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ABSTRACT Characterizing complicated solution phase systems in situ requires advanced modeling techniques to capture the intricate balances between the many chemical species. Due to the error inherent in any scientific measurement, a spectrophotometric titration experiment with nickel(II) and ethylenediamine (en) was repeated six times using an autotitrator to test the replicability of the data and the consistency of the resulting thermodynamic model. All six datasets could be modeled very tightly (R² > 99.9999%) with the following eight complexes: [Ni]²⁺, [Ni₂en]⁴⁺, [Nien]²⁺, [Ni₂en₃]⁴⁺, [Nien₂]²⁺, [Ni₂en₅]⁴⁺, [Nien₃]²⁺, and [Nien₆]²⁺. The logK values for the stepwise associative reactions agree with existing literature values for the majority species ([Nien_{n = 1–3}]²⁺) and matched expectations for the minority species; 95% confidence intervals for each logK value were determined via bootstrapping, which quantifies the variability in the binding constant value that is supported by a given dataset. The repeated experiments, which could not be successfully concatenated together, demonstrate that replication is crucial to capturing all the variability in the logK values. Conversely, bootstrapped confidence intervals across multiple experiments can be readily combined to generate an appropriate range for an experimentally determined binding constant. 

Abstract Spacious M₄L₆tetrahedra can act as catalytic inhibitors for base‐mediated reactions. Upon adding only 5 % of a self‐assembled Fe₄L₆cage complex, the conversion of the conjugate addition between ethylcyanoacetate and β‐nitrostyrene catalyzed by proton sponge can be reduced from 83 % after 75 mins at ambient temperature to <1 % under identical conditions. The mechanism of the catalytic inhibition is unusual: the octacationic Fe₄L₆cage increases the acidity of exogenous water in the acetonitrile reaction solvent by favorably binding the conjugate acid of the basic catalyst. The inhibition only occurs for Fe₄L₆hosts with spacious internal cavities: minimal inhibition is seen with smaller tetrahedra or Fe₂L₃helicates. The surprising tendency of the cationic cage to preferentially bind protonated, cationic ammonium guests is quantified via the comprehensive modeling of spectrophotometric titration datasets. 

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. 

Abstract 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. 

Binding studies are ubiquitous in chemistry, but their extensive usefulness is undermined by false positive and false negative results. Centering on the G-protein mini-Gs, we present a thorough study with both simulated and experimental spectrophotometric titration data to diagnose the validity of both binding and non-binding models. Without the use of statistical tests like Bayesian Information Criterion (BIC) and data reconstruction fractions, spurious binding models may go undetected. Furthermore, if the signal change upon binding is too minute, false negatives can also result. Delineating such issues is paramount to effective science. 

This paper portrays the solution-phase dynamics as copper(II) and ethylenediamine explore a multitude of different complexes. The data from five spectrophotometric titrations were globally analysed, evidencing four predominant species ([Cu]2+, [Cu(en-N,N’)]2+, [Cu(en-N,N’)2]2+, [Cu(en-N)4]2+) along with their molar absorptivity curves and associative binding constants. The data also seem to support a fifth species, [Cu2(µ-en-N,N’)]4+, in which ethylenediamine bridges two Cu(II) centres. The thermodynamic stability of all five species is corroborated by ab initio computational calculations. The potential existence of [Cu(en-N)4]2+ highlights the suprachelate effect – going beyond the chelate effect – where multidenticity is overtaken by monodenticity. Such dangling multidentate ligands are available to bind to additional metal centres and thus build towards self-assembling supramolecules. 

Binding constants (K) are foundational to supramolecular chemistry and quantified by modelling spectroscopic (NMR, UV-vis) titration data according to chemical equilibria. Spurred by growth in data science, the tools and methods for determining K values have accelerated in recent years. To share these advances, we provided a Workshop on Quantifying Binding Constants at ISMSC 2023 in Iceland and herein share the objectives, processes, and recommendations. We framed this short course in terms of learning to drive, from the basics ‘under the hood’, to ‘behind the wheel’, and navigating ‘the open road’. These steps are crucial in the ‘drive to K-town’, where participants appreciate the importance of building, analysing, and comparing models. K-town is where they assess the hazards of incomplete models, inaccurate K values, and incorrect uncertainty assessment. We conclude with the Supramolecular Chemist’s Pledge as a starting point for considering quality control in determining K values.