3374
J . Phys. Chem. 1988, 92, 3374-3379
this state; the Raman wave function is the state prepared by the laser. We have provided a pictorial overview of this state and we are now in a position to explore its unique properties. In our picture, a single trajectory provides all the necessary information. The dynamics of I $ ( t ) ) contains the absorption spectrum, the Raman wave function prepared by the laser at any frequency, and even the eigenstates of the excited-state surface. It also makes it clear that, by choosing the laser frequency, we essentially have the ability to choose which part of the dynamics we will study. The connection between time and detuning means that by detuning the excitation source we limit the time over which the dynamics contribute to the spectrum. The further off resonance we tune the laser, the more we limit the time. Another way to put it is that the off-resonance spectra provide information about the local FC region, whereas on-resonance spectra provide information about the equilibrium position in the case of a bound excited state or the large internuclear separations for a repulsive potential. We find that it is not necessary to make a distinction between Raman spectroscopy and fluorescence. One formula, and moreover the same trajectory, will produce both. We conclude that these are two extremes of one physical process. As the incident laser frequency is tuned from off to on resonance, the spectrum continuously go from Raman to fluorescence (if the
excited-state lifetime is long with respect to a vibrational period). The dissociative case presents an interesting halfway point where, no matter how narrow the bandwidth of the laser, it is impossible to create an eigenstate by simple photon absorption. We find it interesting that in these two extremes the states that the laser prepares exhibit very clear differences. For normal off-resonance Raman, the Raman wave function is purely imaginary, whereas for what would normally be called fluorescence, the Raman wave function is purely real. That is why we chose to designate the repulsive case as the halfway point since here the Raman wave function is complex with equal amounts of real and imaginary components. In our treatment, we have excluded, for the sake of simplicity, many important effects, such as the nonconstancy of the transition moment with intermolecular separation and the influence of more than one excited state on the process. These will be dealt with in future work.
Acknowledgment. This work has been supported by NSF Grant CHE-8507168 and by the donors of the Petroleum Research Fund, administered by the American Chemical Society. We thank Professor Judy Ozment and the Eric Heller group for helpful suggestions and David Tannor for introducing us to the grid method used in these calculations.
Time-Dependent Study of the Absorption and Emission Spectra of 0, Stewart 0. Williams and Dan G. Imre* Department of Chemistry, University of Washington, Seattle, Washington 981 95 (Received: October 19, 1987)
We use a time-dependent theory to investigate the absorption spectrum to the B3Z; state, as well as the emission spectrum corresponding to laser excitation to u’= 4 of the B32; state of the O2molecule. We present detailed discussion of the relationship between the dynamics and the resulting spectra and correlate our results with experimental data.
I. Introduction In recent papers,’-2 we used a time-dependent theory to take an in-depth look at the Raman process. In this paper, we will use this the0ry~9~ to investigate various spectroscopic results for the O2molecule. We will concentrate on the B3Z; excited state of 02,which is the state responsible for the Schumann-Runge (S-R) bands. Because of the extensive work done on the S-R band^,^,^ this band system and indeed the B state are well characterized. The minimum in the B-state potential is at 1.6 A, which represents from the ground state a fairly large displacement of -0.4 of 02.Approximately 21 bound states have been identified on the B excited in fact, it has a shallow dissociation energy of 8121 cm-’ (0.037 au). Because of the large displacement of the minimum in the B-state potential from that of the ground-state potential, and because of the shallowness of the B-state potential (1) Williams, S. 0.;Imre, D. G. J . Phys. Chem., preceding paper in this issue. (2) Williams, S. 0.; Imre, D. G., manuscript in preparation. (3) Tannor, D. J.; Heller, E. J. J . Chem. Phys. 1982, 77, 202. (4) Heller, E. J.; Sunberg, R. L.; Tannor, D. J. Chem. Phys. Lett. 1982, 93, 586. (5) Bethke, G. W. J. Chem. Phys. 1959, 31, 669. (6) Ackerman, M.; Biaume, F.J. Mol. Spectrosc. 1970, 35, 73. (7) Goldstein, R.; Mastrup, F. N. J. Opt. SOC.Am. 1966, 56, 765. (8) Bhartendu; Currie, B. W. Can. J. Phys. 1963, 41, 1929. (9) Julienne, P. S.; Krauss, M. J . Mol. Spectrosc. 1975, 56, 270. (10) Herzberg, G. Spectra ofDiatomic Molecules, 2nd ed.;Van Nostrand: New York, 1950. ( 1 1 ) Krupenie, P. H. J. Phys. Chem. ReJ Data 1972, 1 , 423.
0022-3654/88/2092-3374$01.50/0
well, most of the Franck-Condon (FC) envelope is above the dissociation limit for the B state as reflected by FC factors and absorption s p e c t r ~ m . ~ ~ * * ’ ~ Both ab initio9 and detailed high-resolution experimental studies6 have revealed that there are variations in the line widths for different vibrational levels of the B state. This effect has been shown to be due to predissociation. The predissociation is dominated by the (at least for v’ = 4),9 which crosses the B3Z,state at 1.875 A, which is close to the turning point for u’ = 4. As a result, the lifetime for v’ = 4 is 1 ps. Because of this, we will ihtroduce a phenomenological lifetime r in our calculations. In general, one would expect a fluorescence spectrum from a resonant excitation to a discrete state. However, when O2is excited by an excimer laser at 193 nm, which is resonant with a few rotational levels of u’ = 4 of the B state, the dispersed emission spectrum obtained by us and by Shibuya and Stuhl12 shows that the spectrum cannot be unambiguously characterized as either fluorescence or Raman and in fact appears to be a hybrid. It was this result that first prompted us to undertake this study. The results we presented in ref 1 and 2 showed that indeed hybrid spectra could be expected in a variety of situations. The O2 spectrum provided an example where the two “parts” of the spectrum are of the same order of magnitude and neither can be ignored. Thus this spectrum could serve as a test of our approach. As we mentioned above, the absorption spectrum shows a few discrete vibrational levels but most of the FC envelope is in the continuum. The absorption spectrum in itself presents a challenge
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(12) Shibuya, K.; Stuhl, F. J . Chem. Phys. 1982, 76, 1184. Q 1988 American Chemical Society
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since in a traditional FC analysis one would need to calculate eigenfunctions up to and above the dissociation limit. In the time-dependent formalization, the dynamics on the excited state is rather complex. We expect most of the wave packet to proceed directly to dissociation and only a small fraction to remain trapped in the well. This type of dynamics cannot easily be simulated semiclassically. Thus we carry out a fully quantum mechanical propagation of the dynamics on the excited state. Our analysis presents an intuitive picture of the experiment. It provides a graphic illustration of the state the laser actually prepares and how it evolves in time. In section 11, we present a brief outline of the theory. For a more complete treatment, see ref 1-4 and references cited therein. In the following sections, we apply the theory to 02. 11. Numerical Technique and Theory We have used a time-dependent treatment of absorption and emission spectroscopy in recent articles.',2 A variety of systems were investigated in those studies. In summary, it was shown that the absorption spectrum is given E(w)
0:
S__eiw'(4(o)l4(t)) dt
(1)
and the emission spectrum is given by
Z(wJ
S m e ' ~ ~ ( R ( w , q ) l R ( w , 4dt, t ) ) -m
where
140) = Wizlxi) is the initial wave packet, p is the transition dipole moment, and Ixi) is the ground-state wave function.
The first is controlled by nature. Shy of changing I~#J~), which is usually the ground-state vibrational wave function, the dynamics of 140) on the excited-state potential is determined by the excited-state Hamiltonian. Where, then, does the sensitivity of the emission spectrum to the incident laser frequency originate? The answer is in the equation for the Raman wave function. Note the Raman wave function itself is a half Fourier transform of I4(t)). The frequency 0' that goes into this equation is the laser frequency. Thus the laser projects out of I4(t))components with frequency w'. When the laser is tuned in resonance with a vibrational level of the excited state and that level has a long lifetime, the laser will project the eigenstate resonant with the laser frequency and the spectrum will appear as a fluorescence spectrum. However, if the lifetime of the state is short or when the laser is not exactly in resonance, the Raman wave function will not be identical with the eigenstate and the spectrum may appear as pure Raman or a hybrid. These effects are most noticeable when we are trying to project out a state with small FC factors, as in the case of u' = 4 in 02. To summarize, the first photon prepares a Raman wave function whose shape is determined by the dynamics of I d ( t ) ) , the lifetime of the excited state, and the laser frequency. The emission spectrum is then a Fourier transform of the autocorrelation function of the Raman wave function and the time-evolving Raman wave function on the ground-state potential. We implement eq 1 and 2 to obtain the absorption and emission spectra for O2 using the Fourier transform grid method as developed by Kosloff et al.I33l4 For both the ground state and the B state we used RKR potential curves from ref l l. We assumed that the transition moment is constant with respect to nuclear geometry. To calculate the initial ground state wave function of 02, pi),we placed a Gaussian I$o)(with we = 1580.4cm-') on the ground-state surface and extracted IXi) usingiJ6J7
is the evolving wave packet on the excited state propagated by the excited-state Hamiltonian Hex. W =
WI
- W,
+ Ei/h
where wI is the excitation energy, Ei is the energy of the initial wave packet, and w, is the frequency of the scattered light.
is the Raman wave function.
IR(w,q,t)) = e i H ~ r / h ~ ~ l l R ( W , q ) ) represents the Raman wave function propagated on the ground electronic state. r is the lifetime of the intermediate state. According to this formalism, at time t = 0 the laser transfers the initial ground-state wave function I+o) to the excited-state is not an eigenstate of the excited-state Hamiltonian surface. Ic$~) Hexand becomes a moving wave packet Id(t)) on the excited state. The dynamics of 14(t))is determined by the excited-state Hamiltonian. All the dynamic and spectroscopic information is contained in I $ ( t ) ) as shown by examination of eq 1 (absorption) and 2 (emission). The absorption spectrum is the Fourier transform of the auto correlation (dol+(t)). A single wave packet and a single trajectory (time-evolving wave packet) contain all the information necessary to obtain the complete absorption spectrum. In O2 this means that the dynamics of I @ ( t ) ) must be such that it produces both a continuum as well as a discrete set of vibrational states. The equation for the emission spectrum is remarkably similar to that for the absorption spectrum, where IR(w,q)),the Raman wave function, replaces the initial state Ido).It is the dynamics of IR(w,q)) on the ground-state p ~ t e n t i a l ' . ~that . ~ determines the complete emission spectrum. The Raman wave function is created by the first photon: IR(w,q)) = Jre'"'r-f/r14(f)) dt. Here I' represents the effective lifetime due to curve crossing. Two factors determine the Raman wave function: the dynamics of I4(t))and the laser frequency w'.
where uois the zero-point energy for the ground-state potential. We checked for convergence of IXi) by placing IXi) on the ground-state potential and observing ( X i p i ( t ) ) .(Xipi(t))should equal 1 if (Xil is the true ground-state wave function. 111. Results for O2 a. Absorption. Experimental results for absorption into the B state of O2 show that most of the spectrum is above the dissociation limit of 02.However, there is some vibrational structure in the low-energy region below the dissociation limit of the B state, which is responsible for the S R bands. The FC factors for absorption into these bands are very mall."^'^ For example, for absorption into u ' = 4,the FC value is 3 X We begin our study by observing the dynamics of I+(t)) on the excited B state as shown in Figure 1. Two scales are shown in Figure 1 to illustrate the complex dynamics on the excited-state potential surface. Consistent with the known absorption spectrum, most of Id(t)) proceeds directly to dissociation. Note also the rapid spreading in I4(t)) which is a result of the large change in vibrational frequency between the ground state and excited state, and the highly anharmonic B-state potential. Although most of the wave packet has energy above the dissociation limit, there is a small fraction (just barely apparent in this sequence) that does not have sufficient energy to dissociate. It is this small fraction shown in the expanded scale of Figure 1B that remains in the bound region and will eventually manifest itself in the structured portion of the absorption spectrum. In Figure 2 we show the correlation function ( 4 0 1 ~ ( t ) ) . Consistent with the trajectory (Figure l), as the initial wave packet (13) Kosloff, D.; Kosloff, R. J . Comput. Phys. 1983, 52, 35. (14) Kosloff, R.; Kosloff, D. J . Chem. Phys. 1983, 79, 1823. (15) Lewis, B. R.; Berzine, L.; Carver, J. H. J . Quant. Spectrosc. Radiar. Transfer 1987, 37, 219 and 255. (16) Frederick, J. H.; Heller, E. J. J . Chem. Phys., in press. (17) Davis, M. J.; Heller, E. J. J. Chem. Phys. 1981, 75, 3916.
3376 The Journal of Physical Chemistry, Vol. 92, No. 12, 1988
*]I,
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accelerates from the FC region, ($ol+(t)) decays rapidly. At longer times, small recurrences can be seen. These recurrences are due to the low-energy part of 1+(t)) as explained above. The absorption spectrum which is given by the Fourier transform of (4014(t)) (eq 1) is shown in Figure 3. At first glance, the spectrum appears as one continuous band. However, on close examination of the low-energy part, sharp vibrational bands are observed. On one hand, in order to produce structure in the absorption spectrum, I4(t)),or part of Iq4(t)),must return to the FC region. On the other hand, to produce a continuous absorption spectrum, there cannot be recurrences in (&l4(t)). It is the dynamics of a single trajectory which contains the information
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for the complete spectrum. I4(t)) then must bifurcate such that the high-energy components proceed directly to dissociation while its low-energy components remain trapped in the bound region. This was demonstrated in Figure 1. This study illustrates how a single trajectory can produce two very different features in the absorption spectrum. It should also be noted that our numerical method is capable of generating absorption features corresponding to very weak FC factors. In general, absorption spectra showing this behavior are indicative of the wave packet breaking up; that is, while some of the wave packet is trapped, the other continues into a large density of states, in this case the dissociation continuum. b. The Emission Spectrum. For these studies, we will concentrate on the emission produced from excitation to u’ = 4. In Figure 4a, we show the experimental emission spectrum repro-
Absorption and Emission Spectra of 0,
The Journal of Physical Chemistry, Vol. 92, No. 12, 1988 3377 1 A
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FREQUENCY tau1 Figure 4. (a) Experimental emission spectrum for excitation to v’ = 4 on the B surface. For this experiment, the 193-nm ArF laser line was used as the excitation source. (b) Calculated FC factors for v’= 4, that X’Z,(v?. The results presented in this figure were is, B3Z[(v’=4) simulated from ref 12.
-
duced from ref 12. The experimental spectrum was due to laser excitation using the ArF (193 nm) laser, which is resonant to u’ = 4 on the B state of 02.In Figure 4b, a simple FC calculation was done for overlap between u’ = 4 on the B-state and the ground-state wave functions. Note the FC calculation and the experimental spectrum are very similar for high vibrational levels (u” > 3). The calculation completely fails to reproduce the observed intensity in v” = 1 and 2. The fact that Figure 4a shows appreciable intensity into u ” = 1,2, and 3 and that the calculation based on eigenstates fails to reproduce the observed spectrum implies that short time (and indeed short-time dynamics) must be importantl,2 or, in other words, the laser does not prepare u’ = 4. This short-time dynamics can be due either to an inherent short lifetime on the excited surface or to excitation that is not exactly on resonance.’V2 In ref 1 and 2, we have shown that both of these effects are strongest when the excitation source is tuned into a spectral region of low FC, which in this case is very true, since (vf=41v’’=0) is very small. Since there is such a small component of u’= 4 in the initial wave function, then it will take a very long time to filter out u’ = 4 from I d ( t ) ) . For this case with a lifetime on the order of 1 ps, it is not clear whether the short lifetime can account for such large intensity in u” = 1 and 2 as observed in the spectrum. To test the lifetime effect on the emission spectrum, we present Raman wave functions and their associated spectra in Figure 5 . Four Raman wave functions are shown. They were all obtained by using the same laser frequency, tuned into resonance with u’ = 4, but with different lifetimes (I’). Lifetimes were varied from 150 to 1000 fs. All the Raman wave functions show a component which strongly resembles u’= 4, four nodes are observed, and this part of the wave function is centered about 1.6 8, the B-state equilibrium geometry. However, for all lifetimes there is another part to the Raman wave function which is clearly not u’= 4. That part resides in the FC region. Figure 5 illustrates that, as the lifetime increases, the component of u’ = 4 in the Raman wave function increases at the same time; the intensity pattern in the emission spectrum is changing. The short lifetime spectrum is dominated by emission into u ” = 1 and 2 and a weak fluorescence
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Figure 5. Raman wave functions and associated emission spectra for excitation to v’ = 4 as a function of lifetime. Results shown are for lifetimes of (a) 150, (b) 200, (c) 300, and (d) 1000 fs. For these four plots, the laser was on resonance with u t = 4 of the B state.
part, whereas in the long-lifetime spectrum [Figure 5d], ut’= 1 is barely observed. The spectrum that best represents the experimental one corresponds to lifetime of about 200 fs, which is too short by a factor of 5 as compared to the known lifetime.g Nevertheless, it is very informative to note that even for a 1-ps lifetime, the laser does not prepare purely u’ = 4; rather there is a large component of the initial wave packet that lingers on. Whether this would play a role in the predissociation dynamics of u’ = 4 is not clear. The picture that emerges from Figure 5 is very intuitive. For a short time, before the laser filters out the components of Id(t)) that are not resonant with it, the complete wave packet contributes to IR(w,q)). For a very short time, JR(w,q))takes the form of the part that is localized in the FC region. At later times, the off-resonance components of Id(t)) have been filtered out and the only contributions come from u t = 4 since it is on resonance with the laser. In this case, u’= 4 is only an extremely small component of I4(t))and thus it will take a long time for its contribution to IR(w,q)) to become appreciable as compared to the short time which is determined by the complete wave packet. Thus as time goes on we expect the short time to become less important and the u‘= 4 part to dominate. Indeed, that is what we observe, when comparing parts b and d of Figure 5, a change in lifetime from 200 to 1000 fsec, we find a change of a factor of 5 between the u t = 4 component and the short-time part of IR(w,q)). Our lifetime studies force us to conclude that the lifetime in itself cannot provide the explanation for the experimental spectrum. The best fit does not correspond to the known lifetime. As we have mentioned earlier, there are two factors that can contribute to the shape of the Raman wave function and hence the spectrum: the lifetime and the frequency. In this experiment, an excimer laser operated at 193 mm is used. The line width of the laser is on the order of -100 cm-I. The laser beam was generated in a cavity filled with air, and the laser travels through 0,-filled air for a long distance, in our case 14 ft. By the time the laser beam reaches the cell, the frequency components which are resonant with 0, lines have been completely absorbed by atmospheric 02.In essence, the experiment was performed with
3378
The Journal of Physical Chemistry, Vol. 92, No. 12, 1988
Williams and Imre
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Figure 6. Raman wave functions and associated spectrum as a function of determining frequency from u’ = 4. Results shown are for determining by (a) 20, (b) 22, (c) 24, and (d) 50 au. In each case, the lifetime on the excited B surface was 1 ps.
light that was not resonant with any O2 absorption lines. Since there are many rotational transitions to be considered and a complex line shape for the excitation source, we represent the laser as a narrow band and the transition as a single line to test the effect of detuning slightly from the absorption features. The detuning frequency that best fits the experimental spectrum is an effectiue detuning frequency. Figure 6 represents Raman wave functions for different detuning from u’ = 4 and their corresponding spectra. To best simulate the experimental conditions, the laser was detuned to lower energies; that is, the laser is red shifted with respect to resonant excitation to u’ = 4. The lifetime for all these studies was taken to be the known lifetime of 1 ps. Note that the effect of detuning is to increase the relative contribution of the short-time contribution. We conclude that the best fit to the experimental spectrum is for an effective detuning frequency of -20 cm-I, which is reasonable considering the experimental setup. It is not clear how to estimate the amount of detuning in the experiment since, for any experiment done in the atmosphere, the O2 present will absorb the laser light at the required frequency before it gets to the absorption cell (unless the path of the laser is continuously purged free of 0 2 )Therefore, . it is obvious that the laser light that makes it to the absorption cell will have “holes” due to absorption of O2 in the atmosphere, at frequencies corresponding to resonant excitation to various rovibrational levels; hence, the excitation would not be on resonance with any rovibrational level of 02. In another experiment,’* an injection locked excimer was used and the laser and the laser beam path were purged free of 02. The laser was tuned to one of the rotational transitions. This spectrum shows no intensity into u” = 1 or 2 as we would predict (see Figure 5d). However, in this case, a set of filters was used to eliminate scattered laser light and it is not clear whether the low vibrational levels are missing due to the careful experimental (18) Massey, G. A.; Lemon, C . J. IEEE J . Quuntum Electron. 1984, 20, 454.
T
.
0
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Figure 7. (a) Amplitude of the Raman wave function and associated spectrum for excitation to u‘ = 4 on the B state with a lifetime of -200 fs. (b) Real part and (c) imaginary part of the wave function in (a) with their normalized emission spectrum.
arrangement or the presence of filters. Kelley and Hudson19 reported experiments on O2 using 188- and 184-nm light. With the 184-nm light, they were able to make a resonant transition from u” = 0 to u’ = 6. The subsequent emission spectrum that they measured followed the FC factors for emission from u’ = 6 , and unlike the emission spectrum for excitation with an excimer laser to u’ = 4, there was very little intensity into u” = 1 and 2. This observation is consistent with our study (see Figure 5d) since (a) the excitation is right on resonance, (b) u ’ = 6 has a higher and (c) u t = 6 has a longer lifetime than FC factor (1.7 X u ’ = 4.9 With excitation at 188 nm, the resonance was from u” = 1 to u ’ = 12. However, at the same time there is an off-resonance excitation from u” = 0 (Le., 188 nm is close to the 0-8 transition). As a result, there are two contributions to the emission spectrum: a fluorescence portion due to the emission from u’ = 12 (weakened due to population of U” = 1) and a Raman portion due to emission starting in u” = 0, with fundamental most intense. Therefore, the total spectrum does not follow the FC factors for emission from u’ = 12. c. Raman us Fluorescence. The spectra in Figures 4-6 illustrate very nicely another point raised before about which part (real or imaginary) of the Raman wave function contributes to the Raman spectrum and which part is responsible for the fluorescence spectrum.’ In Figure 7 we present I(rlR)I2,the real part of ( r ( R ) ,and the imaginary part of ( r l R ) . According to Figure 7, the imaginary part of ( r ( R )is localized in the FC, where as the real part represents the eigenstate on the excited state (u’ = 4). The total spectrum will be given by the sum of the spectrum produced by the real and that produced by the imaginary part of ( r l R ) . These are also presented in Figure 7. Note that the part of the spectrum that can be reproduced by a simple FC calculation is produced by the real part, where as the Raman lines (intensity into u” = 1, 2, and 3) is represented by the imaginary part. In fact, a more in-depth investigation’ shows that, for a bound potential, the Raman lines are due to the imaginary part of ( r l R ) ,while the real part of )rlR) contributes to thefluorescence lines. How much real or imaginary components are present in ( r l R ) depends on the lifetime of the intermediate state (Le., excited B state) and (19) Kelley, P. B.; Hudson, B. S. Chem. Phys. Lett. 1985, 114, 451
J. Phys. Chem. 1988, 92, 3379-3386
3379
on the amount of detuning-the shorter the lifetime and the larger the detuning, then the bigger the imaginary component.
function and the fluorescence lines to the real part of the Raman wave function.
IV. Conclusion We have provided an in-depth look at some aspects of the dynamics on the B3Z; state of O2and showed how this dynamics is responsible for features in the absorption and emission spectra. In particular for the emission spectrum, we have examined the origin of the various contributions and demonstrated that the Raman lines are due to the imaginary part of the Raman wave
Acknowledgment. This work has been supported by NSF Grant CHE-8507168 and by the donors of the Petroleum Research Fund, administered by the American Chemical Society. We thank Professor Eric Heller and his group for helpful suggestions and Professor David Tannor for introducing us to the grid method used in these calculations. Registry No. 01, 7782-44-7.
A Strongly Hydrogen-Bonded Molecular Solid, Isonicotinic Acid: Raman Spectra of the -C’’O,H and -C”O,D Species and Infrared and Raman Spectra of the -C“O,H Acid E. Spinner Protein Chemistry Group, John Curtin School of Medical Research, The Australian National University, Canberra, A.C.T. 2601, Australia (Received: October 9, 1987; In Final Form: January 7, 1988)
While the infrared spectrum of solid isonicotinic OD acid differs from that of the OH acid by far more than one might expect, that of the 180Hacid is very similar to that of the 160H acid in regard to the broad 0-H stretching absorption plateau from ca. 1340 to 660 cm-I. The labeling results permit extensive vibrational assignment and show which of the inverted bands (“transmission windows”) are due to intramolecular vibrational coupling and which to coupling across the Ha-N bond. The Raman spectra mostly do not differ from one another by more than ordinarily expected for D or I8O isotopic substitution. The first instances of inverted Raman bands have been observed. Some high-pressure infrared spectra reported by Hamann can now be explained more fully. A further absorption continuum, weak and broad, but distinct from the hydroxyl stretching continuum, appears to be centered around 450 cm-l and is suggested to be due to H-N or D-N hydrogen-bond stretching. Overall, the results indicate that the oD-.N hydrogen bond is not significantly longer than the oH-.N bond, and the unexpected large infrared spectral differences appear to be due essentially to the vibration amplitude being much smaller for the atom. The presence of spectral continua is discussed briefly with reference to ergodicity theory. than for the
Introduction Isonicotinic acid is the first molecular solid to have an infrared spectrum that is highly anomalous (Hadiis’ “type iin4) in (a) having a very broad very intense 0-H stretching band at extraordinarily low frequencies and (b) showing inverted bands (“transmission windows”)s. From more extensive work6 which showed that on 0-deuteriation the hydroxyl stretching band is not merely much reduced in intensity but is actually shifted to higher frequencies (rather than lowered by the usual factor of 0.73), it was predicted that the crystal consists of OH-N chains with an extremely short hydrogen bond. A subsequent X-ray diffraction study7 showed this to be the case; in predicting a length r(O,-N) “near 2.4 A” Spinner6had omitted to take into account that the van der Waals radius of nitrogen (1.5 A) is8 about 0.1 A greater than that of oxygen (1.40 8,). The r(OH-N) actually found,7 2.58 A, is thus roughly equivalent to an r(OH--O)of 2.48 A, which is within the hydrogen-bond-length range known4s9J0 Yoshida, S.; Asai, M. Chem. Pharm. Bull. (Tokyo) 1959, 7 , 162. Hadii, D. Vestn. Slouensk. Kemijsk. Drusf. 1958, 5, 21. Evans, J. C. Spectrochim. Acta 1960, 16, 994; Ibid. 1962, 18, 507. Hadii, D. Pure Appl. Chem. 1965, 11, 435; Chimia 1972, 26, 7. Albert, N.; Badger, R. M. J. Chem. Phys. 1958, 29, 1193. Spinner, E. Aust. J. Chem. 1974, 27, 1149. Takusagawa, F.; Shimada, A. Acta Crystallogr. B 1976, 32, 1925. Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Cornel1 University Press: Ithaca, NY, 1960; p 260. (9) Currie, M.; Speakman, J. C. J . Chem. SOC.A 1970, 1923. (IO) Hadii, D.; Orel, B.; Novak, A. Spectrochim. Acta, Part A 1973, 29, 1745. Novak, A. Struct. Bonding (Berlin) 1974, 18, 177. (1) (2) (3) (4) (5) (6) (7) (8)
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to give rise to Yype ii” spectra. The conclusion6that the very short OH...N bond does not approach the quasi-symmetrical O’/”-H-“I2+ type, too, was reached independently from the X-ray diffraction r e ~ u l t s . ~(Evans3 had predicted the presence of “symmetrical hydrogen bonds”.) The main questions posed by the above results, which the present work was intended to answer, were as follows: (1) Is the anomalous and remarkably large difference between the infrared spectra of isonicotinic O H and OD acids evident also in the Raman spectra? (2) Does this difference imply that the OD*..N bond is appreciably longer than the OH**” bond? (3) What information is obtainable from the inverted bands? It is pointed out here that (1) Raman spectral studies of compounds showing highly anomalous stretching frequency ratios v(0-D st)/v(O-H st) are not numerous; (2) cases where r(OD--O)exceeds r ( O r 0 ) by about 0.06 8, in around 2.50 8, are known;” (3) some spectacular conversions of normal absorption bands into deep inverted bands following application of external pressure (up to 40 kbar) were reported by Hamann12 for both OH and O D isonicotinic acid. In studies of strong hydrogen bonding, labeling with oxygen-18 holds considerable promise in vibrational assignment, especially of inverted bands. It does not seem to have been used so far. There are conceivable complications, and a study of an %-H-.N bonded system prior to studies of 180H-.0 systems seems desirable; isonicotinic acid seems an ideal candidate. (11) Hamilton, W. C.; Ibers, J. A. Acta Crysrallogr. 1963, 16, 1209. Delaplane, R. G.; Ibers, J. A.; Ferraro, J. R.; Rush, J. J. J . Chem. Phys. 1969, 50, 1920, and references cited therein. (12) Hamann, S. D. Ausr. J . Chem. 1977, 30, 71
0 1988 American Chemical Society
