THEOUTERCOORDINATION SPHERE
The Outer Coordination Sphere. I.
3299
Nuclear Magnetic Resonance Relaxation
Time Effects Produced by Paramagnetic Ions with Nonlabile Inner Coordination Spheres‘
by Thomas R. Stengle and Cooper H. Langford Chemistry Departments, U n i w e a y of Massachusetts, Amherst, Massachusetts, and Amherst College, Amherst, Massachusetts (Received February 86, 1966)
The effects of various paramagnetic Cr(II1) complexes with well-defined, nonlabile inner coordination spheres on the transverse relaxation times of F19n.m.r. signals from F- and PFe- have been determined in aqueous solution. The effects of the paramagnetic ions on nuclei in the second coordination sphere are seen to be substantial. The chemical evidence (concentration dependence, structure dependence, etc.) suggests that a consistent interpretation of the effects may be given in terms of relative outer-sphere coordinating tendencies. The interpretation emphasizes the importance of the interaction between innersphere ligands and solvent molecules.
Introduction The composition of the solvation sphere of a complex ion has been t,he subject of some study in the past. Despite a number of investigations, a controversy still exists as to whether an ion such as tris(ethy1enediamine)chromium(III) in aqueous solution will have its first solvation sphere composed completely of water molecules, or whether an anion may enter this “second coordination sphere’’ and form an “outer-sphere” complex. In recent work on inorganic reaction mechanisms, the second coordination sphere has come under increasing scrutiny. For example Tobe and Watts,2 Schmidt and T a ~ b e and , ~ Langford and Johnson4 have discussed ligand interchange reactions between the first and second coordination spheres of Co(111) complexes in a way that assumed that outersphere complexes were well-defined entities in solution. However, the status of such entities is by no means clear, especially with respect to aqueous solutions. There is need for experimental data derived from short-range interactions between a complex with a well-defined (nonlabile) inner coordination sphere and ligands (anions) in solution. The best extant experiments5-’ study outer-sphere complexing by observing modifications of the ultra-
violet spectrum of the complex that are dependent upon anion concentration, but even this technique has led to some serious disagreements. Evans and Nancollas* derived outer-sphere association constants of 74 and 46 for the hexaamminecobalt(II1) ion with chloride and bromide in good agreement with predictions from Bjerrum’sg theory, whereas King, et uE.,l0 studied the same systems over a wider range of halide concentration (and incidentally a wide range of perchlorate concentration which should not be regarded as innocuous) and concluded that the outer-sphere association constant was less than 0.2, so small that it seemed that the ions could not desolvate each other (1) Presented in part at the 145th National Meeting of the American Chemical Society, New York, N. Y., Sept. 1963. (2) M. L.Tobe and D. 71;. Watts, J . Chem. SOC.,4614 (1962). (3) W.Schmidt and H. Taube, Znorg. Chem., 2 , 698 (1963). (4) C. H.Langford and M. P. Johnson, J . Am. Chem. SOC.,86, 229 (1964). (5) H.Taube and F. A. Posey, ibid., 75, 1463 (1953). (6) F. A. Posey and H. Taube, ibid., 78, 15 (1956). (7) N. Fogel, J. Tai, and J. Yarborough, ibid., 84, 1145 (1962). (8) M. G. Evans and G. H. Nancollas, Trans. Faraday SOC.,49, 363 (1953). (9) N. Bjerrum, Kgl. Danske Vdenskab. Selskab, 7 , No. 9 (1926). (10)E. L. King, J. H. Espenson, and R. E. Visco, J . Phys. Chem., 63, 755 (1959).
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to form an outer-sphere complex. This discrepancy with the results of Evans and h’ancollas8 is discussed in detail by King, et al.’O Recently Aleill studied the association between hexaaquochromium(II1) ion and perchlorate ion using an n.m.r. technique. The effect of the paramagnetic ion on the chemical shift of 0’’ nuclei in enriched water was measured as a function of chromium and C104- concentration. From these data it was concluded that the perchlorate ion does enter the second coordination sphere of C I - ( H ~ O ) ~and ~ + that the ratio of Clod- to water in the second sphere is of the same order of magnitude as in the bulk solution. The “equilibrium constant’’ for the association cannot be calculated from this datum alone, but it would appear that its value is small, probably less than unity. In this work a new method of studying outer-sphere association is proposed. This technique is based on the effect of a paramagnetic ion on the relaxation time of nearby nuclei. This interaction is short ranged and leads to a significant reduction in the relaxation time of nuclei which are quite close to the paramagnetic center. In this work we studied the association between a nonlabile Cr(II1) complex and a fluorine-containing anion. In a typical experiment, the spin-spin relaxation time of the F19 nucleus was determined in a 0.25 M solution of KPF6, and this was compared with the value obtained when the solution was also ma,de 0.1 M in a Cr(II1) complex. The addition of the paramagnetic complex resulted in a large reduction of the spin-spin relaxation time of the Fl9 signal (as evidenced by a broadening of the n.m.r. line). Since the interaction of the paramagnetic ion with the F19nucleus is short ranged, most, but not all, of the effect must arise from those PF6- ions which are in the second coordination sphere of the Cr(II1) complex ion. To a rough approximation, the magnitude of the line broadening is proportional to the fraction of the PFa- ions which are in association with the complex ion. Although there is no way of determining the value of the proportionality constant a priori, a great deal of useful information can be obtained from a study of the trends of outer-sphere association with changes in concentration, temperature, and the nature of both the cation and anion. Although all the details of the mechanism of the relaxation are not yet clear, the important study of Bloembergen and Morgan12 seems to justify the following assumptions: (1) the observed relaxation rate is the average over all different nuclear environments weighted for the probability that the nucleus is in the given environment; (2) the decrease of the relaxation time results predominantly from those F19-containing The Journal of Physical Chemistry
THOMAS R. STENGLE AND COOPER H. LANGFORD
anions which are actually in “contact” with (ie., in the second coordination sphere of) the paramagnetic ions; and (3) in the relaxation mechanism of an F19 nucleus in the second coordination sphere of a Cr(111) complex, the spin-exchange interaction is only of secondary importance when compared with the dipolar interaction. Assumption 1 is valid if the exchange of the FIB nuclei is rapid between the various environments when compared with the reciprocal of the difference of the Larmor frequencies for the environments and the relaxation time of the F19 nucleus in the paramagnetic environment. These are the conditions given by eq. 10(d) of ref. 13. Such lability is certainly expected for outer-sphere interactions, and the assumption is confirmed by the temperature dependence of the relaxation times. For a dipole-dipole mechanism in the fast-exchange case, one’ expects the relaxation time of a fluorine nucleus to decrease with decreasing temperature according to the temperature dependence of the correlation time. For Cr(II1) ions, the diffusion correlation time predominates’* which would lead to an activation energy of 2 or 3 kcal. mole-’ for the relaxation process. The experimental temperature dependence of the relaxation time is governed by the heat of association of the second-sphere complex as well as by the activation energy of the relaxation process. The experimental values of 2.5 and 5.0 kcal. mole-’ for the two systems studied are in agreement with this analysis and lead to heats of association between zero and -2.5 kcal. mole-’. The solution of the Bloch equations with chemical exchange has been discussed by McConnell16 and by Swift and Connick.13 In the fast-exchange case, the observed relaxation time, Tz, is given by eq. 1
where PA is the probability that the nucleus is in environment A, T 2 A is the relaxation time in environment A, and p~ and T ~ B refer to the same quantities in environment B. Taking A to be the bulk solution (diamagnetic environment) and B to be the second coordination sphere (paramagnetic environment), we can determine the probability of finding the F19-containing anion in the second coordination sphere of the (11) M. Alei, I m r g . Chem., 3, 44 (1964). (12) N. Bloembergen and L. 0. Morgan, J. Chem. Phys., 34, 842 (1961). (13) T.J. Swift and R. E. Connick, ibid., 37,307 (1962). (14) Z. Luz and S. Meiboom, ibid., 40, 2686 (1964). (15) H.M.McConnell, ibid., 28, 430 (1958).
THEOUTERCOORDINATION SPHERE
paramagnetic complex if the other quantities are known. The relaxation time TU is simply the relaxation time in a solution which is free of paramagnetic ions. At the outset, TZB cannot be determined. For reasonably dilute solutions, PA is nearly unity; therefore, p~ will be proportional to the quantity Av - AYA, where Av is the line width at half-height and is related to the relaxation time by the equation Av = l/?rTz. Assumption 2 is suggested since all proposed mechanisms of interaction are short ranged. The two effects which can lead to relaxation are the nuclear magnetic dipole-electron magnetic dipole interactions and the isotropic spin-exchange mechanism.l2 It is well known that the field of a dipole falls off as r--3 which leads to l / T z ~varying as +. The spinexchange mechanism depends on the value of the wave function of the paramagnetic electrons at the position of the FIBnucleus. Since the paramagnetic electrons of the Cr(II1) ion are localized in tzgnonbonding orbitals, the wave function will rapidly approach zero a t large distances from the metal atom. This interaction is much shorter ranged than the dipolar term. It seems that interactions beyond the second sphere must be wholly dipolar in nature. In estimating that part of the quantity Av - AUA which is due to interactions beyond the second sphere, a geometrical factor of 4 d must be taken into account. This allow fw the increasing number of ions which can be contained within a shell of fixed thickness as the radius increases. Therefore, interactions beyond the second sphere must be small, falling off a t least as rapidly as r4. They are large enough to be observable, but it is certain that they will be much smaller than second-sphere interactions. If TZBchanges in a regular fashion from one Cr(II1) complex to another, it is possible to make direct comparisons of experimental data for different complexes. This will be true if the predominant mechanism of relaxation in the second sphere is dipolar; this is assumption 3. The results of several studies may be cited in support of this contention. The data of Morgan, et aZ.,16 on the proton relaxation times in aqueous solutions of Cr(1II) complexes have been satisfactorily explained in terms of the size of the ion and its solvation. The spin-exchange mechanism, if present, did not vary widely from one complex to the next. More recently Morgan and Nolle1' made a detailed study of the proton resonance in aqueous solu~ ~an ' attempt to elucidate the retions of C ~ ( H Z C ) )in laxation mechanism in the jirst coordination sphere. Although their data cannot be explained in terms of a dipolar mechanism alone, it seems that this effect is responsible for a major part of the relaxation. Since
3301
the dipolar interaction falls off less rapidly with distance than any other interaction, it is reasonable to suppose that it is the predominant interaction present in the second sphere. Finally our results show that the size of the complex ion is not the most important factor causing variations from one complex to another as would be expected if the spin-exchange mechanism were of paramount importance.
Experimental Section Materials. Potassium hexafluorophosphate was obtained from Matheson Coleman and Bell and recrystallized from water. Sodium fluoride was prepared by neutralizing primary standard sodium carbonate with reagent grade HF. This procedure was necessary because most reagent grade fluoride salts contain enough paramagnetic impurities to cause difficulty. This is due to the extreme sensitivity of the relaxation time of F- to the presence of small amounts of paramagnetic ions which have labile first coordination spheres. l8 For example, a concentration of M manganous ion is sufficient to cause appreciable broadening of the F- line. This problem is not encountered with KPF6, since the PF6- ion has little tendency to enter a first coordination sphere. The chromic complexes K,[Cr(ox),] -3Hz0 and cis[Cr(en)zClz]C119 were prepared by standard methods.z0 ,I simple and convenient synthesis of [Cr(en), ]C13 and iC I m i ,IC13 was developed. Hexa(uren)chroinium(III) chloride \E as dissolved in anhydrous dimethylformamide and refluxed for 20 min. with exceSs ligand. First a red color developed in the solution, and finally a yellow precipitate separated. The precipitate was recrystallized from an ethanol-water mixture a t room temperature. The compounds were obtained in about 25% yield, and their identities were established by analysis for chloride ion. The yields are comparable to those obtained by the standard method.21 N.7n.r. Measurements. N.m.r. spectra were recorded on a Varian DP-56.4 spectrometer. The instrument was equipped with a thermostated probe which maintained the temperature within limits of &lo. Values of Tz were obtained from measurements of the width a t half-height of the recorded absorption lines. Care was taken to demonstrate that saturation was not oc('1
(16) L. 0. Morgan, A. W. Nolle, R. L. Hull, and J. Murphy, J. Chem. Phys., 25, 206 (1956). (17) L. 0. Morgan and A . W. Nolle, ibid., 31, 365 (1959). (18) V. M. Vdovenko, L. L. Pavlova, and V. A. Shcherbakov, Zh. Strukt. Khim., 3, 707 (1962); Chem. Abstr., 58, 7528e (1963). (19) ox = oxalato, en = ethylenediamine, pn = 1,2-diaminopropane. (20) D. M. Yost, Inorg. Syn., 1, 37 (1939); C. L. Rollinson and J. C. Bailar, Jr., zbid., 2, 200 (1946). (21) C. L. Rollinson and J. C. Bailar, Jr., ibid., 2, 196 (1946).
Volums 69,Number 10 October 1966
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THOMAS R. STENGLE AND COOPER H. LANGFORD
curring and affecting the line width. The accuracy of the T Z measurements was limited by the poor signalto-noise ratio at large line widths. I n general the line widths are reliable to h l C.P.S.or *lo%,, whichever is larger. In some favorable cases an accuracy of =k5% was achieved. An attempt was made to determine relaxation times by the spin-echo technique. This method was not sensitive enough to be of utility at the concentrations used in this study, and in general more reliable data were obtained from steady-state absorption curves.
501 0.0 5
0
C,
Line-width measurements were made on KPFe in solution with several Cr(II1) complexes. The variation of the line width was observed as a function of metal ion concentration; the results are given in Figure 1. The same results for NaF solutions are shown in Figure 2. Temperature dependence data for two Cr(II1) complexes in KPFs solution are shown in Figure 3. These data are suggestive of the temperature dependence of TZBand thus support the assumption of fast exchange in the second sphere. I n the slow-exchange case the temperature dependence would be that of a reaction rate constant, which would have oppositc sign.15 It is not possible to determine the heat of association from the temperature-dependence data, since the temperature dependence of T 2is~known only approximately.
The probability that an anion is in the second coordination sphere of a Cr(I1.T) complex is p~ (neglecting effects beyond the second sphere). The relationship between the line width ( A v ) and p~ niay be obtained from eq. 1. In most of our experiments the concentrations are such that PA is near unity. The quantity T ~ may A be evaluated from AVA = l/nTzA, where AVAis the line width in the absence of Cr(II1) complex. Equation 1then becomes ~ ( Av AVA) = ~ B / T ~ B
3001 i”
2
+ x = MX
= [MXl/C, and
PI
= [MXI/[Ml[Xl
o.io
0.05 (YOLESILITERI
Figure 2. Variation of line width in saturated (ca. 1 M ) NaF solution: 1, Cr(pn)&lS; 2, Cr(en)&ls; 3, [Cr(en)&l~]Cl; 4, K3Cr(ox),.
I
I
3.2
4
3.4 I
3.6
,os
Figure 3. Temperature dependence of line width in 0.25 M KPFs solution: 1, 0.05 M K&I(OX)~;2, 0.05 M Cr(en)&l3.
(3)
Here nil represents the Cr(II1) complex ion with a fixed inner coordination sphere, X the FlS-containing anion, and MX the first outer-sphere complex. Following the The Journal of Physicul Chemistry
c,
(2)
If we apply the law of mass action to the equilibrium between a second-sphere complex and the ions from which it is formed, we have RiI
0.20
IUOLEEILITERI
Figure 1. Variation of line width in 0.25 M KPFs solution with Cr(II1) complex concentration: 1, Cr( en)3Cls; 2, [Cr(en)&lzlC1; 3, K8Cr(ox)a; 4, Cr(H@)s(NO,)a; 5, Cr(pn)&la.
0
Discussion
a1
0.15
0.10
Results
usual notation, a1 is the degree of monocomplex formation, and is the formation constant for this complex. The concentrations of the species in 3 are de-
THEOUTERCOORDINATION SPHERE
3303
on the relative values of CY^. For example, in Figure 1 the slope of the Cr(en)a3+line is three times larger than the slope of the Cr(HtO)s3+ line. Hence we can say must be at Zeasf three times the that o1 for p~ = [MXJ/C, and p~ = a1C,/Cx (4) value for Cr(Hz0)s3+. where C, is the analytical concentration of the F19The ratio of the values of Av - AVAfor a given comcontaining anion. This treatment predicts that linearplex at two C, values (C, constant) gives the p~ ratio ity is to be expected in the plots in Figures 1 and 2 at with the unknown quantity TZB canceled. Assuming low values of C,n. The deviation from linearity for various p1 values, the PB ratios may be calculated, and the calculated ratios may be compared with experiment some complexes at high C, indicates substantial complexing. I n such cases we no longer have [XI = Cx, to determine the approximate value of PI. Unfortuwhich is a necessary condition that a1be constant. nately, the present experimental requirement of large C, (to observe the resonance) limits such experiments Assuming for the present that, for a given anion, T ~ isBthe same for a series of Cr(II1) ions, the quantity to 01 values between 1 and 10. In some cases, misleading values may be obtained when higher complexing (Av - AVA)is proportional to a1, Therefore the relainterferes with the analysis in terms of monocomplex tive slopes in Figure 1 provide a measure of the relaformation. Moreover, activity effects are expected tive values of a1 for the PFs- complexes. Figure 2 yields the ordering of a1 values for F- outer-sphere to be important. Very approximate values of p1 complexes. For both anions, the order of decreasing were obtained as follows: Cr(ox)s3- with PFs-, PI = > Cr(en)zClz+ > 0; Cr(en)s3+ with PFs-, p1 = 1; Cr(en)zClz+with complexation is: C r ( ~ n ) > ~ Cr(en)33+ ~+ C r ( ~ x ) ~ ~The - . interesting ion Cr(Hz0)63+,which lies F-, 81 = 3; Cr(en)33+with F-, 01 > 10. These values below Cr(en)&lz+ for complexation with PFs-, was necseem reasonable in the light of the prior literat~re.5-7~11 tZ3 essarily omitted from the F- measurements because of solubility limitations. We shall attempt to give an over-all evaluation of If we remove the assumption that T ~ is‘the B same for the n.m.r. method. For a series of complexes of very all of the Cr(II1) complex ions, we can no longer obsimilar electronic structure, it provides a simple way tain quantitative data on the variation of the cyl values. to determine relative degrees of outer-sphere complexHowever, some important qualitative information will ing. If the association is weak, an approximate value result if the T ~ values B can be shown to vary in a reguof the first outer-sphere association constant is oblar manner with the size of the complex ion. The two tained. The value cannot be obtained preci~ely,~‘ factors which must be considered are the strength of but what is more important is that the n.m.r. method the interaction between the paramagnetic electron does appear to detect genuine second-sphere associaand the FI9 nucleus and the correlation time for this tion because of its “short-range” character. Although interaction. The magnitude of the interaction will the results of themeasurements on the C r ( o ~ ) systems ~~depend on the inverse sixth power of the distance be(in which no ion association is likely to take place) tween the interacting centers. This will lead to a rapid suggest some broadening due to “third-sphere” effects, decrease of the relaxation rate, ~ / T , Bwith , increasing it is small, approximately independent of the source radius of the Cr(II1) ion. The tumbling correlation of Fig, and leads to a PI value of zero. timez2will depend on the size of the ion in such a way Using only relative degrees of outer-sphere associaas to increase the relaxation rate with increasing size. tion obtained from the data in Figure 1 and 2, it is For a sphere turning in a viscous medium, it can be possible to comment on the factors which influence shown12 that the relaxation rate will vary directly with second-sphere complexing. As expected, electrostatic the third power of the radius. Hence the magnitude forces are quite important; Figures 4 and 5 present of the diDolar interaction will be the medominant factor ‘I1 deterlnining the dependence Of l/TzB On ion (22) If the correlation time for the interaction is determined by the electron spin relaxation time, ~ / T z Bwill depend on factors other size. The relaxation rate will be smaller for larger than the size of the Cr(II1) ion. However, the temperature-dependions. ence data of Luz and Meiboom“ and our data for the Cr(ox)ra-Our results show an increase in the F’9 line width PFa- system (in which it is likely that no ion pairs are formed) indicate an activation energy for the relaxation process of 2.5 kcal. mole Its the size of the ~ ~ ( 1 1 1 complex ) increases. hi^ is which is consistent with a tumbling and not an electron spin relaxation mechanism. the opposite of what would be expected on the basis (23) R. G. Pearson and F. Basolo, J . Am. Chem. SOC.,78, 4878 of the change of TZBwith ion size, and can only be noted by bracketing, and C, is the analytical concentration of the Cr(II1) complex. The definitions of p~ and a1lead to
-1,
Values Of
in Of ‘On The the Slopes in Figures 1 and 2 will place a limit
(1956). (24) It is quite possible that thermodynamic constants for weak ion associations of this type oannot be precisely defined.
Volume 69. Number IO October 1966
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THOMAS R. STENGLEAND COOPERH. LANGFORD
The possibility that this effect arises from a lowering of the charge due to hydrolysis can be dismissed because the line broadening does not increase in more acid solutions. The anomalous behavior of the hexaaquochromium(111) ion is easily explained, It is able to form strong hydrogen bonds with second-sphere water molecules ‘0 3 2 I O 0 -I -2 - 3 L and these must be broken for association to occur. This viewpoint provides a clue to the other major CHARQE TYPE anomaly revealed by Figures 1 and 2, Le., the increasing Figure 4. Variation of line width in 0.25 M KPFs solution with association of the hexamine ions as the radius increases. charge type of Cr(II1) complex, C, = 0.05 M : 1, Cr(pn)&lr; This behavior is’shown in the ions Cr(en)aa+ and 2, Cr(en)sCls; 3, Cr( HzO),( NO&; 4, [Cr(en)zClz]C1;5, K & r ( ~ x ) ~ . Cr(pn)Sa+;the latter has the larger radius, and also the greater tendency to associate with anions. Although simple electrostatic considerations suggest that increasing ionic radius would lead to lower association, it is clear that increasing radius, especially in the form of added 200 Lo‘ organic groups, reduces solvation by water. Thus as the water molecules of the second sphere become easier to replace, the association increases. The process is easily seen from the point of view of coordination chemistry. Association requires removal of one secondsphere “ligand” and its replacement by another, a CHAROE TYPE process which does depend on the details of the structure of the first coordination sphere. Note that it is Figure 5. Variation of line width in saturated (cu. 1M ) NaF probably not necessary to postulate any covalent solution with charge type of Cr(II1) complex, C, = 0.025 M : 1, Cr(pn)K%; 2, Cr(en)sCls; 3, [Cr(en)zCla]Cl; 4, KsCr(ox)s. bonding to the second sphere, it is simply necessary to use considerations of electrostatics and hydrogen bonding with sufficient regard for microstructure. line broadening as a function of the charge on the Cr(111) complex. Generally, the degree of association Acknowledgments. This investigation was supported increases with increasing positive charge on the Cr(II1) by the Directorate of Chemical Sciences, Air Force complex as a simple electrostatic model would predict. Office of Scientific Research Grant No. 212-63, and in However, the nature of the ligands in thefirst coordinaits early stage by a grant from the Research Corporation sphere also influences the degree of second-sphere tion. The authors are indebted to Mr. James D. association. Despite its high positive charge, Cr(Hz0)ea+ McNeil for his help in the preparation of some of the shows only a m a l l tendency to associate with PFa-. compounds.
300Y’
The J o u d of Physical Chemietry
