Calculation of equilibrium constants from multiwavelength spectroscopic data-I Mathematical considerations.

Multiwavelength spectrophotometric and spectroscopic data in general contain considerably more information about complexation equilibria than potentiometric data do. With the construction of a fully automatic titration set-up built into a high-precision spectrophotometer, the problems related to the wider use of this method have shifted from the quality of the primary data to the complexity of their numerical treatment. Matrix algebra is used to show how these problems can be overcome. An algorithm is described for calculation of stability constants and absorption spectra, together with the associated standard errors, at a reasonable expense of computer time. Problems in finding the minimum in a multidimensional parameter space are reduced by elimination of the molar absorptivities from the algorithm for the iterative refinement. Numerical safety and speed of calculation are improved by use of analytical instead of numerical derivatives. The number of data to be fitted is decreased by principal-component analysis.