The exponents method for calculating equilibrium concentrations of complex species in solution

✍ Scribed by Frederico F. Campos; John S. Rollett

• Publisher: John Wiley and Sons
• Year: 1995
• Tongue: English
• Weight: 820 KB
• Volume: 16
• Category: Article
• ISSN: 0192-8651
• DOI: 10.1002/jcc.540160503

✦ Synopsis

The exponents method for calculating the concentrations of species in multimetal-multiligand systems is introduced. This method uses the Newton-Raphson method with restricted step iteration, which guarantees a monotonically decreasing objective function. Variable transformation and scaling are performed to avoid underflows and overflows during the calculations. A special linear solver using the eigenvalues and eigenvectors of the Jacobian matrix is implemented for overcoming disastrous singularity of this matrix, and the singular value decomposition method is applied for setting the initial guess. In addition, polynomial extrapolation is used for improving the performance when simulating a diagram of concentrations of species. The method was tested with 14 systems of different sizes over the whole pH range and presented robust and efficient behavior. 0 1995 by John Wiley & Sons, Inc. each ligand, and the protonic concentration are known as well as the stability constant for each of the metal-ligand complex reactions, then the problem is to calculate the concentration of metals and ligands in the unbound state. Afterward, the concentrations of the various species of metal-ligand complex can be determined. Conversely, when the equilibrium constants are unknown, they may be found known concentrations using repeated solutions of the forward problem. introduction he calculation of complex species concentra-T tions in large multimetal-multiligand systems in solution has great utility in several areas of chemistry. If the total concentration of each metal,