On the influence of dynamical effects on reactivity descriptors

A redefinition of global conceptual density functional theory reactivity indexes by means of the cubic expansions of the energy

In the present work, a new definition of the conceptual density functional theory reactivity indexes is proposed, based on a cubic interpolation of the energy as function of number of electrons as well as a generalization of the net electrophilicity index. This new proposal takes into account both the influence of hyperhardness on the reactivity and a weighted average of the electrodonating and electroacepting powers. Thus, the presented redefinition incorporates corrections and additional degrees of freedom to the prior CDFT indexes. Numerical support for global descriptors is presented for 30 benzhydrylium ions (i.e., charged electrophiles) and 15 alkyl and aryl nucleophiles taken as reference cases from the Mayr Database of Reactivity Parameters. In the best-case scenario, the descriptors correlated better with the electrophilicity parameter (r2 = 0.981) than with the nucleophilicity parameter (r2 = 0.827).

Revisiting nucleophilicity: an index for chemical reactivity from a CDFT approach

CONTEXT

Understanding and predicting the nucleophilic reactivity are paramount in elucidating organic chemical reactions and designing new synthetic pathways. In this study, we propose a nucleophilicity index within the framework of Conceptual Density Functional Theory (CDFT). Through rigorous theoretical formulations, we introduce an original quantum reactivity descriptor that captures the nucleophilic propensity of molecules based on their electronic structure and chemical environment. Subsequently, this proposed index is applied to a series of nucleophiles (pyrrolidines derivatives), spanning a diverse range of chemical functionalities. Our computational assessments reveal insightful correlations between the predicted nucleophilicity index and experimental observations of nucleophilic behavior. Thereby, they offer a promising avenue for advancing the understanding of organic reactivity and guiding synthetic efforts.

METHODS

Experimentally, Mayr's experimental parameters accounting for nucleophilicity were selected for the pyrrolidines. This study used DFT calculations at the B3LYP/Aug-cc-pVTZ level of theory using the Gaussian 16 program. Geometry optimization was thus performed, and the methodology employed for the computation of quantum reactivity descriptor is presented. Solvent effect was also taken into account using IEFPCM, and empirical dispersion correction (GD3) was employed.

Aza-Michael Addition in Explicit Solvent: A Relative Energy Gradient-Interacting Quantum Atoms Study

Aza-Michael additions are key reactions in organic synthesis. We investigate, from a theoretical and computational point of view, several examples ranging from weak to strong electrophiles in dimethylsulfoxide treated as explicit solvent. We use the REG-IQA method, which is a quantum topological energy decomposition (Interacting Quantum Atoms, IQA) coupled to a chemical-interpretation calculator (Relative Energy Gradient, REG). We focus on the rate-limiting addition step in order to unravel the different events taking place in this step, and understand the influence of solvent on the reaction, with an eye on predicting the Mayr electrophilicity. For the first time, a link is established between an REG-IQA analysis and experimental values.

The computational road to reactivity scales

Reactivity scales are useful research tools for chemists, both experimental and computational. However, to determine the reactivity of a single molecule, multiple measurements need to be carried out, which is a time-consuming and resource-intensive task. In this Tutorial Review, we present alternative approaches for the efficient generation of quantitative structure-reactivity relationships that are based on quantum chemistry, supervised learning, and uncertainty quantification. First published in 2002, we observe a tendency for these relationships to become not only more predictive but also more interpretable over time.

ElectroPredictor: An Application to Predict Mayr's Electrophilicity E through Implementation of an Ensemble Model Based on Machine Learning Algorithms

Electrophilicity (E) is one of the most important parameters to understand the reactivity of an organic molecule. Although the theoretical electrophilicity index (ω) has been associated with E in a small homologous series, the use of w to predict E in a structurally heterogeneous set of compounds is not a trivial task. In this study, a robust ensemble model is created using Mayr's database of reactivity parameters. A combination of topological and quantum mechanical descriptors and different machine learning algorithms are employed for the model's development. The predictability of the model is assessed using different statistical parameters, and its validation is examined, including a training/test partition, an applicability domain, and a y-scrambling test. The global ensemble model presents a Q5-fold2 of 0.909 and a Qext2 of 0.912, demonstrating an excellent predictability performance of E values and showing that w is not a good descriptor for the prediction of E, especially for the case of neutral compounds. ElectroPredictor, a noncommercial Python application (https://github.com/mmoreno1/ElectroPredictor), is developed to predict E. QM9, a well-known large dataset containing 133885 neutral molecules, is used to perform a virtual screening (94.0% coverage). Finally, the 10 most electrophilic molecules are analyzed as possible new Mayr's electrophiles, which have not yet been experimentally tested. This study confirms the necessity to build an ensemble model using nonlinear machine learning algorithms, topographic descriptors, and separating molecules into charged and neutral compounds to predict E with precision.

Uncertainty Quantification of Reactivity Scales

According to Mayr, polar organic synthesis can be rationalized by a simple empirical relationship linking bimolecular rate constants to as few as three reactivity parameters. Here, we propose an extension to Mayr's reactivity method that is rooted in uncertainty quantification and transforms the reactivity parameters into probability distributions. Through uncertainty propagation, these distributions can be transformed into uncertainty estimates for bimolecular rate constants. Chemists can exploit these virtual error bars to enhance synthesis planning and to decrease the ambiguity of conclusions drawn from experimental data. We demonstrate the above at the example of the reference data set released by Mayr and co-workers [J. Am. Chem. Soc. 2001, 123, 9500; J. Am. Chem. Soc. 2012, 134, 13902]. As by-product of the new approach, we obtain revised reactivity parameters for 36 π-nucleophiles and 32 benzhydrylium ions.

A statistical thermodynamics view of electron density polarisation: application to chemical selectivity

A fundamental link between conceptual density functional theory and statistical thermodynamics is herein drawn, showing that intermolecular electrostatic interactions can be understood in terms of effective work and heat exchange. From a more detailed analysis of the heat exchange in a perturbation theory framework, an associated entropy can be subsequently derived, which appears to be a suitable descriptor for the local polarisability of the electron density. A general rule of thumb is evidenced: the more the perturbation can be spread, both through space and among the excited states, the larger the heat exchange and entropy.

Atom-Condensed Fukui Function in Condensed Phases and Biological Systems and Its Application to Enzymatic Fixation of Carbon Dioxide

Local reactivity descriptors such as atom-condensed Fukui functions are promising computational tools to study chemical reactivity at specific sites within a molecule. Their applications have been mainly focused on isolated molecules in their most stable conformation without considering the effects of the surroundings. Here we propose to combine quantum mechanics/molecular mechanics Born-Oppenheimer molecular dynamics simulations to obtain the microstates (configurations) of a molecular system using different representations of the molecular environment and calculate Boltzmann-weighted atom-condensed local reactivity descriptors based on conceptual density functional theory. Our approach takes the conformational fluctuations of the molecular system and the polarization of its electron density by the environment into account, allowing us to analyze the effect of the molecular environment on reactivity. In this contribution, we apply the method mentioned above to the catalytic fixation of carbon dioxide by crotonyl-CoA carboxylase/reductase and study if the enzyme alters the reactivity of its substrate compared with an aqueous solution. Our main result is that the protein environment activates the substrate by the elimination of solute-solvent hydrogen bonds from aqueous solution in the two elementary steps of the reaction mechanism: the nucleophilic attack of a hydride anion from NADPH on the α,β-unsaturated thioester and the electrophilic attack of carbon dioxide on the formed enolate species.