J . Phys. Chem. 1988, 92, 2067-2071
2067
59C0Nuclear Magnetic Resonance Study of the Interactions of the Trls(ethylenediamine)cobalt( I II)Cation with Various Anions in Aqueous Solution Yuich Masuda* and Hideo Yamaterat Department of Chemistry, Faculty of Science, Tokyo Metropolitan University, Fukasawa. Setagaya- ku, Tokyo 158, Japan (Received: February 27, 1987; In Final Form: October 15, 1987)
The chemical shift and the spin-lattice relaxation time of the 59C0nuclear magnetic resonance were measured for aqueous solutions of various tris(ethylenediamine)cobalt(III) salts. For solutions of the complex salt with divalent anions such as sulfate, L-tartrate, and succinate, remarkable shifts to higher field were observed with increase in the concentration, whereas only slight shifts were observed for the univalent-anion salts such as perchlorate, chloride, and iodide, but not for the acetate which showed a considerable higher field shift. These concentration dependences of the s9C0 chemical shifts were well-explained by assuming ion association. The shift to higher field was attributed to the hydrogen bonding of the complex ion with anions and to the ob-to-le1conformational change of the ethylenediamine chelate rings accompanying ion-pair formation. The 59C0 spin-lattice relaxation rate of the [Co(en),13+ion in aqueous solution also showed concentration dependences more or less similar to those for the chemical shift; Le., it considerably increased with increasing concentration for the divalent-anion salts and acetate, whereas only slight increases were shown for the salts of other univalent anions. These concentrationdependences of the relaxation rates were also treated by assuming ion association. The electric field gradients at the 59C0nuclear site were estimated for the [Co(en),13+ion paired with various anions from the observed 59C0 relaxation rates. An appreciable decrease in the electric field gradient along the C3axis of the [Co(en),13+ion is shown for the ion pair with the sulfate ion.
Introduction The 59C0resonance of octahedral cobalt(II1) complexes shows chemical shifts widely distributed (- 19 000 ppm) depending on the ligands. The remarkable variation has been attributed to the paramagnetic term of the chemical shift; the energy separation AE between the ground 'Al,(Oh) state and the excited ITlg(Oh) state(s), appearing in the denominator of this term, is small ( 20000 cm-I) and appreciably varies with different ligands.] The 59C0chemical shift is also sensitive to changes even in the outer sphere of cobalt(II1) complex ions in solution. For example, 10-20 ppm higher field shifts of the 59C0resonance were observed for the hexacyanocobaltate(II1) ion when it is ion paired with various and solvent effects up to nearly 100 ppm were reported for various Co(II1) complexes." The 59C0chemical shift is a good probe for the ion-ion and ion-solvent interactions in solutions containing Co(II1) complex ions. The 59C0spin-lattice relaxation time ( T I )or line width ( v I p ) is also sensitive to the change of environment in the outer sphere of diamagnetic Co(II1) complexes, especially when the complex is of high symmetry such as regular octahedron (Oh).3,536The 59C0relaxation rate (= TI-') or line width is proportional to the product of the magnitude of the principal-axis component of the electric field gradient (efg) at the 59C0 nuclear site and the correlation time of the fluctuation of that efg with reference to the external magnetic field, H o e This efg is essentially zero in cobalt(II1) complexes of cubic (0,) symmetry. Therefore, the changes in the outer-sphere environment of those complex ions, such as ion-pair formation and solvation, directly reflect on the change of the spin-lattice relaxation time (or line width) of the 5 9 cresonance. ~ The tris(ethylenediamine)cobalt(III) ion is one of the highly symmetrical complex ions with a relatively small efg at the cobalt nuclear site.' This paper presents the effects of ion-pair formation on the 59C0chemical shift and spin-lattice relaxation rate of the [Co(en),13+ ion and attempts a quantitative analysis of the concentration dependences of chemical shift and spin-lattice relaxation rate, taking ion association into consideration. The results are compared with those of previous spectroscopic studies such as visible-ultraviolet absorption and circular dichroism studiess-I0 and also with our previous results on the IH and I3C relaxation rates of the [Co(en),l3' ion." N
'Department of Chemistry, Faculty of Science, Nagoya University, Frocho, Chikusa-ku, Nagoya 464, Japan.
0022-365418812092-2067$0 1.50/0
Experimental Section Various salts of [Co(en)J3+ (sulfate, L-tartrate, succinate, acetate, perchlorate, and iodide) were prepared by the ion-exchange technique. The procedure was mentioned in detail previously." Each complex salt was dissolved in water which was twice distilled after ion-exchange treatment. The concentration of the solution used for N M R measurements ranged between 0.003 and 0.15 M. The removal of dissolved aerial oxygen was omitted. Several measurements were also made with degassed sample solutions, but the degassing was found to result in no meaningful effects on the observed 59C0chemical shifts and TI values. The N M R spectra were determined by using a JEOL FX90Q FT N M R apparatus operating at 21.4 MHz for the observation of 59C0 resonance. The measurements were carried out under proton-decoupled conditions with a 10-mm (diameter) tube; a 5-mm coaxial tube contained D20solution of 0.01 M [Co(NH3)6]C13for the internal lock and the 59C0chemical shift reference. The temperature was maintained at 33 f 0.5 OC. The spin-lattice relaxation time (TI) was determined by using the usual inversion-recovery methodI2 of (-1 80' pulse-t-90' pulse-T-), pulse sequence. The delay time ( T ) was 10 times as large as TI, and the signal was detected at more than 12 time intervals (t). The TI value was determined from the analysis of the signal intensities at different time intervals ( t ) , as reported previously.".13 Results and Discussion 59C0Chemical Shift. Figure 1 shows the concentration dependences of the 59C0 chemical shifts for the various salts of (1) Griffith, J. S.; Orgel, L. E. Trans. Faraday SOC.1957, 53, 601. (2) Deiville, A.; Laszlo, P.; Stockis, A. J. Am. Chem. SOC.1981, 103, 5991. (3) Eaton, D. R.; Rogerson, C. V.; Sandercock, A. C. J . Phys. Chem. 1982, 86, 1365. (4) Au-Yeung, S. C. F.; Eaton, D. R. J . Magn. Reson. 1983, 52, 366. (5) Ader, R.; Loewenstein, A. J . Magn. Reson. 1971, 5 , 248. (6) Craighead, K. L.; Bryant, R. G. J. Phys. Chem. 1975,79, 1602. Rose, K.; Bryant, R. G. J . M a p . Reson. 1979, 35, 223. Russell, K. G.; Bryant, R. G . J . Phys. Chem. 1984, 88, 4299. (7) Scott, B. A,; Bernheim, R. A. J . Chem. Phys. 1966, 44, 2004. (8) Larsson, R.; Mason, S. F.; Norman, B. J. J. Chem. SOC.A 1966, 301. Mason, S. F.; Norman, B. J. J . Chem. SOC.A 1966, 307. (9) Yoneda, H.; Taura, T. Chem. Lett. 1977, 63. (10) Tanaka, N.; Kobayashi, Y.; Kanda, M. Bull. Chem. SOC.Jpn. 1967, 48, 2839. (11) Masuda, Y.; Yamatera, H. J . Phys. Chem. 1983,87, 5339. (12) Farrar, H. C.; Becker, E. D. PIuse and Fourier Transform N M R ; Academic: New York, 1971; Chapter 2. (13) Kowallewski, J.; Levy, G. C.; Johnson, L. F.; Palmer, L. J. J . Magn. Reson. 1977, 26, 533.
0 1988 American Chemical Society
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Masuda and Yamatera
The Journal of Physical Chemistry, Vol. 92, No. 7, 1988 d b /DDm
TABLE I: "Co Chemical Shifts for the [C~(en),]~'ions Paired with Various Anions (at 33.0 "C) anion
c10,c1-
30
1AcO-
suc2-
20
L-Tart2-c
so42-
A6(MX)
-1.0 -3.0 -8.0 20 31 30 32
log
(KO
/dm3 mol-')
1 .4" 1 .7" 1.5" 1 .6b 2.gb 2.9b,c 3.0b
"Takahashi, T.; Koiso, T. Bull. Chem. SOC.Jpn. 1976, 47, 2784; 1978, 51, 308. bReference 1 1 . c T h e values for the A-[Co(en),]'+-~Tart2- ion pair.
in the ion pair. The order of the increase in AG(MX) may reflect the tendency for the anions to form hydrogen bonds. For example, the mobility of water molecules around an anion decreases in the 0.05
0
0.10
I- = C104- > C1- > (H,O) > AcO- > L-tartrate2- > S042-
0.15
(4)
[complex s a l t I /mol
Figure 1. Relationship between the 59C0chemical shift and the [Co(en)JX,, concentration, [complex salt], in aqueous solution at 33.0 "C. (Higher field shift is taken to be plus.)
[Co(en)#+ in aqueous solutions. The resonance peak appreciably shifted to higher field with increasing concentration of the complex salt for the sulfate, L-tartrate, and succinate solutions, whereas only slight changes in the chemical shift were observed for the solutions of the chloride, iodide, and perchlorate. These differences in the concentration dependence among the various complex salts can be attributed to the differences in the interaction between the complex ion and the anion in solution. In an attempt to explain quantitatively these concentration dependences of the chemical shift, the chemical shift changes are attributed to ion-pair formation with the equilibrium M+X=MX (1) where M, X, and MX denote the [Co(en),13+ ion, an anion, and their 1:l ion pair, respectively. The ion-association constant at infinite dilution, K O , for the equilibrium (1) is expressed by K O
(2)
yMX[MXl /YuYX[MI [XI
where yi represents the activity coefficient of each species. The ion-paired and unpaired [Co(en),l3+ ions are assumed to show characteristic 59C0shifts, 6(MX) and 6(M), respectively, and 6(M) is determined by extrapolation of the observed chemical shifts, 6, to infinite dilution. Then, the observed chemical shift change relative to 6(M), A6 = 6 - 6(M), is represented by A6 = xMXAb(MX)
(3)
where A6(MX) = 6(MX) - 6(M) and xMX denotes the mole fraction of the M X ion pair in the total complex ion. The xMX values can be determined by using the ion-association constant previously reported" and the activity coefficients, yi,calculated from the extended Debye-Hiickel f0rmu1a.I~ Then, the A6(MX) value for each ion pair was determined so as to give best reproduction of experimentally obtained A6 values. The A6(MX) values t h u s obtained are listed in Table I, and the A6 values calculated with these K O and A6(MX) values are shown by solid lines in Figure 1. Remarkable higher field shifts were shown by the ion pairs with divalent anions, especially with sulfate. For the ion pairs with univalent anions except for acetate, small lower field shifts were observed. These differences in the A6(MX) values correspond to the diversity of the interaction of the [Co(en),l3' ion with the anion (14) For example
+
l o g y , = (q.5115zM21"2)/(1 + 0.3291a11'2) o.1zM21
where I is the ionic strength and z is the charge of the M3+ ion. The ion m), the value reported by size parameter, a, was taken as 6 6X Koiso et al. (Bull. Chem. SOC.Jpn. 1976, 47, 2784).
f(=
This order qualitatively corresponds to the increase in the ability for an anion to form hydrogen bonds with water molecules. If hydrogen bonding between the anion and the N-H protons of the [Co(en),13+ion follows the same or a similar order, a higher value of AG(MX) in Table I indicates stronger hydrogen bonding in the ion pair. Small negative values of A6(MX) for the ion pairs with the univalent anions, except for acetate, show that hydrogen bonds between the univalent anions and the N-H protons of [Co(en),13+ are weaker than those between water molecules and the N-H protons. A similar correlation between the magnitude of 59C0 chemical shifts and the strength of the second sphere hydrogen bonding has been found for several Co(II1) complex ions in various solvents of different hydrogen-bonding a b i l i t i e ~ . ~ . ' ~ The change of the chemical shift upon ion-pair formation, A6(MX), may in part be attributed to deformation of the coordination sphere of the Co(II1) ion.I5 Even a slight change in the arrangement of the six nitrogen atoms of [Co(en),13+ will result in some shift in the 5gC0resonance." The ethylenediamine chelate rings of the [Co(en),13+ ion can take the le1 conformation (with the C-C bond nearly parallel to the C, axis) or the ob (with the oblique C-C bond),8s18-21the former being slightly preferred to the latter in aqueous solution. When hydrogen bonds are formed between N-H protons of [Co(en),13+ and a sulfate ion, the le1 conformation is stabilized so extensively that almost all the complex ions exist in the le13 type (with all three chelate rings in the It is also known that a shift of the o6-lel le1 equilibrium is caused by introduction of a methyl group to the chelate ring. Thus, A-[Co(R-pn),I3+ (pn = 1,2-propanediamine) is almost exclusively of the le13 type, whereas h - [ C ~ ( R - p n ) ~ ] ~ ' is of the 0b3 type. The le13 type complex ion shows a shift 80-90 ppm higher than that of ob3 type.22 This chemical shift difference between the le13 and ob3 conformations of the 1,2-propanediamine chelate is assumed to be transferable to the case of the ethylenediamine chelate and that the conformations of the three ethylenediamine chelate rings in the ion-paired [ C ~ ( e n )3+~ ]ion are regarded to be all le1 ( 4type).'8*19Considering that the conformation is 80% le1 and 20% ob for the unpaired [Co(en),13' in water,23the chemical shift for the ion-paired complex ion is (15) Hertz, H. G. In Water, A Comprehensiue Treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 3, Chapter 7. (16) Masuda, Y.; Yamatera, H., unpublished results. (17) Au-Yeung, S. C. F.; Eaton, D. R. J . Magn. Reson. 1983, 52, 351. (18) Yoshikawa, Y. Chem. Lett. 1980, 1385. (19) Sargeson, A. M. Transition Metal Chem. ( N . Y . ) 1966, 3, 303. (20) Duesler, E. N.; Raymond, K. N. Inorg. Chem. 1971, 10, 1486. (21) The conformations le1 and ob represent that the C-C axis of the ethylenediamine chelate ring is approximately parallel and tilted to the C3axis of the [Co(en)J3* ion, respectively (Corey, J.; Bailar, Jr., J. C. J . Am. Chem. SOC.1959, 81, 2620). One of the N-H bonds of each amino group is also parallel to the C3 axis in the /el conformation, while in the ob conformation all of the N-H bonds are tilted. (22) Koike, Y.; Yajima, F.; Yamazaki, A,; Fujiwara, S. Chem. Lett. 1974,
177.
The Journal of Physical Chemistry, Vol. 92, No. 7, 1988 2069
Tris(ethylenediamine)cobalt(III) Salts
TABLE II: 59C0 Relaxation Rates and Quadrupole Coupling Constants at Infinite Dilution for the [ C ~ ( e n ) ~ Ions ] ~ + Paired with Various Anions (at 33.0 "C)
R, /si-'
(e2dMX)Q/h)/
PS
MHz
(e2QqA/h)'/ MHz
so:-
93 90 105 144 190 206 199
32 34 38 52 54 58 87
2.7 2.6 2.6 2.7 2.9 2.9 2.4
-0.40 -0.61 -0.44 -0.40 -0.60 -0.60 -0.80
unpaired
100
32
2.8
Rlo(MX)/
200
anion
clod-
c1I-
AcOsuc2L-Tart2-b
150
100
I
0.05
I
0.10
7" .(MX)"/
"Reference 1 1 . bValues for the A - [ C ~ ( e n ) ~ ] ' + - ~ - T a rion t ~ - pair. 'See ref 28 and 29.
c1-(-e -)
0
S-'
The values of RIo(MX),i.e., R1(MX) at infinite dilution, given in Table I1 were obtained in the following way. It is a reasonable
I
0.15
[complex s a l t 1 /mol dm-3
Figure 2. Relationship between the 59C0 relaxation rate and the [Co(en)JX, concentration, [complex salt], in aqueous solution a t 33.0 O C .
estimated to be ca. 17 ppm higher field relative to that for the unpaired ion. The ob-to-le1 conformational change associated with ion pairing is an important factor of the higher field shift in the sulfate ion pair. The same is essentially true for the succinate and L-tartrate ion pairs, although the shift is not so large as that for the sulfate ion pair.' An order of anions similar to (4) has also been reported in regard to the change in the circular dichroism (CD) spectra of the [Co(en),13' ion in aqueous solutions containing various The tendency of the anion-induced increase and decrease in the rotational strength of the A, and E components, respectively, of the 'Tl,(Oh) IAlg(Oh)transition of the C D spectra is well-correlated to the higher field shift of ion pairs of various anions. 59C0Spin-Lattice Relaxation Rate. The concentration dependences of the 59C0spin-lattice relaxation rates, R,(= l/Tl), for various salts of [Co(en),l3+ are shown in Figure 2. An appreciable increase in the relaxation rate was observed in the solutions of the salts with divalent anions. Univalent anions (chloride, perchlorate, and iodide), except for acetate, coexisting in solution only slightly affect the relaxation rate. The concentration dependences of the R,values are also analyzed in a manner similar to that for the 59C0chemical shift mentioned above. Thus, an observed R,value at a given concentration is represented by the weighted average of the relaxation rates, RI(MX) and Rl(M), for the paired and the unpaired [Co(en),13'
-
R I = (1 - XMX)RI(M)+ XMXRI(MX) The magnetic relaxation of 59C0nucleus ( I = 7/2) is mainly caused by the interaction of its electric quadrupole moment with the electric field gradient (efg) at the nuclear site. At the extreme narrowing limit, the 59C0spin-lattice relaxation rate is given byz5
R, = (2a2/49)(eZQq/h)2~q
(5)
where T~ represents the correlation time of the reorientation of the principal axis of the efg and eQ and eq are the quadrupole cm2)26and the moments of the 59C0nucleus (Q = 0.404 X efg along the principla axis at the nuclear site, respectively. The efg is assumed to be axially symmetrical in eq 5 for the sake of simplicity. The relaxation rates for the ion-paired and the unpaired [Co(en),13+ ion, R,(MX) and R,(M), can also be represented by eq 5 with parameters related to each species: eq(MX), T,(MX) and eq(M), Tq(M). (23) Sandmeier, J. L.; Blackmer, G. L. J . Am. Chem. SOC.1970,92,5238. (24) Masuda, Y.; Yamatera, H. J . Phys. Chem. 1984, 88, 3425. (25) Abragam, A. The Principles of Nuclear Magnetism; Clarendon: Oxford, 1961; p 314. (26) Ehrenstein, D. V.; Kopfermann, H.; Penselin, S. Z . Phys. 1960, 159, 230.
approximation here to assume that distortion of the octahedral coordination sphere of the six nitrogen atoms of [Co(en),13' is the only cause of the efg a t the 59C0site, eq in eq 5 . The coordination octahedron of the complex ion is compressed along the C3axis.27 This distortion brings about a positive value of efg along the principal axis, which coincides with the C, axis of the [Co(en),],+ ion. Then, the correlation time of the fluctuation of this efg, rqin eq 5 , can be replaced by the rotational correlation time of the C3 axis of the complex ion or the correlation time of the rotation around an axis perpendicular to the C, axis, T ~ The . rotational correlation times of the ion-paired and unpaired [Co(en),],' ions were previously obtained from the measurements of the 'H and I3C relaxation rates of the [Co(en),13' ion and were shown to be proportional to the viscosity of the solution." Then it is reasonable to assume that the 59C0relaxation rates, R,(MXJ and R,(M), of the ion-paired and the unpaired complex ion are also proportional to the viscosity of the solution. With this assumption, the relaxation rate observed at a given concentration and viscosity is expressed by the following equation consisting of terms proportional to the relaxation rates of the ion-paired and the unpaired complex ion at infinite dilution, R l o ( M X ) and Rlo(M), respectively
R, = (v/vo)(l -XMX)RIo(M) + (v/'J?o)XMXRIo(MX)
(6)
where 7 and vo represent the viscosity of the solution and that of pure water, respectively. In a manner similar t6 those in previous studies on the I3C and 'H relaxation the Rl0(MX) values are determined by eq 6 with R,and values measured at various concentrations and also with ion-association constants, K O , listed in Table I. The resulting R,O(MX) values are listed for various ion pairs in Table 11, and the R I values calculated on the basis of these Rlo(MX), 7,and K O values are shown in Figure 2 by solid lines. The difference between the Rlo(MX) and Rlo(M) values which are shown in Table I1 reflects the change of eq and/or rq in eq 5 caused by ion pairing. Comparing their results on the "C and 59C0relaxation rates, Bryant et al. concluded that the increase in the s9C0relaxation rate in the presence of sulfate ions in aqueous solution is mainly caused by the change in the rotational correlation time of the [Co(en),13+ ion.6 However, it should be noted that the rotational correlation time determined by the I3C relaxation rate is related to the rotation of C-H vectors of the ethylenediamine ligands in the [Co(en),13+ ion, while the rotational correlation time obtained from the 59C0relaxation rate ( T in ~ eq 5 ) is concerned with the rotation of the C3 axis of the [Co(en),l3+ ion which coincides with the principal axis of efg at the 59C0 nuclear site, Le., T~ = T L . ~If the rotational motion of the complex ion shows anisotropy, these two rotational correlation times should be different from each other. A previous investigation showed that the rotational motion of the unpaired [Co(en)J3+ ion was (27) Iwata, M.; Nakatsu, K.; Saito, Y . Acta Crystallogr., Sect. B 1969, 825, 2562.
2070
Masuda and Yamatera
The Journal of Physical Chemistry, Vol. 92, No. 7, 1988 n
i i.
c3 Figure 3. Simplified description of the structure of the ion pair lel, [Co(en),]'+-SO,*-.
nearly isotropic, whereas a large anisotropy was observed in the rotational motion of the [Co(en),13+ ion paired with divalent anions; the rotational motion ofthe C3axis was much slower than that around the C3axis." On the basis of the rotational correlation time of the C3 axis, T " ~ ( M X )previously , obtained" and the Rlo(MX) value obtained in the present experiment, the eq(MX) value was estimated from eq 5 . The value of e2Qq(MX)/h thus obtained for each ion pair is listed in Table 11. The effect of ion-pair formation on the eq(MX) or $Qq(MX)/h values is generally slight (a few percent), in agreement with the view of the Bryant et a1.,6 although the decrease in the e2Qq(MX)/h value was noticeable (- 17%) for the ion pair with sulfate ion. The electrostatic effect of the anion in the ion pair is first examined as a possible cause of e2Qq(MX)/h deviating from e2Qq(M)/h. For the sake of simplicity, the anion is regarded as a charged sphere and is placed on the C, axis of the [Co(en),13+ ion at a distance of cationanion contact.28 This structure should be stabilized by the attraction between the positively charged NH hydrogens of [Co(en),13+ and the anion. (See Figure 3.) In this structure, the negative charge of the anion causes an negative efg along the C3axis at the 59C0nuclear site. The magnitude of this efg, eqA, was estimated by electrostatics for each ion pair2' and is listed in Table I1 in the form of e2QqA/halong with the value of e2Qq(MX)/h derived from experiments. No systematic correlation can be seen between the experimental e2Qq(MX)/h and the calculated e2QqA/hvalues. This suggests that an analysis in more detail including the dynamic behavior of the ion pairs is needed. When two causes exist to produce an electric field gradient at a quadrupolar nucleus (59C0),their effect on the nuclear magnetic relaxation rate depends on the degree of their c o r r e l a t i ~ n . ~ Three ~ cases are examined below. Case 1 . The case of extremely strong correlation is first considered: when an anion, sitting on the principal axis of the inherent (28) The ionic radius is taken to be 3.6 A (= 3.6 X m) for [Co3+, 2.4 A for ClO;, 1.8 A for Cl-, 2.2 A for I-, 2.4 A for acetate, 3.0 for succinate and L-tartrate, and 2.3 A for SO4*-. The succinate and tartrate ions deviate considerably from a sphere and have several oxygen atoms of different kinds. These anions can be regarded as a charged sphere, when the anion in the ion pair undergoes conformational changes with a time constant shorter than r , ( M X ) . The time constants of these conformational changes are estimated to be less than 10 ps (Masuda, Y . ;Yamatera, H., unpublished data). (29) The quadrupole coupling constant caused by a charge placed on the C, axis of [ C ~ ( e n ) , ] ~was + calculated by the equation
A"),]
e2qQ/h = (eQ/h)(l + y,)ze/r3 where y- is the Sternheimer antishielding parameter. The value of (1 + yD) is estimated to be about 8 for Co3+(Das, T. P.;Pomeqntz, M. Phys. Rev. 1961, 223,2070). The parameter r is the distance between the center of the anionic charge and Co3+. (30) The general treatment and discussion for the relaxation of a quadrupole nucleus in this condition are given in the review: Hortz, M. Prog. Nucl. Magn. Reson. Spectrosc. 1986, 18, 321.
efg of the [Co(en),13+ ion, is so tightly bound to the cation that the ion pair can be regarded to be rigid during its rotational motion. In this case, the main axis component of the efg caused by the anionic charge on the C3 axis, eqA, is added to that of inherent efg of the [Co(en),13' ion, eq,, and fluctuates with a correlation time, T,, which is identical with that of the rotation of the principal axis of efg (the C3 axis) of the complex ion, T ~ ( M X ) Then, . the 59C0relaxation rate of the ion-paired [Co(en)J3' ion is represented by
where 7 , is equal to T,(MX) previously obtained from I3C and 'H relaxation experiments. Considering that eqA has a negative value (and IeqAl < leqol), eqeff(MX)will be appreciably smaller than eq, (= eq(M)). Case 2. In this case the anion in the ion pair freely moves around the cation with little correlation with the rotation of the complex cation. In this extreme,31there is no correlation between the rotational motion of the C3 axis of the complex ion and that of the vector connecting the centers of the cation and the anion; Le., the inherent efg (eq,) and the anion-induced efg (eqA) independently contribute to the s9C0 relaxation rate with their respective correlation times ( 7 , and T ~ )and , then s9C0relaxation rate is given by32
The effective magnitude of eq, eqefr(MX),will be larger than eq, (= eq(M)), owing to a positive value of (eqA)%A in eq 8. Case 3. If the potential surface for the anion surrounding the complex cation has a shallow depression, the anion moving around the cation is likely to stay at the depression for a while before going to other positions. In this case, the cross correlation term between the fluctuation of the two efg's, eq, and eqA, cannot be negligible. Although the evaluation of this cross term is difficult, the value will range between 2eqAeqo~,(MX) (
