6020
J . Phys. Chem. 1989, 93, 6020-6024
Violet Emission of CN Produced in the Reaction of Ar(3P,,,) with BrCN. 1. Nascent Vibrational and Rotational Distributions of CN(B22?) Kazuhiro Kanda,+ Haruhiko Ito,t Kiyohiko Someda,' Kaoru Suzuki, Tamotsu Kondow, and Kozo Kuchitsu*,s Department of Chemistry, Faculty of Science, The University of Tokyo, Bunkyo- ku. Tokyo 1 1 3, Japan (Received: December 7 , 1988)
The CN(B2Z+-X2Z+)emission spectrum, produced in the dissociative excitation reaction of BrCN with Ar(3Po,2)at thermal collision energy, was observed by using the flowing afterglow method. The effect of collisional relaxation of the excited electronic states of CN by the ground-state Ar atoms was minimized by lowering the ambient argon pressure to less than 10 mTorr. The "nascent" rovibrational distribution of CN(B2Z+)was determined by spectral simulation. A surprisal analysis of the nascent rovibrational distribution of CN(B2Z+)indicated that the dominant pathway of the reaction of BrCN with Ar(3Po,2) was energy transfer, instead of argon complex formation of ion-pair exciplex formation.
1. Introduction The mechanism of the dissociative excitation reaction of cyanides, XCN (X = H, C1, Br, I), with heavy rare-gas metastable atoms, Rgm(Rg = Ar, Kr, Xe), does not seem to be fully settled.'+ Three mechanisms have so far been proposed and discussed. ( I ) Energy transfer, where an excited state of a cyanide, (XCN)*, is an intermediate:1*2,6-8 Rgm XCN (XCN)* Rg
+
-
+ CN(B2Z+) + X
(XCN)* (1) (11) Complex formation, where direct dissociation of a transient supermolecule, (RgXCN) *, leads to the product:2-6 Rgm
-
+ XCN
(RgXCN)*
-
(RgXCN)*
CN(B2Z+)
+ Rg + X
(2) (111) Exciplex formation, where an excited rare-gas cyanide, (Rg+CN-)*, is an i n t e r ~ n e d i a t e : ~ - ~ , ~ Rgm XCN (Rg+CN-)* X
+
--
+ CN(B2Z+) + Rg
(Rg+CN-)* (3) Exciplex formation was reported to be dominant in the reaction of Xem with XCN (X = C1, Br, I).3-s%9However, the energytransfer mechanism was favored in the following cases studied in our laboratory under both flow and beam conditions by the following criteria: (1) a surprisal analysis of the vibrational and rotational distributions of the CN(B2Z+) fragment in the reaction of Arm with H C N at thermal collision energy: (2) a comparison of the energy disposals in the reaction of Xem with BrCN and ClCN with those of photon- and electron-impact dissociation^,^ and (3) an analysis of the polarization of the CN(B-X) emission produced in the reaction of Armwith BrCN at collision energies of several eIectronvoIts.* The present study is our continued effort to investigate the mechanism of the reaction of Armwith BrCN at thermal collision energy producing CN(B2Z+) Arm + BrCN CN(B2Z+) Ar + Br (4)
-
+
by way of a surprisal analysis on the nascent rovibrational distribution of the CN(B2Z+)state. The flowing afterglow method is suitable for studying this reaction at thermal collision energy, because strong signals can be obtained easily and a reliable rovibrational distribution can be derived. For this purpose, it is necessary to minimize the effect of collisional relaxation by keeping Present address: Department of Fundamental Science, College of Science and Engineering, Iwaki Meisei University, Iwaki, Fukushima 970, Japan. *Present address: Institute for Molecular Science, Okazaki 444, Japan. 8 Present address: Department of Chemistry, Nagaoka University of Technology, Nagaoka, Niigata 940-21, Japan.
the ambient pressure at the reaction region as low as possible. The pressure at the discharge region is on the order of 1 Torr in order to sustain a stable and quiet discharge, and the lowest practicable ambient pressure has so far been -200 m T o r r . l ~ i O ~The i i experimental conditions have been improved in the present study, so that the CN(B-X) emission spectrum can be observed at an argon pressure of 10 mTorr or lower in the reaction region. The rovibrational distribution measured in this "low-pressure region" is found to be remarkably different from those measured at pressures higher than 200 mTorr reported in previous studies.]J0~li An analysis of the pressure dependence shows that this difference is due to collisional relaxation. The rovibrational distribution of the CN(B2Z+)state obtained at an argon pressure lower than 10 mTorr can be regarded as "nascent", and this distribution is used to refine the discussion on the reaction mechanism.
2. Experimental Section The flowing afterglow apparatus reported previousIyl2was used after modification. A flow tube of IO-cm diameter and -70-cm length was pumped by a mechanical booster pump (500 LIS). Argon metastable atoms were produced in a Pyrex discharge tube with a 15-mm 0.d. by a microwave discharge (2.45 GHz, 100 W). Ionic species produced in the discharge were eliminated by using a pair of grids, which were placed between the discharge section and the reaction zone. The inside diameter of the discharge tube was reduced to -3 mm at its end in order to keep the argon pressure sufficiently high at the discharge section to maintain a stable discharge and yet to reduce the argon pressure in the flow tube below 10 mTorr. Cyanogen bromide (Nakarai Chemical; purity 90%) was admixed
-
(1) Coxon, J. A.; Setser, D. W.; Duewer, W. H. J. Cfiem.Pfiys. 1973,58, 2244. (2) Berry, M. J. Chem. Pfiys. Lett. 1974, 29, 323. (3) Setser, D. W.; Dreiling, T. D.; Breashears, H. C.; Kolts, J. H. Furuduy Discuss. Cfiem.Sor. 1979, 67, 255. (4) Kolts, J. H.; Velazco, J . E.; Setser, D. W. J . Chem. Pfiys. 1979, 71, 1247. (5) Hennessy, R. J.; Ono, Y.; Simons, J. P. Chem. Pfiys. Lett. 1980, 75, 47. (6) Ozaki, Y.; Kondow, T.; Kuchitsu, K. Cfiem. Pfiys. 1983, 77, 223. (7) Fukuda, Y.; Suzuki, K.; Kondow, T.;Kuchitsu, K. Cfiem.Pfiys. 1984, 87, 389. (8) Nagata, T.; Kondow, T.; Kuchitsu, K.; Tabayashi, K.; Ohshima, S.; Shobatake, K. J. Phys. Chem. 1985, 89, 2916. (9) Tyndall, G. W.; de Vries, M. S.; Cobb, C. L.; Martin, R. M. J . Cfiem. Phys. 1987,87, 5830. (10) Urisu, T.; Kuchitsu, K. J. Pfiotocfiem. 1973/74, 2, 409. (11) Yencha, A. J.; Ozaki, Y.; Kondow, T.;Kuchitsu, K. Cfiem. Pfiys. 1980, 51, 343. (12) Nishiyama, I.; Ozaki, Y.; Suzuki, K.; Kuchitsu, K. Cfiem.Phys. Lett. 1979, 67, 258.
0022-365418912093-6020$01.50/0 0 1989 American Chemical Society
Vibrational and Rotational Distributions of CN(B2Z+) 0
13
12
11
A?,
‘i??“:’
‘y42‘ ‘7
Av=O
47
Av=l
47 47
2I
4 3
19
L
330mTorr
6021
Av =O
14 I
\e
17
The Journal of Physical Chemistry, Vol. 93, No. 16, 1989 v’
11
(a) obs.
44mTorr
9mTorr 388
392
396
400
404
inm
Figure 1. Argon pressure dependences of the observed emission spectra of the Au = 0 sequence in the tail bands of the CN(B2Z+-X22+) transition at Ar pressures of (a) 330 mTorr, (b) 44 mTorr, and (c) 9 mTorr.
to the flow 15 cm downstream from the discharge region. The emission was observed by a 1-m monochromator (Spex Model 1704) with a slit width of 10 pm (spectral resolution: 0.1-A fwhm). The signal was detected by a photomultiplier (Hamamatsu Model R585) and by a photon-counting circuitry. The spectral response of the detection system was calibrated by use of a standard halogen lamp (Ushio Electric Co.). The active species in the low-pressure argon flow (PArC 10 mTorr) responsible for the production of CN(B2Z+) under the present experimental conditions can be ascribed to Ar(3Po,2).This conclusion was derived by the following measurements: (1) The delay between the 50-Hz ripple of microwave discharge and the cortesponding time dependence of the CN(B-X) emission was measured by an oscill~scope,’~ and a delay of 2 ms was observed between the discharge and the CN(B-X) emission. This delay corresponds to a flow speed of -300 m/s. This measurement also confirmed that the contribution of photodissociation by the UV photons present at the discharge was negligible under the present experimental conditions. ( 2 ) Charged species were detected by use of a Langmuir p r ~ b e , ’ ~which ? ’ ~ was placed at about 2 cm downstream from the reaction zone. The dependence of the CN(B-X) emission intensity, measured by the monochromator, on the voltage applied to the grids was independent of the grid voltage above 15 V, and it was completely different from those of the electron or argon ion currents monitored with the Langmuir probe. Therefore, the grid voltage was fixed to 17 V in the present experiment in order to exclude the contribution of charged particles to the emission.
3. Results and Analysis 3.1. Observed Spectra. Figure 1 shows the CN(B2Z+-X2Z+) emission spectra produced in reaction 4 at several argon pressures. Remarkable changes were observed in the perturbed rotational lines and in the intensities of the vibrational bands corresponding to u ’ = 12, 14, 17, and 18 when the argon pressure was reduced from 280 to 9 mTorr. However, no essential changes were observed in the relative intensities of other vibrational bands at Ar pressures ranging between 9 and 50 mTorr. Therefore, the rovibrational distributions obtained at 9-50 mTorr can be regarded as “nascent”. This conclusion is further supported by the following consideration of the collisional frequency: The cross section for the rotational relaxation of the CN(B22+) fragment by collision with an Ar atom was reported to be 85 A’.‘’ By use of this value the average collision time at an Ar pressure in the range 9-50 mTorr is estimated to be 1.1-6.3 ps. This means that the CN( B28+) fragments suffer only about 0.010-0.056 collision during their radiative lifetimes, 64 ns.16 The details of the pressure (13) Fukuda, Y. Ph.D. Thesis, University of Tokyo, 1983. (14) Suzuki,K.; Nishiyama, I.; Ozaki, Y.; Kuchitsu, K. Chem. Phys. Lett. 1978, 58, 145. (15) Duewer, W. H.; Coxon, J. A.; Setser, D. U’.J . Chem. Phys. 1972, 56, 4355. (16) DuriC, D. L.; Erman, P.; Lansson, M. Phys. Scr. 1978, 18, 39.
382
384
386
nm
Figure 2. Observed and best fit simulated emission spectra of the Au = 0 sequence in the main bands of the CN(BZZ+-XZZ+)transition at an argon pressure of 9 mTorr.
dependence of the spectra will be discussed in a forthcoming publication.” The spectra of the 0-0 and 1-0 sequences of the CN(B-X) emission produced by reaction 4 were measured, an example of which is shown in Figure 2. No emission of the Br atom was observed. 3.2. Assignment of Rotational Lines. The rotational distributions were analyzed on the basis of the following assignment: The rotational lines of the vibrational bands Au = 0, u’ = 0-15 and Av = 1, u ’ = 9, 18, and 19 were assigned with respect to the reported wave number^.'^-^^ In the 0-0 and 1-1 bands, the rotational lines were assigned up to about N’ = 120.23The rotational lines in the 16-16 and 17-16 vibrational bands were assigned by a comparison of the observed and calculated wavenumbers, which agreed within estimated uncertainties. 3.3. Rotational Distributions. The rotational lines of the tail bands and those with N ’ > 30 of the main band system ( u ’ l 6) were well resolved. The rotational temperatures were determined from the relative intensities of these rotational lines by the following method: The emission intensity of a transition from (u’, N ’ ) to (u”, N ” ) is given byZ5 ,
, I T
, --
( 2 N ’ + l ) c P dN’ Lr,
where u and N represent the vibrational and rotational quantum numbers, respectively, v is the transition frequency, and S is the rotational line strength connecting the rotational state N’ to N ” . The Franck-Condon factor, q, in which the N dependence was taken into account as a polynomial approximation, was computed on the basis of the RKR potentials of the B2Z+and X2Z+ states that were calculated from reported molecular constant^.'^^^*^^+^^ The r-centroid (ru,u,,)dependence of the electronic transition moment, Re(rdd,), was explicitly taken into account in eq 5, since (17) Kanda, K.; Ito, H.; Ozaki, Y.; Suzuki, K.; Kondow, K.; Kuchitsu, K. Manuscript in preparation. (18) Uhler, H. S.; Patterson, R. A. Astrophys. J . 1915, 42, 434. (19) Jenkins, F. A. Phys. Rev. 1928, 31, 539. (20) Douglas, A. E.; Routly, P. M. Astrophys. J . Suppl. Ser. 1954, I , 295. (21) Engleman, R., Jr. J . Mol. Spectrosc. 1974, 49, 106. (22) Schoonveld, L.; Sundaram, S. Astrophys. J . Suppl. Ser. 1979, 41, 669. (23) Ito, H.; Ozaki, Y . ;Suzuki, K.; Kondow, T.; Kuchitsu, K. J . Mol. Spectrosc. 1988, 127, 283. (24) Gorbal, M. R.; Savadatti, M. I. J . Quant. Spectrosc. Raditat. Transfer 1980, 24, 471. (25) Herzberg, G. Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules; Van Nostrand: Princeton, NJ, 1950. (26) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure IV. Constants o/Diatomic Molecules; Van Nostrand: Princeton, NJ, 1979. (27) Ito, H.; Ozaki, Y.; Nagata, T.; Kondow, T.; Kuchitsu, K.; Takatsuka, K.; Nakamura, H.; Osamura, Y . Chem. Phys. 1985, 98, 81.
6022
The Journal of Physical Chemistry, Vol. 93, No. 16, 1989
K a n d a et a l . TABLE I: Rotational Distributions of CN(B2Z+) Produced in the Reaction of BrCN with Ar(3Po.2)a
1.
V‘
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
TlfH/K (500)b
15200 13900 12700 12300 9900 8700 6500 6000 5300 4600 4100 2800 2000 2800 2100 2000 1100 900 1100 800 600
(400)’
(500)’ (500)’ (800)’ (800)’ (1000)’ ( 1 500)‘ (800)’
(700)’ (300)’ (300)’ (200)’ (400)’ (200)’ (200)’
(100)’
T2IK 1000 (200)‘
Eroi.dIeV 1.31 (7) 1.20 (8) 1.09 (6) 1.06 (9) 0.85 (11) 0.75 (1 1) 0.56 (14) 0.5 1 (1 6) 0.46 (14) 0.36 (13) 0.36 (6) 0.24 (6) 0.17 (6) 0.24 (7) 0.20 ( 5 ) 0.17 ( 5 ) 0.09 ( 5 )
1000 (200)‘ 1000 (200)‘ 1000 (200)‘ 800 (200)c 800 (200)c 800 (200)‘ 800 (200)‘ 600 (200)‘ 400 (150)c 300 (100)’ 300 (100)’ 200 (100)’ 250 (100)’ 150 (80)’ 200 150 (SO)*
(100)’ (100)’
100 (50)’ 100 (50)’ 100
(200)c
80 (40)‘
0.08 (3) 0.09 (3) 0.07 (4) 0.05 (3)
8, 1.1 (3) 1.3 (3) 1.5 (3) 1.4 ( 5 ) 2.3 (7) 2.7 (9) 4.2 (15) 4.4 (1 6) 4.6 (18) 5.9 (22) 5.4 (11) 8.2 (21) 10.8 (29) 6.5 (20) 7.3 (20) 7.6 (23) 13.7 (48) 15.2 (54) 10.3 (30) 12.1 (51) 14.3 (68)
‘The vibrational quantum number, the rotational energy, and the rotational surprisal parameter in the case of n.,ib = 1.6 are denoted as u’, Erot,d, and e,, respectively. ’The rotational temperature was determined by a Boltzmann plot. Numbers in parentheses represent standard errors in units of the last significant digit. cThe rotational temperature was determined by a simulation analysis (see section 3.3). Numbers in parentheses represent possible uncertainties estimated by a simulation analysis in units of the last significant digit.
- - -0 o
___/
10
15
20 i
Figure 4. Relative vibrational populations for u’ = 10-20 in the C N (B2Z+, u‘-X2Z+, u”) system: ( 0 )nascent vibrational populations observed in the present study at PA, = 9 mTorr; (0)ref 10, PA,= 0.28 Torr; (0) ref 9, PA, = 0.3 Torr; (A) ref 1, PA, = 1.8 Torr. rotational t e m p e r a t u r e for e a c h vibrational s t a t e was assumed t o b e t h a t obtained by t h e procedure described in section 3.3. T h e slit function was assumed t o be Gaussian a n d was determined from t h e observed line shape of t h e Hg 313.7-nm a t o m i c line. The i n t e n s i t y a n o m a l i e s a r i s i n g f r o m the p e r t u r b a t i o n s , B28+-A2ni,l,3&33 ~ 2 2 + - 4 ~1,33-36 + B 2 ~ + - 4 n 33,37 B28+-x22+,33
and A211i-X22+,38were taken i n t o account in t h e s i m ~ l a t i o n . ~ ~ * ~ ~
(28) Danylewych, L. L.; Nicholls, R . W. Proc. R. SOC.London, A 1978, 360. 557. (29) Ashfold, M. N. R.; Simons, J . P. J . Chem. SOC.,Faraday Trans. 2 1977, 73, 858.
(30) Meakin, P.;Harris, D. 0. J . Mol. Specrrosc. 1972, 44, 219. (31) Cook, T. J.; Levy, D. H. J . Chem. Phys. 1973, 58, 3547. (32) Ozaki, Y.; Nagata, T.; Suzuki, K.; Kondow, T.; Kuchitsu, K. Chem. Phys. 1983, 80, 73. (33) Ito, H.; Ozaki, Y.; Nagata, T.; Kondow, T.; Kuchitsu, K. Can. J . Phys. 1984, 62, 1586. (34) Coxon, J. A.; Ramsay, D. A.; Setser, D. W. Can. J . Phys. 1975, 53, 145. (35) Miller, T. A.; Freund, R. S.; Field, R. W. J . Chem. Phys. 1976.65, 3790. (36) Cook, J. M.; Zegarski, B. R.; Miller, T. A. J . Chem. Phys. 1979, 70, 3739. (37) Ozaki, Y.;Ito, H.; Suzuki, K.; Kondow, T.; Kuchitsu, K. Chem. Phys. 1983, 80, 85.
Vibrational and Rotational Distributions of CN(B2B+)
The Journal of Physical Chemistry, Vol. 93, No. 16, 1989 6023 Nv
TABLE 11: Energy Disposal of CN(B2E+) Produced in the Reaction of BrCN with Ar(3Po,2)a Evib/eV Erot/eV EtrIeV
1.9 (2) 0.6 (1 )
Evib/Ecx
ErotlEcx
0.39 (4) 0.12 (1)
2.4 (2)
Etr I E e x
0.49 (4)
11
I
‘Numbers in parentheses represent standard error in units of the last significant digit.
The vibrational distribution determined by this analysis is shown in Figure 4. The vibrational distribution obtained in the present study at low argon pressure is very different from those obtained in previous studies at moderate argon pressures’J0*” (see Figure 4). The vibrational populations of u ’ = 12, 14, 17, and 18 increase with the argon pressure, whereas none of the other populations are pressure dependent. The v’= 12, 14, 17, and 18 levels are strongly and collisions with perturbed by CN(AZIIi,4E+, and 411),1,3&37 the ground-state argon atoms enhance the populations of these states. The mechanism of this collision-induced enhancement in the population will be discussed in a separate paper.” 3.5. Auerage Energies. The average vibrational energy, Evib, and the average rotational energy, Era,of the CN(B2Z+)fragment are represented by Evib
= EN,&
(9)
u‘
and Erot
I
0
u‘
where Ed is the vibrational energy of the u’ state and is defined in eq 8. The average translational energy is expressed by
Etr = E c x - ( E v i b + Erot)
(11)
where E,, is the available excess energy defined as E,, = E(Ar(3Po,z))+ EinPCN + E,, - Do(Br-CN) hcvW(CN(B-X)) (12) where E(Ar(3P02)) is the excitation energy of the argon metastable atom. Since Ar(3Pz)is reported to be the dominant active species in an experiment under similar experimental condition^,^^ E( A I ~ ~ P ,is~ assumed )) to be the excitation energy of Ar(3Pz),11.55 eV. The initial internal energy of BrCN, EinPICN,consists of the rotational and vibrational energies. The rotational energy of BrCN is calculated from
ErotBrCN = kT
(13)
to be 0.026 eV at 300 K. The vibrational energy of BrCN is represented as
15
20
V‘
Figure 5. Relative vibrational populations with estimated error bars plotted against the vibrational quantum number u‘ of the CN(B22+) state. The solid curve represents the best fit prediction based on a linear surprisal analysis.
By use of these values, E,, amounts to 4.87 eV. The average vibrational, rotational, and translational energies of C N ( B2Z+) estimated in the present study are listed in Table 11. 4. Discussion 4.1. Surprisal Analysis. The observed vibrational distributions and average rotational energies are analyzed below on the basis of the surprisal analysis!1 The vibrational distribution is assumed to follow a linear surprisal type as4I
(10)
= ENulErot$ur
-
I
10
5
Nut0: But-1(1 - f d ) ” v i b exp(-Xfd)
(17)
f”1= Ed/ECX
(18)
where
k is a surprisal parameter, and n,$, is a parameter related to the degrees of freedom of the nuclear motions involved in the energy disposal. The value of 4 i b reflects the reaction m e c h a n i ~ m . ~ ~ ~ ~ ~ The parameters n,,b and X are adjusted by a nonlinear least-squares fitting43so as to reproduce the observed vibrational distributions. The best fit curve is shown in Figure 5. The optimum values of r& and are found to be 1.6 f 0.5 and -0.7 f 0.9, respectively. The rotational distribution for a given u’is also assumed to be a linear surprisal type with a surprisal parameter 8ut41 N u , f ,= (2J’
+ 1)(1 - gr)bt exp(-Bdgr)
(19)
where gr = B,d’(J’
+ l)/(Eex - E , )
(20) and the parameter nrotis the rotational energy disposal, being set equal to nvib- 1 (see Appendix I). From Ndjt in eq 19, the average rotational energy for a given vibrational level can be obtained by
3
EVlbBrCN = E.,,[C(N,BICNE,,(u) i=l
u
- E,,(0))/EN,B’CNl u
(14)
where NuBrCN
= exp[-(E,,(v) - E”,(O))/kTl
(15)
and a”,is the degree of degeneracy of vi. and EJu) is expressed as (u + 0.5)hvi;EvibBrCN is then estimated to be 0.009 eV. The total internal energy of BrCN EintBrCN
= ,yotBrCN
+ EvibBrCN ,
(16)
is 0.035 eV. The average collision energy of the reaction system, Ed, at 300 K is estimated to be 0.078 eV, D,(Br-CN) is the bond dissociation energy, 3.60 eV,40and hcvw(CN(B-X)) is 3.19 eV.26 (38) Kotlar, A. J.; Field, R. W.; Steinfeld, J. 1.; Coxon, J. A. J . Mol. Spectrosc. 1980, 80, 86. (39) Golde, M. F.;Ho, Y.-S.J . Chem. Phys. 1985, 82, 3160. (40) Davis, D. D.; Okabe, H. J . Chem. Phys. 1968, 49, 5526.
where JmaX is obtained by solving The surprisal parameter Bd is adjusted by a least-squares fitting so as to reproduce the observed average rotational energies. The adjusted values of flu, are listed in Table I. 4.2. Dissociation Mechanism. The parameter nvib estimated in the foregoing gives information on the dissociation mechanism. If the reaction proceeds mainly by energy transfer (see Introduction) Arm + BrCN BrCN* Ar BrCN*
-
+ CN(BzZ+) + Br
(23)
(41) Levine, R. D.; Bernstein, R. B. Acc. Chem. Res. 1974, 7, 393. (42) Someda, K.; Kondow, T.; Kuchitsu, K. J . Phys. Chem. 1986, 90, 4044. (43) Nakagawa, T.; Oyanagi, Y . In Recent Developments in Statisrical Influence and Data Analysis; Matsusita, K., Ed.; North Holland: Amsterdam, 1980.
6024
The Journal of Physical Chemistry, Vol, 93, No. 16, 1989
only a small amount of the available energy is expected to be disposed as the translational energy in the first step of this two-step dissociation, because this mechanism corresponds to direct resonance dissociation. Therefore, the overall reaction via energy transfer can be regarded as “two-body dissociation”. In this case, nvib is calculated to be 1.5. [Note: From eq A2 in Appendix I, nvib is 1.5 and 3.0 for two-body and three-body dissociations, respectively, since the respective values of N,, are 3 and 6.1 On the other hand, complex formation Arm
+ BrCN
(ArBrCN)’
-
-
(ArBrCN)’
CN(B22+)
+ Ar + Br
(24)
is a three-body dissociation, for which nvib is calculated to be 3.0 [see note in text above]. The mechanism of exciplex formation, where an excited rare-gas cyanide is formed as an intermediate Arm + BrCN (Ar+CN-)*
-
+ Br CN(B2Z+) + Ar (Ar+CN-)*
(25)
is a two-step reaction, where each step is composed of two-body dissociation. In this mechanism, the maximum value of nvib is calculated to be 3.0. If a substantial amount of energy is disposed in the first step, however, nvib should be less than 3.0. The value of nvib obtained in the present least-squares analysis, 1.6 f 0.5, falls close to that expected for a two-body dissociation. Since the nvib value obtained is significantly less than 3.0, it can be concluded that the reaction does not proceed via complex formation (three-body dissociation) nor exciplex formation (two-step, two-body dissociation). Accordingly, the mechanism of the reaction under consideration is dominantly “energy transfer”. 4.3. Vibrational and Rotational Excitation. The dynamics of vibrational and rotational excitation can be discussed by the unimolecular dissociation of BrCN*, because reaction 4 is now shown to be dominantly energy transfer. The negative value of X indicates that vbrational excitation of the CN(B2Z+)fragment is more effective than that predicted statistically. On the other hand, the positive value of Our implies that rotational excitation does not occur effectively. The above observation is explicable if it is assumed that the Br-C stretching and C-N stretching modes of BrCN, v i and v3, respectively, are excited in the precursor stete but that the Br-C-N bending mode is not. This assumption is consistent with the linear equilibrium structure of the ion-core BrCN+(X211)u and with the lengthening of the C-N bond from 1 158 A for BrCN to 1.217 A for BI-CN’.~~ Hence, in the dissociation of (BrCN)*, the Br atom should separate nearly along the direction of the C-N axis. In order to confirm this statement, the fly-away angle of Br, 8,is calculated. This angle is related to the impact parameter, 6, by 6 = r sin 8 (26) I
where r is the distance between the Br atom and the center of mass of CN. The average impact parameter of the dissociating Br and C N fragments is calculated by the following procedure: The conservation of angular momentum can be expressed as pb X v = -hJ’ (27)
Kanda et al. energy) is much smaller than that of C N (0.648 eV). The conservation of energy is represented as pc2/2 + B,J’(J’ 1 ) + E , = E,,
+
(28) From eq 27 and 28, the o’J’-dependent impact parameter butJ, is calculated to be
+
bc,jt = hJf/(2p(E,, - BJ’(J’ l)))’/’ (29) The impact parameter averaged over the vibrational and rotational distributions is estimated by b= L’
Nu,( ENdJ,bu,j / ND,j,) / Nu, J‘
J’
(30)
D’
to give b i= 0.35 21. The average angle between the molecular axis of BrCN and the fly-away direction of Br is thus calculated (If the rotational motion of BrCN is taken into to be -8’. account, this angle can be even smaller.) This small fly-away angle supports the conclusion deduced from the Out values that the dissociation of BrCN* occurs almost collinearly. 4.4. Possible Precursor State(s) of BrCN Producing CN(B2Z+). The probability of energy transfer from Armto a manifold of BrCN is mainly determined by the state density in the vicinity of the energy of Arm. There are three Rydberg manifolds, A, B, and C, that converge to X 2 n , A2Z+, and B 2 n of BrCN+, respectively, in the energy region close to the electronic energy of Arm (1 1.6 eV).45,48349Manifold A is produced by promotion of the 2~ electron and converges to the ionization potentials 11.88 eV (BrCN+(X2n3/2))and 12.07 eV (BrCN+(X211i12)),while manifold B is brought about by promotion of the 4u electron and converges to the ionization potential 13.58 eV (BrCN+(A22+)). In addition, promotion of the I T electron results in the production of manifold C, which converges to the ionization potential 14.2 eV (BrCN+(B2n)). The state density of manifold A at 11.6 eV is expected to be much larger than that of manifold B or C, because the energy gap between the ionization potential and the excess energy of metastable argon is the smallest in the case of manifold A. Therefore, the excited states of BrCN that contribute primarily to the present reaction are assigned to the Rydberg states converging to BrCN+(X2n). These Rydberg states are probably predissociative. Acknowledgment. We are grateful to Drs. Y . Ozaki, T. Nagata, and Y . Fukuda for their helpful discussions. The present study was supported by a Grant-in-Aid for Scientific Research by the Ministry of Education, Science and Culture of Japan. K.S. is grateful to Itoh Science Foundation for partial financial support.
I. Values of n in the Prior Distribution A general functional form of the power n is given42by n = [(Ntr + Nrot)/2I Nvib - 1 (AI) where Ntr, Nrot,and Nnbare the numbers of the degrees of freedom of translation, rotation, and vibration, respectively. In the present case, nvlbis given by Appendix
+ Nr0t)/~1-
%ib = since Nro,= 2. Since nrot
(A21
Ntr/2
= [Ntr/21 - 1
(A31
= nvib - 1
(A41
it can be shown that
where b is the impact parameter, p is the reduced mass of Br and CN, v is the relative velocity of the two fragments, and J ’ is the angular momentum of C N . A similar and more rigorous expression has been presented in the case of photodissociation by Carrington& and by Simons and T a ~ k e r .When ~ ~ eq 27 is derived, the orbital angular momentum of the outgoing Ar atom is disregarded, because the translational energy of the Ar atom is small in the present energy-transfer reaction. Furthermore, the rotational motion of BrCN is negligible in comparison with that of CN, because the rotational energy of BrCN (0.026 eV, thermal
Supplementary Material Available: Three figures of (1) observed and best fit simulated emission spectra of the Av = 0 sequence in the tail bands of the CN(B22+-X2Z+) transition, (2) observed and best fit simulated emission spectra of the Av = 1 sequence of the CN( B22+-X2B+)transition, (3) rotational lines of the Av = 0 sequence in the main bands of the CN(B22+-X22+) transition and their assignments (3 pages). Ordering information is given on any current masthead page.
Allan, M.; Maier, J. P. Chem. Phys. Lett. 1976, 41, 231. Hollas, J. M.; Sutherley, T. A. Mol. Phys. 1971, 22, 213. Carrington, T. J. Chem. Phys. 1964, 41, 2012. Simons, J. P.; Tasker, P. W. Mol. Phys. 1974, 27, 1691.
(48) Lake, R. F.; Thompson, H. Proc. Roy SOC.London, A 1970, 317, 187. (49) Heilbronner, H.; Hornung, V.; Muszkat, K. A. Helu. Chim. Acta 1970, 53, 347.
%ot
~~~~
(44) (45) (46) (47)
