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This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes. Article pubs.acs.org/accounts Philicities, Fugalities, and Equilibrium Constants Herbert Mayr* and Armin R. Ofial Department Chemie, Ludwig-Maximilians-Universität München, Butenandtstrasse 5-13 (Haus F), 81377 München, Germany CONSPECTUS: 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 alkylsubstituted 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. Hammond’s postulate4 and its quantification by Leffler are consequences of such considerations.5 Until 1969, it seemed to be even possible to derive the position of the transition state from the Leffler−Hammond coefficient α, which defines the fraction of the change of the Gibbs energy of reaction, which is reflected by the change of the Gibbs energy of activation.5 As illustrated in Figure 3, an α value close to 0 was considered to be indicative of an early (reactant-like) transition state, whereas an α value close to 1 was associated with a late (product-like) transition state. This interpretation collapsed in 1. INTRODUCTION Our comprehension of organic reactivities is coined by thinking in thermodynamic terms. A typical example for this approach is illustrated by Figure 1, which shows that the rate constants for the reactions of 1-chlorobutane with different families of anions correlate linearly with their Brønsted basicities expressed by pKaH, i.e., the acidity constants of their conjugate acids.1,2 This behavior has commonly been rationalized by the Bell−Evans− Polanyi principle (Figure 2), which models the transition states through the intersection of two correlation lines: one for the breaking of a bond in the reactant and one for the formation of the new bond in the product.3 © 2016 American Chemical Society Received: February 9, 2016 Published: April 25, 2016 952 DOI: 10.1021/acs.accounts.6b00071 Acc. Chem. Res. 2016, 49, 952−965 Article Accounts of Chemical Research Scheme 1. Nitroalkane Anomaly (Data from ref 6) sum of α for forward and backward reaction must be 1.00, the resulting value of α = −0.31 for the backward reaction leads to the counterintuitive conclusion that less basic nitronate anions are protonated faster than more basic ones.6 The term “nitroalkane anomaly”, commonly used to describe this phenomenon, may lead to the assumption that the behavior of nitroalkanes is unique. However, Leffler−Hammond coefficients outside the range 0 < α < 1 are just spectacular cases demonstrating that α cannot be a measure for the position of the transition state. The fact that the transition state cannot generally be described by a merger of reactant and product configurations has meticulously been analyzed by Jencks,7 Williams,8 Shaik,9 Bernasconi,10 and many others as quoted in refs 7−10. Pross noted that α is ∞ for a series of identity reactions11 because variation of Y affects ΔG⧧ while ΔG° stays 0 (Scheme 2). Figure 1. Relationships between S N 2 reactivities toward 1chlorobutane and Brønsted basicities (with data from refs 1 and 2). Scheme 2. Pross’ Analysis of Identity Reactions11 Figure 2. Illustration of the Bell−Evans−Polanyi principle.3 Prior to a general analysis of rate-equilibrium relationships let us summarize the definitions of the key terms used in this Account. According to IUPAC recommendations, Lewis acidity and basicity are thermodynamic terms, while -philicity and -fugality refer to kinetics (Chart 1).12 Electron-deficient species, which may either be ionic or neutral (R+, E), can be regarded as Lewis acids, electrophiles, or electrofuges, depending on the properties which are considered. While Lewis acidities refer to the equilibrium constants of their reactions with electron-surplus compounds, electrophilicities refer to the rate constants of their reactions with X− or Nu, and electrofugalities refer to the rate constants of the corresponding backward reactions. Analogously, Lewis basicities, nucleophilicities, and nucleofugalities describe different properties of electron-surplus compounds, and statements that a certain species X− behaves either as a nucleophile or a base are obsolete. When the solvated proton is selected as the reference Lewis acid, we arrive at the lower part of Chart 1, which shows that Brønsted basicity is a special case of Lewis basicity, while H−X can be considered as a special type of Lewis pair. We think that much confusion in teaching comes from the hybrid terms “kinetic basicity” and “kinetic acidity”, which intermix kinetics and thermodynamics. Though everybody understands what “kinetic acidity” means, use of this term suggests that the complementary term should be “thermodynamic acidity” and thus obscures the generally accepted convention that “acidity” by itself represents a thermodynamic property. For that reason, Figure 3. Hammond−Leffler’s α as an alleged measure for the position of the transition state. 1969, when Bordwell observed α = 1.31 for the deprotonation of substituted 1-nitro-1-phenylethanes, indicating that variation of the substituents X affects the energies of the transition states more than the energies of the products (Scheme 1).6 As the 953 DOI: 10.1021/acs.accounts.6b00071 Acc. Chem. Res. 2016, 49, 952−965 Article Accounts of Chemical Research Chart 1. Relationships Between Kinetic and Thermodynamic Terms we recommend to replace the terms “kinetic basicity” and “kinetic acidity” by “protophilicity” and “protofugality”, respectively; “protophilicity” has previously been employed nonuniformly to describe rate as well as equilibrium constants of proton transfer reactions. With the definitions in Chart 1, philicity and fugality refer consistently to kinetic properties, while acidity and basicity are exclusively associated with equilibrium constants and not with kinetics. Please note that Lewis acidity and basicity as well as the corresponding philicities and fugalities refer to a certain reference compound. As there is an infinite number of potential reference compounds, there is also an infinite number of Lewis acidity and basicity scales as well as of philicity and fugality scales. This Account will be restricted to reactions with carboncentered Lewis acids. expressed by KA (eq 2), Hine suggested to derive carbon basicities relative to OH− (KAR, eq 4) by multiplication of the tabulated Brønsted basicities KA with the equilibrium constants KHARA defined by eq 3. KA R R−OH + A− HoooI R−A + OH− (1) KA H−OH + A− ⇌ H−A + OH− KHA RA (2) R−OH + H−A HoooooI R−A + H−OH (3) KA R = KAKHA RA (4) However, when using the term “carbon basicity” in several of our recent papers, we have realized that it was often misinterpreted as “basicities of carbon-centered Lewis bases” (i.e., basicities of carbanions). For that reason, we decided not to use this term any longer and instead employ the less ambiguous expression “Lewis basicities toward carbon-centered Lewis acids”.14 Of course, there are thousands of carbon-centered Lewis acids which might be selected as reference acids for a Lewis basicity scale. The choice is limited by the fact, however, that direct experimental determinations of the equilibrium constants K, as described by eq 5, are only possible when the reactants LA or LB coexist in comparable concentrations with the Lewis adducts LA←LB. 2. LEWIS ACIDITIES AND BASICITIES Most investigated rate-equilibrium relationships for organic reactions are Brønsted correlations, i.e., correlations of rate constants for certain reaction series with the pKa or pKaH values of the corresponding reactants. The interpretation of these correlations is not straightforward, however, when the rate constants refer to reactions with C-, N-, Si-, or B-centered electrophiles, while the equilibrium constants (pKa or pKaH) refer to reactions with the proton. Given that reactions with carbon-centered electrophiles are of particular importance in organic chemistry, Hine introduced the term “carbon basicity” for characterizing relative Lewis basicities with respect to carbon centered Lewis acids.13 The equilibrium constants KAR for the (hypothetical) reaction 1 reflect the relative basicities of A− and HO− toward R+. As the relative Brønsted basicities of A− and HO− toward H+ are K LA + LB ⇌ LA←LB (5) To directly compare Lewis bases of widely differing strengths, we selected a series of benzhydrylium ions Ar2CH+ as reference Lewis acids (Table 1), whose strengths are varied 954 DOI: 10.1021/acs.accounts.6b00071 Acc. Chem. Res. 2016, 49, 952−965 Article Accounts of Chemical Research by substituents in para- and meta-position, while the steric shielding of the reaction center is kept constant. It was found that these equilibrium constants can be described by the sum of a base-independent Lewis acidity parameter LA and an acid-independent Lewis basicity parameter LB (eq 6), which were obtained by subjecting 115 equilibrium constants (log K) for the reactions of the benzhydrylium ions E1+−E20+ with 37 Lewis bases in CH2Cl2 at 20 °C to least-squares minimization with the definition LA[(4-MeOC6H4)2CH+] = 0.0. The resulting Lewis acidity parameters LACH2Cl2 are listed in Table 1 and the corresponding Lewis basicities LB have been reported in ref 14. Table 1. Reference Lewis Acids E1+−E33+, Their Lewis Acidities LACH2Cl2 and LAMeCN, and Calculated Methyl Anion Affinities ΔGMA (for 20 °C, data from ref 14) log K = LA + LB (6) The good fit of the experimental equilibrium constants to the correlation lines in Figure 5 shows that the relative strengths of the Lewis bases are independent of the nature of the benzhydrylium ions and justifies enforcing a slope of unity in the least-squares minimization according to eq 6. When the Lewis bases are ordered according to increasing LB from left to right and Lewis acids are ordered according to increasing LA from top to bottom, as depicted in Figure 6, Lewis adducts, which are located on the diagonal from bottom left to top right, are formed with an equilibrium constant of K = 1 at 20 °C. The multicolor corridor in Figure 6 refers to equilibrium constants in the range 1 < K (M−1) < 106, i.e., equilibrium constants which can easily be measured in millimolar solutions. While Lewis acids and bases in the blue sector do not coordinate in millimolar solution, Lewis adducts in the red corridor are formed almost quantitatively. Similar presentations can analogously be constructed for other solvents. Only small changes of the relative Lewis basicities can be expected when benzhydrylium ions are replaced by other types of carbocations as references, but significant changes of the ranking of the Lewis basicities will occur when charges are generated or destroyed during Lewis acid−Lewis base coordination. Lewis basicities determined with respect to benzhydrylium ions furthermore do not apply for interactions with very bulky reference acids (frustrated Lewis pairs)15 or when the Lewis adducts are stabilized or destabilized by anomeric16 or inverse anomeric effects,17 respectively. Multiplication of the Lewis acidities LA listed in Table 1 with −2.303RT yields standard Gibbs energies (20 °C) ΔG° for the reactions of the corresponding Lewis acids with a Lewis base of LB = 0. Figure 7 shows that these Gibbs energies correlate linearly with quantum chemically calculated methyl anion affinities ΔGMA of the corresponding benzhydrylium ions in the gas phase. Since the calculated methyl anion affinities ΔGMA correlate linearly with the corresponding H−, H2N−, and HO− affinities with a slope of 1.0,18,19 the abscissa of Figure 7 can be replaced by the affinity toward other anions. The linearity of this correlation indicates the absence of differential solvation of these benzhydrylium ions in dichloromethane. By this correlation calculated gas phase data can be transferred into equilibrium constants in solution without employing quantum chemical solvent models. Analogous correlations with slopes of ΔΔG° CH 2 Cl 2 / ΔΔG°gas phase = 0.84−0.95 have been found for reactions with neutral Lewis bases (pyridine, NH3, PH3, H2CCH−NH2), indicating that the differences of the Lewis acidities of benzhydrylium ions toward neutral Lewis bases are only slightly smaller in the CH2Cl2 solution than in the gas phase.19 a As reliable equilibrium constants in MeCN could only be determined with highly stabilized benzhydrylium ions, the Lewis acidity scale in MeCN was fixed at LA(E1+) = −12.76, the LA for E1+ in CH2Cl2 solution. bBenzhydrylium ions with p-phenoxy or p-phenylamino groups deviate from the correlation used to calculate LAMeCN (see ref 14). cFrom LAMeCN = 0.878LACH2Cl2 − 1.60 (ref 14). dCalculated from ΔGMA by the correlation equation shown in Figure 7. eHighly reactive carbocations undergo Ritter reactions with MeCN. In this way, we characterized strong Lewis bases through photometric determination of the equilibrium constants K for their reactions with highly stabilized benzhydrylium ions, whereas weak Lewis bases were calibrated through their reactions with less stabilized benzhydrylium ions (Figure 4).14 955 DOI: 10.1021/acs.accounts.6b00071 Acc. Chem. Res. 2016, 49, 952−965 Article Accounts of Chemical Research Figure 4. Benzhydrylium ions as reference Lewis acids for the determination of Lewis basicities.14 Figure 5. Plot of log K for reactions of benzhydrylium ions E+ with Lewis bases in CH2Cl2 at 20 °C against the Lewis acidity parameters LACH2Cl2 of the benzhydrylium ions (with data from ref 14). with α values between 0.48 and 0.73 again shows that α cannot be related to the position of the transition state. If α were a measure of the position of the transition state, one had to postulate that variation of the carbocations in each of the depicted reaction series does not affect the transition structures, i.e., that the positions of the transition states for slow reactions with highly stabilized carbocations (bottom left) and for the fast reactions with highly reactive carbocations (top right) would be identical. This scenario is totally unrealistic because some of these reaction series include also reactions with rate constants of >(1−10) × 106 M−1 s−1, i.e., reactions 3. CORRELATIONS BETWEEN PHILICITIES AND EQUILIBRIUM CONSTANTS 3.1. Electrophilicity vs Lewis Acidity Figure 8 shows that the rate constants for the reactions of different types of nucleophiles with benzhydrylium ions correlate linearly with the corresponding Lewis acidities.14 Unlike in many Brønsted correlations (correlations with pKa values), rate and equilibrium constants now refer to the same reactions. The amazingly long linearity of these correlations 956 DOI: 10.1021/acs.accounts.6b00071 Acc. Chem. Res. 2016, 49, 952−965 Article Accounts of Chemical Research Figure 6. When do Lewis acids and bases coordinate? (Reproduced with permission from ref 14 Copyright 2015 American Chemical Society). of reaction ΔG° and the intrinsic barrier ΔG0⧧, which corresponds to ΔG⧧ for a reaction with ΔG° = 0. Differentiation of eq 7 gives eq 8, which simplifies to eq 9 (see Chart 2) for |ΔG°| ≪ ΔG0⧧, which applies for the reactions under consideration. According to eq 9 (see Chart 2), a linear correlation between ΔG⧧ and ΔG° can only exist if ΔG0⧧ remains constant throughout the reaction series (α = 1/2) or varies proportionally with ΔG°. Values of α > 1/2, as observed for most reaction series of Figure 8, imply that ΔG0⧧ decreases with increasing exergonicity, which might be explained by an increasing contribution of the HOMO−LUMO interaction, corresponding to increasing importance of inner-sphere electron transfer. 3.2. Nucleophilicity vs Lewis Basicity Since rate constants (log k) and equilibrium constants (log K) in Figure 9 refer to the same reactions, one of the problems which hamper the straightforward interpretation of many Brønsted correlations (rate constants for reactions with R−X vs equilibrium constants for interaction with H+, see Figure 1) has been eliminated. As shown in Figure 9, rate constants correlate very poorly with equilibrium constants even when reactions of nucleophiles with the same central atom are compared. Thus, DABCO (1,4diazabicyclo[2.2.2]octane) is a much stronger nucleophile (i.e., reacts much faster) than NMI (N-methylimidazole) though being a slightly weaker Lewis base. One has to conclude, therefore, that the slightly higher Lewis basicity (ΔG°) of NMI compared to DABCO is overcompensated by the significantly higher intrinsic barrier (ΔG0⧧) for the reaction of NMI. As the intrinsic barriers are related to the reorganization energies λ (= 4ΔG0⧧),21,22 the low nucleophilic reactivities of the imidazoles indicate that more structural reorganization, Figure 7. Correlation of ΔG° (= −2.303RT·LACH2Cl2) for the reactions with a Lewis base (LB = 0) with calculated methyl anion affinities ΔGMA of E1+−E20+ (20 °C, with data from Table 1). with activation enthalpies of ΔH⧧ = 0, where electrophiles and nucleophiles combine without crossing an enthalpic barrier.20 A theoretical rationalization for this behavior is missing. According to Marcus theory (eq 7 (see Chart 2)),21,22 the Gibbs energy of activation ΔG⧧ depends on the Gibbs energy 957 DOI: 10.1021/acs.accounts.6b00071 Acc. Chem. Res. 2016, 49, 952−965 Article Accounts of Chemical Research Figure 8. Correlation of log k2 for the reactions of benzhydrylium ions E1+−E20+ with different nucleophiles in CH2Cl2 versus the corresponding Lewis acidities LACH2Cl2 (from Table 1).14 Chart 2. Marcus Equation for Group Transfer Reactions including solvent reorganization, is required when imidazolium ions are generated from imidazoles than when quaternary ammonium ions are generated from tertiary amines. A rationalization for this behavior may be achieved by the activation strain model.24 The different ranking of nucleophilicity and Lewis basicity has previously been illustrated by the comparison of DABCO and DMAP.25 Though DABCO reacts 103 times faster (i. e., is more nucleophilic) with benzhydrylium ions than DMAP, the low Lewis basicity of DABCO accounts for the fact that it does not give a Lewis adduct with highly stabilized benzhydrylium ions despite of extrapolated rate constants between 106 to 107 M−1 s−1, corresponding to reactions on the millisecond time scale in millimolar solutions (Figure 10). This example rationalizes why one cannot find carbenium ions, which react slowly with tertiary amines. Because of the low intrinsic barriers, reactions of carbocations with tertiary amines are either extremely fast or do not occur at all.26 This point is furthermore illustrated by Figure 9: Though eq 10 predicts fast reactions between E2+ and all nucleophiles depicted there, the 958 DOI: 10.1021/acs.accounts.6b00071 Acc. Chem. Res. 2016, 49, 952−965 Article Accounts of Chemical Research Figure 9. Correlation of log k for the reactions of nucleophiles with E2+ and E8+ (in MeCN at 20 °C) with the corresponding equilibrium constants14 (closed circles, experimental rate constants from references quoted in ref 23; open symbols, log k extrapolated by using eq 10). Figure 10. Differentiation of nucleophilicity and Lewis basicity for DABCO and DMAP (in MeCN, 20 °C, data from ref 25). aExtrapolated value from this graph. bFrom eq 6 using data from ref 14. open red circles indicate electrophile-nucleophile combinations which do not give adducts in millimolar solutions because of the high reversibility. Figure 9 shows that Cl− is a much stronger nucleophile in acetonitrile than N-methylimidazole (NMI). Scheme 3 thus illustrates that in the synthesis of 1,3-dialkylated imidazolium ions27 the weak nucleophile NMI replaces the strong nucleophile Cl−. The reaction works, because imidazole is a stronger Lewis base than chloride. Analogously the formation of carboxylic esters from carboxylate anions and benzyl bromide (Scheme 3)28 is possible because carboxylate anions are stronger Lewis bases than bromide anions. It should be noted, however, that the relative Lewis basicities of anionic and neutral Lewis bases Scheme 3. Substitutions of strong nucleophiles by weak nucleophiles depend on the nature of the solvent, and the ordering shown in Figure 9 will be different in other solvents. 959 DOI: 10.1021/acs.accounts.6b00071 Acc. Chem. Res. 2016, 49, 952−965 Article Accounts of Chemical Research Large differences in intrinsic barriers also account for the fact that in many reactions of ambident nucleophiles, the products of kinetic control differ from those formed under thermodynamically controlled conditions. The thiocyanate anion, for example, gives thiocyanates with C-centered electrophiles under conditions of kinetic control, and isothiocyanates under conditions of thermodynamic control (Scheme 4).29 Earlier attempts to explain ambident reactivities by the ‘hard− soft acid−base principle’ or the Klopman-Salem concept have been discredited.30 Figure 12. Gibbs energy profiles for the deprotonation of nitromethane (left) and 2-nitropropane (right) by HO− (H2O, 25 °C).32 Scheme 4. Thiocyanate Anion as a Typical Example for an Ambident Nucleophile analogous for different carboxylate leaving groups in different solvents. In all series, the benzhydrylium ions E1+ and E3+ with annelated 5-membered heterocycles are generated more slowly than benzhydrylium ions E2+ and E4+of similar Lewis acidity, but with annelated 6-membered rings. Since we were unable to measure equilibrium constants with carbenium ions which are less stabilized than E20+, we cannot extend Figure 13 to the right. To include also the less stabilized carbenium ions E21+-E33+ in the electrofugality-Lewis acidity correlations, we plotted the solvolysis rate constants log ks against the calculated gas phase methyl anion affinities ΔGMA. Figure 14 shows the same pattern as Figure 13, which was to be expected because of the linear correlation between LACH2Cl2 and ΔGMA shown in Figure 7. Why are there good correlations between rate and equilibrium constants for weakly stabilized and destabilized benzhydrylium ions on the right of Figures 13 and 14, but poor correlations for stabilized benzhydrylium ions on the left? From the laser-flash photolytically measured rate constants of the reactions of chloride and bromide ions with weakly stabilized and nonstabilized benzhydrylium ions, we know that all reactions of chloride and bromide ions with the carbocations are diffusion-controlled in the solvents used for the solvolyses, i.e., these reactions do not have a barrier or their barrier is lower than that due to diffusion.33 According to the principle of microscopic reversibility, there also cannot be a barrier for the reverse reaction, i.e., the transition states of the heterolytic cleavages of (E20−E33)−X correspond to the ion-pairs (Figure 15a). Since the benzhydryl halides (E1−E13)+Cl− are ionic in the common solvolytic media, the covalent benzhydryl carboxylates (E1−E13)−O2CR were employed to investigate the rates of solvolytic generation of the amino-substituted benzhydrylium ions E1+−E13+. Direct rate measurements of the reactions of these carbocations with carboxylate ions in the corresponding solvents showed that these ion combinations proceed via significant barriers,34 as illustrated in Figure 15b, which implies that also the transition states of the heterolytic cleavages of (E1−E13)−O2CR do not correspond to the carbocations. Thus, the scatter in the left part of the correlations in Figures 13 and 14 is due to the fact that the barrier for the ionization step does not only depend on the “stabilities” of the resulting carbocations but also on the different magnitudes of the intrinsic barriers. In conclusion, these analyses show that only solvolysis rates of substrates leading to highly reactive carbenium ions give accurate information about their Lewis acidities (thermodynamic stabilities), whereas solvolysis rates of substrates, which give rise to highly stabilized carbenium ions, cannot directly be associated with “carbocation stabilities”. Detailed investigations of trityl solvolyses confirmed this interpretation.35 4. CORRELATIONS BETWEEN FUGALITIES AND EQUILIBRIUM CONSTANTS 4.1. Nucleofugality vs Lewis Basicity Various reference reactions for establishing nucleofugality rankings have previously been discussed.31 In heterolytic bond fissions, the change in nucleofugality usually reflects a fraction of the change in Lewis basicity. However, structural modification may also have a greater effect on nucleofugality than on Lewis basicity. As K = k→/k←, the 103-times faster reaction of DABCO compared to DMAP (despite the 340times higher Lewis basicity of DMAP, Figure 10) implies that the stronger nucleophile DABCO is also a 230 000-times better nucleofuge than DMAP. The low reorganization energies for the reactions of trialkylamines account for the high nucleophilicity and nucleofugality of DABCO (Figure 11). Figure 11. Gibbs energy profiles for the reactions of DABCO and DMAP with E2+ (MeCN, 20 °C, with data from Figure 10, structure for −CH(jul)2, see Table 1). This situation is similar to that for the deprotonation of nitroalkanes: Nitromethide is a stronger Brønsted base (nitromethane is less acidic than 2-nitropropane) and a better protofuge than 2-nitropropan-2-ide, i.e., the thermodynamically less stable nitromethyl anion is formed faster (Figure 12).6,32 4.2. Electrofugality vs Lewis Acidity Plots of solvolysis rate constants for benzhydrylium derivatives Ar2 CH-X against the Lewis acidities of the resulting benzhydrylium ions are linear in the right part of Figure 13, but show a poor correlation on the left.14 The deviations from the correlation lines are not random, however, but are 960 DOI: 10.1021/acs.accounts.6b00071 Acc. Chem. Res. 2016, 49, 952−965 Article Accounts of Chemical Research Figure 13. Correlation of solvolysis rate constants log kS (25 °C) for (E1-E20)-X with the Lewis acidities LACH2Cl2 of benzhydrylium ions E1+-E20+ (PNB = p-nitrobenzoate, DNB = 3,5-dinitrobenzoate, 80A = 80/20 acetone/water; 90A = 90/10 acetone/water; 80AN = 80/20 acetonitrile/water; data from ref 14). Figure 14. Correlation for log ks for the solvolysis reactions of (E1−E33)−X with the methyl anion affinities ΔGMA(gas phase) of E1+−E33+ (with data from ref 14, DCM = dichloromethane, for further abbreviations see Figure 13). 5. RELATIONSHIPS BETWEEN PHILICITIES AND FUGALITIES correlations. For that purpose, the kinetics of reactions of stable carbocations and Michael acceptors with π-, n-, and σnucleophiles were determined, and it was found that the resulting second-order rate constants at 20 °C can be described by eq 10, which characterizes electrophiles by one solventindependent electrophilicity parameter E and nucleophiles by two solvent-dependent parameters, nucleophilicity N and susceptibility sN. The calculation of absolute rate constants by the Marcus equation (eq 7 (see Chart 2)) does not only require knowledge of the Gibbs energies of reaction ΔG° but also of the intrinsic barriers ΔG0⧧. As the latter are not easily accessible, we have developed an empirical method to predict rate constants for the reactions of electrophiles with nucleophiles from rate−rate 961 DOI: 10.1021/acs.accounts.6b00071 Acc. Chem. Res. 2016, 49, 952−965 Article Accounts of Chemical Research benzhydrylium ions and structurally related Michael acceptors (reference electrophiles) with an accuracy of better than a factor of 2. Rate constants with other carbocations, Michael acceptors, and electron-deficient arenes are predicted with an accuracy of better than a factor of 10−100, which is considered satisfactory in view of the reactivity range of 40 orders of magnitude. Additional electrophile-specific susceptibilities are needed to correlate SN2 reactions.37 Analogously, electrofugality and nucleofugality scales38 were constructed by subjecting 628 solvolysis rate constants k25 °C for different benzhydryl derivatives to a least-squares minimization on the basis of eq 11. Electrofugality parameters Ef for 39 benzhydrylium ions and nucleofuge-specific parameters Nf and sf for 101 common leaving groups in different solvents (definition, Ef = 0 for (4-MeOC6H4)2CH+ and sf = 1 for Cl− in ethanol) were thus obtained. Many additional parameters have recently been reported by Kronja and co-workers.39 Figure 15. SN1 Reactions with diffusion-controlled (a) and activationcontrolled (b) ion recombination. log k 20 ° C = s N(E + N ) (10) log k 25 ° C = sf (Nf + Ef ) These parameters were obtained by subjecting a large number of experimental rate constants to a least-squares minimization on the basis of eq 10, with the definitions E[(4MeOC6H4)2CH+] = 0 and sN(2-methyl-pent-1-ene in CH2Cl2) = 1.06 (formerly 1.00).20,36 While the definition of solventindependent electrophilicity parameters E, which shifts all solvent effects into the nucleophile-specific parameters N and sN, works well for reactions with carbocations and quinone methides (reference electrophiles), consideration of electrophile-specific solvent effects will become necessary when electrophiles as aldehydes or SN2 substrates are considered. As illustrated in Figure 16 for the reactions of C-nucleophiles with benzhydrylium ions, the rate−rate correlations remain linear up to rate constants of 108 M−1 s−1 and only bend when the diffusion limit is approached. So far, 1033 nucleophiles and 272 electrophiles have been characterized, and the data are collected in a freely accessible database.23 Equation 10, which covers a reactivity range of 40 orders of magnitude, predicts absolute rate constants for the reactions of nucleophiles with (11) The excellent correlations shown in Figure 17 justify the treatment of the electrofugalities Ef of benzhydrylium ions as solvent-independent parameters, which shifts all solvent effects into the nucleofuge-specific parameters Nf and sf. The underlying assumption that carbocation solvation changes proportionally with Ef does not generally hold for other types of carbocations with the consequence that application of eq 11 to such systems leads to aberrations up to factors 50. When one plots electrofugality vs electrophilicity, one observes a linear correlation for benzhydrylium ions with E > −2 and a large scatter for those with E < −2 (Figure 18).38 This result is not surprising, because linear correlations between philicities and fugalities can only exist if rate constants are linearly related to equilibrium constants (eq 12), and it was shown above that the linear relationship between electrofugalities and Lewis acidities (Figures 13 and 14) and between electrophilicities and Lewis acidities (Figure 8) only hold for alkoxy- and less stabilized benzhydrylium ions but not for Figure 16. Plot of log k2 versus E for the reactions of benzhydryl cations with π-nucleophiles (CH2Cl2, 20 °C). Open symbols indicate rate constants k2 > 108 M−1 s−1, which were not used for the correlation analysis. (Reproduced with permission from ref 20 Copyright 2012 American Chemical Society). 962 DOI: 10.1021/acs.accounts.6b00071 Acc. Chem. Res. 2016, 49, 952−965 Article Accounts of Chemical Research Figure 17. Plots of solvolysis rate constants log k (at 25 °C) for benzhydryl halides and various esters vs the electrofugality parameters Ef of benzhydrylium ions. Mixtures of solvents are given as (v/v); A = acetone, E = ethanol, TFE = 2,2,2-trifluoroethanol. (Reproduced with permission from ref 38 Copyright 2010 American Chemical Society). J. P. Richard has shown that α-CF3-substituted benzyl cations react with nucleophiles with similar rates as their CH3substituted analogues though they are 107 times more slowly generated in solvolysis reactions (Scheme 5).40 Scheme 5. Comparison of Rates of Generation (as SN1 Intermediates) and Electrophilic Reactivities of α-Methyl and α-Trifluoromethyl Substituted Benzyl Cations (Data from ref 40, TFE = 2,2,2-trifluoroethanol) Figure 18. Correlation of electrofugality Ef and electrophilicity E of benzhydrylium ions (with data from ref 38). highly stabilized amino-substituted analogues. Though the deviations of the amino-substituted benzhydrylium ions from the correlation lines in Figure 8 are small, they are not random and show the same pattern for reactions with different nucleophiles. log k = α log K + c (12) While most chemists are well aware of the fact that the intuitive expectation that strong nucleophiles are weak nucleofuges (based on the Bell−Evans−Polanyi principle) does not always hold (iodide ions are good nucleophiles and good nucleofuges), the left part of Figure 18 illustrates that also the inverse relationship between electrofugalities and electrophilicities does not generally hold. Because of the low SN1 reactivities of vinyl halides, vinyl cations have long been considered to be highly unstable intermediates.41 However, the almost identical gas phase hydride affinities of the benzyl (1002 kJ/mol) and αphenylvinyl cation (1004 kJ/mol)42 indicate that vinyl cations do not have very low thermodynamic stabilities and that the low rates of their formation are due to the high intrinsic 963 DOI: 10.1021/acs.accounts.6b00071 Acc. Chem. Res. 2016, 49, 952−965 Article Accounts of Chemical Research barriers. Scheme 6 illustrates the fact that the triaryl substituted vinyl cation, which is generated 108 times more slowly than the to the LMU München in 1996. He is a member of the Bavarian Academy of Sciences and the German National Academy of Sciences. His work focuses on the quantification of organic reactivity. Scheme 6. Comparison of SN1 Rates and Electrophilic Reactivities of Vinyl and Benzhydryl Derivatives Armin R. Ofial studied chemistry at the TU Darmstadt (doctoral degree 1996). Since 1997 he has been a Research Associate at the LMU München where he habilitated in 2013. His research interests include reactions of iminium ions, chemical kinetics, and C−H bond functionalizations. ■ ACKNOWLEDGMENTS Dedicated to Professor George A. Olah. We thank all associates who have contributed to the development of this concept and Professor Reinhard Brückner (Freiburg) for helpful comments. ■ Extrapolated from measurements at 120 °C, ref 43. bCalculated from data in ref 38. cFrom ref 44. dFrom ref 45. a bis(p-tolyl)methylium ion, reacts even slightly slower with trifluoroethanol than the rapidly generated bis(p-tolyl)methylium ion. 6. CONCLUSION The Bell−Evans−Polanyi principle, commonly used to rationalize relationships between rate and equilibrium constants within reaction series, remains to be the first guide for predicting the influence of structural variation on the rates of polar organic reactions. 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