Infrared multiphoton dissociation of 2chloro1,1,1,2tetrafluoroethane in a molecularbeamAtsushi Yokoyama, Keiichi Yokoyama, and Ginji Fujisawa Citation: The Journal of Chemical Physics 100, 6487 (1994); doi: 10.1063/1.467057 View online: http://dx.doi.org/10.1063/1.467057 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/100/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in An International Standard Formulation for the Thermodynamic Properties of 1,1,1,2Tetrafluoroethane (HFC134a) for Temperatures from 170 K to 455 K and Pressures up to 70 MPa J. Phys. Chem. Ref. Data 23, 657 (1994); 10.1063/1.555958 Thermophysical properties of gaseous refrigerants from speed of sound measurements. I. Apparatus,model, and results for 1,1,1,2tetrafluoroethane R134a J. Chem. Phys. 93, 2741 (1990); 10.1063/1.458913 Infrared multiphoton dissociation of RDX in a molecular beam J. Chem. Phys. 88, 801 (1988); 10.1063/1.454158 Infrared multiphoton dissociation of 1chloro1fluoro ethylene: Competitive reactions and pressuredependence J. Chem. Phys. 79, 816 (1983); 10.1063/1.445881 Far Infrared Spectrum and the Barrier to Internal Rotation in 1,1,1,2Tetrafluoroethane J. Chem. Phys. 30, 582 (1959); 10.1063/1.1729991

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

128.192.114.19 On: Thu, 18 Dec 2014 10:47:16

Infrared multiphoton dissociation of 2-chloro-1, 1,1 ,2-tetrafluoroethane in a molecular beam

Atsushi Yokoyama, Keiichi Yokoyama, and Ginji Fujisawa Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki-ken 319-lI, Japan

(Received 27 September 1993; accepted 20 January 1994)

Mechanism and dynamics of the infrared multiphoton dissociation of 2-chloro-l, 1,1,2-tetrafluoroethane have been studied using a photofragmentation translational spectroscopy. The molecule dissociates competitively through three-centered elimination of HCI and C-CI bond rupture. The HCI elimination reaction accounts for 74% of the total primary dissociation yields. The center-of-mass translational energy distribution for the HCI elimination indicates that an exit barrier of several kcallmol exists along the reaction coordinate on the potential energy surface. The infrared multi photon dissociation of CF3CF produced by the HCI elimination from CF3CHCIF also occurs as a secondary process through its dissociation into two CF2 molecules. The average excitation energy of dissociating CF3CHCIF has been determined to be about 20 kcallmol above the C-Cl dissociation threshold of the molecule by comparing the observed center-of-mass translational energy distribution for the C-CI bond rupture reaction with that calculated by Rice-Ramsperger­Kassel-Marcus (RRKM) theory.

I. INTRODUCTION

Since infrared multiphoton dissociation (IRMPD) occurs under collision free conditions, this allows us to study uni­molecular dissociation reactions without interference of sec­ondary reactions of primary products with ambient mol­ecules. A photo fragmentation translational spectroscopy (PTS) is a powerful experimental technique for studying photodissociation mechanisms and dynamics of systems un­dergoing complex dissociation pathways including several primary and secondary dissociation channels.! The technique has been successfully applied to studies on IRMPD of many molecules by Lee et al. 2 In their studies on simple bond rup­tures of several halogenated methanes and ethanes, they have elucidated that Rice-Ramsperger-Kassel-Marcus (RRKM) theory can predict the translational energy distributions of products from the reactions with no exit barrier.3 Thus, in this case we can estimate the average excitation energy of dissociating molecules by comparing an observed transla­tional energy with calculated ones. On the other hand, trans­lational energy distributions for HCI elimination reactions with an exit barrier cannot be predicted by RRKM theory, because the amount of the energy released as translational energy depends on the dynamics of dissociation beyond the transition state.

In the case of three-centered HCI elimination from halo­genated methanes such as CF2HCI, CHCI2F,4 and CHCI3 ,5

the translational energy distribution peaked at several kcall mol, and at least more than half of the exit barrier is released as translational energy. On the other hand, the translational energy distribution for the three-centered HCI elimination from CF2CHCI (Ref. 4) peaked at 0 kcal/mol, as in the case of simple bond ruptures with no exit barrier. Kim and Setser6

have suggested that the exit barrier was small for the three­centered HCI elimination from I, I ,2-trichloroethane. These observations may indicate that exit barrier is very small for the three-centered HCI elimination from chlorinated ethanes

and ethenes in contrast to halogenated methanes. However, there are few examples to draw the conclusion.

Infrared multi photon dissociation of 2-chloro-l, I, I ,2-tetrafluoroethane (CTEFE) has been studied as a working molecule for tritium separation from water by laser isotope separation.7,s Kato et al.9 have reported that the molecule dissociated competitively through three-centered HCI elimi­nation and C-CI bond rupture channels. They also observed CF2 as a secondary dissociation product, but the secondary dissociation mechanism was not elucidated.

In this paper, we try to elucidate the dissociation mecha­nism including secondary dissociation channel and examine whether an exit barrier exists for the three-centered HCI elimination from CTEFE.

II. EXPERIMENT

A molecular beam machine for the PTS is shown in Fig. 1. The design concept of this machine is similar to that of a rotatable source machine constructed by Lee et at.1O This machine consists of three parts; a source region, a main re­gion, and a detector region. The molecular beam was formed by expanding CTEFE (PCR Research Chemicals) at the stag­nation pressure of 200 Torr into the source region through a 0.1 mm diam nozzle. The nozzle was heated at 250°C to enhance multiphoton absorption and prevent the formation of clusters. The source region was pumped to about 10-4 Torr by a combination of a 6 in. oil diffusion pump and a 1500 lis turbomolecular pump while the beam was running. The mo­lecular beam was collimated by being passed through two skimmers attached to two walls of a differential pumping region between the source and detector regions. Then, the beam was crossed with the laser beam at the center of the main region. The main region was pumped to about 10-7

Torr by a 10 in. oil diffusion pump. Copper panels cooled at 77 K were set in the main region to aid pumping capability.

J. Chern. Phys. 100 (9), 1 May 1994 0021-9606194/100(9)/6487/5/$6.00 © 1994 American Institute of Physics 6487 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

128.192.114.19 On: Thu, 18 Dec 2014 10:47:16

6488 Yokoyama, Yokoyama, and Fujisawa: Dissociation of 2-chloro-1 ,1 ,1 ,2-tetrafluoroethane

FIG. 1. Experimental arrangement: (1) molecular beam nozzle, (2) quadru­pole mass spectrometer, (3) 200 Us magnetically suspended turbomolecular pump, (4) 300 Us magnetically suspended turbomolecular pump, (5) IO in. oil diffusion pump, (6) 6 in. oil diffusion pump, (7) CO2 laser, (8) multi­channel scalar, and (9) pulse generator.

Laser beam from a TEA CO2 laser (Lumonics TEA-841) with a temporary pulse form of a 100 ns spike followed by 5 fLS tail was focused with a 30 cm focal length ZnSe lens. The size of laser spot was 3X3 mm2 at the interaction region of the laser and the molecular beam. The CTEFE was excited at 9.294 JLm with the laser fluence of 3 or 19 J/cm2

• The neutral fragments flying through two differential" pumping regions were ionized by electron bombardment at the electron energy of 100 e V, mass selected, and detected by a quadrupole mass spectrometer (Extrel C50) in the detector region. The ionizer of the quadrupole mass spectrometer was located at 44.0 cm away from the interaction region. The detector region was pumped to about 10- 10 Torr by a 300 lis magnetically sus­pended turbomolecular pump. The wall surrounding the ion­izer was cooled at 77 K. We obtained the time-of-flight (TOF) spectra of the fragments by recording ion signals of the fragments on a multichannel scaler as a function of their flight time from the interaction region to the detector. Each TOF spectrum was obtained by accumulating signals for 200 000-1 200 000 laser shots. The source region can be rotated with respect to the laser beam axis, and the spectra were obtained at beam-to-detector angles of 5° and 10°. The velocity distribution of the molecular beam was measured by a conventional TOF method. The molecular beam was chopped to ca. 8 JLS pulse by a slotted wheel and the TOF spectra of the molecular beam was measured at the detector angle of 0°.

III. RESULTS AND ANALYSIS

Signals of fragments were observed at ml e = 31, 32, 35, 36, 50, 51, 69, and 82. A TOF spectrum at ml e = 36 (HCl +)

,..... ....... ..... c ;:;

.ci I-<

~ >. ....... ..... en c aJ

.......

.5

1.0

0.8

0.6

0.4

0.2 1

" -. 0.0

.. : --.

0.0 500

Hel +

e =10 deg.

.. ..... --- I

1000 1500 Flight Time (f1 sec)

FIG. 2. TOP spectrum at mle= 36. Solid line represents the calculated TOP spectrum of HCl produced by reaction (I).

is shown in Fig. 2. This signal must come from HCI pro­duced by the three-centered HCI elimination:

CF3CHClF--.CF3CF+HCl .:lH~(calc)=79.3 kcallmol. (I)

The heat of reaction .:lHo(calc) was estimated by ab initio molecular orbital (MO) calculations at the MP2IECPDZPII HFIECPDZP level. lI The solid line in Fig. 2 represents the time-of-flight (TOF) spectrum calculated using the transla­tional energy distribution, peE), for reaction (I). The peE) was determined by the forward convolution method12 and is shown in Fig. 3.

The peak in the TOF spectrum at mle=82 (C2HFj), shown in Fig. 4, comes from CF3CHF produced by the C-Cl bond rupture reaction:

CF3CHClF--.CF3CHF+CI .:lHo(calc)=80.3 kcallmol. (II)

The primary ion of the CF3CHF could not be observed. This may be due to the fragmentation of the radical by electron bombardment, because the radical is internally excited. The counterpart of this fragment is observed as the slow compo­nent in the TOF spectrum at ml e = 35 (CI +) as shown in Fig. 5. The fast component in the spectrum is the daughter ion of HCl. Although the ml e = 3 1 (CF+) TOF spectrum at 19 J/cm2 looks like one component, the maximum velocity of

1.0

O. 0 '-----'--_"'----"'=--...... --1

o 5 10 15 20 25 Translational Energy (kcal/mol)

FIG. 3. Center-of-mass translational energy distribution for reaction (I).

J. Chern. Phys., Vol. 100, No.9, 1 May 1994 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

128.192.114.19 On: Thu, 18 Dec 2014 10:47:16

Yokoyama, Yokoyama, and Fujisawa: Dissociation of 2-chloro-1 ,1,1 ,2-tetrafluoroethane 6489

1.0 t '" CzHF3 ..... .~ 0.8 c e =5 deg. ::>

.ci 0.6 I-< ~ '-' 0.4 ' . >. -..... .

'U) 0.2 . .. c <I.l ..... .= O. 0 ·c" .:-. .

0.0 500 1000 1500 Flight Time (fJ. sec)

FIG. 4. TOF spectrum at mle = 82. Solid line represents the calculated TOF spectrum of C2HF3CI produced by reaction (II).

the fragment producing CF+ decreases with decreasing the laser fluence as shown in Fig. 6. Therefore, the TOF spec­trum at 19 J/cm2 consists of two components, and the fast component is due to a secondary photodissociation product. This component also appears in the TOF spectrum at ml e = 50 (CF;) as shown in Fig. 7, but not in the spectrum at mle=69 (CFt). Although we carefully searched mass spec­tra of CF3CF, which is the counterpart of HCI from reaction (I), no signal could be detected at mle= 100 (C2Ft), 81 (C2Ft), 62 (C2Ft), and 43 (C2F+) at the laser fluence of 19 J/cm2

• Therefore, most of CF3CF dissociated to fragments containing one carbon atom through a secondary photodisso­ciation process. If the process were the C-C bond rupture of CF3CF:

CF3CF-.CF3+CF AH~(ca1c)=75 kcaUmol, (III)

signal from the fragment contributing to the fast component in the ml e = 50 TOF spectrum should also appear in the TOF spectrum at ml e = 69, and the fast component in the ml e = 3 1 TOF spectrum should be faster than the fast component in the ml e = 50 TOF spectrum. Therefore, reaction (III) does not contribute to the secondary photodissociation process. The secondary dissociation product must be CF2 produced by the following concerted process:

~ ...... 1.0

·8 o~ 8 ::>

-e 0.6 ~

';. 0.4 ..... ...... '" C <I.l ..... C ~

0.2

0.0

0.0

CIt

e =10 deg.

500 1000 1500 Flight Time (IJ. sec)

FIG. 5. TOF spectrum at mle=35. Fast component (- -) is due to HCI from reaction (I), and slow component (- . -) is due to CI from reaction (II).

1.0 .f'. CF

t ~

.t'I!"'" ..... • .-< 0.8 ".,~ c e =10 deg. ::> ~'i'N: ..d 0.6 I· "'::;:1e I-< ",0,.:( . ~ -<to ... ~~ '-' 0.4 ." ~o ,~"o' >. . ~."o:(> ; . 1 ......

..-< 0.2 l ~o .,_ (0 ". •

'" :(f:j": W;\ c " S; "" <I.l ..... o.~ ''iJf~!. 0.0 c o 0l~.!o:l •

~

90 ·v" •

0.0 500 1000 1500 Flight Time (fJ. sec)

FIG. 6. TOF spectra at ml e = 3 1 at the laser fiuence of 3 (0) and 19 J/cm2

(e).

CF3CF-.CF2+ CF2 AHo( calc) =37 kcaUmol. (IV)

The peE) for reaction (IV) is shown in Fig. 8. It peaks at ca. 3 kcaUmol with the average energy of 4.7 kcaUmol, and is similar to that for the concerted HCI elimination reaction shown in Fig. 3. Since a typical peE) for simple bond rup­ture peaks at around 0 kcallmol, the peE) should peak at around 0 kcallmol if reaction (III) contributed to the second­ary photodissociation. On the other hand, the peE) for reac­tion (IV) should peak at nonzero energy, because the poten­tial energy surface for this reaction must have an exit barrier. Therefore, this peE) also supports the conclusion that the secondary photodissociation proceeds not through reaction (III) but through reaction (IV).

'" .....

1.0

0.8

0.6

0.4

'§ 0.2

t;> 1.0 • .-<

gj <I.l ...... .=

0.8

0.6

0.4

0.2

o

::, <to.

500

CF t Z

e =10 deg.

1000 1500 Flight Time (IJ. sec)

FIG. 7. TOF spectra at ml e = 3 1 and 50. Laser fiuence was 19 J/cm2: - - -

CF2 from reaction (IV), - - C2F4 from reaction (I), - . - C2HF4 from reaction (II).

J. Chern. Phys., Vol. 100, No.9, 1 May 1994 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

128.192.114.19 On: Thu, 18 Dec 2014 10:47:16

6490 Yokoyama, Yokoyama, and Fujisawa: Dissociation of 2-chloro-1, 1,1 ,2-tetrafluoroethane

1.0

'" ...... ...... .::: ;::l

..ci ~ 0.5 m ~

'" w ~

CL..

0.0 0 5 10 15 20 25

Translational Energy (kcal/mol)

FIG. 8. Translational energy distribution for reaction (IV).

The branching ratio of reaction (I) to reaction (II) is defined by the ratio of the HCI concentration to the CI con­centration. The ratio is determined to be 2.8 from the total HCl + and Cl + signal intensities measured at the beam-to­detector angle of 10°. The procedure for calculating the true branching ratio from the ion signals measured in the mass spectrometer was the same as that described in Ref. 13. The relative ionization cross sections of HCI and CI were calcu­lated by the following empirical formula of the maximum ionization cross section: 13

u= 36 ;;;-18,

where a is the polarizability in unit of A3. The values of the polarizabilities for CI and HCI are 2.1814 and 2.63,15 respec­tively.

IV. DISCUSSION

A. Translational energy distribution for the C-CI bond rupture

The observed PCE) for reaction (II) is shown in Fig. 9. The calculated RRKM P(E),s for the C-CI bond rupture of CF3CHCIF with excess energies of 15, 20, and 25 kcallmol are also shown in this figure. The transition state was deter-

1.0

'" ...... ...... .::: ;::l

..ci 0.5 ~ m ~

'" w ~

CL..

0.0 0 5 10

Translational Energy (kcal/mol)

FIG. 9. Translational energy distributions for reaction (II): - Observed distribution; - .. - 15 kcallmol excess energy; - . - 20 kcallmol excess energy; - - 25 kcallmol excess energy.

TABLE 1. Parameters used in RRKM calculations.

Transition state

CF3CHClF C-CI rupture HCI elimination

Frequency (cm- I)

3235 3326 1652 1448 1488 1359 1355 1321 1308 1336 1226 1305 1246 1213 1045 1202 1179 997 1140 873 910 916 735 720 840 675 705 702 557 570 576 522 511 531 419 401 456 353 286 382 219 243 325 111 169 242 11l 108 191 87 47 76

Moment of inertia (amu IV) 165 173 162 267 485 346 331 547 411

Critical energy (kcallmo1) 79.2 8004

mined to be at the C-Cl bond length where the state density is minimum. The potential energy along the C-Cl bond length was modeled with a Morse potential determined from the C-Cl stretching frequency of the normal CF3CHCIF molecule and its C-Cl bond dissociation energy obtained by the ab initio MO calculation. Two C-Cl bending frequencies as a function of the C-CI bond length were calculated ac­cording to the equation:

n(r) = n( ro)exp[ - (r- ro)! a],

where r is the C-Cl bond length, ro is its equilibrium length, and a is a constant. The value of a was chosen to be 1.04 A, which was used in the RRKM calculations for the several simple bond rupture reactions of halogenated methanes.4

Other 15 frequencies at the transition state were taken from the frequencies of CF3CHF. The frequencies of CF3CHCIF and CF3CHF were obtained by the ab initio MO calculations . The parameters used in the RRKM calculations are summa­rized in Table I. The calculated distribution shows that the probability is maximum at 0 kcallmol and decreases mono­tonically with increasing the translational energy. On the other hand, the observed peE) peaks around 0.5 kcallmol. The peak position is not highly accurate, because signals from HCl overlap with signals from Cl in the ml e = 35 TOF spectrum, and because the velocity of CF3CHF is not sensi­tive to the shape of the peE) in this energy range. However, it is certain that the peE) peaks at >0.3 kcallmol. This peak is probably due to a centrifugal energy barrier.16 By the com­parison of the observed peE) with the calculated ones, the

J. Chern. Phys., Vol. 100, No.9, 1 May 1994 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

128.192.114.19 On: Thu, 18 Dec 2014 10:47:16

Yokoyama, Yokoyama, and Fujisawa: Dissociation of 2-chloro-1 ,1 ,1 ,2-tetrafluoroethane 6491

average excitation level of dissociating CF3CHClF is esti­mated to be about 20 kcallmol above the C-Cl bond disso­ciation threshold.

B. Translational energy distribution for the three-centered HCI elimination

The P(E) for reaction (I) peaks at ca. 3 kcallmol as shown in Fig. 3, and the average energy is 5 kcallmol. In the case of the three-centered HCl elimination from CHClF2

with an exit barrier of 7 kcal/mol, the peak and average energies of the P(E) were about 5 and 8 kcallmol, respectively.4 If the fraction of the peak energy to the exit barrier is the same for the three-centered HCl eliminations from CHClF2 and CF3CHClF, the exit barrier of about 4 kcallmol should exist in the potential energy surface for the three-centered HCl elimination from CF3CHClF. From the pressure dependence of the cis-trans isomerization rates of CHClCHCl, Kim and Setser6 estimated the internal energy distribution of CHClCHCl produced by H migration of CH2ClCCI following the three-centered DCl elimination from CH2ClCDCI2 :

CH2ClCDCl2-tCH2ClCCI + DCl,

CH2ClCCI-tCHClCHCI.

(V)

(VI)

They inferred that the exit barrier for reaction (V) was zero or nearly zero from the analysis of their experimental data. This seems to be different from our result on CTEFE. How­ever, the internal energy distribution of CHClCHCl is not so sensitive to the small potential energy release associated with reaction (V), because the internal energy, which consist of the excess energy partitioned statistically to CHClCHCl (ca. 20 kcallmol) and the potential energy change of reaction (VI) (ca. 50 kcal/mol), is much larger than a typical exit barrier for a three-centered HCI elimination. In the case of CTEFE translational energy comes from the excess energy and the exit barrier. Since about 1.8 kcallmol is expected to be re­leased as the translational energy as a result of the statistical partitioning of the excess energy (about 19 kcallmol) to all vibrational degrees of freedom, the contribution of the excess energy to the translational energy is less than that of the typical exit barrier. Therefore, our measurement is sensitive to the height of the exit barrier, and the exit barrier of several kcallmol should exist along the reaction coordinate on the potential energy surface of three-centered HCI eliminations even from chlorinated ethanes.

The P(E) for the three-centered HCI elimination from CF2CHCI peaks at nearly zero kcal/mol.4 This characteristic is similar to the P(E) for simple bond ruptures with no exit barrier. In our experiment for the IRMPD of CHCICCI2 ,17

the P(E) for the three-centered HCI elimination from CHCICCl2 also peaks at around 0 kcallmol. Therefore, the exit barrier for the three-centered HCI elimination from ha­logenated ethenes should be very small.

C. Branching ratio of the HCI elimination to the C-CI bond rupture

The measured branching ratio of reaction (I) to reaction (II) is 2.8. The RRKM rate constants of the CTEFE mol-

ecules having the internal energy of 99 kcallmol, which is the average excitation energy of the dissociating CF3CHCIF, are 0.58 and 0.52 I1-S-

1 for the C-Cl bond rupture and Hel elimination reactions, respectively. The frequencies of the transition state for the three-centered HCI elimination, listed in Table I, are estimated from those for the three-centered HCI elimination from CF2CICHCIF obtained by the ab initio MO calculation. The RRKM branching ratio is calculated to be 0.9. This value does not agree with the experimental one. The experimental value can be reproduced when the critical energy for the HCI elimination is assumed to be 1.2 kcallmol lower than that for the C-CI bond rupture, while the ab initio value is 1.2 kcallmol higher. This discrepancy is not signifi­cant when we consider the reliability for the method adopted.

V. CONCLUSION

2-chloro-l, 1,1 ,2-tetrafluoroethane molecules with the average internal energy of ca. 99 kcallmol dissociate com­petitively through C-CI bond rupture [reaction(II)] and three-centered HCI elimination [reaction(I)]. The P(E) for the three-centered Hel elimination indicates the existence of the exit barrier for this reaction, as in the case of the three­centered Hel elimination reactions from chlorinated meth­anes. The IRMPD of CF3CF, a product from reaction (I), also occurred as a secondary process through its dissociation to two CF2 molecules [reaction(IV)].

ACKNOWLEDGMENT

The authors wish to thank Professor Y. T. Lee for his kind advice on the construction of the molecular beam ma­chine used in this experiment.

1 For example, A. Yokoyama, X. Zhao, E. J. Hintsa, R. E. Continetti, and Y. T. Lee, J. Chern. Phys. 92, 4222 (1990).

2p. A. Schulz, Aa. S. Sudbo, D. J. Krajnovich, H. S. Kwok, Y. R. Shen, and Y. T. Lee, Annu. Rev. Phys. Chern. 30, 379 (1979), and references therein.

3 Aa. S. Sudbo, P. A. Schulz, E. R. Grant, Y. R. Shen, and Y. T. Lee, J. Chern. Phys. 70, 912 (1979).

4 Aa. S. Sudbo, P. A. Schulz, Y. R. Shen, and Y. T. Lee, J. Chern. Phys. 69, 2312 (1978).

51. P. Herman, F. Magnotta, R. Buss, and Y. T. Lee, J. Chern. Phys. 79, 1789 (1983).

6K. C. Kim and D. W. Setser, J. Phys. Chern. 78, 2166 (1974). 7 O. Kurihara, K. Takeuchi, S. Satooka, and Y. Makide, J. Nuc!. Sci. Tech­

no!. 20, 617 (1983). 8K. Takeuchi, S. Satooka, and Y. Makide, J. Nucl. Sci. Technol. 21, 959

(1984). 9S. Kato, Y. Makide, T. Tominaga, and K. Takeuchi, Laser Chern. 8, 211

(1988). 10 A. M. Wodtke and Y. T. Lee, J. Phys. Chern. 89, 4744 (1985). 11 K. Yokoyama, A. Yokoyama, and G. Fujisawa (manuscript in preparation). 12 Algorithm for the calculation was originally developed by Y. T. Lee group

in U.C. Berkeley. 13D. Krajnovich, F. Huisken, Z. Zhang, Y. R. Shen, and Y. T. Lee, J. Chern.

Phys. 77, 5977 (1982). 14T. M. Miller and B. Bederson, Adv. At. Mol. Phys. 13, I (1977). 15 Kagakubinran, edited by Nihonkagakukai (Maruzen, Tokyo, 1984), in

Japanese. 16D. J. Krajnovich, Ph.D. thesis, University of California, 1983. 17K. Yokoyama, A. Yokoyama, and G. Fujisawa (manuscript in preparation).

J. Chem. Phys., Vol. 100, No.9, 1 May 1994 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

128.192.114.19 On: Thu, 18 Dec 2014 10:47:16