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Electronic spectra of 2-acetylanthracene
Volume 134, number 3
CHEMICAL PHYSICS LETTERS
27 February 1987
ELECTRONIC SPECTRA OF 2-ACETYLANTHRACENE V. SWAYAMBUNATHAN and E.C. LIM Chemistry Department, Wayne State University,Detroit, MI 48202, USA Received 2 I November 1986
The electronic spectrum of 2-acetylanthracene in a supersonic free jet reveals the existence of two rotational isomers with % 196 cm-‘difference between their S, origins. In low-temperature rigid glasses, 2-acetylanthracene forms stable dimers. The probable structure of this dimer is also briefly discussed.
1. Introduction 2-acetylanthracene (2-acan) is one of the carbonyl derivatives of anthracene in which the acetyl substituent occupies the least electron-rich position of the anthracene ring and also lies very close to the axis of the longitudinally polarized Lb transition. The acetyl substituent, when it occupies the 9-position of the anthracene ring, is prevented from lying coplanar with the aromatic ring in the ground electronic state due to severe per&planar repulsions. Our earlier studies have shown that electronic excitation leads to a geometry change from non-planar to a nearly coplanar structure in 9-acetylanthracene [ 1,2]. But molecular models show that at the 2-position, the acetyl substituent experiences negligible steric repulsion from the ring hydrogens and as a result, 2-acan has a nearly coplanar structure even in the ground electronic state. In this paper, we discuss the electronic spectra of this carbonyl anthracene in a nonpolar solvent at room temperature, in a supersonic free jet and also in a low-temperature rigid glass.
2. Experimental The fluorescence excitation spectrum of jet-cooled 2-acan was obtained with a continuous free-jet apparatus described earlier [ 3,4]. The sample vapor was seeded in z 200 Torr of argon and expanded into a vacuum chamber through a Pyrex nozzle whose one
end was tapered to produce a pinhole opening of ~200 pm. A Nd:YAG laser pumped dye laser (Quanta-Ray) in conjunction with a wavelength extension system (Quanta-Ray) was used as the excitation source. The spectrum was recorded by collecting fluorescence through a Corning 3-73 sharp cutoff filter. The fluorescence and excitation spectra of 2-acan in condensed phase were recorded using an Aminco SPF-500 spectrophotometer. A specially designed dewar was used for measurements at low temperatures. The fluorescence decays were measured using a cavity-dumped dye laser which was synchronously pumped by a mode-locked Nd:YAG laser (SpectraPhysics). The detection system was a time-correlated single-photon counting system. 2-acetylanthracene was synthesized according to the procedure of Hawkins [ 51. The method involves isomerization of 9-acetylanthracene in the presence of aluminium chloride to yield the desired product. The crude product was purified by several recrystallizations first from ethyl acetate and then from light petroleum (boiling point 80- 100 ’ C ) . The purity was determined by gas chromatography to be greater than 99%. Methylcyclohexane (MC & B spectroquality solvent) was used without further purification. It was, however, stored over molecular sieves (type 3A). 3. Results and discussion Fig. 1 shows the fluorescence excitation and dispersed fluorescence spectra of 2-acan in methylcy-
0 009-26 14/87/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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Volume 134, number 3
c
L 4-d-LI
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Fig. 1. Excitation and fluorescence spectra of 2-acetylanthracene (2.7 x 10-r M) in methylcyclohexane at room temperature.
clohexane at room temperature. The O-O bands in excitation and emission spectra are very nearly overlapping in position indicating the absence of substantial change in geometry on electronic excitation. But the excitation and fluorescence spectra do not exhibit mirror-image relationship and this can be attributed to the emergence of the longitudinally polarized ‘Lb transition, which is very weak in anthracene and 9-carbonyl-substituted anthracenes [ 1,2,4]. The IL,, transition becomes more intense and red-shifted in 2-acan because the substituent lies very close to the long axis of the molecule. Similar substituent effects are well known for naphthalene derivatives [ 61: the ‘L, band experiences large bathochromic and hyperchromic shifts from a substituent at the l-position, whereas the ‘Lb band experiences similar shifts from a substituent at the 2position of the naphthalene ring. The fluorescence excitation spectrum of 2-acan can be analyzed by dividing it into two regions (fig. 1). The bands in region I can be assigned to ‘Lb transition and those in region II can be assigned to ‘L, transition on the basis of the results of Tamaki [ 71. Tamaki studied the changes in the absorption spectra of 2-( substituted benzoyl) anthracenes in hexane and found that the bands in region I exhibit bathochromic and hyperchromic shifts on introducing electron-withdrawing groups into the para position of the phenyl ring, whereas the bands in region II remain largely unaffected by such changes in the substituent. Since the substituent lies close to the long axis, only the ‘Lb transition can be expected to be 256
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355 385 WAVELENGTW m-n
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Fig. 2. Fluorescence excitation spectrum of 2-acetylanthracene seeded in a supersonic expansion of argon ( z 200 Torr). Nozzle temperature z 150°C and the nozzle-to-laser distance zz 1.0 cm.
influenced by the changes in the substituent and therefore, the bands in regions I and II were assigned respectively to ‘L,, and ‘L, transitions. The absorption spectrum of 2-acan is similar to that of 2-benzoylanthracene in many respects and therefore, similar assignments are valid for 2-acan also [ 71. The assignment of the lowest energy emitting state to ‘Lb is also supported by a calculation of the radiative lifetime (r: ) of this molecule. By making use of the experimentally determined quantum yield (0.04) and fluorescence lifetime (1.5 ns) , it is easy to estimate rf” to be 37.5 ns. This value is more than twice the radiative lifetime (16.6 ns) of the ‘L, transition of anthracene [ 81. Fig. 2 shows the normalized fluorescence excitation spectrum of jet-cooled 2-acan. As expected from the near coplanarity of the molecule in the ground state, the spectrum shows a very strong O-Oband(A) located at 3853.1 A. This band can be readily assigned to the origin of the ‘Lb transition because it is redshifted relative to the S, origin of anthracene (36 10.8 A) by x 1742 cm- ‘. Such a large red-shift is not expected for the origin of the ‘L, transition in 2-acan because the acetyl substituent does not lie along the short axis of the molecule. Also the spectrum shows the absence of a long progression in any vibration indicating that there is no substantial change in the geometry of this molecule on electronic excitation. The two fairly low frequency bands located at 47 cm- ’ (B) and 127 cm- ’ (C) can be assigned respectively to -COCH3 and -CH3 torsion on the basis of
27 February 1987
CHEMICAL PHYSICS LETTERS
Volume 134, number 3
l#Jq jp-&_ -_ R=CH3
Fig. 3. The rotational isomers of 2-acetylanthracene.
comparison with the frequencies of similar vibrations in acetophenone [ 91. One of the most interesting features of the fluorescence excitation spectrum of jet-cooled 2-acan is the appearance of a fairly strong band located at = 196 cm- ’ (D) on the lower-energy side of the electronic origin. The relative intensity of this band was found to be almost invariant to changes in the carrier gas pressure and also the nature of the carrier gas. On the basis of this observation, it is highly unlikely that this band is a hot band, sequence band or that of a van der Waals complex formed between the carrier gas and the seeded molecule. It is, therefore, quite likely that this band represents the electronic origin of the second rotational isomer of 2-acan. Such an assignment is also supported by the appearance from this new origin of a band (E) which can be assigned to -CHs torsion ( x 127 cm-’ ). The two rotational isomers of 2-acan are shown in fig. 3. The existence of two rotational isomers with slightly different electronic origins has also been observed in the electronic spectra of jet-cooled P-naphthol and metasubstituted phenols [ lo]. We think the x 196 cm- ’ difference in the electronic origins of the two 2-acan isomers represents the change in the potential for the internal rotation of the -COCH., group on electronic excitation. The difference arises essentially due to different x-bond orders of the C l-C2 (0.80) and C2-C3 (0.40) bonds of the anthracene ring in the ground state. Using the results of a molecular mechanics study on 2-methylbutadiene done by Liljefors and Allinger [ 111, it is possible to predict that the more stable of the two isomers in the ground state will be the one in which the -CHJ group eclipses Cl (structure II) and not C3 of the anthracene ring system [ 121. Fig. 4 shows the fluorescence and excitation spectra of 2-acan in methylcyclohexane at 77 K. Also shown in the same figure are the room-temperature
:
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----______
600 widikLml
Fig. 4. Excitation and fluorescence spectra of 2-acetylanthracene in methylcyclohexane at room temperature (solid lines) and at 77 K (broken lines). The two spectra are shown separately so that their features can be seen clearly.
spectra. In rigid glass, the fluorescence and excitation spectra ( ‘h, region) are both red-shifted and also broader compared to the room-temperature spectra. These spectral features indicate the occurrence of aggregation in rigid glasses, leading probably to the formation of stable ground-state dimers of 2-acan. We think the formation of higher aggregates (e.g., trimers, tetramers, etc.) is highly unlikely due to the low concentration of the solute (=2.7x lop5 M at room temperature). The weak band at z 400 nm, corresponding to the O-O fluorescence band of the monomer at room temperature, suggests that the dimerization process may not be entirely complete, but a small amount of the monomer may still be present even at 77 K. The fluorescence decay curve of 2-acan is also slightly non-exponential at 77 K. The decay time of the major component is z 19 ns and the slight non-exponentiality may be due to the presence of the monomer. Although the dispersed emission spectrum of 2acan in rigid glass is broader and red-shifted compared to the room-temperature spectrum, it does not resemble. in any way the “excimer-type” emission observed for the sandwich dimers of anthracene and other 9-substituted anthracenes (e.g., 9-methyl-, 9chloro- and 9-bromo-anthracenes) in rigid glasses by Chandross et al. [ 131. Also the x 19 ns fluorescence lifetime measured for 2-acan dimer is much shorter compared to the lifetimes measured for the sandwich dimers of the abovementioned compounds [ 141 (anthracene: 200 ns; 9-methylanthracene: 220 ns; 9chloroanthracene: 180 ns). On the basis of these experimental observations, it is highly unlikely that the 2-acan dimer has a structure similar to that proposed for the sandwich dimers of the 9-substituted 257
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anthracenes mentioned above, viz., symmetrical tram sandwich configuration. The most probable structure of the 2-acan dimer may then be something similar to that proposed for the stable dimer of anthracene [ 15,161. In this structure, the long axes of the two anthracene rings are parallel or nearly parallel, while the angle between the short in-plane axes is = 60” with the acetyl groups of the two molecules pointing in opposite directions, viz., trans structure. Further studies are currently in progress to understand the dynamics of this aggregation process and also the structure of this dimer in low-temperature solvent matrices of different rigidity. Acknowledgement
This work was supported by the National Science Foundation. VS is thankful to Lubrizol Corporation and Wayne State University Graduate School for the award of a predoctoral fellowship. We are also thankful to Professor N.L. Allinger for helpful comments. References [ 1] V. Swayambunathan and EC. Lim, J. Phys. Chem. 89 (1985) 3960.
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[2] V. Swayambunathan and E.C. Lim, J. Phys. Chem., submitted for publication. [3] H. Saigusaand E.C. Lim, J. Chem. Phys. 78 (1983) 91. [4] V. Swayambunathan and EC. Lim, J. Phys. Chem., submitted for publication. [5] E.G.E. Hawkins, J. Chem. Sot. (1957) 3858. [6] H.H. Jaffe and M. Orchin, Theory and applications of ultraviolet spectroscopy (Wiley, New York, 1962) p. 242. [ 71 T. Tamaki, Bull. Chem. Sot. Japan 5 1 (1978) 2817. [8] LB. Berlman, Handbook of fluorescence spectra of aromatic molecules (Academic Press, New York, 1965) p. 356. [ 91 A. Duben, L. Goodman and M. Koyanagi, in Excited states, Vol. 1, ed. E.C. Lim (Academic Press, New York, 1974) p. 295. [ lo] A. Oikawa, H. Abe, N. Mikami and M. Ito, J. Phys. Chem. 88 (1984) 5180. [ 111 T. Liljefors and N.L. Allinger, J. Comput. Chem. 6 (1985) 478. [ 121 N.L. Allinger, private communication. [ 131 E.A. Chandross and J. Ferguson, J. Chem. Phys. 45 (1966) 3554. [ 141 J. Ferguson, A.W.H. Mau and J.M. Morris, Australian J. Chem. 26 (1973) 91. [ 151 E.A. Chandross, J. Ferguson and E.G. McRae, J. Chem. Phys. 45 (1966) 3546. [ 161 J. Ferguson, A.W.H. Mau and J.M. Morris, Australian J. Chem. 26 (1973) 103.
CHEMICAL PHYSICS LETTERS
27 February 1987
ELECTRONIC SPECTRA OF 2-ACETYLANTHRACENE V. SWAYAMBUNATHAN and E.C. LIM Chemistry Department, Wayne State University,Detroit, MI 48202, USA Received 2 I November 1986
The electronic spectrum of 2-acetylanthracene in a supersonic free jet reveals the existence of two rotational isomers with % 196 cm-‘difference between their S, origins. In low-temperature rigid glasses, 2-acetylanthracene forms stable dimers. The probable structure of this dimer is also briefly discussed.
1. Introduction 2-acetylanthracene (2-acan) is one of the carbonyl derivatives of anthracene in which the acetyl substituent occupies the least electron-rich position of the anthracene ring and also lies very close to the axis of the longitudinally polarized Lb transition. The acetyl substituent, when it occupies the 9-position of the anthracene ring, is prevented from lying coplanar with the aromatic ring in the ground electronic state due to severe per&planar repulsions. Our earlier studies have shown that electronic excitation leads to a geometry change from non-planar to a nearly coplanar structure in 9-acetylanthracene [ 1,2]. But molecular models show that at the 2-position, the acetyl substituent experiences negligible steric repulsion from the ring hydrogens and as a result, 2-acan has a nearly coplanar structure even in the ground electronic state. In this paper, we discuss the electronic spectra of this carbonyl anthracene in a nonpolar solvent at room temperature, in a supersonic free jet and also in a low-temperature rigid glass.
2. Experimental The fluorescence excitation spectrum of jet-cooled 2-acan was obtained with a continuous free-jet apparatus described earlier [ 3,4]. The sample vapor was seeded in z 200 Torr of argon and expanded into a vacuum chamber through a Pyrex nozzle whose one
end was tapered to produce a pinhole opening of ~200 pm. A Nd:YAG laser pumped dye laser (Quanta-Ray) in conjunction with a wavelength extension system (Quanta-Ray) was used as the excitation source. The spectrum was recorded by collecting fluorescence through a Corning 3-73 sharp cutoff filter. The fluorescence and excitation spectra of 2-acan in condensed phase were recorded using an Aminco SPF-500 spectrophotometer. A specially designed dewar was used for measurements at low temperatures. The fluorescence decays were measured using a cavity-dumped dye laser which was synchronously pumped by a mode-locked Nd:YAG laser (SpectraPhysics). The detection system was a time-correlated single-photon counting system. 2-acetylanthracene was synthesized according to the procedure of Hawkins [ 51. The method involves isomerization of 9-acetylanthracene in the presence of aluminium chloride to yield the desired product. The crude product was purified by several recrystallizations first from ethyl acetate and then from light petroleum (boiling point 80- 100 ’ C ) . The purity was determined by gas chromatography to be greater than 99%. Methylcyclohexane (MC & B spectroquality solvent) was used without further purification. It was, however, stored over molecular sieves (type 3A). 3. Results and discussion Fig. 1 shows the fluorescence excitation and dispersed fluorescence spectra of 2-acan in methylcy-
0 009-26 14/87/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
255
27 February 1981
CHEMICAL PHYSICS LETTERS
Volume 134, number 3
c
L 4-d-LI
275
375
475
575
Fig. 1. Excitation and fluorescence spectra of 2-acetylanthracene (2.7 x 10-r M) in methylcyclohexane at room temperature.
clohexane at room temperature. The O-O bands in excitation and emission spectra are very nearly overlapping in position indicating the absence of substantial change in geometry on electronic excitation. But the excitation and fluorescence spectra do not exhibit mirror-image relationship and this can be attributed to the emergence of the longitudinally polarized ‘Lb transition, which is very weak in anthracene and 9-carbonyl-substituted anthracenes [ 1,2,4]. The IL,, transition becomes more intense and red-shifted in 2-acan because the substituent lies very close to the long axis of the molecule. Similar substituent effects are well known for naphthalene derivatives [ 61: the ‘L, band experiences large bathochromic and hyperchromic shifts from a substituent at the l-position, whereas the ‘Lb band experiences similar shifts from a substituent at the 2position of the naphthalene ring. The fluorescence excitation spectrum of 2-acan can be analyzed by dividing it into two regions (fig. 1). The bands in region I can be assigned to ‘Lb transition and those in region II can be assigned to ‘L, transition on the basis of the results of Tamaki [ 71. Tamaki studied the changes in the absorption spectra of 2-( substituted benzoyl) anthracenes in hexane and found that the bands in region I exhibit bathochromic and hyperchromic shifts on introducing electron-withdrawing groups into the para position of the phenyl ring, whereas the bands in region II remain largely unaffected by such changes in the substituent. Since the substituent lies close to the long axis, only the ‘Lb transition can be expected to be 256
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391
Fig. 2. Fluorescence excitation spectrum of 2-acetylanthracene seeded in a supersonic expansion of argon ( z 200 Torr). Nozzle temperature z 150°C and the nozzle-to-laser distance zz 1.0 cm.
influenced by the changes in the substituent and therefore, the bands in regions I and II were assigned respectively to ‘L,, and ‘L, transitions. The absorption spectrum of 2-acan is similar to that of 2-benzoylanthracene in many respects and therefore, similar assignments are valid for 2-acan also [ 71. The assignment of the lowest energy emitting state to ‘Lb is also supported by a calculation of the radiative lifetime (r: ) of this molecule. By making use of the experimentally determined quantum yield (0.04) and fluorescence lifetime (1.5 ns) , it is easy to estimate rf” to be 37.5 ns. This value is more than twice the radiative lifetime (16.6 ns) of the ‘L, transition of anthracene [ 81. Fig. 2 shows the normalized fluorescence excitation spectrum of jet-cooled 2-acan. As expected from the near coplanarity of the molecule in the ground state, the spectrum shows a very strong O-Oband(A) located at 3853.1 A. This band can be readily assigned to the origin of the ‘Lb transition because it is redshifted relative to the S, origin of anthracene (36 10.8 A) by x 1742 cm- ‘. Such a large red-shift is not expected for the origin of the ‘L, transition in 2-acan because the acetyl substituent does not lie along the short axis of the molecule. Also the spectrum shows the absence of a long progression in any vibration indicating that there is no substantial change in the geometry of this molecule on electronic excitation. The two fairly low frequency bands located at 47 cm- ’ (B) and 127 cm- ’ (C) can be assigned respectively to -COCH3 and -CH3 torsion on the basis of
27 February 1987
CHEMICAL PHYSICS LETTERS
Volume 134, number 3
l#Jq jp-&_ -_ R=CH3
Fig. 3. The rotational isomers of 2-acetylanthracene.
comparison with the frequencies of similar vibrations in acetophenone [ 91. One of the most interesting features of the fluorescence excitation spectrum of jet-cooled 2-acan is the appearance of a fairly strong band located at = 196 cm- ’ (D) on the lower-energy side of the electronic origin. The relative intensity of this band was found to be almost invariant to changes in the carrier gas pressure and also the nature of the carrier gas. On the basis of this observation, it is highly unlikely that this band is a hot band, sequence band or that of a van der Waals complex formed between the carrier gas and the seeded molecule. It is, therefore, quite likely that this band represents the electronic origin of the second rotational isomer of 2-acan. Such an assignment is also supported by the appearance from this new origin of a band (E) which can be assigned to -CHs torsion ( x 127 cm-’ ). The two rotational isomers of 2-acan are shown in fig. 3. The existence of two rotational isomers with slightly different electronic origins has also been observed in the electronic spectra of jet-cooled P-naphthol and metasubstituted phenols [ lo]. We think the x 196 cm- ’ difference in the electronic origins of the two 2-acan isomers represents the change in the potential for the internal rotation of the -COCH., group on electronic excitation. The difference arises essentially due to different x-bond orders of the C l-C2 (0.80) and C2-C3 (0.40) bonds of the anthracene ring in the ground state. Using the results of a molecular mechanics study on 2-methylbutadiene done by Liljefors and Allinger [ 111, it is possible to predict that the more stable of the two isomers in the ground state will be the one in which the -CHJ group eclipses Cl (structure II) and not C3 of the anthracene ring system [ 121. Fig. 4 shows the fluorescence and excitation spectra of 2-acan in methylcyclohexane at 77 K. Also shown in the same figure are the room-temperature
:
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----______
600 widikLml
Fig. 4. Excitation and fluorescence spectra of 2-acetylanthracene in methylcyclohexane at room temperature (solid lines) and at 77 K (broken lines). The two spectra are shown separately so that their features can be seen clearly.
spectra. In rigid glass, the fluorescence and excitation spectra ( ‘h, region) are both red-shifted and also broader compared to the room-temperature spectra. These spectral features indicate the occurrence of aggregation in rigid glasses, leading probably to the formation of stable ground-state dimers of 2-acan. We think the formation of higher aggregates (e.g., trimers, tetramers, etc.) is highly unlikely due to the low concentration of the solute (=2.7x lop5 M at room temperature). The weak band at z 400 nm, corresponding to the O-O fluorescence band of the monomer at room temperature, suggests that the dimerization process may not be entirely complete, but a small amount of the monomer may still be present even at 77 K. The fluorescence decay curve of 2-acan is also slightly non-exponential at 77 K. The decay time of the major component is z 19 ns and the slight non-exponentiality may be due to the presence of the monomer. Although the dispersed emission spectrum of 2acan in rigid glass is broader and red-shifted compared to the room-temperature spectrum, it does not resemble. in any way the “excimer-type” emission observed for the sandwich dimers of anthracene and other 9-substituted anthracenes (e.g., 9-methyl-, 9chloro- and 9-bromo-anthracenes) in rigid glasses by Chandross et al. [ 131. Also the x 19 ns fluorescence lifetime measured for 2-acan dimer is much shorter compared to the lifetimes measured for the sandwich dimers of the abovementioned compounds [ 141 (anthracene: 200 ns; 9-methylanthracene: 220 ns; 9chloroanthracene: 180 ns). On the basis of these experimental observations, it is highly unlikely that the 2-acan dimer has a structure similar to that proposed for the sandwich dimers of the 9-substituted 257
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anthracenes mentioned above, viz., symmetrical tram sandwich configuration. The most probable structure of the 2-acan dimer may then be something similar to that proposed for the stable dimer of anthracene [ 15,161. In this structure, the long axes of the two anthracene rings are parallel or nearly parallel, while the angle between the short in-plane axes is = 60” with the acetyl groups of the two molecules pointing in opposite directions, viz., trans structure. Further studies are currently in progress to understand the dynamics of this aggregation process and also the structure of this dimer in low-temperature solvent matrices of different rigidity. Acknowledgement
This work was supported by the National Science Foundation. VS is thankful to Lubrizol Corporation and Wayne State University Graduate School for the award of a predoctoral fellowship. We are also thankful to Professor N.L. Allinger for helpful comments. References [ 1] V. Swayambunathan and EC. Lim, J. Phys. Chem. 89 (1985) 3960.
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[2] V. Swayambunathan and E.C. Lim, J. Phys. Chem., submitted for publication. [3] H. Saigusaand E.C. Lim, J. Chem. Phys. 78 (1983) 91. [4] V. Swayambunathan and EC. Lim, J. Phys. Chem., submitted for publication. [5] E.G.E. Hawkins, J. Chem. Sot. (1957) 3858. [6] H.H. Jaffe and M. Orchin, Theory and applications of ultraviolet spectroscopy (Wiley, New York, 1962) p. 242. [ 71 T. Tamaki, Bull. Chem. Sot. Japan 5 1 (1978) 2817. [8] LB. Berlman, Handbook of fluorescence spectra of aromatic molecules (Academic Press, New York, 1965) p. 356. [ 91 A. Duben, L. Goodman and M. Koyanagi, in Excited states, Vol. 1, ed. E.C. Lim (Academic Press, New York, 1974) p. 295. [ lo] A. Oikawa, H. Abe, N. Mikami and M. Ito, J. Phys. Chem. 88 (1984) 5180. [ 111 T. Liljefors and N.L. Allinger, J. Comput. Chem. 6 (1985) 478. [ 121 N.L. Allinger, private communication. [ 131 E.A. Chandross and J. Ferguson, J. Chem. Phys. 45 (1966) 3554. [ 141 J. Ferguson, A.W.H. Mau and J.M. Morris, Australian J. Chem. 26 (1973) 91. [ 151 E.A. Chandross, J. Ferguson and E.G. McRae, J. Chem. Phys. 45 (1966) 3546. [ 161 J. Ferguson, A.W.H. Mau and J.M. Morris, Australian J. Chem. 26 (1973) 103.