Radiative and Nonradiative Relaxation Dynamics of Sulfur Dioxide

J. Phys. Chem. 1983,87,3926-3933

3926

Radiative and Nonradiative Relaxation Dynamics of Sulfur Dioxide Excited in the 3000-3300-A Region. Fluorescence Emission Spectra and Lifetimes of Single Rotational Levels Dennls L. Holtermann,+Edward K. C. Lee,’ Department of Chemistry, University of California, Irvine, California 927 17

and Roger Nanes Department of physics, California State University, Fu//erton,California 92634 (Received: January 6, 1983)

Emission spectra from single rotational levels (SRL’s)of SO2excited in the 3000-3400-A region have been recorded and are found to be in agreement with the earlier emission study of single vibronic levels (SVL’s)by Shaw et al. The ratio of continuum to discrete emission is observed to increase with increasing excitation energy and pressure. Zero-pressure lifetimes of 41 SRL’s in 7 different vibronic levels have been measured and show a systematic decrease with increasing excitation energy. These lifetime variations and changes in the continuum vs. discrete emission have been interpreted in terms of a mixed vibronic state involving the zero-order ‘A2 state and ‘B1 state perturbed to varying degrees by the Renner-Teller interaction with the lA1 ground state.

Introduction The photophysics of SO2 excited in the 3000-3300-A region has been a subject of numerous recent investigations, and timely reviews are available.’I2 The complexity of the electronic absorption spectrum in this UV region (which involves two electronic transitions lA2 ‘Al and ‘B1 lAJ has made possible relatively unambiguous assignments for only a small number of vibrational levels of the excited state^.^!^ The presence of extensive perturbations makes the rotational analysis very difficult, but molecular geometries and rotational constants for some vibronic levels have been successfully determined.4 Recent studies of single vibronic level (SVL) fluorescence spectra by Shaw et al.5 gave further credence to the explanation that the bulk of the emission is due to the zero-order ‘B1 levels spread among the lA2 levels. Since studies of single rotational level (SRL) fluorescence spectra and lifetimes can provide more detailed information regarding the nature of radiative and nonradiative processes in small we initiated such studies on S02.7,8Here, we wish to report in detail the fiidings of our continuing study on the SRL photophysics of SO2.

-

-

Experimental Section Narrow-band, tunable laser excitation between 3000 and 3300 A was used to prepare SRL’s of SO2at 0.1-10 mtorr and room temperature, -296 K. The laser had a bandwidth of -0.2 cm-’ (in the UV) and a pulse width of -1 p s . The SRL’s selected for the present study were identified from fluorescence excitation spectra using the rotational level assignments given by Hamada and Merer.4 Nearly all of the 41 levels studied were selected from the P P subband excitation region where the line-by-line identification was achieved with the least difficulty. The SO2 sample was contained in a cylindrical fluorescence cell (38 L) equipped with White optics (total absorption path length of 812 cm for 28 traversals of laser) and Welsh optics for collecting fluorescence emission. The fluorescence was dispersed by a 1-m monochromator, and the photomultiplier output was processed by a gated integrator and a signal averager. A 100-MHz wave-form recorder was used for fluorescence lifetime measurements. The details of the ‘Present address: Chevron Research Co., Richmond, CA 94802.

experimental setup and procedure are described elsehere.^^^ Figure 1shows typical fluorescence excitation spectra obtained for finding the PPK,,(5’’) transitions of interest for the 3226- and 3210-A bands. Since SO2 in the ground and excited electronic states is a near-prolate rotor, and since nuclear spin statistics eliminate one-half of all asymmetry doublets, we shall use the symmetric rotor notation, i.e., J and K , for convenience.

Results and Discussion Relative Fluorescence Q u a n t u m Yield The strong vibrational progression commencing at 3130 A has been given the designation A, B, C, ... bands by Clements.’O Since the frequency-doubled output using Rhodamine 6G dye covers the region of the D-L bands, SVL relative fluorescence quantum yields (@f,rel, proportional to If/Ia) were measured from the low-resolution (-6-cm-’ bandwidth) fluorescence excitation spectrum shown in Figure 2 and the absorption spectrum of Mettee.” The precision of the present measurement is probably &30%, adequate for a crude comparison with the earlier SVL measurement of Shaw et al.5a A more precise measurement would require a very demanding study involving SRL’S.~Since the valley (between peaks) is nonzero in the fluorescence excitation spectrum (see Figure 2) and in the absorption spectrum,”J2 the values of +f,rel were evaluated by two (1) E. K. C. Lee and G. L. Loper in “Radiationless Transitions”, S. H. Lin, Ed., Academic Press, New York, 1980, p 1. (2) J. Heicklen, N. Kelley, and K. Partymiller, Reu. Chem. Intermed., 3, 315 (1980). (3) J. C. D. Brand and R. Nanes, J . Mol. Spectroc., 46, 194 (1973). (4) (a) Y . Hamada and A. J. Merer, Can. J . Phys., 52, 1443 (1974); (b) ibid., 53, 2555 (1975). (5) (a) R. J. Shaw, J. E. Kent, and M. F. O’Dwyer, J . Mol. Spectrosc., 82, 1 (1980); (b) Chem. Phys., 18, 155, 165 (1976). (6) K. Shibuya, P. W. Fairchild, and E. K. C. Lee, J . Chem. Phys., 75, 3397 (1981). (7) D. L. Holtermann, E. K. C. Lee, and R. Nanes, Chem. Phys. Lett., 75, 91 (1980). (8) (a) B. G. MacDonald and E. K. C. Lee, J . Phys. Chem., 86, 323 (1982); (b) B. G. MacDonald, Ph.D. Thesis, University of California, Irvine. CA. 1981. (9) ‘Paper 1, D. L. Holtermann, E. K. C. Lee, and R. Nanes, J . Chem. Phys., 77, 5327 (1982). (10) J. H. Clements, Phys. Reu., 47, 224 (1935). (11) H. D. Mettee, J. Chem. Phys., 49, 1784 (1968).

0022-3654/83/2087-3926$0 1.50/0 0 1983 American Chemical Society

The Journal of Physical Chemistty, Vol. 87, No. 20, 1983 3927

Relaxation Dynamics of Excited SOp SO,

‘ 3 2 2 6 i ’ ’P,(J’’) I5

13

‘3210i’ ’P,(J”)

/I

TABLE I:

at 2.2 mtorr of SO,

t

I / 10 9 = J ”

method l b

m

> +

I 1

.-

v)

c aJ

c C

-

H

C

.-0

In

.-v) E

W

a

-I

-I

31055.7

30930.7

u laser (cm-l)

Figure 1. Fluorescence excitation spectra (-0.2-cm-’ laser bandwidth) of the ’P,(J”) subband of the 3226-A band taken at 4.0 mtorr of SO, and the PPe(J”)subband of the 3210-A band taken at 3.8 mtorr of so,. h

-0

I’

I

L

Relative Fluorescence Quantum Yields

(@f,rel)a for Several Bands in t h e 2920-3080-8 Region

I

J

I

I

I

I

G

method 2c

band

If

Ia

@f,rel

D E F G H J K L

4.5 9.0 7.0 15.5 12.2 15.5 13.3 15.4

10.4 14.4 15.2 18.4 16.6 17.6 15.8 15.6

0.4, 0.6, 0.4, 0.8, 0.7, 0.8, 0.8, 0.9,

I’f 3.7 7.8 5.5 13.3 8.8 10.9 7.8 9.2

I’a

7.0 11.0 11.4 14.0 11.0 10.6 7.4 7.0

d

@‘f,rel oSf,rel

0.5, 0.7, 0.4, 0.9, 0.8, 1.0, 1.0, 1.3,

6 9 1 30 11 9 30 NA

a The absolute fluorescence quantum yields extrapolated t o zero-pressure (@ fO) have been measured t o be 0.86 i 0.39 a t 2960 8 and 0.97 i 0.43 a t 3 0 2 0 A in the 1-50mtorr range (Mettee, ref 11). If and I, are relative band intensities measured from the zero base line in fluorescence (this work) and absorption (Mettee, ref ll), respecI‘f and I ’ , are relative band intensities measured tively, for fluorescence (this work) and absorption (Mettee, ref ll), respectively, usin a sloping base line for the underlving “continuum”. The measurement of Shaw e t al. (;e f ‘Sa),

fi

aJ

c V

@

L L

0

0

C

3 v

>r

A

.-c

TI

v)

c

aJ

C

V

aJ

0,

c

L

c Y

L

0 V

C

C

.-0 v) .-v) E w

3 Y

z1

.-cv) 2925

2975

3025

3075

Ae,(A)

Flgure 2. Low-resolution fluorescence excitation spectrum (top trace) in the 2920-3080-A region taken at a 6-cm-’ laser bandwidth with 2.2 mtorr of SO2. The background signal (lower trace) corresponds to an evacuated cell. Total fluorescence emission was observed in both cases.

different methods. In method 1,both the peak absorption and emission intensities ( I , and If,respectively) were measured from the zero base line. In method 2, the intensities were measured from the sloping base line connecting the valleys on each side of the peak and reported as Wfsel I $ j I i . The differences between values obtained by the two methods as shown in Table I are not significant in view of the probable errors involved, i30%. Our values of @f,rel vary by a factor of -2 going from the D band to the L band, whereas the values reported by Shaw et al.5 show a much greater variation. Mettee has measured the absolute values of (extrapolated to zero pressure) to be 0.86 f 0.39 a t 2960 A near the F band and 0.97 f 0.43 at 3020 A near the J band.ll According to our fluorescence lifetime measurement to be discussed later, the halfquenching pressures (Pliz)for SOzvary from 0.6 mtorr for an SRL in the B band to 1.4 mtorr for an SRL in the E band. Therefore, an appropriate pressure correction must be made to obtain the zero-pressure values from the observed afvalues at 2.2 mtorr of SOz. Consequently, we estimate that the values of ‘P? between the D and L bands are close to unity. (12) S. J. Strickler and D.B.Howell, J. Chem. Phys., 49, 1947 (1968).

C

aJ

4-

C U

C

.-0Ln .-

v)

E w

3000

3400

3000

4200

Xcm ( A ) Figure 3. Pressure dependence of the vibrationally resolved emission following excitation of the PP,(7) transition in the E band at 32 813.2 cm-’. The emission spectra were recorded with -4-A spectral band-pass and an integrator gate width of 10 ps. The final vibrational states to which the emission terminates are indicated. I n a sample with 232 mtorr of SO, phosphorescence emission peaks commencing at -3900 A have been observed (as reported in ref 1l), but only weak signals were observed because of discrimination by the short gate width used.

Fluorescence Emission Spectra. The emission from SRL’s excited in the E band was studied most extensively, because this band shows the least amount of perturbation in the Clement’s letter bands.4b Low-resolution emission spectra resulting from the E PP7(7) excitation show vibrational structure with the strong progressions, nv,, nv, + 2v2, and nvz (see Figure 3), similar to the emission spectrum resulting from SVL excitation reported by Shaw

3928

The Journal of Physical Chemistry, Vol. 87, No. 20, 1983

Holtermann et al.

TABLE 11: Calculated and Observed Resonance Transition Frequenciesa of t h e Emission Terminating o n t h e ut''= 1 Level Following E p P , ( J " ) Excitation with J" Varying from 8 t o 1 5 A v , cm-'

'Q

'R

'P

PQ

J"

calcd

obsd

calcd

obsd

calcd

obsd

calcd

obsd

PR (calcd)

7

57.4 59.9 61.2 62.5 63.8 66.3

58.2 60.7 58.7 63.2 64.4 67.7

52.9 54.2 54.8 55.5 56.1 57.4

b 54.2 52.2 55.1 58.0 59.4

47.8 47.8 47.8 47.8 47.8 47.8

b b b 48.6 49.1 47.8

6.4 7.0 7.7 8.3 9.6

5.7 6.8 8.1 8.1 9.9

13.4 14.7 16.0 18.5

8 10 11 12 14

Too weak to be observed.

a Frequencies (expressed as Au i n c m - ' ) are given relative t o the PP transition frequency. (This is the case for all PR transitions, and these are not tabulated.)

TABLE 111: Calculated and Observed Resonance Emission Intensitiesa of the Emission Terminating on t h e Following E pP,(J") Excitation with J" Varying from 8 to 15

= 1 Level,

Y,"

emission intensities

'Q

'R

'P

P&

J'

calcd

obsd

calcd

obsd

calcd

obsd

calcd

obsd

PR (calcd)

rJ

0.87 0.89 0.90 0.92 0.94 1.00

0.80 0.90 0.73 0.79 0.60 0.70

0.12 0.30 0.37 0.43 0.48 0.55

b 0.47 0.38 0.45 0.70 0.47

0.01 0.05 0.08 0.11 0.14 0.22

b b b 0.08 0.18 0.24

0.23 0.34 0.43 0.52 0.70

0.30 0.35 0.35 0.26 0.41

0.014 0.024 0.035 0.055

8 10 11 12 14

a Relative intensities are normalized to the PP transition intensity. Intensities were calculated by the Honl-London formula for perpendicular transition. b Too weak t o be observed. (This is the case for all PR transitions and these are not tabulated. ) I

( a ) 3252

I

I

i 'P8(8)

I

I

I

I

I

1

T5 1

47mtorr

-0 0,

4-

V

__

z - 4 "I

2 L 338"

3 2.

3163

323:

X,

3240

7283

332-

3365

36:-

(Ai

,

0 V C

3 v

Flgure 4. Medium-resolutlon (1-A spectral band-pass) emission spectra resulting from excitation of the PPs(8)transition in the E band at 32 798.9 cm-'. The spectra were taken with the emission filter set, Corning 7-54/4-96 for run a and Corning 7-54/Schott WG 360 for run b. The doublet feature of each vibronic set corresponds to the p-form and r-form subbands. Note the r-form emission line to the blue of the scattered laser line.

et aL5 A t relatively low pressure (see Figure 3c, 0.7 mtorr of SO2)the emission due to the underlying "continuum" so prevalent a t high pressure (see Figure 3a, 34 mtorr of SO2)is absent. The 4.2-mtorr sample shows some continuum emission. However, the ratio of the continuum emission intensity to the "structured" emission intensity appears to level off between 34 and 232 mtorr of SO,. The probable cause for this observation will be discussed later. Medium-resolution emission spectra resulting from excitation of E PP8(8)taken with 1-A spectral band-pass are shown in Figure 4. Each vibronic emission peak shows a doublet feature with p-form (m= -1) and ;-form (m = +I) subbands, as noted previously.7,9 The separation between the two subbands increases with the quantum number K and to a lesser degree with the quantum number J . At 0.4-A spectral resolution, for example, all six rotational subbands (PP, PQ, PR, 'P, 'Q, and 'R) of the emission from the K' = 7 , J' = 14 level can be resolved. The calculated and observed resonance transition frequencies from the J' = 7-14 levels on the K' = 7 stack are shown in Table

ZI c I-

VI

C

-

a)

+

c

C

.-0 VI .-VI E

( c ) 3210% P ',

(9)

$1

5 , 0 tort

m

W

4000

3800

36000

A,,

3400

3200

(A)

Flgure 5. Low-resolution (4-A spectral band-pass) emission S ectra: (a) 3252-A band, pPs(8)excitation at -30690 cm"; (b) 3226- band, pP4(7)excitation at 30970.2 cm-'; (c) 3210-A band, PPs(9)excitation at 3, 056,9 c m - ~ ,

1

11, and the calculated and observed resonance emission intensities for the corresponding levels are shown in Table 111. The intensity calculations were performed by using the symmetric rotor approximation. In most cases, agreement between the calculated and observed values is

The Journal of Physical Chemistry, Vol. 87, No. 20, 1983

Relaxation Dynamics of Excited SO2

I

I

1

0,1

( c ) 'L' 2 9 4 5

4000

3800

i4 . 5 m t o r r 3600

340:

,

,

3200

,

d 3000

X,,(A) Flgure 6. Low-resolution (4-A spectral band-pass) emission spectra: (a) B band, PP,o(lO) excitation at 32078.3 cm-'; (b) G band, pP1,(14) excitation at 33 154.1 cm-'; (c) L band, 2945-A excitation.

satisfactory within the accuracy of the measurement involved. The most serious discrepancies appear in the 'R branch with J' = 12 and 14, 'Q with J' = 12, and P Q with J' = 14. These discrepancies may be due to local perturbations, but no serious attempt has been made to examine this further. The low-resolution emission spectra for other SRL's taken at -5 mtorr are shown in Figures 5 and 6. Since the absorption becomes weaker a t longer wavelengths, the 3252-A spectrum is considerably noisier than the 3226-A or 3210-A spectrum in Figure 5. However, it is clear that the ratio of the continuum emission intensity to the structured emission intensity increases with the excitation energy (from 3252 to 2945 A). It is apparent that, in the cases of B PPlo(lO)and G pPl3(14) excitations (see Figure 6, a and b), the r-p doublets are clearly visible even in this low-resolution spectrum. The doublet and triplet features observed in some cases (e.g., 32 120-cm-' excitation) by Shaw et al.5 may be due to the r-p doublets a t high K' values as well as other vibronic origins as they suggest. Shaw et aL5"classified their SVL emission spectra into three categories according to the excitation region: region 1 for the weak bands preceding the A band, region 2 for the A-D bands, and region 3 for the E-L bands. Our spectra in Figure 5 belong in region 1, although their lowest excitation energy SVL spectrum was taken at 30972 cm-I corresponding to our second lowest excitation energy SRL spectrum at 30 970.2 cm-'. Our SRL spectra at 30 690 and 30 970.2 cm-I are very similar (compare Figure 5, a and b). In region 1, the nvl progression (with n,, = 2) dominates over nu, + 2v3 and nvl + v2 progressions, but the nvl + v2 progression emerges to be more prominent over the nvl + 2v3 progression for 31 056.9-cm-' excitation. In region 2, the nv, + 2v3 progression becomes nearly inactive. The peak intensity resides at n = 1 in the strong nv, progression which still dominates over nv, + v2 and nvl + 2v2 In region

I

!

3929

1

i

J

'lpB'

001 0

I

I

I

I

1

2

3

4

I

I

5

6

Pso2 (mtorr) Figure 7. Stern-Volmer plots for a representative SRL in each of the four low-lying vibronic levels excited. Similar plots for the B and E bands are given elsewhere.'

3, the nvl progression again dominates, but now two Franck-Condon maxima occur at nmax= 0-1 and nmax= 4 for the E and G bands. An intensity minimum occurs in nv, at n = 3 for the E band and n = 2 for the G band. In the L band, the nvl progression has fewer members with Franck-Condon maxima at n = 1 and 3. It is important to recognize that the r-form peak blue to the scattered laser line (p form) gives the intensity information for the n = 0 member of the nvl progression in both E and G bands in our SRL spectra. Overall, our SRL spectra are very similar to SVL spectra reported by Shaw et al.5a and support much of their interpretation. The symmetric stretch ( vl) progression is most prominent, and its FC maximum shifts from n = 2 a t low excitation energy to n = 0-1 a t high excitation energy. Progressions involving v2 (bending mode) are very weak at low excitation energy but become stronger and longer at high excitation energy. There is irregular and limited activity of the antisymmetric stretch mode (VJ. The absence of v2 activity in the emission from the level reached by PP4(7) excitation of the ,A2 (081) level (3226 A)4cis quite puzzling, contrary to what is expected from the Franck-Condon principle. Zero-PressureLifetimes (TO) and Electronic Quenching Cross Section for Self-Quenching ( Q ~ , ~ )In . our previous report (paper 1),9the measurements of the pressure dependence of the fluorescence decay times ( 7 ) due to collisional electronic quenching of SO,* (excited by B PPlo(10) and E PP7(7)excitation) with a variety of foreign gases have been reported. From the Stern-Volmer relationship, the values of TO and QQ,M (M = foreign gas) have been obtained for these two SRL's. In addition, a mechanism for collision-induced quenching via collision complex formation between SO2* and M was presented. In Table IV, the results of and aQ,A (A = SO2) obtained for 41 SRL's in 7 different vibronic levels are presented. The experimental details appear in paper l.9 The SRL lifetimes were measured by monitoring the p-form subband emission to the ul" = 1 level using a spectral band-pass of 2-6 A. The

3930 The Journal of Physical Chemistry, Vol. 87,No. 20, 1983 TABLE IV : Zero-Pressure Lifetimes Sections ( O Q , A ) f o r SRL's of SO,'

--

(TO),

Half-Quenching Pressure (Pi,,), Self-Quenching Rate Constants ( k Q , A ) ,and Cross

-

~

rot. trans or u e X , c m - '

vibration band 3274 A ( 3 0 552 c m - ' ) [ 1 4 1 I d 3252 A ( 3 0 753 c m - ' ) [ 2 2 1 I d 3226 A ( 3 0 9 9 5 c m - ' ) [081Id

Erot,b

level (J',K')

cm-'

-30524 -30527 -30690 PP,(7) pP,(8) (11) (15) PP,(8)

20.4 45.6 63.1 95.4 55.6 66.6 80.1 41.5 51.1 63.3

(10) 3210 A ( 3 1 150 cm

(12) pp,('i)

I )

Holtermann et al.

56.1 73.0 78.7 85.1 ?

B ( 3 2 1 8 7 cm..')

E ( 3 2 8 7 1 cm

81.3 87.0 93.4 102.5 115.9 123.6 31.0 44.3 48.7 59.4 65.6

I )

(15,ll) (13,12) (14,12)

TO, w s

-

2600 -2600 -2730 3082 3107 3125 3158 3117 3128 3142 3257 3266 3277 3273 3291 3297 3303

55.0 I 4.2 43.5 i 5.0 29.8 i 3.6 40.4 i 5.2 33.2 i 6.4 23.2 i 4.7 38.1 t 7.4 29.3 i 4 . 8 40.4 i 5.0 34.7 i 5.1 36.1 i 7.1 3 0 . 6 i 3.3 51.4 k 10.6 28.1 i 1.2 25.5 t 2.3 30.6 i 3.6 27.9 i 2.6 31.6 i 7.2 15.6 i 0.5 15.3 t 0 . 5 21.5 i- 1 . 2 1 5 . 5 I 0.5 15.5 i 0.7 21.0 t 0 . 9 15.4 i 1.3 14.6 i 0.1 14.5 i 0.5 17.0 f 0.6 10.5 i 0.5 15.7 i 0.7 1 4 . 2 2 1.1 1 4 . 2 i 0.7 14.6 i- 1.7 1 4 . 2 i- 1 . 5 24.1 i 2.6 20.7 t 1 . 0 24.5 i 1.2 18.0 i- 0.4 25.3 i 1.2 18.7 i 0.7 17.4 i 0.6

?'

4331 4337 4343 4351 4365 4372 5065 4983 4987 4998

500-1

'?

?

59.9 70.6 83.8 99.5

4998 5009 5023 j039

75.6 81.5 88.1 177.2 176.7 185.9

5475 5481 5486 3578 3580 3588

>

G ( 3 3 3 3 1 cm-I)

cm

>

pi]~, mtorr 0.35 0.4 1 0.74 0.48 0.50 0.78 0.43 0.69 0.47 0.55 0.44 0.58 0.33 0.58

0.64 0.53 0.60 0.49 0.82 0.79 0.55 0.76

0.74 0.57 0.97 0.85 0.90 0.73 1.31 1.07 0.84 1.05 1.20 1.41 0.88 0.60 0.47 0.67 0.49 0.68 0.71

10-'kQ,.?,

torr-' s-

5.23 i 0.07 5.67 i 0 . 1 6 4.54 i 0.21 5.13 I0.14 6.07 i 0.26 5.51 i 0.43 6.08 t 0.27 4.95 f 0.35 5.38 f 0.18 5.28 k 0.21 6.30 i 0.33 5.66 z 0 . 1 9 5.96 i 0.24 6.12 i 0.08 6.12 i 0.19 6.19 i 0.18 6.00 f 0.16 6 . 4 9 I 0.28 7.83 c 0.13 8.25 i 0.14 8 . 4 9 i 0.17 8.46 i 0.13 8.70 i 0.19 8 . 3 3 z 0.14 6.70 r 0 . 3 9 8.03 i 0.24 7.67 5 0 . 1 9 8.09 2 0.14 7.29 i 0.29 5 . 9 5 i 0.19 8.34 i 0 . 4 7 6.69 i 0.26 5.69 ?r 0 . 5 9 5.04 i 0.53 4.74 i 0.30 8 . 0 3 i 0.16 8.77 i 0 . 1 3 8.36 i 0.09 8.13 r 0 . 1 2 7.87 i 0,13 8 . 1 3 i 0.13

u Q . ~x,

361 i 5 391 1 1 1 313 i 1 4 354 t 1 0 419 I 18 380 i 30 420 i 1 9 3 4 1 i 24 366 i 1 2 364 i 1 4 4 3 5 i 23 391 i 11 411 i; 1 7 422 i 6 1 2 2 i 11 427 i 1 2 413 t 11 447 i 1 9 540 i 9 5 6 9 i 10 386 i 1 2 584 L 10 600 ?- 1 3 575i 1 0 1558 62 I i 27 22 529 t 1 3 558 ' 1 0 5 0 3 i 20 411 i 1 3 376 I32 161 i 1 8 393 t 4 1 348 i- 37 327 21 554 i 11 603 i 9 377 i 6 561 I8 343 I 9 561 7 9

' The lifetimes were measured by monitoring the p-form subband emission t o the vi'' = 1 level by using a spectral bandpass of 6 A for the 3 2 7 4 - 8 and 3 2 5 2 - 4 bands, 4 A for the 3226-A and 3210-X bands, 3 A for the B band, and 2 A for the E and G bands. Excited-state rotational energy (relative to the J ' = 0 , K ' = 0 level) was calculated by using rotational constants given in ref 4. ' E , , is the energy above the ' A , * ~ - ' A , electronic origin ( T , = 27930 c m - 1 ) . 4 a Vibrational assignment given in ref 4a. TABLE V: Average SRL Values of the Zero-Pressure Lifetime (7') and t h e Self-Quenching Cross Section ( U Q , A ) ~

-__--__---

vibr band, A 3274 3252 3226 3210

no. of samples 2 1 7 ?.

I

3107 ( B )

6

3043 ( E ) 3001 ( G )

9 6

K ? ?

3 , 6, 7 6-8 8,9 5, 6, 7 8, 1 1 , 1 2

"Q+ , T O ) , /.I$

49z 4 30 34 I6 33 i 9 17 i 3 14 I 2 21 i 3

'

\

376 313 378 417

I

10

i

31 14

t

576 = 20

488 i 79 567 + 22

0

Data taken from Table I\'. 0

importance of single rotational level excitation has been discussed in paper 1 and el~ewhere.~ Under the experimental conditions used, the fluorescence decays were found to be single exponential and obey the linear Stern-Volmer plot as shown in Figure 7. The variation of the TO values as a function of the vibration-rotation energy (calculated as E , in the A 'A, manifold with TO= 27930 cm-')* is shown in Figure 8, and the average SRL values, ( T O ) and ( uQ,*),for each band are summarized in Table V.

L

9---4--

3100

3200

E,,

3300 4300

4400

4900

( c m - ' ) : T,(27930

5000 5400

5500

5600

cm-I for 'A21

Figure?. Zero-pressure lifetime (7') vs. the vibration-rotation energy in the A 'A, manifold. Excitation frequencies (in cm-') are indicated for the three points on the left.

In view of the fluorescence quantum yield data presented earlier, Le., af = 1 for the SOz* in question, the radiationless relaxation for isolated SO,* can certainly be

The Journal of Physical Chemistry, Vol. 87, No. 20, 1983 3931

Relaxation Dynamics of Excited SO2

TABLE VI: Estimates of Radiative Lifetimes for t h e Discrete and Continuum Absorptions Matched to t h e Total Integrated Absorption Coefficient in t h e 2900-8System' discrete absorption, % ' 100 25

7.Q

PS

10

0.6 2.4 6.0

4

15.0

T c , PS -

0.80 0.67 0.63

a These values were calculated by eq 1, using the value of Trad f 0.6 I J S given by Strickler and Howell" (see text for details).

ignored, as expected for an intermediate-case m01ecule.l~ Therefore, the lifetime variation under collision-free condition can be interpreted strictly as the variation in the radiative lifetime. Of course, the anomalously long lifetime behavior of SO2* due to the Douglas effect14has been much studied in recent years. 1 7 8 13,15-17 Inspection of the data in Table IV shows neither large variation nor any clear correlation between lifetime and J'and K'quantum numbers. The average SRL values of TO listed in Table V fall into two regions: The ( T O ) values in region a (3274-3210 A) are 2-3 times longer than those in region b (3107-3001 8,). The dividing line between regions a and b appears to be roughly the same as the dividing line between regions 1and 2 in SVL fluorescence designated by Shaw et aL5" It falls close to the presumed electronic origin of the 'B, state (31240 cm-l) suggested by Shaw et al.5a The (aQ,A)values in region a are somewhat lower than those in region b, but the observed differences are not considered significant. Radiative Lifetime and t h e Nature of Perturbation. It is generally accepted that two electronic transitions contribute to the 2900-A absorption system of SO2. The room-temperature spectrum shows banded structure superimposed on a very dense and congested background of weak and unanalyzable transitions. The recognizable structure, which has yielded to partial rotational analysis,4 is attributed to the electric dipole-forbidden lA2-lA1 transition made allowed by vibronic coupling of 'A2 to the 'B1 state through the antisymmetric stretching vibration ~3'(b2).The 'B1 state is severely perturbed by the dense manifold of high vibrational levels of the 'Al ground state by Renner-Teller interaction and 'B, transfers this perturbation, as well as its oscillator strength, to the lA2 state by means of the vibronic coupling between the two states. This massive Renner-Teller perturbation acts to destroy much of the vibrational and rotational structure normally expected for lB1-lA1, and this transition is presumed to give rise to the dense underlying group of irregular transitions which appears as a "continuum" even at moderate resolution. The extent to which the lA2-lA1 and 'B1-IA1 transitions contribute to the integrated absorption coefficient of the 2900-8, system is known only with qualitative significance. However, since radiative lifetimes can be estimated from the integrated absorption coefficient of a molecular electronic transition,ls we can estimate the fractional contri9

9

(13) (a) J. Jortner, S. A. Rice, and R. M. Hochstrasser, Adu. Photochem., 7,149 (1969); (b) P. Avouris, W. M. Gelbart, and M. A. El-Sayed, Chem. Rev., 77, 793 (1977). (14) A. E. Douglas, J. Chem. Phys., 45, 1007 (1966). (15) L. E. Brus and J. R. McDonald, J. Chem. Phys., 61, 97 (1974). (16) F. Su, J. W. Bottenheim, H. W. Sidebottom, J. G. Calvert, and E. K. Damon, Int. J . Chem. Kinet., 10, 125 (1978). (17) (a) H. Watanabe, Y. Hyodo, S. Tsuchiya, and S. Koda, Chem. Phys. Lett., 81, 439 (1981); (b) J . Phys. Chem., 86, 685 (1982).

TABLE VII: Various Coupling Schemes and Expected Radiative Lifetimes for Excited Levels in the 2900-8System of SO, character of excited level 'B, (zero order) 'A, + 'B, 'A, + ( ' B l + ( ' B ] t 'A,)' 'A, (zero order)

Trads I.rs

-1 -10-50 -100 > 100 (electric-dipole forbidden)

-

a Excitation of an analyzed SRL in the 'A, state and observations of the rotationally resolved emission diminishes the probability of sampling these levels.

bution of the structured absorption to the total absorption in the 2900-A system using the value of 7,,d = 0.6 ps determined by Strickler and Howell.12 Four different values of the percent contribution to the total absorption coefficient by the structured absorption are assumed. The lifetimes estimated from the expression 1/7rad

= fs/?s +

- fs)/.c

(1)

are tabulated in Table VI. In this equation, Trad is Strickler and Howell's value of 0.6 ps, T~ is the lifetime of the structured absorption, 7, is the lifetime of the continuum absorption, and f , is the fraction of the structured absorption. It is important to note that the Renner-Teller interaction, which is responsible for the continuum, does not change the integrated absorption coefficient, but merely dilutes the oscillator strength throughout the many transitions into which the lB1-'A1 transition degenerates as a result of the pert~rbati0n.l~ On the other hand, the interaction lengthens the lifetime of levels belonging to the dense manifold of mixed 'Bl + lA1 states. T h e T , values in Table V I do not t a k e account of these anomalously lengthened lifetimes and should be viewed as characteristic of zero-order 'B1 state lifetimes. For the structured absorption, the fact that a partial rotational analysis has been possible4implies that little or no perturbation affects a certain number of these states. Since most of the SRL's studied here belong to this group, comparison of the observed lifetimes with the 7,values in Table VI allows an estimate of the fraction of the oscillator strength attributable to the structured absorption. The lifetimes observed for the B, E, and G bands in region b (see Figure 8 and Table V) are consistent with 7, = 15 ps, which indicates 4% discrete absorption. Since measured lifetimes of other SRL's are all longer than this, Table VI suggests that the 4% figure can be taken as an upper limit. Since the sampled levels are associated with a vibronically allowed transition, a 4 % (or less) contribution to the total oscillator strength is a reasonable figure, but a test of the validity of this conjecture would require a rather extensive and detailed characterization of the entire 2900-8, absorption system and does not appear possible a t the present time. To interpret the lifetime data presented in Table V, the excited vibronic state is proposed to be a mixed state, i.e. $ = Caj$F

+ Z b j $ y l + C ~ ~ $ ~ ( ~ 1 +(2)~ 1 )

where the second and third terms in eq 2 provide the oscillator strength to the 'A2 state. As implied by eq 2, two types of 'B1 vibronic levels are considered, one which is relatively free of lAl contamination and another which is strongly mixed with the lA1 state. It is expected that the unperturbed lB1 levels should have a normal (i.e., -0.6 (18) S. J. Strickler and R. A. Berg, J . Chem. Phys., 37, 814 (1962).

3932 The Journal of Physical Chemistry, Vol. 87, No. 20, 1983

radiative lifetime whereas the perturbed 'B, levels should have an anomalously long radiative lifetime. In its vibronic interaction with lA,, the 'B1 state transfers different degrees of perturbation which then characterize the lifetimes of the SOz excited rovibronic states. Table VI1 presents a correlation between the character of the excited levels and an order of magnitude estimate for the radiative lifetime expected for the different types of levels. Hamada and Merer first recognized the possibility of identifying the zero-order lB, states ( T , , ~ il: 1 ps in Table VII) from the K' = 0 manifold, since these levels should be immune from the Renner-Teller coupling with 'Al in first order. An unsuccessful search for these levels by Hamada and Merer led them to suggest that asymmetry effects, i.e. departure of the molecule from a symmetric rotor, may transfer the Renner-Teller perturbation to the K' = 0 levels by mixing with the K' = 2 manifold. If correct, this would make observations of "pure" lB1 levels very unlikely. Recently, lifetimes as short as 3-5 ps have been reported for emissions from the E band in a supersonic nozzle jet.I7 This is the shortest lifetime reported for SO, to date and may be due to emission from a relatively pure 'B, level. On the other hand, this result conflicts with the reported lifetime of -10-18 ps for the E band, also observed in a supersonic expansion.8 Watanabe et have observed a biexponential decay and measured the J' dependence of the ratio Iso/ILO(intensity of the short-lived component vs. that of the long-lived component) for a given value of K' = 0, 1, and 2. They found that the ratio Iso/ILo decreased with increasing J ' a n d increased with increasing K'. If the trend in this observation is applied to the higher K' values studied in our work, we should expect that our fluorescence decay with high K' values should have relatively high values of the ratio Iso/Il,ocompared to their values at low K'. Since their T~ values are 3-5 ps and our 7 values are 10-55 ps, it is difficult to reconcile our data with theirs. However, our 7 values are compatible with those reported for K' = 0 and 1 from the supersonic jet study in our laboratory.8 Thus, the question of the existence of unperturbed, zero-order, 'B1 states having lifetimes approaching the 0.6-ps value of Strickler and Howell remains unanswered at the present time. The heavily perturbed lB, levels, which include those that are mixed with 'A2 (entry 3 in Table VII) and those that have no 'Az character at all (entry 4 in Table VII), probably account for the very long lifetimes observed by Brus and McDonald15 and Su et a1.16 A sampling preference for excitation of levels which could be rotationally analyzed as well as observation of the discrete rotationally resolved emission probably biases the present results against observation of the very long lifetimes. The lifetimes reported here are believed to correlate with the 'A, levels that are mixed with lB1 states that are not strongly perturbed by the 'A, ground state (entry 2 in Table VII). The division of the lifetime data into two regions with the dividing line appearing at the approximate origin of ~ *consistent with the the 'B,-'A, transition (31 240 ~ m - l ) is greater 'A2--'B, mixing expected to occur above the 'B, origin. This imparts greater 'B1 character (shorter lifetimes) to the ,Az state and, for the levels excited here, the enhanced "pure" 'B, character results in shorter lifetimes. In addition, the downward trend in lifetimes toward higher excitation energy in region b may reflect the FranckCondon shift in the matrix elements that couple the 'A, and IBI states. Theoretical computationlgpredicts a large ps)

(19) I. H. Hillier and V. R. Saunders, Mol. Phys., 22, 193 (1971).

Holtermann et al.

difference in bond angle between the two states (for 'A,, rso = 1.585 A and LOSO = 100.3'; and for lBl, rso = 1.565 A and LOSO = 125.0'1, and this geometry difference may result in stronger coupling between 'Az and 'B, a t higher energies. Again, increased lB1 character of the levels would impart shorter lifetimes. It can be noted from Figure 8 and Table V that the G band appears to reverse the trend toward shorter lifetimes with increasing energy and it may be that the Franck-Condon maximum occurs between the E and G bands. This appears to contradict the observation of an anomalous decrease in the relative fluorescence quantum yield reported for the F band by Shaw et al.5a No explanation is offered for this at the present time. The increased mixing between the IAz and 'B, states in region b will also couple the 'Az levels more strongly to the continuum. As a consequence, the effect of collisions will be to populate the heavily perturbed 'B, levels and the continuum emission from these levels is observed. When intramolecular or collision-induced vibrational energy redistribution occurs in S1 aromatics at high vibrational energy, sharp vibrational structure in emission becomes obscured by a continuum emission.20 Such processes may also be important in SO2*. As pointed out earlier, the ratio of the continuum to the structured emission intensity appears to level off at some pressure below 232 mtorr. Not enough information is available in our study to offer a definitive explanation for this, but one possibility is that saturation of the continuum is reached when collisional population of the triplet states starts becoming significant. No mention has yet been made here concerning the involvement of the triplet manifold in the relaxation dynamics of SOz in the 3300-3000-A region. It is well-known from the magnetic rotation spectrumz1and the Zeeman effectzz that this band system in SOz exhibits strong magnetic activity despite the fact that it is a singlet system of a nonlinear molecule and should not possess a magnetic moment. The magnetic sensitivity is so great that, for a magnetic field of 9.6 kG, the rotational structure of the E band is virtually destroyed. In order to account for the magnitude of the effect, Brand et al.*' attributed the large magnetic moment to two effects: (i) orbital angular momentum gained by the 'B1 state from the laglinear configuration through its Renner-Teller interaction with the 'Al state and transferred to 'A, by vibronic interaction, and (ii) spin angular momentum gained by spin-orbit interaction between 'Az and high vibrational levels of a low-lying 3B2state. Brand et ai.zz required both mechanisms i and ii since neither could amount for the magnitude of the observed Zeeman splittings by itself. Re~ e n t l y ,a, ~weak magnetic field has been observed to produce quantum beats in the fluorescence from the J ' = 1, K' = 1 level of the E band in jet-cooled SOz. Mechanism i and/or ii is presumed responsible for the magnetic moment of this level although it was not possible to tell which mechanism dominates. Explanation of the Zeeman activity in the rotational structure requires both mechanisms i and ii, whereas the interpretation given here for the observed lifetimes appears to favor mechanism ii as being operative for the structured absorption, such as in the E band, etc. Both mechanisms i and ii would have a lengthening effect on lifetimes in the 'Az state but, in view of the different coupling schemes presented in Table VII, mechanism i would influence only (20) See C. S. Parmenter, J. Phys. Chem., 86, 1735 (1982). (21) P. Kusch and F. W. Loomis, Phys. Reu., 5 5 , 850 (1939). (22) J. C. D. Brand, J. L. Hardwick, D. R. Humphrey, Y. Harnada, and A. J. Merer, Can. J . Chem., 54, 186 (1976). (23) H. Watanabe, S. Tsuchiya, and S. Koda, J . Phys. Chem., 87.906 (1983).

3933

J. Phys. Chem. 1983, 87, 3933-3942

the Rennel-Teller perturbed ‘B1 levels which, as discussed above, are presumed to form the background of weak transitions responsible for the continuum. Mechanism ii directly couples the ‘A2 and 3B2states and will therefore involve all ‘A2 levels, including those that have relatively pure ‘B1 character (entry 2 in Table VII). Thus, if mechanism ii is operative, the levels sampled in the present work derive their l M 0 - p lifetimes, ~ at least in part, from spin-orbit coupling to the triplet manifold.

-

Acknowledgment. This research has been supported by the National Science Foundation Grants CHE-79-25451 and CHE-82-17121 at the University of California at Irvine. Partial support for the collisional relaxation study by the Department of Energy (Office of Basic Energy Sciences) Contract DE-AT-03-76-ER-70217 is gratefully acknowledged. R e g i s t r y No. SO2, 7446-09-5.

Kinetics and Mechanism of the CH 4- N, Reaction. Temperature- and Pressure-Dependence Studies and Transition-State-Theory Analysis Michael R. Berman”’ and M. C. Lln’ Chemistry Division, Naval Research Laboratory, Washington, D.C. 20375 (Received: January 10, 1983)

-

The reaction CH + N2 products was studied at 297 K at total pressures between 25 and 787 torr. The second-order reaction rate constant was found to be pressure dependent, varying by a factor of 9.6 in this range. This reaction was also studied in the range 297-675 K at 100-torr total pressure. The rate constant decreases with increasing temperature and cannot be adequately described by a linear fit in this range. Transitionstate-RRKM-theory calculations for the reaction proceeding through a long-lived intermediate,HCN,, successfully describe the data. Stabilization of the adduct is the primary reaction channel at lower temperatures while metathesis dominates above 1000 K. These calculations provide a consistent description of these and previous data from flame studies.

I. Introduction The reaction of CH with N2 is of considerable importance due to its role in the chemistry of planetary atmospheres and hydrocarbon flames. This reaction is included in models of both the chemistry of the nitrogen- and hydrocarbon-rich atmosphere of Titan’ and the production of nitric oxide in hydrocarbon flame front^.^-^ The CH N2 reaction is alluring to modelers of such systems in that it represents the least endoergic pathway for a hydrocarbon fragment to break the N=N bond enabling the incorporation of N atoms and other nitrogen-containing compounds into subsequent reaction schemes. A clear understanding of the kinetics and mechanisms of this basic reaction is critical for evaluating the complex systems typically found in atmospheric and combustion environments. Recent interest in the CH + N2 reaction has been part of an effort to unravel the mechanism of NO formation in hydrocarbon/air flames. The production of NO in these hydrocarbon flame fronts cannot be described by the Zeldovich mechanism6 which successfully accounts for NO production in the postcombustion region. Fenimore2 proposed the reactions of carbon or hydrocarbon radicals with Nz CH + N, HCN + Nt4S) (1) Cz + N2 2CN (2) followed by oxidation of the products to account for the production of NO in the reaction zone of these flames. Blauwens et al.,3 using molecular beam sampling with

+

-

-

NRC/NRL Postdoctoral Research Associate (1981-1982). Present address: McDonnell Douglas Research Laboratories, St. Louis, MO 63166.

mass-spectrometric detection to measure absolute radical and molecule concentrations, found that the production of this so-called “prompt” NO could be represented by either reaction 1 or 3. They evaluated rate constants for CH2

+ N2 * HCN + NH

(3)

each process finding activation energies of 11.0 and 22.5 kcal/mol, respectively, noting that these values are applicable only if the observed NO was produced solely by the reaction considered. Matsui and Nomaguchi4 found that the amount of prompt NO is proportional to the CH radical concentration and evaluated a rate constant for reaction 1 having an activation energy of 13.6 kcal/mol. However, they detected CH radicals indirectly and did not consider CH2 radicals. Miyauchi et ale7found that HCN was formed prior to the prompt NO, supporting reactions 1 and/or 3. In this case, they did not include reaction 1 in their analysis due to the spin change involved. They used instead reaction 3 as the source of HCN and evaluated a rate constant for this reaction having an activation energy of 35.2 kcal/mol. The objection to reaction 1 on the grounds of spin consideration, however, has been (1)D. F. Strobel, Planet. Space Sci., 30, 839 (1982). (2) C. P. Fenimore, “13th Symposium (International) on Combustion”, The Combustion Institute, Pittsburgh, PA, 1971, p 373. (3) J. Blauwens, B. Smets, and J. Peeters, “16th Symposium (International) on Combustion”, The Combustion Institute, Pittsburgh, PA, 1977, p 1055. (4) Y. Mataui and T. Nomaguchi, Combust. Flame, 32, 205 (1978). (5) J. Duterque, N. Avezard, and R. Borghi, Combust. Sci. Technol., 25, 85 (1981). (6) Ya. B. Zeldovich, Acta Physicochim. URSS, 21, 577 (1946). (7) T. Miyauchi, Y. Mori, and A. Imamura, “16th Symposium (International) on Combustion”, The Combustion Institute, Pittsburgh, PA, 1977, p 1073.

This article not subject to U S . Copyright. Published 1983 by the American Chemical Society