A comparison between theoretical and experimental models of electrophilicity and nucleophilicity

Exploring the electronic structure of knotted proteins: the case of two ornithine transcarbamylase family

CONTEXT

Geometrical knots are rare structural arrangements in proteins in which the polypeptide chain ties itself into a knot, which is very intriguing due to the uncertainty of their impact on the protein properties. Presently, classical molecular dynamics is the most employed technique in the few studies found on this topic, so any information on how the presence of knots affects the reactivity and electronic properties of proteins is even scarcer. Using the electronic structure methods and quantum chemical descriptors analysis, we found that the same amino-acid residues in the knot core have statistically larger values for the unknotted protein, for both hard-hard and soft-soft interaction descriptors. In addition, we present a computationally feasible protocol, where we show it is possible to separate the contribution of the geometrical knot to the reactivity and other electronic structure properties.

METHODS

In order to investigate these systems, we used PRIMoRDiA, a new software developed by our research group, to explore the electronic structure of biological macromolecules. We evaluated several local quantum chemical descriptors to unveil relevant patterns potentially originating from the presence of the geometrical knot in two proteins, belonging to the ornithine transcarbamylase family. We compared several sampled structures from these two enzymes that are highly similar in both tertiary structure and function, but one of them has a knot whereas the other does not. The sampling was carried out through molecular dynamics simulations using ff14SB force field along 50 ns, and the semiempirical convergence was performed with PM7 Hamiltonian.

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.

Secondary Amine Catalysis in Enzyme Design: Broadening Protein Template Diversity through Genetic Code Expansion

Secondary amines, due to their reactivity, can transform protein templates into catalytically active entities, accelerating the development of artificial enzymes. However, existing methods, predominantly reliant on modified ligands or N-terminal prolines, impose significant limitations on template selection. In this study, genetic code expansion was used to break this boundary, enabling secondary amines to be incorporated into alternative proteins and positions of choice. Pyrrolysine analogues carrying different secondary amines could be incorporated into superfolder green fluorescent protein (sfGFP), multidrug-binding LmrR and nucleotide-binding dihydrofolate reductase (DHFR). Notably, the analogue containing a D-proline moiety demonstrated both proteolytic stability and catalytic activity, conferring LmrR and DHFR with the desired transfer hydrogenation activity. While the LmrR variants were confined to the biomimetic 1-benzyl-1,4-dihydronicotinamide (BNAH) as the hydride source, the optimal DHFR variant favorably used the pro-R hydride from NADPH for stereoselective reactions (e.r. up to 92 : 8), highlighting that a switch of protein template could broaden the nucleophile option for catalysis. Owing to the cofactor compatibility, the DHFR-based secondary amine catalysis could be integrated into an enzymatic recycling scheme. This established method shows substantial potential in enzyme design, applicable from studies on enzyme evolution to the development of new biocatalysts.

What defines electrophilicity in carbonyl compounds

The origin of the electrophilicity of a series of cyclohexanones and benzaldehydes is investigated using the activation strain model and quantitative Kohn-Sham molecular orbital (MO) theory. We find that this electrophilicity is mainly determined by the electrostatic attractions between the carbonyl compound and the nucleophile (cyanide) along the entire reaction coordinate. Donor-acceptor frontier molecular orbital interactions, on which the current rationale behind electrophilicity trends is based, appear to have little or no significant influence on the reactivity of these carbonyl compounds.

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.

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.

Bond Energies of Enamines

Energetics of reactive intermediates underlies their reactivity. The availability of these data provides a rational basis for understanding and predicting a chemical reaction. We reported here a comprehensive computational study on the energetics of enamine intermediates that are fundamental in carbonyl chemistry. Accurate density functional theory (DFT) calculations were performed to determine the bond energies of enamines and their derived radical intermediates. These efforts led to the compilation of a database of enamine energetics including a thermodynamic index such as free-energy stability, bond dissociation energy (BDE), and acid dissociation constant (pK _a) as well as a kinetic index such as nucleophilicity and electrophilicity. These data were validated by relating to experimentally determined parameters and their relevance and utility were discussed in the context of modern enamine catalysis. It was found that pK _a values of enamine radical cations correlated well with redox potentials of their parent enamines, the former could be used to rationalize the proton-transfer behavior of enamine radical cations. An analysis of the BDE of enamine radical cations indicated that these species underwent facile β-C-H hydrogen transfer, in line with the known oxidative enamine catalysis. The enamine energetics offers the possibility of a systematic evaluation of the reactivities of enamines and related radicals, which would provide useful guidance in exploring new enamine transformations.

Influence of solvent mixture on nucleophilicity parameters: the case of pyrrolidine in methanol-acetonitrile

The course of organic chemical reactions is efficiently modelled through the concepts of “electrophiles” and “nucleophiles” (meaning electron-seeking and nucleus-seeking reactive species). On the one hand, an advanced approach of the correlation of the nucleophilicity parameters N and electrophilicity E has been delivered from the linear free energy relationship log k (20 °C) = s(N + E). On the other hand, the general influence of the solvent mixtures, which are very often employed in preparative synthetic chemistry, has been poorly explored theoretically and experimentally, to date. Herein, we combined experimental and theoretical studies of the solvent influence on pyrrolidine nucleophilicity. We determined the nucleophilicity parameters N and s of pyrrolidine at 20 °C in CH₃OH/CH₃CN mixtures containing 0, 20, 40, 60, 80 and 100% CH₃CN by kinetic investigations of their nucleophilic substitution reactions to a series of 2-methoxy-3-X-5-nitrothiophenes 1a–e (X = NO₂, CN, COCH₃, CO₂CH₃, CONH₂). Depending on the resulting solvation medium, the N parameters range from 15.72 to 18.32 on the empirical nucleophilicity scale of Mayr. The nucleophilicity parameters N first evolve linearly with the content of acetonitrile up to 60% CH₃CN by volume, but is non linear for higher amounts. We designed a general computation protocol to investigate the solvent effect at the atomistic scale. The nucleophilicity in solvent mixtures was evaluated by combining classical molecular dynamic (MD) simulations of solvated pyrrolidine and a few density functional theory (DFT) calculations of Parr nucleophilicity. The pyrrolidine theoretical nucleophilicity 1/ω obtained in various CH₃OH/CH₃CN mixtures are in excellent agreement with Mayr's nucleophilicity (N) parameters measured. Analyses of the molecular dynamic trajectories reveal that the decrease of the nucleophilicity in methanol rich mixtures arises predominantly from the solvation of the pyrrolidine by methanol molecules through strong hydrogen bonds. Last, we proposed a simple model to predict and accurately reproduce the experimentally obtained nucleophilicity values.

Combined experiments and modelling rationalize the large influence of solvent composition on pyrrolidine nucleophilicity.

Kinetics and Mechanism of Oxirane Formation by Darzens Condensation of Ketones: Quantification of the Electrophilicities of Ketones

The kinetics of epoxide formation by Darzens condensation of aliphatic ketones 1 with arylsulfonyl-substituted chloromethyl anions 2 (ArSO₂CHCl^-) have been determined photometrically in DMSO solution at 20 °C. The reactions proceed via nucleophilic attack of the carbanions at the carbonyl group to give intermediate halohydrin anions 4, which subsequently cyclize with formation of the oxiranes 3. Protonation of the reaction mixture obtained in THF solution at low temperature allowed the intermediates to be trapped and the corresponding halohydrins 4-H to be isolated. Crossover experiments, i.e., deprotonation of the halohydrins 4-H in the presence of a trapping reagent for the regenerated arylsulfonyl-substituted chloromethyl anions 2, provided the relative rates of backward ( k_-CC) and ring closure ( k_rc) reactions of the intermediates. Combination of the kinetic data ( k₂^exptl) with the splitting ratio ( k_-CC/ k_rc) gave the second-order rate constants k_CC for the attack of the carbanions 2 at the ketones 1. These k_CC values and the previously reported reactivity parameters N and s_N for the arylsulfonyl-substituted chloromethyl anions 2 allowed us to use the linear free energy relationship log k₂(20 °C) = s_N( N + E) for deriving the electrophilicity parameters E of the ketones 1 and thus predict potential nucleophilic reaction partners. Density functional theory calculations of the intrinsic reaction pathways showed that the reactions of the ketones 1 with the chloromethyl anions 2 yield two rotational isomers of the intermediate halohydrin anions 4, only one of which can cyclize while the other undergoes retroaddition because the barrier for rotation is higher than that for reversal to the reactants 1 and 2. The electrophilicity parameters E correlate moderately with the lowest unoccupied molecular orbital energies of the carbonyl groups, very poorly with Parr's electrophilicity indices, and best with the methyl anion affinities calculated for DMSO solution.

Do dihydroxymagnesium carboxylates form Grignard-type reagents? A theoretical investigation on decarboxylative fragmentation

Dihydroxymagnesium carboxylates [(OH)₂MgO₂CR] were probed for decarboxylation on a theoretical level, by utilizing both Møller-Plesset perturbation theory (MP2) and density functional theory (B3LYP-DFT) computations. This study is connected to the question of whether this recently introduced, astrobiologically relevant chemical class may form Grignard-type reagent molecules. To extract trends for a broad molecular mass range, different linear alkyl chain lengths between C₄ and C₁₁ were computed. The forward energy barrier for decarboxylation reactions increases linearly as a function of the ligand's chain length. Decarboxylation-type fragmentations of these organomagnesium compounds seem to be improbable in non-catalytic, low energetic environments. A high forward energy barrier (E_MP2 > 55 kcal mol^-1) towards a described transition state restricts the release of CO₂. Nevertheless, we propose the release of CO₂ on a theoretical level, as been revealed via an intramolecular nucleophilic attack mechanism. Once the challenging transition state for decarboxylation is overcome, a stable Mg-C bond is formed. These mechanistic insights were gained by help of natural bond orbital analysis. The Cα atom (first carbon atom in the ligand chain attached to the carboxyl group) is thought to prefer binding towards the electrophilic magnesium coordination center, rather than towards the electrophilic CO₂-carbon atom. Additionally, the putatively formed Grignard-type OH-bearing product molecules possess a more polarized Mg-C bond in comparison to RMgCl species. Therefore, carbanion formation from OH-bearing Grignard-type molecules is made feasible for triggering C-C bond formation reactions. Graphical abstract This study asks whether recently introduced, astrobiologically dihydroxymagnesium carboxylates form Grignard-type reagent molecules via decarboxylative fragmentation.

Quantification and Theoretical Analysis of the Electrophilicities of Michael Acceptors

In order to quantify the electrophilic reactivities of common Michael acceptors, we measured the kinetics of the reactions of monoacceptor-substituted ethylenes (H₂C═CH-Acc, 1) and styrenes (PhCH═CH-Acc, 2) with pyridinium ylides 3, sulfonium ylide 4, and sulfonyl-substituted chloromethyl anion 5. Substitution of the 57 measured second-order rate constants (log k) and the previously reported nucleophile-specific parameters N and s_N for 3-5 into the correlation log k = s_N(E + N) allowed us to calculate 15 new empirical electrophilicity parameters E for Michael acceptors 1 and 2. The use of the same parameters s_N, N, and E for these different types of reactions shows that all reactions proceed via a common rate-determining step, the nucleophilic attack of 3-5 at the Michael acceptors with formation of acyclic intermediates, which subsequently cyclize to give tetrahydroindolizines (stepwise 1,3-dipolar cycloadditions with 3) and cyclopropanes (with 4 and 5), respectively. The electrophilicity parameters E thus determined can be used to calculate the rates of the reactions of Michael acceptors 1 and 2 with any nucleophile of known N and s_N. DFT calculations were performed to confirm the suggested reaction mechanisms and to elucidate the origin of the electrophilic reactivities. While electrophilicities E correlate poorly with the LUMO energies and with Parr's electrophilicity index ω, good correlations were found between the experimentally observed electrophilic reactivities of 44 Michael acceptors and their calculated methyl anion affinities, particularly when solvation by dimethyl sulfoxide was taken into account by applying the SMD continuum solvation model. Because of the large structural variety of Michael acceptors considered for these correlations, which cover a reactivity range of 17 orders of magnitude, we consider the calculation of methyl anion affinities to be the method of choice for a rapid estimate of electrophilic reactivities.

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%).

Revisiting the Dielectric Constant Effect on the Nucleophile and Leaving Group of Prototypical Backside SN2 Reactions: A Reaction Force and Atomic Contribution Analysis

The solvent effect on the nucleophile and leaving group atoms of the prototypical F^- + CH₃Cl → CH₃F + Cl^- backside bimolecular nucleophilic substitution reaction (S_N2) is analyzed employing the reaction force and the atomic contributions methods on the intrinsic reaction coordinate (IRC). Solvent effects were accounted for using the polarizable continuum solvent model. Calculations were performed employing 11 dielectric constants, ε, ranging from 1.0 to 78.5, to cover a wide spectrum of solvents. The reaction force data reveal that the solvent mainly influences the region of the IRC preceding the energy barrier, where the structural rearrangement to reach the transition state occurs. A detailed analysis of the atomic role in the reaction as a function of ε reveals that the nucleophile and the carbon atom are the ones that contribute the most to the energy barrier. In addition, we investigated the effect of the choice of nucleophile and leaving group on the ΔE₀ and ΔE^‡ of Y^- + CH₃X → YCH₃ + X^- (X, Y = F, Cl, Br, I) in aqueous solution. Our analysis allowed us to find relationships between the atomic contributions to the activation energy and leaving group ability and nucleophilicity.

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.

HETEROATOM EFFECTS ON THE TRIAFLUAVENE AND HEAVIER ANALOGUES, XC5H4AND XC5H3(X =C,Si,Ge,N,P, ANDAs): DFT CALCULATIONS

DFT calculations were carried out on molecular structure of triafluavenes and their heavier analogues, X C5H4and X C5H3; 1Xand 2X(X = C , Si , Ge , N , P , and As ); by using B3LYP/6-311++G** and MP2/6-311++G** //B3LYP/6-311++G** levels of theory with the Gaussian 03 program. The thermal energies (E), enthalpies (H), and free Gibbs energies (G) of 1Xand 2Xwere calculated. The geometrical parameters, natural bonding orbital charge at atoms HOMO and LUMO, the chemical hardness (η), chemical potential (μ), electrophilicity (ω), and the maximum amount of electronic charge, ΔNmax, were obtained. The NICS calculations were preformed for both rings of 1Xas well as 2Xdue to determination of the aromatic character of each rings. Molecular electrostatic potential maps were plotted and the infrared and ultraviolet spectra were calculated for 1Xand 2X.