2280
J. Phys. Chem. 1983, 87, 2280-2282
Coriolis Effects on Intramolecular Vibrational Relaxation: Rotational Contour Dependence of Pyrimidine Fluorescence B. E. Forch, K. 1. Chen, H. Salgusa, and E. C. Llm’ Department of Chemlstfy, Wayne State Universlty, Detrolt, Mlchlgan 48202 (Received: March 23, 1983)
The rotational contour dependence of the fluorescence of pyrimidine indicates that the second-order Coriolis interactions play an important role in intramolecular vibrational relaxation.
Introduction The role of level densities in electronic relaxation (ER) of isolated molecules is well recognized, as evidenced by the classificationscheme for intramolecular level structure.’ The classification is based on the magnitude of the density (pl) of the background triple manifold {ll)),relative to their decay with (yJ, at the energy of the optically prepared singlet excited state (Is)). The “small molecule” limit is characterized by ylpl > 1. In between these two limiting cases lies the “intermediate” case in which the background states, although moderately dense, are still well separated relative to their decay width, i.e., ylpl < 1. In the small molecule limit, ER from Is) to (11)j cannot occur, although in the statistical limit ER occurs irreversibly. In the intermediate case the density of final states is insufficient to drive irreversibly ER. Instead, these molecules exhibit collisionfree fluorescence decay that can be described as the sum of two exponential terms.2 Theories of strong coupling intermediate-case molecules, based on the model of Lahmani, Tramer, and T r i ~ indicate ,~ that the fast decay represents the evolution of a primary singlet state into mixed singlet and triplet states (molecular eigenstates), while the slow decay is due to population decay of the molecular eigenstates. The ratio of the fast-decay preexponential to the slow-decay preexponential is thought to be a measure of the number of zero-order triplet levels strongly coupled to the optically prepared singlet state. The level structures pertinent to intramolecular vibrational relaxation (IVR) in the lowest excited singlet state (S,) can be similarly divided into three classification^.^ The small molecule limit corresponds to the case in which the density of background vibrational levels in S1is too small to allow IVR, and the statistical limit corresponds to the case where the vibrational density is high enough to make IVR irreversible. The fluorescence from the small-molecule limit is a discrete emission, which can be identified as resonance fluorescence, while that from the statistical limit is composed of congested, red-shifted, emission that can be attributed to the vibrationally relaxed species. In the intermediate case the density of the background vibrational levels is not high enough to drive truely irreversible IVR, and the fluorescence spectrum displays features due to relaxed as well as unrelaxed species. The intensity of the relaxed fluorescence, relative to that of the unrelaxed fluorescence, is a measure of the density of the background vibrational levels coupled to the (1)A. Nitzan, J. Jortner, and P. M. Rentzepis, Proc. R. SOC.London, Ser. A , 327,367 (1972). ( 2 ) See, for an excellent summary of this topic, D. M. Bartels and K. G.Spears, J. Phys. Chem., 86,5180 (1982). (3)F. Lahmani, A. Tramer, and C. Tric, J. Chem. Phys., 60, 4431 (1974). (4)K.F.Freed and A. Nitzan, J. Chem. Phys., 73,4765 (1980). 0022-365418312087-2280$01.50/0
optically prepared vibrational level. It has recently been shown that, while molecular rotations have little or no effect on ER of molecules belonging to the statistical limit, they have important influence on ER of molecules belonging to the small-molecule limit and intermediate-case ~oupling.~ Thus, rotational excitation can induce changes from small-molecule decay behavior to intermediate-casedecay behavior, while a reverse change can be brought about by rotational ~ o o l i n g .The ~ occurrence of rotational state dependence of ER is due to the need to consider rovibronic levels, rather than vibronic levels, for the number of effectively coupled triplet levels.68 Since vibration-rotation energy as well as angular momentum are conserved during the IVR process, rotations could also play an important role in IVR.9J0 In particular, the second-order Coriolis interactions, which couple different vibrational levels in the same electronic state, could increase the effective density of the background rovibronic states coupled to the optically prepared rovibronic state, thus leading to an increased efficiency of IVR. The purpose of this Letter is to present rotational contour dependence of pyrimidine fluorescence, which indicates that the second-order Coriolis interactions play an important role in the IVR of molecular with intermediate level structure. Experimental Section The pyrimidine (Aldrich) vapor sample was contained in a large volume, multipath aluminum cell equipped with White excitation optics and Welsch fluorescence optics. An absorption path of -2.3 m was obtained by using the multipath cell. Pressures were measured with a MKS Baratron pressure gauge and a Veeco ionization gauge. The laser used to record absorption and fluorescence (emission and excitation) spectra was a Nd:YAG pumped dye laser (Quanta-Ray DCR2A and PDL-l), which was frequency doubled through a Quanta-Ray wavelength extension system (WEX-1). The fluorescence spectra were dispersed through a 1-m Czerny-Turner spectrometer (Jarrell-Ash) used in the second order of a 1180 grooves/” grating, blazed at 500 nm. Both the fluorescence and fluorescence-excitation spectra were recorded at room temperature after normalization to the laser power, as described el~ewhere.~The absorption (5)H.Saigusa and E. C. Lim, J. Chem. Phys., 78, 91 (1973),and references therein. (6)D.B. McDonald, G. R. Fleming, and S. A. Rice, Chem. Phvs., 60, 335 (1981). (7)H.Saigusa and E. C. Lim, Chem. Phys. Lett., 88, 455 (1982). (8)B. J. Van der Meer, H. Th. Jonkman, J. Kommandeur, W. L. Meerts, and W.A. Majewski, Chem. Phys. Lett., 92,565 (1982). (9)H. Saigusa, B. E. Forch, and E. C. Lim, J.Chem. Phys., 78,2795 (1983). (10)C. S. Parmenter, J.Phys. Chem., 86,1735 (1982).
0 1983 American Chemical Society
Letters
The Journal of Physical Chemistry, Vol. 87, No. 13, 1983
RELAXED FL
305
345
11
%-
385
WAVELENGTH / nm Figure 1. Dispersed fluorescence from cdlision-free pyrimidine (- 100 mtorr) at room temperature obtained by exciting the 12; absorption at 0 2025 cm-’.
+
spectra was obtained by monitoring the transmitted intensity of the dye laser, in the presence and absence of pyrimidine, as it was scanned through the wavelength region of the absorption band. A Hamamatsu R928 photomultiplier with gated integrators (PAR 162 with Model 164 and 165 gated integrators) were used for detection.
Results and Discussion The 3200-A absorption system of pyrimidine is due to the dipole-allowed electronic transition to the lowest excited singlet state of the na*(B1) character, and it is characterized by the appearance of long progressions in several totally symmetric modes.ll Optical excitation of pyrimidine vapor into vibronic levels lower than about lo00 cm-’ above the electronic origin of the ‘Bl(na*) leads to the appearance of well-resolved resonance fluorescence with relatively simple and easily analyzed structure.12 As one pumps high-lying vibronic levels, the discrete spectrum characteristic of resonance fluorescence is replaced by congested emission. In the intermediate range of the excitation energy, both types of emission appear, as illustrated by the dispersed fluorescence spectrum generated by pumping 12; (0 + 2025 cm-’) level of pyrimidine (Figure 1). A substantial portion of the congested feature (to the red of the discrete feature) must be due to IVR that occur in the excited electronic state, since far more background appears in the fluorescence than would be expected on the basis of the excitation of the absorption background.l0 Rotational contour dependence of the quantum yields of “discrete” unrelaxed fluorescence, and/or “congested” related fluorescence, can therefore provide information concerning possible Coriolis effects on IVR. Figure 2 compares the fluorescence excitation spectrum (along the rotational contour of the 12; band) of unrelaxed fluorescence at 315.4 nm with that of relaxed fluorescence at 350.0 nm. It should be noted that the two spectra are markedly different. Thus, while the fluorescence excitation spectra of the relaxed emission mimics the rotational contour of the 12; absorption band (vide infra), the fluorescence excitation spectrum of the unrelaxed emission is noticeably sharper than the corresponding absorption, with its major intensity lying on the high-frequency side of the q branch. In order to obtain the relative quantum yield of unrelaxed fluorescence over the rotational contour of the 12; band, we have divided the fluorescence excitation spectrum of the unrelaxed emission by the absorption spectrum of the (11) K. K. Innes, H. D. McSwiney, J. D. Simmons, and S. G. Tilford, J. Mol. Spectrosc., 31, 76 (1969). (12)A. E. W. Knight, C. M. Lawburgh, and C. S. Permenter, J. Chem. Phys., 63,4336 (1975).
2281
+lo
0
-10
wavenumber / cm-1 Flgure 2. Fluorescence excltatlon spectra of the unrelaxed fluorescence monitored at 315.4 nm and relaxed fluorescence monitored at 350.0 nm, obtained by scanning the dye laser through the wavelength reglon of the 12; absorption. The posltlon of the ”band origin” was arbitrarily taken to be at the Q-branch maximum.
ij
ABS.
I
‘r
\
v
2. /,
P 0 -10 wavenumber/cm-l
+10
Figure 3. Comparison of the excitation spectrum of the unrelaxed fluorescence monitored at 315.4 nm (solid curve) with the 12; absorption spectrum (dashed curve). The lower two curves represent the excitation-frequencydependence of the relative quantum yield of the unrelaxed fluorescence, obtained by dividing the excitation spectrum by the absorption spectrum. The quantum yield spectrum 1 was obtained by normalizing the peaks of the excitation and absorption spectra, while the spectrum 2 was obtained by normalizing the excltatlon and absorption backgrounds in the P-branch edge.
same sample taken under the identical experimental conditions. The result, which is shown in Figure 3, clearly demonstrates that the quantum yield of the unrelaxed fluorescence exhibits a sharp maximum at the high-frequency side of the Q branch. The excitation-frequency dependence of the fluorescenceyield in the P branch varies considerably depending upon whether the quantum yield spectrum is obtained by normalizing the peaks of the absorption and excitation spectra or by normalizing the backgrounds on the P-branch edge. Since neither procedure truly corrects for the emission background arising from the excitation of the absorption background (we do not know the exact shape of the absorption background),
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The Journal of Physical Chemistty, Vol. 87, No. 13, 1983
Letters
only the fact that the quantum yield of the unrelaxed fluorescence is the greatest in the high-frequency side of the Q branch has quantitative significance. The large Q-branch quantum yield maximum is most likly related to the inefficiency of the second-order Coriolis interactions in this spectral region of the absorption band. For a symmetric-top molecule, the matrix elements of Coriolis interactions between two nondegenerate vibrational levels (r and s) is given by13J4 2'/'BQflJ(J + 1) - K ( K l)]'" (1)
+
where fl is defined by Qrs
=
f/z[(~r/vs)'/~
+ (~s/vr)'/~I
and {is a Coriolis constant. The rotational line strength pertinent to the intensity distribution in the 12; absorption are given by Honl-London formula for a parallel band15
P branch Q branch R branch
3-P
+ 1)
AJK = J(2J
Ecz AJK = J(J
+ 1)
(J+ 1)2- P = (J+ 1 ) ( 2 J + 1)
It should be noted that in the P and R branches the line strength formulas favor transitions to levels with K' = 0 over those with large values of K', while in the Q branch the maximum intensity is expected for transitions to levels with K' = J'. Comparison of eq 1 and 2 therefore shows that the most efficiently pumped levels in the Q branch, i.e., K' = J', is least active in the second-order Coriolis interactions, while the most efficiently pumped levels in the P and R branches, i.e., K' = 0, are most active in the Coriolis coupling. The quantum yield of the unrelaxed fluorescence is therefore expected to be much larger for the Q-branch excitation than for the R-branch or P-branch excitation, if the second-order Coriolis interactions influence IVR. To investigate whether this expectation is predicted by the rotational contour dependence of the matrix elements of the Coriolis coupling, we have calculated the average value of [J'(J'+1) - K'(K'+ 1)]lI2 as a function of excitation frequency using a computer pro(13) C. Di Lauro and I. M. Mills, J. Mol. Spectrosc., 21, 386 (1966). (14) T.Oka, J.Chem. Phys., 47, 5410 (1967). (15) G. Herzberg, 'Molecular Spectra and Molecular Structure of Polyatomic Molecules", Van Nostrand, Princeton, NJ, 1966, p 266.
Flgure 4. A plote of the average value of [ J ' ( J ' + l ) - K'(K' +1)] "* at room temperature' as a function of the excitation frequency. The plot Is based on the rotational constants for the zero-point level of 'B,(nr'). The rotational constants are not known for the 12; level.
gram modeled after that of Bartels and Spears.2 As can be seen in Figure 4, the second-order Coriolis interactions exhibit a sharp minimum in the same spectral region as the peak in the quantum yield data. We may therefore conclude that the maximum in the quantum yield of the unrelaxed fluorescence occurs in the Q branch because the Coriolis interactions between rovibrational levels are least effective for molecules excited in this spectral region of the absorption band. In conclusion, the results of the present investigation suggest that the second-order Coriolis interactions play an important role in the IVR process. More recent experiments on jet-cooled pyrimidine show that the excitation frequency dependence of the quantum yield of the relaxed fluorescence at various temperatures follows that of the matrix elements of the second-order Coriolis interactions,16 further confirming the role of the Coriolis interactions in the IVR process.
Acknowledgment. We are very grateful to Professor Takeshi Oka for enlightening discussions and guidance concerning Coriolis interactions, and to Professor Kenneth Spears and Dr. David Bartels for sending us the computer program used in ref 2. This work wm supported by a grant (CHE-8119202)from the National Science Foundation. ~
(16) K.T. Chen, B. E. Forch, and E. C. Lim, to be submitted for publication.
