SN2 versus E2 Competition of F- and PH2- Revisited.

We have quantum chemically analyzed the competition between the bimolecular nucleophilic substitution (SN2) and base-induced elimination (E2) pathways for F- + CH3CH2Cl and PH2- + CH3CH2Cl using the activation strain model and Kohn-Sham molecular orbital theory at ZORA-OLYP/QZ4P. Herein, we correct an earlier study that intuitively attributed the mechanistic preferences of F- and PH2-, i.e., E2 and SN2, respectively, to a supposedly unfavorable shift in the polarity of the abstracted β-proton along the PH2--induced E2 pathway while claiming that ″...no correlation between the thermodynamic basicity and E2 rate should be expected.″ Our analyses, however, unequivocally show that it is simply the 6 kcal mol-1 higher proton affinity of F- that enables this base to engage in a more stabilizing orbital interaction with CH3CH2Cl and hence to preferentially react via the E2 pathway, despite the higher characteristic distortivity (more destabilizing activation strain) associated with this pathway. On the other hand, the less basic PH2- has a weaker stabilizing interaction with CH3CH2Cl and is, therefore, unable to overcome the characteristic distortivity of the E2 pathway. Therefore, the mechanistic preference of PH2- is steered to the SN2 reaction channel (less-destabilizing activation strain).

Introduction

The bimolecular nucleophilic substitution (SN2) and base-induced bimolecular elimination (E2) reactions are two elementary reactions in the field of organic chemistry.[1,2] These two reactions are, in principle, always in competition with each other (Scheme ), which might cause unwanted side reactions and hampers the applicability of these reactions in synthetic chemistry. Moreover, the SN2/E2 competition plays a paramount role in the development of modern mechanistic organic chemical insights.[3] Therefore, over the past decades, the SN2/E2 competition has been extensively studied, both experimentally[4] and computationally.[5]

Scheme 1

Generic SN2 and E2 Reactions

An important indicator of the reaction pathway preference is the basicity of the Lewis base, which is closely related to the proton affinity (PA). In general, a weak Lewis base (low proton affinity) will have a weak acid–base-like interaction with the substrate, and hence the mechanistic preference will be determined by the characteristic distortivity (i.e., degree of activation strain) accompanying a reaction pathway. This factor is always more favorable (i.e., less destabilizing) for the less-distortive SN2 pathway, making the Lewis base a nucleophile. In contrast, a strong interacting Lewis base (high proton affinity) is, due to its strong acid–base-like interaction with the substrate, able to overcome the highly destabilizing characteristic distortivity and favors the stronger interacting E2 pathway, reacting as a protophile.[6]

F– and PH2– are ideal model Lewis bases that can be exploited to assess the competition between SN2 and E2 pathways since they display opposing reactivity preferences,[7] even though it was believed that these two Lewis bases were essentially equal in terms of basicity (experimental PA: F– = 371.4 kcal mol–1, PH2– = 367.1 kcal mol–1).[8,9] Scott Gronert concluded, in a previous study, that F—acts as a protophile and abstracts the β-proton via the E2 pathway, whereas PH2—acts as a nucleophile and attacks at the α-carbon center following the SN2 pathway.[7a] This selectivity was ascribed to the fact that, along the E2 pathway, proton transfer to the third-row Lewis base PH2– involves a charge reorganization of the transferring hydrogen atom from protonic, when bonded to the substrate, to hydridic, once it is coordinated to PH2–. Thus, Gronert states in this study: “Intuitively, this shift in polarity [charge reorganization] should involve a significant [E2] barrier,”[7a] which ultimately leads to a preference for the SN2 pathway. In addition, the author emphasizes that “...no correlation between thermodynamic basicity and E2 rate should be expected.”[7a]

Here, we show that the rationale, proposed by Gronert,[7a] behind the opposing SN2/E2 preferences of the Lewis bases F– and PH2– is incorrect and that the observed selectivity does, on the contrary, find its origin in the difference in thermodynamic basicity. To this end, we have performed an in-depth computational study to unravel the physical mechanism behind the SN2/E2 preferences of the Lewis bases F– and PH2– with the model substrate chloroethane (CH3CH2Cl) (Scheme ). The activation strain model (ASM)[10] in combination with Kohn–Sham molecular orbital (KS-MO)[11a] theory and the matching energy decomposition analysis (EDA)[11b,11c] were employed to provide quantitative insight into the factor controlling the SN2/E2 preference of the aforementioned reactions. This methodological approach facilitates the analysis of the potential energy surface and, more importantly, the activation barrier, by decomposing the total energy of the system into physically meaningful and easily interpretable terms, proving to be valuable for understanding the reactivity of, amongst others, nucleophilic substitution and elimination reactions.[12]

Scheme 2

Schematic Overview of the Computationally Analyzed SN2 and E2 Reactions of F– (a) and PH2– (b) with Chloroethane 1

Results and Discussion

The thermodynamic basicity of an anion in the gas phase is usually measured by means of its proton affinity (PA), which is the negative of the enthalpy change for a gas-phase reaction such as eq :where X– = F– and PH2–. A high proton affinity indicates a stronger Lewis base and a weaker conjugated acid. The computed proton affinities (ΔHPA) of the Lewis bases at ZORA-OLYP/QZ4P level are not similar. They, namely, differ by 6 kcal mol–1 (375.0 and 368.8 kcal mol–1, F– and PH2–, respectively), which is, as we will show later, large enough to significantly affect the thermodynamic basicity and hence the preferred reaction pathway. Note that our computed proton affinities compare well with previously reported theoretically[5] and experimentally[7,8] obtained proton affinities.

The reaction pathways of the bimolecular nucleophilic substitution (SN2) and base-induced elimination (E2) reactions of Lewis bases F– and PH2– with chloroethane (1), together with their transition state structures, are shown in Figure . In analogy with previous computational studies,[5f,5g] we established that the F– Lewis base has a strong preference for the E2 reaction pathway, whereas the SN2 pathway is slightly favored by the PH2– Lewis base. The E2 reaction pathway for the attack with the F– Lewis base proceeds with an activation barrier that is almost 5 kcal mol–1 lower in energy than for the SN2 reaction pathway, but the latter results in a more stable product complex. For the reaction with PH2–, both the activation barrier and the product complex are in favor of the SN2 reaction pathway. These findings are in line with Ren, Wong, and co-workers, who also found that F– prefers the E2 reaction channel, whereas PH2– reacts via an SN2 channel.[7b] These results already show that the differences in the proton affinities of the herein studied Lewis acids are significant enough to alter the preferred reaction pathway.

Figure 1

(a) Reaction profiles of the SN2 and E2 reactions between 1 and the Lewis bases F– and PH2– (in kcal mol–1), computed at ZORA-OLYP/QZ4P. (b) Transition state structures with key bond lengths (in Å) for the SN2 and E2 reactions between 1 and the Lewis bases F– and PH2–.

To gain quantitative insight into the physical factors leading to the preferred reaction pathway (SN2 or E2), we turned to the activation strain model (ASM) of reactivity.[10] First, we focus on the reaction with the strong Lewis base F–, as shown in Figure a. The previously mentioned preference for the E2 reaction pathway originates solely from a significantly more stabilizing interaction energy, which is strong enough to overcome the accompanied highly destabilizing characteristic distortivity (activation strain) associated with this pathway. Note that the distortion, characteristic of the E2 reaction, is inherently higher than that for the SN2 reaction because along the former reaction pathway two bonds of 1 (Cα–Cl and Cβ–H) are being broken, while for the latter, only one (Cα–Cl) is being broken.[6] To understand why the E2 pathway goes with a stronger interaction, we employed a canonical energy decomposition analysis (EDA).[11b,11c] We found that the significantly more stabilizing orbital interactions, together with the more favorable electrostatic interaction, for the E2 reaction pathway leads to the observed lower activation barrier of this reaction compared to the SN2 analog (Figure b).

Figure 2

(a) Activation strain analysis and (b) energy decomposition analysis of the SN2 and E2 reactions between 1 and F–, where the energy values are projected on the Cα···Cl bond stretch; (c) molecular orbital diagram of the most important HOMOF––LUMO orbital interaction computed at consistent geometries with a Cα···Cl bond stretch of 0.404 Å, computed at ZORA-OLYP/QZ4P.

The origin of the more stabilizing orbital interactions of the E2 reaction pathway can be analyzed and explained by means of a Kohn–Sham molecular orbital analysis (KS-MO).[11a,13] We have quantified the key occupied–unoccupied orbital interaction between the 2p atomic orbital (AO) of F– (HOMOF–) and the antibonding σ*C–Cl unoccupied orbital of 1 (LUMO) that participate in the acid–base-like interaction between the reactants at consistent geometries with a Cα···Cl bond stretch of 0.404 Å (Figure c). The stronger orbital interaction of the E2 pathway is caused by both a smaller HOMOF––LUMO energy gap, as a consequence of a more stable LUMO, and a better orbital overlap, compared to the SN2 pathway. The characteristic distortivity of both pathways has an immediate, but independent, impact on the electronic structure of 1. The LUMO has antibonding character not only in the Cα–Cl bond, but also in the Cβ–H bond. Thus, when both bonds are elongated, as a result of the characteristic distortion along the E2 pathway, the antibonding overlap of both bonds is reduced, which stabilizes, i.e., lowers the energy of, the LUMO and, therefore, makes the substrate more acidic.[5f,5g,6] In comparison, the LUMO benefits solely from the decreasing antibonding overlap of the Cα–Cl bond and, therefore, lowers to a lesser extent, making the substrate less acidic than along the E2 pathway. Furthermore, the more favorable orbital overlap of the E2 pathway is a direct response of the shorter distance between F– and 1 compared to the SN2 pathway. Thus, the strongly stabilizing interactions between F– and 1 pushes the preference toward the pathway that involves the more destabilizing activation strain (E2 elimination).

Next, we turn to the SN2 and E2 reactions between PH2–and 1, where the SN2 pathway is now favored over the E2 pathway. By applying the ASM, we found that in contrast with the reactions involving F–, the interaction between the weaker Lewis base PH2– and the substrate is not able to overcome the higher activation strain characteristic for the E2 reaction (Figure a). Our EDA clearly shows that all energy terms of the SN2 and E2 pathways are at the early stage of the reaction nearly superimposed (Figure b), resulting in an identical interaction energy. Thus, the preference for the SN2 pathway is exclusively governed by the less destabilizing characteristic distortion, which, in turn, is a result of only one bond-breaking event (Cα–Cl) compared to the E2 pathway, where two bonds of 1 are being broken (Cα–Cl and Cβ–H).

Figure 3

(a) Activation strain analysis and (b) energy decomposition analysis of the SN2 and E2 reactions between 1 and PH2–, where the energy values are projected on the Cα···Cl bond stretch, computed at ZORA-OLYP/QZ4P. (c) Schematic molecular orbital diagram of the most important HOMOX––LUMO orbital interaction, where X– = F– or PH2–.

At last, we wish to understand why the E2 reaction between F– and 1 goes with a more stabilizing interaction energy compared to the PH2– analog. The difference between the two Lewis bases can be ascribed to the differences in the orbital energy of their interacting lone pair HOMOs, which, in turn, translates into the intrinsic differences in acid–base-like interactions with the substrate. As shown in Figure c, the HOMO of F– is higher in energy (i.e., less stable) than the corresponding HOMOPH2–, making the former a stronger Lewis base. This can be explained by the size of the orbitals of the Lewis base. F– has a less stable HOMO due to the compactness of fluorine AOs, which experiences more destabilizing Coulomb repulsion between the electrons compared to the heavier and larger HOMOPH2–. As a result, the more basic Lewis base F– is able to form a stronger acid–base-like complex with the previously mentioned more acidic E2 substrate (i.e., small HOMOF––LUMO gap), compared to the weaker base PH2– (i.e., large HOMOPH2––LUMO gap), and is, therefore, able to generate a sufficiently stabilizing interaction with the substrate to overcome the characteristic distortion accompanying the E2 reaction pathway. Thus, interestingly, while PH2– indeed reacts via a higher activation barrier than F–, as found by Scott Gronert,[7a] this has little to do with the shift in polarity (i.e., charge reorganization), but instead with the fact that PH2– is a weaker Lewis base and hence interacts in a less favorable manner with the substrate.

Conclusions

In the competition between bimolecular nucleophilic substitution (SN2) and base-induced elimination (E2) reactions, the mechanistic preference is influenced by many factors, including the basicity of the Lewis base. In this work, we have corrected the rationale postulated by Scott Gronert[7a] that explained the opposing SN2/E2 preferences of the Lewis bases F– and PH2– to the charge reorganization of the transferring hydrogen atom upon reacting with PH2– and, explicitly, not by their differences in thermodynamic basicity. Alternatively, we found that these two classical Lewis bases do exhibit sufficiently different proton affinities, which ultimately leads to opposite mechanistic preferences; namely, the stronger Lewis base F– prefers to react via the E2 pathway, while the weaker Lewis base PH2– follows the SN2 pathway.

Our activation strain analysis revealed the underlying physical mechanisms behind the SN2/E2 preferences of the herein studied systems. We found that the E2 preference for the more basic Lewis base F–originates from a stronger interaction with the substrate, as a result of more stabilizing orbital interactions, which is able to overcome the more destabilizing activation strain that goes with the high characteristic distortion of the E2 pathway. This higher extent of distortion also causes the substrate’s LUMO to drop further and become more stable along the E2 pathway than the SN2 pathway. In other words, the substrate becomes effectively more acidic along the E2 pathway and engages in a stronger orbital interaction with the Lewis base, due to a smaller HOMOF––LUMO energy gap, compared to the SN2 pathway.

This behavior is different for PH2–. Here, the weaker Lewis base PH2– interacts in a less stabilizing fashion with the substrate and is, thus, not able to overcome the highly destabilizing characteristic activation strain of the E2 reaction. Therefore, the preference for the SN2 pathway is exclusively governed by the less destabilizing activation strain. The striking difference in the strength of the interaction between the two herein studied Lewis bases and the substrate can be ascribed to the differences in the orbital energy of their interacting lone pair HOMOs, which also explains the difference in thermodynamic basicity. The stronger base F– (higher-energy HOMO) interacts more strongly with the more acidic substrate along the E2 reaction pathway, forming a more stable acid–base-like complex, compared to the much weaker base PH2– (lower-energy HOMO); hence, it is able to overcome the characteristic distortion accompanying the E2 reaction pathway.

Methods

Computational Details

All density functional theory (DFT) calculations were performed using the Amsterdam Density Functional (ADF2018.105) software package.[14] The generalized gradient approximation (GGA) exchange-correlation functional OLYP was used for all computations, which consists of the optimized exchange (OPTX) functional proposed by Handy and co-workers[15a], and the Lee–Yang–Parr (LYP) correlation functional.[15b] Our previous benchmark studies have shown that OLYP reproduces SN2 barriers from highly correlated ab initio within only a few kcal mol–1.[16] Scalar relativistic effects are accounted for using the zeroth-order regular approximation (ZORA).[17] The basis set used, denoted as QZ4P, is of quadruple-ζ quality for all atoms and has been improved by four sets of polarization functions.[18] This large basis set is required for small anionic species such as F–.[16b] The accuracies of the fit scheme (Zlm fit) and the integration grid (Becke grid) were, for all calculations, set to VERYGOOD.[19] No symmetry constraints were used during the analyses. All calculated stationary points have been verified by performing a vibrational analysis calculation,[20] to be energy minima (no imaginary frequencies) or transition states (only one imaginary frequency). The character of the normal mode associated with the imaginary frequency of the transition state has been inspected to ensure that it is associated with the reaction of interest. The potential energy surfaces of the studied SN2 and E2 reactions were obtained by performing intrinsic reaction coordinate (IRC) calculations,[21] which, in turn, were analyzed using the PyFrag 2019 program.[22] The optimized structures were illustrated using CYLview.[23]

Thermochemistry

Bond enthalpies, i.e., proton affinities (PA), are calculated at 298.15 K and 1 atm (ΔHPA) from electronic bond energies (ΔE) and vibrational frequencies using standard thermochemistry relations for an ideal gas [eq ].[24]Here, ΔEtrans,298, ΔErot,298, and ΔEvib,0 are the differences between the complex (i.e., HF and PH3, the protonated Lewis bases) and the separate species (i.e., H+ + F– and H+ + PH2–, the proton and the Lewis base) in translational, rotational, and zero-point vibrational energy, respectively. The last term, Δ(ΔEvib,0)298, is the change in the vibrational energy difference when going from 0 to 298.15 K. The molar work term Δ(pV) is (Δn)RT, where Δn = +1, for one complex (HF or PH3) dissociating into two separate species, namely the H+ and Lewis base.

Activation Strain and Energy Decomposition Analysis

The activation strain model (ASM) of chemical reactivity,[10] also known as the distortion/interaction model,[25] is a fragment-based approach in which the potential energy surface (PES) can be described with respect to, and understood in terms of the characteristics of, the reactants. It considers the rigidity of the reactants and to which extent they need to deform during the reaction plus their capability to interact with each other as the reaction proceeds. With the help of this model, we decompose the total energy, ΔE(ζ), into the strain and interaction energy, ΔEstrain(ζ) and ΔEint(ζ), respectively, and project these values onto the reaction coordinate ζ [eq ].In this equation, the strain energy, ΔEstrain(ζ), is the penalty that needs to be paid to deform the reactants from their equilibrium to the geometry they adopt during the reaction at point ζ of the reaction coordinate. On the other hand, the interaction energy, ΔEint(ζ), accounts for all the chemical interactions that occur between these two deformed reactants along the reaction coordinate.

The interaction energy between the deformed reactants can be further analyzed in terms of quantitative Kohn–Sham molecular orbital (KS-MO) theory together with a canonical energy decomposition analysis (EDA).[11] The EDA decomposes the ΔEint(ζ) into the following three energy terms [eq ]:Herein, ΔVelstat(ζ) is the classical electrostatic interaction between the unperturbed charge distributions of the (deformed) reactants and is usually attractive. The Pauli repulsion, ΔEPauli(ζ), includes the destabilizing interaction between the fully occupied orbitals of both fragments due to the Pauli principle. The orbital interaction energy, ΔEoi(ζ), accounts for, amongst others, charge transfer between the fragments, such as HOMO–LUMO interactions.

In the herein presented activation strain and accompanied energy decomposition diagrams, the energy terms are projected onto the carbon–leaving group (Cα–Cl) distance. This critical reaction coordinate undergoes a well-defined change during the reaction from the reactant complex via the transition state to the product and is shown to be a valid reaction coordinate for studying SN2/E2 reactions.[12]