Intrinsic Relative Scales of Electrophilicity and Nucleophilicity

One-Bond-Nucleophilicity and -Electrophilicity Parameters: An Efficient Ordering System for 1,3-Dipolar Cycloadditions

Diazoalkanes are ambiphilic 1,3-dipoles that undergo fast Huisgen cycloadditions with both electron-rich and electron-poor dipolarophiles but react slowly with alkenes of low polarity. Frontier molecular orbital (FMO) theory considering the 3-center-4-electron π-system of the propargyl fragment of diazoalkanes is commonly applied to rationalize these reactivity trends. However, we recently found that a change in the mechanism from cycloadditions to azo couplings takes place due to the existence of a previously overlooked lower-lying unoccupied molecular orbital. We now propose an alternative approach to analyze 1,3-dipolar cycloaddition reactions, which relies on the linear free energy relationship lg k₂(20 °C) = s_N(N + E) (eq 1) with two solvent-dependent parameters (N, s_N) to characterize nucleophiles and one parameter (E) for electrophiles. Rate constants for the cycloadditions of diazoalkanes with dipolarophiles were measured and compared with those calculated for the formation of zwitterions by eq 1. The difference between experimental and predicted Gibbs energies of activation is interpreted as the energy of concert, i.e., the stabilization of the transition states by the concerted formation of two new bonds. By linking the plot of lg k₂ vs N for nucleophilic dipolarophiles with that of lg k₂ vs E for electrophilic dipolarophiles, one obtains V-shaped plots which provide absolute rate constants for the stepwise reactions on the borderlines. These plots furthermore predict relative reactivities of dipolarophiles in concerted, highly asynchronous cycloadditions more precisely than the classical correlations of rate constants with FMO energies or ionization potentials. DFT calculations using the SMD solvent model confirm these interpretations.

A machine learning approach for predicting the nucleophilicity of organic molecules

Nucleophilicity provides important information about the chemical reactivity of organic molecules. Experimental determination of the nucleophilicity parameter is a tedious and resource-intensive approach. Herein, we present a novel machine learning protocol that uses key structural descriptors to predict the nucleophilicities of organic molecules, which agree well with the experimental values. A data driven approach was used where quantum mechanical molecular and thermodynamic descriptors from a wide range of structurally diverse nucleophiles and relevant solvents were extracted and modelled using advanced algorithms against the experimentally available nucleophilicity values. Despite the structural diversity of nucleophiles, we are able to achieve statistically robust models with a high predictive power using tree-based and neural network algorithms trained on an in-house developed unique dataset consisting of 752 nucleophilicity values and 27 molecular descriptors.

Nucleophilicity Prediction via Multivariate Linear Regression Analysis

The concept of nucleophilicity is at the basis of most transformations in chemistry. Understanding and predicting the relative reactivity of different nucleophiles is therefore of paramount importance. Mayr’s nucleophilicity scale likely represents the most complete collection of reactivity data, which currently includes over 1200 nucleophiles. Several attempts have been made to theoretically predict Mayr’s nucleophilicity parameters N based on calculation of molecular properties, but a general model accounting for different classes of nucleophiles could not be obtained so far. We herein show that multivariate linear regression analysis is a suitable tool for obtaining a simple model predicting N for virtually any class of nucleophiles in different solvents for a set of 341 data points. The key descriptors of the model were found to account for the proton affinity, solvation energies, and sterics.

Machine Learning Methods to Predict Density Functional Theory B3LYP Energies of HOMO and LUMO Orbitals

Machine learning algorithms were explored for the fast estimation of HOMO and LUMO orbital energies calculated by DFT B3LYP, on the basis of molecular descriptors exclusively based on connectivity. The whole project involved the retrieval and generation of molecular structures, quantum chemical calculations for a database with >111 000 structures, development of new molecular descriptors, and training/validation of machine learning models. Several machine learning algorithms were screened, and an applicability domain was defined based on Euclidean distances to the training set. Random forest models predicted an external test set of 9989 compounds achieving mean absolute error (MAE) up to 0.15 and 0.16 eV for the HOMO and LUMO orbitals, respectively. The impact of the quantum chemical calculation protocol was assessed with a subset of compounds. Inclusion of the orbital energy calculated by PM7 as an additional descriptor significantly improved the quality of estimations (reducing the MAE in >30%).

A quantitative approach to polar organic reactivity

A method is presented which allows one to predict toxic effects which are triggered by the formation of covalent bonds between electron-deficient (electrophilic) compounds and biological electron-rich (nucleophilic) targets, as proteins or nucleic acids. It is based on our comprehensive nucleophilicity and electrophilicity scales, which we constructed as an aid for the planning of organic syntheses. For the construction of these scales, rate constants for the reactions of benzhydrylium ions (aryl2CH(+)) and structurally related quinone methides with nucleophiles have been measured and correlated by the equation lg k(20 °C) = sN(E + N), which yields absolute rate constants k (L mol(-1) s(-1)) from one parameter for electrophiles (the electrophilicity E) and two for nucleophiles (the nucleophilicity parameter N and the susceptibility sN). A freely accessible database (http://www.cup.uni-muenchen.de/oc/mayr/DBintro.html) is described, which presently comprises data for 1000 nucleophiles and 260 electrophiles and provides links to the original literature reports. The kinetic scales are complemented by a thermodynamic counterpart, which enables one to calculate association constants K (L mol(-1)) of electrophiles with nucleophiles from the empirical Lewis acidity parameters LA and Lewis basicity parameters LB by the equation lg K (20°C) = LA + LB.

Understanding the Highly Varying pKa of Arylamines. A Perspective from the Average Local Ionization Condensed-to-Atom Framework

The highly varying experimental pKa values for 36 arylamines spanning 7 orders of magnitude is carefully examined. Within this framework, a valence condensed-to-atom model for the average ionization energy is introduced and tested. The theoretical approach is connected to orbital Fukui functions directly mapped into semilocal or regional site-specific responses. It is revealed that the average local ionization energies associated with the amino nitrogen atom is linearly correlated to the basicity of the substituted arylamines, properly reproducing the experimental ordering of basicity. The condensed-to-atom descriptor exhibits a high predictive power, providing a new direct reactivity evaluation of significant value.

Scales of Lewis basicities toward C-centered Lewis acids (carbocations)

Equilibria for the reactions of benzhydryl cations (Ar2CH(+)) with phosphines, tert-amines, pyridines, and related Lewis bases were determined photometrically in CH2Cl2 and CH3CN solution at 20 °C. The measured equilibrium constants can be expressed by the sum of two parameters, defined as the Lewis Acidity (LA) of the benzhydrylium ions and the Lewis basicity (LB) of the phosphines, pyridines, etc. Least-squares minimization of log K = LA + LB with the definition LA = 0 for (4-MeOC6H4)2CH(+) gave a Lewis acidity scale for 18 benzhydrylium ions covering 18 orders of magnitude in CH2Cl2 as well as Lewis basicities (with respect to C-centered Lewis acids) for 56 bases. The Lewis acidities correlated linearly with the quantum chemically calculated (B3LYP/6-311++G(3df,2pd)//B3LYP/6-31G(d,p) level) methyl anion affinities of the corresponding benzhydrylium ions, which can be used as reference compounds for characterizing a wide variety of Lewis bases. The equilibrium measurements were complemented by isothermal titration calorimetry studies. Rates of SN1 solvolyses of benzhydryl chlorides, bromides, and tosylates derived from E(13-33)(+), i.e., from highly reactive carbocations, correlate excellently with the corresponding Lewis acidities and the quantum chemically calculated methyl anion affinities. This correlation does not hold for solvolyses of derivatives of the better stabilized amino-substituted benzhydrylium ions E(1-12)(+). In contrast, the correlation between electrophilic reactivities and Lewis acidities (or methyl anion affinities) is linear for all donor-substituted benzhydrylium ions E(1-21)(+), while the acceptor-substituted benzhydrylium ions E(26-33)(+) react more slowly than expected from their thermodynamic stabilities. The boundaries of linear rate-equilibrium relationships were thus defined.

Reactivity of polychlorinated biphenyls in nucleophilic and electrophilic substitutions

To explain the chemical reactivity of polychlorinated biphenyls in nucleophilic (S(N)) and electrophilic (S(E)) substitutions, quantum chemical calculations were carried out at the B3LYP/6-31G(d) level of the Density Functional Theory in gas phase. Carbon atomic charges in biphenyl structure were calculated by the Atoms-in-Molecules method. Chemical hardness and global electrophilicity index parameters were determined for congeners. A comparison of calculated descriptors and experimental data for congener reactivity in the S(N) and S(E) reactions was made. It is shown that interactions in the S(N) mechanism are reactions of the hard acid-hard base type, these are the most effective in case of highly chlorinated substrates. To explain the congener reactivity in the SE reactions, correct descriptors were not established. The obtained results can be used to carry out chemical transformations of the polychlorinated biphenyls in order to prepare them for microbiological destruction or preservation.