NOBORU HIROTA
138
vary and generally decrease as the size of the metal ion increases. The species with small dipole interaction is assigned to the solvent-shared dimer ion pair.l' Therefore, the equilibrium in this system is shown by R'i: -6 R'
@ 6-C IR - R&-5 @ @ O0-C /.R @)
R'
R '
@@@
R'
(B)
(A)
The relative concentration of (B) with respect to (A) was found to be 1.1 at 77°K for sodium hexamethylacetone and increases very rapidly with temperature. A t room temperature it is safe to state that the dominant component is the solvent-shared ion pairz0 (B). Details of the structure and equilibria involving ketyls will be reported elsewhere. F . Spin Density at the Alkali Metal. Several investigators previously reported the values of alkali metal splittings for many radical ion pairs. Several theoretical estimates2" were also made and estimated values were compared with the experimental values. However, the alkali metal splittings depend on the structures of the ion pairs and the exact structures were not known for most cases. It is desirable to obtain the splitting in the system in which the ion pair is a real contact ion pair. The largest alkali metal splittings and the corresponding spin densities obtained in this investigation are tabulated for Na, K, and Cs. K
cs
2.14 (DEE, $23") 6.77
0.060 (DEE,
1.36 (MTHF, -80") 1.66
2.94 (DBE,
0.230 (DEE,
$50') 9.29
-80') 2.80
Na
f a M , KaUSS
Naphthalene
1
'
(PM
-
x
10-8
LYM, gauss
Anthracene p~
x
10-3
-80") 0.73
0.64 (MTHF, -80") 0.78
The alkali metal splittings given here are larger than those previously reported.2n6 The values for potassium and cesium may be close to the values for the contact ion pairs. The value for the sodium contact ion pair would possibly be larger than the value given here. Spin densities on the alkali metal ion depend largely on the nature of the positive and negative ion. Spin densities at the sodium nucleus are undoubtedly larger than at the potassium and cesium nuclei. In order to test the validity of the various mechanisms to produce alkali metal splitting, clear-cut experimental data for t,he splittings in the known ion pair structure must be obtained. We are presently carrying out a The Journal of Physical Chemistry
more systematic survey of the alkali metal splittings in order to clarify the mechanism producing - it.
Acknowledgments. The author thanks Professor R. Kreilick of the University of Rochester for stimulating discussions. He is also indebted to Messrs. R. Carra: way, W. Schook, and T. Takeshita for their assistance in obtaining and analyzing some of the epr spectra. Financial support from the National Science Foundation (GP-5040) is greatly appreciated.
Discussion J. R. BOLTON (University of Minnesota, Minneapolis). Would you care to comment on the negative value of AS" for the ionpair equilibrium?
N. HIROTA. The negative value of AS' in going from a tight ion pair to a loose ion pair is considered to be due to the difference in the solvation of solvent molecules to the positive ions in two different ion pairs. It is considered that the better solvation in a loose ion pair than in a tight ion pair brings more partial ordering of the solvent molecules around the positive ions. This situation is shown in the article by a model, though the model is speculative and mainly for illustrative purposes.
J. L. DYE (Michigan State University, East Lansing). Since solvents such as tetrahydrofuran can dissolve some alkali metals, perhaps the high-temperature form is partaking of "monomer" character such as one has in metal-amine solutions. N. HIROTA. Although the sodium splitting increases at higher temperatures, the spin density a t the alkali metal nucleus is still and this ion pair seems to be quite difvery small ( p 5~ ferent from the "monomer" in metal-amine solutions. The correlation between the sodium splitting and the proton splitting (Figure 7 ) indicates that the positive and negative ions come closer in the high-temperature form of the ion pair, and i t a p pears that the close approach of two ions is primarily responsible for the larger metal splitting. The alkali metal splitting would increase by the mechanism, such as charge transfer, when two come closer. The alkali metal splittings are usually larger in DEE than in DME or THE. I do not think that sodium and potassium dissolve in DEE, though they dissolve in DME a t lower temperatures. G. VINCOW (University of Washington, Seattle). Would you care to comment on possible differences in the structures of loose ion pairs 3 and 4 which might account for the kinetic differences observed? N. HIROTA. Since a loose ion pair 3 is interconverting rapidly with a tight ion pair 2, probable structure of ion pair 3 would be a solvent-shared (or separated) ion pair, such as shown by 3 or 4 of the model given in section IV.A.l. I do not have any definite answer as to the structure of the loose ion pair 4. The main reason to suggest that this is an ion pair rather than a free ion is the observation that the rates of electron transfer are rather slow and the activation energies are rather high. At this stage I would just like to mention some possibilities and wait for further investigations. One possibility is that the loose ion pair 4 is a solvent-separated ion pair in which ions are separated (20) This conclusion was also obtained from the recent investigation by G. R. Luckhurst, Mol. Phys., 9 , 179 (1965).
LINEWIDTHSAND FREQUENCY SHIFTSIN ESRSPECTRA
with two or more solvent molecules, although I do not know if this structure can explain the kinetic data reasonably. The other possibility is that the ions may exist as an ion cluster with solvent moledes between ions rather than the ordinary one-to-one ion pair.
E. DE BOER(University of Nijmegen, Netherlands). Do you have an explanation for the reversal of the sign of the spin density at the Li nucleus for the Li-fluorenone ion-pair when you change the temperature? N. HIROTA.You have suggested that there are two different mechanisms to produce spin density at metal nucleus, one to produce positive spin density and the other to produce negative spin density, and that the sign depends on the relative importance of two mechanism [Rec. Trav. Chim., 84,609 (1965)l. I
139
think this is another example to support your suggestion. If the Li ion sits on the nodal plane of 2pn orbital of fluorenone, and the vibration of the Li ion perpendicular to this plane is small, the positive contribution is expected to be very small because of the small overlap integral between the 2 p orbital ~ of ketyl ion and the s orbital of the Li ion. Furthermore, if the Li ion separates more from the negative ion as the temperature dependence of CIS splitting seems to indicate, this contribution would quickly decrease a t lower temperatures. The negative contribution, on the other hand, may not be so sensitive to the position and the separation aa the positive contribution and may survive at lower temperatures. However, further investigations seem to be necessary in order to understand fully the reversal of the sign as well as the mechanisms to produce alkali metal splittings.
Line Widths and Frequency Shifts in Electron Spin Resonance Spectral
by George K. Fraenkei Departmat of Chemistry, Columbia University, New York, New York lOOdY
(Received September dY, 1966)
A general account is given of the most important types of line-width variations which occur in the electron spin resonance spectra of dilute solutions of free radicals. The effects considered include modulations of the isotropic hyperfine splittings and of the anisotropic gtensor and electron-nuclear magnetic dipole interactions. The influence of fluctuating interactions on the positions of the hyperfine lines (frequency shifts) is also discussed. General formulas are obtained either from intuitive arguments or quoted without proof from the results of the relaxation-matrix theory. Several model systems are discussed, and a brief survey is included of applications to structural problems of chemical interest.
I. Introduction In the past few years, the widths of the hyperfine lines in the electron spin resonance spectra of free radicals has been the subject of considerable investigation. At first, the line-width variations which were observed appeared to represent relatively isolated examples, but as the work progressed, it became increasingly evident that many of the phenomena were quite general and of considerable importance. On the one hand, the proper interpretation of many spectra is only possible if t,he line-width effects are taken into account. More interestingly, line-width studies can be used to obtain information about structural problems. Recent work
has provided data, for example, about intramolecular and intermolecular motions, ion-pair and other radicalsolvent interactions, and n-electron spin-density distributions. Since the theoretical formulations2*3are quite general and, concomitantly, complex, a useful purpose would undoubtedly be served at this time by presenting in as simple a form as possible the salient and most frequently applicable aspects of the theory (1) This research was supported in part through National Science Foundation Grant No. NSF-GP-4188. (2) (a) D. Kivelson, J . C h a . P h ~ a .27, , 1087 (1957); (b) D. Kivelson, ibid., 33, 1094 (1960). (3) J. H. Freed and G. K. Fraenkel, ibid., 39, 326 (1963).
Volume 71,Number 1 January 1967
