14618
J. Phys. Chem. 1996, 100, 14618-14624
Cobalt-59 Nuclear Magnetic Relaxation Studies of Aqueous Octahedral Cobalt(III) Complexes Christopher W. Kirby, Connie M. Puranda, and William P. Power* Guelph-Waterloo Centre for Graduate Work in Chemistry, Department of Chemistry, UniVersity of Waterloo, Waterloo, Ontario N2L 3G1, Canada ReceiVed: May 16, 1996; In Final Form: June 10, 1996X
Variable-temperature 59Co nuclear magnetic longitudinal relaxation and line width measurements have been performed on dilute aqueous solutions of 12 octahedral cobalt(III) complexes spanning a large range of isotropic chemical shifts (-1-12 570 ppm) at two fields (4.7 and 11.7 T). A variable-concentration 59Co longitudinal relaxation study of Na[Co(ethylenediaminetetraacetate)] was performed, and the results of this study indicated a need for the use of dilute solutions. The quadrupolar mechanism of relaxation was found to be dominant for 59Co nuclei in diamagnetic octahedral complexes in aqueous solution, and values of the quadrupolar coupling constants in all 12 complexes have been determined. At temperatures above 323 K, the spin-rotation relaxation mechanism contributes to the overall rate of relaxation for 59Co in cobalt(III) complexes with high local symmetry or large moments of inertia. Previous claims that the chemical shielding anisotropy mechanism of relaxation is also a major contributor to the total 59Co relaxation in cobalt(III) complexes are apparently unjustified. We believe that the previous incorrect conclusions were due to concentration-dependent relaxation behavior that we and others have recently observed. An approximate absolute chemical shielding scale for cobalt is also presented.
Introduction Cobalt-59 has been a nucleus of interest from the early days of NMR.1 Its high magnetogyric ratio (γ ) 6.3175 × 107 rad T-1 s-1, close to that of 13C)2 and its high natural abundance (100%) make it a sensitive nucleus for NMR studies. Even with its high receptivity, 59Co NMR spectroscopy is difficult owing to its large chemical shift range (over 18 000 ppm)3 and the inherent wide lines of this nucleus. The large chemical shift range, for which no absolute shielding reference exists, results from a variety of factors, the most significant of which is the large value of 〈r-3〉3d for cobalt.4 The wide lines arise from efficient relaxation, which might be expected to occur via the quadrupolar mechanism, since 59Co has a nuclear spin quantum number (I) of 7/2. The relaxation mechanisms of cobalt nuclei have been the topic of several 59Co NMR studies. Ader and Loewenstein5 studied the spin-lattice relaxation times (T1’s) of aqueous Co(CN)63-, Co(NH3)63+, and Co(en)33+ with variation of the counterion, the temperature, the concentration, the solvent, and the field. The dominant relaxation mechanism of the cobalt nucleus in these complexes was found to be the quadrupolar mechanism. It was proposed that the nonzero electric field gradient (efg) necessary for quadrupolar relaxation to occur is produced by ionic association of the cobalt complex with the counterion. A linear relationship between ln(T1) and 1000/T was observed over a broad temperature range for Co(en)33+. This linear relationship was observed to hold below 323 K for Co(CN)63- and Co(NH3)63+. However, at temperatures above 323 K, the relaxation times were less than expected if relaxation were solely quadrupolar in origin. The three suggestions were presented as explanations of this behavior: introduction of spinrotation relaxation at higher temperatures, nonexponential behavior of the rotational correlation times, or temperaturedependent quadrupolar coupling constants. A subsequent multi* Address correspondence to this author. Phone: 519-888-4567, ext. 3626. FAX: 519-746-0435. E-mail:
[email protected]. X Abstract published in AdVance ACS Abstracts, August 1, 1996.
S0022-3654(96)01425-6 CCC: $12.00
nuclear study by Jordan6 of the cobalt hexaammine cation in dimethyl sulfoxide solution provided evidence for the participation of the spin-rotation mechanism only at higher temperature. Other interpretations of the mechanism of cobalt relaxation abound in the literature. Doddrell and co-workers7 completed a room-temperature 59Co T1 study of a series of saturated aqueous solutions for complexes with close to octahedral symmetry. Valiev’s vibrationally induced nuclear spin relaxation model8 was suggested as the origin of unexpectedly efficient 59Co relaxation in symmetric cobalt(III) complexes, where shorter 59Co relaxation times were measured in larger complexes (e.g., Co(tropolonato)3) than in smaller complexes (e.g., Co(acac)3) with the “same” local symmetry (i.e., both of these complexes have six oxygen atoms around the cobalt center). Valiev’s model was treated subsequently with a full theoretical approach for a series of quadrupolar nuclei by Brown and Colpa,9 who pointed out that vibrational excitation was not necessary to create transient electric field gradients at the quadrupolar cobalt nuclei, since static electric field gradients exist in both cobalt complexes studied by Doddrell and co-workers. Osten and Jameson10 calculated relaxation rates for a series of quadrupolar nuclei in tetrahedral environments using the vibrationally induced nuclear spin relaxation model and obtained estimates of the relaxation rates that were orders of magnitude too small compared to experimentally observed relaxation rates. The alternative models of collision-deformation by van der Waals interactions (an “intermolecular” effect) and octopole-induced electric field gradients predicted relaxation rates of the correct order of magnitude. Bryant and co-workers11 have also published a series of papers dealing with relaxation in highly symmetric cobalt complexes. They found that perturbations in the first coordination sphere caused large changes in relaxation rates of the central cobalt nucleus,11d presumably due to changes in the cobalt quadrupolar coupling constant, while the second coordination sphere made little to no contribution to the strength of the quadrupolar interaction.11a Subsequent studies indicated that © 1996 American Chemical Society
Cobalt-59 Relaxation in Octahedral Complexes
J. Phys. Chem., Vol. 100, No. 35, 1996 14619
second sphere coordination induced time-dependent changes in the electric field gradient at the central atom, which was used as a measure of “ion-pairing” in the ionic solutions.11e This ion-pairing effect is similar to the ideas presented by Ader and Loewenstein5 and has been reported most recently in the cobalt relaxation of ∆-[Co(R,R-chxn)3]3+ (chxn ) trans-(1R,2R)-1,2diaminocyclohexane).12 Bryant also concluded that scalar relaxation of the second kind13 from 59Co coupled to 14N in high-symmetry N-bonded cobalt complexes contributes to the spin-spin relaxation (T2) in these complexes.11bc In 1983, Eaton and co-workers published a series of 59Co NMR T2 (Via line width measurements)14 and T1 studies15 of cobalt complexes that varied from high symmetry (e.g., Co(CN)63- with Oh symmetry) to low symmetry (e.g., cisCo(NH3)4CO3+ with C2V symmetry). Complexes with less than Oh symmetry were found to have 59Co relaxation times that decreased with increasing field strength, evidence that chemical shielding anisotropy was contributing to the relaxation of the “low-symmetry” complexes. According to their interpretation, the antisymmetric part of the chemical shielding tensor dominated the relaxation of these complexes because T1 values were found to be less than the corresponding T2 values. These studies have been brought into question recently in a review of the chemical shielding tensor.16 According to symmetry arguments presented by Anet and O’Leary, a molecule with D4h symmetry (e.g., trans-CoX4Y2) must possess an antisymmetric contribution of zero while the symmetric part of the tensor must be large. Therefore, if relaxation was through the chemical shielding anisotropy mechanism of relaxation, one would expect T1 to be greater than T2, in contradiction to the experimental data reported by Eaton. Also, large values of the antisymmetric contributions are required to explain their relaxation data. One possible source of error in several of the studies discussed may be the use of saturated solutions. A recent 59Co relaxation study of Co(acac)3 in acetonitrile, conducted as a function of both temperature and concentration,17 indicated that the Debye expression
τc )
Vη kT
(1)
is valid for the Co(acac)3-acetonitrile system only at concentrations below 80 mM at concentrations greater than 80 mM, there were substantial deviations from behavior as predicted by this expression. This demonstrates the importance of performing relaxation studies using dilute solutions. In (1), η is the solution viscosity, k is Boltzmann’s constant, T is temperature, V is the volume of a complex, and τc is the rotational correlation time. If the concentration of a solution is increased, η (hence τc) increases. In extreme narrowing conditions, τc ∝ T1-1, and the relaxation rate should vary linearly with concentration when this expression is valid. In this study, the 59Co longitudinal relaxation rates and line widths of 12 octahedral cobalt(III) complexes have been measured as a function of both temperature and magnetic field strength. Dilute solutions were used in light of the results of a recent Co(acac)3-acetonitrile study17 as well as variableconcentration 59Co relaxation times of aqueous Na[Co(edta)] (edta ) ethylenediaminetetraacetate) presented in this work. Characterization of spin-rotation relaxation in several complexes permitted an estimate of the absolute chemical shielding scale for cobalt. Theory Nuclear spin relaxation describes the rate at which the nuclear spin system approaches equilibrium parallel to (longitudinal or
“spin-lattice” relaxation rate, T1-1) and perpendicular to (transverse or “spin-spin” relaxation rate, T2-1) the applied magnetic field direction. For relaxation to occur, a local magnetic field must be present fluctuating at rates comparable to the Larmor frequency. These fluctuations are described in terms of the spectral density, J(ωo),18
J(ωo) )
2τc
(2)
1 + ωo2τc2
where ωo is the angular Larmor frequency. The temperature dependence of nuclear spin relaxation is normally defined completely by the spectral density terms through the dependence of correlation time (τc) on temperature. However, this does not preclude an additional temperature dependence of the fluctuating local field. The relaxation mechanisms pertinent for octahedral cobalt(III) complexes in solution have been suggested to be the quadrupolar mechanism (Q) as well as other relaxation mechanisms as described in the Introduction including the chemical shielding anisotropy (CSA) and the spin-rotation (SR) mechanisms of relaxation. The relaxation rates for Q, CSA, and SR under extreme narrowing conditions (ωo2τ2 , 1) can be described as19
T1Q-1 )
( )( {
2 3π2 e q33Q 10 h
T1CSA-1 ) γ2Bo2
2
1+
)( (
) )}
ηQ2 2I + 3 τ 3 I2(2I - 1) 2 2
ηCS 2 a2 2 τ (σ ) τ1 + (∆σs)2 1 + 3 15 3 2
T1SR-1 )
2 kT 3p
τJτl )
2
θjcij2τJj ∑ i,j)x,y,z θj
l(l + 1)kT
T1Total-1 ) ∑T1λ-1
(3)
(4)
(5)
(6) (7)
λ
where eQ is the nuclear quadrupole moment, eq33 is the unique component of the efg tensor (a second rank tensor), ηQ is the asymmetry of the efg tensor [ηQ ) (eq11 - eq22)/(eq33)], I is the nuclear spin quantum number, and τl is the time over which fluctuations of first or second (l ) 1 or 2) rank tensors occur (commonly referred to as the correlation time). For CSA relaxation, σa is the antisymmetric part of the chemical shielding (CS) tensor, ∆σs is the anisotropy of the symmetric part of the CS tensor (a second-rank tensor) [∆σs ) σ33 - 1/2(σ11 + σ22)], and ηCS is the asymmetry of the CS tensor [ηCS ) (σ11 - σ22)/ (σ33 - σiso)]. Under spin-rotation, θj is the moment of inertia tensor, cij are the direction cosines of the SR tensor in the principal axis system of θj, and τJ is the angular momentum correlation time. In (7), λ denotes the different relaxation mechanisms (e.g., Q, CSA, SR); the sum of the individual rates results in the total relaxation rate for a nucleus. The expressions for T2 are similar to those for T1 with the addition of a zero-frequency spectral density term J(0) for all mechanisms except SR.19 The longitudinal (T1) and transverse (T2) relaxation time constants are equal for most mechanisms of relaxation under extreme narrowing conditions. Two exceptions to this arise: when a relaxation mechanism, such as scalar relaxation of the second kind, contributes to transverse relaxation with little to no influence on the longitudinal relaxation; when
14620 J. Phys. Chem., Vol. 100, No. 35, 1996
Kirby et al.
TABLE 1: Summary of the 59Co NMR Data Acquired at 294 K (Ambient Temperature) and 11.7 Ti compound
δiso (ppm)
concentration (mM)
synthesis
∆ν1/2 (Hz)
T2*
T1
K3[Co(CN)6] [Co(NH3)6]Cl3 [Co(NH3)5(NO2)]Cl2 Co(acac)3 [Co(sepulchrate)]Cl3 trans-[Co(NH3)4(NO2)2]NO3 cis-[Co(NH3)4(NO2)2]NO3 fac-Co(CN)3(NH3)3 [Co(NH3)5CO3]NO3‚1/2H2O cis-[Co(NH3)4CO3]NO3 [Co(NH3)5Cl]Cl2 Na[Co(edta)]
-1 8076 7565 12570 6931 7157 7227 3289 9053 9662 8793 10237
32.5 42.6 43.7
