Dynamics of triplet states in beam-isolated benzaldehyde - The

Sep 1, 1991 - Wilton L. Virgo, Kyle L. Bittinger, Adam H. Steeves, and Robert W. Field. The Journal of Physical Chemistry A 2007 111 (49), 12534-12537...
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7154

J. Phys. Chem. 1991, 95, 7154-7164

ARTICLES Dynamics of Triplet States In Beam-Isolated Benzaldehyde Ofer Sneh and Ori Cheshnovsky* School of Chemistry, The Sackler Faculty of Exact Sciences, Tel- Auiv University, 69978 Tel Aviv, Israel (Received: June 26, 1990; In Final Form: April 18, 1991)

The radiative and nonradiative dynamics of benzaldehyde in the 0-3750-cm-' energy interval above the TI origin were explored. The relative radiative rates were extracted by combining two different simultaneous measurements: laser-induced phosphorescence (LIP) and surface ejection of electrons by laser excited metastables (SEELEM). The ratio of the LIP signal and the SEELEM signal is proportional to the pure radiative rate. The details of the dynamics were rationalized as a development in the coupling of three electronic states. The Tl(3nns*)-T2(3mr*)vibronic coupling increases regularly in the region between 400 and =2000 cm-' of excess vibrational energy above the TI origin. Starting from the excess energy of the SIorigin (1730 cm-I), the SI excitations are coupled to the sparse TI-T2 background. We have shown that the line profile and dynamics of the SI manifold in the 173&25OO-~m-~ region can be described in terms of the interaction of an optically active state with a background of almost dark states, in accordance with the theory of radiationless transitions. From our spectroscopicdata we have estimated the density of coupled states to be about 200 states/cm-' and the coupling strength to be 0.05 cm-I. The SI content in the region due to the congestion of the triplet states. Finally, the T2 coupled states is gradually diluted in the 173&2500-~m-~ character is eroded probably due to the larger density of TI states. The TI-T2 and the coupling mechanisms were studied.

1. Introduction

The radiative and radiationless processes in benzaldehyde, the simplest aromatic carbonyl molecule, were extensively examined in condensed and gaseous phases. Indirect evidence for the existence of two nearly degenerate 3nr* and 37rr*triplet states were obtained from cold matrices experiments (resolved phosphorescence),'-$ phosphorescence lifetime,$ and T So a b ~ r p t i o n ' . ~ ) , and from resolved phosphorescence measurements of room temperature vaporse9 The interplay between these solvent-shifted triplet states determines the dynamics of the benzaldehyde-triplet-state in solutions. The oscillator strength of the Tl(3nr*)state can be estimated from lifetime measurement in cold nonpolar solvents to be&,,* 106.5 In polar solvents the phosphorescence lifetime has extended up to 265 ms (f< ]OB)? together with a considerable change in the resolved phosphorescence spectra's6 and the T So excitation spectra.6 These observations were attributed to "level-crossing" of the 'r17r* and the ' r r * states in the polar solvents.5*6~10 Polar solvents usually raise the energy of n r * states but stabilize the rr* states.I0 The 3nr*-31rr* energy gap in isolated benzaldehyde was estimated to be 0-1500 cm-1.'93J*6A polar solvent can easily invert the order of states, so that the state is the origin of phosphorescence. The 265 ms is only a lower limit for the T 2 ( 3 r ~ *pure ) radiative lifetime, due to possible competing decay processes. The obtained ratio of 102-103 in the relative oscillator strength of hr*and 3r57*states is typical of hetero-

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(1) Olmted 111, J.; El-Sayed, M. A. J . Mol. Spcrrosc. 1971, 40, 71. (2) Robinson, G.W. J . Chem. Phys. 1954, 22, 1384. (3) Goodman, L.; Lamotte, M.; Koyanagi, M. Chem. Phys. 1980.47.329. (4) Koyanagi, M.; Futami, H.; Nakashima, K. J . Chem. fhys. 1988,89, 2662. (5) Goodman, L.; Koyanagi, M.Mol. fhorochem. 1972,4, 369. (6) Koyanagi, M.; Goodman, L. J . Chem. fhys. 1972,57, 1809. (7) Kearns, D. R.; Case, W. A. J . Am. Chem. Soc. 1966,88, 5087. (8) Koyanagi, M.; Nakashima, K.; Goodman, L. Chem. Phys. 1985,92, 435. (9) Koyanagi, M.; Goodman, L. Chem. Phys. 1979,39, 237. (IO) Dukn, A. J.; Gocdmann, L.; Koyanagi, M. In ExclredSmes; Lim, E. C., Ed.;Academic Press: New York, 1974; Vol. 1 , p 295.

0022-3654/91/2095-7154$02.50/0

atom-saturated hydrocarbons.lJI Recently, studies of the triplet and singlet excitation spectroscopy of isolated benzaldehyde in supersonic jets have been reported by Ohmory et ai.,'* Villa et ai.,I3 and Villa.'' They have found a 1730-cm-' triplet-singlet energy gap in the isolated molecule in accordance with previous measurements in condensed phase'" and in the gaseous phase? The observed triplet features were attributed to the 3nr* electronic state (with the larger oscillator strength). No direct observation of the pure 3 r r * spectral features has been reported, probably due to their much lower oscillator strength. No clear evidence for the existence of the two coupled states have been found in the sensitized phosphorescence (SP) spectra of Ohmory et al.'* or in the laser induced phosphorescence (LIP) data of Villa et A slight congestion of spectral lines in exvibrational energy of 1000-1350 cm-' above the T,origin has been observed. It was attributed to the onset of the T2(3rr*)bands, borrowing intensity from the nearby T1(3n~*) states.'*I4 Spectral background that appeared in the multiphoton ionization (MPI) spectra of Villa et al." and Villa'' was attributed to curve crossing of the T l ( h * ) and the T2('rr*) potential surfaces" in relation to some cold matrices finding^.^ The focus of the present work is on the decay dynamics of the triplet manifold and singlet manifold of the isolated benzaldehyde. Central in these studies is an experimental technique for the detection of triplet-states in supersonic beams. It is based on surface electron ejection by laser-excited metastables (SEELEM) from low work-function surfaces. By combining several experimental methods (SEELEM, laser-induced phosphorescence (LIP), and MPI) we have measured the total decay rates and the relative radiative rates of vibronic states in the range of 0-3700 cm-l above the T I origin. We will rationalize the details of the energy dependence of the various decay rates in terms of the interaction (11) Lower, S.K.; El-Sayed, M. A. Chem. Rev. 1966, 66, 199. (12) Ohmori, N.; Suzuki, T.; Ito, M. J . fhys. Chem. 1988, 92, 1087. (13) Villa, E.; Amirav, A,; Chen, W.; Lim, E. C. Chrm. fhys. tetr. 1988, 147, 43. (14) Villa, E. Ph.D. Dissertation, Wayne State University, Detroit, MI, p 63. Q 1991 American Chemical Society

Triplet States in Beam-Isolated Benzaldehyde

The Journal of Physical Chemistry, Vol. 95, No. 19, 1991 7155

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Figure 1. Schematic side view of the experimental apparatus: ( I ) heatable pulsed nozzle; (2) heatable sample reservoir; (3) skimmer; (4) excitation zone; (5) beam baffle; (6) LIP viewing zone; (7) LIP detector, (8) SEELEM detector; (9) translational stage; (IO) differentially pumped Willson seal; (1 1) MPI detector; (12) first chamber pumping port; (13) second chamber pumping port; (14) third chamber pumping port.

of three electronic states: the T I ( 3 n ~ * )the , T 2 ( 3 ~ ~ and * ) , the S l ( h r * ) states. Finally, we will show that the dynamics of the vibronic levels of the SIstate in benzaldehyde provides an opportunity to simultaneously observe the diluted vibronic states of the SItogether with the almost "dark" states of the background triplet. 2. Experimental Section A. Experimental Apparatus. Several descriptions of our experimental system have been given p r e v i o ~ s l y . ~ ~ Here, - * ~ we emphasize mainly specific details of the current configuration. Figure 1 sketches a schematic side view of the experimental apparatus. It is built of three vacuum chambers with differential pumping. The basic pressures during an experiment are lv, and lo-' Torr in the first, second, and third vacuum chambers, respectively. Benzaldehyde is cooled by supersonic expansion from a heatable pulsed nozzle20 (0.5-0.7-mm diameter, 400-ps pulse width) in the first chamber. Ar (0.3-2.5 bar), He (0.4-2 bar), or H2 (2 bar) is passed through a liquid sample of benzaldehyde contained in a heatable sample reservoir, kept at 35 O C . The nozzle temperature is maintained at 100 O C . The beam generated by the pulsed nozzle is skimmed 40-100 mm downstream into the differentially pumped second chamber. In this chamber the molecules are excited by a pulsed dye laser (Lambda Physik EMG-50 + FL2002) with IO-ns pulse duration. The MPI experiments are performed in this chamber. Ions are collected and detected on a multichannel plates assembly that is perpendicular to the supersonic and the laser beams. After travelling in the second chamber, the beam, which contains the excited molecules, is baffled to the main (third) chamber. This chamber includes the movable assemblies of the SEELEM detector and the LIP photomultiplier. The SEELEM detector is coaxial with the beam axis, while the LIP detector is perpendicular to it. B. Detecton and Detecting Scbemes. B.1. SEELEM. The SEELEM detector assembly has been described in detail elsewhere.Ig Its central element is a low-work-function surface, which emits electrons with high efficiency when hit by the excited molecules. This surface, which serves as the detector cathode, is inclined in three directions: toward the molecular beam, the alkali oven, and an electron multiplier. The low-work-function surface is maintained by a stable continuous deposition of alkali-metal vapors on the metallic substrate (0.01-10 monolayers/s). (15) Sneh, 0.;Cheshnovsky, 0. Chem. Phys. Len. 1986, 130, 53. (16) Sneh, 0.;Cheshnovsky, 0. Chcm. Phys. Lerr. 1988. 146, 216. Amirav, A.; Cheshnovsky, 0. J . Chem. Phys. 1989, 91, (17) Sneh, 0.; 3532. (18) Sneh, 0.;DOnn-Kittenplon, D.; Cheshnovsky, 0. J . Chem. Phys. 1989, 91, 7331. (19) Sneh, 0.;Cheshnovsky, 0. J . Isr. Chem. Soe. 1990, 30, 13. (20) Bahat, D.; Cheshnovsky, 0.;Even, U.; Lavie, N.; Magen, Y . J . Phys. Chem. 1987, 91, 2460.

4000

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Figure 2. Simultaneous LIP (top) and SEELEM (bottom) spectra of benzaldehyde excited at the first 1800 cm-' above the TI origin. 1 Torr of benzaldehyde was expanded in 0.5 bar of He. The flight times of the LIP and the SEELEM signals were 108 and 133 ps, respectively. The alkali metal (usually potassium or potassium/sodium alloys) is evaporated from a small oven and baffled by a double radiation shield. The cathode surface is closed by a fine mesh and biased at -400 V relative to the front face of the electron multiplier, in order to maximize the electron collection efficiency. The electron multiplier consists of a two multichannel plates stack, with a 105-106 gain. The sensitivity of the SEELEM detector is stable within 3% over 10 h of continuous work. The detection efficiency is specific to the metastable molecule and varies between and 0.05 for molecules in which the triplet electronic energy exceeds the surface work function. The distance of the SEELEM detector from the excitation zone is variable between 20 and 400 nm. This interval corresponds to flight times varying from 6 to 500 ps in the various expansion gases. B.2. Delayed LIP. Laser-induced phosphorescence (LIP) experiments in supersonic beams introduce two major problems: (1) fluorescence from impurities and laser stray light signals can surpass the low LIP signal; (2) poor integrated light collection efficiency of the detector due to short viewing time (2-10 ps) as compared with the long pure radiative lifetime (>1 ms). The problems of fluorescence and laser stray light were partly handled by Villa et al.I3 and Penner et a1.,21+22 who collected the light downstream from the excitation zone. We improved this idea by inhibiting the photomultiplier during the excitation.Is Pratt and co-workers have improved substantially the light collection effi~iency.~~-~' Our new LIP scheme is free of stray light and fluorescence and provides a long viewing time (up to 80 ps in Ar expansion) and a large viewing solid angle (-0.8 steradian). The photomultiplier is located in the third chamber 30-40 mm above the beam axis, without any imaging. This configuration provides a large viewing solid angle, which is almost constant while the molecules propagate below the photomultiplier (1-in. diameter, Hamamatsu R-1104). The molecules are excited in the second chamber. Thus, the fluorescence and laser stray light reaching the photomultiplier are reduced by 4 orders of magnitude relative to a configuration where the detector is in the excitation chamber. This novel ~~~

(21) Penner, A.; Oreg, Y.; Villa, E.; Lim, E. C.; Amirav, A. Chcm. Phys. Lerr. 1988, 150, 243. (22) Penner, A.; Amirav, A. J . Chcm. Phys. 1988, 92, 5079. Pratt, D. W. J . Phys. Chcm. 1983, (23) Spangler, L. H.; Matsumoto, Y.; 87, 478 1. (24) Spangler, L. H.; Pratt, D. W. J . Chcm. Phys. 1986,84,4789. (25) Tomer, J. L.; Holtzclaw, K. W.; Pratt, D. W. J . Chcm. Phys. 1988, 88, 1528. (26) Tomer. J. L.; Spangler, L. H.; Pratt, D. W. J . Am. Chcm. Sa.1988, 110, 1615. (27) Holtzclaw, K. W.; Spangler, L. H.; Pratt, D. W. Chcm. Phys. krr. 1989, 161, 347.

7156 The Journal of Physical Chemistry, Vol. 95, No. 19, 199I1

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Figure 3. Time-of-flight traces of the LIP (solid line) and the SEELEM (dashed line) signals taken simultaneously at the SI origin excitation. The whole detecting event is being characterized in the trace shape. The LIP trace contains a low signal which appears 30 ps following the excitation (in He) and relates to the entering of the excited molecules into the main chamber. During the 90-1 30-p time period the LIP signal peaked while the excited molecules travel below the photomultiplier. The LIP trace terminates while the molecules meet the inclined SEELEM surface and the SEELEM signal builds up.

Sneh and Cheshnovsky lifetimes, ensuring the absence of discernible geometrical effects in the decay lifetimes measurements. C.2. Simultaneous SEELEM and LIP Measurements and Spectroscopy. The simultaneous SEELEM and LIP measurements were performed in two ways: (a) Accurate ratio evaluation: The excitation laser was tuned to a given transition and the TOF traces were averaged. (b) Spectroscopy: A simultaneous wavelength-dependent spectra of SEELEM and LIP were taken. The signals were processed by using gated amplifiers and fed into the A/D ports of our computer. The computer averaged the data, normalized it to the laser intensity and controlled the excitation wavelength. The spectral resolution was about 0.3 cm-I. C.3. MPI Measurements. The MPI experiments were performed in two modes: (a) Low-resolution TOF experiments: The laser was tuned to a given excitation and the mass spectrometric TOF signal was averaged. (b) Spectroscopy: The gated MPI and SEELEM signals were taken simultaneously, processed by using gated amplifiers, and fed into the A/D ports of our computer.

3. Results A. Vibronic and Rovibronic Spectroscopy. The simultaneous SEELEM and LIP spectra of benzaldehyde excited to its T I and SIelectronic states are displayed in Figures 2 and 4, respectively. The shortest measured lifetime of the main spectral features was 600 ps (section B3). The LIP and SEELEM spectra were taken with 108- and 137-ps delays, respectively. The difference between configuration allows the detection of a single LIP photon per laser these delay times is much smaller than the lifetimes of the excited pulse. The vacuum has to be better than 5 X lo-’ Torr for reliable states. Thus, practically, the spectra were taken simultaneously. triplet lifetime and SEELEM experiments. Thus, any attempt Note the different relative intensities of the various transitions in the LIP and the SEELEM spectra. These differences will be to measure simultaneously SEELEM and LIP calls for rarefied discussed in section 3C. beam LIP experiments. With our improved S / N ratio we could Figure 2 displays the spectra of the directly excited triplet states measure LIP in rarefied beams (e&, in Ar expansion: mean free in the energy range between the T I and SIorigins. Note the path X > 5 m, beam velocity uB H 500 m/s and Mach no. M excellent S/N ratio of both spectra for this very weak transition 20 and collision rate lower than 5 s-l). Note the excellent S / N (f N l V S )despite the low density in the beam. The main spectral ratio in the LIP spectrum of Figure 2 (top). In these spectra the molecules were excited 120 mm downstream the nozzle. Due to features coincide with the previously reported SP measurements of Ohmori et al.lz and the LIP spectroscopy of Villa et al.” The the long delay between excitation and detection this technique shortest decay lifetime in this region is 1.3 ms. Consequently, is limited to long-lived phosphorescent states. our 108-ps delayed LIP spectrum resembles the intensities of the Figure 3 displays the simultaneously measured time of flight short-delay (1 5 M S ) LIP experiment of Villa et al.” (TOF) LIP (solid line) and SEELEM (dashed line) traces. The Our spectra, however, differ from the MPI spectra of Villa et LIP trace contains a low signal that appears 30 ps after the laser aI.l3 and Villa,I4 in the relative intensities and the rotational excitation (in He) and marks the entrance of the excited beam structure. Our spectra also lack any background in the 400into the main chamber. The LIP signal peaks 90-130 ps after 1730-cm-’ energy range above the TI origin. Villa et al. attributed the excitation, as the excited molecules travel below the photothe differences in the relative intensities of the MPI and LIP multiplier. The LIP signal decays as the molecules pass further spectra to lifetimes effects. The very long lifetimes (compared toward the inclined SEELEM surface while the SEELEM signal to the 15-ps time scale of Villa et al.”) which we have measured builds up. (section 3B) preclude this explanation. We have found that high B.3. MPI. A 150-mm focal length Supraseal lens was used laser intensities produce MPI spectrum, which is quite similar to to focus the laser beam. The ions were collected by an electrostatic that of Villa et aLI3and Villa.I4 At low laser intensities, however, lens and amplified by a two-multichannel-plates stack. the MPI spectrum resembles the SEELEM spectrum. These C. Experimental Procedures. C.1. Lifetimes Measurements. Lifetime measurements were performed by tuning the excitation results will be discussed iq section 3E. Figure 4 displays the spectra of benzaldehyde excited in the wavelength to a given optical transition and measuring the 2000-cm-I energy range above the SIelectronic origin. The main SEELEM TOF signal in several excitation-detector distances. spectral features in the first 1500-cm-l range are consistent with The signals were taken and averaged with a signal averager the spectral locations of Ohmori et a1.I2 (Le-Croy 9400). Due to the finite velocity distribution of the Note that the line profiles of the transitions to the SImanifold molecules in the beam, the traces width was TOF dependent. The integrals of the traces were fit to single exponential decays (section are wider than those of the direct transitions to the triplet manifold. B3). Figure 5 displays the rovibronic spectra of the TIand SIelectronic The interrogation of long decay lifetimes in supersonic beams origins on the same energy scale. The shape of the T I 0-0 exdemands the use of highly collimated and sparse beams to ensure citation resembles a parallel oblate transition which is dominated collisionless conditions on the triplet lifetime time s ~ a l e . ~ * * ~by ~ a prominent Q branch (although triplet excitations are governed by different selection rulesmthe detailed analysis is difficult and Paying the penalty of 200-fold decrease in the beam density we have excited the molecules in a skimmed beam 100-120 mm irrelevant for our discussion). The line profile of the SI origin, downstream the nozzle. The lifetimes were verified to be indewhich is a parallel transition, is much broader and lacks the pendent of the backing pressure in the beam. The lifetime of the P-Q-R shape. These spectral differences are discussed in sections SI origin was measured in two different expansion gases. This 3D and 4D. experiment generated two different time scales in the flight tube B. Triplet Lifetimes. Decay curves of seven prominent spectral due to different gas velocities. The measurements yielded identical features in the benzaldehyde spectra (E, of 0-3750 cm-’) are displayed in Figure 6. The best single-exponential fits and their (28) Cheshnovsky, 0.; Amirav, A. Chem. Phys. Lrtr. 1984, 109. 368. (29) Sneh, 0.; Cheshnovoky, 0. Chem. Phys. Lett. 1986, 130.487.

(30) Hougen, J. T. Can. J . Phys. 1964,42, 1363.

The Journal of Physical Chemistry, Vol. 95, No. 19, 1991 7157

Triplet States in Beam-Isolated Benzaldehyde

WAVELENGTH

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Figure 4. Simultaneous LIP (top) and SEELEM (bottom) spectra of benzaldehyde excited at the first 2000 cm-' above the SI origin. 1 Torr of benzaldehyde was expanded in 0.5 bar of He. The flight times of the LIP and the SEELEM signals were 108 and 133 ps, respectively.

TABLE I: Relative Radiative Rates and Triplet Lifetime of Range above the TIorigin Benzaldehyde in the 0-3700-~m-~ wavelength,

A

exvib energy"

3970 3940 3906 3903 3893 3888 3850 3878 3871 3803 3792 3776 3774 3773 3771 3751 3715 3696 3688 3680 3662 3660 3657 3642 3638 3625 3616 3600 3570 3558 3544 3542 3539 3534 3522 3515 3492 3490 3487

0 I92 41 5 434 500 533 787 599 646 1 IO8 I I84 1296 1310 1317 1331 1473 1731 1869 1928 1987 2120 2135 2158 2270 2301 2399 2468 2591 2824 2919 3030 3046 3070 31 10 3206 3262 3450 3466 3491

re1 SEELEM intensity! 96 100

18 4 2 2 2 4 3 1

3 21 9 18 31 7

IO 2200 180 215 340 55 90 I45 125 55 110

800 125 900 930 400 2000 1250 360 390 180 100

210 200

re1

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TT. US

1.00 35002g? 0.98 13505; 0.97 0.93 0.81 0.85 0.77 0.82 0.68 0.75 0.79 1300fg 0.69 0.69 0.66 17002% 0.63 0.66 1.05 6002% 0.98 0.89 0.91 750!km 0.86 0.81 0.77 0.82 0.80 0.81 0.76 1000f2$ 0.82 0.84 90021% 0.85 800~150 0.93 0.87 800~100 0.92 0.97 0.86 850~150 1.08 1.06 1.07 1.10

'Above the TIorigin. *The TIorigin was taken as 100%.CRelative to kr of the TIorigin.

accuracy limits are summarized in Table I. The lifetime of the TI origin was found to be 3.5 ms. Since longer lifetimes were not measured in our experimental apparatus, it could well be that this lifetime resulted from experimental artifacts. We consider 3.5 ms as a lower limit for the real decay time. The phosphorescence lifetime of the Tl(n**) origin was mea. ~ lifetime sured in cold nonpolar matrices to be 1.5-2 m ~ The

ENERGY (cm-l) Figure 5. SI0-0 SEELEM line profile (bottom) compared to the TI 0-0 SEELEM line profile (top).

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Figure 6. Decay curves of seven prominent benzaldehyde spectral features and the best fitted exponential decay lifetime: (1) T, 0 1 , 3970 A, 7 = 3.5 ms; (2)3792 A, T = 1350 s; (3) 3773 A, T = 1700 ps; (4) SI 0-0,3715A,T = 600ps;(5) 3616 1 , 7 = 1 ms;(6)3542 A, T = 800 ps; (7)3522 A, 7 = 850 ps. The SI0-0 was measured both in He (open circle) and Ar (full circle) expansion to ensure the absence of substantial geometrical effects (section B3).

was found to be slightly temperature dependent in the range 4-77 K. We take 5 ms as a reasonable upper limit for the origin lifetime. This assumption introduces upper limits for all other lifetimes. In Figure 7 we display these rates as a function of excess triplet vibrational energy. C. Relative Radiative Rates. The LIP signal was sampled with a 25-ps gate (At) and is proportional to the expression

IA&

exp(-krD)[ 1 - exp(-&At)]/& (1)

Here I Ais the ~ absorption intensity, kr is the pure radiative rate, k = ~ / T Tis the total decay rate, 77 is the triplet lifetime, and t D

Sneh and Cheshnovsky

7158 The Journal of Physical Chemistry, Vol. 95, No. 19, 1991 I

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F l a r e 7. Excess energy dependence of the total decay rate. The open circle represent the phosphorescence lifetime data which had been taken at nonpolar matrices.s The open square represents the estimated decay rate of the triplet manifold (section D3 and Figure 14).

-8

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ENERGY (cm-1)

Figure 9. Prominent rotational dependence of the pure radiation rate manifested on the P branch of the T I 0-0. This rotational dependence is characteristic in all the directly excited triplet states.

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Flpre 8. Excess energy dependence of the radiative rates (normalized to the rate k, at the TI 0-0). The open squares represent the estimated pure radiative decay rates of the triplet manifold (section D3 and Figurts IO and 11).

k v, z W

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is the sampling delay time which have elapsed since the excitation. The 25-ps sampling time of the LIP signal was short compared to the long lifetimes of the transitions (kAt < 0.04) and eq 1 can be approximated as ILIp

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(2)

The SEELEM technique detects the population of the excited

and thus the SEELEM signal IseeLeM is proportional to IAmexp(-krD). The ratio of the LIP and the SEELEM signals is proportional to the pure radiative rates: ILiP/IseeLeM

0:

kr

(3)

If the difference between the LIP and the SEELEM delay times is not negligible relative to the state lifetime rT the ratio of eq 3 must be corrected to tDLIP fCg,,,

Thus the excess energy dependence of the pure radiative lifetimes

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ENERGY (cm-1) Figure 10. Simultaneous rovibronic LIP and SEELEM spectra (bottom) at the vicinity of the SI 0-0. The LIP spectrum is narrower than the SEELEM spectrum. The LIP spectrum was divided by the SEELEM one to provide the pure radiative rate line profile (top). The T, line profile was fitted to a constant plus Lorentzian shape (eq 5 ) . The relative heights of the constant hT and the Lorentzian hs, serve in the analysis of eqs 7-9.

can be evaluated by comparing the SEELEM and LIP spectra. The relative pure radiative rates, normalized to the rate at the T I origin are summarized in Table I and presented in Figure 8. The relative intensities were measured accurately by tuning the excitation laser to a given transition and averaging the SEELEM and LIP signals simultaneously. Every vibronic state was measured several times, and the accuracy was better than 2%. Special precaution was taken to eliminate detector saturation effects. Figure 9 shows a slight rotational effect on the pure radiative lifetime on the P-branch part of the rotational envelope. We will not discuss this dependence, since benzaldehyde differs much from

The Journal of Physical Chemistry, Vol. 95, No. 19, 1991 7159

Triplet States in Beam-Isolated Benzaldehyde I

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ENERGY ( c m - ' ) ENERGY (cm-I) Figure 11. Simultaneous rovibronic LIP (dotted line) and SEELEM (solid line) spectra (bottom). This figure demonstratethe erosion of the Lorentzian part of the radiative rate line profile with the excess vibrational energy above the SIorigin (top): (a) 240 cm-l of excess energy; the Lorentzian part is only 24% of the peak k, amplitude; (b) at the excess energy of 800 cm-' above the SIorigin the Lorentzian part is

completely eroded.

a "symmetric-top" molecule, and the analysis of the rotational contour is complex. D. Dynamics of SIExcitations. Figure 10 displays the simultaneous measured LIP and SEELEM spectra of the SI0-0 transition. The profile of the relative radiative rate, obtained by dividing the LIP trace by the SEELEM trace, is not constant over this peak. To verify that this effect does not result from nonlinearity of the LIP or SEELEM detectors, the same experiment was repeated with a 75-fold attenuation of the laser! The radiative rate line profile was fitted to a Lorentzian shape riding on a constant background: k,=A+B

(A/2I2 [(A/2)2 + AE2]

where A is the Lorentzian full width at half-maximum (fwhm), A is the constant part of the rate, B is the Lorentzian amplitude, and hE is the energy deviation from the peak of the radiative rate profile. The best fit (shown in Figure 10) is obtained with the parameters: A = 4 cm-I, A = 0.63, and B = 0.37. The polarization of the SI Sotransition in benzaldehyde was 'A' transition3'J2 and should have assigned as a parallel 'A" had (under our 0.3-cm-I resolution) a profile similar to the TI So transition. Therefore, we conclude that the SIline profile with 0.3-cm-I resolution is a congestion of many parallel type (SI TJ So transitions. The constant part of the pure radiative rate line profile results from the T I oscillator strength, while the intersystem coupling of the SIorigin to the background triplet results in a Lorentzian-like line shape.33 Practically, the line profiles of both the LIP and the SEELEM spectra are the convolution of the Lorentzian profile with the rotational envelope of the molecular eigenstates. In our analysis we have assumed that the rotational envelope of each vibronic state is identical with the envelope of the T I 0 transition and have deconvoluted the k, (pure radiative rate) line profile resulting in Ad = 0.6, Bd = 0.4, and 4 = 3.8 cm-l. The

--

-

(31) Shimada, R.;Goodman. L. J. Chem. Phys. 1%5,43, 2027. (32) Hayashi, H.; Nagakura, S . Mol. Phys. 1974,27,969. (33) Bixon, M.;Jortner, J. J. Chrm. Phys. 1968, 48, 715.

+

+

Figure 12. LIP (top) and SEELEM (bottom) rovibronic spectra of the SI 0 (solid line) compared to the convoluted spectra (dotted line, section D3). The beam conditions resulted in a very cold rotational

envelope. 0.6 constant part multiplied by the 1.05 relative radiative rate at the SIorigin (Table I) provides a value of 0.63 for the relative radiative rate of the triplet states, which is close to the value of the nearest directly excited triplet levels (Table I and the open squares of Figure 8). At higher SIexcitations the Lorentzian part of the radiative rate line profile is gradually eroded with the e x w vibrational energy (Figure 11). From 2500 cm-' above the T I origin (about 800 cm-I above the SIorigin) the LIP and SEELEM line profiles are practically identical and the radiative rate profile of the SIvibronic excitations is constant. Due to Franck-Condon overlap only the Lorentzian part of the oscillator strength (related to the SI So excitation) contributes to the absorption. However, the LIP spectra (which is proportional to the product of absorption and radiative rate; section C3) includes also the constant part of the radiative rate. The convolution of a A,, = 3.8 cm-' Lorentzian with the TI origin rotational envelope fits well the SEELEM line profile. Accordingly, the LIP line profile is well reproduced by the convolution of this Lorentzian multiplied by the radiative rate line shape, with the TI 0-0 rotational envelope. Figure 12 compares the experimental and the convoluted line profiles. To check the validity of our convolution procedure, we have repeated it in different rotational temperature. We have convoluted the profiles with a warm T I 0-0 rotational envelope and compared them to the experimental spectra of the SI0-0 excitation, taken at the same warm conditions (Figure 13). The line profiles fit well by using the same oscillator strength parameters (&,Bd, A,,), as in the cold-temperature convolution. We may conclude that the &-TI coupling is rotationally independent. The coupling of the SI0-0 state to the triplet background is reflected also in the profile of the total decay rate. Figure 14 displays the SEELEM line profile of the SI0 4 excitation taken at two different flight times. The spectrum taken at 186 ps is obviously narrower than the one taken at 538 ps. The 352-p flight time difference is more than half of the lifetime at the excitation peak ( 7 = 600 ps). This allows the evaluation of the total decay line profile: 1 In [Dpak/oE,] k@,) = -600 ps At where D = SEELEM'86/SEELEM538is the ratio between the SEELEM signals at 186 and 538 p, respectively. DWk and DE, are the values of this ratio at the line peak and at every excitation energy respectively, and Ar = 352 p is the time difference between

-

Sneh and Cheshnovsky

7160 The Journal of Physical Chemistry, Vol. 95, No. 19, 15191

7

I

I

I

0

I

TI 0-0

W

26960

26930

26900

ENERGY (cm-1) Figure 13. LIP (top) and SEELEM (bottom) rovibronic spectra of the SI0 (solid line) compared to the convoluted spectra (dotted line, section D3). The beam conditions resulted in a hot rotational envelope.

I

I

25210

25180

1

1

25150

ENERGY (cm-1)

Figure 15. Laser intensity dependence of the MPI spectra of the TI 0-0 rotational envelope. The contour of the SEELEM spectrum, taken simultaneously with the MPI spectra (a-e) does not depend on the laser intensity. The MPI spectra consist of the wavelength-dependenttotal ion count. The various laser intensities were obtained with neutral density filters and were loo%, 5046,251, IO%, and 5% of the ~5 GW/cm2 laser intensity, for the a-e spectra, respectively. Note that the low intensity MPI spectrum (e) is practically identical with the SEELEM spectrum

(0.

a Y

I

1

26960

I

26930

I

26900

I

ENERGY (cm-I1 Figure 14. Rwibronic SEELEM spectra taken at the delay times of 186 and 538 ps (bottom). The 186-ps spectrum is narrower than the 538-w spectrum. The spectra were computer treated according to q 6 to provide the line profile of the total decay rate k, (top). The line shape of the decay rate was fitted well to a constant 650-s-' rate plus a 1000-s-' Lorentzian profile with a 3.8-cm-I width (section D3).

these measurements. The line profile fits well to a constant background and a Lorentzian shape given by eq 5 with A = 650 s-I, B = loo0 s-l, and A = 4 cm-I (dotted line). The decay lifetime associated with the triplet states (1 / A = 7 N 1.5 ms) is close to the value of the pure triplet states at the adjacent energy region (open square at Figure 7). E. Multiphoton Ionization. The total ion current was detected in the multiphoton ionization (MPI) experiments. The MPI spectrum was measured simultaneously with SEELEM as a reference for the excitation conditions. We have found that the line shape in the MPI spectra depends strongly on the laser intensity. Figure 15 displays the T I 0 rotational envelope taken

at several laser intensities. Throughout these experiments the SEELEM spectrum was independent of the laser intensity. The MPI spectrum, taken at low laser intensity, is practically identical with the SEELEM spectrum. This fact ensures the absence of short time dynamics that might have distorted our delayed LIP and SEELEM measurements. At higher laser intensities, some of the MPI spectral features become more pronounced. Finally, at the highest intensity (>5 GW/cm-2) the spectrum smears and resembles the spectra of Villa et aLI3 and VillaI4 in all respects: the absence of the Q branch, the spectral background and the electric field effects at the 3770-3795-A wavelength interval. The low-resolution TOF traces of the MPI ions indicate the onset of extensive fragmentation at laser intensities in which the spectrum begins to smear. Fra mentation processes in MPI excitations are well establi~hed.~.~ Villa et al." and Villa" had rationalized some unique spectral features in their MPI spectra as rotational-dependent radiationless processes after the second photon absorption. Our findings imply that the competing fragmentation is more than a threephoton effect. Our MPI results show that the spectral background in the MPI experiments of Villa et al.I3J4is a high-order effect and should not be invoked as a spectroscopic mark of the T2 manifold.

f

4. Discussion

Starting from its origin, the SImanifold of benzaldehyde is unique. The line width of the SIexcitations are about 3.8 cm-' wide, the total decay lifetimes of about 1 ms, and the pure radiative lifetime is comparable to the lifetime of the triplet manifold. We conclude that the SImanifold is heavily mixed with triplet. As will be shown in section D4 these wide lines are composed of a congestion of (Sl-TJ mixed states which are not resolved by our (34) Bosel, U.;N e w r , H. J.; Schlag, E.W.J . Am. Chem.Soe. 1981,103, 5058. (35) Cooper, C. D.; Williamson, A. D.; Miller, J. C.; Compton, R. N. J . Chem. Phys. 1980, 73, 1527.

Triplet States in Beam-Isolated Benzaldehyde

The Journal of Physical Chemistry, Vol. 95, No.19, 1991 7161

laser (ah ci 0.3 cm-I). We expect the time-dependent decay, of the SIvibronic levels, to include a short component of the order of nanoseconds. This time scale could not be probed in our experiments. Beyond this time scale, the SImanifold should be treated as a continuation of the triplet manifold. The origin of the excess vibrational energy scale in our discussion will be the T I origin. A. Excess Energy Dependence of the Total Decay Rates. The excess energy dependences of both the pure radiative rate (Figure 8) and the total decay rate (Figure 7) have some common features. The rates at the SIorigin are nearly twice the values extrapolated from the lower triplet manifold. In the 800-cm-’ range above the SIorigin the decay rates return to the typical rates of the triplet manifold. As was pointed in section D3, the 1730-2500-~m-~ energy range was characterized by a gradual disappearance of the additional Lorentzian part in the line profile of the total and the pure radiative rate. A similar excess energy dependence of the triplet decay rates above the SIorigin was obtained in ~ y r i m i d i n e . ~ ~In ” ~this molecule the SI-T, energy gap is 2540 cm-I. The radiationless rates at 1000 cm-I following the pyrimidine SIorigin show the same irregularity in the excess energy dependence as in benzaldehyde. In contrast, the excess energy dependence of the triplet * ~ ~very *’~ decay at the vicinity of the SIorigin in p y r a ~ i n e ~ *was monotonic (TI-SI energy gap of 4050 cm-I). We conclude, that in the energy region above the SIorigin of benzaldehyde (and pyrimidine), the density of zero-order triplet states is too low for a triplet-dominated radiationless decay. Thus, the total decay includes also contributions of the SIcharacter. The influence of the singlet on the total decay is manifested also in the Lorentzian profile of the total decay rate at the SIorigin (Figure 14). The singlet contribution in the decay rate vanishes at higher excess energies, on further dilution of the singlet character. The same arguments hold for the energy dependence of the pure radiative rates. The line profiles in the 1700-3750 cm-I are composed of many SI+ T states (section D3). In the 17002500-cm-’ region the bands are expected to contain more SI character at their center, as the profile of the relative radiative rate in the SIorigin indicates (Figure 10). The bands in the energy region above 2500 cm-’ have constant radiative rate across their profiles (Figure 1 I). The total decay rates (ignoring the SIdominated 1700-2500cm-I range: open square in Figure 7) gradually increase over the 0-3750-cm-’ energy interval. This mild change is not typical for heteroaromatic molecules. Very often, heteroaromatic molecules with close 3 n ~ and * 37r7r* states show fast increase in the decay rates with excess vibrational energy, due to extensive 3n7r*-37r7r* coupling.’&-“ In pyrazine and methylpyrazine, we have obtained a change of more than 4 orders of magnitude in the nonradiative rates at the first 4000 cm-’ above the T I origin. Such a large dynamic range of the decay can be also deduced from measurements of and aniline.42 The total energy rates of benzaldehyde in the 3750 cm-l excess energy range are comparable with the radiative rate ( 7 , cv 2-5 ms5). Without an accurate knowledge of the radiative rates, it is difficult to extract the nonradiative decay rates from the total decay rates. Consequently, we will not discuss the nonradiative decay rates of the benzaldehyde triplet. B. Excess Energy Dependence of the Radiative Rates. The excess energy dependence of the radiative rates can be divided into four energy regions: (36) Dietz, T. G.; Duncan, M. A.; Pulu, A. C.; Smalley. R. E. J . Phys. Chem. 1982, 86, 4026. (37) Smalley, R. E. J . Phys. Chem. 1982. 86, 3504. (38) Sobolewski, A. L. Chem. Phys. 1987, 115,469. (39) Lim, E. C.In ExciredSrares, Lim, E. C., Ed.;Academic Press: New York, 1977; Vol 111. p 305. (40) Wassam Jr., W. A.; Lim, E. C. J . Chem. Phys. 1978.68.433, (41) Hochstrasser, R. M.; Marzzacco, C. A. In Molecular luminescence; Lim, E. C., Ed.; Benjamin: New York, 1969; p 631. (42) Knee, J . L.; Johnson, P. M. J . Chem. Phys. 1984,80, 13.

(a) 0-400 cm-’: the rates are practically constant. (b) 400-1700 cm-l: a sharp decrease down to about 60% of the rate at the T I origin, followed by a gradual change. (c) 1700-2500 cm-I: SI-influenced region, where the decay rate increases at the SIorigin and gradually decreases with cnergy. (d) 2500-3750 cm-I: the rates increase monotonically to the rate of the T I origin. Several mechanisms can be invoked to explain this very irregular energy dependence of the triplet radiative rates. We will start by rejecting the mechanisms that we consider irrelevant to our case: (a) Rotational effects: Penner et al. have claimed that the spin-orbit coupling in gas-phase molecules is rotational dependent.21 According to their proposed mechanism, strong spin-rotation coupling may cause spin-orbit d e ~ o u p l i n gin~ all ~ except which are one of the 25 3 spin-rotation orientations (MJ21927) available in each Jstate. Vibrational mixing stimulated by Coriolis coupling may cause a reduction in the spin-orbit coupling of the excited states. A total randomization of the spin-rotation orientation at the intramolecular vibrational redistribution (IVR) region would reduce the radiative rate to zero (especially at low J). These predictions oppose the experimental results in the high-energy region. (b) Vibronic-induced spin-orbit coupling: Vibronic induced spin-orbit coupling may become the main intersystem coupling term if the direct mechanism is symmetry forbidden.”.” This coupling is excess energy dependent and will decrease with vibronic mixing. Vibronic induced spin-orbit coupling is typically 3 orders of magnitude weaker than the direct electronic coupling.u The Ti So oscillator strength in benzaldehyde is f cv lod. Such strong T S oscillator strength is unlikely to be vibronically induced. At the energy region of IVR such a coupling mechanism would disappear. This prediction is in contrast to the experimental increase in the radiative rates above 2500 cm-I. (c) Absorption/emission mirror symmetry breakdown: Radiative rates may drop in electronic transitions that lack a b sorption/emission mirror ~ y m m e t r y . ~This ~ . ~mirror symmetry breakdown originates from Duschinsky rotation of the normal coordinates at the excited state.The Duschinsky rotation may induce irregularity in the pure radiative rates. This effect cannot be responsible for the irregularity in the radiative rate of benzaldehyde, since the intensity-lifetime relations expected in Duschinsky rotations are not fulfilled.4s.46 In our view the interaction of the nearly degenerate 3n7r* and 37r17* states is responsible for the excess energy dependence of the radiative rates: Interaction of the Proximate ’n** and ’TT* States. The radiative dynamics over the whole excess energy range is well explained by the 3n7r*-)7r7r*states coupling. The existence of almost degenerate 3n7r* and ’mr* states was predicted by series of experiments.I”J”I4 The 3n7r*--’7r7r*energy gap is probably less than 400 cm-I (section B3). Above the origin of the ’a**,the ’nr* states are diluted with the dark 37r7r* vibronic states. This dilution reduces the radiative rate of the coupled states. It resembles the known Douglas effect in small molecule^^^-^^*^ and was also demonstrated at the S2origin in isoquinoline.” The nonmonotonic variations in the pure radiative lifetime in the energy interval of 400-1730 cm-I (Figure 8) results from resonances. Since the two triplet states are accidental ’r17r*-~mr* nearly degenerate, the expected dilution is around 50%. The reduction in the radiative decay rates in the 12W1700-cm-1region is indeed close to this value (60%). The above trend is hindered over the range of 1700-2500 cm-I (Si influenced). The values of the radiative rates tend to stabilize again in the energy region of 3300-3750 cm-’, where the SI

+

--

(43) Ohta, N.; Takemura, T. J . Chem. Phys. 1989, 91,4477. (44) Wild, U. P. In Triplet Stores; Springer-Verlag: Berlin, 1975; Vol. 11, p 1 . (45) Amirav, A.; Horwitz, C.; Jortner, J. J . Chem. Phys. 1988,88,3092. (46) Warren, J. A.; Hayes, J. M.; Small, G. J. Chem. Phys. 1986,102,313. (47) Duschinsky, F. Acra Phys. U.R.S.S. 1937, 7 , 551. (48) Douglas, A. G. J . Chem. Phys. 1966, 45, 1007.

7162 The Journal of Physical Chemistry, Vol. 95, No. 19, 1991

Sneh and Cheshnovsky

character is negligible. The decay-rate values are 1.05-1,IO of the TI origin rate. The monotonic increase in the radiative rate above the energy of 2500 cm’ may reflect the growth of the Tl()nr*) character in the triplet states. A possible explanation is, that the density of the TI states grows faster than the T2state due to their lower origin. This may reduce the dilution of the T l ( 3 n ~ *states ) by the T2 manifold. C. nr*-mr* Vibronic Coupling Mechanism. The issue of vibronic coupling between proximate electronic states was extensivel treated both t h e ~ r e t i c a l l y ~and ~ l experimental-

Z E R O ORDER

STATES

MOLECULR

EIGENSTATS

ABSORPTION

EMISSION

PROFILE

P&ikE

’I

-

ly,17.1*.3139.49,~o

Three regions of coupling can be distinguished: weak coupling, where the energy gap between the coupled states is much larger than the coupling interaction; intermediate coupling where the gap is somewhat larger than the interaction; strong coupling, where the energy gap is smaller or comparable to the energy gap. In our discussion we shall relate to the two latter cases only. Intermediite Coupling Case. Here the interaction between the two states results in strong changes of the force constants along the promoting vibrational mode. The lower potential curve becomes much more shallow while the upper curve is steep. Still, each state preserves most of its electronic The consequences of this coupling is a constant radiative lifetime along the vibrational manifold (due to the constant electronic character) and a strong vibrational energy dependence of the radiationless transitions from the lower mixed state to the ground state. The latter property results from the large frequency change between the ground and the excited stateU3* A nice example of this case is revealed in the radiative and nonradiative dynamics of p y r a ~ i n e . ~The ~ ~radiative ~ ~ ~ ~ rates ’ of the modified TI states are constant, while the nonradiative rates change by 4 orders of magnitude over the first 2000 cm-’ of excess vibrational energy. In this case, the modified T2transitions are much weaker than those of the T I , and thus they are absent in the spectrum. Strong Coupling Case. The Bom-Oppenheimer approximation is violated. The two states are strongly coupled and mixed.sJO The extent of mixing of the two states strongly depend on the specific vibrational levels. Consequently, the variations of the radiative rates along the vibronic transitions are strong. General theoretical estimates do not predict strong frequency changes of the vibrational levels in the strong coupling case. The results of the current work indicate that the Tl-T2 coupling of benzaldehyde serves as a good example for the strong coupling case. The triplet radiative rates vary strongly with the vibronic levels. The above conclusion is in accordance with the small TI-T2 energy We have not measured the nonradiative ISC rates of the triplet manifold (section A4); however, the results of the total decay rates do not show dramatic changes, unlike the case of pyrazine. D. Dynamics of the SIExcitations. Bixon and Jortner have predicted that the dilution of a doorway state among a manifold of equal, dense and equally spaced dark states should result in a Lorentzian line shape.33 Even et aLsl (in LIF studies of zinc tetrabenzoporphine) and Amirav and J ~ r t n e (in r ~ absorption ~ studies of isolated azulene) have demonstrated such a Lorentzian broadening of “zerO-ordermvibronic levels due to their interaction with background states in the ‘statistical limit” regime. The uniqueness of the present results lies in the simultaneous observation of the diluted doorway and the background states. The simultaneous observation of the diluted state of the SIorigin of benzaldehyde together with the almost ‘dark” states of the background triplet is possible due to the distinct molecular properties of benzaldehyde. First, the background triplet states carries some oscillator strength and can be directly excited from the ground state of the isolated molecule. Second, the energy gap 1700 i cm-l, is small between the singlet and triplet manifolds, = (49) Madej, S. L.; Gillispie, G. D.; Lim, E. C. Chem. Phys. 1918, 32, 1. (50) Villa, E.: Amirav, A.; Lim, E. C. J . Phys. Chcm. 1988, 92, 5393. (51) Even, U.; Jortner, J.; Friedman, J. J . Phys. Chcm. 1982, 70. 2273. (52) Amirav, A.; Jortner, J. J . Chem. Phys. 1984,81, 4200.

t

c U

LL

z

LL

3i l2 io-

Figure 16. Energy level diagram demonstrating the coupling scheme as well as the resulted absorption and emission rate line profiles of SI zaldehyde. The molecular eigenstates in the vicinity of the SIexcitations are the outcome of the interaction of single zero-order singlet states coupled to many zero-order triplet states. The singlet character of the molecular eigenstates accounts for the radiative rate of the states. It constitutesof a constant electronically coupled singlet character ( 2 ) and a resonant vibronically coupled SIcharacter shapcd as a Lorentzian and peaked at the SIzero-order excitations (1). Due to the dilution of the SIdoorway state the dominant character of the states is triplet (3). Due to Franck-Condon overlap only the SI resonant part (having a S, vi-

Fn-

brational function) is reflected in the (vibronic) absorption line profile. However the emission rate line profile (Figure 2, top) includes also the nonresonant singlet character of the molecular eigenstates. enough so that only moderate dilution of the doorway state persists in the SIorigin. The constant part of the radiative rate line profile (Figure IO) results from the optically ‘dark” triplet background (oscillator strength N 10”). The intersystem coupling of the SIorigin to the triplet background results in a Lorentzian-like pure radiative rate that rides on top of the background. The energy level diagram of Figure 16 illustrates this physical picture. Note that due to the Franck-Condon overlap only the Lorentzian SIpart of the mixed states {SI+ T) carries absorption oscillator strength. Both parts (SIand T) contribute to the emission rate, resulting in the superposition of the constant background and the Lorentzian. The spectroscopy of benzaldehyde provides a rare opportunity to quantitatively determine the basic parameters of the theory of radiationless transitions (RT): the density of states p and the coupling strength between the doorway and the background states V. This determination is made possible by the simultaneous measurement of the relative heights of the Lorentzian part hs, and the constant part hT of the radiative rate line profile, together with the coupling width (A,the Lorentzian width) and the known oscillator strengths of both TI and SI and respectively). Note that the SIoscillator strength (5 X 10-4 ) is much larger than the TI oscillator strength (0.8-1.6X lods). The fact that even on the peak of the SI0-0 where the SIcontribution to the radiative rate is maximal, hs is close to hT, results from the dilution of the single SI0-0 state with a large number, N H 1.48pA (1.48A is the full integral over a Lorentzian), of triplet states over an energy range wider than the laser bandwidth. At the vicinity of the SIorigin the average oscillator strength of the triplet manifold, fT, is 0.63fT, = (5-10) X IO-’ (section 3D).

vi., L

The Journal of Physical Chemistry, Vol. 95, No. 19, I991 7163

Triplet States in Beam-Isolated Benzaldehyde The basic assumption in our analysis is that the ratio between the Lorentzian amplitude (hs,) and the constant part of the pure radiative rate profile (hT) equals the ratio between the diluted SI oscillator strength and the triplet oscillator strength: (7) This relation combined with the basic equation, which predicts the coupling width33A = 2rpV2, is sufficient for the evaluation of the average values of both p and K p = - fs, -

fTA

hT H

AS,

140-270 states/cm-I

(8)

We have performed another independent analysis to evaluate V. This analysis is based only on the experimental findings of this work and the measured SIintegrated oscillator strength.S3 In the framework of the Born-Oppenheimer description, the oscillator strength of the TI states of benzaldehyde is proportional to their SIcontent.ll*u The two transitions (SI So and T I So) have the same symmetry for the transition dipole moment and SIis the nearest IANsinglet state. Thus, the molecular eigenstates of the directly excited triplet states can be approximated as $ cy alT) + BlS,). This description is supported by our success in the convolutions displayed in Figures 12 and 13 (see section D3). The top of the "Q" branch at the T I origin of benzaldehyde is substantially broader than the bandwidth of our laser. The absorbance there, T1(O-O)Abr can be expressed as p and

+

+

TI(O-O)Ab= [TI 0-0 Franck-Condon factor] [SIoscillator strength] [the SI content in the T I origin] [number of excited K states on the peak of the Q-branch that are simultaneously excited by our (0.3-cm-' resolution) laser] Tl(0-0)Ab

0.35EfslX

(10)

where X H d2is the SIcontent in the T I states due to spin-orbit coupling between these states, 0.35 is the estimated FranckCondon factor of the T I origin (from our spectrum) and E is an experimental factor including also the number of the rotational states excited by our laser (6X = 0.3 cm-l) and the number of molecules in the excitation region. The absorbance at the peak of the SI origin SI(O-O)Ab,max is given by SI(O-O)Ab,max = [oscillator strength of a single molecular eigenstate] [Franck-Condon factor] [number of excited (SI T) states that are simultaneously excited by our (0.3-cm-l resolution) laser]

The experimental ratio of the SEELEM amplitudes at the peaks of the SIand the TI origins corrected to the excitation time is 22. Thus, the division of eq 10 by eq 1 1 yields SI(O-O)Ab,max = 0 . 0 3 6 ~= 22 resulting in p

We estimate the Franck-Condon factor of the SI0-0 to be 0.17. The peak amplitude at the SIstates includes also the contributions of the P, Q,and R branches of other vibronic transitions from the Lorentzian band. The evaluation of this effect, by numerical convolution results in a proportional factor that is 1.7E. The number of (SI+ TI vibronic eigenstates excited by our laser is bXp = 0 . 3 ~ .At the peak of the SI 0-0 the SIcontribution per eigenstate, to the oscillator strength of the molecular eigenstates is 0.42 of the oscillator strength at the TI origin. This value was calculated by multiplying the relative radiative rate at the peak of the SI0-0 (1 .OS) by the fraction of the Lorentzian amplitude (0.40) (sections C3 and D3). Note, that only the S,part of the vibronic states contributes to the absorption due to Franck-Condon overlap considerations. The above estimates result in the expression for the absorbance at the SIorigin. (53) Kanda. Y.; Kaseda, H.; Matumura, T. Spectroehim. Acta 1964,20, 1387.

H

210 states/cm-'

(13)

The similarity between the two independent estimates for the density of states (eqs 8 and 13) demonstrates the consistency of the basic model of radiationless transitions. Note that with this density of states, the coupling of the SIorigin to the triplet In background fits the case of "intermediate level this coupling case the mixed eigenstates are well separated in energy. Variable radiative lifetimes over the package of mixed eigenstates, as observed by us, is anticipated. We have used the algorithm of Stein and Rabinovitch" and the vibrational frequencies of benzaldehydeSto calculate the T I vibrational density of states. We have obtained the value of 10 states/cm-' at the SIorigin by assuming the existence of only one triplet state. Under the assumption of two nearly degenerate states (TI + T2) we have calculated 20 vibronic states/cm-'. This value is substantially lower than the above experimental estimate. We are faced with the problem of the "missing statesn in the theory of radiationless transitions. This problem has been thoroughly discussed in the literature of p y r a ~ i n e . ~ ~ - ~ ~ Over the energy range of 1730-2500 cm-' the calculated density of states increases by a factor of 9 (up to 175 states/cm-'). This increase is insufficient to explain the further dilution of the SI character and the vanishing of the Lorentzian shaped SIvibronic states contribution to the SI+ T oscillator strength. We are left with the puzzle of the discrepancy between the experimental evidence for higher densities of states and the counting algorithm. Obviously, the dynamics both in the SIorigin vicinity and in the 800 cm-' above it indicates that the density of states p is much larger at these values of excess vibrational energy. We have integrated over the Lorentzian part of the relative radiative rate of the SI0-0 excitation in order to estimate the SI content of the TI electronic state: fs, = integration over the Lorentzian part of the k, line shape at the SI0-0, normalized to the TI0-0 k, and multiplied by Xfss,, the oscillator strength at the T I 0-0

[(3.8/2)*

+

Sl(O-O)Ab,max = 1.7Efs,(O.42X)(O.17 X 0 . 3 ~ ) (1 1)

(12)

+ AE2] d E

x=2x

495Xfsl

(14)

10-3

This value is the square of the SIcontent in T I (X = B2) due to nonresonant interaction of the SIand the TI electronic states and does not depend on the SIvibronic level. The SIoscillator strength was measured by Kanda et al. to be 5.5 X Combining this result with eq 14, we estimate the Tl(3nr*) oscillator strength to be 1.1 X 10" and the pure radiative lifetime T , H 2.2 ps. This calculated value is close to the phosphorescence lifetime in nonpolar solvents5and to our measured lifetime, at the T I origin. Similar considerations can be applied to calculate the integrated nonradiative internal conversion rates of the SIorigin. As displayed in Figure 14 the total decay rate at the SI0-0 vicinity includes a constant part of 650 s-I (associated with the decay of the triplet manifold) combined with a 3.8-cm-' width Lorentzian ~

~~~

Stein, S. E.; Rabinovitch, B. S. J . Chem. Phys. 1971, 58, 2438. Amirav, A. Chem. Phys. 1986, 108,403. Amirav, A. Chem. Phys. 1988, 126, 327. Amirav, A.; Orcg, Y. Chem. Phys. 1988, 126, 343. Amirav, A. Chem. Phys. 1988, 126, 365. Kommandeur, J.; van der Meer,B. J.; Jonkman, H. Th. In Inrromolecular Dynumics; Jortner, J., Pullman, B., Eds.; Reidel: Dordrecht, 1982; (54) (55) (56) (57) (58) (59)

p 259.

J. Phys. Chem. 1991,95,7164-7171

7164

shape (peaked 1000 s-l above the background). The integrated decay rate of the SIorigin ks,(Sl0 4 ) is evaluated by integrating over the Lorentzian part of the total decay line profile: * (3.8/2)2 dE ks,(Sl04)= 1 0 0 0 ~ ~ AE2] -_ [(3.8/2)2

+

N

lo6 s-I

(15) This value can be regarded as the hypothetical total decay rate of the unperturbed SI0 4 state to the So ground state. The dilution of the SI state by the triplet manifold reduces the actual decay rate to our measured values. The radiative rate of the SIstate can be estimated from the integrated oscillator strengths3to be 2.5 X lo5 s-l. Thus, the So Sl(O-O)integrated internal conversion (IC) rate klc(SI0-0) can be extracted by subtracting the SIradiative rate from the total decay rate: klc(SI0-0) N 7.5 X IO5

-

-

In contrast, the So T ISC rate is associated with the constant part of the total decay rate line profile. The 650-s-l decay rate of the background includes the radiative as well as the ISC rates. The radiative rate of the triplet manifold in the vicinity of the SIorigin was measured to be 0.63 of the k, at the TI origin (section D3). This enables a crude estimate for the ISC rate of the (TI T2}levels to S,,. Using 2.2 ms as the TI M) radiative rate results in 360 s-l for the ISC rate in the vicinity of the SIorigin. Together, the above analysis produces a consistent and comprehensive picture of a single allowed excited state coupled to an almost "dark" sparse background. Our findings are consistent with the predictions of Bixon and J ~ r t n e r . ~ ' Actually, the applicability of the theory of radiationless transitions is not obvious for benzaldehyde. In real systems, like benzaldehyde, where the states width 6 H 10" cm-I is much smaller than the levels average energy distance of vibronic states, e = p-l > 3 X IO-' cm-', and the coupling strength varies randomly, the simple model of equally spaced equally coupled states33may be inadequate. This fact was demonstrated in the high-resolution domain, in the case of pyrazine SI excitation^.^^*^ It is gratifying

+

(60) Kommandeur, J.; Majewski, W.A.; Meats, Annu. Rev. Phys. Chem. 1987, 38,433.

W.L.; Pratt. D. W.

that a 0.3-cm-I excitation resolution averages completely the individuality of the states dynamics (only 45-90 states averaging). This means that the applicability of the simple model in predicting the general coupling and dynamics lies beyond the limits of its basic assumptions. Finally, we would like to emphasize that although the oscillator strength of a doorway state is several orders of magnitude larger than that of the "dark" manifold, the contribution of the dark states to the pure radiative rate is not necessarily negligible. The fact that the k, wavelength-dependent profile of an excitation can be a superposition of a Lorentzian and a constant calls for precaution in the analysis of the time-dependent decay of coherently excited Lorentzian bundle of states (excitation width, Aw larger than A). The coherent excitation of a Lorentzian bundle of states may result in a biexponential decay. The short component of that decay cannot be explained solely by the observed coupling width measured from either absorption or excitation experiments.

5. Conclusions The radiative dynamics in the 0-3750-cm-l energy interval above the benzaldehyde T I origin was explored. The details of the dynamics were rationalized as an interplay in the coupling of three electronic states. The TI(3nr*)-T2(3rr*)vibronic coupling increases irregularly in the region between 400 and -2OOO cm-I. Above the energy of the SI origin (1730 cm-I), the SI excitations are coupled to the sparse Tl-T2 background. The line profile and the dynamics of the SImanifold in the 1730-25OO-cm-' region can be described in terms of the interaction of an optically active state with a background of almost dark states, in accordance with the theory of radiationless transitions. The SI content in the coupled states is diluted along the 1730-2500-cm-' region with the congestion of the density of the triplet states. Finally, with larger excess energy, the T2 character is eroded probably due to the larger density of T I states. Acknowledgment. We thank Joshua Jortner and Aviv Amirav for stimulatingdiscussions throughout this project. This research was supported by the Fund for Basic Research, administered by the Israel Academy of Sciences and Humanities and the James Franck German-Israeli Binational Program in Laser-Matter Interaction. Registry No. Benzaldehyde, 100-52-7.

High Overtone Resonance Raman Spectra of Photodissociating Nitromethane in Solution David L. Phillips and Anne B. Myers* Department of Chemistry, University of Rochester, Rochester, New York 14627 (Received: February 5, 1991; In Final Form: May 1, 1991)

Resonance Raman spectra of nitromethane have been obtained in cyclohexane,acetonitrile, and water solvents with excitation at 218 and 200 nm and in the vapor at 218 nm. Fully deuterated nitromethane has also been examined in both vapor and solution phases. Resolvable Raman lines are observed at energies up to 15ooO cm-l, which is approximately the.lowest dissociation limit (to ground-state C H 3 0 + NO). The spectra in solution and in the vapor are qualitatively similar in that overtone progressions in the NO2 symmetric stretch dominate, but the higher signal-to-noise ratio of the solution-phase data allows many weaker transitions to be observed as well. The vibrational frequencies and bandwidths are interpreted qualitatively to explore solvation effects on the ground-state potential surface. The resonance Raman intensitiesare modeled with a simple theoretical treatment employing wave packet propagation on a single electronic surface. This approach does a reasonable job of reproducing the relative and absolute solution-phaseintensities, but some deviations between experimental and calculated combination band intensities are observed.

Introduction Nitromethane belongs to a class of small molecules having relatively intense and structure]- absorption s w r a in the quartz 'Author to whom correspondence should bc addressed.

0022-3654/91/2095-7164$02.50/0

ultraviolet that photodissociate with near-unity quantum yields. The photodissociation dynamics of such mokules are ideally suited for study by a combination of ground-state resonance Raman spectroscopy, which is most sensitive to the dynamics on that part of the excited-state potential surface closest to the Q 1991 American Chemical Society