Competing E2 and SN2 Mechanisms for the F– + CH3CH2I Reaction

Article pubs.acs.org/JPCA

Competing E2 and SN2 Mechanisms for the F− + CH3CH2I Reaction Li Yang,† Jiaxu Zhang,*,† Jing Xie,‡ Xinyou Ma,§ Linyao Zhang,† Chenyang Zhao,† and William L. Hase§ †

School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, People’s Republic of China Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States § Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States ‡

S Supporting Information *

ABSTRACT: Anti-E2, syn-E2, inv-, and ret-SN2 reaction channels for the gas-phase reaction of F− + CH3CH2I were characterized with a variety of electronic structure calculations. Geometrical analysis confirmed synchronous E2-type transition states for the elimination of the current reaction, instead of nonconcerted processes through E1cb-like and E1-like mechanisms. Importantly, the controversy concerning the reactant complex for anti-E2 and inv-SN2 paths has been clarified in the present work. A positive barrier of +19.2 kcal/mol for ret-SN2 shows the least feasibility to occur at room temperature. Negative activation energies (−16.9, −16.0, and −4.9 kcal/mol, respectively) for inv-SN2, anti-E2, and syn-E2 indicate that inv-SN2 and antiE2 mechanisms significantly prevail over the eclipsed elimination. Varying the leaving group for a series of reactions F− + CH3CH2Y (Y = F, Cl, Br, and I) leads to monotonically decreasing barriers, which relates to the gradually looser TS structures following the order F > Cl > Br > I. The reactivity of each channel nearly holds unchanged except for the perturbation between anti-E2 and inv-SN2. RRKM calculation reveals that the reaction of the fluorine ion with ethyl iodide occurs predominately via anti-E2 elimination, and the inv-SN2 pathway is suppressed, although it is energetically favored. This phenomenon indicates that, in evaluating the competition between E2 and SN2 processes, the kinetic or dynamical factors may play a significant role. By comparison with benchmark CCSD(T) energies, MP2, CAM-B3LYP, and M06 methods are recommended to perform dynamics simulations of the title reaction. Brickelhaupt12 and Truhlar13 groups for anti-E2, syn-E2, and SN2 pathways to update the conclusions about the accuracy of ab initio methods and various density functionals. Pliego Jr. and co-worker14 investigated the reaction between KF and ethyl bromide catalyzed by 18-crown-6 using theoretical calculations. They concluded that the K+ ion can favor the SN2 reaction over the anti-E2 pathway, while the crown ether ring hinders the syn-E2 route. In this paper, the reaction of a solvated free fluoride ion with ethyl bromide has been calculated in order to understand the role of a polar environment in determining reactivity. An essential issue in experiment is that the E2/SN2 branching ratios are hard to determine as a result of the difficulty in distinguishing these two reactions.4,17 It is assumed that the dynamics or kinetics play an important role in the contest between E2 and SN2 because the barrier heights for both channels are extremely close, as observed on the static PES profile. In this aspect, chemical dynamics simulations successfully brought to light an understanding of these experiments at the atomistic level and thus are highly desired. On the other hand, comprehensive discussions focused on the

1. INTRODUCTION Bimolecular nucleophilic reactions, elimination (E2) and substitution (SN2), are both fundamental reactions in organic chemistry.1,2 In many cases, E2 and SN2 reactions are competitive. The model system X− + CH3CH2Y (X = F, Cl, ClO, CH3O, CN, et al.; Y = F, Cl, Br, and I) has been the subject of various investigations in the solution phase and gas phase experimentally.3−6

An increasing number of ab initio calculations give important clues to the understanding of the E2/SN2 competition and rules with respect to the nature and structure of the bases, described by the reaction’s potential energy surface (PES).7−16 In early theoretical studies, Yamabe et al.7 revealed the mechanism of the E2 reaction and found a totally different transition state (TS) geometry for E2 compared with that for the SN2 reaction by investigating X− + CH3CH2Y (X = F, Cl; Y = F, Cl) systems. Gronert et al.10 explored the F− (PH2−) + CH3CH2Cl reactions and revealed that both SN2 and E2 reactions are feasible for first-row nucleophiles, whereas the E2 reaction is prohibited for second-row nucleophiles. Later, the benchmark for the PESs of X− + CH3CH2X (X = F, Cl) was been established by the © 2017 American Chemical Society

Received: September 21, 2016 Revised: January 10, 2017 Published: January 17, 2017 1078

DOI: 10.1021/acs.jpca.6b09546 J. Phys. Chem. A 2017, 121, 1078−1085

Article

The Journal of Physical Chemistry A competition between SN2 and E2 mechanisms of the identity reaction system X− + CH3CH2X or the influences led by nucleophiles.7−9,12,13 In contrast, fewer efforts were put on the nonidentity system X− + CH3CH2Y and the effects of leaving group ability, which was mostly confined to F and Cl. In particular, there is still a lack of study of the reactions of ions with alkyl iodide. Very recently, Wester and co-workers investigated a series of reactions X− + RY (X = F, Cl; R = CH3, C2H5, iC3H7, tC4H9; and Y = Cl, I), which exhibited a transition from the dominant SN2 to dominant E2 by substitution of the α-carbon.18 Interpreting the dynamics and kinetics by either statistical calculations or chemical dynamics simulations requires accurate PESs. In the current work, we report a study of the PES for the F− + CH3CH2I reaction in detail, employing a variety of methodologies. The purpose of this study is 4-fold. (1) The character of the PES profile with iodine included as the leaving group is built, and the controversy corresponding to the reactant complex (RC) for E2/SN2 is highlighted. (2) It is of interest to compare with the PES features of F− + CH3CH2Y (Y = F, Cl, Br, and I) to study the effects on E2/SN2 competition mechanisms led by different leaving groups. (3) The reaction kinetics and the branching ratio between the competitive pathways are evaluated and discussed by RRKM theory. (4) Considering that no previous computational methods or experimental data are available for the current reaction, it is important to evaluate and validate the performance of various electronic structure methods against the ab initio benchmark to choose an appropriate method for direct dynamics simulations.

Figure 1. Scheme reaction energy profiles (kcal/mol) for E2 and SN2 reactions of F− + CH3CH2I at the CCSD(T)PP/t//MP2/ECP/d level of theory.

previously.7−9,12,13 The base-induced bimolecular elimination could proceed via anti- and syn-elimination (anti-E2 and synE2) pathways and form product CH2CH2 + HF + I−. For the anionic SN2 reactions, F− could attack the carbon on the either back side (inv-SN2) or front side (ret-SN2) referring to I−, leading to product CH3CH2F + I−. As shown in Figure 1, the F− + CH3CH2I reaction is exothermic, with the energies of two products being −26.2 (E2) and −44.0 kcal/mol (SN2). The CCSD(T) barrier of the syn-E2 is 11.1 kcal/mol higher than that of the anti-E2 pathway, indicating that the latter is favored in the E2 reaction. Because of the severe steric repulsion resulting from the proximity between the nucleophile fluorine ion and the leaving group iodine, the front side SN2 barrier is much higher in energy (cal. 19.2 kcal/mol) than that of inv-SN2, signifying that the ret-SN2 pathway is the most unfavorable. The inv-SN2 is slightly preferred over the anti-E2, with the barrier height differing by 0.9 kcal/mol. The preference of the four channels for the F− + CH3CH2I reaction is basically similar to that of F− + CH3CH2Y (Y = F, Cl, Br).7,8,12−14 As shown in Table 1, notably, the existence of all stationary points on the CCSD(T) PES has been predicted by MP2 and DFT functionals except for B3LYP, which failed in locating the TSs of anti-E2 and inv-SN2. This failure has also been found for F− + CH3CH2F by Gronert and co-workers.36 The difficulty in distinguishing the preference for the inv-SN2 or anti-E2 pathway lies in both experiments and the calculated PES profile. The barrier heights of the two channels are very close and are sensitive to calculation methods and basis sets.4−7,12,14 The branching ratio of inv-SN2/anti-E2, as well as that of anti-E2/syn-E2, remains unidentified. On the other hand, the actual atomic level of the mechanisms for a reaction often deviate from the reaction path defined by the IRC, and the dynamic simulations are vital. In order to choose an appropriate method for simulations, the geometries, vibrational frequencies, and energies obtained by a variety of computational methods have been discussed and are compared in section 3.3. 3.2. Geometrical Character. Figure 2 depicts structures and geometry parameters of all stationary points along the reaction coordinate for the F− + CH3CH2I reaction obtained at the MP2/ECP/d level of theory. Initially, reactants F− and staggered ethyl iodide can form a RC. Controversy concerning

2. COMPUTATIONAL METHOD Bimolecular nucleophilic elimination and substitution of F− + CH3CH2I were investigated at different levels of theory. All of the critical structures were fully optimized using MP219,20 and various density functional theory (DFT)21−24 methods, that is, CAM-B3LYP, M06-2X, BhandH, B3LYP, and M06, combined with the ECP/d basis set. To test the effect of basis sets, another basis set ECP/t was also used for MP2 and CAMB3LYP calculations. The basis sets ECP/d and ECP/t have been defined previously.25−29 To guarantee the correct connection of the minima of the TS, the intrinsic reaction coordinate (IRC)30 was calculated at the MP2/ECP/d level. Higher level coupled cluster theory with triple excitations treated perturbatively CCSD(T) calculations31 were performed based on MP2/ECP/d optimized geometries, serving as the benchmark for the current reaction. The basis set, denoted as PP/t,32 was used for the coupled cluster single-point energy calculations, which has been shown to successfully represent the nature of the methyl iodide systems.33,34 All calculations were carried out using the Gaussian0935 program. 3. RESULTS AND DISCUSSION 3.1. Benchmark PES. A schematic reaction coordinate PES diagram at the CCSD(T)/PP/t level of theory for the F− + CH3CH2I reaction is given in Figure 1. Table 1 displays the energies relative to the separated reactants without zero-point energy (ZPE) for the stationary points calculated with various methods and basis sets. As depicted in Figure 1, both E2 and the SN2 reactions of F− + CH3CH2I have the shape of a doublewell PES with a TS connecting a RC and a product complex (PC) as revealed for X− + CH3CH2Y (X, Y = F, Cl) 1079

DOI: 10.1021/acs.jpca.6b09546 J. Phys. Chem. A 2017, 121, 1078−1085

Article

The Journal of Physical Chemistry A Table 1. Electronic Structure Theory Energies (kcal/mol) for F− + CH3CH2I without ZPEa MP2 −

HF + C2H4 + I (E2) CH3CH2F + I− (SN2) inv-SN2-TS ret-SN2-TS anti-E2-TS syn-E2-TS aRC/cRC bRC/dRC cPC/dPC bPC aPC

CAM-B3LYP

ECP/d

ECP/t

ECP/d

ECP/t

−26.3 −42.1 −15.4 21.5 −15.8 −4.2 −18.7 −19.4 −51.8 −49.0 −41.5

−21.4 −38.0 −13.3 23.8 −14.9 −3.9 −18.3 −19.0 −49.4 −47.5 −38.5

−31.9 −51.8 −18.3 16.0 −18.7 −7.1 −19.3 −19.8 −58.8 −52.3 −44.2

−31.7 −51.0 −16.8 17.8 −17.2 −5.9 −18.5 −19.0 −57.8 −51.9 −43.6

M06-2x

BhandH

B3LYP

M06

ECP/d −36.6 −55.5 −20.4 14.6 −20.6 −8.9 −21.8 −21.0 −64.0 −57.2 −50.7

−30.7 −58.8 −24.1 11.6 −24.4 −13.4 −24.5 −25.2 −68.2 −55.6 −48.8

CCSD(T)

exptlb

PP/t −33.2 −50.0 − 12.1 − −9.7 − −19.6 −56.6 −52.6 −44.4

−29.7 −48.2 −20.4 12.2 −19.5 −8.8 −20.8 −20.8 −56.4 −49.9 −42.9

−26.2 −44.0 −16.9 19.2 −16.0 −4.9 −19.6 −20.1 −54.0 −50.9 −42.7

−37.6 ± 0.1 −48.7 ± 0.3

Energies are in kcal/mol with respect to the F− + CH3CH2I reactants and are at 0 K. bThe reaction enthalpies of reaction at 0 K with ZPE calculated from standard molar enthalpies of formation in ref 37. a

compared to those of CH3CH2I and HF, and the C−C bond contracts to 1.466 Å. The variation trends of the syn-E2-TS geometry are similar to those found for anti-E2, supporting the fact that both elimination channels have E2-type TSs. 3.3. Comparisons of Different Methods. 3.3.A. Structure Parameters. The geometries determined for all stationary points are listed in Table S1 of the Supporting Information. As shown in Table S1, the differences in geometries led by varying the basis set from ECP/d and ECP/t are discussed for MP2 and CAM-B3LYP, respectively. Generally, there are only small differences in bond distances (less than 0.05 Å) and bond angles (less than 1.0°) for both methods with different basis sets. MP2 exhibits relatively larger changes in the geometry with increasing size of the basis set. The Cβ−Hβ−F angle in syn-E2-TS and the Cα−Hα−F angle in bRC vary by 1.4 and 2.1° for the two basis sets. F−Cα−I and I−Cα−Cβ bond angles in cPC differ by 2.4 and 1.9°, respectively. The only difference larger than 1° for the CAM-B3LYP method lies in the F−Cα−I angle (1.2°) in cPC. The results suggest that the ECP/d basis set is sufficient to describe the geometrical character of the F− + CH3CH2I reaction. Except that B3LYP failed to locate TSs of anti-E2 and invSN2 and their RCs, in general, the geometrical parameters obtained by DFT methods with ECP/d agree well with those obtained by the MP2 method. The largest difference lies in bond the angle Cβ−Hβ−F of anti-E2-TS, and it is nearly 180° obtained by MP2 and CAM-B3LYP. For BhandH and M06-2X, this angle bends 5 and 10° from the linear form, respectively. In addition, for the bond angles F−Cα−I and I−Cα−Cβ of cPC, the differences between M06-2X and MP2 are 3.2 and 3.7°. 3.3.B. Vibrational Frequencies. Vibrational frequencies are listed in Table S3. They are generally similar for various theories, with a relative discrepancy [νDFT(i) − νMP2(i)]/ νMP2(i) for each ith vibrational mode of less than 5% for most of the modes except for the imaginary frequency of the TS. MP2 gives much larger imaginary values for TSs than DFT does. For inv-SN2-TS, MP2 gives values 1.15 (for M06-2X)− 1.45 (for CAM-B3LYP) times larger than the DFT functional values. For anti-E2-TS, the imaginary values dramatically dropped from 806 cm−1 for MP2 to 109−841 cm−1 for DFT functionals, indicating that DFT gives much looser geometries and flatter saddle points on the energy hypersurface than MP2. The imaginary frequencies obtained by B3LYP are much lower than other functionals when compared to those of MP2, that is, the relative values MP2/CAM-B3LYP/M06-2X/M06/

whether anti-E2 and inv-SN2 reaction pathways share the same prereactive minimum has been reported in previous work for the F− + CH3CH2Cl reaction. Cardini et al.16 clarified this discrepancy and found that after tightening the convergence criteria or performing further annealing two distinct minima would move to coincide to one. They also pointed out the important role of dispersity and the size of basis sets in complex determination. In the present work, a single prereactive minimum, aRC (cRC), is obtained for anti-E2 and inv-SN2, ascribed to the use of a large basis set and sufficient consideration of dispersion. This initial reaction complex is a weakly bonded, ion−dipole complex with the F− situated on the opposite side of the C−I bond. In this complex, the geometry of the CH3CH2I varies little, and the C−I bond elongates slightly due to interaction with F− (C−I = 2.215 Å in aRC and 2.160 Å in CH3CH2I). The C−C bond shortens around 0.01 Å for the convenience of F− shifting to βhydrogen, as shown in Figure 2. The syn-E2 and ret-SN2 paths also share a common hydrogen-bonded minimum along the reaction coordinate, bRC (dRC), which has a distinct structure from that of aRC (cRC); see Figure 2. Instead of interacting with C and β-hydrogen, the nucleophile interacts with a αhydrogen, leading to the elongation of both C−I and C−Hα bonds compared with CH3CH2I. Bunnett and Cram7,37−39 pointed out that the TS for a E2 reaction may vary from nonconcerted processes corresponding to the E1cb-like and E1-like mechanisms to the synchronous E2-type TS. For the E2-type reaction,37 proton transfer, C−C double-bond formation, and leaving group departure occur simultaneously, which can be identified by the geometry of the TS. The deprotonation of β-hydrogen at anti and syn with respect to the Cα−I bond leads to two distinct TSs, anti-E2-TS and syn-E2-TS. The anti-E2-TS is perfectly periplanar and has an I−Cα−Cβ−Hβ dihedral angle of 180°. It has a nearly linear Cβ−Hβ−F angle and a long Cβ−Hβ distance of 1.302 Å. The Hβ−F distance (1.277 Å) is also relatively long, indicating the the proton Hβ transports midway between Cβ and F. The C−I bond is elongated to 2.381 Å, whereas the C−C bond (1.454 Å) is much shorter than that in ethyl iodide (1.524 Å), indicating that it is a concerted process of leaving group expulsion and partial double bond formation. Although the synE2 TS for the reaction of F− with CH3CH2I is not completely eclipsed, it is nearly syn periplanar with an I−Cα−Cβ−Hβ dihedral angle of 2.6°. The angle of Cβ−Hβ−F slightly bends (173.3°). The Cβ−Hβ, Cα−I, and Hβ−F bonds are stretched 1080

DOI: 10.1021/acs.jpca.6b09546 J. Phys. Chem. A 2017, 121, 1078−1085

Article

The Journal of Physical Chemistry A

BhandH/B3LYP are 1:0.89:0.96:0.83:0.99:0.80 and 1:0.73:0.74:1.46:0.75:0.42 for ret-SN2-TS and syn-E2-TS, respectively. It suggests that B3LYP has a much flatter PES shape in proximity of the TS, which could be the reason why inv-SN2-TS, anti-E2-TS, and their RCs cannot be located. The effects of the basis set on frequencies are discussed for MP2 and CAM-B3LYP methods. Enlarging the basis set from ECP/d to ECP/t has less influence on the frequencies of the minima, with a relative uncertainty less than 5%, than that on the imaginary frequencies of saddle points. Usually, enlargement of the basis set increases the imaginary frequencies, suggesting that the augment basis set plays a role in “tightening” the geometry. We tried the ECP/t basis set to locate TSs of inv-SN2 and anti-E2 with the B3LYP method and obtained inv-SN2-TS but still failed to locate anti-E2-TS, illustrating again that there is a very flat region around the B3LYP saddle point and the unusually loose TS geometry is hard to achieve. 3.3.C. Energies. Reaction energies with ZPE for two product channels HF + CH2CH2 + I− (P1) and I− + CH3CH2F (P2) are listed in Table S2. The experimental reaction exothermicities with ZPE at 0 K are −37.6 and −48.7 kcal/mol for elimination product P1 and substitution product P2, respectively.40 CAM-B3LYP and B3LYP give the best agreement with the experiment, which differs by 0.7−2.6 kcal/mol, whereas CCSD(T) predicts less negative values. Augmenting the basis set does not improve the performance. As listed in Table 1, when comparing the relative energies with CCSD(T) benchmark values for all of the stationary points, MP2 gives the best accuracy with the largest difference less than 2.3 kcal/mol. In reference to CCSD(T), the mean absolute errors are 1.2 (MP2), 2.8 (CAM-B3LYP), 6.0 (M06-2X), 7.8 (BhandH), and 2.8 kcal/mol (M06), respectively. Obviously, among various DFT functionals, CAM-B3LYP and M06 agree better with benchmark than other functionals, and therefore, they are recommended to perform dynamics simulations. To investigate the reactivity of the four paths, we compare both the overall barrier (the energy difference between the TS and the separated reactants) and the central barrier (the energy discrepancy of the TS and RC), as listed in Tables 1 and 2. Usually, the rate constant is determined by the overall barrier. For the F− + CH3CH2I reaction, the order of overall barrier heights inv-SN2-TS < anti-E2-TS < syn-E2-TS < ret-SN2-TS is less dependent on the level of theory. The difference in energy between inv-SN2-TS and anti-E2-TS becomes even smaller for MP2 and DFT functionals compared to that for CCSD(T), less than 0.4 kcal/mol. With the exception of CAM-B3LYP, most of the DFT functionals substantially underestimated the overall barrier heights compared with MP2 and CCSD(T) results, ∼4 kcal/mol lower. As shown in Table 2, the same preferential sequence of four pathways is also reflected by central barriers with both MP2 and various DFT approaches. It is noted that the DFT methods yield central barriers generally smaller than those of MP2 and CCSD(T) methods. In particular, for both anti-E2-TS and invSN2-TS, density functional approaches even further underestimate these values, varying from 0.1 to 1.4 kcal/mol, resulting in difficulty and failure in locating these TSs for some DFT functional, that is, B3LYP. 3.4. Effects of Leaving Group on F− + CH3CH2Y (Y = F, Cl, Br, and I) Reactions. In this section, we explore the effects of leaving group on a series of reactions F− + CH3CH2Y (Y = F, Cl, Br, and I),12,14−16,36 by comparing their PESs. Although

Figure 2. Stationary point geometries and structural parameters optimized at the MP2/ECP/d level of theory. Bond lengths are in angstroms, and bond angles are in degrees. 1081

DOI: 10.1021/acs.jpca.6b09546 J. Phys. Chem. A 2017, 121, 1078−1085

Article

The Journal of Physical Chemistry A Table 2. Central Barriers (in kcal/mol) for Base-Induced Elimination and Displacement Reactions without ZPE MP2 inv-SN2-TS anti-E2-TS syn-E2-TS ret-SN2-TS

CAM-B3LYP

ECP/d

ECP/t

ECP/d

ECP/t

3.3 2.9 15.2 40.9

5.0 3.4 15.1 42.8

1.0 0.6 12.7 35.8

1.7 1.3 13.1 36.8

M06-2x

BhandH

B3LYP

M06

ECP/d 1.4 1.2 12.1 35.6

0.4 0.1 11.8 36.8

− − 9.9 31.7

CCSD(T) PP/t

0.4 1.3 12.0 33.0

2.7 3.6 15.2 39.3

saddle point on the PES and can be responsible for the lower and lower barrier height with the increasing leaving group ability of F < Cl < Br < I. Discussions concerning the preference between anti-E2 and inv-SN2 have been emphasized because the central barriers of them are essentially close. Bichelhaupt computed ab initio benchmarks and concluded that anti-E2 dominates for F− + CH3CH2F.12 Brauman pointed out that anti-E2 is entropically favored, and although both inv-SN2 and anti-E2 paths are viable, the latter mechanism would most likely dominate for reactions of F− with alkyl chlorides.42 This result was affirmed by the G2(+) calculations.15 Pliego Jr. found the same trend for the F− + CH3CH2Br reaction.14 In the following, RRKM theory has been employed to evaluate the branching ratio of inv-SN2/ anti-E2, as well as the anti-E2/syn-E2 for F− + CH3CH2I reaction, and the reaction kinetics is discussed. 3.5. E2/SN2 Reaction Kinetics and Branching Ratio. There is much interest in considering the above PES for the F− + CH3CH2I reaction and the resulting possible dynamics and kinetics for the four reaction pathways. With the statistical model, TS theory is used to calculate the rate constant for the front side SN2 pathway with a potential energy barrier, while the prereaction complexes must be considered for the remaining three pathways with a submerged barrier.43 Including the prereaction complex, the rate constant for each of the latter three pathways is given by k = kas[kr/(kr + kdis)], where kas is the reactant association rate constant to form the prereaction complex, kr is the rate constant for the complex to form products, and kdis is the rate constant for the complex to dissociate to the reactants. Though the barrier for kr is much lower than that for kdis, the two reactions may be competitive because the TS for kr is much “tighter” than the variational TS for kdis. In addition, F− + CH3CH2I association gives rise to large angular momenta for the complex, resulting in a much larger “rotational barrier” at the TS for kr because it has substantially smaller moments of inertia than those for the dissociation variational TS. If kr ≫ kdis, the rate constant for the pathway is simply kas. Rate constants determined for the OH−(H2O)n + CH3I, n = 0−2, reactions from both experiments44−46 and direct chemical dynamics simulations44−46 provide some insight into the effect of the submerged barrier on the rate constant. (The submerged barriers given below are the values, without ZPE, for the B97-1/ ECP/d theory used for the simulations.) For reaction with OH−, the energy of the submerged barrier is −18.7 kcal/mol and the experimental and simulation rate constants are only 25% smaller than the collision capture association rate constant for temperatures of 210−500 K.44 For reaction with OH−(H2O), the submerged barrier is −13.9 kcal/mol and the experimental and simulation rate constants are 1.5−2.1 times smaller than the collision capture rate constants for temperatures of 213−398 K. 4 5 For reaction with OH−(H2O)2,46 the submerged barrier is −8.8 kcal/mol and the simulation rate constant at 387 K is ∼2 times smaller than

they are studied at different levels of theory, at least reasonable comparisons of their essential and pivotal characters are possible. In general, there are two base-induced E2 elimination reactions and two SN2 reactions, and the double-well potential has been suggested for all four reactions. The sequences of reactivity for the four reaction channels of each reaction are less dependent on the level of theory and show the following decreasing order anti‐E2 > (or < ) inv‐S N 2 > syn‐E2 > ret‐S N2

Despite these common features, the variation of leaving group ability from fluorine to iodine still leads to differences in reaction exothermicities, overall barriers, TS structures, and thus the mechanisms. Their corresponding relative energies and selective geometrical parameters are summarized in Tables S4 and S5. As shown in Table S4, the identity reaction F− + CH3CH2F is endothermic for both SN2 and E2 pathways,12 whereas the nonidentity reaction is exothermic and becomes more and more exothermic along the leaving group ability Cl < Br < I, with energies of −19.3, −22.3, and −26.2 kcal/mol for E2 and −32.1, −39.4, and −44.0 kcal/mol for SN2, respectively. Nibbering pointed out that the overall barrier is decisive for the reaction rate in the gas phase, particularly under lowpressure conditions.41 The effects of nucleophile have been investigated widely;3,10,15 in contrast, relatively little work has been reported on the leaving group ability of the E2 reaction. It can be seen from Table S4 that the calculated overall barriers for ret-SN2 and syn-E2 are higher than those of inv-SN2 and anti-E2, respectively, indicating that inv-SN2 and anti-E2 are energetically favorable in the reactions of F− with CH3CH2Y (Y = F, Cl, Br, I). Therefore, we will focus only on inv-SN2 and anti-E2 in the following discussion. The overall barrier of the F− + CH3CH2Y (Y = F, Cl, Br, I) reaction for inv-SN2 exhibits a monotonic decrease with values of 2.20, −12.62, −13.38, and −16.9 kcal/mol, as shown in Figure S4, respectively, as the leaving group ability goes from fluoride to iodide. Again, the barrier for anti-E2 generally shows the same behavior, namely, −1.27, −14.74, −13.38, and −16.0 kcal/mol, except for Y = Cl and Br, which may be ascribed to the different levels of theory. These trends can be clearly related to the geometric looseness of the TSs’ bonds as a result of the different leaving group ability. The key TS structural parameters for inv-SN2 and anti-E2 are collected in Table S5. Variation of the leaving group along Y = F, Cl, Br, and I causes universal elongation for each bond length, as shown in Table S5, that is, the Cα−Y bond length increases as 1.865, 2.200, 2.379, and 2.447 Å for inv-SN2 TS, respectively, implying a more and more noncompact TS geometry. A similar situation is also found in anti-E2 TS, in which the Cα−Y and F−Hβ bonds progressively increase following the order F < Cl < Br < I. It should be noted that this is a general trend and some fluctuations are supposed to be led by the variety of calculation methods. The gradually looser TS structure relates to the flatter 1082

DOI: 10.1021/acs.jpca.6b09546 J. Phys. Chem. A 2017, 121, 1078−1085

Article

The Journal of Physical Chemistry A

the respective barriers for these three reactions at the CCSD(T)/PP/t level of theory are −16.0, −4.9, and −16.9 kcal/mol, respectively. Syn-E2 and inv-SN2 have similar reaction probabilities, but their respective submerged barriers are −4.9 and −16.9 kcal/mol! A modified statistical model was used to approximate the branching between the reaction pathways with submerged barriers. The probability for each pathway was assumed to be proportional to the number of states at its TS. This analysis requires the angular momentum for the F− + CH3CH2I reactive collisions; the largest impact parameter, bmax, leading to reaction is 6.0 Å, giving rise to an orbital angular momentum of lmax = μbmaxνrel = 747ℏ and rotational quantum number J = 747. Setting the rotational angular momentum at the TS equal to the orbital angular momentum l, the relative number of states at the anti-E2/syn-E2/inv-SN2 TSs was calculated for a collision energy of 1.9 eV to compare with the simulation result.54 The K quantum number, for rotational motion, was assumed to be an active degree of freedom.55 The resulting anti-E2/syn-E2/invSN2 branching values for angular momenta resulting from b = 0, bmax/2, and bmax are 6.7:1.2:1.0, 5.3:1.2:1.0, and 10.9:0.25:1.0, in qualitative agreement with the 3.6:1.3:1.0 proportion determined from the simulations. As discussed above, this result is quite unexpected because anti-E2 and inv-SN2 have similar TS energetics on the PES. This result may arise from multiple factors. One is the kinetic or dynamical factor, that is, the steric effects. When considering the geometrical characteristic of CH3CH2I, F− has three targets, that is, the β-hydrogen, αhydrogen, and α-carbon, and it can readily attack any hydrogen in the broader space in contrast to the crowded environment of α-carbon. From another point of view, the F− lone-pair orbital prefers to overlap with the unoccupied H orbital instead of the occupied sp3 hybrid orbitals of carbon. In terms of the PES, these properties give rise to higher/lower vibrational frequencies at the TSs for the three reaction pathways, affecting their branching ratios.

the collision capture value. The experimental rate constant is ∼9 times smaller than the simulation value, suggesting that the submerged barrier is higher in energy than the B97-1/ECP/d value of −8.8 kcal/mol. In light of the above results for OH−(H2O)n + CH3I, the F− + CH3CH2I rate constants for the inv-SN2 and anti-E2 pathways may be well approximated by their kas values. However, the rate constant for the syn-E2 pathway, with a submerged barrier much higher in energy, may be substantially less than its kas value. The above analyses are based on the statistical model that assumes that the prereaction complex is formed for each pathway and the dynamics are indirect. However, both experimental and simulations studies of SN2 reactions have shown that the indirect mechanism is only important at low collision energies.47−51 For the Cl− plus CH3Cl, CH3Br, and CH3I SN2 reactions, there is a transition from a dominant indirect to direct reaction at collision energies of 0.5−0.8,47,48 0.3−0.6,49,50 and 0.2−0.4 eV,51 for CH3Cl, CH3Br, and CH3I, respectively. Cl− + CH3Cl does not have a submerged barrier, the Cl− + CH3Br submerged barrier is ∼−2.5 kcal/mol, and that for Cl− + CH3I is ∼−5.5 kcal/mol.52 For OH− + CH3I, the B97-1/ECP/d submerged barrier is −18.7 kcal/mol and the transition from a dominant indirect to direct reaction mechanism occurs at an even lower collision energy.44 For temperatures of 300−500 K, which correspond to a collision energy of 0.04−0.06 eV, ∼45% of the SN2 reaction is indirect, while ∼65% of proton transfer is indirect. In considering these results for the F− + CH3CH2I reaction, the atomistic dynamics for the inv-SN2 and anti-E2 pathways with deep submerged barriers may have an appreciable direct component for temperatures of 300−500 K, while the dynamics for syn-E2, with a much higher submerged barrier, may be predominantly indirect. The above illustrates that, in future studies, classical chemical dynamics simulations will be very important to investigate the atomistic dynamics of the F− + CH3CH2I reaction at low collision temperatures (energies) of 200−500 K. ZPE effects are expected to be unimportant for the three pathways with submerged barriers, and classical simulations are expected to give accurate results.45 However, for the ret-SN2 pathway, with a large barrier, classical simulations will allow reaction without ZPE at the barrier. For the three pathways with submerged barriers, the simulations will give (1) the percentages of indirect/direct dynamics for each pathway and, thus, the importance of forming the prereaction complexes; (2) the attribution of the F− + CH3CH2I ion−molecule capture cross section to formation of each of the prereaction reaction complexes; and (3) the importance of nonstatistical, nonRRKM dynamics for the prereaction complexes. The results from item (2) are needed to apply the statistical model. The results from (3) will establish whether the statistical model may be accurately applied. For X− + CH3Y SN2 reactions, extensive nonstatistical dynamics have been found for the X−···CH3Y prereaction complexes.52,53 Preliminary, incomplete direct dynamics simulations have been performed for the F− + CH3CH2I reaction at a 1.9 eV collision energy, using the M06/ECP/d method.18 As expected, the reaction is predominantly direct, with 72 and 75% direct for the SN2 and E2 pathways, respectively. The branching found for the three reaction pathways with submerged barriers is 3.6:1.3:1.0 for anti-E2/syn-E2/inv-SN2, which is not the result predicted by simply considering the reaction energetics because

4. SUMMARY The work here investigated the properties of all stationary points and the competition mechanisms between E2 and SN2 in the reaction F− + CH3CH2I by various methodologies. The geometrical characters showed that the TSs for the eliminations were the concerted E2-type. The overall barriers of the TSs are all under the energy reference of reactants, except for ret-SN2TS with a barrier of 19.2 kcal/mol above the reactants, suggesting that front side SN2 with retention configuration is the least favorable pathway. The anti-E2 is favored over syn-E2, whereas there is no obvious prevalence of anti-E2 over inv-SN2 with very close barrier heights of 0.9 kcal/mol difference at the CCSD(T) level of theory. Anti-E2 and inv-SN2 channels share a common RC, and the energy difference between the RC and TS is not independent of methods. We found that DFT predicts a smaller activation energy (