The molar absorptivity curves for [NiLn(MeOH)6-n]2+ L = pyridine, 3-methylpyridine, 4-methylpyridine, n = 1 – 4, have been simultaneously deduced by modeling composite absorbance data of a series of equilibrium solutions in dry methanol using equilibrium-restricted factor analysis, a technique for obtaining spectral and thermodynamic information for component species involved in solution equilibria. Furthermore, the stepwise formation constants at 296 K have been determined with a high degree of accuracy. For pyridine, logK1-4 = 1.272(6), 0.669(9), 0.14(2), -0.32(2), respectively. For 3-methylpyridine, logK1-4 = 1.802(9), 1.16 (1), 0.32(1), -0.46(1), respectively. For 4-methylpyridine, logK1-4 = 2.808(9), 1.114(4), 0.411(4), -0.421(9), respectively. Unrestricted factor analysis was used to confirm the precise number of unique complexes in each case. The only additional complex for which some evidence was found was the pentakis version of the pyridine complex.
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Properly handling negative values in the calculation of binding constants by physicochemical modeling of spectroscopic titration data
To implement equilibrium hard‐modeling of spectroscopic titration data, the analyst must make a variety of crucial data processing choices that address negative absorbance and molar absorptivity values. The efficacy of three such methodological options is evaluated via high‐throughput Monte Carlo simulations, root‐mean‐square error surface mapping, and two mathematical theorems. Accuracy of the calculated binding constant values constitutes the key figure of merit used to compare different data analysis approaches. First, using singular value decomposition to filter the raw absorbance data prior to modeling often reduces the number of negative values involved but has little effect on the calculated binding constant despite its ability to address spectrometer noise. Second, both truncation of negative molar absorptivity values and the fast nonnegative least squares algorithms are superior to unconstrained regression because they avoid local minima; however, they introduce bias into the calculated binding constants in the presence of negative baseline offsets. Finally, we establish two theorems showing that negative values are best addressed when all the chemical solutions leading to the raw absorbance data are the result of mixing exactly two distinct stock solutions. This allows the raw absorbance data to be shifted up, eliminating negative baseline offsets, without affecting the concentration matrix, residual matrix, or calculated binding constants. Otherwise, the data cannot be safely upshifted. A comprehensive protocol for analyzing experimental absorbance datasets with is included.
more » « less- NSF-PAR ID:
- 10459182
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Journal of Chemometrics
- Volume:
- 33
- Issue:
- 11
- ISSN:
- 0886-9383
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Computation of binding constants from spectrophotometric titration data is a very popular application of chemometric hard modeling. However, the calculated values are misleading if the correct binding model is not used. Given that many supramolecular systems of interest feature unknown speciation, a priori determination of binding stoichiometry constitutes an important unsolved problem in chemometrics. We present a new and reliable algorithm for accomplishing this task, implemented using a hybrid particle swarm optimization technique. Simultaneous optimization of stoichiometry ratios and binding constants allows the optimal binding model to be calculated in just a few minutes for systems with up to four reactions. Simulated data studies demonstrate that the algorithm finds the correct stoichiometry with up to nine reactions in the absence of noise, including accurately determining species with unusual stoichiometry, such as H2G5. Application to four experimental datasets shows the algorithm is robust to experimental errors for a variety of chemical systems and binding models. This algorithm will facilitate the discovery of complex binding models, increase efficiency in titration analysis, and avert incorrect stoichiometry models, thereby improving the reliability of binding constant information in spectrophotometric titrations.
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