Experimental Tests of the Theory of Radiationless Transitions

Pyrazine (1,4-diazabenzene) has played a central role in the development of the theory of radiationless transitions. In this paper, we will describe studies of the decay behavior a:qd orescence quantum yield of the isolated molecule and several of its isotopically labelled derivatives following pulsed dye laser excitation of "single" rotational levels of the 1B3u (nzr*) state in a seeded supersonic jet, both in the presence and absence of an external magnetic field. We shall demonstrate that pyrazine can be transformed from a "small" molecule to a "large" molecule by very small perturbations’ e.g., by climbing up the rotational ladder of the first excited singlet state, by isotopic labeling, and/or by applying de magnetic fields of the order of 100 G. Thus, the experiments provide important tests of the predictions of the theory for the first time. Specifically, we will show that, under "intermediate-case" conditions, (1) the fast component of the decay is indeed coherent in nature, (2) the coupled state is triplet in character (and, thus, that the process we are monitoring is intersystem crossing (ISC)), (3) nuclear spin is conserved in ISC, (4) rotations and small magnetic fields play an important role because of the angular momentum selection rules for ISC, and (5) the levels mixed by the magnetic field are most likely the fine-structure components of the different angular momentum levels of the mixed, singlet-triplet state. The relationship of these results to those of other workers in the field will also be discussed.


INTRODUCTION
The azabenzenes, particularly pyrazine (1,4-diazabenzene), have played a major role in the development of the theory of radiationless transitions. This is because they typically exhibit, unlike small molecules and large, statistical ones, a fluorescence quantum yield " A paper presented at the International Conference on Photochemistry and Photobiology, Alexandria, Egypt, January [5][6][7][8][9][10]1983. Work supported by the National Science Foundation (CHE-8021082) and the North Atlantic Treaty Organization (31.80/CI). which is pressure dependent and a fluorescence decay which is nonexponential. These properties, which place most azabenzenes in the "intermediate-case" category of the theory, are believed to derive from relatively small singlet-triplet energy gaps and relatively large intramolecular couplings between these zero-order states. Thus, it is imagined that the states in the vicinity of the singlet origin are mixed states which possess both singlet and triplet character, and that the decay properties of the "prepared" state depend not only on the characteristics of the molecule, but also on those of the exciting light; i.e., on its spectral distribution and its temporal behavior.
In an early, and elegant, treatment of this problem, Tramer and co-workers 2 suggested that the fluorescence decay of pyrazine could, under most conditions, be described as a sum of two exponential components. It was argued that the rapidly decaying component represents the evolution in time of a coherent superposition of molecular states having only singlet character into a set of quasi, stationary mixed singlet-triplet states, and that the slowly decaying component represents the subsequent evolution of an incoherent superposition of the independent decays of each of these quasistationary states. These slow decays may be either radiative or nonradiative, depending on the nature of the coupled state. This model, and its refined versions, accounts for most of the observed dynamic properties of the azabenzenes and many other intermediate-case molecules. 3 Our entry into this field was prompted by the recognition that most previous experimental tests of the predictions of the theory have been carried out under conditions where either the spectral width or the coherence width of the excitation source was large compared to the reciprocal level densities (p-l) typical of the "intermediate-case" molecule. Pyrazine has, for example, a background density of states of the order of 100/cm -1 in the vicinity of the singlet origin. 4 This means that very little in the way of detailed information about the nature of these mixed states (the molecular eigenstates) can be obtained from experiments performed with light sources having large (e.g., lcm-) spectral widths or subnanosecond pulse durations. Instead, one should move in the other direction if one wishes to provide further, and more stringent, tests of the theory. Towards this end, we have been performing, in the past few months, a number of experiments on pyrazine using our new supersonic jet apparatus and 1B3u PYRAZINE. EXPERIMENTAL TESTS 93 a 5 ns pulse duration dye laser with a spectral width of 0.06 cm -1 (2 GHz). We are particularly interested in the dependence of level densities on angular momentum quantum numbers, and on small magnetic fields. Presented herein are the results of some of these experiments which, although incomplete, already demonstrate the validity of our approach. Figure 1 shows a portion of the fluorescence excitation spectrum of 1B3, (nr*) pyrazine expanded in a pulsed supersonic jet of helium (P0 1 atm, x/D 40-100). Here, the (doubled) wavelength of our Quanta-Ray Nd/a'YAG pumped dye laser is scanned over the region 3250-3100 with an autotracking system, and the total fluorescence is detected by an EMI 9813QB photomultiplier tube, PAR162/165 boxcar integrator, and recorder. Immediately apparent are the high resolution capabilities of this technique, well known to workers in the field. In spite of the low quantum yield (,--10-3), we have also found that dispersed fluorescence spectra of pyrazine are relatively easy to obtain. Figure 2 shows a typical spectrum, recorded while exciting the 0o band and scanning the wavelength of an 0.25 m detection monochromator using 1 mm slits. Since the transition is electronically allowed, the strongest band in the spectrum is the resonance line which serves as an origin for a progression in the ground state in-plane stretching mode, Us, of symmetry b2g. This band 1B3u PYRAZINE. EXPERIMENTAL TESTS 95 also serves as an origin for a progression in P6a. At higher resolution, using 150 tz slits, additional structure is resolved in some of the bands.

SPECTROSCOPY
Resonance emission is also observed in the dispersed fluorescence spectra recorded while exciting the 6a0 and 50 vibronic bands. This indicates that intramolecular vibrational relaxation in the excited state is incomplete on the time scale of the emission process. Detailed studies of this effect, both in the presence and absence of collisions, are in progress.
Our main interest in the present work is in the rotationally resolved fluorescence excitation spectrum shown in Figure 3 Figure  4 a plot of the fluorescence intensity as a function of field from 0-150 G. Here, we excite in the Q branch of the 0 band, and detect the total emission with a 1 s aperture duration on the boxcar integrator. Strong magnetic field quenching is observed; the fluorescence intensity is reduced to ---1/2 of its zero-field value at fields in excess of 120 G, and the half-width of the Lorentzian-type curve is about 25 G. From these facts we can conclude that the coupled state is triplet in origin since large g values are necessary to account for such strong mixing effects at low fields. excited? Is nuclear spin, as well as electron spin, important? And what role is played by small magnetic fields? To answer these questions, we probe the decay behavior of the excited state directly under a variety of conditions. Typically, this decay is biexponential in nature, as shown in Figure 5. Here, we excite in the Q branch of pyrazine-h4, and detect the emission as a function of time by scanning, slowly, the gate of the boxcar integrator with an aperture duration of 2 ns. A fit I00 2.00 ,300 TIME (ns) Of this curve to a function of the form gives lifetimes of ---5 and --200 ns and a preexponential factor ratio, A //A-, of 1. Nascent quantum beats are also observed under these conditions.
In the theory of the intermediate case, the time dependence of the fluorescence intensity is usually represented as a sum of coherent and incoherent terms, viz.
Here, n and m denote quasi-stationary molecular eigenstates with energies E, and E,,, widths y. and y,,, and singlet amplitudes C, and C*,.. If the number of coupled states (N) is large (strong-coupling limit), then the "coherent" contribution to the decay (the Y'..F.,. terms) should decay roughly exponentially on a time scale A-, where A 2,rvZp/t and v is the coupling matrix element; this is the "dephasing" From what has been said so far, it would appear that pyrazine is, indeed, a classic example of the intermediate-case molecule. But, can we find other evidence to support this view? In particular, can we demonstrate that the fast component is, in fact, coherent? The answer is, yes, by measurements of the decay characteristics with simultaneous analysis of the polarization of the emitted light. In these experiments, we tuned the laser to a particular line in the P-or R-branch and used a Biomation 8100 transient recorder to improve the signal-to-noise, thus sacrificing the higher time resolution available from the boxcar integrator. Figure 6 illustrates the behavior observed during the first 400 nsec of the decay following excitation of the R1 line (J'= 2) with the linearly polarized laser pulse. Curve A was obtained with a polarization analyzer oriented to transmit parallel-polarized light (III) and curve B was obtained with the analyzer oriented to transmit perpendicularly-polarized light (Ix). Each curve is a sum of 1000 scans, has been corrected for the small contribution (< 1%) of scattered light, and is, as before, biexponential in character.
The derived values of z/ and -_ are the same in both curves. However, the contribution of the fast component, as measured by the A +/Aratios, is significantly different. This is shown more clearly by curve C, a curve computed from A and B, which represents the time dependence of the degree of polarization, This curve demonstrates that the fluorescence is polarized, although the degree of polarization is small, and that the time profile of the depolarization curve is nonexponential in nature.
We believe the situation in Figure 6 is very reminiscent of a zero-field "level-crossing," previously observed in many atoms and small molecules 5 but not, heretofore, in molecules the size of pyrazine. There, one prepares a coherent superposition of the magnetic sublevels of that group of states which lies within the spectral width of the radiation field. This superposition corresponds to an orientation of molecules in the excited state which results, in the case of linearlypolarized excitation, in an alignment of the excited state magnetic moment along a fixed axis. The subsequent emission is then polarized along this axis. Although additional experiments are necessary to completely specify the molecular eigenstates of pyrazine, J (representing the total angular momentum, including electron spin), and M (the projection of J onto a space-fixed axis) are both good quantum numbers. Thus, just as in the traditional level crossing experiment, two states, In, J', M + 1) and Ira, J', M 1), can be excited coherently from the [O,J",M) state due to the selection rule AM +1. The resulting emissions from these states are left (r-) and right circularly polarized (tr/) waves whose superposition will be linearly polarized. The degrees of polarization expected from lines originating in J' 2 and terminating in J"= 3, 2, and 1 are 14, -64, and 45%, respectively. 6 However, in our experiment we collect all of the emission from J'= 2, in accord with the selection rule AJ 0, + 1, so it is not surprising that the residual polarization observed at 0 is small. The interesting question is; what is the mechanism responsible for the depolarization in time? Molecular collisions can depolarize the emission, but we think the effect of collisions under our experimental conditions is negligible, especially at short times. We believe, instead, that the depolarization is caused by a dephasing of the molecular eigenstates. Recall that the application of an external magnetic field in a level-crossing situation introduces a frequency difference Ato 2gBHz/h between the IJ', M + 1) and [J', M 1) states. This frequency shift produces a phase shift of Ab 2gBHz/h between the tr + and o-components of the emitted light which, in turn, causes the plane of polarization to be rotated by a n angle of 0 Ab/2 gHz/h, so that the emission is depolarized. The most commonly known example of this effect is the magnetic depolarization of atomic resonance fluorescence, the so-called Hanle effect. 7 However, similar effects might be expected even in zero-field if non degenerate levels are excited coherently. This is clearly the case in pyrazine. Here, there exists a finite frequency difference Ato,,,=(E,-E,)/h between [n,J',M) and Im, J',M) states in the absence of a field, and the dephasing of these states, occurring at a frequency of the order of Ato,,, (which, in turn, is directly related to the coherence width of the excitation source), causes a very fast depolarization of the fluorescence. A slower depolarization, associated with the dephasing of coherently prepared M states, might also be expected at longer times, yielding an overall decay which is nonexponential in nature.

Magnetic quenching. Coherent or incoherent?
Having demonstrated that the decay of S pyrazine is at least partly coherent in nature, we next ask whether the magnetic quenching of the fluorescence is associated mainly with the coherent or the incoherent component. Again, this question can be answered simply; Figure  7  peak ot the decay curve, with an aperture duration of 2 ns; whereas curve B was obtained with a delay of 100 ns with respect to the peak, with a 1 Is aperture duration. Clearly, it is the incoherent component which is more strongly quenched; theory would suggest, then, that the number of strongly coupled levels is markedly increased by the field.
J'-dependence ter Horst, Pratt, and Kommandeur s were the first to observe that the decay behavior of $1 pyrazine is strongly dependent on the rotational quantum number of the upper state. Because of certain ambiguities in that work, we have repeated the experiments with some care, and show in Figure 8 some of our own results. We observe, as did ter Horst, et al. 8 a growing in of a short component as a function of J' By fitting well over 150 curves of this type to Eq. (1), we have found, as shown in Figure 9, that the ratio of preexponential factors, A //A-, increases approximately linearly with 2J'+ 1 for J'= 1-7. Similar results have been obtained by ter Horst, in more recent work, 9 and by Saigusa and Lim, 1 albeit under rather different conditions. We also find that a particular J', whether prepared by excitation via R-branch transition from the level J"= J'-1 or by excitation via a P-branch transition from the level J"=J'+ 1, has the same A//A value. Finally, we note that neither /, nor z_, are J'-dependent within experimental error. These three results, taken together, give us some important clues about the origins of these effects. First, theory suggests, in the strong coupling limit, that the slow component should decay with a rate which is given by ('-)-3,siN + /, (4) Since N clearly increases with J', whereas rdoes not, we must have 3't >> ,s/N; i.e., the incoherent decay rate is primarily determined by the triplet character of the prepared state. A triplet decay rate of 3.4x 106 s -1 for pyrazine excited at the S So origin has been measured by Dietz, et al., in agreement with this conclusion. Second, from the fact that -+ is also independent of J', it follows from the relations (-+)---2rcA and A. 2rv2p that v2p is not influenced by rotational excitation, assuming that we excite, in any given experiment, all of the singlet character associated with a particular J'. So how can we explain the results in Figure 9? Very simply, or so it would seem. Recall that p is a measure of the vibronic level density in the triplet manifold, and takes no account of angular momentum selection rules. But for intersystem crossing, the total angular momentum J must be conserved, as well as its projection P on the top axis. 12 If we populate, in the zero-order description, a given singlet level having the quantum number Js( Ns), then the rotational selection rule for ISC is AN NT-Ns 0, 4-1. There are also selection rules on K, derived from the requirement that ZiP 0, but the fact that Pand R-branch excitations terminating in the same J' have the same A +/Avalues strongly suggests that K is not a good quantum number in ISC. Several factors may be responsible for this, including deviations from symmetric top behavior in the singlet state and a variety of non-rigid body couplings in the triplet state. Thus, all "K" states for a given N of the singlet state can couple to all "K" states of a given N-+ 1, N-, or N--1 state of the triplet. As the number of possible "K" states increases as 2J'+ 1, the number of coupled states also increases as 2J'+ 1, as observed. Positive proof that rotational angular momentum selection rules are involved in the ISC process has been provided by other experiments on isotopically labeled pyrazines, 13 which show that the number of coupled states is proportional to (2J' + 1)p/tr, where tr is the number of irreducible representations to which the nuclear spin functions belong (the so-called symmetry number). Symmetry plays an important role in this problem because it restricts the number of states with which the initially prepared state can interact.
191nllneti f|eltl effects on the tlecn Figure 10 shows a representative example of the effect of small magnetic fields on the decay behavior of "individual" rotational levels of $1 pyrazine. Here, we excite a single line in the P or R branch and detect the transient response with a boxcar whose gate, of duration 2 ns, is swept slowly across the decay curve at different fields. We find that, just as with increasing J' (cf. Figure 8), there is an increase in the contribution of the fast component with increasing field but that neither z/, nor z_, are influenced by the field. Plots of A//A vs. H for four selected J' values are shown in Figure 11. Clearly, the number of coupled states increases in a sigmoidal fashion with the field, reaching a plateau at fields on the order of 100 G. Similar effects have been observed by Felker, et al. TM using pulses of 15 ps duration.
The data in Figure 11 provide rather convincing evidence for a quantum-mechanical mixing process. But what is the detailed nature of this process? It is known that triplet pyrazine, examined in a low temperature crystal by ODMR techniques, has fine-structure splittings of the order of 1 GHz. 5 If this were also true of triplet pyrazine near the singlet origin, then we might anticipate that the effect of the field is to mix the three fine-structure components of each triplet rotational level via the electron Zeeman interaction, thereby increas-  Figure 11 which shows that, for each J', the ratio of the A //Avalue in "high" field to that in zero field is approximately three. Felker, et al. TM observed the same behavior and also interpreted their results as being due to finestructure mixing.
One problem remains. This is that the fields required for mixing two states separated by 1 GHz should be much larger than those employed here, even for states with large (i.e., triplet) g values. One way to reduce these energy denominators would be to invoke the hyperfine interaction which, although second order in zero field, is strong enough to couple the nuclear spins to the electron spins at low fields. Nuclear spin would then be decoupled from rotation, and the symmetry restrictions noted above could be relaxed, leading to an increase in the A //Avalues. A simple test of this idea was performed by preparing specifically deuterated pyrazines and examining their decay properties. Fortunately, the deuterium shifts in the excitation spectra are fairly large, as shown in Figure 12. Therefore, it is not necessary to prepare isotopically pure samples but only to excite, separately, the Q branches of the do, dl, d2, d3, and d4 species. Figure  13 shows the results obtained for the d3 molecule at fields of 0 and 120 G. Comparison of the zero field curve with that in Figure 5 shows that deuterium substitution produces the expected increase in the number of coupled states. But the d3 molecule also shows a marked magnetic field effect; A//A is again increased by about three on going from 0 to 120 G. This would not be the case if rotational levels of different symmetry in zero field were being mixed, because the d3 molecule has a symmetry number of one. All isotopically labeled molecules behave in much the same fashion.
We are left with only one alternative. This is that, in fact, the fine-structure components are separated by much less than 1 GHz in the vicinity of the singlet origin, and are, indeed, strongly mixed by fields of the order of 100 G, as originally suggested by Zewail and co-workers. TM An average separation of the order of 100 MHz in zero field would be required to explain the observations. Is this reasonable?
The answer is, gratifyingly, yes. Evidence supporting this view comes from three different sources. First, as already noted, more refined density of state calculations, taking rotations and nuclear spin into account, suggest that (2J'+l)p/rlOO/cmnear the singlet origin. 4'6 Second, as discussed elsewhere in these Proceedings, Kommandeur and co-workers 6 have recently obtained ultra high-1B3u PYRAZINE. EXPERIMENTAL TESTS 111 resolution excitation spectra which reveal, for the first time, that each of the Pand R-branch lines in Figure 3 in fact consists of a number of components. The average spacing of these presumed molecular eigenstates is about 100 MHz. But it remains to show that turning on a small field increases the number of these states by a factor of three; i.e., that it is the fine-structure components which are mixed by the field. Since we do not have access to a narrow-band cw laser, we have taken a different approach. Recall from Herzberg that the J 0 angular momentum state of a Hund's case (b) molecule with $ 0 is not split by the fine-structure interaction. 17 An analogous FIGURE 14 pyrazine-h4. TIMF ns Magnetic field dependence of the decay of the J'=0 level of 1B3, situation should exist for the molecular eigenstates of pyrazine even though N and S may not be well defined. That is, there is only one way that "N" and "S" can be combined to produced J 0, whereas there are three ways for all other J. Therefore, if we excite the P1 line of pyrazine (i.e., J' 0), we expect no magnetic field effect if the role of the field is to mix the equivalent of the fine-structure components of the true molecular eigenstates. This is exactly what is observed, as shown in Figure 14. Not only does the J'= 0 decay not have a fast component in zero field, but also there is no growing in of a fast component at higher fields, unlike all other J'. We therefore conclude that the levels mixed by the field in the latter cases are the three fine-structure components of each J' (J' 0), components whose average separation is much less than that of the "pure" triplet. We thus have an explanation for the remarkable influence of small magnetic fields on the static and dynamic properties of "S" pyrazine.
The fact that the level spacing in the vicinity of the singlet origin is very much less than that predicted by the zero order picture may also have profound implications for other types of radiationless processes.

SUMMARY
By performing time-resolved measurements of the fluorescence intensity of "Sl" pyrazine under collision-free conditions, we have shown that the decay of the initially prepared state is both coherent and incoherent in nature, placing the molecule solidly in the category of the intermediate case of the theory of radiationless transitions. Indeed, most of the predictions of the theory are verified experimentally, provided the underlying assumptions are carefully stated and proper account is taken of the appropriate angular momentum selection rules. Our experiments in the presence of small magnetic fields have shown that the coupled state is triplet in origin, and thus that the nonradiative process we are monitoring is intersystem crossing. For such a process, zJ 0; thus, the number of coupled states is strongly dependent on the rotational state which is initially excited.
At low J', we approach the weak-coupling limit whereas at high J', we approach the strong-coupling limit, especially for deuterated molecules. The triplet character of the prepared state plays the dominant role in determining the decay rate of the slow, or incoherent, 1B3u PYRAZINE. EXPERIMENTAL TESTS 113 component. Because of symmetry selection rules, nuclear spin is conserved in intersystem crossing.
Magnetic field experiments have also shown that the levels mixed by the field are the fine-structure components associated with each J', except for J'= 0. However, because the fields required to mix these levels are much smaller than the frequency separations in the coupled but separate manifolds of the singlet and triplet states, we are led inescapably to the conclusion that the true molecular eigenstates in the vicinity of the $1 origin 0t pyrazine are mixed "ST" states with very small (e.g., 100 MHz) energy differences. Supporting evidence for this conclusion has recently been provided by the experiments of Kommandeur, et al. 16 To paraphrase G. N. Lewis,18 it is no longer necessary to assume, as did Tramer and co-workers, 2 the existence of these mixed states.
Molecular eigenstates are real, and their properties can be measured.
But, in order to obtain the maximum possible information about these states, it is necessary to use light sources with very small coherence widths. Narrow band, single frequency, doubled dye lasers with high UV outputs are one possibility, but so also are coherent microwave and radiofrequency sources for which the Doppler broadening problems in the gas phase will be much less severe. We hope, in the next few months, to be addressing some of these problems in our laboratories. If we can succeed in preparing a single, or a small group of these states, then we can test a number of other features of the theory, such as the assumption that there is only one off-diagonal matrix element, and that there is a uniform density of triplet levels. We can also determine whether a single molecular eigenstate shows any dynamic behavior at all, and, at the other end of the scale, probe the origins of chaos in quantum mechanical systems. Thus, a number of challenges remain for the experimentalist who seeks a "grand unified theory" of the radiationless process.