Further relationships between theoretical and experimental models 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.

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.

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%).

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.

Gas-phase chemistry of benzyl cations in dissociation of N-benzylammonium and N-benzyliminium ions studied by mass spectrometry

In this study, the fragmentation reactions of various N-benzylammonium and N-benzyliminium ions were investigated by electrospray ionization mass spectrometry. In general, the dissociation of N-benzylated cations generates benzyl cations easily. Formation of ion/neutral complex intermediates consisting of the benzyl cations and the neutral fragments was observed. The intra-complex reactions included electrophilic aromatic substitution, hydride transfer, electron transfer, proton transfer, and nucleophilic aromatic substitution. These five types of reactions almost covered all the potential reactivities of benzyl cations in chemical reactions. Benzyl cations are well-known as Lewis acid and electrophile in reactions, but the present study showed that the gas-phase reactivities of some suitably ring-substituted benzyl cations were far richer. The 4-methylbenzyl cation was found to react as a Brønsted acid, benzyl cations bearing a strong electron-withdrawing group were found to react as electron acceptors, and para-halogen-substituted benzyl cations could react as substrates for nucleophilic attack at the phenyl ring. The reactions of benzyl cations were also related to the neutral counterparts. For example, in electron transfer reaction, the neutral counterpart should have low ionization energy and in nucleophilic aromatic substitution reaction, the neutral counterpart should be piperazine or analogues. This study provided a panoramic view of the reactions of benzyl cations with neutral N-containing species in the gas phase.

Substituent electrophilicities in the NMR spectra of barbituric derivatives

Comparison of the (1) H and (13)  C NMR spectra of a series of substituted 5-benzylidene-N,N'-dimethylbarbituric acids (1) revealed chemical-shift variations of different centers that correlated with the theoretical electrophilicities or with the substituent electrophilic constant σ(ω) , in an example of the usefulness of these DFT-based indices.