A Unified Framework for Understanding Nucleophilicity and Protophilicity in the SN2/E2 Competition

Abstract The concepts of nucleophilicity and protophilicity are fundamental and ubiquitous in chemistry. A case in point is bimolecular nucleophilic substitution (SN2) and base‐induced elimination (E2). A Lewis base acting as a strong nucleophile is needed for SN2 reactions, whereas a Lewis base acting as a strong protophile (i.e., base) is required for E2 reactions. A complicating factor is, however, the fact that a good nucleophile is often a strong protophile. Nevertheless, a sound, physical model that explains, in a transparent manner, when an electron‐rich Lewis base acts as a protophile or a nucleophile, which is not just phenomenological, is currently lacking in the literature. To address this fundamental question, the potential energy surfaces of the SN2 and E2 reactions of X−+C2H5Y model systems with X, Y = F, Cl, Br, I, and At, are explored by using relativistic density functional theory at ZORA‐OLYP/TZ2P. These explorations have yielded a consistent overview of reactivity trends over a wide range in reactivity and pathways. Activation strain analyses of these reactions reveal the factors that determine the shape of the potential energy surfaces and hence govern the propensity of the Lewis base to act as a nucleophile or protophile. The concepts of “characteristic distortivity” and “transition state acidity” of a reaction are introduced, which have the potential to enable chemists to better understand and design reactions for synthesis.


Introduction
The ability to rationally design chemical reactions is one of the fundamental challenges in chemistry.U nraveling the processes that dictate the courser eactants take along ap otential energy surface( PES) paves the way to such design and may lead to the discovery of new chemistry.T wo prototypical reactions in organic chemistry that feature in many routes in organic synthesis are bimolecular nucleophilic substitution (S N 2) and baseinduced elimination (E2). [1,2] S N 2r eactions (i.e.,n ucleophilic attack) are in principle alwaysi nc ompetition with E2 reactions (i.e.,p rotophilic attack),w hich opens the possibility and the necessity to actively tune reactivity toward the desired path-way to maximize the formationoft he targetedc ompound and to avoid unwanted side products (see Scheme 1).
Over the past decades, valuable insights have emerged from experimental [3] and theoretical studies [4] on the trends in S N 2 and E2 reactivity,a sw ell as the nature of the reactions' potential energy surfaces. [2a] The direct competition between substitution and elimination pathways of anionic Lewis bases with alkyl substrates is af undamental problem and the factors that influence this competition in solution have been studied extensively. [4j, 5, 6] Recently,W ue tal. [7] explored the competition between gas phase S N 2and E2 pathways for arange of anionic Lewis bases reacting with ethyl chloride. They consolidated our earlierf inding that the unfavorably high activation strain, DE°s train ,o ft he E2 pathway can be overruled by as trongly sta-bilizing transition state (TS) interaction, DE°i nt ,e ventually leading to ap reference forE 2o ver S N 2. [4c] Nucleophilicity and leaving group ability in S N 2r eactions have been related to various properties of X À (the nucleophile) and Y( the leaving group), [8] such as electronegativity,s ize, polarizability,a nd others. Nevertheless, the state of the art is to some extents till phenomenological. More recently,i tw as established that the height of S N 2 reactionb arriers is directly determined by the stability of the nucleophile's (X À )h ighest occupied molecular orbital (HOMO) and by the strengtho ft he substrate's carbon-leaving group bond (CÀY): ah ighere lectron-donatingc apability of the X À HOMO or aw eaker CÀYb ond leads to al ower barrier and vice versa. [4i] The same relations were found by Shaik et al. by using the valenceb ond (VB) model,w ho predicted that the height of the S N 2b arrier depends on the vertical ionization energy of the nucleophile (I X:-)m inus the electron affinity of the CÀY bond (A CÀY ). [4q,r] Where I X:-is directly relatedt ot he energy of the HOMO and A CÀY is dominated by the strength of the CÀY bond.
Herein,w ed evelop,b ased on quantum chemical analyses, a unified model that provides chemists with the tools to readily understand the dualityo fL ewis bases, that is their nucleophilic or protophilic character.T ot his end, we have explored and analyzed the potential energy surfaces along the reactionc oordinates of the S N 2s ubstitution, anti-E2 elimination (E2-a), and syn-E2 elimination (E2-s) reactions of X À + C 2 H 5 Y, with X, Y = F, Cl, Br,I ,a nd At, by using relativistic density functional theory (DFT) at ZORA-OLYP/TZ2P. [9] The C 2 H 5 Ys ubstrate allows us to probe the direct competition between S N 2a nd E2, and our findings can be extended to any substrate where the acidic hydrogen and the leaving group are electronicallyc oupled. In the first place, thesee xplorations provide us with ac onsistent overview of reactivity trendso ver aw ide range of reactivities and pathways. More importantly,a nalyses of these consistent reactivity data based on the activation strain model (ASM)o f reactivity [4c, 10] reveal the factorst hat determine the shape of the potential energy surfaces and hence govern the propensity of the Lewis base to act as an ucleophile or protophile, namely:( i) the "characteristic distortivity" of the substrate, which is associated with ap articular reactionm echanism; (ii)the electron-donating capabilityo ft he Lewis base, which enters into an acid-base like interaction with the substrate; and (iii)the strength of the C a -leaving group bond. In the course of our analyses, we develop the concepts of "intrinsic nucleophilicity", "apparent nucleophilicity", and "transition state acidity", which are associatedw ithaparticulart ype of reaction. These concepts will provide chemistsw ith rational design principles that will enable the design of selectives ynthetic routes to targeted products.

Main trends in reactivity
The resultso fo ur ZORA-OLYP/TZ2P computations on the S N 2 and E2 reactions in Scheme1 are collected in Table 1, in Figure 1- Figure 8, and in the Supporting Information. Ta ble 1 containst he energies of stationary points along the variousr eaction profiles relative to the energy of the infinitely separated reactants. Structural datao fs tationary points are shown in Figure 1f or the two representative reactions 1b and 2a;f ull structurald ata fora ll stationary points are provided in Figure S1 and Ta bleS1i nt he Supporting Information.
In mostc ases, the S N 2, anti-E2, and syn-E2 model reactions proceedv ia ar eactant complex (RC) andatransition state (TS) towardsaproduct complex (PC), which may eventually dissociate into products (see Ta ble 1and Figure 1);exceptionsare discussedl ater on. Schematic representations of such reaction profiles are shown in Figure 2a for an exothermic reaction. In the case of anti-E2 elimination, the initial transition state (TS1) constitutes the actual elimination process and leads to an intermediate complex (INT) in which the conjugated acid forms an X-H···p complex with the newly formed ethylene and the leaving group Y À hydrogen binds to an ethylene C a ÀHb ond (see Figure 1f or selected structures and Figure 2b for as chematic anti-E2 reactionp rofile). From here, migration of XH to the leaving group leads, via as econd transition state (TS2), to the PC, H 2 C=CH-H··· À YHX, which,f or our model reactions, [11] is identicaltot hat of syn-E2 elimination. In all cases,T S1 is higher in energy than TS2 and, therefore, rate-determining for the overall anti-E2 pathway.T he energeticallyf avoredp roducts for both anti-E2 and syn-E2 pathways are C 2 H 4 + YHX À ,t hat is, the olefin plus the leavingg roup, microsolvated by the conjugate acid. An umber of clear and general trendsi nr eactivity can be discerned. Reaction barriers alwaysi ncrease as the Lewis base X À becomes less basic, along F À ,C l À ,B r À ,I À ,a nd At À (see Ta ble 1). [12] Note that in the gas phase, it is possible to have negative barriers with respect to the separater eactants, because under these conditions, in many cases, the nucleophile forms an encounter complex (sometimes referred to as an iondipolec omplex) with the substrate, which is stabilized by both electrostatic and donor-acceptor orbitali nteractions. Interestingly,r eaction barriers rise more rapidly along this series for E2 than for S N 2r eactions (note that TS1 is rate-determining for all anti-E2 reactions). This trend can be found for all of the C 2 H 5 Y substrates. As ac onsequence, the preferred reaction pathway switches from anti-E2, in the cases where F À attacks the substrate,t oS N 2f or the heavierh alide anions. For example, along F À ,C l À ,B r À ,I À ,a nd At À + C 2 H 5 Cl, the S N 2r eaction barrier( S N 2-TS in Ta ble 1) moderately increases from À17.5 to + 4.0, + 8.5, + 12.4, and + 13.0 kcal mol À1 ,r espectively,w hereas the anti-E2 barrier( E2-a-TS1 in Ta ble 1) rises more steeply from À23.3 to + 10.7, + 21.4, + 31.1, and + 33.9 kcal mol À1 ,r espectively.T hus, although anti-E2 prevails for the more basic halide F À ,w ith a reactionb arriert hat is 5.8 kcal mol À1 lower than the S N 2p athway,t he S N 2p athway dictates for all heavier,less basic, halides, with an anti-E2 barrier for At À that is 20.9 kcal mol À1 higher than the S N 2p athway.T his is in line with the work of Shaik et al.,w ho showed, with the use of valence bond (VB) theory, that strong Lewis bases prefer the E2 pathway. [13] The syn-E2 pathway is in all cases less reactive than anti-E2.
Our computations show that less basic halides, that is, those with al ower protona ffinity,a re both worse nucleophiles and worse protophiles, in the sense that they lead to higherb arriers for substitution (nucleophilic attack) as well as for elimination (protophilica ttack) reactions along the series F À < Cl À < Br À < I À < At À .T hus, if there were no competing E2 channels, for example, in the aforementioned reaction systems X À + CH 3 Y, [4i] as tronger Lewis base is ab etter nucleophile. This is what we designate as "intrinsic nucleophilicity".H owever, our computations also show that the lowering of reaction barriers for the protophilic attack benefits more from increasing the basicity than that for the nucleophilic attack. Thus, if the basicity becomes stronge nough, the protophilic character Table 1. Energies relative to reactants (in kcal mol À1 )o ft he stationary points occurring in S N 2, anti-E2, and syn-E2 reactions of X E2-a-TS2 of X À prevails. In this situation of mechanistic competition, we speak about the "apparent nucleophilicity". Note that weaker Lewis bases proceed with ar educed intrinsic nucleophilicity (i.e.,h igherS N 2b arrier) but an enhanced apparent nucleophilicity (i.e.,m ore favorable S N 2b arrier compared with E2 barrier).T he origin of theset rends is analyzed and explained later on, on the basis of the activation strain model (ASM) of reactivity [4c, 10] and quantitativem olecular orbital (MO) theory. [15] Special features of particular reactions The prior discussed trends in S N 2v ersusE 2r eactivity hold for all reactions ystems. But the precise shape of the PES differs in   af ew instances to the extent that the processb ecomess pontaneous,t he reverse barrier disappears, or the product complex becomes labile and leads to as pontaneousf ollow-up reaction.
In the case of the rather exothermic reactions that occur between F À and C 2 H 5 Br,C 2 H 5 I, or C 2 H 5 At, the barrier for the anti-E2 pathway disappearsa nd F À spontaneously abstracts a bproton from C 2 H 5 X( X= Br,I ,A t) to form the product complex E2-a-PC, C 2 H 4 ··· À YHX, withoutt he occurrenceo fastable reactant complex or transition state. The latter has become a shouldero nt he PES alongt he reactionc oordinate, as schematically depicted in Figure 2c.T he barrier for the S N 2r eaction has also disappeared for these reactants, which is in line with our previously obtained results fort he S N 2r eactions F À + CH 3 Br and CH 3 I. [4i] However,t he steepest descent path upon the encounter of the F À + C 2 H 5 Xr eactants leads into the anti-E2 and not the S N 2channel.
The highly endothermic nucleophilic substitutions between Br À ,I À ,a nd At À + C 2 H 5 Fh ave, by symmetry,n or everse barrier (see Figure 2d,r ed dotted curve). Interestingly,w hen following the three forward S N 2p rocesses, we nevertheless do find saddle-pointsa t2 6.5, 32.1, and 33.6 kcal mol À1 ,r espectively (listed in Table 1, as S N 2-TS). This transitions tate is achieved after the actual substitution stage, as the reaction systems begin to deviate from the actual S N 2p ath.W hat happens is that the emergingl eaving group, Y À = F À ,i sarelativelys trong Lewis base, which induces ab arrier-free E2 elimination from the comparatively reactive C 2 H 5 Xm olecule (X = Br,I ,A t) formed in the S N 2r eaction (Scheme 2). This is schematically depicted in Figure 2d,b lue curve. Successive S N 2 + E2 multi-step reactions have also been observed by using mass spectroscopic techniques in other reaction systems. [16] Eventually,t he same E2-a-P product, C 2 H 4 ···FHX À ,i sf ormed as in ad irect E2 reaction between the originalr eactants. For example, in the case of Br À + C 2 H 5 F, the S N 2p athway,w ith ab arriero fo nly 26.5 kcal mol À1 ,d ominates the direct anti-E2 reaction, with ab arrier of 46.0 kcal mol À1 .Y et, also the S N 2p athway leads, via aconcerted S N 2 + E2 mechanism, to the formation of C 2 H 4 and FHBr À and not C 2 H 5 Br and F À .

Activation strain analyses
The results of our activation strain analysis( ASA) [4c, 10] for the representative S N 2a nd anti-E2 reactions of X À and C 2 H 5 Y( X, Y = F, Cl) are collected in Figure 3a nd Figure 5( see Figure S2 in the Supporting Information for all data). The activation strain model involves the decomposition of the electronic energy (DE)i nto two distinct energy terms, namely,t he strain energy (DE strain )a nd the interaction energy (DE int ). The strain energy results from the deformation of the individualr eactants and the interaction energy between the deformed reactants along the reactionc oordinate, defined, in this case, as the stretch of the a-carbon-leaving group (C a ÀY) bond. This criticalr eactionc oordinate undergoesawell-defined change during the reaction from the reactantc omplex via the transition state to the product and is shown to be av alid reactionc oordinate fors tudying substitution reactions. [4i, 17] Note that the syn-E2 pathway always goes with ah igher reactionb arrier than the anti-E2 pathway and, therefore, is excluded from this analysis. In Figure 3, we showh ow the nature of the Lewis base X À (left column) and the leaving group Y( right column) influences the decompositiono ft he potentiale nergy surface (PES) along the reactionc oordinate (z), cf. Eq. (1), for the S N 2r eaction (upper row) and anti-E2 reaction (lower row). The solid curves represent the PES (DE), whereas the dashed and dotted curves represent the strain (DE strain )a nd interaction (DE int )e nergy,r espectively.P anels (a) and (c) comparec urveso fF À + C 2 H 5 F( black) and Cl À + C 2 H 5 F( red) for S N 2a nd anti-E2 reactions, respectively, whereas panels (b) and (d)c ompare curveso fC l À + C 2 H 5 F( red) and Cl À + C 2 H 5 Cl (blue) for S N 2a nd anti-E2 reactions, respectively.N ote that the left andr ight columns sharer eaction 1a, that is, Cl À + C 2 H 5 F. This series is representative for the observede ffects induced by Lewis base and/or leaving group variationsa long the various model reactions. Figure 3a indicates that, in the S N 2r eaction, as tronger nucleophile enhances, in agreement with its increased intrinsic nucleophilicity,t he stabilizing interaction energy over the entire course of the reaction, whereas the strain energy is minimally affected. The reasonf or this more stabilizingi nteraction energy is the stability of the X À n p atomic orbital (AO), which decreases along At À ,I À ,B r À , Cl À ,a nd F À and reduces the corresponding HOMO-LUMO energy gap with the substrate ( Figure 4). [18] This effect can be explained by the size of the AOs of the nucleophile. F À has a less stable HOMO owing to the compactness of fluorine AOs, which experience more destabilizing coulombic repulsion between the electrons compared with the heavier and larger halides. Ab etter leavingg roup, on the other hand, results in a weaker carbon-leaving group bond, that is, lower carbon-leaving group bond enthalpy, [19] which manifests in less destabilizing strain energy,w hereas the interaction energy is hardly affected by varying the leavingg roup (Figure 3b). Similar trends are observed for the E2 reaction. In Figure3c, the variation of the protophile, the situationi ss lightly more complicated as as tronger protophile resultsi na ne arlier proton abstraction,t hat is, an earlierj ump in interaction and strain energy,a longt he reaction coordinate. The interaction energy is largely influenced by the nature of the protophile, because as tronger protophile, due to its enhanced intrinsic nucleophilicity,r esults in am ore stabilizing interaction and, therefore, al ower transition barrier (see above).F urthermore, the nature of the protophile affects the strain energy by abstractingt he proton at different moments along the reaction coordinate, which can be seen as the different positions of the sudden jump in strain energy.T he stronger the base, the earlier it abstracts the proton. Note that the strain energy around the reactanta nd product complexes( i.e.,s tart and end of the activation strain diagram) are nearly consistent and hence not influenced by the nature of the protophile. In line with the S N 2 systems, ab etter leaving group reduces the strain curves, as a result of the prior discussed weaker carbon-leaving group bond, whereas the stabilizing interaction energy remains nearly unchanged (Figure3d). Thus, ab etter Lewis base or leaving group results in both alower S N 2a nd E2 reaction barrier.
To directly analyze and comparet he S N 2a nd E2 pathways, Figure 5shows four panels displayingthe S N 2and E2 pathways of the model reaction: F À + C 2 H 5 F( 1a), F À + C 2 H 5 Cl (1 b), Cl À + C 2 H 5 F( 2a), and Cl À + C 2 H 5 Cl (2 b). Going down ac olumn, we  . Schematic orbital interactiondiagrambetween the filled n p HOMO of X À (F À :left; At À :right) and the LUMO of C 2 H 5 Y( middle). Note that the substrate LUMO has s*antibondingc haracterinb oth the C a ÀYand C b À Hb onds. Chem.E ur.J.2020, 26,15538 -15548 www.chemeurj.org vary the Lewis base, and along ar ow,w ec hange the nature of the leaving group. Note that, for all reactions, the strain and interaction energy curvesf or the E2 reaction display ap rofound difference compared to the S N 2a nalog. As mentioned above,a sudden jump in strain and interaction energy is observed during the E2 reaction. This jump can be attributedt ot he proton abstraction by the Lewis base, which, in E2 reactions, acts as ap rotophile.T he deprotonation of the substrate by the protophile requires al arge deformation in the geometry of the substrate but also resultsi namore stabilizing interaction (see below).
The S N 2p athway intrinsically has al ess destabilizing strain energy than the E2 analog, because alongt he former reaction pathway only one bond (C a ÀY) is being broken, while for the latter two bonds are being broken (C a ÀYand C b ÀH). Thus, the distortion, characteristic for the S N 2p athway,i si nherently lower than the E2 pathway.A tt he same time, the "characteristic distortivity" for both pathways also has direct implications on the electronic structure of the substrate. The LUMO of the substrate has antibonding character in the C a ÀYa nd C b ÀH bonds. The deformation along the S N 2p athway (elongation of C a ÀY) reduces the antibonding overlap for C a ÀY, which,i n turn, stabilizes the LUMO (see Figure 6). For the E2 reaction, this effect is more pronounceda st he antibonding overlap of both the C a ÀYand C b ÀHb onds are being reduced. For the S N 2 pathway,t his results in an intrinsically larger HOMO-LUMO gap than for the E2 pathway,a nd therefore as ignificantly less stabilizing interaction energy between the Lewis base and the substrate, regardless of the Lewis base.
Our activation strain analysisr eveals that, similart ot he strain energy,t he interaction energy may also be translated into as imple concept, that is, it corresponds directly to the strength of the Lewis acid or base. [1,20] Am ore basic Lewis base (higher-energy HOMO) interacts more strongly.I na ddition, am ore acidic substrate (lower-energy LUMO)a lso interacts more strongly.C onsequently,w ep ropose the novel concept of effective acidity of the deformed substrate in the transition state, or "transition state acidity". For an E2 pathway,t he substrate in the transition state is more acidic (lower-energy LUMO), whereas in an S N 2p athway it is less acidic (higherenergy LUMO). As ar esult, the E2 pathways will alwaysd ominate the S N 2p athway in the limit of as trong interaction (more basic Lewis base), which we have observedf or the reactions where X À = F À .
Changing the Lewis base from X À = F À to X À = Cl À has ap rofound effect on the preferred reactionp athway,s hifting the preference from E2 for F À (Figure 5a and b) to S N 2f or Cl À (Figure 5c and d). As previously discussed, when going from F À to Figure 5. Activation straina nalysisoft he differences between the PESs of S N 2( red) and anti-E2 (blue) reactionsofX À + C 2 H 5 Yw ith X, Y = F, Cl.T rends down columns(a!corb!d) show how variationo ft he Lewis baseinfluences the competition, whereas trends along rows (a!bo rc!d) showt he effect of leaving group variation.S olidl inescorrespond to the PES, dashedlinestot he strain energy, andd otted linest ot he interaction energy. Transition states are indicated with dots. Computed at ZORA-OLYP/TZ2P. Cl À the basicity is reduced, whichm anifestsi naless stabilizing interaction energy for both the S N 2a nd E2 reaction pathways. This enhances the apparent nucleophilicity,b ecause the S N 2 barrierb ecomes more favorable compared with the E2 barrier.
The weaker Lewis base Cl À has al ower-energy HOMO (Figure 4), resulting in al arger HOMO-LUMO gap and hence a weaker interaction with the substrate. Duetothis weaker interaction, Cl À is unable to overcome the highly destabilizing characteristic distortivity that inextricably accompanies the E2 reaction.
On the other hand, substituting Yf or ab etter leavingg roup, by going from Y = Ft oY= Cl,r educes the strain curves for the S N 2a nd E2 pathway to as imilare xtent, making the strain al essi mportantf actor,w hereas the interaction curves, which are alwaysi nf avor of E2, remain essentially constant for both pathways. As predicted by our model,t his has the effect of reducingt he apparent nucleophilicity.T hus,t he preference for the E2 pathway is further enhanced (e.g.,f rom F À + C 2 H 5 Ft o F À + C 2 H 5 Cl) or the preference for the S N 2p athway is reduced (e.g.,f rom Cl À + C 2 H 5 Ft oC l À + C 2 H 5 Cl);s ee also Table 1a nd Figure5.A tl ast, we were ablet oe xtrapolate the strain and interaction curves of our model reactions to as implified S N 2a nd E2 limit (see Figure 7a). This plot clearly displays the interaction of the Lewis base with the acidic substrate to be the dominant effect that determines the propensityt owards the S N 2o r E2 reactionpathway.
Our herein presentedmodel also explains the effect of solvation on the S N 2v ersusE 2c ompetition. Solvations tabilizes the lone-pair electrons of aL ewis base and, thus, lowers the Figure 6. Schematic representation of how the LUMO energy is affected by increasinglydistorting the substrate (C 2 H 5 Y) from its equilibrium geometry to the S N 2, and to the E2 pathway. HOMO of X À and reduces its electron-donatingc apability or basicity.A saresponse, the acid-base, that is, HOMO-LUMO, interaction between the Lewis base and substrateg oes from a strongeri nteraction, for example, in the case of F À (Figure 7c), to aw eaker interaction (Figure 7d)a nd, hence, changes the preferred reactionp athway from E2 in the gas phase to S N 2i n solution. [3m, 4b, j, 6a, e] In addition, also for weaker Lewis bases (X À = Cl À ,B r À ,I À ,A t À ), solvation will enhance the apparent nucleophilicity as it increases the E2 reaction barriert oal arger extent than the S N 2r eaction barrier.T hese effects will be more pronounced when the polarity of the solvent increases. [21] Evaluating the generality of the model Next, we seek to test our proposed general model and have, therefore, studied the S N 2/E2 competition of the following three, commonly used, Lewis bases H 3 CHN À ,H 3 CO À ,a nd H 3 CS À with C 2 H 5 Cl. [4b, 7, 22] As previously discussed, strong Lewis bases will have am ore favorable interaction with the substrate than weak Lewis bases and, therefore, the former will be able to overcome the characteristich igh distortivity accompanied with the E2 reaction. Thus, based on the strengtho ft he Lewis base, that is, the stabilityo ft he HOMO, one can predict the preferred reaction pathway.T he energy of the HOMO of the three Lewis bases decreases from H 3 CHN À (e HOMO = 3.3 eV), to H 3 CO À (e HOMO = 2.4 eV), to H 3 CS À (e HOMO = 1.7 eV), whichi ndicates that the Lewis base becomes increasingly weaker. This implies that the strong Lewis base H 3 CHN À will be prone to undergo an E2 reactiona nd that the intrinsic nucleophilicity reduces along the series from H 3 CHN À ,t oH 3 CO À ,t oH 3 CS À .
Ta ble 2d isplays the energies of the stationary points of the S N 2a nd E2 reactionb etween H 3 CX À (X = HN,O ,S )a nd C 2 H 5 Cl. As predicted, based on the stabilityo ft he HOMO of the Lewis base, H 3 CHN À is the most reactive Lewis base, to the extent that both the S N 2a nd E2 reactions are barrierless. We note that the S N 2r eactiono ccurs with aT S-like structure at À13.7 kcal mol À1 but this is as houlder on the reactions' potential energy surface, as shown in Figure 2c,n ot as addle point. Interestingly,e ven though H 3 CO À is am oderate Lewis base, it is stronge nough to result in al ower reaction barrier for the E2 reaction compared to the S N 2r eaction, À12.1 and À9.2 kcal mol À1 ,r espectively.C ontrarily,t he weakest Lewis base of the series, H 3 CS À ,u ndergoes, not unexpectedly,a nS N 2r eaction, with ab arriert hat is 3kcal mol À1 lower than the E2 reaction. Thus, changing the Lewis base from H 3 CHN À to H 3 CO À to H 3 CS À reduces the intrinsic nucleophilicity,a st he S N 2r eaction barriers teadily increases, but enhances the apparent nucleophilicity,b ecause the S N 2r eaction barrier becomes consistently more favorable compared with the E2 barrier.
At last, we applied the activation strain model (ASM) of reactivity to examinei ft he behavior of the Lewis base, that is, nucleophilic or protophilic, is indeed determined by the Lewis acid-base-like interaction between the Lewis base and the substrate. In Figure 8, we focus on the S N 2/E2 competition of H 3 CO À and H 3 CS À ,w hich prefer an E2 and S N 2r eaction, respectively.I tcan clearly be seen that the more basic Lewis base H 3 CO À interacts strongly with the more acidic E2 transition state, which, in turn, manifestsi namore stabilizing interaction energy ( Figure 8a). As ar esult,H 3 CO À is able to overcome the highly destabilizing characteristicd istortivity along the E2 pathway and hence making H 3 CO À ap rotophile. On the other hand, H 3 CS À is aw eaker Lewis base and, for that reason, has a less stabilizing Lewis acid-base-like interaction with C 2 H 5 Cl, resulting in reactionb arriers that are determined by the strain energy ( Figure 8b). As the S N 2r eaction occurs with less destabilizing strain energy,i .e.,al ower characteristicd istortivity, than the E2 pathway, H 3 CO À will act as an ucleophile following the S N 2r eaction. The herein presented resultss how that our proposed model is indeedg eneral and can be used to elucidate the S N 2/E2 competition of ap lethora of Lewis bases.

Conclusion
Bimolecular nucleophilic substitution (S N 2; nucleophilic attack) and base-induced elimination (E2;p rotophilic attack) reactions are both accelerated when the electron-donating capability of the Lewis base increases, but the E2 pathway benefits more and therefore is favored in the case of stronger Lewis bases. Solvation,i ng eneral, stabilizes the HOMO,d ecreasing the electron-donating capability of the Lewis base and thus reduces the preference for E2 or enhances the preference for S N 2( enhanced apparent nucleophilicity), even though the barrier of the latter is also raised (reduced intrinsic nucleophilicity). These insights emerge from ad etailed and consistentq uantum chemicale xploration of av ast range of archetypal model systems X À + C 2 H 5 Y( X, Y = F, Cl, Br,I ,A t) displaying aw ide range in reactivitya nd pathways.
We highlight the main factors determining the shape of the potentiale nergy surface, and hence the propensity of the Lewis base to act as an ucleophile or protophile, to be the structurald eformation of the substrate during the course of the reactioni nc ombination with the nature of the Lewis base and the nature of the leaving group.E ach pathway is associated with ac haracteristic distortivity:h igh and associated with a more destabilizings train fort he E2 pathway,i nw hich two bondsa re broken (C a ÀY, C b ÀH), versus, low and associated with al ess destabilizing strain for the S N 2p athway,i nw hich [ c] An IRC analyses reveals as houlder along the S N 2p otential energy surfacea tÀ13.7 kcal mol À1 ,w hich is characterized by forming the new C a ÀXb ond and breaking the old C a ÀY. Chem.E ur.J.2020, 26,15538 -15548 www.chemeurj.org 2020 The Authors. Published by Wiley-VCH GmbH only one bond is broken (C a ÀY). At the same time, the LUMO of the substrate is C a ÀYa nd C b ÀHa ntibonding and therefore assumes al ower orbital energy along the more distortive E2 pathway,r endering effectively ah igher electron-accepting capability. We refer to this circumstance as the "transition state acidity" of the substrate, which is stronger for E2 than S N 2. Thus, the Lewis acid-base-like interaction between the Lewis base and the substrate in the transition state determines the outcome of the competition: (i)inar egime of weak interaction, that is, if the Lewis base is weak, the strain determines the barrier and this factor is alwaysm ore favorable, i.e.,l ess destabilizing, for the less distortive pathway,S N 2; (ii)ina regime of strong interaction, that is, if the Lewis base is strong, the interaction overrules the strain and determines the barrier, and this factor is alwaysm ore favorable, i.e.,m ore stabilizing, for the more distortive pathway, E2. These findings show that the nucleophilic or protophilic behavior of aL ewis base towards aL ewis-acidic substrate is fundamentally co-determined by the latter.
The introducedc oncepts of "characteristic distortivity" and "transition state acidity", together with the distinction between apparent and intrinsic nucleophilicity,p rovide av ital, qualitative approach for understanding organic reactions in the framework of both MO theory and Lewis't heory of acidsa nd bases. [15,20] This approach rationalizes in ap hysically sound and intuitive manner why strong Lewis bases prefer the protophilic pathway,w hereas weak Lewis bases behave as nucleophiles in S N 2r eactions, and why (stronger) solvation pushes the mechanistic competition from E2 towards S N 2. Thei nsights provided herein elucidate ap lethora of experimental findings and can serve as powerful tools for am ore rational designo fsynthetic routes. We envisage that the scope of our findings extends well beyond the competition between nucleophilic and protophilic reactivity.