Mathematical optimization in the determination of the dissociation constants of a tribasic organic acid by 13C NMR spectroscopy.
The calculation of dissociation constants from the chemical shifts of (13)C NMR spectra leads to a complicated non-linear equation. Two different mathematical methods for solution of this equation have been chosen--an iterative step method and a matrix pseudo-inversion method. When the iteration method is used the initial guesses for the parameters, the initial value of the step size and the escalation of the iteration must be optimized. For comparison the matrix pseudo-inversion method was used because it gives a unique result. With the optimized step method the results were as accurate or even better than those obtained with the matrix method. Although it takes time to optimize the system, the step method is the more suitable method of solving the problem. The matrix inversion can be done only with a computer with 13 significant digits and exponent capacity larger than +/- 38.
Salonen
A M
AM
Department of Chemistry and Biochemistry, university of Turku, SF-20500 Turku, Finland.