Chemical Ph3mics 1~8 (1984) 135-1425=: __ '-: :-'" --- :- North-Holland, Amste rdam

" " - -'" -''- - -.2_-- -: - "

P H O T O D I S S O C I A T I O N O F M O L E C U L A R B E A M S O F I t A L O G E N A T E D H Y D R O C A R B O N S AT 193-nm

Masahiro K A W A S A K I , Kazuo KASATANI , Hiroyasu SATO

Chemistry Department of Resources, Faculty of Engineering, Afi'e Universi¢); Tsu 514, Japan

and

Hisanori S H I N O H A R A and Nobuyuki N I S H I Institute for Molecular Science, Okazaki 444, Japan

Received 19 October 1983; in final form 19 March 1984

Molecular beams of halogenated hydrocarbons conta ining chlorine and bromine a toms were photodissociated using an excimer laser at 193 nm. Molecules photodissociated were HCCBr, H C C C H 2 Br, HCCCHzCI, CH3CI, C2HsCI and i-C3H7C1. The t ime-of-f l ight-distr ibut ions of the photof ragments were measured in o rder to s tudy the pr imary processes and the

- dissociation dynamics. General izat ions consis tent with the da ta are that a tomic products (RX---, R + X ) result f rom direct dissociation o f the C - X repulsive singlet state, molecular e l iminat ion (RX --* g ' + HX) is a result of a crossover to the ground state and triplet states are involved in the photodissociat ion of alkyne compounds .

1. Introduction

-The photodynamics of halogenated hydro- carbons have been studied mainly by photofrag- ment spectroscopy. Riley and Wilson [1] and Dzvonik et al. [2] have reported that, when methyl- iodide is photodissociated at its first absorpt ion band, the dissociation lifetime is as short as 0.1 ps for the process

2 C H a I ~ C H 3 + I( Pl/2)"

Chou et al. [3] have suggested another minor pro- cess for near U V photolysis

CH3I --* C H , + HI .

The pr imary processes of CH3CI and CH3Br in U V photolysis have been reported to be direct breaking of the C - X bond [41. Photoabsorpt ion of alkyl halides may result in both atomic and molec- ular elimination, . _ ._

R x - - : R+X, (1) L , _. R'-V:HX~-- (2)

When a methylene radical reacts with methyl halides: a vibrationally excited ground-state alkyl halide C 2 H s X * is formed which undergoes an H X molecular elimination reaction.-This suggests that if RX* is formed from an intermediate state in process (2) the translational energy (ET) distribu- tion P ( E T ) for H X photofragments must differ f rom P ( E T ) for X photofragments formed in pro- cess (1). Unimolecular dissociations of halogenated methanes induced by I R laser light have been studied by S u d r o et al. [6] and P ( E T ) can be described b y a statistical theory of unimolecular reactions. The direct rupture of the C - X bond induced by U V absorpt ion may result in a non- statistical distribution of P ( E T ) , e.g., a Poisson distribution.

When a molecule has two chromophores, Li.e. o and -n systems, photoabsorpt ion causes two excita- tion mechanisms- (i) direct excitation of the C - X bond and (ii) energy flow from the ~r bond to the C - X b o n d . The resulting bond dissociation pro- c e s s competes with internal "conversion and inter- system crossing processes. We have photodi'ssoci- a ted H C C X a n d - H C C C H 2 X molecules as model

0301-0104/84/$03.00 © Elsevier Science Publishers B.V. _ (Nor th-Hol land physics Publishing Division)

136 AL Kawasaki et aL / Photadissociation of halogenate of hydrocarbons

compounds to understand intramolecular processes using photofragment spectroscopy, i.e. measuring time-of-flight and angular distributions of photo- fragments.

2. Experimental

The photofragment spectrometer has been de- scribed in detail elsewhere [7]. Briefly. the super- sonic nozzle molecular beam was photodissociated by 193 nm excimer laser light (~-20000 shots). Photofragments were detected by a quadrupole mass filter (Q-mass) with an electron bombard- merit ionizer at a flight path of 6.9, 8.0 or 16 cm. The Q-mass, operat ing at unit mass resolution, was placed in the reaction chamber for the 6.9 and 8.0 cm flight path. while for the 16 cm flight path the detector chamber was separated from the reac- t ion chamber and pumped differentially by a turbo molecular pump and an ion pump. Using a suit- able jacobian factor [8], the time-of-flight (TOF) data are converted to a center-of-mass reference- frame translational energy distribution P ( E T ) after subtracting the drift t ime in the mass-filter tube. For an angular distribution measurement, a pile- of-plate polarizer was used to polarize the excimer laser light. The plane of polarization was rotated with respect to the detector axis. Commercial ly available chemicals were used as received. Bromoacetylene was prepared by the method of Bashford et al. [9]. Purification was done by vacuum distillation.

laME OF FLIGHT !/as o 2oo 400 6oo B00 | " t - i ~ i

Z '"'~'i , , i '

- I ~ ~ '

r ' ' n r ' ' ! J t t !

O 200 400 600 800 lOO0 TIME AFIER LASER PULSE l.a..q

Fig. I. Time-of-flight distribution for re~e= 79 Br + signals from HCCBr at 193 nm. Solid line: background signal~. Flight length l = 8 cm.

probabil i ty P , ( E T ) was low in the low E T region. This results f rom the fact that the detector axis is at right-angles to the molecular beam axis. The apparatus of Sudbo et al. [6] has the advantage that the angle between the detec tor and the molec- ular beam axis can be varied. Assuming a simple model, we can safely suggest that Pr(ET>~40 k J / m o l ) is larger than 0.9 [10]. Three peaks appear in the translational energy distr ibution P ( E T ) of bromoacetylene in fig. 2. The energy difference of the two peaks corresponds approximately to the energy difference of Br(2p3/:) and Br*(2P1/2), that is 44 k J / m o l .

HCCBr + h v - - - ~ HC 2 + Br(-'P3/2), (3) . 2

HC, + Br ( P,/2)- (4)

3. Results

3.1. Bromoacetytene and propargylbromide

In fig. 1 the signal of m / e = 79 corresponding to Br + is plot ted versus flight time for the photoly- sis of HCCBr molecular beams at 193 rim. A background signal was observed to arise with time when the Q-mass was placed in the reaction cham- ber due to scattering o f paren t molecules. The m / e = 25 (C2 H) signal was d r o w a e d in the high background noise level. When the heavier, slowly moving fragments were observed, the detect ion

3

~ Z o

o . .

J I i

- ~ " - ~ ItCCCH2Br/Br A

- 2 " , , . . . . " - ...... | \ ",, -i

50 100 150 2O0

To to l T r t ans l o t t ono l Energy E T / kJ.mo1-1

F i g . 2. T o t a l c . m . t r a n s l a t i o n a l e n e r g y d i s t r i b u t i o n P ( E T ) o b -

t a i n e d from Br and HBr pbotofragments for the pbotolysis of HCCBr and HC2CHzBr at 193 nm. - - - - - HCCBr/Br; - - HC2CH2Br/Br; ... HC2CH2Br/HBr.

M. Kawasaki et al. / Photodissociation of halogenate of hydrocarbons

The lowest one seems to peak towa~rd zero. F rom fig. 2 we can safe ly-conclude t h a t - i t peaks at E r < 20 k J / m o l . -

In fig. 3 T O F spectra are p lo t t ed for m/e = 79 (Br +) and m/e = 80 (HBr +) signals generated for photolysis of H C C C H 2 B r at 193 rim. HBr + sig- nals have a broad T O F distribution, while Br + signals consist of two distributions: a fast narrow one and a slow broad one. In the electron- bombardmen t ionizer a dissociative ionization oc- c u r s :

e

x - , x + ; (5)

e

HXL~_ H X + '

X + " (6)

Thus, the Br + signal may arise not only from Br photofragments bu t also from H B r photofrag- merits. The cracking pattern is reported to be B r + / H B r + =0 .45 in the electron bombardmen t ionizer [11]. The relative intensity of the (m/e--- 80)~(re~e=79) signals was found to be much

~ 2

$.

111

~ 2

: l

°

o )

f I i 1 J,

N

%

o HCCCH2Br/Br

~o

I I 1 I I I I I - -

B BCCC82Br/BBr !-!..

. . - . . - : - o . . ":"2: "- :" . . . . "" . . ~ ' A

-:2":I--" "" "b:" - I , ! h . El"- ~:: " . I . O ~1 2 8 1 3 3 1 3 0 . 4 0 1 3 5 0 0

TIME AFTER LASER PULSE / us

Fig. 3. T O F d is t r ibu t ions for Br (m' /e = 79) a n d H B r ( m / e = 80) signals. 1 =- 6.9 era fo r H C C C H z B r photo lys is at 193 nm.

1 3 7

s m a l l e r than u n i t y in the T O F measurement. The slow component in the T O F signal of Br is mainly due to slowly moving Br photofragments and partly due to HB r photofragments:

f a s t

R x + F R + x , (7) Islow

R + X, (8) Islow t

R + HX. (9)

Fig. 2 shows P(ET) curves obtained from these T O F distributions. The P(ET) curve for Br from H C C C H 2 B r shows two peaks at 30 and 120 k J / t oo l . The energy difference is too large to be the s p i n - o r b i t ene rgy d i f f e rence b e t w e e n Br*(2P1/2) and Br(2P3/2). If we assume a phase space model [12] for process (8), fT defined as the ratio ET/E~v t is given by 1 / ( 2 n + 2) for the prior distr ibution P°(fT)=f~/2(1--fT) "+1/2, where n is the number of modes over which the vibrational energy is distributed. Suppose that light atoms are inactive in energy partition and the number of skeletal a toms is four, then n ----- 6 for H C C C H a B r or f r = 0 . 1 . This is in fair agreement with the experimentally obtained value of 30 k J / t oo l , when D O is estimated to be the same as for C H s - B r , i.e. 288 k J / t oo l , or the available energy Eav I = 334 k J / t oo l . As shown in fig. 2, P ( E T ) for HBr from H C C C H 2 B r seems to peak toward-zero or experi- mentally at ET < 20 k J / m o l while P(Er) for Br has two peaks. This fact also indicates that process (9) is represented by a statistical model.

3.2. Methylchloride, ethylchloride, iso-propylchloride and propargylchloride

Figs. 4 and 5 show the T O F distributions mea- sured for the photolysis of CH3C1, C2H5C1, i - C3H7C1 and HCCCH2CI at 193 nm. These mole- cules gave the same narrow peaks in the T O F of m / e = 35 CI + signals. A broad distribution of rn/e = 36 HCI + was observed in C2H5C1 ph0toly- sis. it has a quite weak "intensity compared_to C1 +. The photolysis of HCCCH2CI results in the com- binat ion of the narrow and broad distributions for m / e = 36 signals. This is because role = 36 signals -¢eere obtained both from C~-ar is ing from C3H ~

138 i~t. Kawasaki et a L / Photodissociation o f halogenate o? hydrocarbons

III

.,o'~ e . .

o

t k I,l

\.1.

31

e .

e

s t -

,.-,0 - - -:-":-" ":":'::'" :---''-'-'-':'" -""f " 13 l O 0 2~

TIME AFTER LASER PULSE / ]Is

Fig. 4. T O F d i s t r i b u t i o n s for r e ~ e = 35 ( C I " ) simaals f rom C H 3 C I a t 193 nm. 1 = 1 6 c-m; 100000 l a se r shots .

photofragments by dissociative ionization in the mass spectrometer and HC1 ~ from HCI photo- fragments. When C3H ~- signals were observed, C3H 3 photofragments showed the same fast nar- row distribution as Cl counter photofragments. HCI fragments could not be detected for the pho- tolysis of CH3CI and i-C3H7C1 by our apparatus.

The primary processes are essentially the same as (7)-(9) except that the relative intensity of (8) to (7) is reduced for chlorides compared to bromides. The TOF distributions are converted into P (ET) curves in figs. 6 and 7 for CI and HCI fragments, respectively. For CI, P (ET) peaks at E T = 140 and 240 k J / t o o l and for HCI a t E T < 20 kJ /mo l . The results are summarized in table 1 along with those of other molecules.

3.3. angular distribution

The TOF signal intensity of m / e = 35 was mea- sured for photolysis of HCCCH2CI at four angles (0, ~ / 4 , ~r/2, 3-rr/4) of the polarization direction of the laser light with respect to the detector axis. Each point is obtained from 7500 laser shots. In fig. g the peak heiojats are plotted as a function of the four laboratory angles. This function seems to be anisotropic with a parallel transition moment.

If photoabsorption is due to the triple bond, the angle between the transition moment and dissocia- tion direction will be close to the magic angle, and the angular distribution would be isotropic [13]. I f the C-CI bond absorbs a photon, an anisotropic distribution is expected. The experimental results suggest that the o* transition of the C - C I bond has been excited. The dissociative state has a rather short lifetime in the order of ps.

T a b l e 1

T o t a l t r a n s l a t i o n a l ene rg ies

P a r e n t P r i m a r y P ( E T ) p e a k

m o l e c u l e p roces s (kJ m o l - I )

H C C B r --~ C 2 H + Br 75 40

< 20

H C C C H 2 Br --* C 3 H 3 + Br 120

3O

C 3 H 2 + H B r < 20 C H 3 C I -'~ C H 3 + CI 240

C2H5C1 -*' C 2 H s + CI 150 -'* C 2 H 4 + HCI < 20

i -C3H7 CI --* C 3 H 7 + C I 140

H C C C H 2 C i -* C 3 H 3 + C I 140

"-* (23 H 2 + HCI ~: 20

==

E

-__ M . K a w ~ i ; t ~ / P h o t ~ s 6 c i a t i o n o f h a l o g e n a t e o f h.~'drocar/~ns _" - - ~ -:------139

L ~ 2 7 - " 'm - " - r -

O - " °

- - ! 5 0 - 1 5 0 - 250 . -

- b C 2 H s C l I C I T o t a l T r a n s l a t i o n a l E n e r g y E T / k J , m o 1 - 1 -

. . - , : " . ' . . . , . . . . .

" | .. T " " '

m ' . . . . . ' ~ 1

~" c C I H 7 C l / C I

• t . ."~, : .-" • , . : ; . . : . .

.,~a - - 'i _

- - d C 2 H s C I / H C I §

e f - : ' ~ : - • : "~%. , . .

J . o o ~ i l l l i I" I I I I

e HCCCX2CI /HCI , C3H 3

J a t , a t j .

b - ( - . H

; la f~t

. "¢ . . . . . . - - - : • \ . _ . - ' % , -

L . 8

~ , 2 ~ I I I I

-~

Fig. 6. P ( E T ) calculated from the T O F distribution of CI fragments obtained in the photolysis o f CH3CI ( . . . . . ), C2H5C! ( . . . ) , HCCCH2CI ( : ), and (CH3)2CHCI (---).

3 i , " , , ,

2 ! .q -

T:t01 TranslotlolnO01 Energy E T /20k~.mol i Fig. 7. P ( E T ) calculated from the T O F distribution of I /C/ fragments obtained in the photolysis of C2H5C1 ( . . . ) and HC2CH2CI ( )-

~ e -"J - e i I : I - I . I I I t - I

a e @ 4 8 0 6 o 8 8 o Q _

TIME AFTER LASER PULSE I ~ s .

°

==:

~o

3 - -

I I I I '

I | I I

LAB. ANGLE

F / g . 8. Angular : distribution o f CI photofragments from HCCCH2CI at 193 nrn.

• Fig. 5. T O F distributions for C l ( m / e =35) . HCI ( m / e = 36) and C 3 ( m / e = 36) signals. C + signals are obiained from C 3 H ~ p h o t o f r a g m e n t s g e n e r a t e d i n t h e p r o c e s s o f H C C C H z C I

"* C3I- ] [ 3 "'l- CI." ! -~ 6 . 9 c m . _ _

140

4 . D i s c u s s i o n

4.1. P r i m a r y process

M. Ka, a.asaki et al. /_Photodissociation-of halogenate b f h-ydro~-boris -- 2-_--:~ 517:~ ~:~-" 5_ ~ ._- -_: --~ --

tion band , - the f luorescence-quaii tum :yield :-.has_

The first absorption bands in the alkyl halide molecules, called A bands, are observed at = 200 nm in ethyl chloride and bromide. Most recent workers agree that A-band absorption can be de- scribed within the valence shell as n p ' ~ o * (C-X). where np~r is the outermost lone-pair p orbital of the halogen, and o* is the antibonding C - X molecular orbital [14]. The B band is well separated from the A band in alkyl halides, and corresponds to the np 5 ---* np~(n + 1) s I Rydberg transition of the halogen atom. The excitation of CH3CI. C2H5CI. and i-C3H7CI at 193 nm is due to the o* valence state but not to the Rydberg one implying that the dissociation is "direct". Our results for alkyl halide photolysis at 193 nm are summarized from the results in table 1 as:

(1) (2)

RX----I--~ R + X major.

L R" + HX minor.

The evidence for the consistency of the major atomic process (1) with a o* valence excitation is that P (ET) is well represented by an impulsive model or a poissonian one as will be discussed. The expected short lifetime is supported by the anisotropic angular distribution.

Concerning the acetylene derivatives, the chro- mophores are not only o* of C - X but also or* of the triple bond. Both absorption coefficients are comparable with each other at --- 200 nm. The 193 nm excitation of C , H 2 results in the formation of the A ~A u state [16]. The main primary process of the ,~, state is not the decomposition into HC 2 + H nor C 2 + H 2 but the formation of a metastable acetylene. This is the case in the photolysis at 184.9 nm where 13tBu is optically excited [17]. Although the electronic states of the metastable compound have been uncertain, several low-lying triplet states have been experimentally and theo- reucally predicted below 4.7 eV. The triplet state may play an important role in non-radiative processes for acetylene. The absorpt ion of bromoacetylene starts at 250 nm, 100 k.J/mol above the dissociation limit. In this first absorp-

been reported :to be 4~ < 0.1 b y Evans et .al . [18]. This has been interpreted to indicate a weak cou: piing to the background s ta te . The second con- t inuum absorption band peaking at ~ 200 nm may be assigned to both ~* of the triple bond and to o* of the C - B r bond. Because of the large sp in-orbi t interaction, the intersystem crossing must be fast in HCCBr. The translational energy distribution at E-r < 20 k J / t o o l in fig. 2 arise from this process. Concerning two peaks at 75 and 40 k J / m o l , the energy difference corresponds roughly with that between Br(2 P1/2) and ( 2 P3/2)- Although the internal quenching of I*(2P1/2) has been re- ported for the photolysis of alkyl iodides [15], the internal quenching rate o f Br*(ZPI/2) tO Br(2P3/2) should be small because the hydrocarbon group of HCCBr is rather simple; in other words, the vibra- tional energy level density of the HC 2 group is rather sparse.

The primary processes deduced are:

HCCBr + h v - - - ~ HCCBr(S, o*)

t _ , HCCBr(S. ~r*)

fast HCCBr(S, o*) ~ HC2 + Br(Br*) ,

SlOW HCCBr(S. ~r* ) ---* (T) --~ HC~ + Br.

A similar discussion can be applied to propargyl halides:

HCCCH2 X + h v - - ~ HCCCH2X(S, 0 " )

L H C C C H , X(S, ~r* )

fast HCCCHzX(S , o*) --, C 3 H 3 + X,

S|OW

HCCCH2X(S , ~*) -~ (T) U C3H3 + X,

[ s l ° W e 3 H 2 + H X .

The involvement of triplet states is clearly shown when one compares the relative intensities of slow atomic fragments with fast ones in the T O F distri- butions of chloro and bromo compounds (see figs.

3a and 5a). Because of .the large spin::orbit cou- piing of Br, the iow~E.r component generated via triplet s tates is intense for bromo compounds com- pared to chloro compounds.

- - 34. K awasaki et aA- /_ Photodissociation o f halogenate o f fiydrdcarbdns -- - -_- _ ; :-: 141~_

4.2. Dynamics of photodissociation

The dynamics of photodissociation has been recently reviewed-by Shapiro and Bersohn [19]. Photodissoeiation takes place in two distinet steps: molecular excitation followed by fragment separa- tion. The cross section for a transition from the initial molecular state i to the final state n of the fragments is given by

I On, = ~ /1 m ,

where A m is the relative probability amplitude for generation by photon excitation of a state which correlates with the final state ~ of the fragments. S,,n, the scattering matrix for the half collision, is the amplitude for a transition from a fragment state ~ during the motion on the excited potential surface. The photodissociation is classified into two cases: one is "'direct" and the other is "'indi- rect". For the direct process, both S,~ and A m are functions of the potentials of i and n. For the indirect process Azi can be approximately unity and the S,n is predicted by the statistical model if the energy is completely randomized. In one ex- treme model, the so-called F ranck -Condon model, the final state interactions are neglected or S,~ is

taken to be unity. This Would n0t-be the case for alkyl halides. >For example, [in the :CH3I .g, ~- X. transition, the S mat r ix has . moderately large off-[ diagonal elements. Examina t ion o f table 2 reveals that the f-r of the bromides are small-compared to those of the chlorides because-the b romides have more energy transferred by ,the half collision into v ibra t ional energy.- The v i b r a t i o n a l energy trarisferred is a funct ion-of both masses of ph0- tofragments and a characteristic range of a repul- sive potential in a classical impulsive model-[20]. The energy Ev increases with increasing mass and range. In the other extreme model, the final s t a te interaction model assumes that all of the fragment vibrational excitation arises from the final state interaction. The generalized force in a polyatomic molecule generates a Poisson distribution in each vibrational mode. Then, a collection of oscillators, each having a Poisson distribution, has an overall distribution of vibrational energy which is also given by a Poisson distribution. The P ( E T ) of fig. 6 are well represented by poissonians.

The impulsive collision models are given by Riley and Wilson [1]. Two extreme models are spectator and rigid rotor models. The spectator model well predicts the ET/E~v~ value obtained experimentally as shown in table 2. For the case of HCCCHzX, the CH--=C group may be considered as a spectator because of a low to value for the C H 2 rocking mode (~o = 366 e ra - l ) . Another ex- treme is the rigid rotor model where E~v ! is parti- tioned into rotation and translation. In the HCCBr dissociation, if we assume a bent form like the

T a b l e 2 A v e r a g e pa r t i t i on ing o f ava i l ab le e n e r g y

P a r e n t D0(C-X) Ear I ETT m o l e c u l e ( k J / m o l ) ( k J / m o l )

fv ") /v b)

s p e c t a t o r r igid ro to r

H C C - B r 336 286 75 0.26 0.55 1 ( a = ~r) 0.59 ( a = 9 / 2 )

HC,_CH 2 - B r 288 334 120 0.36 0.46 0.76 C H 3 - C 1 339 283 240 0.85 0.85 1 C H 3 C H 2 - C I 339 283 150 0.53 0.63 0.69 ( C H 3) 2 C H - C I 339 283 140 0.49 0.49 0.89 HC2CH 2-C1 339 283 140 0.50 0 .54 0.80

~) A = ~ T / E , , , - b) A s s u m i n g a q u a s i - t r i a t o m i c s t ruc tu re , a = < C C B r . E q u a t i o n s for ca l cu l a t i on o f t hese m o d e l s a re g iven b y Ri ley a n d W i l s o n [I].

142 M'. Kawasaki et aL / Photodissociation of halogenate of hydrocarbons

excited state o f acetylene, the model calculation predicts fT = 0.59 while the experimental value o f ]'1- = 0.26. This implies the vibrational excitation of HC=--C fragments as well as the rotational excita- tion. It is interesting to note that f r for CHsCI is much larger than the f-r values for C2HsCL ( C H 3 ) 2 C H 2 C 1 , a n d H C C C H 2 C I . T h i s r e s u l t i n d i -

c a t e s t h a t n o t o n l y t h e v i b r a t i o n a l e x c i t a t i o n b u t

a l s o t h e r o t a t i o n a l e x c i t a t i o n o f n o n - l i n e a r a l k y l

g r o u p s a r e i m p o r t a n t i n t h e e n e r g y d i s t r i b u t i o n

because of the non-linear s tructure of these parent molecules. Even in the spectator model, rotational excitation is predominant . For example for HCCCHzCI fR and f v are 0.39 and 0.06, respec- tively, assuming the structure o f the parent mole- cule is the same as that of the ground state.

Concerning the P ( E T ) for slow atomic pho- tofragments the S~n is well represented by Ma_xwell-Boltzmann distributions because the dis- sociation is an indirect process:

P ( E T ) CC EIT/2 exp( -- ET/kT).

The characteristic temperature in the above equa- tion is 5300 K (40 k J / m o l ) for Br in HCCCHzBr . The equiparti t ion model among rotation, vibration and translation modes predicts T = 4900 K assum- ing that the vibrational energy is given by E v = n k T . E R = ~ k T , f_. x = ~ k T . a n d E a , q = E v + E" R +

ET where n is defined in section 3.1 ". This is in good agreement with the temperature obtained experimentally.

One must use E v = g ' tkT/[exp(h~, /kT)- - I] if values for a:, are known.

Acknossledgement

The authors thank H. Sawaki for assisting in performing the experiments. Part of this work was

supported by a Grant- in-Aid f rom the Ministry of Educat ion, Science and Culture and by the Joint Studies Program of the Insti tute for Molecular Science.

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