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A cluster expansion method for the complete resolution of microscopic ionization equilibria from NMR titrations

The NMR chemical shift of spin 1/2 nuclei in a polyprotic molecule represents a sensitive probe of microscopic protonation equilibria. However, these equilibria are commonly parametrized in terms of microscopic equilibrium constants, whose number increases very rapidly with the number of ionizable groups. For that reason their determination was considered to be basically impossible except for the cases of the simplest molecules. On the basis of a cluster expansion of the free energy of a microstate, we propose a novel parametrization of this problem that drastically reduces the number of necessary parameters needed to specify the microscopic equilibria. Such cluster parameters can be extracted from NMR titration data in a straightforward way. Once these parameters are known, all microscopic equilibrium constants can be obtained.