Measuring coupling constants Appendix

Attention should be paid to the possible existence of several complexes having different stoichiometries. A necessary preliminary experiment consists of recording the fluorescence and/or excitation spectra under experimental conditions (nature of the solvent, composition of the medium, ionic strength, pH (if it has an effect on the stability constant), etc.) as close as possible to the medium in which a cation must be detected. The variations in the fluorescence intensity for an appropriate couple of excitation and emission wavelengths (or for several emission or excitation wavelengths) as a function of cation concentration must be analyzed in order to determine the stoichiometry and the stability constant of the complexes (Appendix B). As in the case of pH determination (see Section 10.2.1), ratiometric measurements are recommended. 

The following first section of this appendix describes quantities that are measured when registering spectra obtained using various experimental set-ups and their relations with molecular quantities. These relations form the basis of the interpretations of molecular spectra. The second section describes some general properties of a distribution that are used in various chapters of this book when this distribution is the band of a spectram. The third section deals with such concepts as normal modes in the harmonic approximation, while the fourth section deals with force constants, reduced masses, etc., and offers comparisons of these various quantities. The last section provides a more specific calculation of the first and second moment of a band such as which corresponds to a normal mode characterized by a strong anharmonic coupling with a much slower mode. 

Planck s constant as given in the appendix of Ch. 1, a value of 0.06 A is found for 8Qq. This value is not at all small and emphasizes the important geometrical consequence of the anharmonic modulation of the freqnency of by intermonomer modes (4). It gives a value of 0.017 A for 8Qq -8Qq (eq. (7.1)), a value close to 0.02 A, measured by electron diffraction. It shows that the theoretical description of the anharmonic coupling of and intermonomer modes of H-bonds, presented above, not only quite precisely reproduces spectra, but also reproduces such small geometrical effects, which are measured by completely independent methods. The experimentally verified correlation this theoretical description establishes between IR bandshapes and isotopic length variations 8Qq - 8Q° of H-bonds constitutes a strong snpport of its validity. Values of 8 - 5 can be in principle also measured by X-ray... 

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