D. Fiat

Nuclear Magnetic Resonance Studies of Solutions of the Rare‐Earth Ions and Their Complexes. III. Oxygen‐17 and Proton Shifts in Aqueous Solutions and the Nature of Aquo and Mixed Complexes

A nuclear magnetic resonance survey has been undertaken in order to gain a better insight into the nature of the complex species present in aqueous solutions of the rare‐earth ions. Oxygen‐17 and proton chemical shifts of water are reported and the effects of concentration and added anions upon them discussed. Nuclear magnetic resonance evidence is presented, showing that the shifts observed in solutions of the perchlorate salts are due to a single hydrated species persisting over a wide range of concentrations and that no “inner‐sphere” complex is formed with perchlorate. It appears, also, that all the water molecules in the first solvation shell are equivalent with respect to their contribution to the shift, owing to their relatively short residence time. The sign, magnitude, and temperature dependence of the oxygen‐17 shifts as contrasted to those of protons support the suggestion that the former are mainly due to contact interaction, whereas the latter are dominated by dipolar interaction with the unp...

Nuclear Magnetic Resonance Studies of Solutions of the Rare‐Earth Ions and Their Complexes. IV. Concentration and Temperature Dependence of the Oxygen‐17 Transverse Relaxation in Aqueous Solutions

The concentration and temperature dependence of oxygen‐17 linewidths in solutions of rare‐earth perchlorates have been investigated. Empirical models are proposed to account for the observed behavior. An equation relating the apparent relaxation rate to the concentration and to the NMR parameters of the nuclei under conditions of fast chemical exchange has been derived. It was used in the interpretation of the experimental results. Lower limits have been estimated for the rate constants of water exchange between the aquo complexes of Tb3+, Dy3+, Ho3+, Er3+, and Tm3+ and the solvent. These are found to be in the range 0.3–2.6 × 107 sec−1 and to follow the trend of the ionic radii. The upper limit for the activation enthalpy of the exchange process is estimated to be 5 kcal/mole. The upper limits of the electron relaxation times are in the range 2.8–5.0 × 10−13 sec. The temperature dependence of the oxygen‐17 transverse relaxation rates in these systems is discussed in terms of the microdynamic behavior of ...

Magnetic Resonance Studies of Ion Solvation. The Hydration of the Cobaltous Ion

Evidence is presented that cobaltous ion in aqueous solution retains a coordination number of 6 in a temperature range of −10° to +183°C. The temperature dependence of the oxygen‐17 NMR linewidths and chemical shifts of the noncoordinated water were measured. The parameters of water exchange between the first hydration sphere and the bulk were determined and found to be: (τm)27°C=4.2×10−7 sec, ΔH‡=10.4 kcal/mole, ΔS‡=5.3 e.u. The oxygen‐17 hyperfine coupling constant with the unpaired electrons of the cobaltous ion was found to be A/h=—(1.70±0.02)×107 Hz. The relaxation time of the unpaired electrons of the cobaltous ion was calculated and found to be (T1e)183°C=4.6×10−13 sec, assuming T1e=T2e. Earlier observations relevant to those reported here are discussed and, in some cases, reinterpreted.

Effect of chemical exchange on the transverse relaxation rate of nuclei in solution containing paramagnetic ions

Abstract An analysis of the exchange contribution to the transverse relaxation rate of nuclei in bulk solvent molecules, in a dilute solution containing paramagnetic ions, in limiting and intermediate cases, is presented. The conditions under which the absorption mode signal of these nuclei has a Lorentzian line shape are examined in detail. As a result, a constraint on the concentration of the solution under investigation is obtained.

Proton and deuterium magnetic resonance study of the aqueous nickelous complex

The absorption signals of protons and deuterons in bound and nonbound water molecules in the aqueous nickelous system were observed. From the PMR and DMR measurements, the hyperfine coupling constants were calculated and found to be (1.3±0.1)×105 and (2.0±0.2)×104 Hz, respectively. The spin density at the proton (and deuteron) nuclei was calculated to be (2.9±0.3)×10−5 electrons/a.u.3, in accordance with theoretical expectations. The rate constant at 298°K for the exchange of water was found to be 3×104 sec−1, and the activation energy 12 kcal/mole. The relaxation time of the electron at 243°K, assuming T1e =T2e was found to be 1.9×10−12 sec and the activation ernergy 0.8 kcal/mole. The temperature dependence of the proton transverse relaxation rate was studied. It is suggested that in the absence of chemical exchange the transverse relaxation rate is governed both by the relaxation of the nickelous unpaired electrons and by the diffusional motion of the water molecules. Methods of estimating the diffusio...

Orientation dependent spin density matrix of tumbling molecules in thermal equilibrium

The spin state of randomly moving paramagnetic molecules is described by a density matrix ρ(Ω), which is a function of the random molecular coordinate Ω. As a typical example, Ω denotes the orientation of molecules in a liquid. It is shown that in thermal equilibrium ρ(Ω) is equal to a statistical Boltzmann distribution, which is determined by the full Ω‐dependent spin Hamiltonian ℋ(Ω). Thus the effect of the anisotropic part of ℋ(Ω) is not canceled in the case of rapid tumbling. This result is proved using a quantum mechanical description of the lattice, in a way similar to Van Vlecks derivation of the Langevin‐Debye formula for susceptibilities. Based on the same formalism, an extension of the equation of motion of ρ(Ω) (the stochastic Liouville equation) is proposed. The modified equation guarantees the approach of ρ(Ω) to its thermal equilibrium value. The new term in the equation is also discussed in terms of Brownian motion.

Solvation of Co(II) in Methanol and Water Enriched in Oxygen‐17

The solvation sphere of cobaltous ion in oxygen‐17‐enriched methanol and water solutions was observed by oxygen‐17 magnetic resonance. The chemical shift between the coordinated methanol molecules and the bulk methanol and the transverse relaxation times of oxygen‐17 in the two environments were measured in the temperature range of −27.5° to +21°C. The hyperfine coupling constant between the cobaltous ion unpaired electrons and the oxygen‐17 nuclei was found to be temperature independent and its value −(1.70 ± 0.03) × 107 Hz. The relaxation time of the unpaired electrons of the cobaltous ion was calculated and found to be 7 × 10−13 sec at 25°C, assuming T1e = T2e. The dipolar contribution to the relaxation rate of the oxygen‐17 was calculated and found to be about 1% of the hyperfine contribution. The oxygen‐17 chemical shift between the coordinate water molecules and the noncoordinated water molecules and their transverse relaxation times were measured at temperatures of −15°, −10°, and −5°C. The hyperfi...

Hydration of the vanadium (III) ion by oxygen-17 and proton magnetic resonance

Abstract The oxygen-17 and proton magnetic resonance absorption signals of water molecules coordinated to the vanadium (III) ion in aqueous solution have been observed and their temperature dependence studied. The kinetic and thermodynamic parameters of water exchange between the first hydration sphere and the bulk were determined and found to be (τM)25°C = 6.0 × 10−4 sec, ΔH ‡ = 6.2 kcal/mole, ΔS ‡ = −23 e.u. The spin densities at the oxygen and hydrogen nuclei of the coordinated water molecules were found to be −0.0157 and 0.0014 electrons/a.u.3, respectively. This is the first direct determination of negative spin densities in the aquo complexes of the first transition-metal ion series. The temperature dependence of the relaxation time of the unpaired electrons has been obtained. The coordination number was determined and found to be six.

Solvation of the Titanous Ion in Aqueous and Methanol Solutions

The solvation of the titanous ion in aqueous and methanol solutions has been studied by means of proton, deuteron, and oxygen‐17 magnetic resonance. Kinetic parameters for the exchange reaction of the solvent molecules between the coordination sphere and the bulk, hyperfine coupling constants, and relaxation times of the unpaired electron of the titanous ion have been determined. Attempts to interpret the results in view of the uniqueness of the titanous ion among the ions of the first transition‐metal series have also been made.

O−17 Nuclear Magnetic Resonance of Manganese (III) Tris(Acetylacetonate)

The 17O NMR signal of manganese (III) tris(acetylacetonate) was studied in the temperature range 26°—83°. From the temperature dependence of the shift of this signal, a hyperfine interaction constant of 1.88 G is found. This result is used to estimate the covalent character of the σ metal—oxygen bond. An upper limit of 0.077 is found for the mixing coefficient of the oxygen 2s orbitals in the bonding molecular orbitals of the complex. The electron spin transverse relaxation time is estimated from the linewidths of the 1H and 17O resonances to be in the range 10−11 to 10−12 sec.