J . Phys. Chem. 1987, 91, 2076-2079
2076
Rotational Effect on Intramolecular Vibrational Redlstrlbutlon in S, of p -Dlfluorobenzene Vapor Nobuhiro Ohta,* Osamu Sekiguchi, and Hiroaki Baba Division of Chemistry, Research Institute of Applied Electricity, Hokkaido University, Sapporo 060, Japan (Received: June 3, 1986; In Final Form: December I , 1986) The quantum yields and decays of fluorescence from the initially prepared vibronic level and of broad fluorescence from SI levels reached via intramolecular vibrational redistribution (IVR) were measured for p-difluorobenzene vapor at room temperature with excitation across the rotational contour of the 3;5; absorption band belonging to the So SI transition. A comparison between the observed yield spectra and simulated spectra suggests that parallel Coriolis interaction plays a significant role in IVR following excitation into the 3'5' vibrational level in SI.
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Introduction It has been made clear through emission measurements in many research laboratories that intramolecular vibrational rediitribution (IVR) is a general phenomenon in polyatomic molecules, which can be observed with excitation into higher vibrational levels.' However, the mechanism of IVR is not well understood, though there is some evidence to show that molecular rotation plays an important role in IVR.24 In p-difluorobenzene (pDFB) vapor, besides sharp structured fluorescence from the initially prepared vibronic level (IPL), a broad fluorescence was demonstrated by Parmenter and coworkers' to be emitted from S1 levels reached via IVR, provided that the IPL has an excess vibrational energy (AE)of more than 1600 cm-' above the SIorigin. The IVR processes following excitation into the individual vibronic levels of SI were discussed by them, based on an analysis of the intensity ratio between the IPL fluorescence and the broad fluorescence under various pressure conditiom8 Rotation-vibration coupling was suggested by these authors8-I0 to play a n important role in IVR of pDFB, since the experimentally obtained density of levels coupled to the IPL exceeds the theoretical density of S1vibrational levels with suitable symmetry, and since the intensity of the broad fluorescence relative to the IPL fluorescence is dramatically reduced in a supersonic jet in comparison with that in the bulk gas at room temperature. Their experiments were performed with excitation only at a specific position in the rotational contour of each vibronic band. In order to understand fully the effect of molecular rotation on IVR, one should investigate IVR following selective excitation into rovibronic levels with different rotational quantum numbers of J'or K', the prime referring to the excited-state S1. In this paper, we report the quantum yields and decays of the fluorescence from the IPL and of the broad fluorescence from S, levels reached via IVR for pDFB vapor at room temperature, with the excitation performed across the rotational contour of the 3b5; band belonging to the So Si transition. By combining the results of the experiments and computer simulation, we can get an insight into the role of molecular rotation in IVR occurring from the 3I5' vibrational level.
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(1) See, for example; (a) Parmenter, C. S. J . Phys. Chem. 1982,86, 1735. (b) Smalley, R. E. J . Phys. Chem. 1982,86,3504. (c) Zewail, A. H. Faraday Discuss. Chem. SOC.1983, 75, 315. (2) Riedle, E.; Neusser, H. J.; Schlag, E. W. J . Phys. Chem. 1982, 86, 4847. Riedle, E.; Neusser, H. J. J . Chem. Phys. 1984, 80, 4686. (3) Lambert, W. R.; Felker, P. M.; Zewail, A. H. J . Chem. Phys. 1984, 81, 2217. (4) Apel, E. C.; Lee, E. K. C. J . Phys. Chem. 1984,88, 1283. ( 5 ) Nathanson, G. M.; McClelland, G . M. J . Chem. Phys. 1986,84, 3170. (6) Ohta, N.; Sekiguchi, 0.;Baba, H. Chem. Phys. Lett. 1986, 126, 124. (7) Coveleskie, R. A.; Dolson, D. A,; Parmenter, C. S. J . Chem. Phys. 1980, 72, 5774. (8) Coveleskie, R. A.; Dolson, D. A,; Parmenter, C. S . J . Phys. Chem. 1985,89,645. Coveleskie, R. A.; Dolson, D. A.; Parmenter, C. S. Ibid. 1985, 89, 655. Holtzclaw, K. W.; Parmenter, C. S. J . Chem. Phys. 1985,84, 1099. Dolson, D. A.; Holtzclaw, K. W.; Moss, D. B.; Parmenter, C. S. Zbid. 1985, 84, 1119. (9) Holtzclaw, K. W.; Parmenter, C. S . J . Phys. Chem. 1984, 88, 3182. (10) Dolson, D. A.; Holtzclaw, K. W.; Lee, S. H.; Munchak, S.; Parmenter, C. s.;Stone, B. M.; Knight, A. E. W. Laser Chem. 1983, 2, 271.
0022-3654/87/2091-2076$01.50/0
Experimental Section pDFB (Nakarai Chemicals) was purified by repeated vacuum distillation. The sample pressure was determined with a capacitance manometer (MKS Baratron Type 170). All the optical measurements were carried out at room temperature by using a laser spectrophotometric systems."-'3 A pulsed dye laser (Molectron DL14) pumped by a nitrogen laser (Molectron UV22) was used as an exciting light source. The output of the dye laser was doubled by a KPB or KDP crystal. The generated UV light has a spectral bandwidth of -0.5 cm-I and a pulse duration of 3 ns. The fundamental of the laser light was cut before the sample was irradiated, by using an aqueous solution of a mixture of nickel sulfate hexahydrate and cobalt sulfate heptahydrate. The fluorescence was viewed at right angles to the direction of propagation of the exciting laser light which is linearly polarized. As occasion demands, the polarization direction of the laser light was changed by employing a BabinetSolei1 compensator (Oyo Koden). The absorption and excitation spectra were simultaneously measured. The excitation spectra were obtained by monitoring the emission dispersed by a grating monochromator (Nikon G-250). The decay curves of the dispersed emission were measured by attaching a lifetime apparatus, which is equipped with a time-to-amplitude converter, to the laser spectrophotometric system."-13
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Results and Discussion Figure 1 shows the fluorescence spectrum of pDFB vapor obtained with excitation into the 3l5' vibrational level (AI2 = 2069 cm-') of SI. The fluorescence with a sharp spectral feature is seen to be superimposed on the fluorescence with a broad spectral feature. The former fluorescence is known from a vibrational analysis to be emitted from the IPL of 3l5'. As suggested by Parmenter et al.,' the latter fluorescence is considered to be emitted from S1 levels reached via IVR following excitation into the IPL, though a small amount of the broad fluorescence may be emitted from higher SI levels populated by hot band transitions. Figure 2 shows the absorption spectrum along the rotational contour of the 3h5; band and the excitation spectrum at 0.06 Torr obtained by monitoring the IPL fluorescence at 269 nm or the broad fluorescence at 309 nm with a detection bandwidth of 4 nm, together with the relative quantum yield spectrum derived as the intensity ratio between the excitation spectrum and the corresponding absorption spectrum. As mentioned in the experimental section, the exciting light employed is linearly polarized and the fluorescence is viewed at right angles to the direction of propagation. The excitation spectra shown in Figure 2 were obtained by employing the incident laser light polarized perpendicularly to the plane containing the laser beam and the emission detector. During the measurements, we did not use an analysis (11) Baba, H.; Fujita, M.; Ohta, N.; Shindo, Y . J . Specrrosc. SOC.Jpn. 1980, 29, 387. ( 1 2 ) Ohta, N.; Baba, H. J . Chem. Phys. 1982, 76, 1654. (13) Baba, H.; Ohta, N.; Sekiguchi, 0.;Fujita, M.; Uchida, K. J . Phys. Chem. 1983, 87, 943.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 8, 1987 2077
Intramolecular Vibrational Redistribution
r
Ex.
3’5’
F
I1
1$
120
WAVELENGTH (nm 1
Figure 1. Fluorescence spectrum of pDFB vapor with excitation into the 3I5I level of SI at a sample pressure of 1.2 Torr. The spectral resolution is 0.6 nm. The symbols * and ** indicate the wavelengths (269 and 309 nm) at which the IPL fluorescence and the broad fluorescence were monitored, respectively, to obtain the excitation spectra.
WAVENUMBER (cm-’ 1 Figure 3. (a) @ pspectrum ~ along the rotational contour of the 3b5: band corrected for the superposition of background absorption (-); corrected absorption spectrum (...); q p (~0 ) .(b) Absorption spectrum at a tem-
perature of 298 K simulated with the rotational constants reported in ref 14. A ” = 0.188 10, B “ = 0.04764, and C”= 0.03801 cm-l in theground state; A‘ = 0.176 20, B’ = 0.047 87, and C’ = 0.037 65 cm-I in the excited state (. .); distribution of 1’ -); distribution of &‘ (-). In these simulations, the laser line was assumed to have a triangle band shape with a width (fwhm) of 0.5 cm-l, and the maximum J value was limited to
-
(b)
broad
(-e
200.
I
I
I
I
20
to
0
-10
I
-20
I
-3(
WAVENUMBER (cm-’) Figure 2. A set of spectra for the 3A5; band of pDFB vapor. (a) Excitation spectrum monitored through the IPL fluorescence (-- -); absorption spectrum aIPL spectrum (-). (b) Excitation spectrum monitored through the broad fluorescence (-- -); absorption spectrum (. .); abroad spectrum (-). The band origin, denoted by 0, is tentatively assumed to be at 38 907 cm-l. Sample pressures are 0.06 Torr for the excitation and (e..);
yield spectra and 0.8 Torr for the absorption spectra. polarizer for the emission and so did not measure the quantities I,,and I , which are the intensities of fluorescence polarized parallel and perpendicularly to the polarization direction of the laser light, respectively. In such circumstances, the observed intensity nearly +lI,. The excitation spectra which are related corresponds to Il to I , were also obtained by employing the laser light polarized in the plane. However, a significant difference was not observed. Therefore, the excitation spectra shown in Figure 2 are reasonably regarded as the spectra of the total fluorescence whose intensity corresponds to Ill + 21,. The excitation spectrum of the IPL fluorescence is considerably different from the corresponding absorption spectrum, indicating that the quantum yield of the IPL fluorescence (@pIpL) notably depends on the rotational level excited. The peak located at higher wavenumbers, indicated by P, in Figure 2, is lower in absorption intensity than the peak a t lower wavenumbers, indicated by P2, whereas PI is higher in fluorescence intensity than P2 (Figure 2a). In fact, the QIpL spectrum exhibits
a prominent peak at around PI. On the other hand, the difference between the excitation spectrum of the broad fluorescence and the absorption spectrum is quite small, and the quantum yield of the broad fluorescence (abroad) is nearly constant along the rotational contour (Figure 2b). Inspection of Figure 2 will show that a continuous background due, probably, to congested hot bands is superimposed on the 3;s; absorption band. On the other hand, the fluorescence excitation spectrum shown in Figure 2a can be regarded as the excitation spectrum of the IPL fluorescence along the rotational contour of the 3;s; band, since the sharp fluorescence bands at around 269 nm where the fluorescence was monitored to obtain the excitation spectrum are assigned to the vibronic bands of fluorescence emitted from the IPL. Actually, the contribution of the broad congested background which can be assigned to the fluorescence emitted from levels reached via IVR and levels populated by hot band transitions is quite small a t around 269 nm, as is seen in Figure 1. For obtaining the true yield spectrum of the IPL fluorescence from the 3I5l, therefore, the portion of the background was subtracted from the observed absorption spectrum. Figure 3a shows the true QIpL spectrum thus obtained, together with the corrected absorption spectrum. The latter spectrum was obtained by assuming that the background intensity is constant throughout the spectral region of the 3$f, band, and that the constant background intensity is equal to 15% of the absorption intensity observed at peak P,. The decays of the two fluorescence emissions in question were separately measured at 0.06 Torr for three different excitation positions on the rotational contour of the 3A5; band with a detection resolution of 0.6 nm. For each of the excitation positions, the calculated decay curve obtained by convoluting the profile of the excitation laser pulse with a single exponential decay constant was found to fit well the observed decay curve. The lifetimes thus obtained for the IPL fluorescence (7IpL) are shown
2078
Ohta et al.
The Journal of Physical Chemistry, Vol. 91, No. 8, 1987
convoluted by assuming a single-exponential decay implies that the contribution of the fast decaying component is negligibly small. On the basis of the pressure dependence of the fluorescence spectra, Parmenter and co-workerss also suggested that IVR from the 3'5' level in S1 of pDFB vapor is characterized by the intermediate case, in agreement with our present view. The fast fluorescence may be roughly estimated to be about 3% of the total fluorescence in intensity under collision-free conditions, by employing the IVR parameters reported by these authors. Accordingly, the observed yields and decays may be regarded as those of the slow component of fluorescence. Then, the quantum yields and lifetimes can be expressed as f 0 1 l o w s : ~ ~ ~ ' ~
0-0
@IPL abroad
l/TIPL
10
0
-10
-20
-30
WAVENUMBER (cm-' 1 Figure 4. A set of spectra for the 0-0 band of pDFB vapor. Excitation spectrum monitored through the IPL fluorescenceat 278.2 nm with a detection resolution of 0.6 nm (- - -); absorption spectrum (...); Q ~ spectrum (-). See the text for the evaluation of !BIPL. The band origin, denoted by 0, is at 36 837.9 cm-'.I4 Sample pressures are 0.02 Torr for the excitation and yield spectra and 0.16 Torr for the absorption spec-
L
trum. in Figure 3a. The TIPL values a t these excitation positions were also obtained by employing a detection resolution of 4 nm. However, each of them is essentially the same as the one measured with the 0.6-nm resolution. The value of 7 1 p ~a t the excitation position where @IpL exhibits a peak (6.3 nm) is a little smaller than those at the other positions (6.5 and 6.8 ns), but the variation of 7 1 p ~is significantly smaller than that of @pIpL. The lifetimes of the broad fluorescence (Tbroad) are almost the same (4.8 ns) ~ measured. a t the three excitation positions where 7 1 p were For the 0-0 band and the 5; band (AE= 818 cm-' at 5'), the excitation of which induces no broad fluorescence resulting from IVR, the absorption spectrum and the excitation spectrum across the rotational contour obtained at low pressures are identical with each other except that a continuous background is superimposed in the absorption spectrum. The results for the 0band are shown in Figure 4. The fluorescence quantum yield spectrum was obtained as the intensity ratio of the excitation spectrum to the absorption spectrum corrected for the background absorption. The correction of the absorption spectrum was made by assuming that the background intensity is constant throughout the spectral region of the 0-0 band, and that the constant intensity is equal to 5.5% of the intensity at the peak with a maximum. These results indicate that QIPL is independent of the excited rotational level unless IVR occurs. Therefore, the excited rotational level dependence of a 1 p L at the 3'5' vibrational level is reasonably attributed to a rotational effect on IVR. If IVR at the 3l5' level is characterized by the statistical limit of the radiationless transition theory, the IVR rate constant (and hence 1/qPL) is expected to be smaller at peak P, than at any other position, since &IPL is greatest a t PI;moreover, 1 / q P L will be larger than l / ~ - by the IVR rate constant, if electronic decay rates at the IPL and at the emitting levels of the broad emission are equal to each other. Contrary to the results expected from the statistical limit behavior, however, the observed value of 1 / q P L at P1is larger than the others, and 1/7IpL is appreciably smaller than 1/7broad, as mentioned previously. With respect to the rotational level dependence, the relation between QIpL and 7 1 p ~ reminds us of that between the quantum yield and the lifetime of the slow component of fluorescence in pyrimidine vapor excited into the '0 level of S1 where the fluorescence is characterized by the intermediate case b e h a ~ i 0 r . IAccordingly, ~ IVR at the 3l5' level of pDFB is considered to be described by the intermediate case of radiationless transition theory which leads to a biexponential decay of fluorescence. However, the fact that any fluorescence decay measured in the present study is satisfactorily
=
1/7broad
k,'/(k,
+ NkJ
kurN/(ks
+ Nku)
ks/(N+
1) + N k u / ( N +
(1) (2) l)
(3)
Here N is the number of the emitting levels of the broad fluorescence, denoted by U, which are coupled to the IPL; k, and k , and k,' and k,' are, respectively, the total decay constants and the radiative decay constants; the subscripts s and u refer to the IPL and U, respectively. As mentioned previously, QpL varies greatly along the rotational contour with a maximum at PI, whereas @brad does not. These results show that N varies significantly with excitation across the rotational contour with a minimum a t P,, since the ratio @broad/@IpL is proportional to N, as is known from eq 1 and 2. Furthermore, the fact that @broad is nearly independent of the rotational level, in'spite of the considerable variation of N, indicates that Nk, is much larger than k, (see eq 2). Therefore, the number of N is suggested to be quite large, probably more than 10. This view is supported also by the fact that the spectrum of the fluorescence emitted from the levels reached via IVR from the 3l5l exhibits a broad feature as is seen in Figure 1. If the number of N is small, IVR will be restricted in the sense that essentially full recurrence in vibrational distribution occurs on the time scale of the fluorescence lifetime, as mentioned by Zewail et a1.I6 In such circumstances, the quantum beat will be expected in the fluorescence decay, and the fast decaying component of fluorescence will be missing. As mentioned previously, however, the IVR at the 3l5' level of pDFB vapor is regarded as the intermediate case which leads to a biexponential decay of fluorescence, though the contribution of the fast component is considered to be very small. This conclusion agrees with the view that the N value is probably larger than 10. Parmenter and co-workerss estimated the N value to be 1.8 at the 3'5' level by using the chemical timing method. This was obtained for excitation at P2 with an excitation bandwidth of 2 cm-I. By combining their value with eq 1 and our results on @ l p ~ , the N value is indicated to vary approximately from 1 to 3 with excitation along the rotational contour. In that case, @.broad is expected from eq 2 to exhibit a fairly large variation where the ratio of the maximum to the minimum is about 1.5. Contrary to the expected results, however, the observed @broad is nearly constant along the rotational contour, as mentioned previously. Accordingly, the N value of 1.8 seems to be underestimated, though our experimental conditions on excitation are not the same as theirs. As mentioned previously, 7pLslightly varies along the rotational contour with a minimum at P,,indicating that k, is different from k, (see eq 3). It is seen from eq 3 that a decrease of qPL with decreasing N, which corresponds to the present case, occurs when k, is smaller than k,. According to eq 3, Tbrmd is expected to be equal to 7 1 ~ Ac~ . tually, Tbrad is smaller than T ~ L and , nearly independent of the rotational level excited, as mentioned previously. These unexpected results may be attributed to the superposition of the background (14) Cvitas, T.; Hollas, J. M. Mol. Phys. 1970, 18, 793.
(15) van der Werf, R.; Kommandeur, J. Chem. Phys. 1976, 16, 125. (16) Felker, P. M.; Zewail, A. H. Chem. Phys. Lett. 1983, 102, 113; J . Chem. Phys. 1985, 82, 2975.
Intramolecular Vibrational Redistribution
The Journal of Physical Chemistry, Vol. 91, No. 8, 1987 2079
absorption on the 3;5; band which is induced by hot band transitions, since such absorption may induce broad fluorescence whose lifetime is shorter than the value of 7br-d for excitation into 3IS1. Next, we discuss the origin of the rotational effect on IVR of pDFB, which is a nearly prolate symmetric top, on the basis of the results of simulation performed with a computer program to calculate the rotational band contour of an asymmetric rotor.” Rotational analysis has not been made for the 3;5; band, but the rotational constants for the 00 level obtained by Cvitas and Hollas14 may be used as those for the 3l5I level, since the absorption spectrum of the 3;5; band simulated with these constants agrees with the observed spectrum in the sense that two sharp peaks appear, with the peak a t lower wavenumbers being stronger in intensity than the other (see Figure 3). Figure 3b shows the distribution of the ensemble averaged J’ and K,’, Le. J ’ ( = C J ’ A J ’ K , ’ K , ’ v ) / ~ J ~ , ’ K ~and v ) ) K,‘ (=CK,’ f(J’K,’K,’v)/Cf(J’K,’K;v)), for the excited state a t room temperature, wheref(J‘K,‘K:v) is the probability that a molecule is excited into a rotational level with rotational quantum numbers J‘, K,‘, and K,’ at an excitation frequency of v. There is no correlation between the @IpL spectrum shown in Figure 3a and the distribution of J’across the rotational contour. On the other hand, the observed @IpL spectrum shows a peak at the excitation position where K,’ gives a minimum. Thus, it may be said depends on K,‘ and not on J’. qualitatively that aIpL Using the density of rovibronic levels of U, denoted by p , and the matrix element of the interaction between the IPL and U, 3 angular . ~ ~momentum denoted by u, N is given by 2 ~ ~ If~all the quantum numbers are conserved in IVR, as suggested by Nathanson and McClelland19 from the fluorescence polarization measurements, p is regarded as independent of the rotational level , is known excited. Then, will be nearly proportional to u - ~ as from eq 1. On the basis of these considerations, IVR induced by Fermi interaction is known to give @IpL which is independent of the rotational level excited, since the matrix element concerned is independent of the rotational quantum number. On the other hand, IVR induced by Coriolis interaction in the nearly prolate symmetric top will give @IpL which is proportional either to K,’-2 = F(K,’) or to ((J’+ K,’)(J’- K,’ 1) (J’- K,’)(J’+ K,’ l))-l = G(J’,K,’), depending on the kind of Coriolis interaction, since the matrix element concerned is proportional to K’or to (J’(J’ 1) - K’(K’f l)l1l2in the symmetric top.20 F(K,‘) is related to parallel Coriolis interaction induced by rotation around the figure ( z ) axis (in-plane long axis), and G(J’,K,’) is related to perpendicular Coriolis interaction induced by rotation around the x or y axis. The quantum yield spectra simulated on the assumption that the yield is proportional to F(K,’) and to G(J’,K,’) are shown in parts a and b of Figure 5 , respectively. As is seen in Figures 3a and 5b, the observed yield spectrum is entirely different from the yield spectrum simulated by assuming the perpendicular Coriolis interaction. On the other hand, the yield spectrum which was obtained by assuming the parallel Coriolis interaction (Figure sa) agrees with the QIpL spectrum shown in Figure 3a in the sense that a maximum appears near the absorption peak located at higher wavenumbers. Both the distribution of 1’and K,’and the quantum yield spectra shown in Figures 3b and 5 , respectively, were simulated with the
+ +
+
+
(17) Sekiguchi, O.;’Ohta,N.; Baba, H. Chem. Phys. Lett. 1984,106,387. (18) Freed, K. F.; Nitzan, A. J . Chem. Phys. 1980, 73, 4765. (19) Nathanson, G. M.; McClelland, G. M. Chem. Phys. Lett. 1985, 114, 441. (20) Allegrini, M.; Johns, J. W. C.; McKellar, A. R. W. J. Mol. Spectrosc. 1977, 67, 476.
10
0
- 10
-2
WAVENUMBER (cm-’ 1 alpLspectrum simulated by assuming parallel Coriolis interaction; (b) aIpL spectrum simulated by assuming perpendicular Figure 5. (a)
Coriolis interaction. Dotted line shows the simulated absorption spectrum.
rotational constants evaluated from the 0-0 absorption band, as mentioned previously. However, the rotational constants a t the 3l5I level will be slightly different from the employed ones. Then, we examined the dependence both of the distribution of J’and K,’ and of the yield spectrum on the rotational constants employed. The change in A’or B’leads to a change in relative intensity of the two sharp peaks, and the decrease of C’leads to a decrease of energy separation between these two peaks in the simulated absorption spectrum. We could not reproduce the observed absorption spectrum completely. However, the absorption spectrum characterized by two sharp peaks with the lower wavenumber peak being stronger in intensity than the other and by a long tail in the lower wavenumber region could be reproduced when the rotational constants were employed in the following regions: 0.1732 5 A ’ S 0.1812,0.0477 5 B ’ S 0.048 24, and 0.037 25 5 C’50.037 85 cm-l. When the rotational constants were varied in these regions, however, both the distribution of K,’ and the yield spectrum simulated on the assumption that the yield is proportional to F(K,’) are the same as the ones shown in Figures 3b and 5a, respectively, in the sense that K,’ and the quantum yield show a minimum and a maximum, respectively, near the absorption peak located at higher wavenumbers. On the other hand, the yield spectrum simulated on the assumption that the yield is proportional to G(J’,K,’) is always similar to the one shown in Figure 5b, and exhibits two high peaks, in contrast with the observed yield spectrum shown in Figure 3a. Thus, the rotational level dependence of @IpL is considered to be correlated with K,’ at least for excitation into the rotational levels with small quantum numbers of K,‘, e.g., K,‘ 5 10, as is known by comparing the observed yield spectrum with the simulated distribution of K,’ and with the simulated quantum yield spectra. These results strongly suggest that the parallel Coriolis interaction plays an important role in IVR from the 3’5l vibrational level in SIof pDFB vapor, especially for excitation into rotational levels with small values of K,‘.
