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Spectichimiea Acta, Vol. 24A, pp. 31 to 39. Pergamon Preen 1868.Printed in Northern Ireland Influence of high pressures and low temperatures on the absorption spectra of a, a-diphenyl-p-picrylhydrazyl H. W. OFFEN University of California, Santa Barbara, California and K. F. STERRETT Northrop Corporation, Hawthorne, California (Received 24 April 1967) Abstract-The absorption spectrum of a,a-diphenyl-&picrylhydrazyl (DPPH) has been studied in the O-40 kbar range at 295”K, 193°K and 77°K. The influence of these environmental perturbations was investigated for DPPH crystals dispersed in a sodium chloride matrix and for DPPH monomolecularly dispersed in cellulose acetate filma. Near 30 kbar the broad absorption in the visible spectrum of isolated DPPH, attributed to orbital promotion of the odd electron, becomes broader and is displaced 300-600 cm-l (in the 295-77°K temperature range) toward longer wavelengths. For the crystalline material a small pressure dependence of the center of gravity of the visible band is observed. At the higher pressurestwo band peaks, separated by ~900 cm-l emerge from the nearly symmetric band. The second component manifests itself on the short wavelength side of the original, red-shifted peak. The ultraviolet absorption showed a comparable shift for DPPH and a larger shift for the corresponding parent hydrazine in plastics at relatively low pressures. The DPPH system exhibits some unusual environmental responses compared to other rr-systems. The crystal spectra suggest phase changes at higher pressures. INTRODUCTION THE molecule a, a-diphenyl-/?-picrylhydrazyl (DPPH) is a free radical which is stable at room temperature. Its stability and insensitivity to oxygen have made it the DPPH reference standard for electron spin resonance spectroscopy. Although its paramag- netic nature has been well-characterized [l, 21, the electronic spectrum has been virtually neglected. Intensity changes of the broad visible absorption band, which gives DPPH its characteristic deep-blue color, are used in solution kinetic studies and analytical determinations. Since these reactions involve the unpaired electron, the visible band can be attributed to the orbital promotion of the odd electron. Most orbital calculations based on simplified views of its molecular structure have focused on the electronic ground state and the extent of the unpaired electron [l] N. W. LORD and S. M. BLINDER, J. Chem. Phg8.34, 1693 (1961). [2] T. H. BROWN,D. H. ANDERSON and H. S. GUTOWSKY, J. Chem. Php. 53, 720 (1960). 31

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Page 1: Influence of high pressures and low temperatures on the absorption spectra of α,α-diphenyl-β-picrylhydrazyl

Spectichimiea Acta, Vol. 24A, pp. 31 to 39. Pergamon Preen 1868. Printed in Northern Ireland

Influence of high pressures and low temperatures on the absorption spectra of a, a-diphenyl- p-picrylhydrazyl

H. W. OFFEN University of California, Santa Barbara, California

and

K. F. STERRETT Northrop Corporation, Hawthorne, California

(Received 24 April 1967)

Abstract-The absorption spectrum of a,a-diphenyl-&picrylhydrazyl (DPPH) has been studied in the O-40 kbar range at 295”K, 193°K and 77°K. The influence of these environmental perturbations was investigated for DPPH crystals dispersed in a sodium chloride matrix and for DPPH monomolecularly dispersed in cellulose acetate filma. Near 30 kbar the broad absorption in the visible spectrum of isolated DPPH, attributed to orbital promotion of the odd electron, becomes broader and is displaced 300-600 cm-l (in the 295-77°K temperature range) toward longer wavelengths. For the crystalline material a small pressure dependence of the center of gravity of the visible band is observed. At the higher pressures two band peaks, separated by ~900 cm-l emerge from the nearly symmetric band. The second component manifests itself on the short wavelength side of the original, red-shifted peak. The ultraviolet absorption showed a comparable shift for DPPH and a larger shift for the corresponding parent hydrazine in plastics at relatively low pressures. The DPPH system exhibits some unusual environmental responses compared to other rr-systems. The crystal spectra suggest phase changes at higher pressures.

INTRODUCTION

THE molecule a, a-diphenyl-/?-picrylhydrazyl (DPPH) is a free radical which is stable at room temperature. Its stability and insensitivity to oxygen have made it the

DPPH

reference standard for electron spin resonance spectroscopy. Although its paramag- netic nature has been well-characterized [l, 21, the electronic spectrum has been virtually neglected. Intensity changes of the broad visible absorption band, which gives DPPH its characteristic deep-blue color, are used in solution kinetic studies and analytical determinations. Since these reactions involve the unpaired electron, the visible band can be attributed to the orbital promotion of the odd electron. Most orbital calculations based on simplified views of its molecular structure have focused on the electronic ground state and the extent of the unpaired electron

[l] N. W. LORD and S. M. BLINDER, J. Chem. Phg8.34, 1693 (1961). [2] T. H. BROWN, D. H. ANDERSON and H. S. GUTOWSKY, J. Chem. Php. 53, 720 (1960).

31

Page 2: Influence of high pressures and low temperatures on the absorption spectra of α,α-diphenyl-β-picrylhydrazyl

32 H. W. OFFEN and K. F. STERRETT

delocalization [3]. Recently, WALTER [4] conducted an experimental and theoretical study of substituent effects on the spectra of several free radicals including DPPH.

The LCAO-MO calculations reproduce the directions of the spectral shift produced by various substituents on one phenyl ring. Detailed spectral predictions were not possible because the molecular structure was unknown until WILLIAMS [5] very

recently reported an X-ray diffraction study of DPPH crystals. It was concluded that the exceptional stability of this free radical arises primarily from the shielding of the hydrazyl backbone by surrounding parts of the molecule, and not extended conjugation as previously presumed [5].

The present work combines high pressure-low temperature spectroscopic tech- niques to elucidate the electronic structure of DPPH by noting the influence of envi- ronmental perturbation on the electronic absorption spectrum. The effects of high pressures on the electronic absorption spectra of other organic molecules in crystals [S-lo] and in polymer matrices [ 1 l-141 have been characterized to yield band shifts, broadening, and intensity changes. While low temperatures are often employed in molecular spectroscopy, the two techniques have not been combined for the purpose of understanding molecular interactions. It is appropriate that DPPH should be the first example so studied because environmental perturbations of this paramagnetic species are also important in branches of chemistry other than molecular electronic spectroscopy.

EXPERIMENTAL

The high pressure apparatus consists of an optical high pressure cell placed in a “simple squeezer” press [15]. Hydraulic pressure is manually applied to a 50 ton ram, and the oil pressure is registered on conventional gauges. The cell is modeled after previous designs [8, 161. The additional feature is a special window design using single-crystal sodium chloride and oriented sapphire to retain similar optical transmission properties at liquid nitrogen temperatures as can be achieved at room temperature [IS]. For low temperature studies the cell is contained in a styrofoam dewar into which liquid nitrogen is slowly passed. The refrigerant flow is carefully controlled to permit stabilization at intermediate temperatures. The sample temper- ature is read with a copper-constantan thermocouple placed in the steel jacket near the sample. Evacuated window ports extend outside the dewar and are sealed by

[3] R. BERSOHN, Arch. Sci. Qenewa 11, 172 (1958). [4] R. I. WALTER, J. Am. Chem. Sot. 88, 1923, 1930 (1966). [5] D. E. WILL~MS, J. Am. Chem. Sot. S&6665 (1966). [6] S. WIEDERHORN and H. G. DRICKAMER, J. Phye. Chem. Solids 9, 330 (1959). [7] R. B. AUST, W. H. BENTLEY and H. G. DRICKAMER, J. Chem. Phya. 41, 1856 (1964). [S] H. W. OFFEN, Ph.D. Thesis, UCLA (1963). [9] H. W. OFFEN, J. Chem. phy8. 42, 430 (1965).

[lo] H. OHIGASHI, I. SHIROTANI, H. INOEUCHI and S. MINOMURA, J. Chem. Phys. 43,314 (1965). [ll] H. W. OFFEN, J. Chem. Phya. 42,2523 (1965). [12] H. W. OFFEN and E. H. PARK, J. Chem. Phys. 43, 1848 (1965). [13] H. W. OFFEN and R. R. ELIASON, J. Chem. Phys. 43,4096 (1965). [14] A. H. KADHIM and H. W. OFFEN, J. Am. Chem. Sot. 89, 1805 (1967). [15] D. T. GRICJ~S and G. C. KENNEDY, Am. J. Sci. 254, 722 (1956). [16] R. A. FITCH, T. E. SL~KHOUSE and H. G. DRICKAMER, J. Opt. Sot. Am. 47, 1015 (1957). [17] P. W. BRIDUMAN, PTOC. Am. Acad. Arts Sci. 74, 21 (1940). [IS] H. W. OFFEN, R. L. TANQUARY and K. F. STERRETT, J. Appl. Phy8. In press.

Page 3: Influence of high pressures and low temperatures on the absorption spectra of α,α-diphenyl-β-picrylhydrazyl

The absorption spectra of a,a-diphenyl-p-picrylhydrazyl 33

heated quartz discs. Pressure is calibrated by the optical observation of the potas- sium chloride phase transition. The transition pressure of potassium chloride has been measured by BRIDGIMBN [17] at room and dry ice temperatures and has been extrapolated by us to 77°K. Since friction becomes increasingly important at lower temperatures, the pressure calibration becomes somewhat uncertain although several self-consistency checks are available. The absolute error is estimated to be ~10O/~ at 295°K and ~25% at 77’K. Further details will appear elsewhere [lS].

The absorption spectra were recorded photographically (Eastman Kodak plates 103F and SAl) using a 3-meter grating spectrograph (Baird-Atomic). The relative plate darkening was measured on a Jarrell-Ash non-recording microphotometer. The spectra shown in the following figures are obtained from direct readings of the densitometer scale plotted against wavelength for a linear dispersion of 5.43 A/mm in the visible and 2.66 A/mm in the ultraviolet spectrum. In the first three figures, the band maxima are adjusted arbitrarily to the same height. The error in the wave- length scale is less than 2 A.

DPPH was used as received from Eastman Distillation Products. The manu- facturer states that the chemical was recrystallized from benzene and dried in vacua at 80°C for 16 hr so that nearly all solvating molecules have been removed. The crystalline samples were prepared by mixing 0.5% by weight of DPPH with NaCl crushed single crystal, followed by pressing into a 0.010 in. thick pellet with & cylin- drical die commonly used in infrared spectroscopy. The plastic samples were pre- pared by dissolving DPPH (0.5% by weight) and cellulose acetate (39% acetylated) in pure acetone and drying in sir. For some experiments the dried plastic films were degassed to 1O-3 torr. The parent hydrazine (DPPH,) was also embedded in the cellulose acetate matrix for comparative studies of the ultraviolet spectra. The band positions and shape observed for DPPH powder and solid plastic solutions are similar to those reported for crystals [19] and liquid solutions [20, 211 at atmospheric pressure and room temperature.

Crystal

RESULTS

The absorption of DPPH crystals dispersed in a sodium chloride matrix has been studied in the 4500-5800 A spectral range as a function of temperature and pressure. Figure 1 illustrstes the spectral behavior of the blue color of the crystal when subjected to elevated pressures at room temperature. The exact location of the broad, slightly asymmetric band in the 5243-5324 A region depends on the detailed techniques involved in pellet preparation. As pressure is applied to the crystal the band maximum is displaced to longer wavelengths (red shift) by -190’ A in the O-19 kbar interval and thereafter remains stationsry. Simultaneously, progressively higher pressures develop the asymmetric character of the bsnd on the high-energy side of the absorption band. Gradually, this new absorption develops into a separate band at shorter wrtvelengths than the original 1 atm peak. At the highest pressure (38 kbar) achieved in the present work the band splitting is -900 cm-l. There is also

[lQ] H. INOKUCHI, Y. HARADA and Y. MARUYAMA, Bull. Chem. Sot. Jupun 35, 1569 (1962). [20] R. H. POIRIER, E. J. KAHLER and F. BERINGTON, J. Org. Chem. 17, 1437 (1952). [21] A. SUZUKI, M. TAKAHAS I and K. SHIOMI, Bull. Chem. Sot. Japati 36, 644, 998 (1963).

3

Page 4: Influence of high pressures and low temperatures on the absorption spectra of α,α-diphenyl-β-picrylhydrazyl

34 H. W. OXTEN and K. F. STERRETT

Fig. 1. The absorption spectrum of crystalline DPPH at room temperature for the 0, 19, and 38 kbar isobars.

an indication that yet a third band might develop at shorter wavelengths when the pressure is further increased.

When the crystal is cooled, the band becomes broader although its transition energy is unaffected by temperature. The pressure behaviour at the lower tempera- tures is similar to that exhibited at room temperature, particularly near dry ice temperatures: the magnitude of the band splitting as well as the relative intensities of the two bands are the same at 193’K and 295°K at the highest pressures. When the optical cell is immersed in liquid nitrogen, however, the band splitting is no longer discernible, and the strong asymmetry observed at higher temperatures is masked by the increased bandwidth at elevated pressures (see Fig. 2).

These results are obtained reversibly and reproducibly when precautions are taken to limit the periods of light exposure to the actual photographing of the spectro- gram. After a 15 min exposure to visible light from a tungsten-iodine lamp, the band broadens by ~10% and shifts toward the blue by ~30 8. The band maximum continues to be displaced irreversibly toward higher energies and increasingly merges into the underlying continuous absorption as photolysis proceeds. The spectral changes of a partially decomposed sample under pressure differ from those reported above ; for example, a band splitting is then no longer discernible.

Phstic solzction

In order to determine whether the band splitting arises from molecular or crystal interactions, DPPH was also studied in a compressed and/or cooled environment of cellulose acetate. The absorption of DPPH in plastic solution is identical in location, but symmetric and narrower in width compared to crystalline samples at atmospheric pressure and room temperature. The pressure-induced red shift is not accompanied by new absorption. The spectral shift for three temperatures is summarized in Fig. 3.

Page 5: Influence of high pressures and low temperatures on the absorption spectra of α,α-diphenyl-β-picrylhydrazyl

The absorption spectra of a,a-diphenyl-/Lpicrylhydrazyl

I 5000 5250 5;oo 5750

WAVELENGTH (i,

Fig. 2. The absorption spectrum of crystalline DPPH at 77°K for the 0, 18, and 33 kbar isobars.

0

7 z -2oc u

4”

t f m

g

u -4oc %

-600

DPPH - CELLULOSE ACETATE

I 10 20 30

PRESSURE (KBAR)

Fig. 3. The red shift, -Av(cm-l), of the visible absorption band at 295”, 193O, and 77°K for DPPH in celluloee acetate.

Page 6: Influence of high pressures and low temperatures on the absorption spectra of α,α-diphenyl-β-picrylhydrazyl

36 H. W. OF~N and K. F. STERRE~

It is clear that the magnitude of the red shift is smallest at room temperature and that the rate of shift approaches zero above ~15 kbar at room and near dry ice temperatures and at somewhat higher pressures at 77°K. This conclusion is inde- pendent of uncertainties in the pressure calibration.

The symmetric band is increased in width both by lowering temperature and applying pressure. The temperature behavior at one atmosphere parallels that of the crystal. The pressure effect on the spectrum is illustrated for the 77°K isotherm in Fig. 4. It is surprising that the spectrogram, taken soon after the pressure is

L,FzH - CiLLlJLOSE ACETAiE

I I I

5030 5250 5500

WAVELENGTH (i,

Fig. 4. The visible absorption spectrum of DPPH in cellulose acetate at 77°K and for the 0, 18, and 33 kbar isobars. The 1 atm (2) spectrum was photographed

immediately after releasing the pressure.

quickly released, exhibits a band broadened by more than 100% [the curve labeled 1 atm (2) in Fig. 41. The original spectrum is observed upon warming the sample. The same phenomena occur at 193’K upon pressure relaxation, except that the band narrows to its original width within a few minutes. Intensity changes of the band maximum are difficult to evaluate in the present work, but qualitative inspection shows an appreciable decrease in the absorption strength at high pressures and low temperatures for DPPH in cellulose acetate as well as for DPPH crystals.

The plastic samples containing DPPH are also subject to photochemical de- composition. The sample deteriorates especially when residual gases and solvents are removed by extensive pumping to ~10~ torr. The presence of appreciable irreversible reaction is noted by a blue shift and inhomogeneous broadening at high pressures. The photolysis rate increases in the order crystal < fresh plastic sample < degassed sample.

The ultraviolet absorption systems of DPPH and DPPH, have similar transition energies and represent presumably the same orbital promotion. The ultraviolet light (xenon lamp) required to observe this absorption also accelerates the decompo- sition process for both compounds in polymer matrices so that one pressure cycle

Page 7: Influence of high pressures and low temperatures on the absorption spectra of α,α-diphenyl-β-picrylhydrazyl

The absorption spectra of a,a-diphenyl-@-picrylhydrazyl 37

could not be concluded before the band merges into a continuous absorption toward shorter wavelengths. Figure 5 illustrates the effect of pressure on the UV absorption at room temperature (low temperature runs were not made for the W spectra). The redshift of -280 cm-1 at 9 kbar for the 330 m,u band of DPPH is somewhat larger than for the free radical absorption in the visible spectrum. The 314 rnp band of DPPH,, however, showed ~1000 cm-1 red shift at 19 kbar after which the band permanently submerges into the continuum. The data indicate that pressure accelerates the decomposition.

DPPH - CELLULOSE ACETATE T = 295OK

I 3125 3250 3375 3500

WAVELENGTH (A)

li Fig. 5. The ultraviolet absorption spectrum of DPPH in cellulose acetate at room

temperature for the 0, 9, 19, and 38 kbar isobars.

DISCUSSION

The results concerning the blue color band of DPPH in cellulose acetate may be summarized as follows: decreasing the temperature broadens the absorption band and increasing the pressure both increases the bandwidth and produces a band shift toward the red which becomes larger at lower temperatures. In DPPH crystals increasing the pressure produces two absorption bands which become less distinct as the temperature is lowered. It is helpful to put the present pressure and room temperature results for the spectral shift in perspective with VMT* transitions in other molecules. The high molar extinction of both the 5300 d and 3300 A bands (log E N 4.15 and 4.25, respectively) [20] corresponds to a large transition moment resulting from an appreciable charge redistribution in the excited state. The planar conjugated anthracene system has an allowed transition of similar absorption strength and at ~30 kbar shows red shifts of ~800 cm-l and ~1800 cm-l for plastic solutions and crystals, respectively [S]. The net pressure perturbations are evidently smaller for DPPH with regard to this spectral shift comparison. In addition to oscillator strength, important contributions to pressure (and solvent) shifts may be made by signifloant

Page 8: Influence of high pressures and low temperatures on the absorption spectra of α,α-diphenyl-β-picrylhydrazyl

38 H. W. OFFEN and K. F. STERRE~

changes in any of the following during excitation: dipole moment, polarizability or size of cavity occupied by solute in the dielectric medium [12, 221. When the dipole moment is smaller in the excited state than in the ground state, the pressure shift becomes smaller [12, 231. The band broadening upon cooling DPPH is anomalous relative to the common observation that band structure sharpens at lower tempera- tures. We conclude that the DPPH system exhibits some unusual environmental responses and temperature perturbations.

The unique behavior of this organic radical must have its origin in the electronic structure as governed by the arrangement of the atoms in the molecule. The large dipole moment of DPPH in its ground state (4.9D) [24] requires substantial contri- butions of polar valence structures to the ground state description. An increased

charge separation can be achieved by adding to the structure 4,-w---&-Pm(I)

other structures such as +a--~--g--Pic(II) and &-l?--N=P%(III), where the latter structure has achieved stability through donating an’unshared electron pair from the p-nitrogen to the picryl group. Recent X-ray structure analysis predicts an unfavorable relative energy for the latter structure because the picryl carbon bonded to the p-nitrogen lies 0.5 A out of the plane defined by the three u-nitrogen bonds. The small twist angle of -22’ for one phenyl group [5] permits its effective participation in conjugative stabilization with the odd electron on the u-nitrogen. The N-N bond length is intermediate between that of a single and double bond (“three-electron” bond), according to X-ray diffraction [5]. It is then reasonable to conclude that the strong visible absorption arises from a n electron being promoted to the molecular orbital occupied by the unpaired electron to yield an excited state as depicted essentially by structure (II). The consequence could be an increased dipole moment in the excited state. On the basis of this assumption we predict a red shift which is greater than that observed for anthracene at a given pressure. The experimental results do not confirm this prediction. This apparent contradiction is easily resolved when the highly irregular shape of DPPH is compared to the planar anthracene molecule. For example, each nitrogen atom is surrounded by twelve other atoms with less than 3.1 A separation. Strong interactions must arise from this steric crowding. Low frequency torsional motions about single bonds yield a large number of different possible geometrical configurations of the absorbing molecule. This situation evidently exists because a broad, structureless absorption is observed. The pressure shifts can be interpreted to mean that steric repulsion is stronger in the excited state reached in the absorption process from the equilibrium ground state (Franck-Condon principle). The sp2-hybridized lone pair on the nitrogen atom is also subjected to strong repulsive forces in this highly hindered molecule [14]. DPPH is then the first molecule in which steric factors have become evident in pres- sure perturbation studies, provided the above hypothesis proves correct. The parallelism between pressure and solvent shifts evident for simple molecules is then lost for irregularly shaped complex molecules.

Steric factors are also responsible for the greater bandwidths observed at lower

[22] N. S. BAYLISS, J. Chem. Phys. 18,292 (1950); E. G. MCRAE, J. Phys. Chem. 61,562 (1957); N. S. BAYLISS snd E. G. McRm, J. Phys. Chem. 58, 1002 (1954).

[23] W. W. ROBERTSON and A. D. KING, JR., J. Chem. Phys. 34,X11 (1961); W. W. ROBERTSON, A. D. KING, JR. and 0. E. WEIGANG, JR., J. Chem. Phys. 35, 464 (1901).

[24] J. TURKEVICH, P. F. OESPER and C. P. SMYTE~E, J. Am. Chem. Sot. 64, 1179 (1942).

Page 9: Influence of high pressures and low temperatures on the absorption spectra of α,α-diphenyl-β-picrylhydrazyl

The absorption spectra of a,a-diphenyl-B-picrylhydrazyl 39

temperatures and for the feature that dv/dp N 0 above certain pressures, since these phenomena are not observed in simple conjugated organic molecules. Evidently, the slow polymer relaxation at ‘WK from the compressed state at high pressures results in large inhomogeneous interactions which result in doubling the bandwidth from its value in a equilibrium polymer environment. The inhomogeneous polymer relaxation has succeeded in profoundly distorting the potential energy curves defining the two electronic states involved in the transition.

Photolysis of DPPH has been studied both in solution and in the solid state [21, 251. Polymer formation by reaction through the para position of the phenyl ring destroys the free radical absorption, and apparently also affects the ultraviolet band of both DPPH and DPPH,. The course of the photoreduction process requires definitive study at atmospheric pressure before a kinetic study at higher pressures is warranted. It is here only pointed out that photo-induced free radical destruction is also observed in plastics.

It has been noted that the ~T-T* absorption of aromatic crystals [8] is very sensi- tive to pressure. In strong contrast, the DPPH crystal absorption is not displaced by a significant amount at high pressures. Except for the band splitting at the highest pressures, the free radical absorption appears to be rather insensitive to pressure and temperature changes. Yet the electrical conductivity increases sharply in this pressure range, suggesting significant overlap between the appropriate orbitals of neighboring molecules [26]. It is difficult to explain these conductivity results when the spectroscopic pressure measurements are considered. The two absorption bands produced at high pressures cannot be attributed to removal of electronic level degeneracies because this phenomenon is found to be absent in solid solution. Molec- ular crystals which have more than one molecule per unit cell produce exciton interactions which can split excited electronic levels appreciably for strong transi- tions [27, 281. The experimental observation appears to favor new absorption rather than a splitting which should progressively increase with higher pressures. It is then more likely that the phenomenon is due to the appearance of a new crystal structure. Three distinct polymorphic forms of solvent-free DPPH have been identified at atmospheric pressure [29, 301. It is clearly possible that compression would favor a denser crystal structure which would distort the molecular geometry and shift the absorption to higher energy. Pressure studies above 40 kbar would definitely decide between the two alternatives and elucidate the high pressure origin of the third band at shorter wavelengths. The plastic cellulose acetate may also undergo phase changes at lower temperatures and higher pressures. Such solvent transfor- mations upon pressure release may explain the unusual broadening observed.

Acknowledgments-The authors are grateful to R. L. TANQUARY for his assistance in performing the experimental measurements and to Dr. J. W. MOYER for his encouragement and interest. This work was sponsored by the Northrop Corporation’s Independent Research and Development Program and was performed at Northrop Systems Laboratories.

[25] J. N. PITTS, JR., E. A. SCHUCK and J. K. S. WAN, J. Am. Chem. Sot. 86, 296 (1963). [26] H. INOWCHI, I. SHIROTANI and S. MINOMURA, Bull. Chem. Sot. Japan 37, 1234 (1964). [27] A. S. DAVYDOV, Theory of Molecular Excitona (Translated by M. KASHA and

M. OPPENHEIMER, JR.). McGraw-Hill (1962). [28] D. S. MCCLURE, Solid State Phys. 8, 1 (1958). [29] J. A. WEIL and J. K. ANDERSON, J. Chem. Sot. 5567 (1965). [30] D. E. WILLIAMS, J. Chem. Sot. 7535 (1965).