1602
K. L. Craighead and R. G. Bryant
The Insignificance of Second Coordination Sphere Interactions in Cobalt-59 Nuclear Magnetic Resonance Relaxation K. L. Craighead and R. G. Bryant”’ Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455 (Received October 28, 1974: Revised Manuscript Received March 24, 1975) Publication costs assisted by the National lnstitutes of Health
Nuclear magnetic resonance relaxation time measurements are reported which permit evaluation of the electrostatic contribution to field gradients from ions external t o the first coordination sphere of the observed nucleus. I t is concluded that for the tris(ethylenediamine)cobalt(III) ion the presence of phosphate ion in the second coordination sphere makes little if any contribution to the electric field gradient a t the cobalt nucleus. Considerable attention has been focused on the origins of NMR relaxation in aqueous electrolyte solutions.’ For many nuclei the nuclear electric quadrupole interaction dominates; but definitive evidence that any of the theoretical approaches to this problem is correct is lacking. A theory developed by Hertz focuses on electrostatic contributions to the electric field gradient at the observed nucleus and is able to obtain approximate agreement with experimental observation^.^,^ In spite of this result some discussions of NMR data for quadrupole relaxed nuclei have ignored electrostatic contributions to relaxation originating external to the first sphere of interaction and focused only on that part which results from molecules or ions in the first coordination sphere of the observed ion. The present experiment is directed a t assessing the validity of this approach. Tris(ethylenediamine)cobalt(III) chloride is a very wellcharacterized chemically inert coordination complex in which the 59C0 NMR signal is readily observed. The j9C0 nuclear electric quadrupole moment6 is 0.40 in units of 10-24e cm2 which is sufficiently large that the resonance is not detected in some unsymmetrical complexes.6 In alkaline aqueous solutions phosphate ion forms an ion pair with C0(en)3~+ in high yield which has been investigated by several methods.’-l3 The 59C0 NMR signal from this complex is both shifted and broadened by the formation of the ion pair.I4J5 This system therefore provides a direct means of assessing electrostatic contributions to quadrupole relaxation which originate in ionic charges placed external to the first coordination sphere of the ion. The 59C0 NMR relaxation is dominated by the nuclear electric quadrupole relaxation mechanism. In the present case the cobalt nucleus experiences approximately spherical symmetry and the relaxation equation may then take the form2
where TIis the longitudinal relaxation time, I the nuclear spin quantum number, e the unit charge, Q the nuclear electric quadrupole moment, and J the Fourier transform of the time correlation function describing the fluctuations of the components of the electric field gradient tensor. In the limit of extreme narrowing and where a covalent bond is formed this expression becomeslfi
The Journal of Physical Chemistry, Vol. 79,No. 15,1975
1 -=-(-) 2n T T ~ 49
e2qQ h
27
where T is the correlation time for the reorientation of the electric field gradient, q. Usually T may be identified with a rotational correlation time. In either description changes in the relaxation time may reflect changes in either the magnitudes of the field gradient tensor components or in their time dependence. In the present case the magnitude of the electric field gradient a t the cobalt nucleus originating from negative charge on the phosphate ion is to be estimated. An accurate theoretical prediction of the field gradient would require sufficiently precise wave functions for the system to accurately include antishielding effects. The metal system is too large for this approach. A very crude estimate may be made based on electrostatic ideas where the electric field gradient is approximately q ’ h 3 where q’ is the charge and r is the distance from the phosphate ion to the cobalt nucleus. This estimate is expected t o be low because antishielding effects are ignored. If the ligand system about cobalt were absent the antishielding correction to the field gradient would be about a factor of Calculations of this correction for a metal complex have not been reported. Substitution of a reasonable distance into the above expression suggests that the field gradient originating from the phosphate ion will have a negligible effect on the 59C0 relaxation time unless the antishielding factor is on the order of or larger than 10. Although the basis for the estimate of the field gradient may be questioned, the suggestion that the effects observable a t the cobalt nucleus are small or even negligible is supported by the data in Table I. These data show that the 59C0 relaxation rate changes by a factor of about 2.5 upon ion pair formation. This may come about from changes in either the magnitude or time dependence of the field gradient tensor elements. The I3C 2‘1 provides a good measure of the change in the rotational correlation time suffered by the metal complex on formation of the ion pair.ls The 13C data show that the change in the correlation time describing reorientation of the C-H vectors in the complex exceeds a factor of 4 when the ion pair is formed. This result is also consistent with proton and deuterium measurements made on the same c0mp1ex.l~There is a possibility that the correlation time change monitored a t the carbon
1603
Origin of NMR Relaxation in Aqueous Solution
TABLE I: NMR Relaxation Times in Co(enh3+ Ion 13crelaxation
59Coline width, Hz ~~
l/Tl,
rate,
sec-'
~
310
* 27 = 0.7 il/I
pH 13.5, [Co(III)] = 0.1 M
127 i 12
1.34 f 0.1 pH 13.5, [Pod3-]= 0.5 M [Co(III)] = 0.3 M 5.8 f 0.5
pH 13.5, [CO(III)] = 0.1 M pH 13.5, [CO(III)] = 0.3 M a Recorded a t 14.1 MHz as previously reported.20 *Recorded on a Varian XL-100 NMR spectrometer using the inversion recovery method. atoms is larger than that experienced at the cobalt ion because of changes in ligand motion upon formation of the ion pair. Nevertheless it is clear that the correlation time for r,otational motion of the complex is altered by at least a factor of 2. T o the extent that rotation dominates the field gradient time dependence, the measured correlation time change accounts for the observed changes in the 59C0 relaxation rate on ion pair formation. Therefore contributions to the cobalt relaxation rate arising from the electric field of the phosphate ion are small in this instance and the previous neglect of field gradient contributions from ions external to a first coordination sphere appears to be justified.
NOTE ADDED IN PROOF: Alder and Loewenstein have previously approached this problem somewhat differently using an anionic cobalt complex. Their data and interpre-
tation also suggest that in the present case such a field gradient contribution should be small. (R. Alder and A. Loewenstein, J. Mag. Resonance, 5,248 (19711.)
Acknowledgment. This work was supported by the National Institutes of Health, GM-18719, the Research Corporation, and the Chemistry Department and the Graduate School, The University of Minnesota. References a n d Notes Camille and Henry Dreyfus Teacher Scholar. H. G. Hertz in "Water, A Comprehensive Treatise", F. Franks, Ed., Plenum Press, New York, N.Y., 1973, Chapter 7. (a) H. G. Hertz, Ber. Bunsenges. Pbys. Chem., 77, 531 (1973); (b) 77, 688 (1973). H. G. Hertz, et al., Ber. Bunsenges. Pbys. Cbem., 78, 24 (1974). Varian NMR Table, Varian Associates, Palo Alto, Calif., 1968. A. Yamasaki, F. Yajima, and S. Fujiwara, Inorg. Chim. Acta.. 2, 39 (1968). H. L. Smith and B. E. Douglas, Inorg. Chem., 5, 784 (1966). R. Larsson, S. F. Masson, and B. J. Norman, J. Cbem. SOC. A, 301 (1966). S. F. Masson and B. J. Norman, Proc. Cbem. SOC.,London, 339 (1964). S . F. Masson and B. J. Norman, J. Chem. SOC.A, 307 (1966). J. L. Sudmeier and G. L. Blackmer, J. Am. Cbem. SOC.,92, 5238 (1970). J. L. Sudmeier, G. L. Blackmer, C. H.Bradley, and F. A. L. Anet, J. Am. Chem. SOC.,94, 757 (1972). L. R. Froebe and B. E. Douglas, horg. Cbem., 9, 513 (1970). T. H. Martin and B. M. Fung, J. Phys. Cbem., 77, 637 (1973). K. L. Craighead, Ph.D. Thesis, University of Minnesota, 1973. A. Abragam, "The Principles of Nuclear Magnetism", The Clarendon Press, Oxford, 1961, p 314. E. A. C. Lucken. "Nuclear Quadrupole Coupling Constants", Academic Press, New York, N.Y., 1969. A. Allerhand, D. Doddrell, and R. Komoroski, J. Cbem. Pbys., 55, 189 (1971). K. L. Craighead, P. Jones, and R. G. Bryant, unpublished data. K. L. Craighead, J. Am. Chem. SOC.,95, 4434 (1973).
The Journal of Physical Chemistry, Vol. 79, No. 15, 1975
