Microcomputer application of non-linear regression analysis to metal-ligand equilibria.

A non-linear least-squares regression program is described which is suitable for PC-compatible microcomputers. The program is written in GWBASIC, but compiled to run with the Intel 8087 fast numeric processor. Subroutines which simulate functions are compiled separately from the main program. Parameters are optimized by a Gauss-Newton-Marquardt algorithm which can be provided with either analytically or numerically calculated partial derivatives. Multi-component potentiometric titrations are simulated and parameters optimized by using analytical derivatives. Spectrophotometric titrations are also simulated, but absorptivities are optimized by linear regression while stability constants are optimized non-linearly by using numerical derivatives. Provision is made for "global analysis" of parameters. The experimental points can be displayed on screen, along with the "best" fit and the speciation. The program is demonstrated here by the determination of the pK(a) values and stability constants of a hydroxypyridinone ligand and its complexes with Fe(III).