J. Phys. Chem. 1988, 92, 3725-3729
3725
two-dimensional surface for this system, and Carmeli and Nitzan166have interpreted this in terms of a non-Markovian generalized Langevin equation. Recently, Singer, Kuharski, and Chandler'67 estimated the equilibrium solvent effect to be AVTsT 0.6 cm3/mol. This estimate is just the opposite of Jonas's estimate AVTsT -1.5 cm3/mol which is based on the approximation of hard sphere interactions. It seems that the interactions present in this nonpolar system, which are comparable with thermal energies, cannot be approximated by using the intuitive concept of reactant volume changes. Therefore, the data on cyclohexane imply that the transmission coefficient K increases with pressure over the whole density range in contrast to the widely accepted interpretation by Jonas which predicts a decreasing K going through a maximum. A slowly increasing K could be caused by two effects and possibly a combination thereof. First, it is know that RRKM weak collision models show a very smooth transition between their low-pressure limit and transition-state t h e ~ r y l ~ ~(section ~ l J ~ *4). Second, the presence of weakly coupled modes in the molecule could cause a transition to a quasi few degree of freedom system at higher
pressures.19,75~76~103 As mentioned in section 4.4, recent work confirms this prediction.'Og*l10As the calculation of the potential of mean force is hard but feasible, it would be extremely helpful to collect more extensive data on this system covering a wide density and temperature range. In conclusion, the data on cyclohexane still await a definitive interpretation. Our three examples show that, while these are the systems best understood, having been in the focus of study for many years, there exist many uncertainties. In our view, the weak points on the experimental side are that systems are not studied over a wide enough range of densities, temperatures, and solvents. It is also desirable to extend such studies to atom-transfer and polyatomic recombination reactions. On the theoretical side, a small knowledge of the true intramolecular solute potential and the solvent-solute potential makes application of existing theories difficult. Practical procedures for calculating rate constants in polyatomics at low pressures beyond the strong collision approximation, which would take the proper collisional dynamics into account, are still lacking. Finally, ways of incorporating different reaction channels, quantum effects, and all electronic surfaces participating are in their infancy.
(165) Garrity, D. K.; Skinner, J. L. Chem. Phys. Lett. 1983, 95, 46. (166) Carmeli, B.; Nitzan, A. Chem. Phys. Lett. 1984, 106, 329. (167) Singer, S. J.; Kuharski, R. A.; Chandler, D. J . Chem. Phys. 1986, 90, 6015.
Acknowledgment. We thank J. Troe, D. Chandler, P. Hanggi, P. Talkner, D. Thirumalai, H. Grabert, J. Skinner, D. Hsu, and M. Sceats for helpful discussion and correspondence.
ARTICLES Rotational Effects on Intramolecular Radiationless Transitions. The Story of Pyrazine Aviv Amirav School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Auiv 69978 Tel Auiu, Israel (Received: June 8, 1987; In Final Form: November 13, 1987)
The experimental rotational effects on the Sl('B3J excited-statedynamics of pyrazine are briefly summarized. These experiments impose severe constraints on the validity of the general radiationless transitions theory in the limit of intermediate level structure. A model is presented to account for all the problems confronted by the theory in terms of rotationally induced intratriplet vibrational energy redistribution. This new type of intramolecular radiationless transition called vibrational crossing is an interstate process with intrastate vibronic coupling features. From this model two major predictions emerge, which are shown to be fulfilled. We demonstrate that Coriolis coupling is an important and dominant mechanism leading into intramolecular vibrational energy redistribution. The absorption spectrum, fluorescence excitation spectrum, and the resulting emission quantum yield of pyrazine were studied by using dye laser with 2-GHz resolution as a light source. The emission quantum yield decreased with the rotational state. The absorption contour of a single rotational state was broader than the excitation contour, and absorption with a low emission quantum yield is shown between adjacent rotational transitions. The ratio of short time to long time emission (A+/A-) is shown to depend on the rotational temperature following excitation of a single rotational transition. These experimental results combined with the quantitative fit of the inverse emission quantum yield and A+/A- were predicted by the vibrational crossing model and thus strongly support its validity.
Introduction The S1(lB3J state of the pyrazine molecule serves as a touchstone for critical scrutiny of >he theory of radiationless Following the pioneering work of Tramer and co-~orkers,~*' conventional wisdom has attributed intramolecular ~
( 1 ) Bixon, M.; Jortner, J. J. Chem. Phys. 1968, 48, 715. (2) Bixon, M.; Jortner, J.; Dothan, Y. Mol. Phys. 1969, 17, 109. (3) Jortner, J.; Mukamel, S. In Molecular Energy Transfer; Levine, R. D., Jortner, J., Eds.; Wiley: New York, 1979; p 178. (4) Jortner, J.; Levine, R. D. A h . Chem. Phys. 1982, 47, 1 . (5) Nitzan, A.; Jortner, J.; Rentzepis, P. M. Proc. R. Soc. London, A 1972, 327, 367.
0022-3654/88/2092-3725$01.50/0
dynamics in this system to the intermediate level structure (ILS) As detailed experimental results have limit in the become available, this picture became less clear and understandable as the conventional theory in the ILS limit was confronted with a large volume of conflicting pieces of experimental results. These puzzling self-inconsistencies are described in detail elsewhere.* (6) Frad, A,; Lahmani, F.; Tramer, A,; Tric, C. J . Chem. Phys. 1974, 60, 4419. (7) Lahmani, F.; Tramer, A.; Tric, C. J . Chem. Phys. 1974, 60, 4431. (8) Amirav, A. Chem. Phys. 1986, 108, 403.
0 1988 American Chemical Society
3726 The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 H,,pC,H
PYRAZINE
,C.dqH
a
:
SPIN ORBIT
p : CORIOLIS y :SPIN ORBIT
Amirav to reconcile between the experimental results and the theory of radiationless transitions, a new theoretical model was advanced by Amirav.*
Vibrational Crossing: A New Type of Intramolecular Radiationless Transition Following ref 8, the relevant energy level diagram in pyrazine is shown in Figure 1. So is radiatively coupled to SI with AJ = 0, f 1 standard selection rules. SI is strongly coupled to the sparse triplet T manifold, via spin-orbit coupling. The spin-orbit selection rules are AN = 0 and AK anything. T is nonradiatively coupled through an intrastate K”selective Z type Coriolis coupling to T’. (X, Y Coriolis coupling can also be considered.) T’ contains energy levels of T which, due to selection rules, are not allowed to SI by spin-orbit coupling. T’ may decay nonradiatively to So in 7 2 350 ns. From Figure 1, it is implied that a rotational induced vibrational energy redistribution within the triplet state leads to the observed dynamics in pyrazine. This state of affairs can be written as Figure 1. Energy level diagram of pyrazine. T and T’ vibrational-rotational states belong to the same triplet electronic state. T’ states are vibronically coupled via Coriolis coupling to T and are uncoupled to SI via spin-orbit coupling due to selection rules.
The two major problems are the following:* (a) One problem is the problem of the missing states arising from the confrontation of the time-resolved and emission quantum yield data with the ultrahigh-resolution spectral data. The number of spectroscopically observed molecular eigenstates (MEs) is small ( 12) and rotationally i n d e ~ e n d e n t , ~ -whereas l~ the time-re~ o l v e d ’ ~and * ’ ~ quantum yield data6J6 require a much higher number of MEs and a rotational dependence of this number. (b) A second problem is the origin of the short-time-resolved emission component. The number of spectroscopically observed MEs is too small for a true dephasing (at the magnitude observed) to occur in the ILS limit. This problem is further exacerbated by the existence of the short time component in the (biexponential) time-resolved emission of pyrazine, following an incoherent nanosecond laser e ~ c i t a t i o n . ~In J ~addition to this inconsistency, it was shown by Kommandeur and c o - w ~ r k e r s ~that - ’ ~ the amplitude ratio of this short component to the long time emission ( A + / A - )is sharply maximized in the valleys between adjacent rotational transitions where no spectral lines were observed. According to the conventional ILS theory A+IA- should be proportional to the number of coherently excited MEs. The number of spectrally observed MEs is too small for any short component to appear under nanosecond incoherent excitation, and obviously it should not maximize in the “no man’s land” where no MEs are detected. The existence of near-resonance Raman light scattering (NRLS) was therefore invoked in order to account for the observation of this short component?-’* but the short component was subsequently shown to be real with a lifetime of 100-120 P S . ” ~ ’ ~ In order to explain the wealth of experimental results and N
(9) Drabe, K. E.; Kommandeur, J. In Excited State; Lim, E. C . , Innes, K. K., Eds.; Academic: New York, 1988; Vol. 7. (IO) Kommandeur, J.; van der Meer, B. J.; Jonkman, H. Th. In Zntramolecular Dynamics; Jortner, J., Pullman, B., Eds.; Reidel: Dordrecht, 1982; p 259. (1 1) van der Meer, B. J.; Jonkman, H. Th.; Kommandeur, J. Laser Chem. 1983, 2, 77. (12) Jonkman, H. Th.; Drabe, K. E.; Kommandeur, J. Chem. Phys. Lett. 1985, 116, 357. (13) van der Meer, B. J.; Jonkman, H. Th.; Kommandeur, J.; Meerts, W. L.; Majewski, W. A. Chem. Phys. Le??. 1982, 92, 565. (14) Matsumoto, Y.; Spangler, L. H.; Pratt, D. W. Laser Chem. 1983, 2, 91; Chem. Phys. Let?. 1983, 98, 333. (1 5) Saigusa, H.; Lim, E. C. J . Chem. Phys. 1983, 78, 9 1; Chem. Phvs. Left. 1982, 88, 455. (16) Amirav, A.; Jortner, J. J . Chem. Phys. 1986, 84, 1500. (17) Lorincz, A,; Smith, D. D.; Novak, F.; Kosloff, R.; Tannor, D. J.; Rice, S.A. J . Chem. Phys. 1985, 82, 1067. (18) Knee, J. F.; Donay, F. E.; Zewail, A. H. J . Chem. Phys. 1985, 82, 1042.
These matrix elements represent a new type of radiationless transition, which we call vibrational crossing (VC). An intrastate vibrational mixing which is assumed to arise from Coriolis coupling is also associated with increased dilution and hence interstate electronic relaxation of the singlet component of the MEs (intersystem crossing in this case). Thus, vibrational crossing is an interstate radiationless transition with intrastate vibronic coupling features. This model gives a full qualitative and quantitative interpretation of all the debated aspects of pyrazine dynamics.* Basically, MEs originating from the interstate coupling of S,(J’,K’) with the sparse T manifold exhibit a dual behavior with regard to their Coriolis coupling with T’ states, as the matrix elements (VRz) of Z type parallel Coriolis coupling is proportional to K.19,20( K is the precessional-rotational quantum number, and K”is the triplet K quantum number.) The MEs with Sl-T(J”,K”=O) correspond to the small molecule limit (vanishing Coriolis coupling) having a long lifetime (350 ns) and Doppler-limited spectral width. The MEs containing an Sl-T(J”,K”#O) admixture correspond to the large molecule statistical limit being characterized by a short ( N 120-ps) lifetime, low emission quantum yield ( Y = 6 X and a broad homogeneous width of 1.5 GHz. The experimental biexponential decay observed is inhomogeneous in nature, and the rotational dependence of A + / A - and the emission quantum yield is due to the 1 / ( 2 J 1) statistical abundance of MEs with Sl-T(J”,K”=O) character.
+
Model Predictions Two major predictions clearly emerge from this model? 1. Coriolis coupling is an important and dominant vibronic coupling (mechanism) inducing intrastate vibrational energy redistribution. 2. The “missing states” are “grass”, namely, a continuous, broad, short-lived and low quantum yield background; hence, they are very weak in the excitation spectrum but should be amenable to observation in direct absorption spectroscopy. Each rotational line envelope is broader in absorption than in excitation, and the absorption “background” extends to the valley between adjacent rotational transitions. The term “grass” was denoted by D. W. Pratt,2’ while introducingzza multitude of very weak MEs in order to account for the observed short component under nanosecond laser excitation and its magnetic field effect. According to the VC model, however, the “grass” is a continuous low quantum yield (19) Riedle, E.; Neusser, H. J.; Schlag, E. W.; Lin, S. H. J . Phys. Chem. 1984, 88, 198.
(20) Mills, I. M. Pure Appl. Chem. 1965, 1 1 , 325. (21) Presented at the International Conference on Radiationless Transitions, Newport Beach, CA, Jan 7, 1984. (22) Matsumoto, Y . ;Spangler, L. H ; Pratt, D W. J Chem. Phys. 1984, 80. 5542.
Rotational Effects on the Dynamics of Pyrazine
The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 3727
background due to a statistical limit IVR and not due to a true dephasing. In this paper, I shall describe new experimental results demonstrating the verification of these predictions and thus giving additional credence to the validity of the vibrational crossing (VC) model.
Experimental Section Our experimental apparatus and techniques for measuring absorption spectra and absolute fluorescence quantum yield16,23324 were extended to allow the use of our new eximer pumped dye laser as a light source (Lambda Physik EMG53MSC+FL2002E). Absorption spectra and fluorescence excitation spectra of pyrazine cooled in planar supersonic expansions were simultaneously determined by using the dye laser equipped with an etalon and frequency-doubling crystal, having 2-GHz spectral resolution, and using pressure tuning. Pulsed planar jets were generated by expansion of seeded argon through a nozzle slit. Two nozzle slits were used having dimensions of 0.22 X 33 and 0.27 X 90 mm. The repetition rate of both nozzles was 6-9 Hz, and the gas pulse duration was 200-300 hs. The nozzle was at about room temperature (in the range of 15-40 “C), and pyrazine was mixed with argon at the stagnation pressure up to 70 Torr. Laser light after attenuation to a 1 gJ/pulse crossed the beam parallel to the slit at a distance of X = 16 mm from it (10 and 30 mm were also used). The light beam was split by a sapphire window. Before hitting the silicon photodiode detectors (UDT PIN lOD/SB 12-mm diameter followed by a current to voltage converter), the laser beam was fully absorbed in a red dye cell and was turned into a diffuse lower intensity red fluorescence. This was done in order to increase the detector linearity. The attenuation AZ of the light beam due to absorption was determined from the difference in the light intensity before and after crossing the planar jet. The fluorescence intensity IF was monitored by a photomultiplier. The number of laser pulses was doubled compared with the nozzle pulse rate, and a second differentiation was performed between the results obtained with the laser pulse that crossed the pulsed jet and the second untimed laser pulse. This procedure eliminated any stray absorption and resulted in a zero, flat, wavelength-independent base line. The role of collisions was studied by varying both the stagnation pressure of the argon gas and the pyrazine concentration by changing the nozzle temperature. Probing the long-time emission, we have controlled the collision effect which was small and rotationally independent in our experiments. Absolute quantum yield was measured on the peak of R4 transition relative to that of 4-chloro-tram-stilbene in an expansion containing both molecules.23 Time-resolved decay curves were processed in a LeCroy 9400 125-MHz signal averager. Spectral tuning was achieved by means of a pressure transducer in a homemade pressure tuning unit, with dry nitrogen gas. The resolution was 2 GHz, and the long-term stability was 1 GHz/5 min. The spectral region near the 0-0 transition was also studied and found to contain negligible contributions from dimers, van der Waals complexes, impurities, hot bands, and other spectral interferences. Laser stray light was carefully filtered out and had no effect on the experimental results herewith presented.
-
Coriolis Coupling and Intrastate Intramolecular Vibrational Energy Redistribution Recently, there has been considerable experimental and theoretical work on the effect of molecular rotations on electronic intrastate as well as interstrate radiationless processes.8 Most noticeable is the celebrated problem of the onset of “channel three” in benzene. Riedle et aLZShave demonstrated the important role of rotational (J’) and precessional (K’) states in the radiationless transitions of benzene in the region of the onset of channel three (23) Sonnenschein, M.; Amirav, A,; Jortner, J. J . Phys. Chem. 1984,88, 4214. (24) Amirav, A,; Horwitz, C.; Jortner, J. J . Chem. Phys. 1988, 88, 3092. (25) Riedle, E.; Neusser, H. J. J . Chem. Phys. 1984, 80, 4686. Riedle, E.; Neusser, H. J.; Schlag, E. W. J . Phys. Chem. 1982, 86, 4847.
1
E, = l l 6 0 c m - l
A z Ln
E ,,” EXCITATION
..._ ..-
.__
ROTATIONAL ENERGY ( c m - l )
Figure 2. Absorption (solid curve) and fluorescence excitation (dashed curve) spectra and absolute fluorescence quantum yield (full squares and open circles) as a function of excitation frequency in the 1160-cm-’ band of SI of 9-cyanoanthracene. Spectral resolution is 0.8 cm-I. Rotational temperature is -30 K in the spectra and associated full squares and -20 K for the open circles.
where a drastic reduction in the emission quantum yield and lifetime occurs with increasing excess vibrational energy. The K’ = 0 precessional states in each rotational state J’ = 0-1 4 were much narrower than the K‘ # 0 states and appeared as sharp lines in the ultrahigh-resolution spectra. The other J’(K#O) states were much broader and had an order of magnitude smaller emission quantum yield, resulting in a broad and unresolved background “noise” in the spectra. This important effect was a t t r i b ~ t e d ’ ~ , ~ ~ to Z type parallel Coriolis coupling causing a rotationally induced intrastate vibrational energy redistribution (RIVR). On the other hand, Felker and Zewail have beautifully demonstrated quantum beats in the energy-resolved emission spectra of anthracene.26 The existence of these quantum beats as well as the weak rotational effect on their dephasing was invoked as a strong argument for the dominating role of anharmonic coupling on IVR in anthra~ e n e . ~ ’ Further work was therefore required to clarify the generality of Coriolis coupling on intrastate IVR. RecentIy, Amirav et al. have demonstrated the important role of Coriolis coupling in both 9-cyanoanthraceneZ8and a n t h r a ~ e n e . ~ ~ Figure 2 shows the absorption and fluorescence excitation spectra and absolute fluorescence quantum yield of 9-cyanoanthracene as a function of the excitation frequency near the 1160-cm-I vibrational-rotational contour. It is clearly observed that the emission quantum yield is reduced at increased rotational energy on both the P and R branches. This effect was shown to be one of the manifestations of intrastate Coriolis coupling.28 In Figure 3, we show the excitation spectrum of anthracene near its 1380-cm-’ vibration (upper trace) together with its energy-resolved emission spectra when it was excited on different positions and rotational states of its rotational contour. For clarity, only the portion of emission to states near 1380-cm-’ ground-state energy is shown. A remarkable difference is observed upon changing the excitation energy by 1.6 and 3.2 cm-’. An increased rotational energy completely changes the emission trace A into the highly congested trace C, demonstrating the greatly increased number of coupled background states. This increased vibrational density of states due to Coriolis-induced IVR was also noticed by Parmenter and c o - w ~ r k e r sin~ their ~ study of IVR in p-di(26) Felker, P. M.; Zewail, A. H. J . Chem. Phys. 1985, 82, 2961, 2975. (27) Felker, P. M.; Zewail, A. H. J . Chem. Phys. 1985, 82, 2994. (28) Amirav, A.; Jortner, J.; Terazima, M.; Lim, E. C. Chem. Phys. Lett. 1987, 133, 179. (29) Amirav, A. J . Chem. Phys. 1987, 86, 4706. (30) Holtzclaw, K. H.; Parmenter, C. S . J . Phys. Chem. 1984, 88, 3182. Coveleskie, R. A,; Dolson, D. A,; Parmenter, C. S. J . Phys. Chem. 1985, 89, 655.
3728 The Journal of Physical Chemistry, Vol. 92, No. 13, 1988
h,
I C
1
Amirav
: ni.i
LQb,
"." 1
3630
3625
3650
(b) Figure 3. Excitation (upper curve) and energy-resolved emission of anthracene on the spectral range 3600-3650 A. The excitation wavelengths for traces A, B, and C are marked in arrows on the upper excitation spectrum. Note the dramatic rotational dependence of the energy-resolved emission. EMISSION WAVELENGTH
'-4.0
-3.0
-2.0
-1.0
0
WAVVENUMBER(cm-')
Figure 4. Absorption (lower) and fluorescence excitation (middle) spectra of the rotational R branch of pyrazine S1(lB3Jorigin. The upper trace is the ratio of absorption over excitation spectra (l/Q). Laser wavelength is 3237 A, and pressure tuning is used for the fine tuning. Nozzle temperature is 20 O C , and the argon backing pressure is 60 Torr.
fluorobenzene and p-fluorotoluene. The conclusion that emerges from these and other time-resolved experimentsz8is that, in adI dition to anharmonic coupling, Coriolis coupling is very important and it dominates intrastate intramolecular vibrational energy redistribution. If we accept this situation which was found in b e n ~ e n e , ~ ~ ~ ~ ~ 3 9-~yanoanthracene,~~ a n t h r a ~ e n e and , ~ ~ ~ y r i m i d i n e ,then ~ ~ we Rl TRANSITION should naturally suspect that this may also be the case for intratriplet IVR in pyrazine. The triplet vibrational energy in v1 pyrazine at the SI origin is 4060 cm-1,32high enough to enable RIVR. The major difference, however, is that intratriplet RIVR z ....- - - - - .-._.____. in pyrazine is inherently associated with interstate electronic _ _EXCITATION ______---FREQUENCY relaxation, manifesting the essence of the new type of vibrational crossing radiationless transition. Figure 5. Absorption (full line) and fluorescence excitation (dashed line) spectra of the R, rotational transition of pyrazine S1('B3J electronic The "Grass"Is Real! origin. Spectral resolution is 2 GHz. The rotational temperature i s -20 K. The two spectra were simultaneously measured by using an etalon Figure 4 shows the direct absorption spectrum (lower trace), and pressure tuning. fluorescence excitation spectrum (middle trace), and the resulting ratio of absorption over fluorescence traces in the first nine Rthis comparison is that the inverse quantum yield spectrum branch rotational transitions of pyrazine SI origin. Several imquantitatively matches the A+/A- spectrum of Kommandeur and portant observations are made clear from Figure 4: c o - ~ o r k e r s . These ~ ~ are seemingly entirely different experiments, (a) The emission quantum yield strongly depends on the roand yet the results of these two different experimental observables tational quantum number and monotonically reduces with J'. are practically identical. (b) The absorption spectrum shows a substantial background In Figure 5, the R, transition is magnified. This figure clearly in between adjacent rotational transitions, in contrast to the exdemonstrates the fulfillment of the predictions drawn from the citation spectrum. vibrational crossing model. The absorption of R, is broader than (c) The inverse emission quantum yield (1/Q = absorption/ the excitation spectrum, and a clear low quantum yield background fluorescence ratio) strongly oscillates as one crosses each rotational absorption ("grass") is observed on the two sides of the R, trantransition. The ratio of the peaks to valleys can exceed a factor sition. We note that the relative emission quantum yield on the of 20! two sides of R, transition is about 5% of its value in the center (d) The minima in the inverse quantum yield spectrum are on of this transition. the peak of the rotational transitions, while the maxima are located Two remarks are in order concerning Figures 4 and 5 : in the valleys in between adjacent rotational transitions. (a) The largely reduced emission quantum yield in the valleys Comparing these results with the short gated and delayed between rotational transitions not only is in full agreement with excitation spectra of Kommandeur and c o - w o r k e r ~ , ~our - ~ ab~ the vibrational crossing model but also contradicts models based sorption spectrum clearly resembles the short gated spectrum. on near-resonance Raman light scattering (NRLS).9-12 Any Perhaps the most intriguing conclusion that can be drawn from photon which is "Raman scattered" is scattered, and hence, NRLS ~
-
' I
---*I
(31) Forch, B. F.; Lim, E. C. Chem. Phys. Leu. 1984, 110, 593. (32) Villa, E.; Terazima, M.; Lim, E. C. Chem. Phys. Left. 1986, 129, 336.
(33) Reference 10, p 266, Figure 10; ref 12, p 360, Figure 3.
The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 3729
Rotational Effects on the Dynamics of Pyrazine
TR=40’K
TR 120”K
I
0
t
1
1
1
100 200 300 400
1
I
0
TIME(Nsec1
t
/
/
100 200 300 4 TIME(Nsec1
Figure 6. Time-resolved emission of R2and R, rotational transitions of pyrazine SI(’BpU) electronic origin. The laser excited R2and R, transitions at their peak a t the various rotational temperatures indicated. The time resolution width is 26 ns. The nozzle temperature was 35 OC,and the argon backing pressure was controlled in the range 4-60 Torr. The indicated rotational temperature was separately measured from the resulting spectra.
has an emission quantum yield of loo%, which is 2 orders of magnitude higher than some average value of pyrazine emission quantum yield.16 The existence of NRLS and “no man’s land” between rotational transitions implies a much higher quantum yield in the valleys. The experimental results are completely the opposite of this implication. (b) The quantitative fit between the A+/A- spectrum and l / Q spectrum is explained as follows 1 / Q = A / F = ( A L + A s ) / ( A L Q L+ AsQs) (2) where A L and As are the absorption responsible for the short and long time emission component, respectively. QL and Qs are their emission quantum yields, respectively. If we ignore the short component contribution to the fluorescence quantum yield (ALQL >> AsQs), we obtain
(3) l / Q = l / Q ~ ( l + As/AL) According to the vibrational crossing model, As/AL is proportional to A + / A - so we can write 1 / Q = l/QL(1
+ CA+/A-)
(4)
where C is a constant, depending on the detection resolution and lifetimes. Since CA+/A- are high, 1 / Q Lcan be neglected and we obtain
1 / Q = CA+/A-
(5)
as is observed.
The Origin of the Short Component or Rotational Temperature Effects on Experimental Observables of a Single Rotational Transition After establishing the vibrational crossing model, the next relevant and interesting question pertains to the details of the intratriplet RIVR and Coriolis coupling. Addressing this aspect of pyrazine dynamics, we have conducted several additional exp e r i m e n t ~some , ~ ~ of which are shown in Figure 6 . In Figure 6 , we show the time-resolved emission after exciting pyrazine on the peak of its R4 and R2 transitions at various rotational temperatures, which were controlled by changing the argon backing pressure. The conclusion which emerges from these results is that A + / A (34) Amirav, A., submitted to Chem. Phys.
of a single rotational spectral line (and 1 / Q as established in other experiment^)^^ strongly depends on the rotational temperature. In fact, the A + / A - ratio can increase by more than an order of magnitude in R 2 and by a factor of 5 in R4 over the rotational temperature range of 24-120 K. It should be stressed that this increased A+/A- at higher rotational temperature is also associated with increased absorption background between the transitions. From these and other results, as well as computer simulation of pyrazine spectra, we assert that the short component and “grass” are an inhomogeneous superposition emerging from several sources. Any doorway state (J’, K’) is coupled to several groups of triplet (J”, K”) vibronic states; each group of a given triplet K”character has a spectral width (coupling width) that strongly increases with K”as Vbz(Coriolis) a p.Thus, Coriolis coupling results, in addition to an increased available density of states, also in an increased coupling width which manifests itself in the observed absorption spectrum.28 The overall result is that the short component originates mainly from (a) MEs(J”,K’’#O) which are spin-orbit coupled to the excited J’ rotational state; (b) neighboring rotational transitions and especially MEs of high J”and K” of the same branch resulting from high J’transitions; (c) rotational transitions in the Q branch and especially MEs of high J“ and K ” resulting from high J’ transitions; and (d) pyrazine molecules with one I3C and I5N isotope that their Q branch is about 6.4 cm-l to the blue of the regular pyrazine, but their high P-branch transitions strongly depend on the rotational temperature in their i n t e n ~ i t y . ) ~ These high J”, K ” transitions are low amplitude, very broad transitions that “invade” the R branch, generating the short time and low quantum yield emission. Similar behavior is observed in the P branch.34 Finally, we note that the rotational temperature dependence of a single rotational-state time-resolved emission can rationalize several experimental peculiarities and the debated aspects reported in the l i t e r a t ~ r e . * ~ ~ ~
Conclusions The excited-state dynamics of pyrazine shows several experimental unique features, such as a short time emission component and background low quantum yield absorption. These features cannot be accounted for by the general radiationless transitions theory in the ILS limit. A new type of intramolecular radiationless transition, namely, vibrational crossing (VC) which was invoked, could account for all the experimental results. This VC radiationless transition is based upon intratriplet RIVR leading into intersystem crossing of the singlet character of the MEs. A unique feature of VC is that it is an interstate process with intrastate features which, in the case of pyrazine, is determined by the properties of intrastate Coriolis coupling. In this paper, the predictions based upon the existence of VC were demonstrated experimentally. We showed that the “grass” is real and Coriolis coupling is an important and dominant coupling leading into intrastate IVR. A new manifestation of this Coriolis coupling was demonstrated in the rotational temperature dependence of A + / A - on the peak of R4 and R2 transitions. Acknowledgment. My very deep appreciation to Prof. Joshua Jortner for many long, fruitful, and stimulating discussions. I also thank Prof. E. C. Lim for a fruitful collaboration on the subject of rotational effect on radiationless transitions. Finally, my gratitude is given to Mr. Chanan Horwitz for maintaining our new laser. The research was supported by the Fund for Basic Research of the Israel Academy of Sciences. Registry No. Pyrazine, 290-37-9. (35) Terazima, M.; Lim,E. C.Chem. Phys. Lett. 1986, 127, 330.
