Inertial and attractive potential effects on rotation of solitary water molecules in apolar and polar solvents

Deuteron nuclear magnetic resonance spin–lattice relaxation times T1 have been measured for solitary water molecules (D2O) at very low concentrations (8–70 mM) in a series of solvents over a wide range of temperatures; the solvents studied are carbon tetrachloride (10 to 40 °C), benzene (10 to 60 °C), chloroform (−40 to 50 °C), acetonitrile (−40 to 50 °C), and acetone (−40 to 50 °C). The orientational correlation times τ2R for D2O with extremely small moments of inertia (I) in CCl4, C6H6, CHCl3, CH3CN, and (CH3)2CO at 30 °C are, respectively, 96, 224, 230, 625, and 826 fs, which are all by far smaller than the bulk value (2210 fs). The τ2R value is proportional to the proton chemical shift of water in each solvent which is taken as a measure of the strength of solute–solvent interactions in the short range. On the other hand, τ2R is almost inversely proportional to solvent viscosity in disagreement with the simple hydrodynamic friction model. The correlation time (τ*) scaled by the free rotator correlation time √I/kBT is 1.20, 1.01, and 0.89 in CCl4, respectively, at 10, 30, and 40 °C, suggesting a strong inertial effect on the water rotation in the weakly coupled solvent cage. In other solvents, the quantity τ* increases with an increase in the water proton chemical shift, and the larger the τ* value the stronger the temperature dependence. The usefulness of the solvent cage model is illustrated and limitations of primitive models so far often used are discussed.