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Publicly Available Published by De Gruyter March 18, 2017

Philicity, fugality, and equilibrium constants: when do rate-equilibrium relationships break down?

Herbert Mayr EMAIL logo and Armin R. Ofial

Abstract

Linear free energy relationships, in particular relationships between rate and equilibrium constants, are the basis for our rationalization of organic reactivity. Whereas relationships between the kinetic terms nucleophilicity and nucleofugality and the thermodynamic term basicity have been in the focus of interest for many decades, much less attention has been paid to the relationships between electrophilicity, electrofugality, and Lewis acidity. By using p- and m-substituted benzhydrylium ions (Aryl2CH+) as reference electrophiles, reference electrofuges, and reference Lewis acids of widely varying electron demand and constant steric surroundings of the reaction center, we have developed comprehensive reactivity scales which can be employed for classifying polar organic reactivity and for rationally designing synthetic transformations. It is a general rule that structural variations in electron-surplus species, which increase basicities, also increase nucleophilicities and decrease nucleofugalities, and that structural variations in electron-deficient species, which increase Lewis acidities also increase electrophilicities and decrease electrofugalities. Deviations from this behavior are analyzed, and it is shown that variations in intrinsic barriers are responsible for the counterintuitive observations that structural variation in one of the reactants alters the rates of forward and backward reactions in the same direction. A spectacular example of this phenomenon is found in vinyl cation chemistry: Vinyl cations are not only generated several orders of magnitude more slowly in SN1 reactions than benzhydrylium ions of the same Lewis acidity, but also react much more slowly with nucleophiles.

Introduction

The mechanistic investigations of organic reactions in the 1940s to 1970s have paved the way for the rapid development of novel synthetic methods in recent decades [1]. In the meantime the precision of quantum chemical calculations has reached a level that they can be used to derive the thermodynamics of most organic reactions in the gas phase with an accuracy which sometimes even exceeds that of experimental methods. Less reliable are quantum chemical calculations of reactions in solution, in particular when ions are involved as reactants, products, or intermediates, because in such cases solvation makes a major contribution to the energetics of these processes. Though quantum chemical calculations of transition structures have also made tremendous progress in recent decades, calculations of reaction pathways are still rather laborious that they are predominantly used for investigating mechanisms of known reactions and less for designing novel synthetic transformations.

For these reasons, linear free energy correlations still play a major role for quick predictions of organic reactivity. As they also reveal relationships between various kinetic and thermodynamic properties, they are essential tools for our understanding of organic reactivity. Thus, pKa values are generally employed for rationalizing relative reactivities of nucleophiles and leaving group abilities in nucleophilic substitutions [1]. Systematic studies by Bordwell have shown, for example, that the rates of nucleophilic substitutions by sulfonyl-substituted benzyl anions are linearly correlated with their pKaH values, i.e. the Brønsted acidities of their conjugate acids (Fig. 1). This correlation is in line with our intuition, that electron-releasing substituents, which increase the affinity of the benzyl anions toward the proton (pKaH), also enhance their tendency to attack at an alkyl halide.

Fig. 1: Relationship between nucleophilic reactivities of carbanions in DMSO at 25°C and their Brønsted basicities (pKaH=pKa of the corresponding benzylsulfones in DMSO) with data from [2] (photograph of F. G. Bordwell by courtesy of J.-P. Cheng).
Fig. 1:

Relationship between nucleophilic reactivities of carbanions in DMSO at 25°C and their Brønsted basicities (pKaH=pKa of the corresponding benzylsulfones in DMSO) with data from [2] (photograph of F. G. Bordwell by courtesy of J.-P. Cheng).

However, when Bordwell studied the nucleophilic substitutions of butyl chloride with a variety of nucleophiles, separate correlations were observed for the different families of nucleophiles (Fig. 2). The interpretation of these correlations is hampered by the fact that pKaH values measure affinities toward the proton, while the rate constants refer to reactions at a carbon atom. For that reason, we have determined equilibrium constants for the reactions of a variety of nucleophiles with benzhydrylium ions, which we used as prototypes of C-centered Lewis acids [5]. Before turning to that aspect, let us recollect some definitions [6], which will be used throughout this essay (Fig. 3).

Fig. 2: Relationships between Brønsted basicities in DMSO and nucleophilic reactivities toward 1-chlorobutane in DMSO at 25°C (with data from [3], [4]).
Fig. 2:

Relationships between Brønsted basicities in DMSO and nucleophilic reactivities toward 1-chlorobutane in DMSO at 25°C (with data from [3], [4]).

Fig. 3: Relationships between kinetic and thermodynamic terms (from [6]).
Fig. 3:

Relationships between kinetic and thermodynamic terms (from [6]).

A Lewis acid (charged or neutral) is an electron-pair acceptor, a Lewis base (charged or neutral) is an electron-pair donor. We speak about Lewis acidities and Lewis basicities, when we refer to equilibrium constants. However, we use the terms electrophilicity and nucleophilicity when we consider the rates of their combinations, and electrofugality and nucleofugality, when we talk about the rates of their separation. Thus, a Lewis base can always be characterized by its Lewis basicity or nucleophilicity or nucleofugality, whichever property is considered.

As Lewis basicity has to be specified with respect to a certain Lewis acid, and there is an infinite number of potential reference Lewis acids, there is also an infinite number of Lewis basicity scales. The same ambiguity holds for each of these terms. Thus, nucleophilicity must be specified with respect to a certain electrophile, and since there is an infinite number of potential reference electrophiles, there is also an infinite number of nucleophilicity scales. What are the relationships between these scales? Let us first describe the procedures, which we used for developing Lewis acidity/basicity as well as philicity and fugality scales.

Lewis acidity and Lewis basicity

Benzhydrylium ions (Ar2CH+) have been employed as reference C-centered Lewis acids, because their strengths can widely be varied by substituents in p- and m-position, while the steric surroundings of the Lewis-acidic site are kept constant. As photometric determinations of equilibrium constants require the presence of comparable concentrations of reactants and products in the equilibrium mixtures, we have used highly stabilized benzhydrylium ions (weak Lewis acids) to measure association constants with strong Lewis bases and less stabilized benzhydrylium ions (stronger Lewis acids) to measure association constants with weaker Lewis bases, as illustrated in Fig. 4 [7].

Fig. 4: Benzhydrylium ions as reference Lewis acids for the determination of Lewis basicities.
Fig. 4:

Benzhydrylium ions as reference Lewis acids for the determination of Lewis basicities.

As expected, the relative Lewis basicities were found to be almost independent of the substitution of the benzhydrylium ions, which allowed us to express the equilibrium constants by equation (1),

(1)lgK(20°C)=LA+LB

where the strengths of the Lewis acids are characterized by LA and the strengths of the Lewis bases are characterized by LB. In order to get a direct link to the kinetic scales, which we had developed earlier, we defined LA=0 for the dianisylcarbenium ion (4-MeOC6H4)2CH+. A justification for this approach is illustrated by the good fit of the correlations shown in Fig. 5 [7].

Fig. 5: Correlations of lg K (20°C) for the reactions of benzhydrylium ions with Lewis bases in CH2Cl2 with the LA parameters of the benzhydrylium ions (with data from [7]).
Fig. 5:

Correlations of lg K (20°C) for the reactions of benzhydrylium ions with Lewis bases in CH2Cl2 with the LA parameters of the benzhydrylium ions (with data from [7]).

In Fig. 6, we arranged Lewis acids with increasing strengths from top to bottom and Lewis bases with increasing strengths from bottom to top. In millimolar solutions, combinations of Lewis bases and Lewis acids, which are on the same level in Fig. 6 (LA+LB=3), are partially coordinated with each other. A certain Lewis acid will coordinate to a large extent with Lewis bases positioned above its own level in Fig. 6 (LA+LB>3) and will not significantly coordinate with Lewis bases below this level (LA+LB<3). Thus, in dichloromethane solution (mor)2CH+ (LA=−6.82) will form Lewis adducts with donor-substituted pyridines at 20°C, but not with acceptor-substituted pyridines or thioethers. Though equation (1) was developed for benzhydrylium ions as reference Lewis acids, it was found to give good approximations also for the coordinating abilities of other types of carbenium ions [8], [9]; severe deviations occur, however, when very bulky carbenium ions (e. g. tritylium ions) are involved [10], [11]. Such deviations due to steric effects are the basis of the frustrated Lewis pair chemistry [12], [13].

Fig. 6: Ranking of Lewis bases (left, ordered by LB) and Lewis acids (right, ordered by LA), which brings partners with lg K=3 to the same horizontal level (CH2Cl2, 20°C). (with data from [7]).
Fig. 6:

Ranking of Lewis bases (left, ordered by LB) and Lewis acids (right, ordered by LA), which brings partners with lg K=3 to the same horizontal level (CH2Cl2, 20°C). (with data from [7]).

Electrophilicity and nucleophilicity [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]

A strategy analogous to that described above for the construction of Lewis acidity and basicity scales had previously been used for the construction of electrophilicity and nucleophilicity scales. As shown in Fig. 7, weak electrophiles were used to study kinetics of the reactions with strong nucleophiles, and strong electrophiles were employed to study kinetics of the reactions with weak nucleophiles. Since the employed quinone methides (a zwitterionic resonance structure is shown in the first line of Fig. 7) have the same steric surroundings of the reacting site as the benzhydrylium ions, the variation of electrophilicity is exclusively due to electronic effects.

Fig. 7: Benzhydrylium ions as reference electrophiles for the determination of nucleophilicities.
Fig. 7:

Benzhydrylium ions as reference electrophiles for the determination of nucleophilicities.

In order to cover a wide range of reactivity, UV-Vis measurements with conventional spectrometers connected by light-conducting fibers to an all-quartz insertion probe, stopped-flow techniques, and laser-flash generation of benzhydrylium ions have been used side by side [21]. In many cases the formation of the initial adducts shown in Fig. 7 is highly reversible, and the reactions had to be designed in a way, that the initial step is followed by a rapid irreversible step (e. g. protonation of the adduct in the first example of Fig. 7 [27] and Cl transfer from BCl4 in the last [28]). Since the rates of the reactions with different nucleophiles were affected differently by variation of the electrophiles, the rate constants for the electrophile nucleophile combinations (Fig. 7) could not be expressed by an equation analogous to that for the equilibrium constants (eq. 1), i.e. a so-called “constant selectivity relationship” [29], [30]. Excellent correlations were observed, however, when a nucleophile-specific susceptibility parameter sN was included in addition to the nucleophilicity parameter Nu and the electrophilicity parameter E, as shown in equation (2).

(2)lgk(20°C)=Nu+sNE

With the definition E[(4-MeOC6H4)2CH+]=0 and sN=1.0 for allyltrimethylsilane [24] (initially, 2-methyl-pent-1-ene was used as the reference with sN=1.0 [15]) the measured second-order rate constants smaller than 108 L mol−1 s−1 were subjected to a least-squares minimization to derive the reactivity parameters Nu, sN, and E according to equation (2). By defining E as a solvent-independent electrophilicity parameter, all solvent effects on the rates of these reactions are shifted into the nucleophile-specific parameters Nu and sN [22], [26]. Figure 8 shows that this equation holds up to 108 L mol−1 s−1, and deviations only occur when the diffusion limit (3×109 to 5×1010 L mol−1 s−1in water and typical organic solvents) is approached.

Fig. 8: Correlation of second-order rate constants for reactions of various types of nucleophiles with benzhydrylium ions and quinone methides with the corresponding electrophilicity parameters E (in dichloromethane at 20°C if not mentioned otherwise).
Fig. 8:

Correlation of second-order rate constants for reactions of various types of nucleophiles with benzhydrylium ions and quinone methides with the corresponding electrophilicity parameters E (in dichloromethane at 20°C if not mentioned otherwise).

While equation (2) provides reliable predictions of rate constants for the reactions of benzhydrylium ions and quinone methides with a large variety of π-, n-, and σ-nucleophiles (accuracy usually better than factor 2), deviations up to a factor of 10 (in few cases up to 100) have to be tolerated for reactions with other types of carbocations and Michael acceptors. We consider these deviations tolerable, however, in view of the 40 orders of magnitude covered by these correlations.

There is a shortcoming in practical applications of equation (2), however. Synthetic chemists commonly get inspiration from analogies between different classes of compounds and try to transfer knowledge from one field of chemistry into another. If one is familiar with electrophilic aromatic substitutions of pyrroles, for example, one would like to use this knowledge also for predicting potential electrophilic reaction partners of benzenoid arenes, alkenes, diazoalkanes, and hydride donors. In many cases, the reactivity parameters Nu for these nucleophiles, which reflect the relative reactivities toward the dianisyl carbenium ion (ani)2CH+ (E=0), do not directly provide this information. The Nu values of carbanions and nitrogen ylides, for example, which are based on kinetic measurements of their reactions with weak electrophiles, correspond to extrapolated rate constants beyond the diffusion limit and do not have a physical meaning. As they result from wide-ranging extrapolations, the relative magnitudes of Nu for these nucleophiles differ significantly from the relative reactivities of these nucleophiles toward weak electrophiles, as Michael acceptors, which are common reaction partners in organic synthesis.

For that reason, we prefer to characterize nucleophiles not by Nu [equation (2)] but by the parameter N, as defined by equation (3), which is mathematically equivalent to equation (2), because N=Nu/sN [22], [26].

(3)lgk(20°C)=sN(E+N)

As N corresponds to the intercepts of the correlation lines on the abscissa (N=−E for lg k=0), they are usually within or very close to the experimentally studied range and thus are good approximations for the relative reactivities of nucleophiles toward those types of electrophiles, which are commonly used as reaction partners in synthetically used transformations. For that reason, we generally characterize nucleophiles by N, as illustrated in Fig. 9, where electrophiles and nucleophiles are arranged in a way that E+N=−5 for systems on the same level. As sN is typically between 0.5 and 1.1, electrophiles can be expected to react with nucleophiles on the same level in Fig. 9 with rate constants of 3×10−3 to 3×10−6 L mol−1 s−1corresponding to half reaction times of 5 min to 4 days in 1 M solutions at 20°C. One thus can anticipate that at ambient temperature a certain electrophile will react with those nucleophiles, which are positioned above itself in Fig. 9, but not with those below its own position. Of course, this is a very crude approximation because of the neglect of sN. However, when nucleophiles are located significantly above or below the corresponding electrophiles, potential reaction partners can be identified by just looking at the scales. In order to predict the likeliness of reactions of electrophiles with nucleophiles, which are on similar levels in Fig. 9, the simple calculation on the basis of equation (3) cannot be avoided.

Fig. 9: Nucleophilicity (N) and electrophilicity (E) scales arranged in a way that a certain electrophile will react with those nucleophiles, which are positioned above its own level (lg k=N+E>−5) [31].
Fig. 9:

Nucleophilicity (N) and electrophilicity (E) scales arranged in a way that a certain electrophile will react with those nucleophiles, which are positioned above its own level (lg k=N+E>−5) [31].

Some examples may illustrate how the reactivity scales in Fig. 9 were employed as a roadmap [32] for finding new synthetic transformations:

  1. Once the electrophilicity parameter of ethenesulfonyl fluoride (ESF) was determined to be E=−12.09 (level A in Fig. 9) by using sulfur and pyridinium ylides as reference nucleophiles, it was evident that ESF should be capable of undergoing aromatic substitutions with highly reactive pyrroles while it should be inert towards pyrroles with N<7 [33]. In accord with these predictions the product of the attack of ESF at 2,4-dimethylpyrrole (N=10.67) was isolated in 92% yield after 20 min, whereas the less nucleophilic N-methylpyrrole (N=5.85) did not form a product with ESF after 24 h (both reactions at ca 22°C) [33].

  2. Recently, we became interested in the nucleophilic reactivities of iodonium ylides [34]. The second-order rate constants that were obtained from the reactions of iodonium ylides with benzhydrylium ions as reference electrophiles showed that their nucleophilicity parameters are in the range 4.7<N<8.0. Thus, the stabilized iodonium ylides depicted in Fig. 9 are located slightly above the level of the cinammaldehyde-derived iminium ions in the electrophilicity scale of Fig. 9 (level B). This iminium ion, which is generated as an intermediate in organocatalytic reactions using MacMillan’s first-generation catalyst (E=−7.4 [23], [35], [36], [37], [38], [39]), was, therefore, predicted to react smoothly with the studied iodonium ylides. In line with this prediction, kinetic measurements of the reaction of the dimedone-derived iodonium ylide shown in Fig. 9 with the iminium ion depicted at level B, yielded a second-order rate constant, which deviated by only a factor of two from that calculated by equation (3). As a proof of principle for the applicability of iodonium ylides in iminium ion activated reactions, the reaction of the dimedone-derived iodonium ylide with cinnamaldehyde was studied under organocatalytic conditions. In the presence of 20% of (5S)-2,2,3-trimethyl-5-benzyl-4-imidazolidinone (MacMillan generation 1 catalyst) the cyclopropanation product was obtained in an enantiomeric ratio of up to 70/30. Yields of up to 72% of the resulting cyclopropanation products were obtained (in MeCN, 20°C, 24 h) [34], which demonstrated the possible use of iodonium ylides as nucleophiles in iminium-activated reactions.

  3. Though enamines derived from imidazolidinones are much less nucleophilic than enamines derived from pyrrolidine (Fig. 9, 2nd column from left), their nucleophilicity is sufficient (even when generated from aliphatic aldehydes under organocatalytic conditions) to react with tropylium ions (E=−3.7, level C of Fig. 9) and thus arrive at enantioenriched α-cycloheptatrienyl-substituted aldehydes [32].

Electrofugality and nucleofugality

Though strong nucleophiles are generally considered to be poor nucleofuges and strong electrophiles to be poor electrofuges, deviations from these relationships have long been known, and the fugality orders are not just the inverse of the philicity orders which were derived in the preceding chapter. For the development of fugality scales, we selected the rates of SN1 reactions of benzhydryl derivatives. As illustrated in Fig. 10, acceptor-substituted benzhydrylium ions, i.e. poor electrofuges, were used to calibrate the leaving group abilities of good nucleofuges, alkyl- or non-substituted benzhydrylium ions were used to study kinetics of the ionizations of adducts with intermediate nucleofuges, and donor substituted benzhydrylium ions, i.e. good electrofuges, were employed for studying rates of ionizations of adducts incorporating poor nucleofuges.

Fig. 10: The benzhydrylium approach for the determination of nucleofugalities, i.e. leaving group abilities in a certain solvent.
Fig. 10:

The benzhydrylium approach for the determination of nucleofugalities, i.e. leaving group abilities in a certain solvent.

After establishing that the ionization step of the corresponding SN1 reactions was rate-determining, solvolysis rate constants at 25°C [40] were subjected to a least squares minimization according to equation (4) for the determination of the solvent-independent electrofugality parameters Efas well as the parameters Nf and sf, which characterize the leaving group ability of a certain nucleofuge in a specific solvent. Two parameters were pre-defined: Ef=0 for (4-MeOC6H4)2CH+and sf=1.0 for Cl in EtOH.

(4)lgk(25°C)=sf(Ef+Nf)

Subsequent to our 2010 review [41], which reports more than 150 nucleofugalities of ionic and neutral leaving groups in different solvents, a large number of further nucleofuges have been characterized, mostly by the Zagreb group [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52]. When electrofuges and nucleofuges are ordered as shown in Fig. 11, adducts composed from carbocations and leaving groups on the same level ionize with a half-life of approximately 2 h at 25°C [54].

Fig. 11: A semiquantitative model for heterolysis reactions (with data from [41], [52], [53]). Adducts from nucleofuges and electrofuges on the same horizontal line separate heterolytically with a half-life of 2 h at 25°C.
Fig. 11:

A semiquantitative model for heterolysis reactions (with data from [41], [52], [53]). Adducts from nucleofuges and electrofuges on the same horizontal line separate heterolytically with a half-life of 2 h at 25°C.

Just by inspection of Fig. 11 it becomes clear that solvolyses of (4-MeOC6H4)2CH–Cl in typical solvolytic media (aqueous alcohols or aqueous acetone) will occur in the sub-second time regime at room temperature, whereas the solvolyses of the corresponding nitro- and dinitrobenzoates proceed in the conveniently measurable time scale of minutes to hours.

By looking at Fig. 11 one can immediately understand, why H.C. Brown selected 90% aqueous acetone (90A10W) to measure solvolysis rates of substituted cumyl chlorides, ArC(CH3)2Cl, for the determination of σp+ substituent parameters [55]: solvolyses in aqueous alcohols would have been too fast for the instrumentation available at that time.

Figure 11 furthermore gives a clue why Winstein and co-workers used 80% aqueous ethanol as standard solvent for most kinetic studies of solvolysis reactions [56], [57], [58], [59], [60], [61], [62], [63]: This is the solvent mixture, in which tert. alkyl chlorides and bromides solvolyze with conveniently measurable rates at 25°C.

Like the philicity scales discussed in the previous chapter, the fugality scales based on equation (4) provide highly reliable predictions for the heterolytic cleavages of benzhydryl derivatives [64], whereas predictions for other types of substrates are much less accurate, and deviations up to a factor of 100 are encountered [53] – tolerable for qualitative predictions in view of the 20 orders of magnitude covered by equation (4).

Correlations between the different scales

As shown in Fig. 2, pKaH values of structurally different types of anions are not a reliable guide for predicting their nucleophilic reactivities. Using the rate and equilibrium constants for the reactions of nucleophiles with benzhydrylium ions, reported in the previous chapters, we can now examine whether the splitting-up of Brønsted correlations in Fig. 2 is only due to the fact that the pKaH values refer to associations with the proton, while the kinetic data refer to attack of the nucleophiles at a carbon atom.

Figure 12 shows that the correlation between rate and equilibrium constants is also poor when kinetics [31] and thermodynamics [7] refer to the same processes. This observation is in line with earlier conclusions that nucleophilic reactivities do not only depend on the corresponding thermodynamic driving forces but that many other factors have to be considered in addition [65], [66], [67].

Fig. 12: Correlation of the reactivities of nucleophiles toward the 4,4′-(bis(dimethylamino)phenyl)methylium ion (dma)2CH+ with their Lewis basicities LBMeCN (in MeCN at 20°C, open symbols: lg k extrapolated by using eqation (3)).
Fig. 12:

Correlation of the reactivities of nucleophiles toward the 4,4′-(bis(dimethylamino)phenyl)methylium ion (dma)2CH+ with their Lewis basicities LBMeCN (in MeCN at 20°C, open symbols: lg k extrapolated by using eqation (3)).

Due to the scarcity of appropriate data, analogous relationships between Lewis acidity, electrophilicity, and electrofugality of carbocations found much less attention [68], [69], [70], [71], [72], [73], [74], [75], [76], [77]. Using the rate and equilibrium constants for the reactions of p- and m-substituted benzhydrylium ions reported in the sections above, we can now analyze these relationships in detail.

The general trend exhibited by Fig. 13 is in line with expectation: As the electron-donating abilities of the substituents in the benzhydrylium ions decrease from left to right, Lewis acidity LA [7] and electrophilicity E [15] increase, while electrofugality Ef (that is, reactivity in SN1 reactions) [41] decreases.

Fig. 13: Correlations of electrofugality Ef (top) and electrophilicity E (bottom) with Lewis acidities LA of benzhydrylium ions (in dichloromethane at 20°C, with data from [7], [15], [41], see Fig. 6 for abbreviations).
Fig. 13:

Correlations of electrofugality Ef (top) and electrophilicity E (bottom) with Lewis acidities LA of benzhydrylium ions (in dichloromethane at 20°C, with data from [7], [15], [41], see Fig. 6 for abbreviations).

Most interesting is the deviation pattern from this general trend, however. The areas marked in green [(lil)2CH+ and (jul)2CH+] and red [(ind)2CH+, (thq)2CH+, and (pyr)2CH+] characterize benzhydrylium ions with similar Lewis acidities but variable electrophilicities and electrofugalities. The amazing observation: The patterns in the two green and the two red fields are exactly the same, i.e. structural variations within these fields affect electrophilicities and electrofugalties in the same sense. How can one explain this counter-intuitive phenomenon that within these colored fields, a structural variation which increases the electrophilicity of a benzhydrylium ion also increases the rate of its formation in an SN1 reaction?

Marcus equation (5) expresses the Gibbs energy of activation (∆G) as a function of the Gibbs reaction energy (∆G°) and the intrinsic barrier (∆G0), which equals ∆Gfor a reaction with ∆G°=0 [78], [79], [80].

(5)ΔG=ΔG0+0.5ΔG°+((ΔG°)2/16ΔG0)

Figure 14 illustrates rate and equilibrium constants for the reactions of the two best-stabilized benzhydrylium ions of this series, (lil)2CH+ and (jul)2CH+, with an isothiourea derivative [81].

Fig. 14: Comparison of rate and equilibrium constants for the reactions of 2,3,6,7-tetrahydro-5H-thiazolo[3,2-a]pyrimidine with two equally Lewis acidic benzhydrylium ions (with data from [81]).
Fig. 14:

Comparison of rate and equilibrium constants for the reactions of 2,3,6,7-tetrahydro-5H-thiazolo[3,2-a]pyrimidine with two equally Lewis acidic benzhydrylium ions (with data from [81]).

The equal equilibrium constants K for both reactions shown in Fig. 14 imply that (jul)2CH+ and (lil)2CH+ have identical Lewis acidities (i.e. equal ∆G°) [82]. The higher electrophilic reactivity of (jul)2CH+ (i.e. lower ∆G), must, therefore, be due to a lower intrinsic barrier (∆G0). Since a change of the intrinsic barrier affects forward and backward reactions in the same sense, (jul)2CH+must not only be a better electrophile but also a better electrofuge than (lil)2CH+ as shown in Fig. 13. As the intrinsic barriers are related to the reorganization energies λ (λ=4∆G0), we must conclude that reorganization of the five-membered ring in (lil)2CH+ is energetically more demanding than reorganization of the six-membered ring in (jul)2CH+.

The comparison of (ind)2CH+ and (thq)2CH+ in Fig. 13 reveals the same trend. The benzhydrylium ion (ind)2CH+with an annelated 5-membered heterocyclic ring is a weaker electrophile as well as a weaker electrofuge than (thq)2CH+ with an annelated 6-membered heterocyclic ring. The analogous reactivity patterns in the marked areas of Fig. 13 are exemplary for a general phenomenon. Whenever carbocations of similar Lewis acidity (less precise: similar stability) differ in their electrophilicity or electrofugality, the differences are always in the same direction, i.e. the better electrophile is also the better electrofuge.

The same line of arguments has been used to solve an old mystery: Why do vinyl bromide solvolyses show common ion rate depression [83], which is indicative of high selectivity of the intermediate carbocations [84], [85], [86]? Since the low SN1 reactivities of vinyl derivatives had been associated with the formation of highly reactive, unselective intermediate carbocations, it was surprising that in many cases, the intermediate vinyl cations were not immediately trapped by the solvent, but partially underwent recombination with the anionic leaving group.

Quantum chemical calculations showed that the p-anisyl substituted vinyl cation depicted in Fig. 15 has almost the same Lewis acidity (gas phase) toward different anions as the parent benzhydrylium ion [87].

Fig. 15: Calculated (TPSSTPSS/def2TZVP+GD3) gas phase Gibbs energies for the reactions of Br− with sp2- and sp-hybridized carbocations (data from [87]).
Fig. 15:

Calculated (TPSSTPSS/def2TZVP+GD3) gas phase Gibbs energies for the reactions of Br with sp2- and sp-hybridized carbocations (data from [87]).

The 1.5 million slower solvolysis of the vinyl bromide in Fig. 16 must be due, therefore, to the higher intrinsic barrier of the sp2sp rehybridization (right part of Fig. 16) than of the sp3sp2 rehybridization (left part of Fig. 16). In accord with this conclusion, vinyl cations also react more slowly with nucleophiles than trivalent carbenium ions of equal Lewis acidity. Accordingly, laser flash photolytically generated benzhydryl cations have been found to undergo diffusion controlled reactions with bromide ions in various solvents [85], while a barrier of 34 kJ mol−1 has been extrapolated for the reaction of the vinyl cation with Br in 80% aqueous ethanol [87]. Due to the high intrinsic barrier, the transition state of the vinyl bromide solvolysis is not carbocation-like, which explains the occurrence of common ion return.

Fig. 16: Gibbs energy profiles (kJ mol−1) for the ionization of bromodiphenylmethane and 1-bromo-1-(4-methoxyphenyl)-2,2-diphenylethene in 80% aqueous ethanol at 25°C. For the solvolysis step of Ph2C=C(ani)Br, a value of k=1.92×10−4 s−1 was measured at 120°C [88]; reported activation parameters allow extrapolation to the value at 25°C given in this Figure. The rate constant for the Ph2CHBr solvolysis is from [89].
Fig. 16:

Gibbs energy profiles (kJ mol−1) for the ionization of bromodiphenylmethane and 1-bromo-1-(4-methoxyphenyl)-2,2-diphenylethene in 80% aqueous ethanol at 25°C. For the solvolysis step of Ph2C=C(ani)Br, a value of k=1.92×10−4 s−1 was measured at 120°C [88]; reported activation parameters allow extrapolation to the value at 25°C given in this Figure. The rate constant for the Ph2CHBr solvolysis is from [89].

Conclusions

The Marcus equation (eq. 5) describes Gibbs activation energies ΔG by a combination of the Gibbs reaction energy ΔG0 and the intrinsic barrier ΔG0. For that reason, the term “kinetic effect” is ambiguous, as changes in the Gibbs activation energies (ΔΔG) may have a thermodynamic (product-stabilizing factor ΔΔG0) or an intrinsic (ΔΔG0) origin.

While deviations from correlations between nucleophilicity and basicity have often been observed, we have now shown that differences in intrinsic barriers may also cause deviations from the correlations between electrofugalities, electrophilicities, and Lewis acidities. Whereas electrophilicities generally increase and electrofugalities generally decrease with increasing Lewis acidities of carbocations (less precise: “decreasing carbocation stability”), variations in intrinsic barriers may overcompensate variations in the ∆G° term. As a consequence, a carbocation (R1)+ which is more electrophilic than a carbocation (R2)+ of equal Lewis acidity will also have higher electrofugality, i.e. be formed faster in an SN1 reaction.


Dedicated to the memory of George A. Olah, a dear friend and mentor.

Article note:

A collection of invited papers based on presentations at the 23rd IUPAC Conference on Physical Organic Chemistry (ICPOC-23), Sydney, Australia, 3–8 July, 2016.


Acknowledgements

We thank all associates and collaboration partners mentioned in the references for their contributions and Prof. J.-P. Cheng for providing the photograph of Prof. F. G. Bordwell. Financial support by the Deutsche Forschungsgemeinschaft (SFB 749, project B1) is gratefully acknowledged.

References

[1] H. Mayr. Isr. J. Chem.56, 30 (2016).10.1002/ijch.201400200Search in Google Scholar

[2] F. G. Bordwell, J. C. Branca, T. A. Cripe. Isr. J. Chem.26, 357 (1985).10.1002/ijch.198500120Search in Google Scholar

[3] F. G. Bordwell, T. A. Cripe, D. L. Hughes. in Nucleophilicity, J. M. Harris, S. P. McManus (Eds.), pp. 137–153. American Chemical Society, Washington DC (1987).10.1021/ba-1987-0215.ch009Search in Google Scholar

[4] T. A. Cripe. PhD dissertation, Northwestern University, Illinois (1986).Search in Google Scholar

[5] The problem of different references for rate and equilibrium constants in most Brønsted correlations has been discussed by Hine, who suggested a method to determine relative Lewis basicities toward C-centered Lewis acids, which he called “carbon basicities”: J. Hine, R. D. Weimar Jr. J. Am. Chem. Soc.87, 3387 (1965).10.1021/ja01093a018Search in Google Scholar

[6] H. Mayr, A. R. Ofial. Acc. Chem. Res.49, 952 (2016).10.1021/acs.accounts.6b00071Search in Google Scholar PubMed

[7] H. Mayr, J. Ammer, M. Baidya, B. Maji, T. A. Nigst, A. R. Ofial, T. Singer. J. Am. Chem. Soc.137, 2580 (2015).10.1021/ja511639bSearch in Google Scholar PubMed

[8] E. Follet, P. Mayer, H. Mayr. Eur J. Org. Chem. 4050 (2016).10.1002/ejoc.201600572Search in Google Scholar

[9] E. Follet, P. Mayer, G. Berionni. Chem. Eur. J.23, 623 (2017).10.1002/chem.201603963Search in Google Scholar PubMed

[10] M. Horn, H. Mayr. J. Phys. Org. Chem.25, 979 (2012).10.1002/poc.2979Search in Google Scholar

[11] A. R. Ofial. Pure Appl. Chem.87, 341 (2015).10.1515/pac-2014-1116Search in Google Scholar

[12] D. W. Stephan. J. Am. Chem. Soc.137, 10018 (2015).10.1021/jacs.5b06794Search in Google Scholar

[13] D. W. Stephan, G. Erker. Angew. Chem. Int. Ed.54, 6400 (2015).10.1002/anie.201409800Search in Google Scholar

[14] H. Mayr, M. Patz. Angew. Chem. Int. Ed. Engl.33, 938 (1994).10.1002/anie.199409381Search in Google Scholar

[15] H. Mayr, T. Bug, M. F. Gotta, N. Hering, B. Irrgang, B. Janker, B. Kempf, R. Loos, A. R. Ofial, G. Remennikov, H. Schimmel. J. Am. Chem. Soc.123, 9500 (2001).10.1021/ja010890ySearch in Google Scholar

[16] R. Lucius, R. Loos, H. Mayr. Angew. Chem. Int. Ed.41, 91 (2002).10.1002/1521-3773(20020104)41:1<91::AID-ANIE91>3.0.CO;2-PSearch in Google Scholar

[17] H. Mayr, B. Kempf, A. R. Ofial. Acc. Chem. Res.36, 66 (2003).10.1021/ar020094cSearch in Google Scholar

[18] H. Mayr, A. R. Ofial. in Carbocation Chemistry, G. A. Olah, G. K. S. Prakash (Eds.), Chap. 13, pp. 331–358, Wiley, Hoboken (2004).Search in Google Scholar

[19] A. R. Ofial, H. Mayr. Macromol. Symp.215, 353 (2004).10.1002/masy.200451127Search in Google Scholar

[20] H. Mayr, A. R. Ofial. Pure Appl. Chem.77, 1807 (2005).10.1351/pac200577111807Search in Google Scholar

[21] H. Mayr, A. R. Ofial. J. Phys. Org. Chem.21, 584 (2008).10.1002/poc.1325Search in Google Scholar

[22] H. Mayr. Angew. Chem. Int. Ed.50, 3612 (2011).10.1002/anie.201007923Search in Google Scholar

[23] H. Mayr, S. Lakhdar, B. Maji, A. R. Ofial. Beilstein J. Org. Chem.8, 1458 (2012).10.3762/bjoc.8.166Search in Google Scholar

[24] J. Ammer, C. Nolte, H. Mayr. J. Am. Chem. Soc.134, 13902 (2012).10.1021/ja306522bSearch in Google Scholar

[25] M. Horn, L. H. Schappele, G. Lang-Wittkowski, H. Mayr, A. R. Ofial. Chem. Eur. J.19, 249 (2013).10.1002/chem.201202839Search in Google Scholar

[26] H. Mayr, A. R. Ofial. SAR QSAR Environ. Res.26, 619 (2015).10.1080/1062936X.2015.1078409Search in Google Scholar

[27] R. Lucius, H. Mayr. Angew. Chem. Int. Ed.39, 1995 (2000).10.1002/1521-3773(20000602)39:11<1995::AID-ANIE1995>3.0.CO;2-ESearch in Google Scholar

[28] H. Mayr, R. Schneider, C. Schade, J. Bartl, R. Bederke. J. Am. Chem. Soc.112, 4446 (1990).10.1021/ja00167a049Search in Google Scholar

[29] C. D. Ritchie. Acc. Chem. Res.5, 348 (1972).10.1021/ar50058a005Search in Google Scholar

[30] C. D. Ritchie. Can. J. Chem.64, 2239 (1986).10.1139/v86-370Search in Google Scholar

[31] H. Mayr, A. R. Ofial. Mayr’s Database of Reactivity Parameters. Version 2 (2016). http://www.cup.lmu.de/oc/mayr/DBintro.html.Search in Google Scholar

[32] A. Gualandi, L. Mengozzi, E. Manoni, P. G. Cozzi. Chem. Rec.16, 1228 (2016).10.1002/tcr.201500299Search in Google Scholar

[33] Q. Chen, P. Mayer, H. Mayr. Angew. Chem. Int. Ed.55, 12664 (2016).10.1002/anie.201601875Search in Google Scholar

[34] S. Chelli, K. Troshin, P. Mayer, S. Lakhdar, A. R. Ofial, H. Mayr. J. Am. Chem. Soc.138, 10304 (2016).10.1021/jacs.6b05768Search in Google Scholar PubMed

[35] S. Lakhdar, J. Ammer, H. Mayr. Angew. Chem. Int. Ed.50, 9953 (2011).10.1002/anie.201103683Search in Google Scholar PubMed

[36] K. A. Ahrendt, C. J. Borths, D. W. C. MacMillan. J. Am. Chem. Soc.122, 4243 (2000).10.1021/ja000092sSearch in Google Scholar

[37] W. S. Jen, J. J. M. Wiener, D. W. C. MacMillan. J. Am. Chem. Soc.122, 9874 (2000).10.1021/ja005517pSearch in Google Scholar

[38] N. A. Paras, D. W. C. MacMillan. J. Am. Chem. Soc.123, 4370 (2001).10.1021/ja015717gSearch in Google Scholar PubMed

[39] G. Lelais, D. W. C. MacMillan. Aldrichimica Acta39, 79 (2006).Search in Google Scholar

[40] The reference temperature 25°C was selected to make use of the numerous rate constants reported in the literature at this temperature.Search in Google Scholar

[41] N. Streidl, B. Denegri, O. Kronja, H. Mayr. Acc. Chem. Res.43, 1537 (2010).10.1021/ar100091mSearch in Google Scholar PubMed

[42] M. Matic, B. Denegri, O. Kronja. Eur. J. Org. Chem. 6019 (2010).10.1002/ejoc.201000784Search in Google Scholar

[43] B. Denegri, O. Kronja. Croat. Chem. Acta83, 223 (2010).10.1002/ejoc.200901327Search in Google Scholar

[44] S. Juric, B. Denegri, O. Kronja. J. Org. Chem.75, 3851 (2010).10.1021/jo100327cSearch in Google Scholar PubMed

[45] S. Juric, B. Denegri, O. Kronja. J. Phys. Org. Chem.25, 147 (2012).10.1002/poc.1886Search in Google Scholar

[46] M. Matic, B. Denegri, O. Kronja. J. Org. Chem.77, 8986 (2012).10.1021/jo3013308Search in Google Scholar PubMed

[47] M. Matic, B. Denegri, O. Kronja. Croat. Chem. Acta85, 585 (2012).10.5562/cca2179Search in Google Scholar

[48] M. Matic, B. Denegri, O. Kronja. Eur. J. Org. Chem. 1477 (2014).10.1002/ejoc.201301574Search in Google Scholar

[49] S. Juric, O. Kronja. J. Phys. Org. Chem. 28, 314 (2015).10.1002/poc.3412Search in Google Scholar

[50] M. Horn, C. Metz, H. Mayr. Eur. J. Org. Chem. 6476 (2011).10.1002/ejoc.201100912Search in Google Scholar

[51] C. Nolte, J. Ammer, H. Mayr. J. Org. Chem.77, 3325 (2012).10.1021/jo300141zSearch in Google Scholar PubMed

[52] K. Troshin, H. Mayr. J. Org. Chem.78, 2649 (2013).10.1021/jo302766kSearch in Google Scholar PubMed

[53] B. Denegri, A. R. Ofial, S. Juric, A. Streiter, O. Kronja, H. Mayr. Chem. Eur. J.12, 1657 (2006).10.1002/chem.200500847Search in Google Scholar PubMed

[54] For Ef + Nf=–4 and sf=1.0, k=10−4 s−1.Search in Google Scholar

[55] H. C. Brown, J. D. Brady, M. Grayson, W. H. Bonner. J. Am. Chem. Soc.79, 1897 (1957).10.1021/ja01565a035Search in Google Scholar

[56] E. Grunwald, S. Winstein. J. Am. Chem. Soc.70, 846 (1948).10.1021/ja01182a117Search in Google Scholar

[57] S. Winstein, E. Grunwald, H. W. Jones. J. Am. Chem. Soc.73, 2700 (1951).10.1021/ja01150a078Search in Google Scholar

[58] A. H. Fainberg, S. Winstein. J. Am. Chem. Soc.78, 2770 (1956).10.1021/ja01593a033Search in Google Scholar

[59] A. H. Fainberg, S. Winstein. J. Am. Chem. Soc.79, 1597 (1957).10.1021/ja01564a021Search in Google Scholar

[60] A. H. Fainberg, S. Winstein. J. Am. Chem. Soc.79, 1602 (1957).10.1021/ja01564a022Search in Google Scholar

[61] A. H. Fainberg, S. Winstein. J. Am. Chem. Soc.79, 1608 (1957).10.1021/ja01564a023Search in Google Scholar

[62] S. Winstein, A. H. Fainberg, E. Grunwald. J. Am. Chem. Soc.79, 4146 (1957).10.1021/ja01572a046Search in Google Scholar

[63] S. Winstein, A. H. Fainberg. J. Am. Chem. Soc.79, 5937 (1957).10.1021/ja01579a027Search in Google Scholar

[64] H. Mayr, A. R. Ofial. Pure Appl. Chem.81, 667 (2009).10.1351/PAC-CON-08-08-26Search in Google Scholar

[65] J. O. Edwards. J. Am. Chem. Soc.78, 1819 (1956).10.1021/ja01590a012Search in Google Scholar

[66] J. O. Edwards, R. G. Pearson. J. Am. Chem. Soc.84, 16 (1962).10.1021/ja00860a005Search in Google Scholar

[67] J. F. Bunnett. Annu. Rev. Phys. Chem.14, 271 (1963).10.1146/annurev.pc.14.100163.001415Search in Google Scholar

[68] T. L. Amyes, I. W. Stevens, J. P. Richard. J. Org. Chem.58, 6057 (1993).10.1021/jo00074a036Search in Google Scholar

[69] J. P. Richard, T. L. Amyes, L. Bei, V. Stubblefield. J. Am. Chem. Soc.112, 9513 (1990).10.1021/ja00182a010Search in Google Scholar

[70] J. P. Richard, T. L. Amyes, M. M. Toteva. Acc. Chem. Res.34, 981 (2001).10.1021/ar0000556Search in Google Scholar

[71] M. M. Toteva, J. P. Richard. Adv. Phys. Org. Chem.45, 39 (2011).Search in Google Scholar

[72] Y. Tsuji, M. M. Toteva, H. A. Garth, J. P. Richard. J. Am. Chem. Soc.125, 15455 (2003).10.1021/ja037328nSearch in Google Scholar

[73] J. P. Richard, K. B. Williams. J. Am. Chem. Soc.129, 6952 (2007).10.1021/ja071007kSearch in Google Scholar

[74] C. F. Bernasconi. J. Phys. Org. Chem.17, 951 (2004).10.1002/poc.810Search in Google Scholar

[75] C. F. Bernasconi, Z. Rappoport. Acc. Chem. Res.42, 993 (2009).10.1021/ar900048qSearch in Google Scholar

[76] C. F. Bernasconi. Adv. Phys. Org. Chem.44, 223 (2010).10.1016/S0065-3160(08)44005-4Search in Google Scholar

[77] R. More O’Ferrall. Adv. Phys. Org. Chem.44, 19 (2010).Search in Google Scholar

[78] R. A. Marcus. J. Phys. Chem.72, 891 (1968).10.1021/j100849a019Search in Google Scholar

[79] R. A. Marcus. J. Am. Chem. Soc.91, 7224 (1969).10.1021/ja01054a003Search in Google Scholar

[80] W. J. Albery. Annu. Rev. Phys. Chem.31, 227 (1980).10.1146/annurev.pc.31.100180.001303Search in Google Scholar

[81] B. Maji, C. Joannesse, T. A. Nigst, A. D. Smith, H. Mayr. J. Org. Chem.76, 5104 (2011).10.1021/jo200803xSearch in Google Scholar

[82] The small differences of the Lewis acidities of these two carbenium ions shown in Fig. 13 is the result of averaging a large number of equilibrium constants.Search in Google Scholar

[83] P. Stang, Z. Rappoport, M. Hanack, L. R. Subramanian. Vinyl Cations. Academic Press, New York (1979).Search in Google Scholar

[84] D. J. Raber, J. M. Harris, P. v. R. Schleyer. in Ions and Ion Pairs in Organic Reactions, M. Swarcz, (Ed.), Vol. 2, pp. 247–374, Wiley, New York (1974).Search in Google Scholar

[85] S. Minegishi, R. Loos, S. Kobayashi, H. Mayr. J. Am. Chem. Soc.127, 2641 (2005).10.1021/ja045562nSearch in Google Scholar

[86] T. Kitamura, H. Taniguchi. in Dicoordinated Cations, Z. Rappoport, P. J. Stang, (Eds.), Chapter 7, pp 321–376, Wiley, New York (1997).Search in Google Scholar

[87] P. A. Byrne, S. Kobayashi, E.-U. Würthwein, J. Ammer, H. Mayr. J. Am. Chem. Soc.139, 1499 (2017).10.1021/jacs.6b10889Search in Google Scholar

[88] Z. Rappoport, A. Gal. J. Am. Chem. Soc.91, 5246 (1969).10.1021/ja01047a012Search in Google Scholar

[89] K.-T. Liu, C.-P. Chin, Y.-S. Lin, M.-L. Tsao. Tetrahedron Lett.36, 6919 (1995).10.1016/0040-4039(95)01430-PSearch in Google Scholar

Published Online: 2017-03-18
Published in Print: 2017-06-27

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