not exceeding 1.1 units. At each p[H] value, the pH-meter
readings were stable in less than 2 min and no more than two
spectral recordings were required.
7
V. Amendola, L. Fabbrizzi, C. Mangano, P. Pallavicini, A. Poggi
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8
9
The multiwavelength data sets were decomposed into their
principal components by factor analysis with the SPECFIT
program.73–75 The protonation constants and the extinction
coefficients corresponding to each species were subsequently
adjusted to the reduced data sets by the Marquardt nonlinear
least-squares algorithm. Furthermore, the data from each
titration were also processed by the program HYPERQUAD
2000, which allows the simultaneous treatment of potentio-
metric and spectrophotometric data.67 While SPECFIT uses
the measured p[H] values to calculate directly the free H3O+
concentration, the mass-balance equations for all components,
including the hydronium ion, are solved at each titration point
by the program HYPERQUAD. Since the precision of spectro-
photometric and potentiometric measurements is different, it is
of prime importance to define a proper weighing scheme
relying on the error propagation rule, which gives to each type
of observation an approximately equal contribution to the
residual sum of squares. Realistic parameter estimates of the
quadratic absorbance error function (sA = a + bA + cA2)
were evaluated by computing, for each recorded wavelength of
50 replicates of the ligand spectrum, the average absorbance
and its associated standard deviation.67,94
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In a jacketed cell maintained at 25.0(1) 1C and held under an
argon atmosphere, a ca. 15 ꢂ 10ꢀ3 M solution of L1 dissolved
in D2O (SDS, D 4 99.90%) was titrated by addition of small
amounts of a ca. 3.7% diluted DCl solution (Aldrich, 37% by
wt, D 4 99.5%) in D2O with a Gilmont micropipette. After
each titrant addition, a ca. 0.5 mL aliquot was taken from the
titration vessel. Apparent p[H] values, noted p[H]*, were
measured with a combined Ag/AgCl glass semimicroelectrode
(Mettler–Toledo) filled with a saturated KCl/AgCl solution in
water and fitted to a PHM240 (Radiometer-Tacussel) pH-
meter. The electrode was calibrated in water in terms of
hydronium ion concentration according to the procedure
described above. The corrected p[D] values were calculated
according to the formula p[D] = p[H]* + 0.4.96 Deuteration
constants were determined by nonlinear least-squares refine-
ment using the Solver routine available in Excel (Microsoft)
and corrected for the isotopic effect according to the correla-
tion found by Delgado et al.: log KD = 0.32 + 1.044 log KH.82
34 J. Springborg, J. Chem. Soc., Dalton Trans., 2003, 1653–1665.
35 J. Springborg, B. Nielsen, C. E. Olsen and I. Sotofte, J. Chem.
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Acknowledgements
36 J. Springborg, B. Nielsen, C. E. Olsen and I. Sotofte, J. Am. Chem.
Soc., 2002, 124, 5084–5090.
37 M. Rodopoulos, T. Rodopoulos, J. N. Bridson, L. I. Elding, S. J.
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38 F. Denat, S. Lacour, S. Brandes and R. Guilard, Tetrahedron
Lett., 1997, 38, 4417–4420.
This work was supported by the Centre National de la
Recherche Scientifique (CNRS) and the Conseil Regional
´
de Bourgogne. L. F. thanks the Ministere de l’Education
Nationale, de la Recherche et de la Technologie for a Ph.D.
scholarship.
39 S. Brandes, F. Denat, S. Lacour, F. Rabiet, F. Barbette,
P. Pullumbi and R. Guilard, Eur. J. Org. Chem., 1998, 2349–2360.
40 F. Denat, S. Brandes and R. Guilard, Synlett, 2000, 561–575.
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