2892
J. Phys. Chem. 1985,89, 2892-2896
Far-Infrared Spectrum of Solvated Lithium Cations in Tetrahydrofuran S. Chang, M. W. Severson,* and P. P. Schmidt* Department of Chemistry, Oakland University, Rochester, Michigan 48063 (Received: February 1I , 1985)
We report the far-infrared spectra (in the region of 400 cm-') of the following salts at 298 and 110 K: LiCl, LiBr, LiI, LiC104, and LiBF.,. The low-temperature spectra, cooled by liquid nitrogen, were obtained to see if there exists any resolved fine structure which might be useful in determining the nature of the solvation of the lithium cation at ambient temperature. In addition to the experimental results, we report the results of a preliminary Monte Carlo statistical simulation of the spectra for these systems in the liquid and solid states. The simulations are in qualitative agreement with the experimental results. Both the simulations and the experimental spectra indicate that the solvation of the ion at ambient temperatures yields a single band. In the solid crystalline phase, ion-pairing results in a resolution of the spectrum of solvated lithium into two bands. The presence of water, as an impurity, results in the appearance of three bands.
Introduction It is only relatively recently that the far-infrared spectra of the solvated simple cations of the group 1 elements have begun to be investigated;'" the solvation of these ions has been of interest for a much longer time.6 If the structure, mechanics, and thermodynamics of these simpler systems in solution can be understood, then it ought to be possible to understand the solvation of more complicated systems. Spectroscopic studies may be useful for untangling the apparently simple but still elusive structures of solvation, At room temperature, the far-infrared spectra of the simple group 1 cations in a variety of solvents are broad and relatively featureless. The investigators who reported the original far-infrared spectra offered some simple models to account for some of their features.'-5 The most remarkable observation of all, however, is that of a lack of obvious structure. Over a fairly large span in frequency, there is only one spectral maximum and there is no immediately obvious, published spectral suggestion of fine structure or splitting. Our purpose in examining the spectra of these simple systems is to see if there exists any fine structure within the relatively simple structures which are already known in order to see. if the spectra might yield any more definite information about the structure of solvation of the ions. Thus, if more information is available about solvation it may eventually be possible to determine accurate potential energy functions for the ionsolvent intractions that exist in the inner shells of solvation. There is evidence from the far-infrared spectra of the solvated lithium cation in liquid and solid, crystallized solution that ordered, crystalline structures of the solid state persist as majority structures in solution. It is apparent from our experimental results that thermal averaging in the liquid state obliterates any spectral fine structure which could carry over from the solid to the liquid phases. The broad bands of the liquid-state spectra appear as spectral envelopes over the resolved bands of the solid, crystalline state. Several years ago, a preliminary investigation of the spectra of the group 1 cations was made in order to try to assign realistic parameters to representative potential energy function^.^^^ Central to that investigation was the assumption that regular, crystalline-like coordination applied to the structures of the primary shells of solvation. In particular, it was assumed that coordination/ solvation according to one of the cubic symmetry groups applied.
It was found, in contrast to earlier assumptions that, under these conditions, ionic-dipolar contributions to the force constant for the oscillation of the centrally solvated cation in an inertial cage of solvent vanished due to symmetry. This fact was demonstrated simply with the use of the Carlson-Rushbrooke expan~ion.~Thus, apparently, the far-infrared-active spectra of the solvated ions could be used primarily as probes of the repulsive forces which operate between the ion and the solvent in its immediate neighb~rhood.~ The spectrum which follows with the use of such a model and the associated analysis consists of only a single band. Deviations from rigid crystallinity of the primary shell of solvation, which arise due to fluctuations, can be shown relatively easily to have a small effect on the ionic-dipolar contributions to the spectrum. Thus, random displacements of the solvent about positions of equilibrium in a regular arrangement are expected to account only for a broadening of the single-maximum band. For a number of reasons, we suspected that perhaps underneath the envelope there was indeed a fine structure to the spectrum which might suggest the existence of a more complicated, and interesting, system. At room temperature, such fine structure would be statistically washed out. A light ion, such as the lithium cation, for example, might tunnel from its cage of primary solvation to a neighboring vacancy; the tunneling would be observed as a spectral band splitting. In addition, if there is an underlying, permanent asymmetry to the structure of solvation, then, as the sample is cooled, individual bands for each of the degrees of freedom available to the ion should appear in the spectrum. We can report the absence of any obvious permanent structure due to persistent, crystalline solvation of the lithium cation in the liquid or glass phases to temperatures as low as 110 K. There is no evidence of strong, crystallike interactions which would yield spectral fine structure upon the simple cooling of the system. Nevertheless, there is an experimentally observable asymmetry to the spectral envelopes and this asymmetry can be attributed to two modes of vibration which are available to the ion within its cage of solvent; these modes of vibration arise in a majority structures which have a predominantly crystalline character. When the samples are allowed to crystallize, however, a resolution into bands occurs. These resolved bands lie under the envelope of the original single band. In solution, fluctuations of the molecules of solvent within the first shell clearly result in a broadening of the spectrum which is sufficient to obliterate any band structure.
(1) B. W. Maxey and A. I. Popov, J . Am. Chem. Soc., 90, 4470 (1968). (2) B. W. Maxey and A. I. Popov, J . Am. Chem. Soc., 91, 20 (1969). (3) J. L. Wuepper and A. I. Popov, J. Am. Chem. Soc.,92, 1493 (1970). (4) M. K. Wong, W. J. McKinney, and A. I. Popov, J. Phys. Chem., 75, 56 (1971).
(5) W. F. Edgell, J. Lyford, R. Wright, W. Risen, and A. Watts, J. Am. Chem. Soc., 92, 2240 (1970). (6) See,for example, J. Burgess, 'Metal Ions in Solution", Ellis H o r w d ,
Experimental Section Lithium chloride, bromide, iodide, perchlorate, and tetrafluoroborate were obtained from Aldrich and were dried under vacuum prior to use. A sample of 6LiOH was obtained from MSD Isotopes Inc., and was specified as 99% isotopically pure. 6LiC1, 6LiBr, 6LiI, 6LiC104,and 6LiBF4were prepared by neutralizing
Chichester, 1978. (7) P. P. Schmidt, B. S. Pons, and J. M. McKinley, J . Chem. SOC.,Faraday Trans. 2, 76, 919 (1980). (8) P. P. Schmidt, J . Chem. SOC.,Faraday Trans. 2, 78, 123 (1982).
(9) B. C. Carlson and G. S. Rushbrooke, Proc. Comb. Phil. SOC.,46, 626 (1950).
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Far-IR Spectrum of Li Cations in T H F
The Journal of Physical Chemistry, Vol. 89, No. 13. 1985 2893
I
500
400
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cm-' Figure 1. The far-infrared spectra of lithium salts in THF at,298 K: concentration, 0.7 M; path length, 0.1 mm; (a) LiCI, (b) LiBr, (c) LiI, (d) LiC104, (e) LiBF4.
Figure 2. The far-infrared spectra of lithium salts in THF at 110 K: concentration, 0.7 M; path length 0.1 mm; (a) LiCI, (b) LiBr, (c) LiI, (d) LiC104, (e) LiBF4.
an aqeous solution of 6LiOH with the appropriate acid and drying the resulting salt under vacuum. Tetrahydrofuran (THF) was purified by treatment with KOH, to remove peroxides, followed by distillation from Na metal. The effects of the inadequate drying of the salts or the solvent is discussed below. Far-infrared spectra were obtained with an IBM Instruments Inc. IR-98 Fourier transform infrared spectrometer (FTIR) with a helicoil source, 3-pm mylar beamsplitter, and a DTGS detector with a polyethylene window. The sample cell, which was fitted with polyethylene windows, was in thermal contact with a liquid nitrogen reservoir which allowed cooling of the cell to 110 K; sample temperatures were monitored with a copper-constantan thermocouple connected to the cell body. Room temperature spectra were recorded with the spectrometer purged with dry nitrogen. The low-temperature spectra were recorded with the spectrometer under vacuum.
TABLE I: Vibrational Frequencies (cm-I) of Bands due to 'Li+ and 6Li+ Vibrations for CI-,Br-, I-, Clod-, and BF, Salts at 298 and 110 K 298 K 110 K anion 'Li t i 'Li %i c1388 415 370, 415 395, 442 Br380 406 400" 430" I375 376, 403 405, 432 400 Clod397 422 415 439 B F4410 438 422 453
Results Far-infrared spectra for LiCl, LiBr, LiI, LiC104, and LiBF4 in THF a t 298 K are shown in Figure 1. For these spectra a concentration of 0.7 M and path length of 0.1 mm were used. Spectra for the same solutions at 110 K are shown in Figure 2. In each case, the spectrum of pure T H F was used as the reference. Spectra were also obtained with the 6Li isotope of each of the salts. The results are summarized in Table I. The spectral resolution of the solid-phase bands is not due to the spectra of the separated lithium salts.1° The spectra which are observed are the genuine lithium-solvent and ion-pair bands. The spectra due to LiC104 and LiBF4 show bands at 470 and 530 cm-', respectively; these may be assigned to internal vibrations of the a n i ~ n . ' ~ . ' ~ (10) J. R. Ferraro, 'Low-Frequency Vibrations of Inorganic and Coordination Compounds", Plenum Press: New York, 1971. (1 1) N. Metropolis, A. W. Rosenbluth, M.N. Rosenbluth, A. H. Teller, and E.Teller, J . Chem. Phys., 21, 1087 (1953). (12) P. J. Rossky, J. D.Doll, and H. L. Friedman, J . Chem. Phys., 69, 4628 (1978). (13) J. M. McKinley and P. P. Schmidt, J . Chem. SOC.,Forodoy Trons. 2, 78, 067 (1982). (14) J. M. McKinely and P. P. Schmidt, Chem. Phys. Lerr. 110, 379 (1984).
a,
Broad band with apparent doublet structure; see text.
It is reasonable to expect ion pairing to be an important effect in solutions of ions in a weakly solvating solvent such as THF, and previous results have been interpreted this However, larger cation/anion aggregates may form at high salt concentrations, and it is possible that such large aggregates are present in the ranges of concentration we have employed. We have carefully studied the dependence on concentration of the spectra of all of these salts in THF and find no changes in the bands due to the lithium cation for concentrations between 0.05 and 1.O M. On the one hand, the locations of the bands due to lithium in the spectra of the various solutions at 298 K were not affected by the addition of water, although the intensities varied markedly. On the other hand, at 110 K the presence of water had a significant effect. For example, for samples of LiBr which were not adequately dried, the spectrum showed a small band at 509 cm-' in addition to the primary band a t 400 cm-'. Adding more water to the solution resulted in an increase in intensity of this band relative to that at 400 cm-I. Carefully dried samples gave only the 400-cm-' band. Similar results were obtained for the other solutions. Further studies of the interactions of water with the cation/anion/solvent system are in progress. (15) M. H. Abraham and J. Liszi, J . Chem. SOC.,Faraday Trons. 2,74, 1604 (1978). (16) J. K. Wilmshurst, J . Chem. Phys., 36, 2415 (1962). (17) K. Nakamoto, "Infrared and Raman Spectra of Inorganic and Coordination Compounds", Wiley, New York, 1978.
2894 The Journal of Physical Chemistry, Vol. 89, No. 13, 1985 Theoretical Simulation of the Spectra There are data, and there are interpretations of these data, which suggest that the solvation number for the lithium cation is four and that the structure of the first layer of solvent ought to be tetrahedraL6 It is appropriate to note, however, that there are data and interpretations of data which seem to implicate other numbers of solvent and, of course, other structures of solvation.6 We have carried out two kinds of computer simulation in order to try to understand better the experimental results. Our work focuses on tetahedral structures, but we believe our results apply to more cases than simply to the single model system which we consider here. An account of these simulations follows. Classical potential energy functions were employed, that is, only classical electrostatic interactions and simple power-law repulsions were considered; no quantum mechanically derived functions were used. The solvent was modeled as a collection of polarizable spheres with embedded point dipoles. All species, the ions and the dipolar solvent, repelled each other through r-I2 interactions. The individual solvent molecules interacted with each other through the usual direct dipole-dipole term. At the beginning of each kind of calculation, the solvation about the central cation was tetrahedral. In addition, secondary solvent occupied appropriate alternate tetrahedral sites at distances which are greater than those which were used in the primary shell. Finally, an anion was included; it was placed both in the primary shell to simulate tight ion pairing and in the secondary shell to simulate the looser ionic association. It was assumed here, as has been assumed in other calculations, that the solvent behaves inertially compared to lithium. In the sense of the Born-Oppenheimer approximation, the cation oscillates about a position of equilibrium within a massive and rigidly fixed cage of solvent. [The breakdown of this assumption is expected to be seen simply as an environmentally dependent fine structure which should be detected only at very low temperatures.] The potential energy functions which were used are the following: (a) dipole-dipole
Chang et al. bration. Subsequent additional random structures, however, were generated from the last randomly generated structure before the lithium was displaced to its position of equilibrium. With the generation of each configuration according to the usual scheme, the three normal modes of oscillation for the centrally solvated ion are determined. The spectrum for the 0 to 1 transitions of lithium along each of the three available degrees of freedom within its cage was determined as a histogram over a range of frequencies from 0 to 1000 cm-’. In order to determine the values of the force constants for the oscillation of the cation, it is necessary to consider the expansion of the complete potential. If Ri is the vector from the origin (and location of the lithium cation) to the solvent molecule “in,and r is the vectorial displacement of the lithium cation from its position of equilibrium, then an ion-single dipolar solvent contribution to the complete force constant has the form
in which the subscripts i j = x,y,z; in this and the following expressions, the diagonal elements of the force constant matrix are k, and the off-diagonal elements are k,. The ion-pair contribution to the force constant is easily derived from the Laplace expansion of the free-space Green function:
(7) e2Z kjj = -3-XJj RS The remaining contributions to the force constant for the oscillation of the centrally solvated ion are derived with the use of an expansion due to McKinley and Schmidt:’J3J4
in which al and a2 are the vectorial dipole moments on molecules 1 and 2; (b) ion-dipole
The angle between the vector from the cation to the solvent dipole and the orientation of the dipole moment is 0; (c) ion-induced dipole
v, = --e2Za
2 ~ 4
(3)
here a is the polarizability of the solvent; (d) repulsion
v, = B / R I Z
with
(4)
and B is the strength of the repulsion (it is determined in part by the distance of closest approach between the two species). For the simulation of the first kind, the calculation proceeds with the aid of a Monte Carlo/Metropolis et al. sampling routine.” The location of a molecule of solvent is displaced according to the generation of a set of random numbers. This displacement also includes the orientation of the dipole with respect to the laboratory based set of coordinates. Metropolis sampling is carried out until the total energy of the system stabilizes; typically this is accomplished in roughly 50000 sample cycles. In order to accelerate the approach to equilibrium, we used the “smart Monte Carlo” method suggested by Doll et al.12 Once equilibrium had been reached, additional Monte Carlo sampling was carried out in order to build the spectrum. Each time a solvent molecule or the anion was displaced, the lithium cation was moved to its position of equilibrium within that structure for the purpose of determining the frequencies of vi-
where V is the particular potential energy function. The ioninduced dipolar (polarization) contribution to the force constant is therefore
and the r-12 interaction yields
B kij = 168-R16x4 The values of the parameters used in the potential energy functions and in the expressions for the force constants were determined in part from macroscopic quantities. The molar polarizability of the solvent was determined from the refractive index
Far-IR Spectrum of Li Cations in THF
The Journal of Physical Chemistry, Vol. 89, No. 13, 1985 2895 .04T
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Figure 3. The Monte Carlo simulation of the far-infrared spectrum of a solvated lithium halide in T H F (a) 300 K, (b) 100 K.
with the use of the Lorentz-Lorenz equation. The dipole moment of THF is the common value of 1.7 D. The solvent radius is given by Abraham and Liszi.lS Finally, values for the repulsion parameter B were determined with the use of pairwise equilibrium relationships. The effect of anionic radius was taken into account primarily through an adjustment of the ion-pair and anionsolvent repulsion parameters. For the second type of simulation, the evaluation of the force constants within any individual configuration was the same as just described. However, the sampling technique differed from that described above. One problem we found when attempting to simulate solvated systems with small numbers of solvent and ions is the difficulty in knowing what the packing density is. Moreover, we suspect strongly that liquid-phase simulations are acutely sensitive to the microscopic potential energy functions and to the actual, discrete molecular structures of the species involved. The featureless spherical solvent cannot settle into the actual structures which undoubtedly exist. Therefore, in order to atone in part for the transgression of oversimplicity, we constrained the simple model to be crystalline, as presumably it would be in the solid phase. A crystalline configuration of solvent and counteranion was preserved and new random codigurations were generated with referenced to this structure. Metropolis sampling was used to discard high-energy fluctuations. Within each new configuration, the cation was allowed to seek its position of equilibrium prior to the evaluation of the force constants for the oscillations of that species within its cage of solvent and anion.
Discussion Although it is difficult to adjust of some of the parameters of the potential energy functions in order to get an accurate simulation of the spectra in solution, certain trends seem to emerge. The interpretation of these trends, we believe, assists in understanding the experimental spectra. First, for both types of simulation, loose ion pairing between the centrally solvated lithium and the counterion yields a single
b
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Figure 4. A restricted Monte Carlo simulation of the far-infrared spectrum of a solvated lithium halide in a crystallineTHF environment:
(a) tight ion pairing, (b) loose ion pairing. band both in solution and in the solid, presumably crystalline phases. There is, however, underlying structure to these single bands. In the liquid phase, the pronounced feature is an asymmetry in the single band, as indicated in Figure 3; there is an apparent shoulder. This asymmetry resolves into two bands upon cooling to 100 K. In this f i s t kind of simulation an outer boundary to the first shell of solvent was maintained, but there was no attempt to impose any kind of crystalline order. On the other hand, as shown in Figure 4,for tight ion pairing, there is a resolution of the single band into two bands in the solid crystallized phase. One band is clearly a direct ion-pair oscillation band while the other is due to the oscillation of the ion against the neighboring solvent. In the case of a strongly associated impurity, such as water, the splitting of the original single liquid-phase band into a maximum of three. bands in the solid phase is seen. The presence of both the anionic counter charge and the water impurity in the inner layer of solvent lifts completely the original threefold degeneracy of the cation which is surrounded only by solvent in a configuration which belongs to the symmetry class of one of the cubic point groups. The results of our investigations into the modeling of the spectra indicate, a t this time, that an appropriate form of simulation (which preserves some of the simplicity which accompanies the use of spherical solvent) is to consider local crystallinity as we have done together with a less restricted, freer Monte Carlo sampling of the subsequent layers of solvent. Such simulations are presently under consideration. The far-infrared spectra of these solutions at 298 K are quite similar to those reported previously.'-5 For all of the salts a broad band near 400 cm-' is observed; the spectra for 6Li+ substituted salts demonstrate that these bands are due to vibrations primarily involving the lithion ion. As the mass of the lithium ion is much smaller than any of the other particles involved, the reduced mass for the vibration should be approximately equal to the lithium mass, and the isotope shift should be simply the square root of
J. Phys. Chem. 1985,89, 2896-2900 One feature worth noting is the fact that in the solid state the resolved spectral bands appear with approximately equal intensity. Although more work needs to be done on the simulations, we have noted the following. When the anionic counter charge replaces a solvent molecule which (at least at the start of the simulation) occupies the primary or secondary structure of solvation, the effect of the anion on lifting the degeneracy of the vibrations is not as great as it is when the ion tends to be restricted to some other position. Moreover, placing the counter charge in the original cubic structure tends to form a new system which still has a high level of symmetry; the ion-pair axis defines the C, axis of a trigonal bipyramid. Furthermore, the single anionic charge seems to have approximately the same solvating strength as the remaining nearest-neighbor solvent. Under these conditions, it is reasonable to expect that the intensities along the two resolved degrees of freedom might be nearly equal. We note that our spectral simulations do not yet take into account the actual vibrational transition probabilities. Nevertheless, the strength of the axial polarized transition would appear to be twice the strengths of the doubly degenerate, laterally polarized transitions. We conclude that there is substantial evidence that solid-state, local, essentially crystalline structures of solvation about lithium persist in the the liquid, solution phase. It is reasonable to expect that the continued examination of these solid systems should yield more information about solvation as well as accurate potential energy functions for the forces which operate between the ion and its neighboring species.
the ratio of the isotopic masses, or about 8%. This is approximately what is observed. The wavenumber of the band is a strong function of the anion, consistent with the earlier interpretation of ion pairing being an important effect in this relatively weakly solvating solvent.1-5 At 110 K the dependence of the lithium ion band on anion is even more pronounced. LiCl shows a sharp doublet at 370 and 415 cm-I which is symmetrically split about the wavenumber of the single band observed at 298 K, 388 cm-'. The spectrum of LiBr at 110 K shows a broad band centered at about 400 cm-'; this appears to be made up of two overlapping bands at 387 and 421 cm-'. The LiI spectrum shows two sharp bands at 376 and 403 cm-'. The spectrum of LiC104 shows a broad band centered a t about 415 cm-I. There is a shift to higher wavenumber upon going from the solution phase to the solid for LiBr, LiI, and LiClO,, in contrast to the results for LiC1. The band due to lithium in the spectrum of solutions of LiBF, shifts from 410 cm-' at 298 K to 422 cm-' at 110 K, but in this case the band at 110 K appears as a single sharp feature. We have observed that all of these frozen solutions are polycrystalline at low temperatures, but we have no knowledge of the crystal structure. It seems reasonable to assume that the local structure near a Li+ ion is largely determined by the short-ranged cation/anion/solvent interactions. The appearance of two bands (due to vibrations of lithium) in the spectra of the halide salts is consistent with a solvation sheath of tetrahedral or octahedral symmetry about the Li+ cation in which one of the solvent molecules is replaced by an anion. The appearance of a single band in the spectra of the BF4- and C104- salts is consistent with the formation of a looser ion pair. The differences observed for the spectra with different anions may then be attributed to slightly different structures of the solvation sheath. There are slight shifts in the spectral maxima for all species, apart from the chloride salt, on passing from the liquid to the solid states. It appears therefore that the structures formed in the solid differ to some slight extent from those which exist in solution.
Acknowledgment. This work was supported in part by the Office of Naval Research, Arlington, VA. The spectra were obtained on an IBM Instruments, Inc. IR-98 FTIR spectrometer which was purchased with the assistance of a University Instrumentation Grant from the Department of Defense, administered through the Office of Naval Research. Registry No. LiCI, 7447-41-8; LiBr, 7550-35-8; Lil, 10377-51-2; LiCIO,, 7791-03-9;LiBF4, 14283-07-9;Li*, 17341-24-1;THF, 109-99-9.
Structure and Kinetics in Aqueous Solution of Butyl Cellosolve from the Temperature Dependence of Ultrasonic Propertles Sadakatsu Nishikawa* and Kiyoshi Kotegawa Department of Chemistry, Faculty of Science and Engineering, Saga University, Saga 840, Japan (Received: October 2, 1984)
A pulse method ultrasonic absorption apparatus was improved with a microcomputer and a digital micrometer to reduce the period for higher precision absorption measurements. Ultrasonic absorption coefficients in the frequency range of 2.5-220 MHz for aqueous solutions of butyl cellosolve (ethylene glycol monobutyl ether) were measured as a function of concentration and temperature. Abnormal changes in the absorption and velocity were observed near the critical solution temperature. On the other hand, normal relaxational absorptions which were characterized by double relaxations were found in the isotropic phases. They were interpreted by a conventional kinetic approach and were attributed to reactions associated with an interaction between solute and solvent (hydrogen-bonding association) and with aggregation of the solute (hydrophobic interaction). The rate and thermodynamicconstants were determined from the concentration and temperature dependencesof the relaxation frequency and the maximum excess absorption per wavelength.
Introduction We reported ultrasonic absorption and velocity results in aqueous solutions of butyl cellosolve (ethylene glycol monobutyl ether) at 25 O C . 1 The relaxational absorptions were attributed to perturbations of equilibria associated with the solute and solvent
interaction and the aggregation of the solute. By decreasing the hydrophobicity of the solute, e.&, in a solution of propyl cellosolve (ethylene glycol monoProPY1 ether)2 Or with increasing hydrophilicity of the solute, e.g., in a solution of butyl carbitol (diethylene glycol monobutyl ether),3 a clear single relaxational ultrasonic
(1) S. Nishikawa, T. Tanaka, and M. Mashima, J . Phys. Chem., 8 5 , 6 8 6 (1981).
(2) S. Nishikawa, Y. Yamashita, and 55, 1 (1982).
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M. Mashima, Bull. Chem. SOC.Jpn.
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