Table Of ContentComputational
Methods for the
Determination of
Formation Constants
MODERN INORGANIC CHEMISTRY
Series Editor: John P. Fackler, Jr.
Texas A&M University
METAL INTERACTIONS WITH BORON CLUSTERS
Edited by Russell N. Grimes
HOMOGENEOUS CATALYSIS
WITH METAL PHOSPHINE COMPLEXES
Edited by Louis H. Pignolet
THE JAHN-TELLER EFFECT AND
VIBRONIC INTERACTIONS IN MODERN CHEMISTRY
I. B. Bersuker
MOSSBAUER SPECTROSCOPY
APPLIED TO INORGANIC CHEMISTRY, Volume 1
Edited by Gary J. Long
CARBON-FUNCTIONAL ORGANOSILICON COMPOUNDS
Edited by Vaclav Chvalovsky and Jon M. Bellama
COMPUTATIONAL METHODS FOR THE DETERMINATION
OF FORMATION CONSTANTS
Edited by David J. Leggett
A Continuation Order Plan is available for this series. A continuation order will bring
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Computational
Methods for the
Determination of
Formation Constants
Edited by
DAVID J. LEGGETT
Dow Chemical USA
Texas Division
Freeport, Texas
Plenum Press • New York and London
Library of Congress Cataloging in Publication Data
Main entry under title:
Computational methods for the determination of formation constants.
(Modem inorganic chemistry)
Bibliography: p.
Includes index.
1. Phase rule and equilibrium-Data processing. I. Leggett, David J. II. Series.
QD503.C66 1985 541.3'63'0285 85-16991
ISBN-13: 978-1-4684-4936-5 e-ISBN-13: 978-1-4684-4934-1
001: 10.1007/978-1-4684-4934-1
©1985 Plenum Press, New York
Softcover reprint of the hardcover 1st edition 1985
A Division of Plenum Publishing Corporation
233 Spring Street, New York, N.Y. 10013
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording, or otherwise, without written permission from the Publisher
TO
M. J. S. L.
S. R. L.
K. E. L.
Contributors
Alex Avdeef • Syracuse University, Department of Chemistry, Syracuse, New York
13210
Josef Havel • Department of Analytical Chemistry, J. E. Purkyne University,
Kotlarska 2, 611 37 Brno, Czechoslovak~ll
David J. Leggett • Dow Chemical USA, Texas Pivision, Freeport, Texas 77541
Peter M. May • Department of Applied Chemistry, University of Wales, Institute
of Science and Technology, Cardiff CFt ~NU, United Kingdom
Milan Meloun • Department of Analytical Chemistry, University of Chemical
Technology, Leninovo nam. 565, 532 10 Pardubice, Czechoslovakia
I. Nagypal • Computer Center, Institute of Inorganic and Analytical Chemistry,
Lajos Kossuth University, H-401O, Debrecen, Hungary
D. D. Perrin • Medical Chemistry Group, The John Curtin School of Medical
Research, The Australian National University, P.O. Box 334, Canberra City,
A.C.T., 2601, Australia .
Antonio Sabatini • Dipartimento di Chimica dell' Universita di Firenze and
LS.S.E.C.C. - CNR, Florence, Italy
H. Stunzi • Universite de Neuchatel, Institut de Chimj~, Avenue de Bellevaux 51,
CH-2000 Neuchatel, Switzerland
Alberto Vacca • Dipartimento di Chimica dell' Universita di Firenze and
LS.S.E.C.C. - CNR, Florence, Italy
David R. Williams • Department of Applied Chemistry, University of Wales, In
stitute of Science and Technology, Cardiff CFt 3NU, United Kingdom
L. Zekany • Computer Center, Institute of Inorganic and Analytical Chemistry,
Lajos Kossuth University, H-4010, Debrecen, Hungary
vii
Preface
This volume is concerned with methods that are available for the calculation of for
mation constants, in particular computational procedures. Although graphical meth
ods have considerable value in the exploration of primary (raw) data they have been
overtaken by computational methods, which, for the most part, take primary data and
return the refined formation constants. Graphical methods are now considered com
plementary to these general computational procedures.
This volume brings together programs that span the lifetime of computer-assisted
determination of formation constants. On one hand the reader will find listings of
programs that are derived from LETAGROP (b.l961) and the GAUSS-G/SCOGS
(b. 1962) families. On the other hand programs are presented that are the newest mem
bers of the SCOGS lineage and from the on-going MINIQUAD series. One program
is presented that describes a computational approach to the classical Hedstrom
Osterberg methods; another that takes care of electrode calibration in a simple yet
rigorous manner.
Potentiometry and spectrophotometry are the most popular experimental tech
niques for equilibrium studies, and the programs in this volume reflect this. Four
programs handle potentiometric data, two will process spectrophotometric data, and
one makes use of both types of data separately or in combination.
This collection of programs also represents a collection of well-tested numerical
algorithms for the general problem of data fitting. As such the volume will have value
to users not necessarily devoted to full-time solution eqUilibrium studies. Each pro
gram employs a different, and in several instances novel, method for data input.
Every effort has been made to ensure that the codings are accurate. Of course,
each program has been run on the author's computer. More importantly the programs
have also been tested on a Honeywell 66/60 and on a Vax 111780, under the FORTRAN
66 compiler. The input data, supplied by each author and used to test the programs,
have been included. Minor changes were made to some of the· programs to work
around local features of the original machines. The program listings were printed out
using a daisy-wheel printer after being down-loaded from the Vax 111780 to a Dec
Mate word processor. The listings, so produced, clearly distinguish between a zero
and upper case "oh"; D and "oh" are also obviously different.
I would like to take this opportunity to acknowledge the patience and forebear-
ix
x PREFACE
ance of a number of people in what has turned out to be a longer than expected time
to produce the volume: the contributors to'this volume; Plenum as publishers; my
wife.
It would be remiss of me not to acknowledge the positive guidance of Professor
W.A.E. (Pete) McBryde during my graduate student days; but for him none of this
would have been possible.
David 1. Leggett
Contents
1
The Determination of Formation Constants:
An Overview of Computational Methods
for Data Processing
DAVID J. LEGGETT
1. Introduction .......................................................................... 1
2. Direct Search and Univariate Methods ...... .................................... 2
2.1. Grid, Star, and Composite Designs....................................... 2
2.2. Fibonacci and Golden Section............................................. 3
2.3. Hooke and Jeeves, Simplex .................. ......... ..................... 3
2.4. Quadratic and Cubic Interpolation Methods............................. 3
2.5. Summary ..................................................................... 4
3. Least-Squares Methods......................... .................................... 5
3.1. Newton-Raphson ............................................................ 5
3.2. Gauss-Newton................................................. .............. 7
3.3. Levenberg and Marquardt ......... ................ ......................... 10
3.4. Objective Function Differentiation......................... ............... 11
4. Other Methods.............................................. ......................... 11
4.1. Curve Fitting................................................................. 11
4.2. HOSK Method............................................................... 12
5. Summary ...................................................................... ....... 13
6. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2
Strategies for Solution Equilibria Studies with
Specific Reference to Spectrophotometry
JOSEF HAVEL and MILAN MELOUN
1. Elucidation ofthe Equilibrium Model ............................................ 19
1.1. Introduction .. " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.2. Experimental Techniques .................................... .............. 21
xi
