Andreas D. Zuberbühler

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.

Reversible cleavage and formation of the dioxygen O-O bond within a dicopper complex

A key step in dioxygen evolution during photosynthesis is the oxidative generation of the O-O bond from water by a manganese cluster consisting of M2(μ-O)2 units (where M is manganese). The reverse reaction, reductive cleavage of the dioxygen O-O bond, is performed at a variety of dicopper and di-iron active sites in enzymes that catalyze important organic oxidations. Both processes can be envisioned to involve the interconversion of dimetal-dioxygen adducts, M2(O2), and isomers having M2(μ-O)2 cores. The viability of this notion has been demonstrated by the identification of an equilibrium between synthetic complexes having [Cu2(μ-η2:η2-O2)]2+ and [Cu2(μ-O)2]2+ cores through kinetic, spectroscopic, and crystallographic studies.

TITFIT, a comprehensive program for numerical treatment of potentiometric data by using analytical derivatives and automatically optimized subroutines with the Newton—Gauss—Marquardt algorithm

TITFIT, a computer program written in HP-enhanced BASIC is able to fit potentiometric titration curves with up to 400 points by using the Newton-Gauss-Marquardt technique supplemented by the use of analytical derivatives. The program contains a part which writes an optimized subroutine as needed by the model. The program also has additional facilities such as visual interactive adjustment of parameters and a plotting subroutine for graphical presentation of the final results. Data can be entered either manually through the keyboard or automatically through an RS-232 serial interface. The performance of the program is discussed for the well studied Ni(2+) glycine system; the results are similar to those already published in the literature.

Comments on potentiometric pH titrations and the relationship between pH-meter reading and hydrogen ion concentration

Abstract It is emphasized and shown that the concept of pH is more complicated than might be thought (and to some extent also unsatisfactory); there are (at least) three pH scales in general use and it is the aim to make this fact recognized. These scales are: (1) an activity scale, where the hydrogen ion activity is measured based on NBS or similar standards by carefully eliminating the liquid-junction potentials of the electrode system via experimental determinations; (2) a practical scale, which has unintentionally developed by convenience over the past ca. 30 years, is based on now generally available combined glass electrodes together with NBS (or related) buffers used for calibration; and (3) a concentration scale which uses strong acids and/or bases for calibration and defines the pH-meter reading in terms of −log[H + ]. Scale (2) is clearly the one least well defined, yet it is also the one most widely used. If a ‘pH’ is measured for a given constant H + concentration in the three scales, its value decreases in the order (1) > (2) > (3). Scales (1) and (3) may be converted into each other by using the single ion activity coefficient of H + , e.g., at 25°C and at ionic strengths of 0.1 and 0.5 M the differences correspond to 0.11 and 0.15 log unit, respectively. The conversion term from scale (2) to (3) corresponds at 25°C and an ionic strength between 0.1 and 0.5 M to about 0.03 log unit. It is evident that any acidity constant, i.e. p K a value, determined for a given system (HA ⇌| A − + H + ) is affected to the same extent; hence, the mentioned conversion factors have to be applied if P K a values determined in different scales are to be compared or used. It may be added that many workers believe that combined glass electrodes measure the hydrogen ion activity and that they are working in sale (1), yet this is not the case, they are actually working in scale (2). Moreover it is also barely (or not at all) recognized that the values in scale (2) are in fact closer to those of scale (3) and not to those of scale (1), as is often assumed. Some general comments regarding potentiometric pH titrations and the determination of equilibrium constants (i.e., p K a values and stability constants of metal ion complexes) are also made, and the advantages of different titration procedures are discussed and pitfalls are pointed out.

Second-order globalisation for the determination of activation parameters in kinetics

Abstract First order global analysis consists of linking common parameters across series of measurements, e.g., reaction kinetics measured at different wavelengths where the rate constants are the same for all kinetic traces at individual wavelengths. This approach is taken a step further in second order globalisation. A series of measurements is linked together by a new superimposed model which encompasses the individual measurements. The mathematics for the non-linear least-squares fit of the global parameters is presented. Two modes are possible depending on whether the linear parameters (absorption spectra) are constant or changing across the series. Factor analysis is incorporated for multivariate measurements. The procedures are exemplified with applications of activation analysis in chemical kinetics. Global analysis of complete temperature and pressure dependences results directly in the activation parameters of interest, i.e., activation enthalpies, entropies and volumes. Due to a significant decrease in the number of parameters to be fitted, the robustness is considerably improved.

Microprocessor-controlled system for automatic acquisition of potentiometric data and their non-linear least-squares fit in equilibrium studies☆

A microprocessor-controlled potentiometric titration apparatus for equilibrium studies is described. The microprocessor controls the stepwise addition of reagent, monitors the pH until it becomes constant and stores the constant value. The data are recorded on magnetic tape by a cassette recorder with an RS232 input-output interface. A non-linear least-squares program based on Marquardts modification of the Newton-Gauss method is discussed and its performance in the calculation of equilibrium constants is exemplified. An HP 9821 desk-top computer accepts the data from the magnetic tape recorder. In addition to a fully automatic fitting procedure, the program allows manual adjustment of the parameters. Three examples are discussed with regard to performance and reproducibility.

Superoxo, μ-peroxo, and μ-oxo complexes from heme/O2 and heme-Cu/O2 reactivity: Copper ligand influences in cytochrome c oxidase models

The O2-reaction chemistry of 1:1 mixtures of (F8)FeII (1; F8 = tetrakis(2,6-diflurorophenyl)porphyrinate) and [(LMe2N)CuI]+ (2; LMe2N = N,N-bis{2-[2-(N′,N′-4-dimethylamino)pyridyl]ethyl}methylamine) is described, to model aspects of the chemistry occurring in cytochrome c oxidase. Spectroscopic investigations, along with stopped-flow kinetics, reveal that low-temperature oxygenation of 1/2 leads to rapid formation of a heme-superoxo species (F8)FeIII-(O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{2}^{-}}}\end{equation*}\end{document}) (3), whether or not 2 is present. Complex 3 subsequently reacts with 2 to form [(F8)FeIII–(O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{2}^{2-}}}\end{equation*}\end{document})–CuII(LMe2N)]+ (4), which thermally converts to [(F8)FeIII–(O)–CuII(LMe2N)]+ (5), which has an unusually bent (Fe–O–Cu) bond moiety. Tridentate chelation, compared with tetradentate, is shown to dramatically lower the ν(O–O) values observed in 4 and give rise to the novel structural features in 5.

Zwei neue computerprogramme zur bestimmung von komplexbildungskonstanten aus potentiometrischen und spektrophotometrischen messungen

Zusammenfassung VARIAT und SPANA, zwei neue Computerprogramme in FORTRAN V zur Bestimmung von Komplexbildungskonstanten aus potentiometrischen und spektrophotometrischen Messungen, werden beschrieben. Die beiden Programme sind so aufeinander abgestimmt, das die Rechnung mit denselben Unterprogrammen moglich ist. Es werden verschiedene bei dieser Art von Analyse wichtige Punkte diskutiert und VARIAT wird mit anderen schon bekannten Programmen verglichen. Da die Konvergenz zu den richtigen Gleichgewichtskonstanten mit VARIAT besonders gut ist, genugt es, ohne eine graphische Vorbehandlung der Daten, grob geschatzte Anfangswerte fur die Konstanten einzusetzen.

Handling of electronic absorption spectra with a desk top computer—I A fully automatic spectrophotometric titration system with on-line data acquisition

A fully automatic system for combined spectrophotometric and pH titrations with on-line digital data acquisition is described for a Cary 118C spectrophotometer. The system consists of a temperature-controlled titration cell, a motor burette, a digital ph-meter, and an HP9820 desk-top computer. The computer controls the stepwise addition of reagent, the wavelength and paper drives, and the recorder pen; the absorption data and the pH-values are obtained on-line. A special interface was constructed from CMOS components. This is compatible with other computers or microprocessors having the necessary input/output facilities. The performance of the system has been tested critically. In 50 min more than 200 data points, each representing the mean of ten individual readings, can be collected, and the number of data points which can be obtained in one run is practically unlimited. The system avoids the cumbersome and error-prone manual handling of a large amount of data, it saves time, and, most important, the results have a high reproducibility.

Handling of electronic absorption spectra with a desk-top computer—II Calculation of stability constants from spectrophotometric titrations

A fully automatic system for combined spectrophotometric and pH titrations was described in Part I. Its performance in the titration of weak acids and metal complexes is discussed, along with a computer program for numerical treatment of the data, based on Marquardts modification of the Newton-Gauss non-linear least-squares method. The deprotonation of p-nitrophenol at concentrations of 4 x 10(-5) and 4 x 10(-6)M was studied in order to test the sensitivity. Results identical within the reproducibility of the pH-meter were obtained: pK(H) = 7.00 +/- 0.01 and 7.02 +/- 0.01, respectively. Three complexation reactions were studied: (1) the interaction of SCN(-) with the Co(2+) complex of 1,4,8,11-tetramethyl-1,4,8,11-tetra-azacyclotetradecane (TMC); five independent experiments gave pK [CoTMC (SCN)(+) right harpoon over left harpoon CoTMC(2+) + SCN(-)] = 3.099 +/- 0.003: (2) the deprotonation of the Cu(2+) complex of 3,7-diazanonanediamide (DANA); five experiments gave pK (CuDANA(2+) right harpoon over left harpoon CuDANAH(+)(-1) + H(+)) = 7.14 +/- 0.01 and pK (CuDANAH(+)(-1) right harpoon over left harpoon CuDANAH(-2) + H(+)) = 8.38 +/- 0.01: (3) for the reaction of Cu(2+) with 1,3,7-triazacyclodecane (L), data from different ligand: metal ratios had to be combined to obtain pK (CuL(2+) right harpoon over left harpoon Cu(2+) + L) = 16.19 +/- 0.01, pK (CuL(2+)(2) right harpoon over left harpoon CuL(2+) + L) = 10.30 +/- 0.01, and pK (Cu(2)L(2) (OH)(2+)(2) right harpoon over left harpoon 2 CuL(2+) + 2 OH(-)) = 14.58 +/- 0.03. Titration curves with a total change in absorbance of as little as 0.03 units could be analysed satisfactorily, extending considerably the useful range of concentrations for spectrophotometric titrations. In combined spectrophotometric/pH titrations the accuracy of the glass electrode is normally the limiting factor. Other equilibrium constants can easily be reproduced with standard errors of less than 0.01 log unit.