for the unfiltered flash light gives ro = 4.8 X l e 8 cm., hence Po = 1 - = 5@/6 and P = 0.935. It can be further that u SI [3a(l - p)]/p for small values of Q, and therefore the mean diffusive displacement is ca. 0.4 X 10-8 cm. based on the above value for
+
P.
The assumption that the liquid is a continuous medium is obviously quite severe in view of such a small calculated diffusive displacement. Required is that the diffusive process take place by a series of very small steps occurring at very high frequency and hence low activation energy. This is consistent with the constantvolume measurements on the diffusion of molecular iodine in carbon tetrachloride24 and the self-diffusion of carbon tetrachloride, 2 5 whereby the temperature coefficients of diffusion are very nearly the temperature (23) L. Monchick,J. Chem. Phys., 24, 381 (1956). (24) E. W. Haycock, B. J. Alder, and J. H. Hildebrand, ibid., 21, 1601 (1953). (25) H. Watts, B. J. Alder, and J. H. Hildebrand, ibid., 23, 659 (1955).
coefficient of kinetic energy. However, in view of the discrepancies between the measured and calculated parameters in the diffusion-controlled rate expression, NoyesZ0 has concluded that a small but significant energy barrier exists for recombination and dissociation processes. Acknowledgments. The author wishes to acknowledge with sincere appreciation the grant of a Science Faculty Fellowship by the National Science Foundation, the opportunity to use the facilities at the Institute of Physical Chemistry, and the help and courtesies extended by Professor Stig Claesson, Docent Lars Lindqvist, and the Institute staff during his year at the University of Uppsala. Through the courtesy of the National Swedish Office for Administrative Rationalization and Economy, Stockholm, free computer machine time was made available; it is a pleasure to acknowledge the assistance of Dr. Lars-Olof Sundelof in the digital programming of these results.
Electron Spin Relaxation in Pseudo-Tetrahedral Cobalt (11) and Nickel (11) Complexes in Solution'a Gerd N. La Marlb
Contribution f r o m the Frick Chemical Laboratory, Princeton University, Princeton, New Jersey 08540. Received April 17, 1965 It is shown that the well-resolved proton magnetic resonance spectra qf the paramagnetic, pseudo-tetrahedral Ni(II) complexes with aminotroponeimines and salicylaldimines, and the Ni(II) and Co(Il) complexes with triarylphosphines, are the result of very short electron resec. The possible laxation times, of magnitude mechanisms responsible f o r these short relaxation times are investigated, and it is concluded that: (1) dynamic interconversion between diamagnetic and paramagnetic forms in solution f o r the Ni(II) complexes is too slow to be the dominant relaxation mechanism; (2) coupling of the zero field splitting to the tumbling of the complex in solution dominates the relaxation time f o r both the Co and N i systems of interest. For the N i complexes, these conclusions are reached by systematic elimination of the other possible mechanisms and by demonstrating that the electronic structures f o r these complexes favor the appearance of large zero field splittings necessary f o r such rapid relaxation. For the Co complexes, it is demonstrated that the short relaxation times can be quantitatively accounted f o r by a zero field splitting constant well within the range of values observed f o r other tetrahedral Co systems. The dferences in p.m.r. line width f o r some triarylphosphine and aminotroponeimine complexes in carbon disulfide and chlorof o r m are shown to be consistent with this relaxation mechanism. (1) (a) This research has been supported by a grant from the National Institutes of Health; (b) Physical Chemistry Laboratory, Swiss Federal Institute of Technology, Zurich, Switzerland.
La Mar
Introduction The appearance of a well-resolved proton magnetic resonance (p.m.r.) signal for paramagnetic complexes is the result2of their unpaired electron(s) possessing a very short relaxation time, Tl, or exchange time, T,. For a sufficiently short electronic relaxation time, the p.m.r. line width for the complex may be only imperceptibly broader than for the diamagnetic ligands. Recently, a number of paramagnetic systems containing tetrahedrally coordinated Ni(II)4-6 and Co(II)' have been investigated, whose p.m.r. spectra are characterized4v8-l4by very narrow line widths (as narrow as 4-5 (2) H. M. McConnell and D. B. Chesnut, J . Chem. Phys., 28, 107 ( 1958).
(3) R. E. Richards, Discussions Faraday SOC.,34, 74 (1962). (4) D. R. Eaton, W. D. Phillips, and D. J. Caldwell, J . Am. Chem. Soc., 85, 397 (1963), and references therein. (5) R. H. Holm and I concerned. the p.m.r. line widths led to relaxation times such that essentially Tl < sec. We may thus conclude that Anisotropy in g-Tensor or Hyperfine Interaction in all probability, the possible rates of interconversion This mechanism, first treated by McConnell, inare all too slow to give rise to the "observed" electron relaxation times. This conclusion is c ~ n f i r m e d ~ ~volves l ~ ~ the coupling of the g-tensor or hyperfine anisotropy to the rapid tumbling of the complex in solution. by p.m.r. studies on the Ni(I1) chelates of pyrromethThis mechanism has been shown to determine the elecenes, whose p.m.r. spectra are characterized by resotron relaxation time in several Cu(I1) complexes. 16, l 8 nances of approximately the same width as for the This mechanism would not be expected to produce Tl ATI, SAI, and TAP systems. This system, however, values as short as encountered in the systems of inhas given no evidence23of participating in any diamagterest, unless the anisotropies were very large.16 For netic e paramagnetic equilibrium in solution, so that the Ni(I1) complexes, there is no hyperfine interaction28 this mechanism can be definitely eliminated. Electron due to the low abundance (1.25 %) of 'Ni. It has been spin relaxation through rapid interconversion between convincingly demonstrated4+-14 that the g-tensor the tetrahedral and square-planar forms of these comanisotropies for these Ni complexes are usually negliplexes can therefore be discarded as the dominant so that this mechanism is eliminated for the case gible, mechanism in all the Ni(I1) systems concerned. of Ni. For the Co system, although there exists hyperIt should be pointed out, however, that for the Ni fine interaction, it would not be expected28to be very complexes, this paramagnetic F? diamagnetic equilibanisotropic because the ion possesses a 4A2ground state. rium does lead to p.m.r. line narrowing by averaging These complexes exhibit some g-tensor anisotropy, 1 2 , 1 3 the line widths for the diamagnetic and paramagnetic but it would also be expectedz8to be small, as observed forms. It has been observed that the p.m.r. lines bein other tetrahedral Co(I1) systems,28,29 and thus not come narrower as the equilibrium shifts toward the contribute significantly to the electron relaxation time. diamagnetic form. 4 , 2 The conclusion reached above is that this interconversion does not significantly deterZero Field Splitting mine the line width for the paramagnetic form. The coupling of the splitting of the ground-state spin Interaction with Low-Lying Orbital States multiplet in the absence of an external magnetic field30 with the random tumbling of the complex in solution has Interaction with low-lying orbital states" is expected been demonstrated 16,l9 to dominate the spin relaxation to be weak for ions which have an orbitally nondegenin various Cr(II1) complexes. As indicated before, this erate ground state, such as Co(I1) in a tetrahedral mechanism has been postulatedLgto be dominant for ligand field,I6 with 4A2as ground state, so that this recomplexes with two or more unpaired electrons. The laxation mechanism is in all probability quite ineffectiveness in reducing the relaxation time depends significant in determining Tl in the case of the Co comon the magnitude of this splitting and the tumbling plexes. Ni(I1) in a tetrahedral field has a 3T2ground Bloembergen and Morgan20 time in solution. l6 state, which could yield low-lying orbital levels in the have attributed the ineffectiveness on Ni(I1) in reducing presence of a small low-symmetry distortion. Howthe proton relaxation time in aqueous solution to rapid ever, studies of the absorption spectraz5for TAP comelectron relaxation via the zero splitting mechanism. plexes indicate that the low-symmetry distortions cause The 4A2ground state of tetrahedral Co(I1) cannot be splittings of approximately 3000 cm.-l of the 3T2 split by either spin-orbit coupling or low-symmetry ground state, which is nearly as large a separation to fields, but the combined effects produce3 a splitting the first excited orbital state as for the analogous Co into two doublets (m,= f 1/2 and m, = i3/2) separated c o m p l e ~ e s , where ~ ! ~ ~ 1004 = -4000 cm.-'. Thereby 2 0 , which can be as large as a few cm.-l. Since the fore this mechanism would not be expected to be Co complexes of interest exhibit low-symmetry disdominant for the NiLX, complexes. t o r t i o n ~((22" ~ ! ~for ~ (TAP)2CoX2, CaVfor (TAP)CoX,-), The separation between the split components of the the conditions for relaxation through this mechanism 3T2ground states for the AT1 and SA1 Ni complexes are present. The magnitude of the zero field splitting have not been estimated. The observed magnetic moments for fully paramagnetic AT14 and SAI1orll constant D has not been determined for these complexes, but it has been shown for other distorted tetracomplexes are -3.3 B.M., considerably below the 3.9hedral Co(I1) complexes that fairly large values for D 4.2 B.M. predicted26and usually foundz7 for strictly can be expected, 3 1 having been 0 b s e r v e d ~ ~ - in 3 ~ the tetrahedral Ni(I1) complexes, indicating a fairly large range 1-5 cm.-l. The complex (TAP)CoX3has a TI splitting of the 3T2ground state.6g25 Since the magnetic essentially identical'l with that of (TAP)2CoX2. For moments for the AT1 and SA1 complexes are essenthis axially distorted complex, the spin Hamiltonian tially i d e r ~ t i c a l ~ ~with ' ~ ~ ' 'those observed6 for the TAP will take the form28*32 complexes with Ni, it might be assumed that the lowsymmetry splitting is of a magnitude similar to the X gfiHS AS1 D [ S z z- '/3S(S l)] (2) TAP complexes (-2000-3000 crn.-l). The effect of neglecting the small anisotropies in g and A . The low-lying orbital levels may therefore be eliminated as contribution to TI from the last term in this spin Hamil-
+
(24) D. R. Eaton and E. A. LaLancette, J. Chem. Phys., 41, 3534 (1964). (25) D. M. L. Goodgame and M. Goodgame, Inorg. Chem., 4, 139 (1965). (26) B. N. Figgis, Nature, 182, 1568 (1958). (27) F. A. Cotton and R. Francis, J . A m . Chem. Soc., 82, 2986 (1960); F. A. Cotton and D. M. L. Goodgame, ibid., 82, 5771 (1960); D. M. L. Goodgame and F. A. Cotton, ibid., 82, 5774 (1960).
+
+
(28) J. S. Griffith, "The Theory of Transition-Metal Ions," Cambridge University Press, London, 1961, Chapter 12. (29) H. A. Weakliem, J. Chem. Phys., 36, 2117 (1962). (30) B. N. Figgis, Trans. Faraday SOC.,56, 1553 (1960). (31) I
