Relationships between carbocation stabilities and electrophilic reactivity parameters, E: quantum mechanical studies of benzhydryl cation structures and stabilities

Illuminating the multiple Lewis acidity of triaryl-boranes via atropisomeric dative adducts

Using the principle that constrained conformational spaces can generate novel and hidden molecular properties, we challenged the commonly held perception that a single-centered Lewis acid reacting with a single-centered Lewis base always forms a single Lewis adduct. Accordingly, the emergence of single-centered but multiple Lewis acidity among sterically hindered and non-symmetric triaryl-boranes is reported. These Lewis acids feature several diastereotopic faces providing multiple binding sites at the same Lewis acid center in the interaction with Lewis bases giving rise to adducts with diastereomeric structures. We demonstrate that with a proper choice of the base, atropisomeric adduct species can be formed that interconvert via the dissociative mechanism rather than conformational isomerism. The existence of this exotic and peculiar molecular phenomenon was experimentally confirmed by the formation of atropisomeric piperidine-borane adducts using state-of-the-art NMR techniques in combination with computational methods.

Electrophile-Arene Affinity: An Energy Scale for Evaluating the Thermodynamics of Electrophilic Dearomatization Reactions

Rational design and development of organic reactions are lofty goals in synthetic chemistry. Quantitative description of the properties of molecules and reactions by physical organic parameters plays an important role in this regard. In this Article, we report an energy scale, namely, electrophile-arene affinity (EAA), for evaluating the thermodynamics of electrophilic dearomatization reactions, a class of important transformations that can rapidly build up molecular complexity and structural diversity by converting planar aromatic compounds into three-dimensional cyclic molecules. The acquisition of EAA data can be readily achieved by theoretically calculating the enthalpy changes (ΔH) of the hypothetical reactions of various (cationic) electrophiles with aromatic systems (taking the 1-methylnaphthalen-2-olate ion as an example in this study). Linear correlations are found between the calculated ΔH values and established physical organic parameters such as the percentage of buried volume %VBur (steric effect), Hammett's σ or Brown's σ+ (electronic effect), and Mayr's E (reaction kinetics). Careful analysis of the ΔH values leads to the rational design of a dearomative alkynylation reaction using alkynyl hypervalent iodonium reagents as the electrophiles.

Methide Affinity Scale: Key Thermodynamic Data Underpinning Catalysis, Organic Synthesis, and Organometallic and Polymer Chemistry

Methide transfer reactions play important roles in many areas of chemistry, including the Grignard reaction, in the transmetalation steps of metal-catalyzed cross-coupling reactions, and in the generation of cationic metal polymerization catalysts. Methide affinities (MAs) are the key thermodynamic quantity that underpin such reactions, and yet comprehensive methide affinity scales are poorly developed. Here, B3LYP-D3BJ/def2-TZVP calculations are used to calculate the energy changes (MAs) for cations (MeZ → Z+ + Me-), neutrals (MeY- → Y + Me-), and anions (MeX2- → X- + Me-) derived from permethyl species of all group s and p elements. The MAs range from 2525.8 for the singlet cation F+ to -820.4 kJ/mol for the tetramethylborate anion, Me4B-. The cations show the clearest trends: the MAs in all cases decrease going down the group, while moving across a period, the MAs increase from group 1 to group 2 and then decrease for group 3, remaining about the same or with a modest increase moving to group 4, and then continue to increase across a period to a maximum for the halogens (group 17). The anions and dianions are sensitive to hypervalency; those elements that cannot expand the octet have very unfavorable MAs (e.g., MA of Me4C requires the formation of Me5C- and of Me4B- requires the formation of Me5B2-). To address whether the anion MeY- and dianion MeZ2- are stable, the vertical detachment energies of the anions and dianions were calculated. All of the anions are thermodynamically stable with respect to electron loss, except for Me4N-, while the dianions are all thermodynamically unstable with respect to electron loss. The kinetic stability of the dianions with respect to methide and electron loss was also evaluated for the lowest MAs. The only dianions that might be kinetically stable and observable in the gas phase are Me4Ca2-, Me4Sr2-, and Me4Ba2-. The dianion CF3CaF32- is predicted to be both thermodynamically and kinetically stable in the gas phase.

Electrophilicity index revisited

This review aims to be a comprehensive, authoritative, critical, and accessible review of general interest to the chemistry community; because the electrophilicity index is a very useful global reactivity descriptor defined within a conceptual density functional theory framework. Our group has also introduced electrophilicity based new global and local reactivity descriptors and also new associated electronic structure principles, which are important indicators of structure, stability, bonding, reactivity, interactions, and dynamics in a wide variety of physico-chemical systems and processes. This index along with its local counterpart augmented by the associated electronic structure principles could properly explain molecular vibrations, internal rotations and various types of chemical reactions. The concept of the electrophilicity index has been extended to dynamical processes, excited states, confined environment, spin-dependent and temperature-dependent situations, biological activity, site selectivity, aromaticity, charge removal and acceptance, presence of external perturbation through solvents, external electric and magnetic fields, and so forth. Although electrophilicity and its local variant can adequately interpret the behavior of a wide variety of systems and different physico-chemical processes involving them, their predictive potential remains to be explored. An exhaustive review on all these aspects will set the tone of the future research in that direction.

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.

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.

4b-Aryltetrahydroindeno[1,2-a]indenes by Acid-Catalyzed Trans­annular Cyclization of Benzannulated Cyclooctene Alcohols

By starting from two simple building blocks, benzannulated cyclooctenones were obtained in three steps. Subsequent Grignard/aryl lithium addition to the ketone yielded the corresponding tertiary alcohols that underwent stereoselective acid-catalyzed transannular cyclization to provide a cis-fused 5/5 bicyclic indanylindane framework exclusively. Subsequent stereoselective nucleophilic addition to the indanyl cation by hydride, water, or electron-rich aromatics furnished the 4b-aryltetrahydroindano[1,2-a]indenes in good to excellent yields (up to 92%) in the trans-C9–C9a form in up to a >99:1 diastereomeric ratio.

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.

Quantum Mechanics and Machine Learning Synergies: Graph Attention Neural Networks to Predict Chemical Reactivity

There is a lack of scalable quantitative measures of reactivity that cover the full range of functional groups in organic chemistry, ranging from highly unreactive C-C bonds to highly reactive naked ions. Measuring reactivity experimentally is costly and time-consuming, and no single method has sufficient dynamic range to cover the astronomical size of chemical reactivity space. In previous quantum chemistry studies, we have introduced Methyl Cation Affinities (MCA*) and Methyl Anion Affinities (MAA*), using a solvation model, as quantitative measures of reactivity for organic functional groups over the broadest range. Although MCA* and MAA* offer good estimates of reactivity parameters, their calculation through Density Functional Theory (DFT) simulations is time-consuming. To circumvent this problem, we first use DFT to calculate MCA* and MAA* for more than 2,400 organic molecules thereby establishing a large data set of chemical reactivity scores. We then design deep learning methods to predict the reactivity of molecular structures and train them using this curated data set in combination with different representations of molecular structures. Using 10-fold cross-validation, we show that graph attention neural networks applied to a relational model of molecular structures produce the most accurate estimates of reactivity, achieving over 91% test accuracy for predicting the MCA* ± 3.0 or MAA* ± 3.0, over 50 orders of magnitude. Finally, we demonstrate the application of these reactivity scores to two tasks: (1) chemical reaction prediction and (2) combinatorial generation of reaction mechanisms. The curated data sets of MCA* and MAA* scores is available through the ChemDB chemoinformatics web portal at cdb.ics.uci.edu under Chemical Reactivities data sets.

Nucleophilicities and Nucleofugalities of Thio- and Selenoethers

Rate constants for the reactions of dialkyl chalcogenides with laser flash photolytically generated benzhydrylium ions have been measured photometrically to integrate them into the comprehensive benzhydrylium‐based nucleophilicity scale. Combining these rate constants with the previously reported equilibrium constants for the same reactions provided the corresponding Marcus intrinsic barriers and made it possible to quantify the leaving group abilities (nucleofugalities) of dialkyl sulfides and dimethyl selenide. Due to the low intrinsic barriers, dialkyl chalcogenides are fairly strong nucleophiles (comparable to pyridine and N‐methylimidazole) as well as good nucleofuges; this makes them useful group‐transfer reagents.

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.

Methyl Anion Affinities of the Canonical Organic Functional Groups

Calculated methyl anion affinities are known to correlate with experimentally determined Mayr E parameters for individual organic functional group classes but not between neutral and cationic organic electrophiles. We demonstrate that methyl anion affinities calculated with a solvation model (MAA*) give a linear correlation with Mayr E parameters for a broad range of functional groups. Methyl anion affinities (MAA*), plotted on the log scale of Mayr E, provide insights into the full range of electrophilicity of organic functional groups. On the Mayr E scale, the electrophilicity toward the methyl anion spans 180 orders of magnitude.

Carbon Atom as an Extremely Strong Nucleophilic and Electrophilic Center: Dendritic Allenes Are Powerful Organic Proton and Hydride Sponges

Gas-phase proton affinities (PAs) and hydride affinities (HAs) of organic bases possessing an allene moiety and substituted with methyl, dimethylamino, cyano, and vinyl substituents were examined with the B3LYP/6-311+G(2df,p)//B3LYP/6-31G(d) model. It was shown that a number of superbases and hyperbases can be obtained, as well as the potent hydride sponges. Methyl or dimethylamino substituents increased the proton affinity of the parent molecule, and the cyano substituents increased its hydride affinity. When the vinyl substituents are placed on allene, both the hydride and the proton affinities increased. A disubstituted allene with two dimethylamino groups is the smallest studied superbase, whereas the allene tetrasubstituted with four vinyl groups gives the smallest superbase possessing only alkene substituents. By introducing the vinyl group as a repeating subunit, one can obtain dendritic structures with the investigated substituents determining its properties. By changing the dimethylamino with the cyano group, a dendrimeric molecule can change from a hyperbase with a proton affinity of 324.6 kcal mol^-1 to a very strong hydride ion acceptor with a hydride affinity of 205.4 kcal mol^-1, while possessing the same proton or hydride ion attachment site.

How the Arrangement of Alkyl Substituents Affects the Stability of Delocalized Carbocations

G-4 calculations are used to explore which carbon atoms of methylated butadienes, methylated cyclopentadienes, and methylated benzenes are most readily protonated to yield delocalized allyl and pentadienyl cations. While it is not surprising that alkylation of the positions bearing formal positive charge stabilizes these cations, several other effects are less obvious. First, alkylation of positions in the delocalized cation that do not bear formal charge is beneficial, to an extent about a quarter to a third as great as at charged positions. Second, alkylation of the position receiving the proton disfavors protonation. Finally, at least in the acyclic systems, the more symmetrical substitution pattern that is 2° at both ends is moderately preferred to the less symmetrical pattern that is 3° at one end and 1° at the other. Taking all three of these factors into account, as well as substitution at the formally charged centers, models the stability of all 94 delocalized cations quite well.

Computational study of vicarious nucleophilic substitution reactions

Vicarious nucleophilic substitution reactions are a versatile way of introducing substituents into aromatic and heteroaromatic electron-deficient compounds. In this project, a kinetic study of these reactions by applying quantum mechanics concepts, such as reaction force, force constant, and electronic reaction flow was proposed. Furthermore, absolute theoretical scales of electrophilicity by applying density functional theory electronic indices were established to classify a series of five and six-membered nitroheteroarenes, and nitrobenzenes with substituents in ortho, meta and para positions. The theoretical model was validated by comparison with experimental kinetic results. Calculations using B3LYP/6-311G(d,p) level of theory allowed analysis of the reactivity patterns and the mechanisms of these chemical reactions. The theoretical scale properly accounts for the activating/deactivating effects promoted by the substituents and agrees with the ability of these substituents to accept or donate electrons, electron acceptor substituents are those that increase electrophilicity, and electron donors those that reduce it.

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.

Solvolytic Behavior of Aryl and Alkyl Carbonates. Impact of the Intrinsic Barrier on Relative Reactivities of Leaving Groups

The effect of negative hyperconjugation on the solvolytic behavior of carbonate diesters has been investigated kinetically by applying the LFER equation log k = s_f(E_f + N_f). The observation that carbonate diesters solvolyze faster than the corresponding carboxylates and that the enhancement of aromatic carbonates is more pronounced indicates that the negative hyperconjugation and π-resonance within the carboxylate moiety is operative in TS. The plots of ΔG^‡ vs approximated Δ_rG° for solvolysis of benzhydryl aryl/alkyl carbonates and benzhydryl carboxylates reveal that a given carbonate solvolyzes over the higher Marcus intrinsic barrier and over the earlier transition state than carboxylate that produces an anion of similar stability. Due to the lag in development of the electronic effects along the reaction coordinate, the impact of the intrinsic barrier on solvolytic behavior of carbonates is more important than in the case of carboxylates and phenolates. Consequently, the solvolytic reaction constants (s_f) are generally lower for carbonates than for carboxylates. Because of considerable lower reaction constants of carbonates, an inversion of relative reactivities between aryl/alkyl carbonate and another leaving group of similar nucleofugality (N_f) may occur if the electrofuge moiety of a substrate is switched.

Philicities, Fugalities, and Equilibrium Constants

The mechanistic model of Organic Chemistry is based on relationships between rate and equilibrium constants. Thus, strong bases are generally considered to be good nucleophiles and poor nucleofuges. Exceptions to this rule have long been known, and the ability of iodide ions to catalyze nucleophilic substitutions, because they are good nucleophiles as well as good nucleofuges, is just a prominent example for exceptions from the general rule. In a reaction series, the Leffler-Hammond parameter α = δΔG(⧧)/δΔG° describes the fraction of the change in the Gibbs energy of reaction, which is reflected in the change of the Gibbs energy of activation. It has long been considered as a measure for the position of the transition state; thus, an α value close to 0 was associated with an early transition state, while an α value close to 1 was considered to be indicative of a late transition state. Bordwell's observation in 1969 that substituent variation in phenylnitromethanes has a larger effect on the rates of deprotonation than on the corresponding equilibrium constants (nitroalkane anomaly) triggered the breakdown of this interpretation. In the past, most systematic investigations of the relationships between rates and equilibria of organic reactions have dealt with proton transfer reactions, because only for few other reaction series complementary kinetic and thermodynamic data have been available. In this Account we report on a more general investigation of the relationships between Lewis basicities, nucleophilicities, and nucleofugalities as well as between Lewis acidities, electrophilicities, and electrofugalities. Definitions of these terms are summarized, and it is suggested to replace the hybrid terms "kinetic basicity" and "kinetic acidity" by "protophilicity" and "protofugality", respectively; in this way, the terms "acidity" and "basicity" are exclusively assigned to thermodynamic properties, while "philicity" and "fugality" refer to kinetics. Benzhydrylium ions (diarylcarbenium ions) with para- and meta-substituents are used as reference compounds for these investigations, because their Lewis acidities and electrophilicities can be varied by many orders of magnitude, while the steric surroundings of the reaction centers are kept constant. The rate constants for their reactions with nucleophiles correlate linearly over a wide range with the Lewis acidities of the benzhydrylium ions: from slow reactions with late transition states to very fast reactions with early, reactant-like transition states (including reactions which proceed without an enthalpic barrier, ΔH(⧧) = 0). Thus, unequivocal evidence is obtained that even within a series of closely related reactions, the Leffler-Hammond α cannot be a measure for the position of the transition state. Differences in intrinsic barriers lead to deviations from the linear rate-equilibrium correlations and give rise to counterintuitive phenomena. Thus, 1,4-diazabicyclo[2.2.2]octane (DABCO) reacts with lower intrinsic barriers than 4-(dimethylamino)pyridine (DMAP) and, therefore, is a stronger nucleophile as well as a better nucleofuge than DMAP. Common synthetically used SN2 reactions are presented, in which weak nucleophiles replace stronger ones. Whereas solvolysis rates of alkoxy- and alkyl-substituted benzhydryl derivatives correlate linearly with the Lewis acidities of the resulting carbenium ions, this is not the case for amino-substituted benzhydrylium ions, where differences in intrinsic barriers play a major role. The common rule that a structural variation, which increases the electrophilicity of a carbocation at the same time reduces its electrofugality, does not hold any longer. The need to systematically analyze the role of intrinsic barriers is emphasized.

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.

Structure of a reactive gold carbenoid

A formal gold-for-chromium transmetalation allowed the gold carbenoid species [Cy3 PAuCAr2 ]NTf2 (11) (Ar=pMeOC6 H4 -) to be obtained in crystalline form. The structure in the solid state suggests that there is only little back donation of electron density from gold to the carbene center of 11 and hence very modest AuC double-bond character; rather, it is the organic ligand framework that is responsible for stabilizing this species by resonance delocalization of the accumulated positive charge. Because 11 is capable of cyclopropanating p-methoxystyrene even at low temperature, the discussion of its structure is deemed relevant for a better understanding of the mechanisms of π-acid catalysis in general.