The hydration state, q, of Dy- and Yb-M8-SPy was determined by measuring the lanthanide induced chemical shift of the free water 17O signal of the two samples, using as a reference (Djanashvili and Peters 2007), and using the equation q = Δ/(<Sz> •F), where Δ = δobs/Pm (δobs is the difference in 17O chemical shifts of the water resonances and Pm is the mole fraction [Ln(III)]/[H2O] = 0.00114). The <Sz> is the reduced value for the average spin polarization [28.591 and 2.591 for Dy and Yb at 333 K, respectively, calculated as in (Pinkerton et al. 1985)], and F ≈ (−2.40 9 104)/T, where F is given in ppm, and T is the absolute temperature. The experiments were conducted in water at 333 K with 19 % H2 17O (Cambridge Isotope Laboratories, Tewkesbury, MA) and 7 % D2O, using 128 scans on a Bruker Avance 600 MHz spectrometer equipped with a room-temperature probe. Chemical shifts were also measured as a function of temperature for both compounds, using 8 scans for each data point with the deuterium providing the lock signal.
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