bis(9-anthryl)alkanes - American Chemical Society

Jan 3, 1986 - ring. On the other hand, theobserved spectrum of 3*+ shows that an unpaired electron is delocalized over two anthracene rings. The hyper...
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J. Phys. Chem. 1986, 90, 4958-4961

Spin Distributions and Molecular Conformations in Cation Radicals of ar ,o-Bis( 9-anthry I)alkanes Atsushi Terahara, Hiroaki Ohya-Nishiguchi,* Noboru Hirota, Department of Chemistry, Faculty of Science, Kyoto Uniuersity, Kyoto 606, Japan

Hiroyuki Higuchi, and Soichi Misumi The Institute of Scientific Industrial Research, Osaka University, Suita, Osaka 565, Japan (Received: January 3. 1986)

Cation radicals of bis(9-anthry1)alkaneshaving one to four -CH2- linkages (1-4) have been investigated by ESR and cyclic voltammetry. The observed ESR spectra of l", 2'+,and 4" indicate that unpaired electrons are localized on only one anthracene ring. On the other hand, the observed spectrum of 3" shows that an unpaired electron is delocalized over two anthracene rings. The hyperfine coupling constants due to the methylene protons observed in 1" and 2" are not equivalent, which concludes that the rotation of the anthracene ring is inhibited because of steric hindrances. Evidence for the intramolecular dimerization in 3" was also provided by cyclic voltammetry. The stabilization energy due to dimerization in 3" was estimated as 0.10 eV. Based on the experimental results, the conformation of 3" is proposed as an intramolecular sandwich-likestructure.

Introduction Compounds in which two chromophores are connected by alkyl chains have been investigated as model compounds to study formation and structures of excimers1.2 and to understand the mechanism of electron transfer in excited m o l e c ~ l e s . ~These compounds can also be useful for the investigation of intramolecular interaction in dimer cation radicals, because the two aromatic rings can be stacked in a sandwich-like structure when the alkyl chain is sufficiently long. Transannular interaction in the cation radicals of such bichromophoric compounds is an interesting subject of study, but there have been no reports on this subject. In a series of work we have studied the dimer cation radicals of naphthalene derivatives and the cation radicals of cyclophane compounds4 in order to obtain information about the transannular interaction in dimer cation radicals. In the present work we have studied the cation radicals of cu,w-bis(9-anthryl)alkanes having one to four -CH2- linkages (1-4) by means of electron spin resonance (ESR) and cyclic voltammetry (CV) to study transannular interaction in their cation radicals. Since these molecules have flexible structures, transannular interaction may play an important role in determining the conformations of cation radicals in solution. It is known that anthracene cation radical associates with neutral anthracene to form a dimer cation radical under proper conditions5 and that the unpaired electron in [2,2]-9,lOanthracenophane cation radical is delocalized over the two anthracene moieties6 Therefore, we may expect that under favorable conditions two anthracene rings in the cation radicals of these compounds may interact with each other, forming intramolecular dimer structures. Formation of such dimer structures (1) (a) Hirayama, F. J . Chem. Phys. 1965, 42, 3163. (b) Chandross, E. A., Demster, C. J. J . Am. Chem. Sot. 1970, 92, 3586.

(2) (a) Castellan, A., Desvergne, J. P.; Bouas-Laurent, H. Chem. Phys. Lett. 1980, 76, 390. (b) Ferguson, J. Ibid. 1980, 76, 398. (c) Hayashi, T.: Mataga, N.; Sakata, Y . ;Misumi, S . ; Morita, M.: Tanaka. J. J . A m . Chem. Soc. 1976, 98, 5910. (d) Hayashi, T.; Suzuki, T.; Mataga, N.; Sakata, Y . ; Misumi, S. J . Phys. Chem. 1977,81, 420. (e) Anderson, B. F.; Ferguson. J.: Morita, M.; Robertson, G. B. J . Am. Chem. Sot. 1979, 101, 1832. (3) (a) Pearson, J . M.; Williams, D. J.; Levy, M. J . Am. Chem. Soc. 1971, 93, 5478. (b) Williams, D. J.; Pearson, J. M.; Levy, M. Ibid 1971, 93, 5483. (4) (a) Terahara, A.; Ohya-Nishiguchi, H.; Hirota, N., Oku, A. J . P h y ~ . Chem. 1986, 90, 1564. (b) Terahara, A,; Ohya-Nishiguchi, H.; Hirota, N.; Sakata, Y.;Misumi, S.; Ishizu, K. Bull. Chem. Sot. Jpn. 1982, 55, 3896. ( c ) Ohya-Nishiguchi, H.: Terahara, '4.; Hirota, N.; Sakata. Y.;Misumi, S. Ibid. 1982, 55, 1782. (5) Howarth, 0. W., Fraenkel, G. K. J . Chem. Phys. 1970, 52, 6258. ( 6 ) Gerson, F.: Kaupp. G.; Ohqa-Nishiguchi. H. .4ngem. Chenl , In[. Ed. Engl. 1971. 16. 657.

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would easily be recognized by the hyperfine structures of the ESR spectra and the stabilization energy measurable by CV.4 We have found here that formation of an intramolecular sandwich-like structure takes place only in 3". The spin distribution and stabilization energy in 3'+ are discussed, compared with those in lo+,2'+, and 4". On the other hand, the hyperfine coupling constants (hfcc) due to the two methylene protons in l'+ and 2'' were found to be nonequivalent, indicating rather rigid conformations of the cation radicals. Probable conformations for 1" and 2" are suggested based on the analysis of the nonequivalent methylene protons by the Heller-McConnell relationship.

Experimental Section Compounds 1 to 4 were synthesized according to the literat ~ r e . ' ~ , 'The cation radicals were generated electrochemically in CH2C12(DCM) by using an electrochemical ESR cell. No stable ESR signals were detected in propionitrile (PN). Chemical oxidation by using concentrated H2S04and CF3S03Hin DCM were also attempted, but the observed ESR signals were weaker except for the case of 3. CV was measured at low temperature (200 K) and room temperature. The experimental details on electrochemical ESR and CV were described in a previous paper.4a Computer simulations have been carried out for both the ESR spectra and the cyclic voltammograms.

Results and Discussion Cyclic Voltammetry. The cyclic voltammogram observed for 1 in DCM at room temperature is shown in Figure lA, as an example. The reversible peak at 0.40 V is due to the redox couple of ferrocene/ferrocene+ used as an internal reference (0.400 V vs. The peak corresponding to the one-electron oxidation of 1 is then assigned to that appearing at 1.15 V. As the temperature is lowered to 200 K, the cathodic peaks for 1 and 2 become apparent (Figure 1B) because of the prolonged lifetimes of the cation radicals. A sharp peak due to the formation of the solid cation radical salt appeared for 4 in the cathodic sweep at 200 K. On the other hand, in the case of 3 a very strong cathodic peak appeared with a peak potential lower than that of the anodic peak at 200 K as shown in Figure 1C. CV was also measured ( 7 ) (a) Dunand, A,; Ferguson, J.; Puza, M.; Robertson, G. B. J . A m . Chem. Soc. 1980, 102, 3524. (b) Daney, M.; Lapouyade, G. F. R.; BouasLaurent, H. Fr. Demande 1977, 2,314,165; Chem. Abstr. 1977,87, 134837h. (c) Applequist, D. E.; Swart, D. J. J . Org. Chem. 1975, 40, 1800. (8) Gagne, R. R.; Cowl, C. A,; Lisensky, G. C. Inorg. Chem. 1980, 19, 2854.

0 1986 American Chemical Society

The Journal of Physical Chemistry, Vol. 90, No. 21, 1986 4959

Molecular Conformations in Cation Radicals

0

0.5

1.0 E /V -.NE

Figure 2. Observed ESR spectrum of 1" by electrochemicaloxidation in CH2CI2at 215 K (A) and the simulated one (B).

1.5

Figure 1. Observed cyclic voltammograms obtained for (A) 1 at room temperature, (B) 1 at 200 K, and (C) 3 at 200 K in CH2C12containing tetrabutylammonium tetrafluoroborate at the sweep rate of 56 mV/s. Peaks denoted by Fc are due to ferrocene (0.400 V v. "E), used as an internal reference.

TABLE I: First Oxidation Potentials (Ell2') and hfcc for 1-4 E1/2', V VS.

NHE compd 1

(A)O

(C)b

1.16

1.15

hfcc, mT position value (10) (1,4,5,8) (2,3,6,7)

(9-CH2) 2

1.10

1.10

(IO) (1,4,5,8) (2,3,6,7) (9-CH2)

3

1.11

1.01

(IO) (1,4,5,8) (2,3,6,7)

(9-CH2) 4

1.12

1.09

MAC

1.12

1.12

(10) (1,4,5,8) (2,3,6,7) (9-CH2) (10) (1,4,5,8) (2,3,6,7) (9-CHJ

0.785 (1 H) 0.260 (4 H ) 0.120 (4 H) 0.912 (1 H ) 0.120 (1 H) 0.780 (1 H) 0.262 (4 H) 0.138 (4 H ) 1.350 (1 H ) 0.370 (1 H ) 0.396 (2 H ) 0.143 (8 H) 0.101 (8 H) 0.241 (2 H ) 0.041 (2 H) 0.720 (1 H ) 0.276 (4 H) 0.138 (4 H) 0.404 (2 H) 0.703 (1 H) 0.285 (2 H) 0.281 (2 H) 0.146 (2 H) 0.1 19 (2 H) 0.779 (3 H )

a Anodic peak potential. *Cathodic peak potential. hfcc are taken from ref 10.

in PN solution, but such a peak of 3" was not observed. In Table I are given the first oxidation potentials ( E , 2°) for 1-4 obtained from CV together with those for 9-methylanthracene (MA) used as the reference compound. The peak potentials of the anodic (A) and cathodic (C) sweeps were estimated in reference to the corresponding peaks of ferrocene. The anodic peak potentials of 1-4 agree well with that of MA, which suggests that the electronic interactions between the two anthracene rings are negligibly small in the neutral states. In the cases of 1, 2, and 4, the potentials of the cathodic peaks agree well with those of the anodic peaks, which shows that the interaction between the two anthracene moieties are also negligible in the cation radicals of these three compounds. On the other hand, the cathodic peak potential for 3 is 0.10 V lower than the anodic peak potential. This fact indicates the existence of some electronic interaction in the cation radical of 3. ESR Spectra. The voltages at which ESR signals due to the cation radicals first appeared were close to EIi2O for all the

compounds. In the cases of 1,2, and 3, the first signals disappeared and different signals probably due to reaction products appeared when the applied voltages were raised more than 1.8 V. In the case of 4, a single sharp signal, which may be attributed to the solid cation radical salt, appeared when the applied voltage was increased. No significant effect of the temperature was observed on the first appearing signals in the range 230-180 K. The ESR spectra of l", 2'+, and 4'' observed at low applied voltages have almost the same line widths of 0.05 mT. In Figure 2A is shown the observed spectrum of 1" as an example. In the case of 1'' the observed spectrum can be analyzed by the hfcc listed in Table I, as the simulated spectrum given in Figure 2B shows. However, the relative intensities of the central lines of the simulated spectrum are a little higher than those found in the observed spectrum, which may be attributed to the effect of the line width alternation due to the electron exchange between the two rings. Similarly the line intensities of the spectrum of 2'" obtained by the electrochemical ESR could not be simulated well, though the spectrum obtained by chemical oxidation in H2SO4 could be simulated reasonably well. The hfcc of the spectrum of 2" obtained by oxidation in concentrated H 2 S 0 4are given in Table I. On the other hand, the ESR spectrum of 4"' could be simulated completely by using the hfcc also listed in Table I. By comparing the hfcc obtained for lo+,2", and 4"with those for MA", it is seen in Table I that the three groups of hfcc due to one, four, and four equivalent protons are close to the three hfcc assigned to the ring protons of the 10, the 1,4,5,8, and the 2,3,6,7 positions in MA", respectively. The assignment of these hfcc are then straightforward. Therefore, it is concluded that on the ESR time scale the spin is localized on one anthracene ring in l", 2'+, and 4". The residual hfcc due to two protons can be assigned to the methylene protons attached to 9 position. It is noted that these two protons are not equivalent in 1'+ and 2'+, while they are equivalent in 4". On the other hand, the ESR spectrum of 3" is very different from those of the others, consisting of a highly resolved spectrum and a broad background. The ESR spectrum of 3" shown in Figure 3A, which was obtained by chemical oxidation using CF3S03Hin DCM, agrees basically with those by electrochemical ESR, but in the former case the relative intensity of the sharp component is higher with better resolution. The origin of the broad background cannot be identified but is probably due to a reaction product or a different conformation of 3'+. The line width of the spectrum of 3" is narrower than those of l a +2", , and 4".The well-resolved spectrum was reconstructed well as shown in Figure 3B by using the hfcc listed in Table I. The total number of protons in 3" is much larger than that in MA" as seen in Table I. The three hfcc of 0.396, 0.143, and 0.101 mT are close to 1 / 2 of the three hfcc due to the ring protons in MA". These characteristics of hfcc in 3" are similar to those found in the dimer cation radicals of a number of aromatic hyd r o c a r b o n ~ Therefore, .~~ it is concluded that the unpaired electron in 3" is delocalized over the two anthracene rings. The assignment

4960 The Journal of Physical Chemistry, Vol. 90, ,Yo. 21, 1986

Terahara et al.

II

A

>'

/

E

Figure 5. Cyclic voltammograms calculated for 3" by assuming intramolecular ( A ) and intermolecular (B) dimer formation. A.

Figure 3. Observed ESR spectrum of 3" in a solution of CF3S03H/ CH2C12at 230 K (A) and the simulated one (B). A . 1'

c . 4:

E . 2'

B.

iCH2 ,C \H2

H

m

C3H6m

Figure 4. Schematic views of the geometries of the P-protons in (A) la+, (B) 2'+, and (C) 4". TABLE 11: Calculated Dihedral Angles of the P-Protons in 1'+-4'+ 1 2'+ 3'+ 4'+ EA'+

.+

hfcc, mT a2

0.910 0.120

1.350 0.370

e, e2

45 75

-2 122

1.81

1.39

a,

0.241 0.041

0.404 0.404

0.36" 0 36

60 60

60 60

1.62

144

Angle, deg 46 74

B2p9,b mT 0 51

"Taken from ref 11. bSee text of hfcc is also straightforward as given in Table I. As in the case of 1'" and 2'+, the hfcc of the methylene protons were separated into two groups. @-ProtonSplitting. The hfcc of the @-protonsin 1". 2'+, and 3'+ are not equivalent and split into two groups as seen in Table I. Furthermore, the hfcc of the equivalent @-protonsin 4'+,3.404 mT, is much smaller than the methyl hfcc in MA", 0.779 mT. The origin of this anomaly must be in the rigid conformation of the methylene groups. It is well-known that the splittings of @-protons, a(CH2), can be correlated to the geometries of alkyl groups by using the Heller-McConnell relationship,' written as

a(CH2) = (Bo + B2 cos' 8 ) p , where 6' are the dihedral angles of the P-protons and p, are the spin densities on the aromatic carbons substituted by alkyl groups. Bo and B, are constants and, in the following argument, we neglect Bo because it has been estimated to be very small from the experimental and theoretical analyses.' The dihedral angles for the two @-protons,0, and e2, and B2~9 can be calculated by combining the above equation for the two P-proton hfcc with 8, + 82 = 120' expected for sp3 configuration. In Table I1 are summarized the angles and B2~9for l'"-4'+ together with those calculated for 9-ethylanthracene cation radical (EA")" for the sake of comparison. The conformations of the ( 9 ) (a) Heller, C.; McConnell, H . M. J . Chem. Phys. 1960, 32. 1535. (b) Sevilla, M. D.; Vincow, G .J . Phys. Chem. 1968, 72, 3647. ( I O ) Bolton. J. R.; Carrington, A,; McLachlan, A. D. Mol. Pk.vs. 1962, 5. 161.

Figure 6. Schematic views of the intramolecular sandwich-likestructure for 3" constructed on the basis of the normal methylene with sp3 configuration (A) and the distorted methylene to explain the experimental result (B).

@-protonsobtained from the calculated angles are schematically shown in Figure 4 for 1, 2, and 4, and Figure 6B for 3. We now compare B@9of 1'+-4'+ with those of MA" and EA" given in Table 11. In the case of MA", we obtain B2p9 = 1.56 mT from cos2 6' = because of free rotation of the methyl group. It is noted that B 2 ~ 9of 1'+-4'+ are somewhat different from each other and also from those of MA" and EA". The observation that B2p9 of 3'+, 0.51 mT, is very small is explained mainly by the small value of p9 due to the delocalization of the unpaired electron into the two rings. Although B2p9 changes corresponding to the changes in both p9 and the structure of the methylene group, p9 of these compounds are considered to be close to those of MA" a i d EA" from the observed hfcc of the ring protons. Therefore the change of B2 induced by the distortion of the methylene groups is probably the main cause of the different values of B2p9. The two @-protonsin 4" are equivalent and have the angle of 60' (Figure 4C). It is then concluded that the @-protonsin 4" exist in an almost fixed conformation and the rotation of the methylene group is restricted by the steric hindrance between the alkyl groups and peri protons. This situation may be similar to the case of 9-ethylanthracene cation radical in which the two P-protons have an equivalent hfcc of 0.36 mT.9 The angles of the @-protonsin 1" deviate from 8 = 60' for the stable conformation as seen in Figure 4A. It is considered that the origin of this deviation is due to the steric hindrance between the two anthracene rings. The deviation is even larger in the case of 2". It is difficult to rationalize the observed conformation by taking into consideration only the steric repulsion between the @-protons and anthracene rings. Intramolecular Sandwich-Like Structure of3". Both ESR and CV results for 3''' indicate unambiguously that the unpaired electron is delocalized over the two anthracene rings. The potential shift of the cathodic peak is similar to those obtained for the dimer cation radicals of naphthalene derivatives4" and fluoranthene." The difference between the anodic and cathodic peak potentials, 0.10 eV, can be regarded as the stabilization energy due to the transannular interaction between the two anthracene rings. In order to confirm that the stabilization is due to the intramolecular dimer formation and not to the intermolecular dimer ( 1 1 ) Backmann, D. 2. Phys. Chem. 1964, 43, 198. (12) Enkelmann, V.; Morra, B. S.; Krohnke, Ch.: Wegner, G.; Heinze, J. Chem. Phys. 1982, 66, 303.

J. Phys. Chem. 1986, 90,4961-4969 formation, we have simulated the cyclic voltammograms for the two cases with a stabilization energy of 0.10 eV (Figure 5).13 The observed CV curve (Figure 1C) is obviously close to Figure 5A in shape and intensity of the anodic peak, further confirming our conclusion. The hfcc due to the ring protons in 3" are close to half the corresponding hfcc in MA'+, and the numbers of the equivalent protons are twice those in MA". Therefore, the symmetry of the relative configuration of the two anthracene rings is considered to be high.4a Constructing molecular models for 3'+ with high s mmetry, we find that the inter-ring distance becomes about 2.5 the dihedral angles of the two- P-protons being 30° and 90° as shown in Figure 6A. However, this model is not considered to be appropriate because the inter-ring distance of 2.5 A is much smaller than those found for the salts of aromatic dimer cation r a d i ~ a l s l (2.9-3.2 ~ . ~ ~ A) and the dihedral angles do not agree with the experimental result. In the actual conformation of 3'+ the inter-ring distance becomes larger than that given in Figure 6A, resulting in the distortion of the propyl chain as shown in Figure 6B.

1,

~

~

~

~~

4961

In the case of 4 a structure in which the two anthracene rings take a parallel sandwich-like structure is also possible, but the inter-ring distance becomes about 4 A. Energy stabilization due to transannular interaction is probably very small at this distance, making this structure unstable. It is difficult to construct a molecular model with the inter-ring distance of about 3 A because of the steric hindrance between the peri protons and alkyl protons. It is not probable that intramolecular dimer formation takes place in 4". This is in agreement with the ESR and CV results. According to the results on the excimer formation of diphenylalkanes and dinaphthylalkanes so far reported,] the efficiency of excimer formation is highest in the compounds linked by propane chains, which agrees well with the result in this work. In the case of anthracene, however, it has been reported that no excimer emission was observed for 32, which may be due to the high reactivity of the excimer having a strong transannular interaction in an eclipsed dimer structure. On the other hand, excimer emissions were observed even in 2 and 4. It is thus concluded that transannular interaction is most efficient in the compound linked by a propane chain in the both excited state and cation radical, but it acts over a longer range in the excited state.

~

(13) Feldberg, S. Electroanal. Chem. 1969, 3, 199-296. (14) Fritz, H. P.; Gebauer, H.; Friedrich, P.; Schubert, U. Angew. Chem., Int. Ed. Engl. 1978, 17, 275.

Registry No. 1, 15080-14-5; le+,103499-74-7; 2, 4709-79-9; 2'+, 95977-51-8; 3, 63934-10-1; 3'+, 103616-09-7; 4, 63934-1 1-2; 4", 103616-10-0; MA, 779-02-2; MA", 34467-27-1.

Rotational Spectra of Rare Gas-Nitrlc Oxide van der Waals Molecules. 2. The Structure and Spectrum of Argon-Nitric Oxide Paul D. A. Mills,+ Colin M. Western,: and Brian J. Howard* Physical Chemistry Laboratory, Oxford University, Oxford, OX1 3QZ, U.K . (Received: January 7, 1986)

The microwave and radio-frequency spectra of the open-shell van der Waals complex Ar-NO are presented. The results show a near T-shaped molecule with a vibrationally averaged intermolecular distance of 3.71 A. Within the complex the orbital angular momentum of NO is largely unquenched, but the barrier to free orbital motion exhibits a minimum with the *-electron out of the plane of the dimer. Nitrogen hyperfine parameters are derived for the complex and are shown to be slightly perturbed from those of the monomer. However, the overall results are consistent with little electron rearrangement on complex formation.

1. Introduction In paper 1 of this series (hereafter referred to as 1) a theory was derived for the rotational energy levels of rare gas-nitric oxide van der Waals molecules. In this paper we will present the rotational spectrum of the argon complex obtained with the molecular beam electric resonance technique. This spectrum will then be analyzed in terms of that theory and the structure, and molecular parameters derived for the complex will be discussed. Both experimental and theoretical studies have previously been made of the argon-nitric oxide system.*-I1 As early as 1973 Novick et aL2reported the strong polarity of ArNO in an electric deflection experiment although no spectroscopy was attempted. Since then there have been investigations of the electronic spectrum of the complex by Langridge-Smith et al.,3 who observed direct photodissociation of the complex following laser excitation to the repulsive wall of the A2Z+state. More recently still, Suto, Achiba, and Kimura4 observed spectra involving "bound-to-bound" transitions to the excited C 2 n state of ArNO using multiphoton ionization techniques. These workers were able to derive dissociation energies for the complex in this excited state as well as for the Ar NO+(XIZ) ion. Present address: Corporate Colloid Science Group, IC1 plc, The Heath Runcorn, Cheshire WA7 4QE, U.K. *Present address: School of Chemistry, University of Bristol, Bristol BS8 ITS, U.K.

0022-3654/86/2090-4961$01.50/0

Molecular beam scattering studies by Thuis and co-workers5-' have probably provided the best experimental data on the argon-nitric oxide anisotropic intermolecular potential. Their measurements of the total collision cross sections, determined with and without orientation of the nitric oxide molecules, were analyzed with the sudden approximation. The later reference contains results that were expressed in terms of a modified Maitland-Smith anisotropic potential containing the previously neglected PI(cos (1) Mills, P. D. A.; Western, C. M.; Howard, B. J. J . Phys. Chem. 1986, 90, 3331.

(2) Novick, S. E.; Davies, P. B.; Dyke, T. R.; Klemperer, W. J . Am. Chem.

SOC. 1973, 95, 8547. (3) Langridge-Smith, P. R. R.; Carrasquillo, E.; Levy, M.; Levy, D. H. J . Chem. Phys. 1981, 74, 6513. (4) Sato, K.; Achiba, Y.; Kimura, K. J . Chem. Phys. 1984, 81, 57. ( 5 ) Stolte, S.; Reuss, J.; Schwartz, H. L. Physicn 1973, 66, 21 1. (6) Thuis, H.; Stolte, S.; Reuss, J. Chem. Phys. 1979, 43, 351. (7) Thuis, H.; Stolte, S.; Reuss, J.; van den Biesen, J. J. H.; van den Meijdenberg, C. J. N. Chem. Phys. 1980, 52, 211. (8) Kalinin, A. P.; Khromov, V. N.; Leonas, V. B. Mol. Phys. 1982, 47, 811. (9) Andresen, P.; Joswig, H.; Pauly, H.; Schinke, R. J . Chem. Phys. 1982, 77, 2204. (10) Nielson, G. C.; Parker, G. A.; Pack, R. T. J . Chem. Phys. 1977, 66, 1396. (1 1) Nielson, G. C.; Parker, G. A,; Pack, R. T. J . Chem. Phys. 1976, 64, 2055.

0 1986 American Chemical Society