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Anomalous Temperature Dependence of N-H Vibrational State in Phenothiazine Crystal: Existence of Weak Hydrogen Bonds Hideyuki Nakayama,* Mikako Mukai,+Ryoji Hagiwara,t and Kikujiro Ishii* Department of Chemistry, Faculty of Science, Gakushuin University, Mejiro 1-5-1, Toshimaku, Tokyo, 171 Japan (Received: November 6, 1989)
Anomalous temperature dependences were found in the frequency and width of the Raman band arising from the N-H stretching vibration in the phenothiazine crystal. The data are discussed first from the viewpoint of the change in the dihedral angle about the N-S axis of the phenothiazine molecule. The N-H stretching frequency calculated by the CNDO/2 method as a function of the dihedral angle seemed to explain the above change qualitatively but cannot explain the large difference among the frequencies in the crystal, neat liquid, solution, and vapor states. The existence of weak hydrogen bonds in the crystal is then discussed. The competing effects of the molecular-orientationchange and the thermal expansion of the crystal on the hydrogen bonds are shown to cause the temperature dependence of the N-H vibrational frequency. The change in the N-H band width is, on the other hand, shown to arise from the coupling of the N-H vibration with the lattice mode.
Introduction
Phenothiazine crystal undergoes a phase transition at T, = 248.8 K at atmospheric pressure from the high-temperature phase with the space group Pbnm to the low-temperature ferroelastic phase with the space group P 2 , / n . 1 - 3 By a Raman scattering study, an optical phonon was found to show a partial softening in the low-temperature phase.* By use of an ultrasonic method, the elastic constant CS5 was found to be softened linearly as the temperature approaches T, in the high-temperature phase.4 From an analysis based on Landau’s phenomenological theory, it was concluded that the phase transition of the phenothiazine crystal takes place primarily as the result of the instability of the transversal acoustic p h ~ n o n . However, ~ the microscopic cause of the phase transition has not been revealed yet. Recently, we measured the Raman spectra of phenothiazine in the intramolecular vibrational region in various states. We found that the N-H stretching band of the crystal shows remarkable behaviors in that the frequency and width increase anomalously as the temperature is raised. This suggests the existence of a special circumstance related to the N-H bond. I n order to analyze these behaviors, first the N-H stretching frequency was calculated by the C N D 0 / 2 methodS as a function of the dihedral angle of the folding about the N-S axis of the phenothiazine (see Figure 1). This is because the molecular orientation has been inferred to change gradually as the temperature is changed,2 and then the dihedral angle is also inferred to change. The calculated results seemed to explain the temperature dependence of the N-H band frequency observed for the crystal. However, these cannot explain the large shifts of the N-H frequencies of the crystal and neat liquid from the vapor state. The consideration of the solvent effect based on the simple dielectric model6 also indicates that these shifts are too large to be attributed to this effect. I t is therefore inferred that weak hydrogen bonds of the N-H-S type exist in the crystal, causing the large shift of the N-H band frequency. It is shown that the crystallographic data’ do not exclude the existence of the weak hydrogen bonds, although the original author did not refer to their existence. The competing effects of the temperature-dependent molecular-orientation change and the thermal expansion of the crystal on the hydrogen-bond strength are shown to explain the observed change in the N-H band frequency. The observed anomaly in the width of the N-H band is, on the other hand, explained by the coupling of the N-H vibration with the lattice mode which shows partial softening on approaching T, in the low-temperature phase. Other results of ‘Present address: Kao Corporation, Bunka 2-1-3, Sumidaku, Tokyo, 131 Japan. Present address: Seiko Instruments Inc., Oyama, Sizuoka Prefecture, 410- I3 Japan.
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TABLE I: Bond Lengths (A) Used in the Calculation N-C 1.399 C-H 1.010 s-c 1.762 N-H 1.090
c-c
1.383
the Raman measurements on phenothiazine in the intramolecular-vibration region will be published elsewhere.* Experimental Section
Raman spectra of phenothiazine were measured with the 514.5or 488.0-nm radiations of the Ar ion laser as the excitation source. The former was used for the crystal and liquid samples and the latter for the vapor. The equipment for the measurements and the samples were almost the same as those used in the previous study.2 The spectra of the single crystal were measured between 90 and 420 K by use of an Oxford D N 1704 cryostat. The spectra of the neat liquid were measured with the sample which was sealed in a Pyrex glass tube under vacuum and melted by a heater wound around the tube. In the measurement on the vapor, a Pyrex glass tube with a pair of Brewster windows and a set of multiple reflection mirrors were used. The powder sample was sealed in the tube under vacuum and heated at -550 K by the flow of hot air. The infrared spectra of the dilute solutions of phenothiazine in n-hexane (0.005 mol/L) and carbon tetrachloride (0.03 mol/L) were measured with a Bomem DA3.02 Fourier transform spectrophotometer.
CND0/2 Calculation The N-H stretching frequency uN-H of the phenothiazine molecule was calculated by evaluating the total energy of the molecule at several points along the vibrational coordinate by assuming that the N-H stretching is a group vibration. The total energy was calculated by means of the C N D 0 / 2 method5 using the MELCOM-COSMO 800111 computer at the Computer Center of Gakushuin University. The calculation was carried out on the following assumptions for the structure of the phenothiazine (1) Nakayama, H.; Ishii, K.; Chijiwa, E.; Wada, M.; Sawada, A. Solid State Commun. 1985, 55, 59. (2) Nakayama, H.; Ishii, K. Chem. Phys. 1987, 114, 431. (3) We have recently found that the phenothiazine crystal also undergoes a phase transition under high pressure. The high-pressure phase has been shown to be the same phase as the low-temperature phase at the atmospheric pressure (Araki, G.; Mukai, M.; Nakayama, H.; Ishii, K. Bull. Chem. SOC., Jpn., in press). (4) Nakayama, H.; Ishii, K.; Sawada, A. Solid State Commun. 1988,67, 119. (5) Pople, J. A,; Beveridge, D. L. Approximate Molecular Orbital Theory; McGraw-Hill: New York, 1970; Chapter 3. (6) Bauer, E.; Magat, M. J. Phys. Radium 1938, 9, 319. (7) McDowell, J. J. H. Acta Crystallogr. 1976, B32, 5. (8) Nakayama, H.; Mukai, M.; Ishii, K. Unpublished results.
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Nakayama et al.
The Journal of Physical Chemistry, Vol. 94, No. 10, I990
Figure I . Structure of phenothiazine molecule and definition of dihedral angle 8 and angle a .
r
-30
5
4820
1
I
I
I
140
160
180
Dihedral angle / d e g . Figure 3. N-H stretching frequency calculated by the CNDO/2 method as a function of the dihedral angle. The scales on the left-hand side and right-hand side stand for the original and corrected values, respectively (see text).
\
- 20 5 e E
-
.Q
10
g
m
I
W
100
200
300 400 Temperature / K
500
Figure 2. Temperature dependences of the frequency and width of the N-H stretching Raman band observed with the c(aa)b polarization where the directions are indicated by using the crystal axis of the hightemperature phase (see ref 1). No correction for the slit width (1.1 cm-') has been made.
molecule: ( I ) The molecule belongs to point group C,. (2) The benzene rings are right hexagonal and rigid. (3) The S and N atoms lie on the line of the intersection of the planes of the two benzene rings. The dihedral angle 8 of the folding of the molecule and the angle a related to the direction of the N-H bond are defined as shown in Figure 1 . The bond lengths used in the calculation are listed in Table I. They are the mean values based on the crystallographic data.7 The calculations were performed as follows. First, the total energy of the molecule was calculated as a function of a at fixed 0 to obtain the N value of the equilibrium conformation at each 0. In these calculations, the N-H bond length was fixed at the value reported in the crystallographical data.7 Next, the total energy was calculated for various N-H bond lengths at each 8 and at N of the equilibrium conformation. Thus, the potential energy data for the N-H stretching were obtained at each 8. The potential energies obtained above were fitted to a thirdorder polynomial of the N-H bond length, and the force constants were obtained from the factor of the quadratic term. The vibrational frequency uN-H was calculated by the harmonic approximation assuming that the remaining part of the molecule except the N-H bond was rigid.
Results and Discussion Temperature Dependences of the Frequency and Width of the N-H Stretching Band of the Crystal. Figure 2 shows the temperature dependences of the frequency and width of the N-H stretching Raman band. In general, the intramolecular vibrations in molecular crystals are not influenced by the change in the crystal field as much as the lattice vibrations, since the potential energies of the intramolecular vibrations are subject almost to the intramolecular bonds. Therefore, the frequencies of the intramolecular vibrations hardly change, or slightly decrease on account of the thermal expansion, as the temperature is raised. However, the frequency of the N-H stretching band shown in Figure 2 increases with temperature, showing a small maximum just below T,. The bandwidth shows, on the other hand, a steep increase just below T, and shows different temperature dependences above and below T,. These characteristic behaviors suggest the existence of a special
-114.645 I 100
I
I
1
140
180
220
1
260
Dihedral A n g l e / d e g . Figure 4. Total energy of the phenothiazine molecule as a function of the dihedral angle. TABLE 11: Values of a (deg) That Minimize the Total Energy at Each 0 (deg) 0
cy
8
a
180
0.00 13.80 14.10
150 140 130
12.41 10.11 8.14
I70 160
circumstance related to the N-H bond. Results of the CNDOJZ Calculation and Comparison with Experimental Data. Figure 3 shows YN-H calculated by the CNDOJZ method as a function of 8. uN-H increases with 8. The magnitude of the calculated uN-H is much larger than the experimental value shown in Figure 2. In the crystal at room temperature, 8 of the phenothiazine molecule is 158.5' and the measured uN-H is 3340 cm-'. On the other hand, the calculated v ~ at-0 =~ 158.5' is 4860 cm-'. This difference is considered to be due to the fact that the calculation was not carried out along the normal coordinate but along the local coordinate of the N-H bond length and also due to the fact that the C N D O / 2 method tends to estimate the value of force constants larger than the correct To check the reliability of the results obtained by the present calculation, we compare other calculated results with the experimental data that have been reported so far. Table I1 shows the values of a that minimize the total energy at each 8. These data indicate that the phenothiazine molecule is stable at the conformation in which the hydrogen atom attaching to the nitrogen lies inside with respect to the dihedral angle. This result is in agreement with the results of the X-ray analysis7 and the calculation by the extended Huckel method.IO Figure 4 shows the total energies at the equilibrium angle of a plotted against 0. This curve predicts that 8 at the equilibrium state is 143'. The potential barrier against the butterfly inversion and the frequency of the butterfly vibration are predicted to be 16.8 kJ/mol and 82.3 cm-', respectively. On the other hand, 0 obtained by the X-ray analysis of the crystal structure and by the measurement of the Kerr (9) Chapter 4 in ref 5 . (10) Kamiya, M.; Akahori, Y.Chem. Pharm. Bull. 1972, 20, 117.
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N-H Vibrational State in Phenothiazine Crystal TABLE 111: Frequency Shift Av (cm-') from the Vapor State, the Square of the Refractive Index R of the Medium, and the Constant C in the Kirkwood-Bauer-Magat Equation (References 6 and 14) solvent Au n2 C 13 1.8816 2.1X10-2 n-hexane carbon tetrachloride neat phenothiazine liquid
16 36
2.1316 2.7)'
2.2 X 3.9 X
constant in benzene solution is 158.5' and 150' f 7 O , respecti~ely.~,"Since 8 in the crystal is influenced by the intermolecular interaction, care must be taken in comparing this with the value calculated for the free molecule. For the inversion barrier, the values obtained from the force constants of C-N-C and C-S-C bendings and by the dielectric measurement in the polystyrene ~'~ matrix are I O kJ/mol and 25 kJ/mol, r e ~ p e c t i v e l y . ~ ~The butterfly vibration was observed at 49 cm-I by Raman measurement on the vapor.8 Comparing the calculated and experimental results described so far, it is concluded that the present calculation tends to yield the absolute value of energy larger than the correct value but that the results can be used for the semiquantitative discussion if we take proper care of this tendency. To correct the deviation of the calculated YN-H from the experimental value, we use the scale on the right-hand side in Figure 3 for This was obtained by multiplying the original value by a factor so that uN+ at 8 = 158.5' coincides with the experimental value. If the temperature dependence of u ~ in- Figure ~ 2 is due to the change of 8, this means that 8 increases with temperature. If this was the case, Figure 3 imples that the change of 6 is about 11 O between 90 and 415 K. Thus, one might attribute the cause of the change of YN-H to the change of 8. However, since uN-H in the liquid, solution, and vapor states falls in the range outside of Figure 3 as will be discussed below, another mechanism of the frequency shift must be sought. Estimation of the Frequency Shift Arising from the Simple Solvent Effect. We observed the N-H Raman band at 3399 and 3435 cm-' for the neat liquid (-460 K) and vapor (-550 K), respectively. We also observed the N-H infrared bands for the solutions in n-hexane and carbon tetrachloride at 3422 and 3419 cm-', respectively, at room temperature. The difference between these frequencies and that of the crystal is too large to be attributed to the difference of 8. Even if the phenothiazine molecule takes the planar structure, the difference in vN-H is 30 cm-' at the most as shown in Figure 3. In studying the frequency shift Au from the vapor to other states, the solvent effect related to the dielectric constant of the surrounding medium is first taken into account. For this purpose, the Kirkwood-Bauer-Magat equation62I4(eq 1) has been widely used:I5
AU - t - 1 _ cu
2t+1
where u is the frequency in the vapor state, t is the dielectric constant of the medium, and C is a constant. Using the values of the square of the refractive indice~'~.''for t, we calculated C as shown in Table 111. The values of C obtained for n-hexane and carbon tetrachloride are almost the same, which indicates that ~~
( I I) Aroney, M. J.; Hoskins, G. M.; Le Ftvre, R. J. W. J . Chem. SOC.( B ) 1968, 1206. (12) Koga, Y.; Takahashi, H.; Higasi, K. Bull. Chem. SOC.Jpn. 1973, 46, 3359. (13) Davies, M.; Swain, J. Trans. Faraday SOC.1971, 67, 1637. (14) Buckingham, A. D. Proc. R. SOC.London 1958, A248, 169. ( 1 5 ) (a) West, W.; Edwards, R. T . J . Chem. Phys. 1937,5, 14. (b) Jones, L. H. Badger, R. M.J . Am. Chem. SOC.1951, 73, 3132. ( I 6) CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, 1986. (17) The square of the refractive index of liquid phenothiazine near the melting point was estimated from the electronic polarization P, = 65.0 cm3/mol (Leonard, N. J.; Sutton, L. E. J . Am. Chem. SOC.1948, 70, 1564) by using the Lorentz-Lorenz equation. The density of the liquid phenothiazine was measured by us to be 1.10 g/cm3 around 470 K.
a Figure 5. Projection of the room-temperature structure of the phenothiazine crystal along the c axis (reproduced according to ref 7). T h e crystal axes a , b, and c in ref 7 a r e read a s b, c, and a , respectively, in our notation (see ref 1). Only the N-H-23 systems a t z = (3/4)c are indicated.
the model of the simple solvent effect holds for these solvents. On the other hand, C for the neat liquid is significantly larger than those obtained for the other two solvents. This difference suggests the existence of an additional intermolecular interaction related to the N-H bond in the neat liquid, This may be a very weak hydrogen bonding or the correlation between the orientations of the neighboring molecules in the liquid. vN-H in the crystal is smaller than that in the liquid by -50 cm-'. The simple solvent effect in the crystal may be almost the same as that in the liquid, since the densities in these two states are of the same order. Therefore, the large shift of vN-H in the crystal cannot be attributed to the simple solvent effect. Existence of Hydrogen Bonds in the Crystal. Figure 5 is the projection of the room-temperature crystal structure along the c axis reproduced from the previous X-ray datae7 The N-He-S systems indicated in this figure are almost linear. The N-S distance 3.695 A 7 is shorter by 0.40 8, than the sum of the N-H bond length (1.09 A) and the van der Waals radii of hydrogen (1.20 A) and sulfur (1.80 A).18 Donohue,19 on the other hand, proposed the use of the H-S distance as the criterion to distinguish hydrogen-bond formation and suggested 2.75 A as the border value. The H-S distance in the phenothiazine crystal is also shorter by 0.13 A than this value. These facts suggest that hydrogen bonds of the N - H . 4 type exist in the phenothiazine crystal although the original worker of the X-ray analysis' has not referred to the existence of these bonds. According to Kuleshova and Zorkii,20 however, the mean value of the N-S distance and its standard deviation in the crystals including N - H . 4 hydrogen bonds are 3.42 and 0.1 1 A, respectively. Taking these into consideration, the N-H-.S hydrogen bond in the phenothiazine crystal is considered to be weak. Lautii and Novak2' reported the relation between the N-S distance of the N-He-S hydrogen bond and YN-H. By extrapolating the curve shown in their paper to the long N-S distance side, we obtain 3360 cm-I as the estimate of the frequency in the phenothiazine crystal. This frequency is comparable with the measured one, 3340 cm-' at 300 K. The extrapolation of the curve of Lautii and Novak2' also gives the estimate of the derivative of vN-H with respect to the N-S distance as -500 cm-I/h;. Using this value, we try to estimate the magnitude of the frequency change caused by the thermal expansion of the crystal. Assuming that the coefficient of the linear expansion of the N-S distance is 1 X lo4 K-I (the typical value of the linear thermal expansion coefficient of organic crystals22),the N-S distance change is estimated to be 4 X lo4 A/K. Therefore, the frequency change is estimated to be -0.2 cm-'/K. This is of the same order as the measured average change Bondi, A. J . Phys. Chem. 1964, 68, 441. Donohue, J. J . Mol. Biol. 1969, 45, 231. Kuleshova, L. N.; Zorkii, P. M. Acta Crystallogr. 1981, B37, 1363. Lautib, A,; Novak, A. Chem. Phys. Lett. 1980; 71, 290. This value was estimated from the volume expansion coefficients of crystals such as anthracene (Kitaigorodsky, A. I. Molecular Crystals and Molecules; Academic Press: New York, 1973; Chapter 5), assuming that the expansion is isotropic. (18) (19) (20) (21) (22)
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in the phenothiazine crystal, 0.07 cm-' between 250 and 350 K, but seems slightly larger. Therefore, the strength of the hydrogen bond is not considered to be changed simply by the linear thermal expansion, It has been suggested that a change in the molecular orientation occurs in the low-temperature phase.2 This change is considered to be the tilt of the molecule against the mirror plane of the high-temperature phase. If this is the case, the tilt weakens the hydrogen bond which is formed on the mirror plane, causing the shift of uN-H to the high-frequency side. It should be noted that uN-H shows a small maximum just below T, (Figure 2). This is considered to be due to the competition of the effect of the thermal contraction which strengthens the hydrogen bond and the opposite effect of the molecular tilt. Actually, the temperature region (220 K-T,) where vN-H shows the anomaly corresponds to the region where the extinction angle, which reflects the molecular orientation, shows a large temperature dependence.] Raman bands related to the vibrations involved in hydrogen bonds are usually broad. This is understood since such vibrations easily couple with the lattice vibrations. The steep increase in the N-H bandwidth of the phenothiazine crystal just below T, (Figure 2) is attributable to the coupling of the N-H vibration with the librational lattice mode which shows a partial softening as the temperature approaching T, in the low-temperature phase.2 The amplitude of this libration may become larger as its frequency is softened. Therefore, the coupling between these vibrations is considered to increase in this temperature region, giving rise to
the acceleration of the relaxation of the excited states of the N-H vibration and to the observed increase in the Raman bandwidths. Conclusion Anomalous temperature dependences observed for the frequency and width of the Raman band arising from the N-H stretching vibration in the phenothiazine crystal were discussed from the viewpoints of the changes in the dihedral angle 0 of the molecule or in the hydrogen-bond state. It was shown by the CNDO/2 calculation that the N-H stretching frequency YN-H increases with 0. However, this mechanism cannot explain the large difference of uN-H in the crystal, neat liquid, solution, and vapor states. To explain the above difference, the existence of hydrogen bonds in the crystal was proposed. It was shown that the crystallographic data do not exclude the existence of the weak hydrogen bonds. The competing effects of the reorientation of the molecule and the thermal expansion of the crystal on the hydrogen-bond strength were shown to cause the anomalous temperature dependence of u ~ - The ~ . anomaly in the bandwidth was, on the other hand, explained by the coupling with the lattice mode. In conclusion, there are weak hydrogen bonds in the phenothiazine crystal. The anomalous behaviors of the N-H stretching Raman band are due to the change in the hydrogen-bond state. Although there is a possibility that the change in the dihedral angle of the molecule contributes to the change in the frequency of the above Raman band, its contribution is considered to be small. Registry No. Phenothiazine, 92-84-2
Electronic Band Structure of Graphite-Boron Nitride Alloys John P. LaFemina Pacific Northwest Laboratory,t P.O.Box 999, Richland, Washington 99352 (Receioed: August 7 , 1989: In Final Form: October 27, 1989)
Extended-Huckel crystal orbital band calculations, frontier crystal orbital analysis, and degenerate-level perturbation theory are used to explore the electronic structure of several graphite-boron nitride alloys: BC3, C3N, BC2N, and their structural isomers. These materials are treated as two-dimensional solids, and the effect of crystal relaxation on the bandgap is considered. Similarities and differences between the band diagrams of these structurally similar materials are discussed and understood in a simple crystal orbital framework.
Introduction
Recent interest in the electronic properties of layer-type crystals has been sparked by the synthesis of several alloys of graphite and boron nitride,'-' materials in which some of the carbon atoms have been replaced by boron atoms (BC3),2,3nitrogen atoms (C3N), or a combination of both boron and nitrogen atoms (BC2N).1,4 Electron and X-rav diffraction studies of these materials indicate graphite-like layer structures with sp2bonding in-plane, and a large distance between layers (>3 A).3,4 In this paper the electronic band structure of the structural isomers of single-layer BC,, C,N, and BC2N (see Figure 1) are examined via extended-Huckel crystal orbital (EHCO) band c a l ~ u l a t i o n s . Since ~ these band diagrams can be thought of in terms of the perturbation of graphite via boron and nitrogen substitution, the degeneracy lifting near the Fermi energy6 (and hence the energy gaps) can be understood in a simple crystal orbital (CO) context by using first-order perturbation theory, the ideas of qualitative crystal orbital theory (QCOT),' and the concept of transferability.a Furthermore, these same principles can be used to qualitatively evaluate the effect of crystal relaxation 'Operated for the US. Department of Energy by Battelle Memorial Institute under Contract DE-AC06-76RLO 1830.
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on the bandgap by examining the leading frontier COS of the system.6 Band Diagrams The weak interlayer interactions permit these materials to be treated as two-dimensional solids in the computation of their electronic band structure and allow for a qualitative understanding (1) (a) Badzian, A. R.; Niemyski, T.; Appenheimer, S.; Olkusnik, E. In Proceedings of the International Conference on Chemical Vapor Deposition; Glaski, F. A,, Ed.; American Nuclear Society: Hinsdale, IL, 1972; Vol. 3. (b) Kosolapova, T. Ya.: Makarenko, 9 . N.; Serebryakova, T. I.; Prilutskii, E. V.; Khorpyakov, 0. T.; Chernsheva, 0. 1. Poroshk. Mefall. (Kieu) 1971, I , 27. (2) Kouvetakis, J.; Kaner, R. 9 . ; Sattler, P.: Bartlett, N. J , Chem. SOC., Chem. Commun. 1968, 1758. (3) Kaner, R. B.; Kouvetakis, J.; Warble, C. E.; Sattler, M. L.; Bartlett, N.Mater. Res. Bull. 1987, 22, 399. (4) Sasaki, T.; Bartlett, N., unpublished, referenced in: Liu, A. Y.: Wentzcovitch, R. M.; Cohen, M. L. Phys. Rev. B 1989, 39, 1760. (5) (a) Whangbo, M. H.; Hoffmann, R.; Woodward, R. 8.Proc. R. SOC. London, Ser. A 1979,366, 23. (b) Whangbo, M. H.; Hoffmann, R. J . Am. Chem. SOC.1978, 100, 6093. ( 6 ) (a) LaFemina, J. P.; Lowe, J. P. In?. J . Quantum Chem. 1986.30.769. (b) LaFemina, J . P.; Lowe, J. P. J. Am. Chem. SOC.1986, 108, 2527. (7) Lowe, J. P.; Kafafi, S. A,; LaFemina, J . P. J . Phys. Chem. 1986, 90, 6602. (8) Lowe, J . P.: Kafafi, S. A. J . Am. Chem. Soc. 1984, 106, 5837.
e 1990 American Chemical Society
