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The exponents method for calculating equilibrium concentrations of complex species in solution
Author(s) -
Campos Frederico F.,
Rollett John S.
Publication year - 1995
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540160503
Subject(s) - jacobian matrix and determinant , extrapolation , eigenvalues and eigenvectors , scaling , mathematics , polynomial , matrix (chemical analysis) , singularity , singular value decomposition , solver , transformation (genetics) , monotonic function , variable (mathematics) , range (aeronautics) , singular value , discretization , mathematical analysis , mathematical optimization , chemistry , physics , algorithm , materials science , biochemistry , geometry , chromatography , quantum mechanics , composite material , gene
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. © 1995 by John Wiley & Sons, Inc.