Gateway coupling between quartet and doublet states of 15N18O studied in molecular beams

21 March 1997

CHEMICAL PHYSICS LETTERS ELSEVIER

Chemical Physics Letters 267 (1997) 294-300

Gateway coupling between quartet and doublet states of 15Nl80 studied in molecular beams Ch. Ottinger, T. Winkler Max-Planck-lnstitut Jfir StriJmung~fi>rschung, Bunsenstr. 10. D-37073 Gfittingen, Germany

Received 20 December t996

Abstract Collision-induced intramolecular electronic energy transfer in NO was studied using a beam of metastable ~5N~80 (a 4H) molecules colliding with Ar atoms in a cell. As in our earlier work on 14NI60 and 15N160, selective excitation of certain NO(B 2H) levels was observed by means of their [3-band emission. In the B, v = 2 level three emitting levels could be uniquely identified in terms of rotational, fine structure and A component quantum numbers. They are gateway-coupled to likewise fully characterized b-state levels, which are collisionally populated from the a state. Weaker and less specific emission from the B, v = 3 level was also observed, but not rotationally assigned.

1. Introduction Electronically excited molecules in metastable states are usually difficult to study experimentally, since they do not combine optically with the ground state. Nevertheless, these long-lived species are kinetically important in many systems such as plasmas and flames, where they can occur in great abundance and may store considerable amounts of energy. One important way of releasing this energy is intramolecular transfer to radiating states. Whenever a metastable and a radiating state belong to different spin multiplicities, s p i n - o r b i t ( S / O ) interaction is thought to provide the necessary coupling. Since this is typically a weak mechanism, it will only operate on pairs of closely spaced levels. These are the so-called gateway levels. They connect the metastable and radiating moieties at certain isolated term values, determined by the condition of near-resonance of the interacting level pair. Due to the accidental nature of

these resonances, the gateway levels are irregularly distributed. The kinetics of gateway-coupled systems have been analyzed, in particular, by Freed and Gelbart [1,2]. In essence, coilisional redistribution within one set of levels of a given spin multiplicity causes the population to flow towards the gateway levels. These possess wavefunctions of mixed spin multiplicity, as a result of the quantum mechanical perturbation by the S / O operator. Thus a fraction of the population of a given spin arriving collisionally at a mixed level will automatically enter the other spin multiplicity. This mechanism of collision-induced intersystem crossing (CI-ISC) has been applied notably to the much-studied singlet ~ triplet transfer in organic molecules [3-5]. Opposite to the case considered above, the energy is here transferred out of the radiating into a dark electronic state. The gateway theory is then used to explain this particular type of electronic quenching.

0009-2614/97/$17.00 Copyright © 1997 Published by Elsevier Science B.V. All rights reserved PH S0009-261 4(97)00102-4

295

Ch. Ottinger, T. Winkler / Chemical Physics Letters 267 (1997) 294-300

Gateway couplings can best be studied in small molecules, where the level density is low, and consequently only few gateways will exist. For any detailed investigation an experimental prerequisite is that single-collision conditions are obtained. Only then is it possible to trace the energy flow from the observed emission back to the metastable levels responsible. The method of choice is clearly a molecular beam arrangement. It permits the the reactions of the metastable molecules in a region well separated from the beam source. The multitude of short-lived excited species which usually prevails in the source region will then not confuse the observations. We have applied this method to a number of diatomics: NO [6-8], N 2 [9-11], CO [12], CN [13] and NH [14]. NO and N 2, in particular, proved to provide textbook examples of well-defined gateway couplings. The case of NO was especially revealing. Here, the detailed results from the beam experiments could clarify earlier, hitherto unexplained, data obtained under the multicollisional conditions of an afterglow [15]. In the afterglow spectra of 14NI60, the 13 bands emitted from the B, v = 0 and 3 levels were conspicuously enhanced. This was shown in Refs. [6,7] to be due to the existence of gateways, leading from the primary reaction product NO (a 41-I) into NO(B 2H, v = 0 and 3) at certain rotational/fine structure/A levels. Similarly, the afterglow spectra of 15N160 showed an enhancement of the B, v = 2 and 3 emission. Our beam experiment on this isotopic species again pinpointed the corresponding gateways. As in 14N160, B, o = 3 is selectively populated by S / O coupling with the a state. B, v = 2, however, has here gateway couplings only with the b a s - state, which itself is coilisionally populated from the a a l l state. The present work continues this series of investigations. In the afterglow experiment [15] with tSNIsO, prominent emission from the B, v ' = 2 and 3 levels was observed. This motivated our search for gateway-type emission of this isotopic species under molecular beam conditions. Guided by the data of Ref. [15], the search focussed on B - X emission from the v ' = 2 and 3 levels. We did, in fact, identify three pairs of NO(B/b) levels which are S / O coupled. The observed highly selective NO(B-X) emission then results from collisional transfer NO(a ~ b) populating, among many other levels, in particular also those

which have partly B character. Thus the process investigated in this work can be summarized by NO(a 41-1)

Ar , NO(b 4~',-/S

2n)

~ N O ( X 2I]) +h~,.

(1)

2. Experimental A supersonic beam of excited ~5N~80 molecules was generated by a strong DC discharge (50 V, 2 A) in the expansion region. It was passed through a target cell filled with 6 mTorr Ar. NO 13 bands emitted from the collision region were spectrall~¢ analyzed by a 0.25 m spectrograph (resolution 2 A FWHM) and detected by a liquid N2-cooled CCD camera. Only 1 bar 1 of the isotopic NO gas was available (supplier Campro Scientific, Emmerich, isotopic purity 99.9% 15N, 99.4% t80). The high gas throughput of the nozzle source then limited the total duration of the experiment to about 25 min. During this time, two adjacent spectral ranges were recorded on the detector, each with an exposure time of 6 × 100 s (i.e. six consecutive, cumulative exposures of 100 s each, with software-controlled elimination of spurious cosmic ray signals in the intervals). The spectrograph dispersion allowed coverage of a = 14 nm wide span in a single exposure. The two (slightly overlapping) spectral sections chosen covered the region from 223 to 251 ,nm. This included those ~5N~80 13 bands from v = 2 and 3, i.e. the two levels to be examined, which have the largest Einstein coefficients. These are the bands with v" = 2, 3 and 4. In order to maximize the signal, in this experiment the collision cell was positioned closer to the discharge source (12 cm) than in previous works [6-8] (25 cm). This increased the 13-band signal about four-fold, as was verified by recording test spectra of 14NI60 and comparing with the intensities observed in Ref. [6]. However, the uniform background from the filament light also increased by the same factor, so that the S / N ratio was only doubled. The time of flight of the molecules from the source to the observation zone was now shorter ( = 120 IXS) than previously, but this is of no consequence for our purpose. The spectrograph wavelength scale was

296

Ch. Ottinger, T. Winkler / Chemical Physics Letters 267 (1997)294-300

carefully calibrated by means of Hg lines from a 'Penray' standard lamp and the well-known 14N160 collision-induced P, R line pairs of 14N160 [6,7]. The estimated accuracy of the measured line wavelengths is + 0.025 nm.

~- 3oo

3. Results and discussion

~ 200

i

. . . .

i

i

. . . .

i

. . . .

2-4

qhllI

ill

3-3

nit.

-7--3-4-,-~

225

230

235

240

I

R 1(9.5) P~(11.5) R ~(19.5) Pt(21.5) R2(19.5) P2(21.5)

227.98 228.28 228.72 (229.28) b (229.28) b 229.83

228.06 228.40 228.78 229.44 229.20 229.88

R 1(9.5) P~(I 1.5) R I(19.5) Pj(21.5) R2(19.5) P:(21.5)

237.46 237.87 238.21 (238.80) b (238.80) b 239.40

237.49 237.86 238.24 238.95 238.70 239.43

R t(9.5) P~( 11.5) R ~(19.5) P~(21.5) R2(19.5) P2(21.5)

247.62 248.03 248.37 (249.00) b (249.00) b 249.64

247.57 247.97 248.36 249.12 248.86 249.64

I 11 III

,

245

250

oped line patterns in the v ' = 2 progression, it was possible to arrive, after some trial and error, at a unique assignment of the major features. They are due to three distinct upper state levels, labeled I, II

2-2

2-4

I~It

Fig. 1. Spectrum of tSNIsO B 2 I I - X 2I] emission induced by collisions of metastable NO(a 4II) molecules in a beam with argon gas. Three partly overlapping P, R line doublets (I, II, lid of the 2-2, 2-3 and 2 - 4 bands are marked. The exact identification of the corresponding three gateway couplings from the NO(b 4X- ) to the B 21I state is discussed in the text. In the 3-2, 3-3 and 3 - 4 bands, broader structures are observed which are probably due to a greater number of unresolved gateways.

Avac calc. (nm)

III

~:

Wavelength [nm]

Avac exp. (nm)

II

t

loo

Line

i

'-I

o

Level a

2-3

i

g

Band

III

. . . .

II F-~qIII

Table 1 Observed and calculated wavelengths of the gateway-induced lines of 15NISO(B-X) emission

II

i

2-3

400

II

Fig. 1 shows the spectrum, recorded as described above from collisions of long-lived excited 15NJ80 molecules with Ar atoms. A rich line structure is observed, repeating itself quasi-periodically in regions of the indicated progressions of 13 bands, 2-2, 2-3, 2-4, and 3-2, 3-3, 3-4. Thus there is no doubt that the collision-induced intramolecular transfer into the B, v' = 2 and 3 levels actually occurs, as expected from the afterglow results [15]. In order to identify the emitting levels, the positions of all rotational lines of the ~5N180 13 bands in question were calculated. To this end, the molecular constants of 14NI60 from Ref. [16] were rescaled in the usual way to allow for isotopic substitution [17]. The A doubling, calculated according to the prescription given in Ref. [18] was isotopically scaled following Ref. [19]. Concentrating at first on the well-devel-

. . . .

15NlSO(B'v'-X'v")

a Emitting levels: (I) B 2FIi/2, v = 2, J = 10.5; (II) B 21rli/2, v = 2, J = 20.5; (Ill) B 2II3/2, v = 2, J = 20.5. b The Pj(21.5) and R2(19.5) lines are blended.

Ch. Ottinger, T. Winkler / Chemical Physics Letters 267 (1997) 294-300

and III, and identified with their rotational/fine structure quantum numbers given at the bottom of Table 1. Each of these gives rise to a P, R line pair in each of the three bands considered. It was, in fact, this criterion which was used as an aid in the assignment. The measured and calculated wavelengths of the total 18 lines are listed in Table 1. The nine line doublets are also marked in Fig. 1. The P1(21.5) and R2(19.5) lines are experimentally resolved, but the blended line is clearly broader, see Fig. 1. In Table 1, the center wavelengths of these three blended lines are given in parentheses. No other line assignment that was tried was able to reproduce the observed line pattern simultaneously in all three bands. Note, however, that some fairly well pronounced line features on the long-wavelength side of the doublets III in Fig. 1 remained unidentified. The relatively unstructured emission in the regions of the 3 - 2 , 3 - 3 and 3 - 4 bands could not be uniquely identified either. Especially in the contours of the two latter bands, broad intensity maxima at low J and at high J are clearly evident. An estimate shows that for J ~< 4 a P, R line doublet emitted from a certain gateway level would not be resolved with the spectrometer bandwidth used. This prevents a unique assignment. Nevertheless, the broad emission features near the bandhead indicate that a considerable number of emitting levels must be contributing. The same is true for the features at high J. Although the P and R lines for a given J ' are here widely separated, no such line doublets could be distinguished in the spectrum. Thus, if the u ' = 3 emission is indeed due to the gateway mechanism, then many of such gateways must exist, clustered at low and high J of ~5N~80 B, u' = 3. An alternative explanation could be some mechanism with a propensity for populating certain groups of rotational levels without, however, possessing the rigorous selectivity of a proper gateway process. For the three clearly identified emitting levels in u' = 2 (Table 1), it was possible to identify precisely the corresponding levels in the quartet manifold which are responsible for the perturbations. As in our previous work on 15Nl60, the rotational plus fine structure term values of the a 4I-I and the b 4~states in the region of interest were calculated and compared with the term values of the levels I, II and III. Details of this calculation and references for the

a

4FI

297

B 2El

b 4E-

52000 v

v

51000

v 4

15

___

5

50000 ''

14

.....

13

4

49000

12

3

48000 UJ

11

~ 47000 >

10

46000

9

2

~

1

~

0

1

'"

8

~

0

45000 7 44000

--

14N~60

15N16O

_ _ _ lSNla O

Fig. 2. Energies of the rotationless vibrational levels (center of gravity of the fine structure multiplets) of the a 41I, B 21-I and

b 42- states of NO. In addition to the levels of 15N~sOrelevant for this work, the 14NI60 levels [7] and 15NI60 levels [8] are also shown as marked. The gateway couplings identified in this work occur between the B, o = 2 and b, o = 1 levels, which come into close resonance when the rotational energy is taken into account.

molecular constants used are given in Ref. [8]. Fig. 2 shows the coarse (vibrational) level structure of the three electronic states, including, for completeness, all three NO isotopes studied by us so far. It is seen that possible candidates for perturbations in B, u = 2 are the a, u = I 1 or the b, v = 1 states, whose rotationless term energies lie, respectively, slightly above and below that of B, v ' = 2. The rotational constant B v of NO(a) is smaller than that of NO(B), while that of NO(b) is larger. Therefore, the rotational term energies of both NO(a) and NO(b) will, at some J, cross those of NO(B), and perturbations can be expected here. However, the calculations showed that, for example, in the case of the B-state level I, of the four a-state fine structure components having the same J of 10.5, the one closest to level I still has an energy mismatch of 65 c m - 1. Compared to the small S / O matrix element between the a and

Ch. Ottinger, T. Winkler / Chemical Physics Letters 267 (1997) 294-300

298

Table 2 Characteristics of the observed perturbations between the B 2H and b Level (I) (ll) (Ill)

B, v = b, v = B, v = b, v = B, v = b, v =

4~

slates of

Energy ( c m - i) 2, 21-I 1/2(10.5) 1, 4~3/~(10.5) 2, z If i;2(20.5) 1, 4E~-/2(20.5) 2, 2~3/2(20.5) 1, 4x-(/2(20.5)

(0 c (f) (f) c (f) (e) ¢ (e)

15N180 a

47557.933 47553.891 47869.556 47873.760 47922.515 47924.513

C3/2

CI/2 b

0.29 0.88 0.44 0.48 0.90 -0.52

0.96 -0.47 0.90 0.88 -0.44 0.86

a Calculated from literature data; for details see Ref. [8]. 3 I b Coefficients of the D = ~- and D = ~- Hund's case (a) wavefunction components. c Deduced from the selection rule e ,~, f and the unique identification of the matching b state level.

B states (expected to be at most 0.01 cm -~, by analogy with 1 4 N I 6 0 [6] and 1 5 N 1 6 0 [8]), t h i s w i d e energy gap precludes any observable perturbation. The same is true for levels II and III, having calculated minimum energy gaps of 11 and 14 cm-1, respectively. Having thus eliminated the a state as a potential perturber, the b state was examined next. Here for each of the three levels I, II and III a matching partner could be found. Table 2 lists the complete characteristics of the three level pairs. Following Ref. [8], in addition to NO(B 2II), the NO(b 4 E - ) levels are also described in terms of a Hund's case (a) 2II basis. The four spin sublevels then appear as the A-doublet ( e / f ) components of the O = 3 and /2 = 2I substates. C3/2 and C~/2 as given in Table 2 are the coefficients of these substates in the overall b-state wavefunction and were obtained, together with the term values, from the diagonalization of the fine structure/rotation Hamiltonian. Note that due to the mixed-/2 nature of the wavefunction, perturbations are possible between states of nominally different /2 (see I and III in Table 2). Since the 'e' and ' f ' b-state components are energetically widely separated, it is clear which of them is responsible for the perturbation. The selection rules e ~ e, f ~ f, e ~ f then also determine uniquely the e / f character of the corresponding B state level. This information could not have been derived directly from the spectrum, since the A splittings in NO(B) and NO(X) are small (<0.01 to =0.1 cm -l [7]). Table 2 can be compared with Table 2 of earlier work [8]. It is seen that the energy mismatch between

the interacting B/b-state level pairs is much greater in 15NlsO ( 2 - 4 cm - I ) than in 15NI60 (0.1-0.3 cm-~). The coupling matrix elements, on the other hand, are of the same order. They were calculated in the present work according to the prescription given in Ref. [7], and are 0.2, 0.7 and 0.8 cm -l for perturbations I, II and III, respectively. This is of the same order as found in Ref. [8] for 15Nl60 ( = 0.50.6 c m - J ) . Considering the energy gap size relative to the matrix element, much weaker gateway effects would have been expected in the present experiment compared to 15Nl60 [8]. This expectation is supported by the case of ~4N260, where the B, v = 2 / b , v = 1 minimum energy mismatch is also several c m - ~ and the coupling matrix element is = 0.4 cm -t. Here no corresponding gateway spikes were actually observed. Yet the 15Nl80 spikes observed in the present work are about as intense as with 15N~60 (compare the 2 - 4 band in Fig. 1 with that in Fig. 3 of Ref. [8], with allowance for the four-fold experimental enhancement of the former). The reason for the apparent anomalously strong gateway coupling in the present case of 1 5 N 1 8 0 is not clear, l

A similar discrepancy can be noted in Table 2 of Ref. [8], where the calculated energy mismatch of the a / B coupling is = 0.06 c m - I , which is about l0 times larger than the a / B coupling matrix element given in Ref. [7]. Nevertheless the corresponding gateway spikes are quite strong in the spectrum of Ref. [8], Fig. 3. The most likely source of these discrepancies is slight errors in the calculated term energies. It is difficult to attain an accuracy of --- 1 c m - l or better uniformly for different vibrational levels a n d / o r electronic states of different isotopic species.

Ch. Ottinger, T. Winkler / Chemical Physics Letters 267 (1997) 294-300

Concerning the quantum numbers of the observed gateways in 15NIsO compared to 15N160, one notices a close relationship between the levels II and III in ~5N180, on the one hand, and in 15Nl60, on the other. The only difference is that in the heavier isotope J is lower by one unit. Qualitatively, it is clear that the B / b perturbation of 15Nt60, if indeed also present in ~SN~sO, should move to a lower rotational quantum number: the isotopic downward shift of the vibrational level B, o = 2 is greater than that of b, v = 1 (see Fig. 2), thereby destroying the near-degeneracy at J = 21.5, but opening up another possibility at some lower J, due to the closer spacing of the rotational levels in the B state compared to the b state. This explains the perturbation of 15Nl80 at J = 20.5. However, even the structure of the emission spectrum is almost the same for the two molecules. In each case, the P, R doublets from levels II and III are interlaced, with overlapping central components (P line from II plus R line from IID. This similarity follows automatically from the fact that the fine structure splittings are isotope independent, and the J values are close to each other. Fig. 3 illustrates this. In the center of this level diagram, the perturbations of levels II and III of 15N160 are shown (heavy energy levels). It so hap]~Rns that the fine structure splitting between the B, 3/2 and 2H~/2 components is almost exactly equal to the splitting between the I2 = ' (e) and (O components of b 4E-. Therefore, the two resonances at levels II and III are linked. Now, if this is the case in 15N~60 at J = 21.5, then it must also be true in ~5NbsO at J = 20.5, since the fine structure splittings are the same within a few wavenumbers (cf. Table 2 and Table 2 of Ref. [8]). This is shown in Fig. 3, where the corresponding level pairs of ISNIsO (dashed lines) are seen to be matched analogously for ~5N~60. One can even understand why in the ~5N~60 spectrum (Ref. [8], Fig. 3) the two blended lines in the center of the line pattern are partially resolved, while in ~5N~80, Fig. 1 of this work, they add up to a single, higher and broader spike: the separation of doublet II from doublet III is essentially isotope independent. The separation of the R line from the P line, however, is -- 10% smaller for J 20.5 of XSNI80 than for J = 21.5 of 15N160. From the interlaced arrangement of the P, R line patterns II and III it then follows that the central P =

49400!

299

B 21-[

a 4[[

b 4~..,

49200! Q 49000

v=12, J=175

48800

48600 E

V=12, J=10.5

4/2 lz2 3,,,~ ~2

-

-

tl <

4/2 it2 ~ 3~2--< s/2

- > - -

3,'2 ~/2

v=3, J=175

~ > ~

312 1/~

V=3, J=10.5

48400

~ 48200 J=21.5

ILl 48000 .0 ¢.0

-.~

47800

J=21.5

vz ~

<.___~ ~ll2_~f~_____

v=2,

3c2

(

)

-- --

~t2 (e}

J=20.5

v'z - - - -

<

:,- - - - ----v=l.

i,'2(~, ,.v2 (e~

J=20.S

~ 47600 v=2,

~2 - - - -

J=10.5

wz ~ - -

(

47400

v=8,

Irz _ _

J=10.5

zcz - -

J - -

14N16 O

• 2 W2

15N16 O

>

== ~---:

I I t I

3#2 If) l~{e)

v=l,

~2(I)

J=105

[ [

v=O, J=10.5

---- ISNIBOI

Fig. 3. Overview of all gateway couplings identified so far in the three isotopic species 14Nt60 [7], 15NI60 [8] and 15NlsO (this work). The latter are framed by a dashed line for clarity. The three double-headed arrows within this box indicate the B z r I / b 4Ecouplings II1, II and I (from top to bottom). This box is an enlarged section of the B, v = 2/b, v = 1 region shown in Fig. 2, but inclusive of rotational and fine structure energies.

line of II and the R line of III are separated by 0.38 nm in 15NI60, but only by 0.25 nm in 15N~80.

4. Conclusion It has been shown that highly product-state specific intramolecular energy transfer occurs in single collisions of metastable 15N~80(a 4H) molecules with Ar atoms. The formation of NO(B 21I, v = 2) in three well-characterized rotation/fine structure levels was observed by means of the corresponding 13-band emission spectra. These three levels were shown to be in accidental near-degeneracy with certain rotation/fine structure levels of the b 4 E - , v = 1 state, with which they are S / O coupled. The collisional process thus consists of an unspecific broadband transfer a 411 ~ b 4 E - , of which only three

300

Ch. Ottinger, 7". Winkler / Chemical Physics Letters 267 (1997) 294-300

product states are observable due to the partially radiative character of their wavefunctions, cf. Eq. (1). This is a special variant of the so-called gateway mechanism. A similar case was reported earlier by us in the ~5NI60 molecule [8]. In that case the more common gateway process, involving direct coupling of the metastable a 41-1 state with the radiating B 2II state without participation of b 4~-, was also observed. Even earlier, in the study of 14N160 [6,7], it was found that here the gateway processes occur only via direct a 4 I I / B 211 coupling. All three studies combined explain anomalous 13-band intensity distributions observed by other workers in the NO afterglow emission [15]. Those vibrational levels which appeared enhanced in that work are the same for which we have found specific gateways leading from the metastable a to the radiating B state. An exception, however, may be the enhanced B, v = 3 emission of 15NI80 reported in Ref. [15]. Here we observed, in the present work an unspecific emission from many v = 3 levels, despite the single-collision conditions.

References [1] W.M. Gelbart and K.F. Freed, Chem. Phys. Lett. 18 (1973) 740. [2] K.F. Freed, Chem. Phys. Lett. 37 (1976) 47. [3] L.G. Anderson, C.S. Parmenter and H.M. Poland, Chem. Phys. 1 (1973) 40 1.

[4] R.A. Beyer, P.F. Zittel and W.C. Lineberger, J. Chem. Phys. 62 (1975) 4016. [5] R.A. Beyer and W.C. Lineberger, J. Chem. Phys. 62 (1975) 4024. [6] Ch. Ottinger and A.F. Vilesov, J. Chem. Phys. 100 (1994) 1805. [7] Ch. Ottinger and A.F. Vilesov, J. Chem. Phys. 100 (1994) 1815. [8] J. Heldt, Ch. Ottinger, A.F. Vilesov, T. Winkler and D.D. Xu, Int. Rev. Phys. Chem. 15 (1996) 65. [9] Ch. Ottinger, L.G. Smirnova and A.F. Vilesov, J. Chem. Phys. 100 (1994) 4848. [10] Ch. Ottinger and A.F. Vilesov, J. Chem. Phys. 100 (1994) 4862. [11] Ch. Ottinger and A.F. Vilesov, J. Chem. Phys. 103 (1995) 9929. [12] Ch. Ottinger, A.F. Vilesov and D.D. Xu, J. Phys. Chem. 99 (1995) 15642. [13] M. de Moor, Ch. Ottinger, A.F. Vilesov and D.D. Xu, J. Chem. Phys. 101 (1994) 9506. [14] Y. Mo and Ch. Ottinger, to be published. [15] A.A. Matveev, A.M. Pravilov and A.F. Vilesov, Chem. Phys. Lett. 217 (1994) 582. [16] R. Engleman, Jr. and P.E. Rouse, J. Mol. Spectrosc. 37 (1971) 240. [17] G. Herzberg, Molecular spectra and molecular structure, Vol. l. Spectra of diatomic molecules (Van Nostrand, New York, 1950). [18] G.W. Faris and P.C. Cosby, J. Chem. Phys. 97 (1992) 7073. [19] C. Amiot, R. Bacis and G. Guelachvili, Can. J. Phys. 56 (1978) 251. [20] K.P. Huber and M. Vervloet, J. Mol. Spectrosc. 129 (1988) 1.