Photophysics and photochemistry of monothioanthraquinone - The

Dec 1, 1987 - Lenoble, Ralph S. Becker. J. Phys. Chem. , 1987, 91 (27), pp 6606–6609. DOI: 10.1021/j100311a010. Publication Date: December 1987...
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J. Phys. Chem. 1987, 91, 6606-6609

6606

rectionality imposes a dynamic coupling between NH4+ and the ligand Z 4 0

Experimental Section The N M R spectra have been measured on the following spectrometers: Bruker SY 200 (IH at 200 MHz, *H at 30.701 MHz, 13Cat 50.288 MHz, I4N at 14.447 MHz, and ISNat 20.265 MHz); Bruker AM400 (IH a t 400 MHz). The chemical shifts are given in ppm downfield from the 'H or "C signals of internal tetramethylsilane. The I4N shifts are given with respect to the tetramethylammonium cation. Ammonium Cryptate Preparation. To ligand 1 (66 mg, 1.75 X lo4 mol), dissolved in 5 mL of chloroform, was added NH4PF6 (31 mg, 1.9 X lo4 mol). After evaporation of the solvent, crystals suitable for X-ray structure determination were obtained by slow evaporation of a water-methanol solution. Anal. Calcd for C18H40F6N306P: c , 40.08; H, 7.42; N, 7.79; Found: c, 40.22; H, 7.27; N, 7.70. (40) One may also note the existence of a correlation between the energy barrier opposing NH4* reorientation in solid ammonium salts and thermochemical data: Johnson, D. A. J . Chem. SOC.,Chem. Commun. 1986. 534.

Stability Constant Determinations. For these measurements an automatic titration unit Metrohm 636 was used. To avoid interference from complexable cations the internal solution of the combined electrode (Metrohm EA 125) was 3M NMe4C1 instead of 3 M KC1. The measurements were performed in a thermostat4 cell (25" f 0.1') under N2 atmosphere. The added base was 0.1 N N M e 4 0 H . The pK, determinations were made by titration M), HCI (3 X of a 4-mL solution containing ligand 1 (1 X M), and NMe4Cl (0.1 M) as supporting electrolyte. For the stability constant measurements the concentrations in the 4-mL M ligand 1, 3 X solution were 1 X M HCl, 5 X M salt (KCl or NH4Cl), and 0.1 M NMe4C1. Analysis of the titration curves with the SCOGS program4I gave the pK,'s of the ligand and the stability constants of the complexes. Registry No. NH,+, 14798-03-9; [NH4*Cl]PF6-,110718-28-0.

Supplementary Material Available: Listing of observed and calculated structure factors for [NH4+C1]PF6-(3 pages). Ordering information is given on any current masthead page. ~

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(41) Sayce, I. G.Talanta 1968, 145, 1397. Program adapted by Vitali, P

Photophysics and Photochemistry of Monothioanthraquinone L. V. Natarajan, Christian Lenoble, and Ralph S. Becker* Department of Chemistry, University of Houston, Houston, Texas 77004 (Received: May 13, 1987)

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The green lO-thioxo-9(lOH)-anthracenone, also known as monothioanthraquinone,exhibits striking spectral differences from that of the pale yellow anthraquinone. An n a* transition exists at 695 nm. No fluorescence is observed, but strong T I crossing. Theoretical phosphorescence is detected with an emission maximum around 950 nm indicating efficient SI calculations employing INDO, CNDO, and PPP methods on the singlet- and triplet-stateenergy levels are in excellent agreement with the experimentally observed ones. An experimental value of -700 cm-l was obtained for the lowest singlet-lowest triplet splitting. Laser flash photolysis in benzene produced a triplet transient with the difference absorption spectrum having maxima at 440 and 600 nm. The lifetime of the triplet transient is 100 ns. The triplet transient is capable of hydrogen abstraction, thus supporting the theoretical calculations which show the lowest triplet state to be of n,a* nature.

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Introduction The literature on anthraquinone (AQ) is extensive, but very little is known about the corresponding sulfur analogue. Monothioanthraquinone (TAQ), although known for a long time, was not synthesized in a stable state until recent1y.l Several unsuccessful early attempts were A simple synthesis of monothioanthraquinone was reported by Raaschl in 1979. TAQ was obtained as green crystals, in striking contrast to the pale yellow anthraquinone. For simple p-quinones (no thiocarbonyl groups), the most important absorption band from the point of view of determining photoreactivity is the one at the longest wavelength and that lies in the region of 400-450 nm (e of 20-100). This band is or has a* singlet-singlet t r a n ~ i t i o n . ~ been assigned as due to an n Fluorescence does not commonly occur in such paraquinones. Almost complete intersystem crossing takes place from the lowest n,?r* single state ultimately to a lowest n,a* triplet state from which phosphorescence occurs.s When viewed with carbonyl compounds, many of the photophysical and photochemical properties of thiocarbonyl compounds are quite different. Because of the relatively low ionization energy

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(1) Raasch, M. S. J. Org. Chem. 1979, 44, 632. (2) Zincke, T.; Glahn, W. Ber. Drsch. Chem. Ges. 1907, 40, 3039. (3) Stevenson, H.A.; Smiles, S. J . Chem. SOC.1930, 1740. (4) Bruce, J. M. In Chemisrry of Quinonoid Compounds; Patai, S., Ed.; Wiley: New York, 1974; Chapter 9, pp 465-538. ( 5 ) Steer, R. P. Rev. Chem. Intermed. 1981, 4 , 1.

of the nonbonding electron in the 3p orbital of the sulfur atom, the lowest lying orbitally forbidden (n,?r*) states are substantially red-shifted in thioketones.6 Thiocarbonyls have large S2-S1 electronic energy gaps, and some of the thiocarbonyls (xanthiones for examples) fluoresce and react chemically from excited states other than S1 (thiobenzoyl derivatives of aromatic hydrocarbons having H atoms in the periposition'). Strong spin-orbit coupling leads to unusual physical and dynamic properties of their triplet states. Thiocarbonyls are also examples of a rare class of compounds which phosphoresce in fluid solution at room temperature! In view of the striking differences in the photobehavior between carbonyl and thiocarbonyl compounds, TAQ-a molecule having both C=O and C-S groups-offers interesting possibilities for photophysical and photochemical studies. The absorption spectrum of AQ shows a strong absorption band at 325 nm and very weak bands at -375 and 405 nm (Figure 1, curve b). The weak bands originate from excitation to a (n,x*) state, and the Corresponding n,a* triplet state is responsible for photoreactions involving hydrogen abstraction.8 The longest wavelength band in TAQ is at 695 nm (see later discussion). AQ does not fluoresce, but strong phosphorescence was detected at 77 K.9 A triplet intersystem crossing yield of 1 was r e p ~ r t e d . ~

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(6) De Mayo, P. Arc. Chem. Res. 1976, 9, 52. (7) Lapouyade, R.;de Mayo, P. Can. J. Chem. 1972, 50, 4068. (8) (a) Hulme, B. E.; Land, E.-J.; Phillips, G. 0.J . Chem. SOC.,Faraday Trans. 2 1972,68,2003, 1992. (b) Hamocnoue, K.; Kajiwara, Y.; Miyake, T.;Nakayama, T.; Hirase, S.; Teranishi, H. Chem. Phys. Lett. 1983,94, 276.

0022-3654f 87 12091-6606%01.50/0 , 0 1987 American Chemical Society I

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The Journal of Physical Chemistry, Vol. 91, No. 27, 1987 6607

Monothioanthraquinone TABLE I: Calculated and Observed Sn compd TAQ

AQb

transition to 'Akw*) 'A2(no,a*) 'Al(a,a*) 'Bl(a,r*) 'A,(*,**) 'A,(r,a*) 'Bl(a,r*)

'Blg(n,a*) 'A,Sn,a*) 'B3,(a,r*) 'Blu(a,a*) 'B3"(r,r*)

E, cm-'

27433 28953 30777 29761 42567

31 012 35376 41452

-.

S. Transition Energies of TAQ and AQ" PPP INDO/S A, nm V, E, cm-' A, nm V, 13374 748 (0.000)

3645 345 325 251.5 235

322.5 282.5 241

(0.500) (0.297) (0.459) (0.600) (0.214)

22408 29677 31727 33382 40040 40682

446 337 315 299.5 250 246

(0.000) (0.340) (0.219) (0.239) (0.123) (0.49)

(0.260) (0.689) (0.910)

23128 23374 34589 41455 43564

432 428 289 241 229.5

(0.000) (0.000) (0.110) (0.397) (1.104)

observed polarzn

z

M-I cm-'

E, cm-' 14388

A, nm 695

log c 1.699

29940

'334

4.140

13803

37000

270

4.41

25 703

24690b 26660b 31453b 37099b 40325b

405 375 318 269 248

1.9 2.06 3.53 4.12 4.58

79 114 3 388 13182 38018

e,

50

x z z X

x z z

"The forbidden a,a*transitions are omitted. bAll experimental data on A 0 are from ref 17.

Transient spectra produced by laser flash photolysis and pulse radiolysis showed that the transient readily abstracted hydrogen from 2-propan01.~~Oxygen quenching was not total since the triplet transient was short-lived (200 ns). In view of the significant differences in absorption between AQ and TAQ and the lack of any photophysical or photochemical data on TAQ, we decided to carefully examine TAQ. In this publication, we report for the first time the results of photophysical and photochemical studies made on TAQ involving (1) transients from laser flash photolysis, (2) steady-state emission and emission lifetimes, (3) state assignments, and (4)theoretical calculations and their comparison with experimental results. To our knowledge, apart from the aliphatic cyclobutane keto thione,I0 TAQ is the first example of an aromatic compound having both C=S and C=O groups on which systematic photophysical and photochemical studies are attempted.

Experimental Section The monothioanthraquinone was synthesized and purified by the procedure given by Raasch.' The nanosecond laser flash experiments were carried out with the third harmonic (A = 355 nm) generated from a mode-locked Nd:YAG laser (200 ps, full width at half-maximum), (fwhm), 13 mJ). The detailed description of the laser setup is given elsewhere.]' The risetime of the detection system (photomultiplier tube and digitizer) was 2 ns. The steady-state phosphorescence measurements were done on a homemade system equipped with a liquid nitrogen cooled germanium-diode detector. The excitation source was 365-nm light from a high-pressure mercury lamp (150 W). Molecular orbital calculations have been performed in the r-electron approximation of Pariser, Parr, and PopleI2with a singly excited CI. The parameters for the carbon and oxygen atoms were taken as proposed by Hinze and JaffeI3 and by Fabiani4 for the sulfur atom. The two-center electron repulsion integrals were estimated by the use of the Mataga-NishimotoI5 approximation. Calculations of the intermediate neglect of differential overlap (INDO) type16 were performed using the INDO/S-CI model.'73'8 The configuration interaction (CI) consisted of 196 selected single excitations. For the triplet calculation, the CNDO/S method was e m p l ~ y e d . 'The ~ ~ ~two-center ~ repulsion integrals were estimated

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(9) (a) Wilkinson, F. J . Phys. Chem. 1962, 66, 2569. (b) Tickle, K.; Wilkinson, F. Trans. Faraday SOC.1965, 61, 1981. (10) Bhattacharya, K.; Das, P. K.; NageshwaraRao, B.; Ramamurthy, V. J. Photochem. 1986, 32, 33 1. (11) Lenoble, C.; Becker, R. S. J. Photochem. 1986, 33, 187. (12) (a) Pariser, R.; Parr, R. G. J. Chem. Phys. 1953, 21, 769. (b) Pople, J. A. Trans. Faraday SOC.1953, 49, 1375. (13) Hinze, J.: Jaffe, M. H. J . Am. Chem. SOC.1962, 84, 540. (14) Fabian, J. Theor. Chim. Acta 1968, It,200. (15) Nishimoto, K.; Mataga, N. Z . Phys. Chem. (Munich) 1957, 12, 355; 1958, 13, 140. (16) Kuroi, T.; Y . Gondo, Res. Bull. Fac. Educ., Oita Univ., Nut. Sei. 1971, 4, 9-16. (17) Ridley, J. E.; Zerner, M. C. Theor. Chim. Acta 1973, 32, 11 1. (18) Ridley, J. E.; Zerner, M. C. Theor. Chim. Acta 1976, 42, 223. (19) Pople, J. A.; Segal, G. A. J. Chem. Phys. 1965, 44, 3289. (20) Del Benc, J.; Jaffe, H. H. J . Chem. Phys. 1968, 48, 1807.

3 600

1

2 290

I

,

j,

I

:_jl 't

700

800

l'\cl

\

'--,

350

-- --

410

WAVELENGTH

470

NM

Figure 1. (a) Absorption spectrum of TAQ in benzene (-). (b) Absorption spectrum of AQ in benzene (-- -). The insert is the absorption spectrum of TAQ in benzene at longer wavelengths. The thick vertical bars are the values for singlet absorption of TAQ obtained from PPP theoretical calculations. The dashed vertical bars are the corresponding value for AQ. In addition, the vertical bars with an asterisk correspond to the n , r * transition as calculated by the INDO/S method.

by the use of the Pariser-Parrz' approximation for the triplet calculation (INDO/S or CNDO/S). The geometry of TAQ was taken to be identical with that of AQ, the only difference being the C=!3 bond length, which was taken to be 1.67 A?' All valence angles were chosen to be 120". 0 1.1111

TAQ

Results and Discussion Figure 1, curve a, shows the absorption of TAQ, as well as AQ, curve b, for comparison. Table I gives the results of calculations of the energies, intensities, and nature of the transitions by the PPP and INDO/S methods for both TAQ and AQ. For comparison, experimentally observed transition energies and oscillator (21) Pariser, R. J . Chem. Phys. 1952, 20, 1499. (22) Sutton, L. E., Ed. Tables of Interatomic Distances and Configuration in Molecules and Ions; The Chemical Society: Burlington House, London,

1958.

Natarajan et al.

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TABLE II: Calculated Triplet Enemy Levels for AQ and TAQ AQ INDO/S state E, cm-' 'B,.(n,r*) 'A&,**) 'BIu(r,r*) 3B2g(r,~*)

28 170 29 645 30606 30 122

CNDO/S state E, cm-I 3Bl,(n,r*) 23974 )AJn,r*) 24 398 3 B l u ( r , r * ) 26 383 3 B 2 , ( ~ , ~ * ) 26709

obsd' state E, cm-'

3(n,r*)

21 978

"0-0 band of phosphorescence spectrum in 3MP at 77 K (ref 6b)

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strengths are also given in Table I. In the case of AQ, the bands at 405 and 375 nm have been assigned as n a* transition^.^^ The remaining bands at higher energies were assigned as a a* transition^.^^ Our calculations (Table I) clearly assign the transitions of AQ in a manner parallel to those given in the literature. In the case of TAQ, on the basis of the experimentally observed low intensity ( 6 = 50) of the 695-nm band and the n,a* state assignment by theory for a long-wavelength transition near this wavelength at 748 nm (Table I), we assign the 695-nm transition a* type. This transition would have the n orbital origin as n on sulfur of the C=S group. A second n a* transition is predicted by theory to be near 446 nm. This transition is not clearly observed experimentally but may correspond to the shoulder near 400 nm seen on the long-wavelength side of the band with a maximum near 334 nm (Figure 1, curve a). Such a transition would be expected where the n orbital origin would be on 0 of the C=O group. Given the difference expected for the electronegativity of oxygen and sulfur, the n a* transition associated with the C=O group would be expected to be at considerably higher energy than that associated with the C=S group. Other bands at 334 and 270 nm are assigned as a a* type transitions based on both their intensity and the theoretically predicted nature (of 1~ a* type). The calculated a,a*transitions based on the PPP method are shown in Figure 1 under the absorption spectra of TAQ on A Q where the height of the bars corresponds to the relative intensity of each transition. The observed absorption band for TAQ with a maximum at 334 nm (29 940 cm-I, t = 14 000) may be interpreted as actually being composed of three allowed a,a* transitions of different polarizations of A,, B1, and A I symmetry based on calculations (see Table I). In the same spectral region (33 000-25 000 cm-I), AQ, based on calculations, shows only one allowed *,a* transition, and only one is seen experimentally a t 31 453 cm-I (see Table I). Figure 2A shows the difference (transient) absorption spectrum in the range 360-760 nm, 10 ns after the laser flash (excitation at 335 nm, 200-ps pulse, -10 mJ) in benzene. This spectrum contains two major peaks a t 440 and 600 nm with 440-nm maximum having the greatest intensity. The negative absorbance in the region of 360-380 nm is observed because of ground-state depletion in the spectral region of So S, absorption. The transient spectrum may be assigned as belonging to that of the TAQ triplet on the basis of the lifetime of 100 ns and the substantial quenching (- 60%) by oxygen. Moreover importantly, the addition of @carotene to TAQ in benzene led to the observation of the triplet transient absorbance spectrum (AOD) of &carotene resulting from energy transfer from the triplet state of TAQ to 0-carotene (no direct excitation of the @-carotenetriplet occurred). The lifetimes of the decay at 440 and 600 nm were the same and equal to 100 ns; also, oxygen quenching was the same for both spectral regions. The combination of these results makes it clear that the absorptions in both spectral regions are associated with triplet-triplet absorption originating from the TI state of TAQ. Also, the triplet decay and corresponding ground-state recovery resulted in a final AOD of zero in all spectral regions indicating only a photophysical process exists in TAQ; that is, no photochemical H atom abstraction occurred in benzene. By comparison, the AOD spectrum of AQ showed an intense

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TAQ INDO/S CNDO/S state E, cm-' state E, cm-' 'A2(ns,r*) 13596 3A2(ns,r*) 11 966 3 A I ( ~ , s * ) 14 390 3 A 1 ( ~ , ~ * ) 15 374 3A2(no,r*) 23 523 3A2(no,r*) 28 374 3Bl(r,r*) 25 521 3B1(r,r*) 28 800

bO-O band of phosphorescence spectrum in benzene at room temperature. 0.1 1 I

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(23) Tushishvili, L. Sh.; Shcheglova, N. A.; Shigorin, D. N.; Dokurikhin, N. S . Russ. J. Phys. Chem. (Engl. Transl.) 1969, 43, 542.

obsdb state E, cm-I 3(n,r*) 12 195

a

$0 WAVELENGTH NM

Figure 2. (A) Difference absorption spectrum of TAQ in benzene ob= 355 nm. (B) Difference tained by laser flash photolysis. hexcitation absorption spectrum of the TAQH radical produced by the addition of = 355 nm. 2-propanol to TAQ in benzene. XSXELtatlOn

maximum at 370 nm with considerably intense peaks at 460 and 550 nm.* (The lifetime of the AQ triplet was of the order of 200 ns.) Table I1 summarizes the results obtained for the calculated triplet energy levels for AQ and TAQ. Both CNDO/S and INDO/S methods were used and compared for the calculations. (The CNDO/S method often gives better results for triplet-state energy levels.) Both calculations give identical results for the state ordering and state assignment of the triplet excited states of AQ and TAQ. The lowest triplet state is found to be of n,a* character for both AQ and TAQ by CNDO/S and INDO/S methods. This is in agreement with the observed hydrogen abstraction (from 2-propanol) by the lowest triplet state of AQ and TAQ (by transient absorption spectroscopy); see later discussion. The calculated energy for the lowest triplet states of AQ and TAQ agrees well with the experimental values except for the INDO/S calculated triplet energy level of AQ which is calculated as -6000 cm-' too high in energy. However, by the CNDO/S method, it is found to be in agreement with the experimental observation that the lowest triplet state of TAQ is -10000 cm-' (28.6 kcal/mol) lower in energy than the lowest triplet state of AQ. It is possible to interpret the maximum at 600 nm observed in the T-T transient spectrum (Figure 2A) based on our triplet-state energy level calculations. The lowest triplet state for TAQ is a 'A2(n,?r*) state. This state is estimated to be approximately 80% pure configuration representing the excitation of an electron from the lone-pair orbital of sulfur (ns) to the lowest unoccupied MO (a*).The other contributions to the state are excitation from the ns orbital to higher unoccupied a MO's. The T, triplet state is a 3Al(r,a*) state located -3400 cm-I above the lowest triplet state TI. T3 is a 3A2(n,a*) state where n represents a lone-pair orbital of the oxygen atom. the two lowest 3(n,7r*) states (3(ns,a*) and 3(n,,,a*)) are separated by 16 300 cm-' ( 600 nm) or 46.7 kcal/mol. Bearing in mind that the symmetry-allowed transition of lowest energy from TI to upper excited states is the T, 3(ns,a*) T33(n,,,a*)transition, this transition could very well correspond

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Monothioanthraquinone

The Journal of Physical Chemistry, Vol. 91, No. 27, 1987 6609

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1 I

720

800

I

900

I

1000 1100 1200

1300 1400

WAVELENGTH N M

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Figure 3. (a) Phosphorescence emission spectrum of TAQ in N,-saturated benzene. (b) 'As %, emission of oxygen excited by energy transer from triplet TAQ.

The energy corresponding to the 0 4 band of the phosphorescence of TAQ is 12 200 cm-'. Based on the behavior of thiobenzophenone and the comparable energy of the lowest triplets of thiobenzophenone and TAQ, the probability of H abstraction by the low-energy triplet of TAQ is not surprising. N o fluorescence of TAQ was detected in benzene at room temperature by exciting in the region of SIor S2. However, we were able to observe strong phosphorescence with a 0-0 band at approximately 820 nm (12 195 cm-I) at room temperature in benzene (Figure 3). By bubbling oxygen in the benzene solution of TAQ, we also observed the partial (-70%) quenching of phosphorescence and the simultaneous rise of the emission of singlet oxygen (IAJ (Figure 3) formed by energy transfer from triplet TAQ. The observations of no fluorescence and strong phosphorescence imply a high triplet intersystem quantum yield. In this respect, TAQ is very similar to AQ. The singlet-triplet splitting for TAQ is calculated to be very low, -700 cm-I based on estimations of the 0-0 band of S,(n-w*) and the 0-0 band of the phosphorescence spectrum of TAQ. This compares with 1400 cm-' obtained for AQ from delayed thermal fluorescence.26 A similar magnitude of decrease in the S-T zero-point energy difference was observed for thiob e n ~ o p h e n o n e(-~ ~1375 cm-') compared to benzophenone2* (2180 cm-I).

to the observed lowest T-T transition at 600 nm by the laser flash photolysis of TAQ in benzene. The lifetime of the TAQ triplet was independent of the initial TAQ concentration in the range of 5 X to 1 X M, implying the absence of any ground-state aggregation or selfM) reduced the quenching. Saturation with oxygen (7.25 X triplet lifetime to 40 ns, leading to a quenching constant of 2.0 X lo9 M-' s-l. This value compares with an oxygen quenching Acknowledgment. The laser flash experiments were performed rate constant of 1.5 X lo9 M-' s-l obtained for AQ.8 at the Center for Fast Kinetics Research (CFKR) at the University Addition of increasing concentrations of 2-propanol to TAQ of Texas at Austin, which is supported by N I H Grant RR-00886, in benzene led to an increase in the TAQ triplet decay rate the Biotechnology Branch of the Division of Research Resources, constant. We obtained a triplet decay rate constant of 3 X lo7 and the University of Texas. We are also grateful to Dr. Michael M-' s-I at a concentration of -1 M 2-propanol. (The decay A. Rodgers of CFKR for the use of a home-assembled phosconstant was 1 X lo7 s-l in pure benzene.) The AOD spectrum phorescence equipment. We also thank Dr. Michael Zerner at obtained in the presence of 2-propanol is shown in Figure 2B. We the University of Florida at Gainesville for providing us with assign this AOD spectrum to be that of the slow-decaying TAQH theoretical programs for computer calculations. radical. The n,** triplet owing to its biradical nature is known to abstract hydrogen from 2-pr0panol.~In our case, it is likely Registry No. TAQ, 68629-85-6;TAQH radical, 1 1 1005-84-6;2propanol, 15552-77-9. that the radical is centered on the sulfur of TAQ as the lowest triplet state has a configurational origin involving the n-orbital origin on sulfur of the C=S group (see discussion above). It was (24) Formosinho, S.J. J. Chem. SOC.,Faraday Trans. 2 1976, 72, 1332. reported for thiobenzophenone that the 0-0 band of phos(25) Kito, N.; Ohno, A. Chem. Commun. 1971, 1338. (26)Carlson, S.A.; Hercules, D. M. J . Am. Chem. SOC.1971, 93, 561 1. phorescence was located at 13 800 cm-I (40 kcal) and H ab(27)Blackwell, D.S. L.; Liao, C. C.; Loufty, R. 0.;de Mayo, P.; Paszyc, straction by this low-energy triplet from 2-propanol was compaS . Mol. Photochem. 1972, 4, 171. rable to that of the benzophenone triplet (23 800 cm-I, 68 kcal), (28) McGlynn, S. P.; Azumi, T.; Kinoshita, M. Molecular Spectroscopy implying a low activation energy for the abstraction p r o ~ e s s . * ~ ~ ~of ~the Triplet Srare; Prentice-Hall: Englewood Cliffs, NJ, 1969.

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