Effects of Methyl Substitution and Leaving Group on E2/SN2 Competition for Reactions of F− with RY (R = CH3, C2H5, iC3H7, tC4H9; Y = Cl, I)

The competition between base-induced elimination (E2) and bimolecular nucleophilic substitution (SN2) is of significant importance in organic chemistry and is influenced by many factors. The electronic structure calculations for the gas-phase reactions of F− + RY (R = CH3, C2H5, iC3H7, tC4H9, and Y = Cl, I) are executed at the MP2 level with aug-cc-pVDZ or ECP/d basis set to investigate the α-methyl substitution effect. The variation in barrier height, reaction enthalpy, and competition of SN2/E2 as a function of methyl-substitution and leaving group ability has been emphasized. And the nature of these rules has been explored. As the degree of methyl substitution on α-carbon increases, the E2 channel becomes more competitive and dominant with R varying from C2H5, iC3H7, to tC4H9. Energy decomposition analysis offers new insights into the competition between E2 and SN2 processes, which suggests that the drop in interaction energy with an increasing degree of substitution cannot compensate for the rapid growth of preparation energy, leading to a rapid increase in the SN2 energy barrier. By altering the leaving group from Cl to I, the barriers of both SN2 and E2 monotonically decrease, and, with the increased number of substituents, they reduce more dramatically, which is attributed to the looser transition state structures with the stronger leaving group ability. Interestingly, ∆E0‡ exhibits a positive linear correlation with reaction enthalpy (∆H) and halogen electronegativity. With the added number of substituents, the differences in ∆E0‡ and ∆H between Y = Cl and I likewise exhibit good linearity.


Potential Energy Surfaces of F − + RY Reactions
The relative energy of stationary points of F − + RCl (R= CH3, C2H5, i C3H7, t C4H9 and Y = Cl, I) calculated by the MP2 method are displayed in Table 1 together with the high-level CCSD(T)-F12b [16,42], CCSD(T) [17] benchmark values, and the available B97-1/aug-cc-pVDZ values [43].The average deviation from the benchmark is 0.11/0.48,0.16/0.13,and 0.16/0.35kcal/mol for CH3Cl/I, C2H5Cl/I, and i C3H7Cl/I, respectively, indicating that the MP2/aug-cc-pVDZ (ECP/d) level is reasonable.The profiles of PES for F − + RY are presented in detail in Figures 1a,b and S1a,b together with the geometrical structures in Figure S2a,d.As shown in Figures 1 and S1, similar to the reaction of F − with ethyl halide, for isopropyl and tert-butyl reactions, four traditional reaction pathways, including base-induced anti and syn elimination (anti-E2 and syn-E2), as well as nucleophilic substitution with inversion and retention of configuration (inv-SN2 and ret-SN2), are predicted by MP2 theory.Inv-SN2 and anti-E2 reactions share the same reactant complex (a/bRC), and ret-SN2 and syn-E2 also utilize a common complex (c/dRC) along the reaction coordinate.With the increased methyl substitution, the difference in PES profiles of the series of reactions lies in the entrance channel.For F − + RY (R = CH3, C2H5, and Y = Cl, I), a hydrogenbonded F•••HC α H2(CH2)Y complex (c/dRCH) is obtained, which can easily convert to an ion-dipole complex F•••H β CH2(CH2)Y (a/bRC) via a low-energy TSRC [16,29,42,[44][45][46][47][48][49][50][51][52].In contrast, for F − + RCl (R = i C3H7, t C4H9 and Y = Cl, I) reactions, only an ion-dipole complex (a/bRC) is found, where F − is situated between α-carbon and β-hydrogen of iso-propyl or tert-butyl moiety, so that F − can attack either target atom to form an inv-SN2 or anti-E2 channel.For the reactant complex F•••H β H2(CH3)CHY (c/dRC) in syn-E2 and ret-SN2 channels, F − and some hydrogen atoms in β-position, instead of α-hydrogen of alkyl halides, have a mild hydrogen-bond interaction.There is no transition state available for the conversion of these two RCs.

Potential Energy Surfaces of F − + RY Reactions
The relative energy of stationary points of F − + RCl (R = CH 3 , C 2 H 5 , i C 3 H 7 , t C 4 H 9 and Y = Cl, I) calculated by the MP2 method are displayed in Table 1 together with the high-level CCSD(T)-F12b [16,42], CCSD(T) [17] benchmark values, and the available B97-1/aug-cc-pVDZ values [43].The average deviation from the benchmark is 0.11/0.48,0.16/0.13,and 0.16/0.35kcal/mol for CH 3 Cl/I, C 2 H 5 Cl/I, and i C 3 H 7 Cl/I, respectively, indicating that the MP2/aug-cc-pVDZ (ECP/d) level is reasonable.The profiles of PES for F − + RY are presented in detail in Figures 1a,b and S1a,b together with the geometrical structures in Figure S2a,d.As shown in Figures 1 and S1, similar to the reaction of F − with ethyl halide, for isopropyl and tert-butyl reactions, four traditional reaction pathways, including baseinduced anti and syn elimination (anti-E2 and syn-E2), as well as nucleophilic substitution with inversion and retention of configuration (inv-S N 2 and ret-S N 2), are predicted by MP2 theory.Inv-S N 2 and anti-E2 reactions share the same reactant complex (a/bRC), and ret-S N 2 and syn-E2 also utilize a common complex (c/dRC) along the reaction coordinate.With the increased methyl substitution, the difference in PES profiles of the series of reactions lies in the entrance channel.For F − + RY (R = CH 3 , C 2 H 5 , and Y = Cl, I), a hydrogenbonded F•••HC α H 2 (CH 2 )Y complex (c/dRC H ) is obtained, which can easily convert to an ion-dipole complex F•••H β CH 2 (CH 2 )Y (a/bRC) via a low-energy TS RC [16,29,42,[44][45][46][47][48][49][50][51][52].In contrast, for F − + RCl (R = i C 3 H 7 , t C 4 H 9 and Y = Cl, I) reactions, only an ion-dipole complex (a/bRC) is found, where F − is situated between α-carbon and β-hydrogen of iso-propyl or tert-butyl moiety, so that F − can attack either target atom to form an inv-S N 2 or anti-E2 channel.For the reactant complex F•••H β H 2 (CH 3 )CHY (c/dRC) in syn-E2 and ret-S N 2 channels, F − and some hydrogen atoms in β-position, instead of α-hydrogen of alkyl halides, have a mild hydrogen-bond interaction.There is no transition state available for the conversion of these two RCs.[43].c The reaction enthalpies of reaction at 0 K with ZPE calculated from tabulated reaction enthalpies in ref. [41].Resulting from the strong steric exclusion between the nucleophile and substrate, the ret-SN2 TS usually gives a much higher overall barrier than other reaction pathways, suggesting it is the least favorable pathway.The barrier for the syn-E2 pathway is usually higher than inv-SN2 and anti-E2 for a similar hindrance effect.Therefore, in the following discussions, the most competitive inv-SN2 and anti-E2 pathways for the series of F − + RY reactions are considered here, and their PES profiles obtained at the MP2 level of theory are characterized in Figure 2 for convenience of comparison.For the F − + CH3Y reaction, F − attacks CH3Y on the back-side via a traditional path along a pre-reaction ion-dipole complex (1bRC), a Walden-inversion transition state (1bTS), and a post-reaction ion-dipole complex FCH3•••Y − (1bPC).The E2 pathways appear with the successive addition of the methyl group besides the SN2 pathways and show similar double well potential characters.The initial association of F − and RY can form an ion-dipole complex a/bRC and, after going over a/bTS, the system drops down to the deep potential energy well a/bPC and then decomposes to products P1 (RF + Cl − /I − ) and P2 (RCH2 = CH2 + HF + Cl − /I − ), respectively.Resulting from the strong steric exclusion between the nucleophile and substrate, the ret-S N 2 TS usually gives a much higher overall barrier than other reaction pathways, suggesting it is the least favorable pathway.The barrier for the syn-E2 pathway is usually higher than inv-S N 2 and anti-E2 for a similar hindrance effect.Therefore, in the following discussions, the most competitive inv-S N 2 and anti-E2 pathways for the series of F − + RY reactions are considered here, and their PES profiles obtained at the MP2 level of theory are characterized in Figure 2 for convenience of comparison.For the F − + CH 3 Y reaction, F − attacks CH 3 Y on the back-side via a traditional path along a pre-reaction ion-dipole complex (1bRC), a Walden-inversion transition state (1bTS), and a post-reaction ion-dipole complex FCH 3 •••Y − (1bPC).The E2 pathways appear with the successive addition of the methyl group besides the S N 2 pathways and show similar double well potential characters.The initial association of F − and RY can form an ion-dipole complex a/bRC and, after going over a/bTS, the system drops down to the deep potential energy well a/bPC and then decomposes to products P1 (RF + Cl − /I − ) and P2 (RCH 2 = CH 2 + HF + Cl − /I − ), respectively.

Effects of α-Methyl Substitution
To explore the effects of the addition of the α-methyl group on the competition of E2 and S N 2 mechanisms, the activation (∆E 0 ‡ ) and the overall barrier (∆E ‡ ) are especially emphasized for discussion as presented in Scheme 2, and the calculated values of the relevant energies are summarized in Table 1.Here, Y = Cl is used as an example.
Exothermicity.As shown in Figure 2, it is clear that all E2 and S N 2 paths for the reaction of F − + RY (R = CH 3 , C 2 H 5 , i C 3 H 7 , t C 4 H 9 , and Y = Cl, I) are highly exothermic, and, for each reaction, the reaction enthalpy ∆H of S N 2 pathways is much more negative than that of E2 pathways, suggesting S N 2 reactions are more exothermic than E2 reactions owing to the strong combination between the F atom and C atoms in the neutral products.By changing R from the methyl to the tert-butyl group, the ∆H of S N 2 pathways slightly drops, while the values of E2 pathways escalate, eventually widening the ∆H gap between E2 and S N 2.

Effects of α-Methyl Substitution
To explore the effects of the addition of the α-methyl group on the competition of E2 and SN2 mechanisms, the activation (∆E0 ‡ ) and the overall barrier (∆E ‡ ) are especially emphasized for discussion as presented in Scheme 2, and the calculated values of the relevant energies are summarized in Table 1.Here, Y = Cl is used as an example.Exothermicity.As shown in Figure 2, it is clear that all E2 and SN2 paths for the reaction of F − + RY (R = CH3, C2H5, i C3H7, t C4H9, and Y = Cl, I) are highly exothermic, and, for each reaction, the reaction enthalpy ∆H of SN2 pathways is much more negative than that of E2 pathways, suggesting SN2 reactions are more exothermic than E2 reactions owing to the strong combination between the F atom and C atoms in the neutral products.By Barrier Height.The variation of ∆E 0 ‡ , ∆E ‡ , and the difference in ∆E 0 ‡ between inv-S N 2 and anti-E2 along the methylation of the α-carbon is illustrated in Figure 3a-c.The horizontal coordinate is the degree of methyl substitution of C α , named n, ranging from 0 to 3. As described in Figure 3a, successively adding methyl groups to the C α dramatically raises the activation barrier (∆E 0 ‡ ) of inv-S N 2 from 3.3 to 6.8 to 11.6 and finally to 20.8 kcal/mol, while the ∆E 0 ‡ of anti-E2 gently escalates from 6.6, 9.1 to 11.2 kcal/mol.Figure 3b depicts the activation barrier difference between the inv-S N 2 and anti-E2 pathways (∆∆E 0 ‡ = ∆E 0 ‡ inv-SN2 − ∆E 0 ‡ anti-E2 ) as n changes from 1 to 3, which is 0.2 and 2.5 kcal/mol for n = 1 and 2, respectively.The significant augment of ∆∆E 0 ‡ for the F − + t C 4 H 9 Cl reaction is observed in doubling the difference to 9.6 kcal/mol.All these results suggest that anti-E2 is becoming more and more competitive.Wester and coworkers [32] have disentangled the dynamics of the competition between anti-E2 and inv-S N 2 in the reaction F − + C 2 H 5 Cl, indicating that anti-E2 is more advantageous.In addition, Gronert [38] also predicted that in the reaction of F − + i C 3 H 7 Cl anti-E2 is completely dominated and substitution should be more competitive with ethyl halides.As the maximum difference between ∆E 0 ‡ (S N 2) and ∆E 0 ‡ (anti-E2) of these three systems, the anti-E2 mechanism will also be the most favorable pathway for F − + t C 4 H 9 Cl (I).
tion of F − + RY (R = CH3, C2H5, i C3H7, t C4H9, and Y = Cl, I) are highly exothermic, and, for each reaction, the reaction enthalpy ∆H of SN2 pathways is much more negative than that of E2 pathways, suggesting SN2 reactions are more exothermic than E2 reactions owing to the strong combination between the F atom and C atoms in the neutral products.By changing R from the methyl to the tert-butyl group, the ∆H of SN2 pathways slightly drops, while the values of E2 pathways escalate, eventually widening the ∆H gap between E2 and SN2.
Barrier Height.The variation of ∆E0 ‡ , ∆E ‡ , and the difference in ∆E0 ‡ between inv-SN2 and anti-E2 along the methylation of the α-carbon is illustrated in Figure 3a-c.The horizontal coordinate is the degree of methyl substitution of C α , named n, ranging from 0 to 3. As described in Figure 3a, successively adding methyl groups to the C α dramatically raises the activation barrier (∆E0 ‡ ) of inv-SN2 from 3.3 to 6.8 to 11.6 and finally to 20.8 kcal/mol, while the ∆E0 ‡ of anti-E2 gently escalates from 6.6, 9.1 to 11.2 kcal/mol.Figure 3b depicts the activation barrier difference between the inv-SN2 and anti-E2 pathways (∆∆E0 ‡ = ∆E0 ‡ inv-SN2 − ∆E0 ‡ anti-E2) as n changes from 1 to 3, which is 0.2 and 2.5 kcal/mol for n = 1 and 2, respectively.The significant augment of ∆∆E0 ‡ for the F − + t C4H9Cl reaction is observed in doubling the difference to 9.6 kcal/mol.All these results suggest that anti-E2 is becoming more and more competitive.Wester and co-workers [32] have disentangled the dynamics of the competition between anti-E2 and inv-SN2 in the reaction F − + C2H5Cl, indicating that anti-E2 is more advantageous.In addition, Gronert [38] also predicted that in the reaction of F − + i C3H7Cl anti-E2 is completely dominated and substitution should be more competitive with ethyl halides.As the maximum difference between ∆E0 ‡ (SN2) and ∆E0 ‡ (anti-E2) of these three systems, the anti-E2 mechanism will also be the most favorable pathway for F − + t C4H9Cl (I).For the variation pattern of overall barriers (∆E ‡ ), the α-methyl group slightly changes the ∆E ‡ of an anti-E2 pathway with values gradually dropping from −11.2, −11.6 to −11.9 kcal/mol but significantly alters the barrier of inv-S N 2 from −12.3 kcal/mol for F − + CH 3 Cl to −2.3 kcal/mol for F − + t C 4 H 9 Cl.Rablen et al. [35] systematically compared the free energies of S N 2/E2 transition states for CN − + RCl reactions at the W1 and G4 levels of electronic structure theory in the presence of a simulated acetonitrile solvent.Their results suggest that the barrier to the E2 reaction reduces by the same magnitude as the barrier to S N 2 raises when methylation of the α-carbon increases.Connor and Gronert [34] studied the impact of αand β-methylation on E2 and S N 2 reactions between a series of alkyl bromides and nucleophiles in the gas phase using both mass spectrometer experiment and computational methods.They found the reduction in S N 2 rate constant and the mounting in E2 rate constant when adding a methyl group to the α-carbon position, which is in line with our findings.
To understand why the increasing alkyl substitution strikingly enhances the ∆E ‡ of the S N 2 reaction and slightly lowers the E2 barrier, we decompose the transition state energy by referring to the activation strain analyses proposed by Bickelhaupt et al. [28,53,54] as shown in Figure 3b.Energy decomposition contributes to a quantitative understanding of how methyl substitution affects the inv-S N 2/anti-E2 reaction barrier.The total energy ∆E ‡ , that is, the difference between reactants and transition states, can be decomposed into preparation energy (∆E prep ) and interaction energy (∆E int ) based on the formula ∆E ‡ = ∆E prep + ∆E int .The ∆E prep is the energy that is needed to overcome the deformation of individual reactants from their equilibrium structure into the geometries of the transition structure.And the interaction energy ∆E int is considered as the energy difference between the individual fragments of transition states' geometries and the transition states.For F − + RCl reactions, the inv-S N 2 goes with less preparation energy than anti-E2, which can be attributed to the different mechanisms.One bond breaking occurs in the inv-S N 2 mechanism, whereas two bond breakings and one C-C bond shrinking occur along the anti-E2 pathway.Hence, the destabilizing distortion characteristic for the anti-E2 reaction pathway is by definition higher than the inv-S N 2 reaction pathway.As previously proposed by Bickelhaupt [53], the C α -Y bond extension of inv-S N 2 reduces the antibonding orbital overlap between C 2p and Y 2p orbitals, which makes the LUMO of the substrate more stable.Obviously, due to the antibonding orbital overlap of both the C α -Y and C β -H bonds being diminished, this stabilization of the LUMO is more significant in the E2 reaction.For inv-S N 2 transition structures, when the degree of CH 3 varies from 0 to 3, ∆E prep increases gradually, indicating the fragments in the transition structures distorted more violently, whereas ∆E int decreases, suggesting the interaction of two parts is stronger.The decline in ∆E int cannot pay for the rapid growth of ∆E prep , resulting in the overall rise in ∆E ‡ .Especially in the F − + t C 4 H 9 Cl reaction, the increase in S N 2 ∆E ‡ is particularly significant.In comparison, the ∆E prep of the anti-E2 transition structure is higher but elevates more slowly than that of the inv-S N 2. Accordingly, the results obtained suggest that, compared to the anti-E2 reaction, the inv-S N 2 reaction is more sensitive to structural changes in the substrate.Therefore, the barrier of inv-S N 2 increases with the increased degree of substitution, resulting in less competitiveness compared to anti-E2, which is in agreement with previous research by Pendás et al. [39].The ∆E int is further broken down into the steric term ∆E steric (∆E steric = ∆E els + ∆E XC + ∆E Pauli ) and the orbital interaction term ∆E orb in order to ascertain the primary contributor to the fluctuation in ∆E int as shown in Figure S3 [55].Obviously, the orbital interaction term ∆E orb is responsible for the interaction energy.The orbital interactions of both S N 2 and E2 decrease as the number of substituents increases.It is noteworthy that the stronger orbital interaction favors the E2 reaction to lower ∆E int compared to its S N 2 analog.This is consistent with the finding by Bickelhaupt et al. [22] for the F − + CH 3 CH 2 Cl reaction.
These results suggest that, with the addition of α-methyl substituent, the anti-E2 reaction is completely dominant considering the energetics from ethyl to butyl reactions in the gas phase.This is consistent with the scattering experimental phenomenon [41] that the character of forward scattering becomes more and more obvious with the increased size of residue R, where scattering into the forward hemisphere is a mechanistic fingerprint of E2 reactions.Further dynamics simulations are desired for revealing the variation in an aspect of dynamical factors.

Effects of Leaving Group
It is of interest to explore the effect of the leaving group along the α-methyl substitution.Figure 4a compares the activation barrier heights of F − + RCl and F − + RI; it can be seen that, as the enhanced leaving group ability varies from Cl to I, both S N 2 and E2 reaction barriers are dropped by similar amounts.More significantly, with the increased number of substituents of n = 0-3 the barrier heights decrease more dramatically from 3.5/3.7,3.8/4.1, to 3.9/4.5 kcal/mol for the S N 2/E2 reaction pathways along Y = Cl to I. Their key TS structural character could be closely related to this change.Variation in the leaving group from Cl to I causes the elongation of the C α -Y bond ∆L (L Cα-I − L Cα-Cl ) ranging from 0.26, 0.29, 0.32 to 0.38Å with n going from 0 to 3 for the TS structure of inv-S N 2. Similarly, the bond elongation ∆L of C α -Y for anti-E2 TS also grows along with methyl substitution degree n.The looser transition states typically align with the reduced barrier heights, resulting in heightened reactivity [20,56,57].

Computational Methods
The stationary points for a series of F − + RY (R = CH3, C2H5, i C3H7, t C4H9 and Y = Cl, I) reactions are studied by second-order Møller-Plesset perturbation MP2 [59,60] with the frozen core (FC) method.The atoms of H, C, F, and Cl are based on Dunning and Woons aug-cc-pVDZ [61,62] basis set.For I, the core electrons use the Wadt and Hay ECP [63] and the valence electrons use a 3s, 3p basis, plus a d-polarization function with a 0.262 exponent, and s, p, and diffuse functions with exponents of 0.034, 0.039, and 0.0873, respectively.
According to previous work, aug-cc-pVDZ basis set has the lowest systematic errors, while G** and aug-cc-pVTZ tend to overestimate and underestimate the single-point energies [64].Aug-cc-pVDZ basis set also showed good agreement with the experiment in previous research on similar reactions [17,30,42].Vibrational analysis is used to determine each stationary point under the harmonic oscillator mode in which balanced structures have no imaginary frequencies and transition states have one normal mode with an imaginary frequency.Furthermore, each transition state is calculated with the internal reaction coordinate (IRC) to make sure that it connects the assumed pre-and post-reaction complexes.The coupled cluster theory with triple excitations treated perturbatively CCSD(T) is often used as a benchmark due to its good accuracy [16,17,25,65].Hence, the relative energies of the stationary points are compared with the high-level CCSD(T)-F12b [16,42] and CCSD(T) [17] benchmark values, and the available B97-1 values [43] for methyl, ethyl, and tert-butyl halide systems, to rationalize the dependability of the computing method.Since there is no report available previously for isopropyl halide reactions, the high-level CCSD(T)/aug-cc-pVTZ or CCSD(T)/ECP/d energy corrections based on MP2 geometries are performed.Gaussian 09 package [66] was used for all computations.Along the leaving group ability changing from Cl, Br to I, a good linear relationship is found between ∆E 0 ‡ and ∆H for both inv-S N 2 and anti-E2 pathways of each F − + RY reaction as presented in Figure 4b.Obviously, the F − + RY reaction set obeys the expression ∆E 0 ‡ = a∆H + C, which connects the barrier with the reaction enthalpy, following the Bell-Evans-Polanyi principle, which is a long-standing chemical theory [58].Furthermore, good relevance is also found between activation barrier difference ∆∆E 0 ‡ and enthalpy difference ∆∆H for Y = Cl and I with the increased degree of substitution of the corresponding S N 2 and E2 pathways as shown in Figure 4c.The above results indicate that, as the leaving group changes from Cl to I, the reaction becomes more exothermic and the barrier drops.Barriers of both inv-S N 2 and anti-E2 reactions are found to exhibit good linear dependences with halogen electronegativity increasing in the order of I (2.66) < Br (2.96) < Cl (3.16) as shown in Figure 4d.The above results suggest the decreased electronegativity of Y is expected to lead to a looser TS structure (elongation of C-Y bond), and further a higher reaction reactivity.

Computational Methods
The stationary points for a series of F − + RY (R = CH 3 , C 2 H 5 , i C 3 H 7 , t C 4 H 9 and Y = Cl, I) reactions are studied by second-order Møller-Plesset perturbation MP2 [59,60] with the frozen core (FC) method.The atoms of H, C, F, and Cl are based on Dunning and Woons aug-cc-pVDZ [61,62] basis set.For I, the core electrons use the Wadt and Hay ECP [63] and the valence electrons use a 3s, 3p basis, plus a d-polarization function with a 0.262 exponent, and s, p, and diffuse functions with exponents of 0.034, 0.039, and 0.0873, respectively.
According to previous work, aug-cc-pVDZ basis set has the lowest systematic errors, while G** and aug-cc-pVTZ tend to overestimate and underestimate the single-point energies [64].Aug-cc-pVDZ basis set also showed good agreement with the experiment in previous research on similar reactions [17,30,42].Vibrational analysis is used to determine each stationary point under the harmonic oscillator mode in which balanced structures have no imaginary frequencies and transition states have one normal mode with an imaginary frequency.Furthermore, each transition state is calculated with the internal reaction coordinate (IRC) to make sure that it connects the assumed pre-and post-reaction complexes.The coupled cluster theory with triple excitations treated perturbatively CCSD(T) is often used as a benchmark due to its good accuracy [16,17,25,65].Hence, the relative energies of the stationary points are compared with the high-level CCSD(T)-F12b [16,42] and CCSD(T) [17] benchmark values, and the available B97-1 values [43] for methyl, ethyl, and tert-butyl halide systems, to rationalize the dependability of the computing method.Since there is no report available previously for isopropyl halide reactions, the high-level CCSD(T)/aug-cc-pVTZ or CCSD(T)/ECP/d energy corrections based on MP2 geometries are performed.Gaussian 09 package [66] was used for all computations.

Conclusions
In this paper, F − ions with a series of α-substituted alkyl chlorides and alkyl iodides in the gas phase are studied by using MP2/aug-cc-pVDZ or MP2/ECP/d methods, and the effect of methyl substituents and leaving group ability on the competition of E2 and S N 2 pathways is investigated.As the degree of methyl substitution increases, the preference for anti-E2 over inv-S N 2 enlarges, and, till R = t C 4 H 9 , anti-E2 becomes overwhelmingly dominant.The prediction of this reaction trend is consistent with the differential scattering experiment [41].This can be explained by energy decomposition analysis.With the increased degree of substitution, the drop in the interaction energy between reactants cannot compensate for the rapid growth of preparation energy resulting from the more distorted transition state structure for the inv-S N 2 reaction pathway.
In the aspect of the leaving group, the barrier heights for both E2 and S N 2 reactions drop more dramatically along Y = Cl to I with the increased number of substituents, which can be attributed to the relaxation of the key transition state structure.Variation in the leaving group from Cl to I results in the larger extension of the C α -Y for the TS structure of anti-E2 and inv-S N 2 with the methyl group going from 0 to 3, and thus the larger reaction activity.Along the leaving group ability changing from Cl, Br to I, a notable linear relationship is found between ∆E 0 ‡ and ∆H for both the inv-S N 2 and anti-E2 channels of each F − + RY reaction, indicating the smaller the reaction barrier, the more negative the reaction enthalpy.These results correspond to the decreasing halogen electronegativity from Cl to I, which results in the more relaxed structural characters of TS and thus the larger reaction probability.This work lays the foundation for our subsequent dynamic simulations.Since it is known that the dynamics of the reaction may deviate from the potential energy surface, dynamics simulations are able to intensify our understanding of the effects of the substitution and leaving group on the competition mechanism between E2 and S N 2 reactions.

Figure 1 .
Figure 1.Potential energy curves and stationary points at MP2/aug-cc-pVDZ level for F − + RCl reactions.The energy (in kcal/mol) is relative to F − + CH3Cl (a) and F − + RCl (b) reactants at 0 K, and does not include ZPE.In (b), the black, blue, and pink numbers represent F − + C2H5Cl, F − + i C3H7Cl, and F − + t C4H9Cl reactions, respectively.

Figure 1 .
Figure 1.Potential energy curves and stationary points at MP2/aug-cc-pVDZ level for F − + RCl reactions.The energy (in kcal/mol) is relative to F − + CH 3 Cl (a) and F − + RCl (b) reactants at 0 K, and does not include ZPE.In (b), the black, blue, and pink numbers represent F − + C 2 H 5 Cl, F − + i C 3 H 7 Cl, and F − + t C 4 H 9 Cl reactions, respectively.

Figure 3 .Figure 3 .
Figure 3. (a) Activation barrier heights ∆E0 ‡ (full line) and overall barrier heights (dashed line) of anti-E2 and inv-SN2 transition states as a function of methyl substitution degree n of C α (n = 0-3).(b) Barrier difference ∆∆E0 ‡ between anti-E2 and inv-SN2 as a function of n (n = 1-3).Values of Y = Cl are Figure 3. (a) Activation barrier heights ∆E 0 ‡ (full line) and overall barrier heights (dashed line) of anti-E2 and inv-S N 2 transition states as a function of methyl substitution degree n of C α (n = 0-3).(b) Barrier difference ∆∆E 0 ‡ between anti-E2 and inv-S N 2 as a function of n (n = 1-3).Values of Y = Cl are reported.All the energies are in kcal/mol.(c) Energy decomposition analysis of the anti-E2 and inv-S N 2 transition structure between F − + (CH 3 ) n CCl (n = 0-3).

Figure 4 .
Figure 4. (a) Comparison of activation barriers between inv-SN2 and anti-E2 TS in the F -+ RY reaction calculated by MP2 method.The correlation of (b) activation barrier heights ∆E0 ‡ and reaction enthalpy ∆H, (c) activation barrier difference ∆∆E0 ‡ and reaction enthalpy ∆∆H between Y = Cl and I, and (d) activation barrier heights and electronegativity of leaving group Y.

Figure 4 .
Figure 4. (a) Comparison of activation barriers between inv-S N 2 and anti-E2 TS in the F − + RY reaction calculated by MP2 method.The correlation of (b) activation barrier heights ∆E 0 ‡ and reaction enthalpy ∆H, (c) activation barrier difference ∆∆E 0 ‡ and reaction enthalpy ∆∆H between Y = Cl and I, and (d) activation barrier heights and electronegativity of leaving group Y.

Figure S2 :
Stationary point structures of E2 and SN2 pathways for (a) F-+ CH3Y, (b) F-+ C2H5Y, (c) F-+ iC3H7Y, (d) F-+ tC4H9Y(Y = Cl, I) reaction optimized at the MP2/aug-cc-pVDZ(ECP/d) theoretical level.Bond distances are in Å, and black/pink line represents Y = Cl/I.; Figure S3: Interaction energy decomposition according to formula ∆E int = (∆E els + ∆E XC + ∆E Pauli ) + ∆E orb = ∆E steric + ∆E orb .∆E els is electrostatic interacton term, ∆E XC is the change of exchange-correlation energy during complexation process, and ∆E Pauli is the Pauli repulsion effect between electrons in occupied orbitals of the fragments and is invariably positive.They combine to form steric term ∆E steric (Dashed line).∆E orb is orbital interaction term and represented by short dotted line.The full line represents ∆E int .

Table 1 .
The relative energies (kcal/mol) for stationary points of the E2 and SN2 pathways on the F − + RY with different methods.

Table 1 .
The relative energies (kcal/mol) for stationary points of the E2 and S N 2 pathways on the F − + RY with different methods.