J. Phys. Chem. 1980, 84, 2913-2920 (15) W. J. Baxter and 5 ; ~ R. Rouze, J. Appl. Phys., 48, 2429 (1975). (16) E. E. Huber, Jr., and C. T. Kirk, Jr., Surf. Sci., 5, 447 (1966). (17) G. A. Somorjal, “Principles of Surface Chemistry”, Prentice-Hall, Englewood Cliffs, NJ, 1972, p 249. (18) A. J. Dekker, “Solid State Physics”,Prentice-Hall, Maruzen, Tokyo, 1957, p 225. (19) J. C. Bolger and A. 8.Mlchaels, “Interface Conversion for Polymer
2913
Coatings”,P. Webs and 0. D. cheever, E&., American Elsevier, New York, 1968, p 3. (20) K. Tanaka in “Catalytic Engineering”,Vol. X, A. Ozaki, K. Tamaru, K. Tanabe, and S. Nishimura, E&., Chijinshokan,Tokyo, 1967, p 790. (21) L. Himmel and P. Kelly, Comments Solid State Phys., 7, 81 (1976). (22) J. Akutsu and H. Klrlhata, Sci. Pap. Inst. Phys. Chem. Res. (Jpn.), 67, 87 (1973).
ESR Studies OF Ion Pair Formation in Solutions of the Triphenyiene Anion Radical‘ M. Thomas Jones” and Raria
H. Ahmed
Department of Chemistty, University of Missouri-Si.
Louis, St. Louis, Missouri 63121 (Received: March 10, 1980)
Ion pair formation of the triphenylene anion radical with alkali metals (Na, K, Rb, Cs) in four solvents (1,2-dimethoxyethane,tetrahydrofuran, methyltetrahydrofuran,and tetrahydropyran)has been studied by ESR and theoretical techniques. The goals of the study were severalfold: one, to characterize the electronic and molecular structure of the triphenylenide anion radical-metal cation pair; two, to determine to what extent the ion pair is dependent upon the alkali metal ion and/or the solvent; three, to demonstrate that physical measurements such as proton hyperfine splitting, metal hyperfine splitting,g values, and optical spectra when combined with the use of molecular orbital calculationsof these same experimentalvariables can be very powerful techniques for the characterization of ion pair structures of radical systems. The results of the study suggest that four distinct species (Le., structures) exist. The most important result is that at high temperature and under conditionswhich favor tight ion pairs, the ion pair no longer possesses a static threefold rotation symmetry.
Introduction The purpose of the study described here is to investigate and to characterize the molecular and electronic structure of the triphenylenide anion radical-alkali metal cation pair. Previously reported ESR studies of the proton and metal hyperfine splitting5 (hfs)24 and optical spectral studies5p6 have established that under certain limited experimental conditions ion pair formation takes place. One of the goals of the study reported here is to investigate the effect of changes in the alkali metal, the solvent and the temperature upon the g values of solutions of alkali metal triphenylenides. Another goal is to demonstrate that experimental measurements of the g value when combined with other experimental data (in this case, proton hfs, metal hfs, and optical spectra) and theoretical calculations of these same experiimental observables can be very powerful tools for ion pair structure determination. Experimental Section Materials. The solvents used in this study (i.e., 1,2dimethoxyethane (DME), tetrahydrofuran (THF), methyltetrahydrofuran (MTHF), and tetrahydropyran (THP)) were prepared by previously described techniques? The alkali metals (sodium, potassium, rubidium, and cesium) were prepared by decomposition of the corresponding azidesa8Triphenylene and dibenzo-18-crown-6 ether were purchased from Aldrich Chemical Co. and used with no further purification. Sample Preparation. The anion radicals were prepared by technique^^^^ which have been previously described. The crown ether was introduced into the reaction vessel at the same time as the triphenylene. The amount of crown ether introduced was in excess relative to the triphenylene by at least a factor of 10 (on a mole-to-mole basis). ESR Spectrometer and g-Value Measurements. The ESR spectrometer arid the techniques used to measure the g values have been previously described in detailgJOand will not be repeated here.
Experimental Results g Values. Four different alkali metal salts &e., sodium, potassium, rubidium, and cesium) were studied in four different solvents (DME, THF, MTHF, and THP). The solvents were selected to represent a variation in ability to solvate alkali metal ions and are listed in order of decreasing solvating ability. In addition, each alkali metal triphenylenide/solvent pair was studied in the presence and the absence of 18-crown-6 ether. The purpose of the addition of the crown ether was to break up the ion pairs and/or to better solvate the alkali metal ions and to study the effect such changes would have upon the observed g values. However, the results do not support the conclusion that in all cases the addition of crown ether leads to a break up of ion-paired species. Of the possible 32 different combinations of alkali metal ion, solvent, and the presence or the absence of crown ether, the experimental results can be obtained for all but four combinations. The Cs/THP pair in the presence and the absence of crown ether cannot be studied because cesium reacts with THP. The Cs/ MTHF samples in the presence and the absence of crown ether can be prepared, but the ESR spectral line widths are so large that it is not possible to obtain accurate enough g-value measurements for meaningful analysis. Figure 1shows a fairly typical set of experimental reoults. The g values are plotted as a function of temperature for all four alkali metal salts in DME in the absence of crown ether. These results are similar to those obtained in two other solvents (THF and MTHF) with the exception of the rubidium salt, which behaves more like the cesium salt in DME. Figure 2 shows the results for the sodium, potassium, and rubidium salts in THP in the absence of crown ether. As a point of reference the g values for potassium in DME for Figure 1are included. The insensitivity of the g values toward changes in temperature for the sodium and potassium triphenylenides in T H P is in strong contrast to the behavior of all of the other combinations studied. We believe this occurs because the two salts are tightly ion
0022-3654/80/2084-2913$01 .00/0 0 1980 American Chemical Society
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The Journal of Physical Chemistry, Vol. 84, No. 22, 1980
Jones and Ahmed 2.00305
t
/
295 9
7
275 -100
-20
-60
T
+20
+60 -60
Flgure 1. Plot of g values as a function of temperature for alkali metal-triphenylenide solutions in DME. 2.00290 r
THP
. Na
-40
O
"C
,
,
40
Flgure 2. Plot of g values as a function of temperature for alkali metal-triphenylenide solutions in THP. The g values for potassium triphenylenide in DME are shown for comparison. MTHF IK K + Crown Ether
2.002906
I
-60
"C
-20
*
+20
Flgure 3. Plot of gvalues as a function of temperature for potassium triphenylenide in MTHF in the presence and absence of crown ether.
paired over the entire temperature range studied. Addition of crown ether to the sodium and potassium salts appears to partially break up to the ion pair with the result that the temperature dependence of the observed g values tends to approach that observed for the sodium and potassium salts in the more polar solvents. The effect of the addition of crown ether to the various alkali metal/solvent pairs is somewhat more difficult to summarize. For one group (i.e., Na/DME, K/DME, Na/THF, and Cs/THF) there is no significant effect upon the g values due to the presence of crown ether in the solution. For a second group (i.e., K/THF, Na/MTHF, K/MTHF, Na/THP, K/THP, and Rb/THP) the effect is essentially as if the temperature scale were shifted to lower values. An example of this behavior is shown in Figure 3 for the K/MTHF system. The remaining combinations displayed more striking effects, an example of which is shown in Figure 4 for Cs/DME. Proton and Metal Hfs. A brief summary of the experimental proton and metal hfs dataz4 is given here because the data are to be compared later with calculated results. Three types of ESR spectra are observed. Type 1 occurs in highly polar solvents such as NH,, hexamethylphosphoramide, acetonitrile, etc. The same spectrum is observed at low temperatures in such solvents as DME, THF, and MTHF. However, as the temperature is increased from approximately the freezing points of each of
suin densitva
line widthb
Type 1 (Free Ion) 1.097 0.041 1.613 0.060 0.066
0.25
1 2 3
Type 2 (Solvent-Separated Ion Pair) 1.277 0.047 1.566 0.058 0.061
0.46
Type 1 2 3 Na(- 100 C) a
-100
+60
1 2 3
3 (Contact Ion Pair)c 1.41 0.052 1.49 0.055 0.059 0.25 1.9 x
0.20
Q = 27 G.
gauss.
270 '
proton hfs (G)
position
,
+20
TABLE I: Proton Hfs and Spin Density Distribution
1% I
oc
Flgure 4. Plot of g values as a function of temperature for cesium trlphenyienide in DME In the presence and absence of crown ether.
280 -
270'
-20
Peak-to-peak component line width in Solvent: diethyl ether. d A, = 316.11.
the latter solvents, a new spectrum (type 2) replaces the low-temperature spectrum. The temperature at which this transition occurs decreases as one goes through the solvent series DME, THF, and MTHF and the alkali metal series lithium to cesium. Finally, at higher temperatures, metal hfs is observed for sodium triphenylenide in MTHF and diethyl ether. The latter spectra are called type 3. Table I gives a brief summary of the hfs data for the three different types of ESR spectra. Optical Spectral Studies. A number of optical spectral studies of triphenylenide solutions have been reported.6*6 One is of particular interest here and will be rather extensively summarized because its results integrate into the model for the ion pair structure which has resulted from the present study. Arick et ala6have very carefully studied the effect of temperature upon the optical spectra of alkali metal triphenylenides (lithium through cesium) in MTHF. They conclude that to explain both optical and ESR spectral changes which are observed, one must introduce four distinctly different species which are in equilibrium. However, at any given temperature and alkali metal/ solvent combination only one or two of the species can be predominantly present. The four species are described below. The representations and definitions of the equilibrium constants of Arick et al.5 have been retained for simplification. Species 1 (Tp-.+Me+), a free ion, exists at low temperatures and in highly polar solvents. Species 2 (Tp-./S/Me+) is a rather highly solvated and solventseparated ion pair. The ESR and optical spectra of species 1and 2 are essentially identical. The ESR spectra are of type 1. Species 3 (Tp-.//Me+) is a solvated and solventseparated ion pair. Its ESR spectra are of type 2. Species 4 (Q-.. Me+) is a contact ion pair which exists at the higher
Ion Pair Formation of lrrlphenylene Anion Radical
temperatures and under some conditions displays metal hfs. The ESR spectra are of type 3. The equilibria between the various species are represented in the following equation: 1 2 3 TP-.+Met Tp-./S/Met Tp--//MeC Kz 4 Tp-. Met
E
The Journal of Physical Chemistry, Vol. 84, No. 22, 1980 2915 Y-Axis
I
t(;l
Species 1 and 2 are predominant at low temperatures and in highly polar solvents. As the temperature is increased and/or the solvent polarity decreased the equilibria are shifted toward the right (i.e., toward species 3 and 4). The existence of :species1 is inferred from the fact that at low temperatures and low radical and counterion concentrations, the optical spectra are concentration dependent. At radical concentrations greater than 5 X lo4 M, the optical spectra are independent of radical concent r a t i ~ n .Experimental ~ measurements of A&ks based on the ESR,3 and o p t i ~ a land , ~ conductivityll studies yield values of zero for sodium triphenylenide in MTHFa and THF'l and -2 f 1 k;cal/mol for potassium triphenylenide in MTHFSSThe small AH, which includes solvation effects, means that tlhe electronic energy levels of the free triphenylenide anion are, at most, only weakly perturbed by the formation of'the first ion pair (Le., species 2). For potassium triphenylenide in MTHF,5 ASdisawas found to be -25 f5 eu. This reflects the difference in the amount of solvation of the two species (i.e., species 1 and 2). Evidence for the equilibrium between species 2 and 3 is derived from both the optical and ESR spectral studies. In the optical studies, two distinct optical spectra are observed, which gradually change into each other through a series of isosbestic points as the temperature is varied. From an analysis of these spectral changes, the thermodynamic parameters which describe the equilibrium (K,) between species 2 and 3 can be obtained. Species 2 and 3 display types 1 and 2 ESR spectra, respectively. The values obtained for AH and A S (i.e., -8.8 f0.5 kcal/mol for sodium triphenylenide and -49 f3 eu, re~pectively)~ in MTHF suggest ,a greater electronic energy level perturbation as well EIS a larger change in solvation upon formation of species 3 from 2 than when species 2 is formed from 1. Species 4 is associated with type 3 ESR spectra (Le., spectra in which the metal hfs is resolved). The optical spectra of species 4 is essentially that of species 3 but shifted toward larger absorption frequencies. No isobestic points are observed. From both the ESR and optical spectra, the thermodynamic parameters which describe the equilibrium (K2)between species 3 and 4 can be derived. The values obtained1 for AH2 and AS2 (i-e.,-5 fl kcal/mol and -19 f4 eu, respectively) for the sodium triphenylenide in MTHF suggest changes in electronic energy levels intermediate to those noted above for the change from species 2 to species 3.
Calculationsa1 Ion Pair Association Energies. Association energies for the alkali metal/triiphenylenide pair were calculated as described by Goldberg.12J3 The calculations were performed for two difftaent triphenylenide molecular structures. In both structures, threefold rotational symmetry in the triphenylenide molecular plane was maintained. In one of the structures, all of the carbon-carbon bond lengths were assumed to be equal. In the other, the relative lengths of the various carbon-carbon bonds were modified to reflect the experimentally determined X-ray structure of the neutral m o l e ~ u l e . ~The ~ J ~changes made in the relative
Flgure 5. The trlphenylene molecular structure. The following bond lengths are reported In ref 15: (a) 1.447 A; (b) 1.416 A, and the average of the rest = 1.396 A.
Figure 6. Contour plot of the calculated ion pair assoclatlon energies for the potassium Ion 3.5 A above the plane of the trlphenylenide ion. The letters A and B label the two sets of minima. The unequal bond length structure was used In the calculations. The contour lines are separated by units of -0.02 /3, where p is the aromatic carbowcarbon resonance Integral. See Figure 7 for a cross section at x = 0 and for varlous metal ion distances above the trlphenylene anion radical plane.
bond lengths were consistent with SCF-type calculations of the bond lengths in triphenylenide as reported by I"aya et al.le Briefly, the bonds of the central ring are longer than the remaining five in the outer rings. The peri bonds are the longest (see Figure 5). Figure 6 shows a contour plot of the ion pair association energies for the potassium cation 3.5 A above the triphenylenide molecular plane for the unequal bond length structure. There are two sets of threefold rotationally symmetric minima. The values of the minima of the two seta are essentially equal. The minima in one set (Figure 6, point A) are much broader than those of the other set (Figure 6, point B). Similar plots are obtained for other distances between the alkali metal ion and the molecular plane. A t shorter distances, the depths of the potential wells are increased. At larger distances, the depths of the potential wells decrease. At sufficiently large distances (>5 A), the cusp centered on the threefold rotational axis disappears, leaving a rather broad, dish-shaped minimum. A series of ion pair association energies calculated along the y axis (x = 0) and bisecting one member of each set of minima for various cation distances above the triphenylenide plane is shown in Figure 7. While the results shown in Figure 6 and 7 were calculated for potassium triphenylenide, they apply equally well to the other alkali metal salts because the calculation is that of a point positive charge interacting with the negative charge distribution of the triphenylenide ion.0J2J3 The contour plot for the equal bond length structure is essentially identical with that shown in Figures 6 and 7
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The Journal of Physical Chemisty, Vol. 84, No. 22, 1980 0.5
r
Jones and Ahmed -0.80
r
A 2.0' -6
'
-4
' -2
I
I
0
A
2
-
'
4
I
6
Flgure 7. Cross-sectional plots of the ion pair association energies for potassium triphenylenide at various separations between the metal ion and the molecular plane. The energies are given In units of fl (the aromatic carbon-carbon resonance integral). The solid lines represent the results for the unequal bond length calculatlon. The dashed lines represent the differences observed when the calculation Is performed for the equal bond length structure. The cross section is for x = 0. The coordinate plotted along the abscissa is y .
with one very important exception. Three new minima which are more or less located over the centers of the outer rings are observed. The positions and size of the other two minima remain essentially unperturbed. In terms of the plots shown in Figure 7, the only si nificant changes occur a t values of y greater than ca. +1 . These are shown in Figure 7 as dashed lines. We believe and will demonstrate (see the section on spin density distribution) that the unequal bond length calculation provides the better description of the triphenylenide ion. The results of the equal bond length calculation have been considered here because two groups of workers have previously reported the existence of minima located over the centers of the outer ringsa3r6Their calculations were based on an equal bond length structure. They did not look for other minima, nor did they report having constructed contour plots such as shown in Figures 6 and 7. .rr Molecular Orbital Energies. The charge density distribution of the unpaired electron within the threefold rotationally symmetric triphenylenide ion is described by a pair of energetically degenerate orbitals. The wave functions which describe these two degenerate orbitals predict different spatial distributions for the unpaired charge density, and they possess different symmetries upon reflection through a plane which is perpendicular to the molecular plane and which contains the threefold rotation axis. One of these wave functions is symmetric (S) and the other antisymmetric (A) with respect to the reflection operation. Just as in the case of the benzene anion radical, a correct prediction of the charge density distribution is obtained by taking an average over the two degenerate orbitals. Generally, the formation of the ion pair removes the orbital degeneracy, An exception occurs when the metal ion resides on the triphenylenide threefold rotation axis. Figure 8 shows how the relative energies of the two orbitals which contain the unpaired electron vary as the metal ion is moved along the y axis ( x = 0) at a distance of 3.5 A above the triphenylenide molecular plane for the unequal bond length structure. The two orbital energies are labeled by their respective reflection symmetries. When the metal ion is closer to the triphenylenide molecular plane, the energy differences are larger, and when it is further from the molecular plane, the energy differences are smaller. The situation is quite similar to that reported for the benzene anion r a d i ~ a l .Just ~ as in the case of the benzene ion, the calculated results are independent of the identity
d
Figure 8. Plot of the orbital energies for the two lowest-energy antlbonding orbitals for potassium trlphenylenide ( x = 0,z = 3.5 A). The coordinate plotted along the absclssa Is y . 6.0R
-2
A
0
2
Flgure 9. Plot of the charge densltles at positions 1 and 2 for the potassium trlphenylenide as the metal Ion moves along the y axis ( x = 0, z = 3.5 A) for the unequal bond length structure.
TABLE 11: Spin (Charge) Density Distribution in the Free Ion
position 1 2 3
exptl spin density 0.041
0.060 0.066
charge density, calcd equal unequal bonds bonds 0.056 0.048 0.056 0.057 0.055 0.062
of the alkali metal ion because a perturbation calculation based on point charges was used. Spin (Charge)Density Dktribution. The Free Ion. The charge density distributions were calculated for the equal and unequal bond length, free ion triphenylenide structures by using the simple Huckel treatment. The results are shown in Table 11. Clearly, the calculations based on the unequal bond length structure are in much better agreement with the experimental results. The results based on the unequal bond length calculations derived from X-ray structural data are not too different (but are in better agreement with experiment) from those reported by van Willigen et alS2wherein they started with the equal bond length calculation and modified the triphenylenide carbon-carbon resonance integrals by using the CoulsonGolebiewski bond order-bond length re1ationship.l' The Ion Pair. Consider, first, motion of the metal ion along the triphenylenide threefold rotation axis. There is essentially no change (i.e., less than 2%) in the charge densities calculated for positions 1 and 2 until the metal is less than 6 A above the triphenylenide molecular plane. This is true for both the equal and unequal bond length triphenylenide structures. As the metal ion is moved closer to the triphenylenide molecular plane, the charge density at position 3 increases and that at positions 1 and 2 decreases. For the unequal bond length calculation, the charge densities at both positions 1 and 2 are reduced b 13% relative to the free ion when the metal ion is 2 above the molecular plane. However, in the case of the equal bond length calculation the rate of decrease of charge density at position 1is much greater than that at position
K
The Journal of Physical Chemistty, Vol. 84, No. 22, 1980 2017
Ion Pair Formation of Triphenylene Anion Radical
TABLE 111: Calculated Charge Densities for Various Molecular Plane-Metal Ion Separations position (triphendenide - ion) position (metal ionP 1 2 3 - -l.--- - . -- -Free Ion (infinite Separation) =-
0.048
0.057
Ion PaiP Minimum “A” (0, -1.2, 2.5) 0.0495 0.052 (0, -1.2, 3.0) 0.051 0.053 ( 0 , - 1 . 0 , 3.5) (0, -0.8, 4.0) (0, -0.8, 4.5)
0.0495 0.049 0.0485
0.0535 0.055 0.055
Ion Pair Minimum “B” (0, 1.0, 2, 5 ) 0.056 0.051 (0, (0, (0, (0,
1.0, 1.0, 0.9, 0.8,
3.0) 3.5) 4.0) 4.5)
0.053 0.052 0.050 0.049
0.052 0.053 0.054 0.055
0.062 0.066 0.063 0.064 0.064 0.063 0.060 0.062 0.062 0.063 0.063
Charge densities are calculated at positions for which the ion pair associatilon energies are at a minimum (See The numbers enclosed in parentheses repreFigure 6). sent the 3c, y, and z coordinates of the metal atom, respectively. 6r
4
P e
2
-8
-4
4
8
Figure 10. Plot of the charge density at the potassium ion in potassium trlphenylenlde as the metal ion moves along the y axis ( x = 0, I =
3.5 A).
2. The charge densities calculated at positions 1 and 2 when the metal ion is 2 A above the triphenylenide molecule are 0.044 and 0.051, respectively. Figure 9 shows the calculated charge density distribution at positions 1and 2 for the unequal bond length structure when the metal ion is 3.5 A above the molecular plane and moved along the y axis (3c = 0). The charge densities shown in Figure 9 were obtained by averaging over the two lowest energy antibonding orbitals shown in Figure 8. When the metal ion is closer to the triphenylenide molecular plane, the distance between the two points at which the charge densities at positions 1and 2 are equal is, decreased. The reverse occurs when metal ion-triphenylenide ion diistance is increased. Table I11 lists calculated charge densities at positions 1and 2 for the two ion-pair association energy minima for selected metal ion-triphenylenide separations. Figure 10 shows the calculated charge density for the unpaired electron at the potassium ion as it is moved along the same locus as indicated above for the charge densities at positions 1 and 2. The value plotted along the ordinate was obtained by taking (1/2(C&/2+l + where i is the atom and N is the total of ?r molecular orbitals. Again, the greater the metal ion-triphenylenide separation the smaller the charge density at the metal ion. Here, however, the results are dependent upon the particular alkali metal ion. For a given distance, the lower the metal atom ionization potential, the larger the calculated, unpaired electron charge demity on the metal ion. The results are
C
Figure 11. Contour plot of the calculated g values for rubidium triphenylenlde where the rubidlum is 3.5 A above the molecular plane. The values of the calculated g’s are A = 2.002 847, B = 2.002 822, and C = 2.002 707. The contour lines are separated by units of -25 x 10-6.
quite similar to those reported for the benzene anion radi~al.~ g Values. The expected effect of the formation of an ion pair upon the triphenylenide g value was calculated by means of the EWMO method, which has been described by Dalgard and Linderberg.lBJg Figure 11shows a contour plot of the g values calculated for rubidium triphenylenide where the metal ion is 3.5 A above the molecular plane. At smaller separations between the metal ion and the molecular plane, the deviations from the calculated free ion g value (2.002 837) are larger. For example, if the deviation at a given point, for a separation of 3.5 A, is positive, then a t a distance of 2.5 A the deviation from the free ion g value is more positive. For larger separations between the metal ion and the molecular plane, the deviations are smaller. As the metal ion/molecular plane distance is increased, the triphenylenide g value approaches its free ion value. The major change observed upon replacing rubidium by one of the other alkali metals in the ion pair is to approximately scale the deviations from the free ion g value by the ratio of the respective spin-orbit interaction parameters. A larger spin-orbit interaction parameter yields larger deviations from the free ion g value and vice versa. For certain combinations (e.g., sodium triphenylenide with R = 3.5 A), the calculated changes in the g value are less than experimental error. Briefly, the calculations predict that for certain ion pair structures there will be measurable changes in the experimentally observable g values if the alkali metal is rubidium or cesium. However, no matter what the ion pair structure in the case of lithium, sodium, or potassium salts, no significant changes in the experimentally observable g values are predicted. There is one difficulty with the use of these particular g-value calculations for orbitally degenerate radicals. The calculations are not capable of taking into account the spin-orbit interaction of the unpaired electron due to the orbital degeneracy of the triphenylenide ion. The significance of the degeneracy and its effect upon the g value is discussed in the next section. Discussion g Values. It has been recognized, since the first accurate g-value measurements for degenerate and nondegenerate organic free radicals were reported,20that g values associated with orbitally degenerate organic free radicals are anomalous in terms of Stone’s theory of g values.21-26As noted earlier, our g-value calculations do not include the effect of orbital degeneracy. Therefore, the calculated g
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The Journal of Physical Chemistty, Vol. 84, No. 22, 1980
values are those expected from a “nondegenerate” triphenylenide ion. The significant result from these calculations is that for the sodium and potassium triphenylenide ion pairs, the g values are predicted to be independent of the ion pair structure because the contribution to the g value from the alkali metal spin-orbit interaction is too small to be experimentally observed. In contrast, certain ion pair structures for the rubidium and cesium salts are predicted to deviate significantly from their fEe ion values. The experimentally reported g values can be understood in these terms. In the case of the sodium and potassium salts in all of the solvents except THP, the observed g values at low temperatures (and other conditions which favor free ion formation) approach a value in the range of 2.003002.00290. The addition of crown ether to solutions of these salts has relatively little effect upon the g value. As the temperature is increased, the g values tend to decrease and approach as asymptote of -2.002 72 (see Figure 1). There is no doubt that ion pair formation occurs at the higher temperature^.^' For example, sodium metal hfs has been observed in solutions of MTHF.2 The optical spectra for the sodium and potassium salts are ~ i m i l a r .Since ~ the g-value calculations suggest that these changes in g value are not due to the spin-orbit contribution arising from the alkali metal of the ion pair, we must investigate other mechanisms. Consider the possibility that the decrease in the g value for the sodium and potassium triphenylenides is due to the removal of the orbital degeneracy because of the ion pair formation. An empirical fit of experimental g-value data to Stone’s theory26allows us to predict what the g value would be a nondegenerate triphenylenide ion. If we assume a value for the energy of the orbital which contains the unpaired electron in the range of -0.68 to -0.72 (see Figure 8), g values of 2.002718 f 11 to 2.002722 A l l , respectively, are predicted.28 The uncertainty represents the root mean square (rms) deviation of the data used to establish the empirical fit.26 These values are quite close to the high-temperature g values observed for sodium and potassium triphenylenide solutions. This constitutes strong evidence in support of the idea that at high temperatures the triphenylenide ion pair is nondegenerate. Note that the nondegeneracy can exist at the same time that the apparent threefold rotational symmetry of the ESR spectrum is preserved. This will be explained in the next section. Consider the behavior of the rubidium and cesium triphenylenides in solution. In most instances after the g value initially drops slightly as the temperature increases, it begins to increase rather strongly. In many instances, but not all, the addition of crown ether to solutions of the two salts tends to cause the g values to behave more like those observed for the sodium and potassium salts. This behavior is consistent with the concept that a nondegenerate ion pair is formed. The formation of the nondegenerate ion pair makes a negative contribution to the triphenylenide ion g value, whereas the presence of the rubidium or cesium makes a positive contribution. At the higher temperatures and in the poorer solvents, the ion pair is tighter and the positive contribution to the g value is the larger of the two, hence the increase in the triphenylenide g value. Moreover, since the cesium spinorbit interaction is larger, the cesium ion pair is expected to show larger positive changes in g than for rubidium. If the above conclusions are correct regarding the removal of the orbital degeneracy, one would expect to observe changes in the spin-lattice relaxation times ( T I )as
Jones and Ahmed
a function of temperature for the triphenylenide ion. Because of ESR spectral line overlap and the inhomogeneous nature of the individual ESR spectral lines, it is not possible to experimentally measure the spin-lattice relaxation time in this system by using CW progressive satuation techniquesB with the kind of accuracy needed to answer this question. However, pulsed ESR techniquesm hold out the promise that such measurement can be made. We plan to make such an attempt in our laboratory in the future. Proposed Ion Pair Structure. The following model for the ion pair structure (actually structures) is based upon the experimentally measured g values, proton hfs, metal hfs, and optical spectra plus the theoretical calculations of these same experimentally observable quantities. The model is built upon the proposal by Arick et al.5 that, depending upon the particular experimental conditions (i.e., solvent, temperature, counterion, etc.), a total of four different species can be identified. To avoid confusion, we shall adopt the notation and labels introduced by h i c k et al. Species 1 . This is the free ion species, i.e., the species found at low temperatures, in highly polar solvents, with the smaller alkali metals, etc. Its g value of -2.003 000 is 280 X 10” units larger than the predicted g value of 2.002 720 for a nondegenerate system with the same unpaired electron orbital energy. Note the rms deviation in the predicted value is 11 X 10”. Therefore the deviation from the predicted nondegenerate value is 25 times the rms uncertainty of the predicted value. Species 2. This is the first “ion pair” structure which is formed as the temperature of the triphenylenide solution is increased. The experimental evidence suggests that the metal is still solvated (less so than in species 1) but now somewhat localized with respect to the triphenylenide ion. Rather small changes in enthalpy of dissociation are observed in going from species 2 to species 1. The values range from zero to -2 f l kcal/m01.~8The positions of the optical absorption frequencies are unchanged as are the ESR spectra as species 2 replaces species 1. These two experimental observations are consistent with a weak perturbation of the energy levels. As a result of the calculations presented earlier, a structure is proposed which places the metal ion more or less on the threefold rotation axis and at a distance greater than 5 A above the triphenylenide molecular plane (Figure 7). At such distances the ion pair association energy curve has a rather flat dish shape centered on the threefold rotation axis, the electronic energy levels are not perturbed enough to cause shifts in the optical absorption frequencies, the ESR spectra (i.e,, proton hfs) are unchanged relative to those of the free ion, there is no contribution to the g value from any of the metal ions as the separation is greater than 5 A, and there is no unpaired electron density transferred to the metal ion at any separation. Species 3. At higher temperatures, the metal ion becomes less solvated, The optical spectra show a change in the absorption frequencies of the triphenylenide ion. This change which involves isosbestic pointe establishes that there is an equilibrium between two different species! The thermodynamic parameters (i.e., the values obtained for the enthalpy and entropy) suggest that there is a significant change in the electronic energy levels (this is supported by the optical and ESR spectral data3) and the extent of s o l ~ a t i o n .It ~ is in this range that the strong temperature dependence of the g value is observed. If one assumes that this particular ion pair structure is characterized by a smaller distance between metal ion and N
Ion Pair Formation of Triphenylene Anion Radical
the triphenylenide ]plane,the ion pair association energy calculations suggest that the metal ion is no longer located on the threefold rotiation axis'but over one member of the two sets of threefold rotationally symmetric minima (See Figure 7). Such a shift produces a significant change in the calculated energy levels. The changes are in agreement with the observed optical spectral shifts.6 This shift away from the threefold rotation axis also produces changes in the calculated charge density at positions 1 and 2 (see Figure 9) and in the g values for rubidium and cesium salts (see Figure 11). Two questions remain to be answered. The first question is which of the two sets of minima shown in Figure 7 is favored? The calculations point toward the minima located near the peiri bonds. These minima are broader, the calculated charge densities are in better agreement with experiment (see Table 111), and the calculated rubidium g values increase (in agreement with experiment) in that area (see Figure 11). The second question is why does one observe an ESR spectrum which is consistent with the existence of threefold rotational symmetry? This can occur if the metal ion is allowed to hop from one of the threefold rotationally symmetric minima to the other at a frequency greater than that of the difference between the positions of the nondegenerate spectral lines. We estimate that a hopping frequency of 1 MHz would be sufficient to accomplish this. Note, however, even with the hopping that any orbital angular momentum which the electron might have developed because of the original orbital degeneracy will be quenched. This is expected to have significant effects upon both the observed g values and the spinlattice relaxation tiimes (TI) (i.e., the g values will fall in the range associated with nondegenerate radicals and the spin-lattice relaxat ion time will be larger). Species 4. Final1,yat the highest temperatures and in the poorest solvents this species is observed. The optical spectra are not characterized by shifts which involve isosbestic points but instead by gradual shifts in the absorption peaks.5 The ESR spectra show changes in the proton hfs splittings at positions 1and 2 (they are tending to move closer together), and the metal hfs is explicitly re~olved.~ In this range it appears that there is little change in the g values for the sodium and potassium salts although the g values for the rubidium and cesium salts continue to increase in value. The thermodynamic parameters (enthalpy and entropy) are smaller in going from species 3 to 4 than in going from species 2 to 3. This suggests that both changes in the energy levels and in solvation are less pronounced. We suggest that the major differences between the structures of species (3 and 4 are a smaller distance between the metal ion and the triphenylenide molecular plane and a less solvated metal ion for species 4. The static x and y positions of the metal ion relative to the ion pair association energy minima are assumed to remain relatively constant, but the metal ion is assumed to jump randomly from one equivalent site of minimum energy to another. The calculated changes in the various experimentally observable parameters for such changes in the structure are consistent with experimental observations. A decrease in the metal ion distance above the triphenylide plane produces much smaller 13hifts in the calculated electronic energy levels than the shift from the threefold rotation axis to a position over one of the ion pair association energy minima. This is in agreement with the observation that the optical absorption spectral peaks show gradual shifts at higher temperatures, but not isobestic points. The ESR spectra of species 4 how that the hfs at positions 1 and
The Journal ofPhyslcal Chemistry, Vol. 84, No. 22, 1980 2919
2 are almost equivalent (see Table I). Calculations of the charge density at positions 1and 2 (see Figure 9) demonstrate that as the metal ion is moved closer to the triphenylide plane the values of the charge densities at positions 1and 2 approach each other. Calculations of the charge density on the metal ion (see Figure 10) show that the metal ion cannot reside on the threefold axis. At a fixed position relative to the ion pair association energy minima, the charge density at the metal ion increases as the distance between the metal ion and the triphenylenide decreases. This is consistent with the experimental observation that the metal hfs increases with increasing temperature.6 Finally, the calculated g values are consistent with experiment. In the case of the sodium and potassium salts, the calculated changes are too small to be observed. If the major change in the g values of these two salts occurs when species 2 converta into species 3 (i.e,, when the shift from a degenerate to a nondegenerate state occurs), then no changes in g value are expected and none is observed. However, for the rubidium and cesium salts a decrease in the metal ion-triphenylenide distance leads to an increase in the predicted g value. This is in agreement with experiment. Conclusions A model for the ion pair structure for the alkali metal triphenylenide system is presented which is consistent with the experimental observations as well as calculations of these same experimental quantities. Our goal to use such information as a tool to study the structure of such species in solution has been accomplished. The experimental and calculated g values were of pivotal importance in deciding which of the two sets of ion pair association energy minima is most likely favored by the metal ion in the ion pair.
Acknowledgment. We acknowledge the support of the Computer Center of the University of Missouri-St. Louis which provided the funds for the calculations. R.H.A. gratefully acknowledges receipt of a Summer Fellowship from the Graduate School. References and Notes Abstracted in part from the Ph.D. dlssertatlon of Raria H. Ahmed, University of Missouri, St. LOUIS,MO, 1979. H. van Wllllgen, J. A. van Broekhoven, and E. de Boer, Mol. Phys., 12, 533 (1967). J. A. van Broekhoven, Thesis, Unhrerstly of Nijmegen, The Netherlands, 1970. B. M. P. Hendrlks and E. de Boer, Mol. Phys., 29, 129 (1975). M. R. Arick, J. A. M. van Broekhoven, F. W. Pijpers, and E. de Boer, J. Am. Chem. Soc., 94, 7531 (1972). (a) R. E. Koning, H. Zandvoort, and P. J. Zandstra, Chem. Phys., 28, 343 (1978). (b) G. J. Holjtlnk, Mol. Phys., 2, 85 (1959). R. D. Ratalzak and M. T. Jones, J. Chem. Phys., 56,3896 (1972). M. J. Felghan and M. T. Jones, J. Am. Chem. Soc., 92,6756 (1970). M. T. Jones and T. C. Kuechler, J. Phys. Chem., 81,360 (1977). M. T. Jones, R. Ahmed, R. Kashup, and V. Rapini, J. Phys. Chem., 83, 1327 (1979). P. Chang, R. V. Slates, and M. Srwarc, J. Phys. Chem., 70,3180 (1966). I. B. Goklberg, Thesis, University of Minnesota, Mlnneapdls, MN, 1969. I. B. Goldberg and J. R. Bolton, J . Phys. Chem., 74, 1965 (1970). A. Klug, Acta Crystallogr.,3, 165 (1950). F. R. Ahmed and J. Totter, Acta. Crystallogr., 16, 503 (1963). Y. J. I'Haya, M. Nakayama, and T. Iwabuchi, Int. J. ckrsnfum. Chem., 5, 227 (1971). C. A. Coulson and A. Goleblewskl, Roc. phys. Soc.,78, 1310 (1981). E. DAlgard and J. Llnderberg, Int. J. Quenrum Chem., 50, 269 (1975). E. DAlgard and J. Llnderberg, J. Chem. Phys., 65, 292 (1976). 8. G. Segal, M. Kaplan, and 0. K. Fraenkel, J . Chem. Phys., 43, 4191 11965). A. J. Stone; Roc. R. SOC. London, Ser. A , 271, 424 (1963). A. J. Stone, Mol. Phys., 6, 509 (1963). A. J. Stone, Mol. Phys., 7, 311 (1964). R. E. Moss and A. J. Perry, Mol. Phys., 22, 789 (1971). M. T. Jones, T. C. Kuechler, and S. Metz, J. M g n . Reson., 10, 149 f19731. > . - - -,R. A. Rouse and M. T. Jones, J . Magn. Reson., 19, 294 (1975).
2920
J. Phys. Chem. 1980, 84, 2920-2922
(27) In the unique case of solutions in THP, it appears that over the whole
solvents used in thls study are molecules of low polarity, so that one would expect rather small electrostatic perturbations from that source in comparison with the aikall metal ions. Moreover, the major effects of the solvent is expectedto manifest itself by reduclngthe magnitude of the electostatic interaction between the anion radical and the alkali metal cation. The effect of solvation upon the calculated results would be as if the anion-cation separation were increased for a bare ion calculation. Also, it Is Importantto recognlze that sohrent pertubations for large molecules such as the triphenylene anlon radlcal where the negative charge density is rather uniformly distributed over the molecular framework Is much less than in the case of anion radicals such as the nitrobenzeneanion radical where 4 0 % of the negatlve charge is located on the nitro group.
temperature range studied sodium and potassium triphenylenide are ion paired. Moreover, the ion pair structure appears to be that observed in the other solvents only at the highest tem eratures. (28) The relationship used was that of Rouse and Jones,' Q)Le., g = 2.002631 - k(1.61 X lo4) - X2(4.65X lo4) where k Is the energy, in unlts of @,of the T molecular orbital which contains the unpalred electron. (29) M. T. Jones and M. Komarynsky, J. Chem. Phys., 56,4404(1972). (30) See, for example, M. Huisjen and J. S. Hyde, Rev. Sci. Instrum.,
45,669 (1974). (31) One of the referees was concerned that solvent effects are not explicitly taken into account in the calculations described herein. The
Cavitatlon-Induced Oxidation of Aerated Aqueous Fe2+ Solutions in the Presence of Aliphatic Alcohols C. Sehgal, R. G. Sutherland, and I?.E. Verrall" Deparfment of Chemistry and Chemical Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N OW0 (Received: March 13, 1980; In Final Form: July 3, 1980)
Ultrasonic oxidation of Fez+increases in the presence of aliphatic alcohols in the order MeOH < EtOH < n-PrOH < n-BuOH. The increased oxidation is explicable on the basis of the possible formation of peroxyhydroxyalkyl radicals as observed in radiation studies and which provide better pathways for the oxidation of Fe2+. These results also indicate that at low solution concentrations (0-20 mM) the physical effects of alcohol addition on the cavitation phenomenon are much less predominant than those arising from its chemical participation.
Introduction Organic compounds are known to have a marked effect on sonoluminescence and other ultrasonically induced chemical rea~tions.l-~ Our previous studies' showed that addition of minute amounts of alcohols to an aqueous medium significantly reduces sonoluminescence. This decrease was attributed to the alcoholic scavenging of hydrogen and hydroxyl radicals formed by the cavitationally induced decomposition of water. In the present studies we report the oxidation of Fez+ to Fe3+ by ultrasound in the presence of alcohols. This work further substantiates the argument that the decrease in sonoluminescence flux caused by alcohols with solution concentrations of 0-20 mM is due to the scavenging of radicals and not to the suppression of cavitation. Also, various researchers6P&l1have shown that there exists a certain analogy between sonochemistry and radiation chemistry. The oxidation of Fe2+to Fe3+in an ultrasonic field is readily described by a mechanism similar to that used for radiation work and supports the above contention. Experimental and Results Aliquots (50-mL) of a Fricke dosimeter solution12containing alcohols (0-20 mM) were insonated at 459 kHz by using equipment and procedures previously described.13 A mixture of ethylene glycol and water (3:2 v/v) was used as a coupling liquid to transmit acoustic energy from the transducer to the insonation cell. The temperature inside the cell was maintained relatively constant at 25 O C by circulating the coupling liquid through a constant-temperature bath (25 f 0.5 "C). After 5 min of insonation the solutions were quenched by addition of a 2% sulfamic acid solution to prevent postinsonation oxidation of the remaining Fez+by the end products of insonation, viz., H202,HNO2, The Fe3+ concentration was determined spectrophotometrically at 304 nm by using a Cary 14 spectrophotometer. 0022-3654/60/2084-2920$0 1 .OO/O
The effects of addition of methanol, ethanol, 1-propanol, and 1-butanol on the chemical oxidation of acidic ferrous M) solution are shown in Figure ammonium sulfate 1. The values of G(Fe3+)o,in the presence of various alcohols were determined on a relative basis by using G(Fe3+)o,= 3.9 ions per 100 eV.16 These results show that the chemical yield (Le., G(Fe3+)o) increases with an increase in alcohol concentration an$ that there is a marked increase in the yield of Fe3+with the number of carbon atoms in the alcohol when different alcohols are added in equimolar quantities. Both of these results show a very close resemblence to the radiation-induced oxidation of Fez+ in the presence of alcohols.16-18
Discussion It is well established that acoustic cavitation decomposes water to produce hydrogen and hydroxyl r a d i c a l ~ . l ~ ~ J ~ J ~ While the formation of hydrated electrons has also been proposed, direct evidence for their existence in an ultrasonic field (US) has not yet been obtained. In any event, in the acidic medium in which the present experiments were conducted, hydrated electrons would readily react with protons to form hydrogen atoms. Therefore, the discussion will be restricted to a consideration of the role played by the reactive species He and .OH.In the airsaturated solution, the hydrogen atoms produced during cavitation will combine with dissolved oxygen to produce perhydroxyl radicals (H02.).sy21Both .OHand H02. radicals are relatively strong oxidizing agents and should be involved in producing the high yield of Fe3+in the Fricke dosimeter system. When added alcohols are present in the solution, it is likely that they penetrate into the cavitation bubbles (see below) and react with the intracavity contents. The alcohols may f i s t scavenge the radicals HOz. and .OH1 to produce RCHOH1J6which then further reacts with 0 2 to give RC(02)HOH.16~22 These organic peroxide radicals oxidize Fez+and so provide better pathways for alcohols 0 1980 Amerlcan Chemical Society
