational state distributions of CHŽ Õ s 0. and CDŽ Õ s 0. were measured under single collision conditions. The distributions measured in the present study were close to those obtained in the previous studies using the 157 nm photodissociation. The rate constants at the room temperature were measured to be Ž2.0 " 0.6. = 10y10 , Ž1.7 " 0.4. = 10y10 and Ž1.4 " 0.3. = 10y10 cm3 moleculey1 sy1 for the reactions with H 2 , HD and D 2 , respectively. The CDrCH branching ratio in the CŽ1 D. q HD reaction was determined to be 1.6 " 0.1. The preference of the CD production suggests that this reaction proceeds mainly via the HCD intermediate complex. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction Atomic carbon is one of the most important species in combustion and hydrocarbon synthesis. Especially, the reaction of electronically excited carbon atom CŽ1 D. with H 2 ; k1
C Ž 1 D . q H 2 ™ CH q H,
Ž 1.
has been of interest in the field of physical chemistry. The central interest is to elucidate whether the reaction is abstractive or insertive in comparison with the OŽ1 D. q H 2 reaction. Reaction Ž1. proceeds with the comparable gas-kinetic rate constant, between 4.15 = 10 y 11 and 3.7 = 10 y 10 cm 3 moleculey1 sy1 w1–3x. Because of the small exoergicity, 25.0 kJ moly1 , the CH product is expected to be dominantly populated in the vibrational ground state. The rotational state distribution of CHŽ Õ s 0. was measured by several groups w3–8x. Jursich and
Wiesenfeld reported that the rotational state distribution matches well a prior distribution w4,5x. They considered that the reaction proceeds via the CH 2 intermediate complex. This mechanism is similar to that of OŽ1 D. q H 2 . On the other hand, Fisher et al. concluded that the abstractive mechanism is also important because the rotational energy fraction is lower than that for the OŽ1 D. q H 2 reaction. The reaction mechanism has not been completely established. Reaction Ž1. has also been studied from the theoretical side w9–13x. The reaction proceeds via the 1AX potential energy surface of CH 2 if the reaction is adiabatic. Blint and Newton calculated the 1AX surface employing a configuration-interaction model combined with a minimum basis set w9x. They reported that the barrier height is approximately zero for the perpendicular approach. This result was supported by the later studies at the higher levels of
0301-0104r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 1 8 3 - 9
K. Sato et al.r Chemical Physics 237 (1998) 195–204
196
theory w11–13x. For the collinear abstraction, Blint and Newton reported that the barrier height is 63 kJ moly1 . Their result suggested a preference of the perpendicular attack of carbon atom. No later workers has studied on the barrier height for the collinear abstraction. A study on the reactions of isotopomers; k 2a
C Ž 1 D . q HD ™ CD q H, k 2b
™ CH q D, k3
C Ž 1 D . q D 2 ™ CD q D,
Ž 2a . Ž 2b . Ž 3.
may provide more detailed information on the reaction dynamics. Especially, the CDrCH branching ratio for reaction Ž2. can be considered to be sensitive probe for the potential energy surface in comparison with the OŽ1 D. q HD reaction w14–25x. However, the isotope effect for reaction Ž1. has not been studied sufficiently. To our knowledge, only one experimental study of the isotope effect was performed by Fisher et al. w3x. They measured the CDrCH branching ratio to be 1.69 and roughly estimated the thermal rate constants for reactions Ž1. and Ž3.. Prior to the experimental study, Whitelock et al. predicted the CDrCH branching ratio to be 2.25 from trajectory calculations on the VB-DIM surface w26x. Their result was considerably larger than the experimental one. In order to obtain the detailed information on the potential energy surface, further studies on the isotope effect are necessary. This study presents laser-induced fluorescence ŽLIF. measurements of the kinetic isotope effect and the CDrCH branching ratio at the room temperature. The reactant CŽ1 D. atom was produced by the 308 nm two-photon dissociation of C 3 O 2 . In order to determine the accurate CDrCH ratio, the effect of possible exchange reactions between CD and CH is discussed in detail.
laser w28x. The product CH or CD was probed through LIF of the A2D § X 2 P transition. The nascent rotational state distributions of CHŽ Õ s 0. and CDŽ Õ s 0. were measured under single collision conditions. A XeCl excimer laser ŽLambda Physik, EMG50. was used as a pump laser. Laser beam of the pump laser was focused by a quartz lens Ž f s 60 cm.. A dye laser ŽLaser Photonics, DL14. pumped by a nitrogen laser ŽLaser Photonics, UV14. was used as a probe laser. CH was probed using the R branch of the Ž0,0. band in the 423–431 nm region. The LIF signals were processed by a digital boxcar integrator ŽNF Circuit Design, BX-531rBP10. and a personal computer ŽEPSON, PC286.. The two lasers and the detection system were synchronized by using a pulserdelay generator ŽStanford Research Systems, DG535.. The typical delay time between pump and probe pulses was 150 ns. The total pressure in the reaction vessel was 90 Pa, while the partial pressure of hydrogen molecule was 45 Pa. The rate constants and the CDrCH branching ratio were measured under rotationally relaxed conditions. Time-resolved measurements of the LIF signal were performed in the presence of 4–79 kPa of He. The pump-probe delay time was changed between 60 ns and 10 ms. For C 3 O 2rH 2rD 2 and C 3 O 2rHD systems, the R lines for CH significantly overlapped with those for CD. However, the Q lines of CH and CD did not overlap each other under rotationally relaxed conditions and could be recorded by a single scan in the 430.4–431.4 nm region. The relative CH andror CD concentrations were measured from the integrated intensity of the Q branch. Carbon suboxide was prepared by the dehydration of malonic acid with phosphorus pentoxide at 400– 420 K w29x. Purification from the main impurity, CO 2 , was achieved by careful pumping on the sample at ; 150 K. H 2 ŽTakachiho Kako., HD ŽMSD Isotopes 98.6%., D 2 ŽShowa Denko. and He ŽNihon Sanso. were used without further purification.
2. Experimental 3. Results A standard pump-and-probe technique was employed. The experimental apparatus was similar to that employed elsewhere w27x. C 3 O 2 was photolyzed to CŽ1 D. q 2CO by focused beam of a XeCl excimer
In the present study, the CH signal was measured by irradiating focused 308 nm light to C 3 O 2rH 2 mixture. In the absence of the focusing lens, no CH
K. Sato et al.r Chemical Physics 237 (1998) 195–204
Fig. 1. Log-log plot of pump-laser power versus the LIF signal. The slope of the solid line is 1.88"0.08.
signal could be measured. This suggests that the CH formation is due to a multiphoton dissociation of C 3 O 2 . Fig. 1 shows the signal-intensity dependence of the pump-laser pulse energy. A slope of a log-log plot of the intensity versus the pulse energy was determined to be 1.88 " 0.08 from Fig. 1. It was concluded that a photofragment of the two-photon dissociation is the source of the CH radical. Fig. 2 shows rotationally resolved spectra of the Ž0,0. band of CH measured under the single collision condition. No rotational lines of the Ž1,1. band was observed. The relative vibrational population of Õ s 1 to Õ s 0 was estimated to be less than 0.03. The relative rotational populations for Õ s 0 were calculated from the peak areas of the rotational lines of the Ž0,0. band. For the A2D § X 2 P transition, RŽ N . rotational line splits into two spin-orbit lines, R 1Ž N . and R 2 Ž N . w30–32x. The spin-orbit lines could be resolved at lower N, but could not be resolved at higher N as shown in Fig. 2. The resolved spin-orbit lines were treated as unresolved line by summing peak areas of the two lines. The Honl-London factors ¨ calculated by the method of Jursich and Wiesenfeld w4x were employed in the population calculation. The relative rotational state distributions of CH and CD are shown in Fig. 3. Fig. 3Ža. compares the CH distribution for reactions Ž1. and Ž2b., while Fig. 3Žb. compares the CD distributions for reactions Ž2a. and Ž3.. For reaction Ž2., overlap of the CH and CD rotational lines were significant. Thus, all the rotational populations could not be derived. There is no
197
Fig. 2. LIF spectrum of CH produced by reaction Ž1. measured at the total pressure of 92 Pa and the pump-probe delay time of 150 ns.
great difference in the CH distribution between reactions Ž1. and Ž2b. and in the CD distribution between reactions Ž2a. and Ž3.. Fig. 4 shows the time variation of the CH signal in the C 3 O 2rH 2 system. A similar plot was also
Fig. 3. Nascent rotational state distributions. Ža. CH distributions for reaction Ž1. Žopen circle. and reaction Ž2b. Žclosed square.. The solid line is the RRHO prior distribution for reaction Ž1. at 300 K Žsee text.. Žb. CD distributions for reaction Ž3. Žopen circle. and reaction Ž2a. Žclosed square.. The solid line is the RRHO prior distribution for reaction Ž3. at 300 K Žsee text..
198
K. Sato et al.r Chemical Physics 237 (1998) 195–204
Fig. 4. Time variation of the CH signal obtained for reaction Ž1.. The total pressure was 40 kPa, while the partial pressures of gases are 40 Pa for H 2 and 130 Pa for C 3 O 2 .
obtained for the C 3 O 2rD 2 system. In the C 3 O 2rHD system, both CH and CD are produced by reaction Ž2.. Fig. 5 shows results obtained at the HD partial pressures of 52, 169 and 367 Pa. The relative intensities of CH and CD signals were plotted as were
Fig. 5. Time variations of the LIF signal for reaction Ž2. obtained at the total pressure of 17 kPa. The partial pressure of HD were 52 Pa Ža., 169 Pa Žb. and 367 Pa Žc.. The open and closed circles represent the results of CH produced by reaction Ž2a. and CD produced by reaction Ž2b., respectively. The solid lines represent curves obtained from the simulations in which the rate constants listed in Table 3 ware used.
Fig. 6. Plot of a parameter Žsee text. versus the partial pressure of H 2 . The partial pressure of C 3 O 2 was 130 Pa. The open circles, the closed circles and the squares represent the results obtained at the total pressures of 4, 16 and 79 kPa, respectively.
measured. All the time-resolved data were fitted by the following double-exponential function; I Ž CH . A eya t y eyb t ,
Ž I.
where a and b are fitting parameters. The a and b parameters were obtained for various experimental conditions. Fig. 6 presents a plot of the a parameter versus the partial pressure of H 2 . The results obtained at various total pressures could be fitted by a single straight line. The similar trends were also observed for the case of D 2 . Fig. 7 shows the similar plot for the reaction of HD. The results for CH and
Fig. 7. Plot of a parameter Žsee text. versus the partial pressure of HD obtained at the total pressure of 17 kPa. The partial pressure of C 3 O 2 was 130 Pa. The open and closed circles represent the results for CH produced by reaction Ž2a. and CD produced by reaction Ž2b., respectively.
K. Sato et al.r Chemical Physics 237 (1998) 195–204
Fig. 8. Plot of b parameter Žsee text. versus the partial pressure of H 2 . The partial pressure of C 3 O 2 was 130 Pa. The open circles, the closed circles and the squares represent the results obtained at the total pressures of 4, 16 and 79 kPa, respectively.
CD could be fitted by a single straight line. Fig. 8 shows a plot for the b parameter versus the partial pressure of H 2 . As shown in Fig. 8, the slope of the fitted line depended on the total pressure. The partial C 3 O 2 pressure dependences of the a and b parameters were also measured at a constant partial pressure of H 2 . The linear dependence upon the pressure of C 3 O 2 was found. In order to obtain the CDrCH branching ratio for reaction Ž2., the relative LIF sensitivities of CD and CH are necessary. The relative sensitivities were obtained from the nascent signal intensities of CH and CD produced by the reaction of CŽ1 D. with an equi-molar mixture of H 2 and D 2 . By using these results and rate constants, k 1 and k 3 , the sensitivity ratio of CD to CH was determined to be 1.4 " 0.1. This result is close to that estimated from spectrum w33x and Flanck– simulations using Honl–London ¨ Condon w34x factors, i.e., 1.3. This means that the experimental result of the sensitivity ratio does not include a significant systematic error.
4. Discussion 4.1. Rotational state distribution The photodissociation of C 3 O 2 has been studied at various wavelengths w35–43x. The mechanism of the two-photon dissociation has not been known.
199
Considerable amount of CH radical was produced by the 308 nm two-photon dissociation of C 3 O 2rH 2 mixture. The energetically possible decomposition ˜ 3 Sq . and products may be CŽ 3 P., CŽ1 D., C 2 OŽX 1 3 C 2 O Ža˜ D .. However, C Ž P . q H 2 ™ CH q H, ˜ 3 Sq . q H 2 ™ CH q HCO and C 2 OŽa˜ 1D. C 2 OŽX qH 2 ™ CH q HCO are energetically inaccessible even though the translational energies of the photofragments are taken into account w44–46x. Thus, CH is produced by the reaction of CŽ1 D. with H 2 under the present experimental condition. The rotational state distribution of CHŽ Õ s 0. has been measured by the previous workers using the 157 nm and 248 nm two-photon dissociations of C 3 O 2 w3–8x. The present result obtained by using the 308 nm two-photon dissociation could be compared with the previous ones. As shown in Fig. 2, the CH signals for N F 13 were measured in the present study. Jursich and Wiesenfeld reported that maximal observable N is 14 for the 157 nm photodissociation w4,5x. Their result is very similar to the present result. This is reasonable because the excitation energy of C 3 O 2 is comparable between the 157 nm and 308 nm two-photon dissociations. On the other hand, Fisher et al. reported that CH for N s 13,14 was not measured though they also employed the 157 nm photodissociation w3x. They suggested that this is because the different LIF transitions were used between two 157 nm studies. They used the B § X transition, while Jursich and Wiesenfeld used the A § X transition. The LIF sensitivity for the B § X transition may be lower than that for the A § X transition. Scott et al. used the 248 nm two-photon dissociation and measured CH for N F 15 w6x. In this case, the translational energy of CŽ1 D. should be higher than that for the present study. Therefore, the maximal N is larger than that observed in the present study. The present results was very similar to the results of the 157 nm photodissociations. CH radical detected in the present study must be produced by reaction Ž1.. Under the single collision conditions, the collision energy between CŽ1 D. and H 2 is not relaxed. However, the maximal N observed for CH, 13, was the same as maximal accessible N expected for the total available energy of 300 K, yD H0 q 52 kT. This may be caused by the small reduced mass of the CŽ1 D.rH 2 system as discussed in the previous 157
K. Sato et al.r Chemical Physics 237 (1998) 195–204
200
nm study w3x. The mean collision energy should be close to that of 300 K. A solid curves in Figs. 3Ža. and 3Žb. are RRHO prior distributions w47x at 300 K for reactions Ž1. and Ž3., respectively. The prior distribution and experimental data were normalized at N s 7. The rotational state distributions matched well the RRHO prior distributions as shown in Fig. 3. This strongly suggests that the reaction proceeds via the long-lived intermediate complex. The adiabatic potential energy surface of the reaction has a deep potential well corresponding to CH 2 Ž1A1 .. The vibrationally excited CH 2 Ž1A 1 . intermediate complex should be produced in the reaction. The lifetime of the CH 2 intermediate may be long compared to the time for the intramolecular vibrational energy redistribution ŽIVR. because the well depth is much larger than the exoergicity, 25.0 kJ moly1 . In such a case, the vibrational energy of the intermediate complex is statistically partitioned into all the degrees of freedom prior to the decomposition. Therefore, the rotational state distribution of the product is close to that predicted from the statistical model. The OŽ1 D. q H 2 reaction is also considered to proceed via the deep potential well of H 2 O. However, it is known that the rotational state distribution of OH is much hotter than the statistical one w16x. Because of its large exoergicity, 182 kJ moly1 , the lifetime of the H 2 O may be short compared to the time for IVR. 4.2. Reaction mechanism and rate constants In order to explain the results such as shown in Figs. 6–8, the following mechanism was considered for the C 3 O 2rH 2 system:
k1
k4
C Ž 1 D . q C 3 O 2 ™ product, k5
CH q H 2 ™ product, k6
CH q C 3 O 2 ™ product.
a s k 1 wH 2 x q k 4 wC 3 O2 x , b s k 5 wH 2 x q k 6 wC 3 O2 x . k 1 could be obtained from the slope of Fig. 6 and the intercept of the plot of the a parameter versus wC 3 O 2 x under a constant H 2 partial pressure. The results obtained from two plots were consistent each other. k 2 and k 3 were obtained by the similar procedure for HD and D 2 , respectively. The results of k 1 –k 3 were listed in Table 1 with error of 95% confidence limit. The results of k 4 obtained from the intercept of Fig. 6 and the slope of the plot versus wC 3 O 2 x were also self consistent. Table 1 compares the present results with the previous ones. Braun et al. measured k 1 monitoring decay curves of CŽ1 D. through the resonance absorption method combined with the photograph technique and reported k 1 to be 4.15 = 10y1 1 cm3 moleculey1 sy1 w1x. This value is much smaller than the present one, 2.0 = 10y1 0 cm3 moleculey1 sy1 . Their results for the reactions, CŽ1 D. q NO, CH 4 and O 2 , are also greatly under-estimated compared to the results of other workers w2x. Husain and Kirsch also used the resonance absorption method but recorded the decay curves through a oscilloscope w2x. Their result, 2.7 = 10y1 0 cm3 moleculey1 sy1 , is close to the present result. By using LIF method, Fisher et al. roughly estimated k 1 and k 3 to be 3.7 = 10y1 0 cm3 moleculey1 sy1 w3x, which is also close to the present result.
Table 1 Rate constants for the CŽ1 D.qH 2 , D 2 and HD at the room temperature
C 3 O 2 q 2 hn ™ C Ž 1 D . q 2CO, C Ž 1 D . q H 2 ™ CH q H,
ŽI.. The fitting parameters in equation ŽI. are represented as functions of wH 2 x and wC 3 O 2 x:
Ž 1. Ž 4.
Reaction CŽ1 D.qH 2
Ž 5. Ž 6.
Assuming the initial concentration of CŽ1 D. to be much smaller than those of H 2 and C 3 O 2 , the time variation of the CH signal is represented by equation
CŽ1 D.qHD CŽ1 D.qD 2 a b
CŽ1 D. Source
Rate constant
C 3 O 2 rFP b C 3 O 2 rFP b C 3 O 2 r157 nm C 3 O 2 r308 nm C 3 O 2 r308 nm C 3 O 2 r157 nm C 3 O 2 r308 nm
0.415 2.6"0.3 3.7"0.2 2.0"0.6 1.7"0.4 3.7"0.4 1.4"0.3
In units of 10y10 cm3 moleculey1 sy1 . Vacuum ultra violet flash photolysis.
Ref. a
w1x w2x w3x this work this work w3x this work
K. Sato et al.r Chemical Physics 237 (1998) 195–204 Table 2 Rate constants for CHqH 2 and CDqD 2 at the room temperature Reaction
pŽkPa.ŽM.
Rate constant
CHqH 2
3.3ŽAr. 3.5ŽHe. 4.0ŽHe. 4.1ŽAr. 4.3ŽAr. 13ŽAr. 13ŽAr. 13ŽAr. 13ŽAr. 13ŽHe. 13ŽAr. 16ŽHe. 17ŽAr. 67ŽHe. 79ŽAr. 80ŽAr. 80ŽHe. 4.0ŽHe. 13ŽAr. 13ŽAr. 17ŽHe.
0.79"0.22 0.400"0.040 0.70"0.14 0.564"0.033 0.545"0.120 1.74"0.20 2.6"0.5 1.40"0.10 1.53"0.04 1.02"0.10 1.35"0.07 1.7"0.1 1.548"0.362 2.53"0.25 4.542"0.600 4.5"0.4 3.2"0.2 0.84"0.32 2.05"0.16 1.63"0.15 2.7"0.4
CDqD 2
a
a
Ref. w48x w55x this work w50x w49x w51x w52x w48x w53x w55x w50x this work w49x w55x w49x w48x this work this work w48x w55x this work
201
rable with the sum of the rotational radius of H 2 and ˚ This suggests that the the C–H bond length, 1.4 A. steric factor is close to unity for this reaction. The rate constant, k 5 , was obtained from the slope of Fig. 8, i.e., the plot of the b parameter versus wH 2 x. The results were summarized in Table 2 along with the previous ones w48–55x. As discussed in the previous studies, k 5 depended on the total pressure. This has been consistently explained by a model in which reaction Ž5. proceeds through formation of vibrationally excited CH 3 w48–55x. The excited CH 3 radicals decompose to products or undergoes vibrational relaxation through the collisions with the third body. Because of the collisional stabilization channel, k 5 depends on the total pressure. As shown in Table 2, the present result at each pressure shows good agreements with the previous ones. The similar trend was observed for the case of D 2 as shown in Table 2. In the C 3 O 2rHD system, the exchange reactions of CH and CD may take place:
In units of 10y11 cm3 moleculey1 sy1 . k7
CH q HD ™ CD q H 2 , As shown in Table 1, the larger the reduced mass of the reactant is, the overall rate constant is smaller, i.e. k 1 ) k 2 ) k 3 . The cross section of reactions Ž1., ˚ 2, Ž2. and Ž3. are evaluated to be 10, 10 and 9.6 A respectively. Though the rate constants are different, the cross sections were close each others for three ˚ deterisotopic reactions. The collision radius, 1.7 A, mined from the result of the cross section is compa-
Ž 7.
k8
CD q HD ™ CH q D 2 .
Ž 8.
In order to study influence of reactions Ž7. and Ž8. on the present result of k 2 , the time variation of the signals were numerically simulated taking into account these reactions. The reactions considered in the simulation were listed in Table 3. The CHrCD sensitivity ratio measured in the C 3 O 2rH 2rD 2 sys-
Table 3 Reactions and rate constants employed in the simulations of the CH and CD signals in the C 3 O 2 rHD system Reaction 1
CŽ D. q HD ™ CH q D CŽ1 D. q HD ™ CD q H CŽ1 D. q C 3 O 2 ™ product CH q HD ™ CD q H 2 CH q HD ™ other product CD q HD ™ CH q D 2 CD q HD ™ other product CH q C 3 O 2 ™ product CD q C 3 O 2 ™ product a b c
Rate constant Ž2a. Ž2b. Ž4. Ž7. Ž8. Ž6.
In units of 10y11 cm3 moleculey1 sy1 . Rate constants treated as the fitting parameter with the estimated fitting errors. Rate constants estimated from the results of the C 3 O 2 rH 2 and C 3 O 2 rD 2 systems.
b
7.0 " 3.0 12.0 " 5.0 b 3.0 c 1.0 " 0.5 b 2.0 " 0.5 b 1.0 " 0.5 b 2.0 " 0.5 b 1.0 c 1.0 c
a
202
K. Sato et al.r Chemical Physics 237 (1998) 195–204
be obtained. The result of the branching ratio, 1.6 " 0.1, is listed in Table 4 along with the previous results. Fisher et al. reported that the CDrCH branching ratio is 1.69 in the non-thermal condition w3x. Their result is close to the present result. Whitelock et al. studied the CDrCH branching ratio using the quasi-classical trajectory ŽQCT. calculations on a VB-DIM surface and evaluated the branching ratio to be 2.25 w26x. The result of the QCT calculation is larger than experimental results. The VB-DIM surface may not well represent the global potential
Table 4 XDrXH isotope branching ratio for the XqHD reactions X
D H0
a
a
Method
Ecoll
XDrXH
Ref.
expt. expt.
- 4.2 1.69"0.07 w3x 3.7 1.6"0.1 this work 12 2.25"0.15 w26x
XDqH XHqD CŽ1 D. y25.8 Fig. 9. Time variations of the CDrCH signal ratio obtained at the total pressure of 17 kPa. The partial pressures of HD were 52 Pa Ža., 169 Pa Žb. and 367 Pa Žc.. The solid and dotted lines are the curve simulated by using k 7 and k 8 listed in Table 3 and that simulated by setting k 7 and k 8 to be zero, respectively Žsee text..
tem was used in the simulation. The best-fitted curves were obtained from comparisons with 15 different time-resolved results. The rate constants deconvoluted from the simulations were listed in Table 3. Fig. 9 shows the time variations of the CDrCH signal ratio. The solid and dotted lines represent the curve simulated by using k 7 and k 8 listed in Table 3 and that simulated by setting k 7 and k 8 to be zero, respectively. The CDrCH signal ratio is sensitive to k 7 and k 8 . However, the time variations of the CH and CD signals, shown in Fig. 5, were not sensitive to these rate constants. In addition, the deconvoluted result of k 2a q k 2b , 1.9 " 0.6, is consistent with k 2 obtained from Fig. 7, 1.7 " 0.4. The influence of reactions Ž7. and Ž8. can be ignored on the estimation of k 2 .
OŽ1 D. y184
FŽ2 P. y137
4.3. Isotope branching ratio As shown in Fig. 9, the CDrCH signal ratio did not greatly change in the 0.06–0.1 ms region. By correcting the signal ratio in this region with the sensitivity ratio, the CDrCH branching ratio could
a b c d
y21.4
y178
y131
QCTr DIM expt. b expt. expt. expt. b expt. c expt. QCTr DIM QCTr MC QCTr SL1 QCTr MCMG expt. expt. expt. QCTr 6SCE QCTr T5A QCTr M5 QCTr SW IOSA d r TS
w18x w20x w14x w18x w18x w23x w26x
13 13 10 10 10 3.7 8.4
1.35"0.20 1.3"0.2 1.13"0.08 1.5"0.2 1.3"0.1 1.33"0.07 5.60"0.27
21
1.09"0.06 w15x
21
1.43"0.18 w15x
24
1.77"0.25 w17x
3.7 ;11 3.7
0.69 0.70 0.66 0.79
w56x w57,58x w14x w59x
3.7
0.95
w59x
3.7
1.03
w59x
3.7
0.79
w60x
8.3
2.18
w61x
In units of kJ moly1 . The multiphoton ionization measurement. The vacuum-ultra-violet LIF measurement. Infinite-order-sudden approximation.
K. Sato et al.r Chemical Physics 237 (1998) 195–204
energy surface. For the reaction of CŽ1 D., QCT calculations on ab initio surfaces have not been performed. In order to obtain detailed information on the potential energy surface, such a study is necessary. The XDrXH branching ratio for the X q HD reaction have been studied for the various reaction systems as shown in Table 4. The isotope branching ratio for the reaction of FŽ2 P. is smaller than unity, 0.7 w56–61x. This reaction is known to proceed via direct abstraction. Since the cross section of H atom is larger than that of D atom due to the rotation of HD, the HF becomes a dominant product in this reaction. On the other hand, the isotope branching ratios are larger than unity for the reactions of CŽ1 D. and OŽ1 D.. These reactions are considered to proceed via the deep potential well. In this case, the XDrXH branching ratio may be determined by the rate constants of unimolecular decomposition of the HXD intermediate complex. The XDrXH branching ratio, G , was evaluated from the following equation which was based on the Kassel equation;
Gs
ka kb
s
Aa Ab
Ea‡
ž / E b‡
2
,
where A is vibrational frequency for the dissociating bond of HXD, E ‡ is the total available energy of the product and subscripts ‘a’ and ‘b’ represent the HXD ™ H q XD and HXD ™ HX q D reactions, respectively. The results were 1.4 and 1.8 for OŽ1 D. and CŽ1 D., respectively. The XD diatomic product is dominantly produced because the elimination of light H atom is faster than that of heavy D atom. The lifetime of the H 2 O intermediate is considered to be short compared to the time for IVR w14–25x. If this is the case, the above treatment is not applicable to the OŽ1 D. q HD reaction. However, the result for OŽ1 D. qualitatively explains the experimental result, 1.13–1.5. The experimental results for the CŽ1 D., 1.6–1.69, is well explained by the above treatment. This result also suggests that the reaction of CŽ1 D. proceeds via the CH 2 intermediate complex. 5. Conclusion The reactions of CŽ1 D. with H 2 , HD and D 2 were investigated using the 308 nm two-photon dissocia-
203
tion of C 3 O 2 . The rate constants for the reactions of three isotopomers were simultaneously measured at the first time. Although the rate constants for three reactions are different, the reaction cross sections were the same. The obtained cross section was 10 ˚ 2 . The reaction proceeds with the rate constant A comparable with the gas-kinetic one. The CDrCH branching ratio and the rotational state distributions were also measured. The CDrCH branching ratio was well explained by the model based on the Kassel equation for the the unimolecular decomposition of HCD. The rotational state distribution matched well the RRHO prior distribution. These results strongly suggests that the long-lived intermediate complex is produced in the reaction. In order to obtain more detailed information on the reaction dynamics, the QCT calculations on the ab initio surface are necessary.
Acknowledgements The authors wish to thank Professor Okitsugu Kajimoto of Kyoto University and Professor Kenji Honma of Himeji Institute of Technology for a technical advice on the 308 nm photodissociation of C 3 O2 .
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