Revisiting the Dielectric Constant Effect on the Nucleophile and

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Revisiting the Dielectric Constant Effect on the Nucleophile and Leaving Group of Prototypical Backside S2 Reactions: a Reaction Force and Atomic Contribution Analysis n

Laura Milena Pedraza-González, Johan Fabian Galindo, Ronald Gonzalez, and Andrés Reyes J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b06517 • Publication Date (Web): 09 Oct 2016 Downloaded from http://pubs.acs.org on October 9, 2016

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The Journal of Physical Chemistry

Revisiting the Dielectric Constant Effect on the Nucleophile and Leaving Group of Prototypical Backside SN2 Reactions: a Reaction Force and Atomic Contribution Analysis Laura Pedraza-González, Johan F. Galindo, Ronald González, and Andrés Reyes∗ Department of Chemistry, Universidad Nacional de Colombia, Av. Cra 30 # 45-03, Bogotá, Colombia E-mail: [email protected] Phone: +(57)3165000 ext. 10616. Fax: +(57)3165440

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Abstract The solvent effect on the nucleophile and leaving group atoms of the prototypical F− + CH3 Cl → CH3 F + Cl− backside bimolecular nucleophilic substitution reaction (SN 2) is analyzed employing the reaction force and the atomic contributions methods on the intrinsic reaction coordinate (IRC). Solvent effects were accounted for using the polarizable continuum solvent model. Calculations were performed employing eleven dielectric constants, ε, ranging from 1.0 to 78.5, to cover a wide spectrum of solvents. The reaction force data reveals that the solvent mainly influences the region of the IRC preceding the energy barrier, where the structural rearrangement to reach the transition state occurs. A detailed analysis of the atomic role in the reaction as a function of ε reveals that the nucleophile and the carbon atom are the ones that contribute the most to the energy barrier. In addition, we investigated the effect of the choice of nucleophile and leaving group on the ∆E0 and ∆E ‡ of Y− + CH3 X → YCH3 + X− (X,Y= F, Cl, Br, I) in aqueous solution. Our analysis allowed us to find relationships between the atomic contributions to the activation energy and leaving group ability and nucleophilicity.

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Introduction The bimolecular nucleophilic substitution (SN 2) reaction is perhaps one of the most studied chemical transformations, both in gas phase and in solution, because of its importance in chemical and biological processes. 1–16 Two different mechanisms have been identified for the SN 2 reaction: frontside and backside attacks. Numerous studies have analyzed the backside SN 2 mechanism in gas phase of prototypical Y− + CH3 X → CH3 Y + X− reactions, with X, Y = F, Cl, Br and I. 6–12,17–21 These studies have found direct connections between physical and chemical properties of the nucleophile (Nu) and the leaving group (LG) such as: polarizability, 18,22,23 electronegativity, 24 molecular size, 23 ionization potential, 25 proton affinity, 24 among others. 20,26–30 and their corresponding nucleophilicity and leaving group ability. Fewer studies have analyzed SN 2 backside reactions in solvent. 31–43 For instance, Olmstead and Brauman 18 reported that the potential energy surfaces (PES) in the gas phase present a double-well shape whereas in solution they are unimodal. Also, that the reactions occurring in solution are slower than those occurring in gas phase. In addition, that the order of relative nucleophilicity of halide ions in reactions taking place in aprotic solvents is similar to that observed in reactions in gas phase and reversed for reactions ocurring in protic solvents. These authors also reported that the relative order of leaving group ability was identical in gas and in all the considered solvents. The F− + CH3 Cl → Cl− + CH3 F reaction has been widely employed as a prototype to study the solvent effect on SN 2 backside reactions. 42,44–46 For this reaction, the experimental energy barrier changes from 7.5 kcal·mol−1 in the gas phase to 26.9 kcal·mol−1 in water. 12,47 In addition, the activity of the nucleophile (F− ) in water is about 100 times less that in gas phase. 48 Although the aforementioned studies have provided key information on the energetics and kinetics of the reaction in gas phase and solution, to the best of our knowledge there are no studies on the role of each atom on the reaction mechanism, and in particular those 3



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of the nucleophile and leaving group. To that aim we propose an atomic analysis of the reactions employing the reaction force and the atomic contribution methodologies. The reaction force method allows dividing the reaction coordinate in three different regions, each region characterized by either structural or electronic rearrangements. 49–52 The atomic contribution method 53 has been used to identify the role of each atom in the reaction mechanism and its contribution to the energy barrier and reaction energy. 54 With the aim of providing new insights into the backside SN 2 reaction mechanism, we analyze the intrinsic reaction coordinate (IRC) of backside SN 2 reactions occurring in gas phase and different solvents, employing both the reaction force and the atomic contributions methods. 49,54 This work is divided in two: In the first part we employ different solvents to perform a systematic analysis of the solvent effect on the IRC of the F− + CH3 Cl → Cl− + CH3 F backside SN 2 reaction and analyze the effect of the different solvents on each atom and on the energy barrier. The PCM solvation model 55,56 was employed in this study as it reproduces the experimental energy barriers and reaction energies for the aforementioned reaction in aqueous phase. In the second part, we study the set of SN 2 reactions: Y− + CH3 X → CH3 Y + X− with X, Y = F, Cl, Br, I in aqueous phase to study the nucleophilicity and leaving-group ability. This article is organized as follows: section 2 outlines the general concepts of reaction force and reaction work as well as their separation into atomic contributions. Section 3 presents and discusses the results. Section 4 provides some concluding remarks and perspectives of this work.

Methodology Here, we summarize the equations of the reaction force and atomic contributions methodologies proposed by Toro-Labbé and co-workers. 49–52,54,57,58

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Reaction force and energy partitions The reaction force, F (ξ), is defined as the negative derivative of the energy of the molecular system, E(ξ), with respect to the intrinsic reaction coordinate, ξ,

F (ξ) = −

dE(ξ) , dξ

(1)

here, E(ξ) is given in mass-weighted Cartesian coordinates (amu1/2 ·bohr). 59,60 The amount of work done by a molecular system advancing from point A (ξA ) to point B (ξB ) along the reaction path is

WAB = −

Z

ξB

(2)

F (ξ)dξ. ξA

As shown in Figure 1 the IRC can be divided in four regions delimited by five points of ξ along F (ξ) (ξmin , ξmax , ξT S , ξR and ξP ). Partial works can be calculated per region: 51,52,61

W1 = − W3 = −

Z

ξmin

ξR Z ξmax

F (ξ)dξ,

W2 = −

F (ξ)dξ,

W4 = −

ξT S

Z

ξT S

F (ξ)dξ,

ξmin Z ξP

F (ξ)dξ.

(3)

ξmax

The reaction energy, ∆E0 , is equal to the sum of these works

∆E0 = W1 + W2 + W3 + W4 .

(4)

The energy barrier, ∆E ‡ , can be obtained as

∆E ‡ = W1 + W2 .

(5)

Alternatively, the reaction can be divided in three regions: a reactant region located in the interval (ξR , ξmin ), a transition state region located in the interval (ξmin , ξmax ) and a product

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Figure 1: Reaction force profile for the F− + CH3 Cl → CH3 F + Cl− backside SN 2 reaction in water. Dotted lines crossing minimum and maximum of the force divide the profile in reactant (W1 ), transition state (W2 + W3 ) and product (W4 ) regions. ξT S = 0 is set for the transition state point, ξR for the reactants and ξP for the products points. region located in the interval (ξmax , ξP ). Toro-Labbé has proposed that structural changes take place in the reactant and product regions, while the transition region corresponds to an electronic rearrangement.

Atomic contributions in the framework of the reaction force method Haas and Chu 53 showed that the reaction work calculated along a reaction path connecting i structures A and B, WAB , can be divided into atomic contributions, wAB :

WAB =

N X

i wAB ,

(6)

i

where N is the number of atoms in the system. i can be calculated numerically by subdividing Toro–Labbé and co–workers showed that wAB

a portion of the IRC path delimited by points A and B in t fragments: 54

i wAB =

X

gti dit .

t

6


(7)

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here, gti is the energy gradient of atom i in structure t and dit is a vector containing the x, y and z displacements of atom i advancing from configuration t to t + 1 along the IRC.

Computational details All calculations in this work were carried out with the Gaussian 09 suite of programs. 62 Geometries of reactants, transition states and products were optimized at the MP2/6-311++G(d,p) level of theory. Calculations involving bromine and iodine atoms employed the LANL2DZ(dp) pseudopotentials 63 (and basis sets). IRC calculations were performed using the Hessian-based Predictor-Corrector integrator (HPC) algorithm 60 in mass-weighted Cartesian coordinates with a step size of 0.010 a0 ·amu1/2 . 59 Stationary points and transition states were confirmed with frequency calculations. Solvation was simulated with the polarizable continuum model (PCM). 55,56 Ten dielectric constants, (ε), in the range [1.9,78.5] were considered to emulate a wide spectrum of solvents. Reaction forces and works were computed numerically by employing the five-point stencil derivation formula 64 and the Simpson 3/8 rule, 64 respectively.

Results and discussion Solvent effect on the F− + CH3 Cl → CH3 F + Cl− backside SN 2 reaction Energy paths for the reactions occurring in gas phase (central barrier) and in the ten selected solvents are presented in Figure 2a. Calculated energy barriers and reaction energies are compiled in Table 1. A detailed analysis of this table reveals that all considered reactions are exothermic. In addition, we observe that an increase in the dielectric constant of the solvent, ε, results in an increase in the energy barriers (∆E ‡ ) and a decrease in the exothermicity of the reaction energies (∆E0 ). We observe that there is a dramatic variation of ∆E ‡ and ∆E0 for values of ε in the range 1.0 (gas phase) to 12.9 (pyridine), followed by a stabilization for

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values of ε greater than 15.9 (2-Butanol).

‡ The computed ∆Ecent value reported in Table 1 for gas phase (7.5 kcal·mol−1 ) is in a good

agreement with experiment (7.5 kcal·mol−1 ). 12 The ∆E ‡ and ∆E0 in water (24.6 kcal·mol−1 and -8.3 kcal·mol−1 , respectively) are also in good agreement with the experimental values (26.9 kcal·mol−1 47 and -8.1 kcal·mol−1 , respectively). 46

Figure 2: Potential energy (a) and reaction force (b) along the intrinsic reaction coordinate for the F− + CH3 Cl → CH3 F + Cl− reaction in gas phase and in ten solvents. ξT S = 0 corresponds to the transition state point, ξR to the reactants and ξP to the products. For the gas phase profiles, ξRC and ξP C correspond to the reactant- and product-complexes. The values in parentheses are the dielectric constants.

We now analyze the solvent effect on the reaction force profiles. As observed in Figure 2b, reaction forces are dramatically affected by ε in the region preceding the transition state (ξ < 0) while they remain practically unaffected in the region succeeding the transition state 8


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Table 1: Reaction works W1 , W2 , W3 , W4 , ∆E0 , ∆E ‡ for the F− + CH3 Cl → CH3 F + Cl− reaction in gas phase and in ten solvents. Values in kcal·mol−1 . Solvent ε Gas phase 1.0 Heptane 1.9 Benzene 2.3 Chloroform 4.8 THF 7.6 Pyridine 12.9 2-Butanol 15.9 Acetone 20.7 Methanol 32.6 DMSO 47.0 Water 78.5 Variance – a

∆E0 -22.92 -16.67 -16.33 -12.38 -10.78 -9.76 -9.81 -9.33 -8.60 -8.48 -8.32 –

∆E ‡ 7.52a 13.84 15.14 19.76 21.59 22.71 22.81 23.32 24.12 24.29 24.56 –

W1 4.09 8.67 9.68 12.60 14.08 14.95 14.96 15.09 15.47 15.59 15.82 14.28

W2 3.44 5.17 5.46 7.16 7.51 7.77 7.85 8.23 8.65 8.70 8.74 2.99

W3 -12.61 -12.60 -12.47 -12.42 -12.69 -12.89 -12.92 -12.97 -13.03 -13.06 -13.08 0.06

W4 -17.83 -17.91 -19.00 -19.73 -19.69 -19.58 -19.69 -19.68 -19.69 -19.71 -19.80 0.54

Central barrier in gas phase.

(ξ > 0). This finding allows us to conclude that solvent effects on the reaction mechanism are mainly brought about by the differences in solvent-solute interactions observed in this region. We observe that a gradual increase of ε induces shifts in ξmin and ξmax toward more negative and positive values, respectively, and increase in the magnitudes of F(ξmin ) and of F(ξmax ). One important finding is that the observed variations in F(ξmin ) and ξmin are about five times higher than those of F(ξmax ) and ξmax , respectively. We now employ reaction work analysis 57,65–67 to gain further insight into the solvent effect on the reaction. As a first step, we divide the IRC in regions employing the reaction force critical points of Figure 2b. Works W1 and W2 are found in the region defined by ξ < 0. Figure 2b shows that this zone is the most affected by changes in the dielectric constant. As reported in Table 1 the variance of W1 is 4.7 times higher than that of W2 . Toro-Labbé proposed that W1 is associated to structural rearrangements of the reactants while W2 is associated to electronic reordering. Therefore, the data suggest that the variation of ε impacts more prominently the amount of work performed to produce structural changes to prepare the complex to reach 9



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the transition state. We now analyze works W3 and W4 found in the region with ξ > 0. As reported in Table 1, the variance of W4 is 6 times higher than that of W3 . Toro-Labbé proposed that W4 is associated mainly to structural relaxation changes and W3 is due mainly to electronic rearrangements. The analysis of these data reveals that the variation of ε impacts more prominently the work incurred in the structural relaxation of the complex to form the product. In the reaction force scheme W2 and W3 belong to the transition state region. As observed in Table 1 the variance of W2 is on average 50 times higher than that of W3 . This clearly indicates that region (ξmin ,ξT S ) is more strongly affected by ε. A combined reaction force and reaction works analysis allowed us to gain a better understanding of the effect of the solvent on the global features of the reaction. For instance, the reaction force analysis revealed that solvent effects concentrate on the reactant region (ξR ,ξmin ). On the other hand, the reaction works analysis showed that solvent variation affects primarily the magnitude of W1 . Until now, we have analyzed the effect of ε on the IRC. We now aim to assess the effect of ε on atomic properties such as nucleophilicity or leaving group ability. To this aim we employ the decomposition of the reaction works into atomic contributions approach presented in the methodology section. The atomic contributions to the total potential energy for the reaction with ε=78.5 (corresponding to water) are shown in Figure 3 (results for the remaining ε in Figures S1-S10 of the SI). As observed, the largest contribution to the energy barrier comes from the carbon atom, followed by the nucleophile F− and the leaving group Cl− . In contrast, the contribution of the hydrogen atoms is negligible. This contribution order is maintained across the ε choice. Atomic contributions to W1 , W2 , W3 , W4 for the reaction occurring in gas phase and in the different solvents are listed in Figure 4. Here, we observe in all cases that carbon and

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Figure 4: Atomic contributions to (a) W1 , (b) W2 , (c) ∆E ‡ (d) W3 (e) W4 and (f) ∆Eo , for the F− + CH3 Cl reaction in gas phase and in ten solvents.

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to the transition state. We now contrast atomic contributions to W2 for the reaction in solvent and in gas phase with the aim of analyzing the effect of the solvent in this region. Data reported in Figure 4b and Tables S1 to S11 of SI reveal that the atomic contributions of the carbon present the greatest variation with the increase in ε. The atomic contribution analysis of regions W1 and W2 shows that the choice of solvent impacts mainly the contributions of the carbon atom and the nucleophile (Figure 4c). Therefore, this finding indicates that differences in the energy barrier of the reaction in solution and gas phase are in great extent determined by the effect of the solvent on the carbon atom and the nucleophile. We now inspect the atomic contributions to W3 in Figure 4d and find that carbon contribution is of at least 79% while the F− contribution is as high as 15%. Surprisingly, these contributions remain practically independent of ε. Figure 4e depicts the atomic contributions to W4 . Here we observe that the carbon contribution is at least 59% and contributions of Cl− and F− are as high as 24% and 16%, respectively. Surprisingly, W4 is the only region where the contribution of the leaving group surpasses that of the nucleophile. We note that atomic contributions are barely affected by the choice of ε. Figure 4f displays the atomic contributions to ∆E0 (W1 +W2 +W3 +W4 ). We observe that, regardless of the solvent, the atomic contributions follow the order |∆E0C |>|∆E0Cl |>|∆EF0 |>|∆EH 0 | with |∆EC 0 | contributing to at least 70% of ∆E0 . The current analysis allows us to conclude that: 1) Any analysis of the solvent effect on the SN 2 reaction based solely on the IRC may lead to wrong conclusions. For instance, it may reveal that the main solvent effects on the reaction profile are concentrated on the region beyond the energy barrier. 2) Our analysis of the energy gradient (Figure 2b) and work per region (Table 1) data reveals that the effect of the solvent on the total reaction energy is practically dictated by its effect on the region preceding the energy barrier. 3) Our

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energy decomposition per atom analysis shows that the effect of the solvent on the kinetics of the reaction will be determined by its impact on the carbon atom and the nucleophile. These results are quite revealing since chemical intuition dictates that the solvent effect on the kinetics of the reaction is caused mainly by its impact on the nucleophile.

Atomic contribution analysis of backside SN 2 reactions in solution: Y− + CH3 X → YCH3 + X− (X, Y = F, Cl, Br, I) We perform this analysis to understand in more detail the role of each atom along the reaction path and their contribution to the energy barriers and reaction energies. Solvation in water was simulated with the polarizable continuum model (PCM) and ε = 78.5. Table 2: ∆E0 , ∆E ‡ , W1 , W2 , W3 and W4 for the Y− + CH3 X → CH3 Y + X− SN 2 reactions in water. Values in kcal·mol−1 . Reaction ∆E0 ∆E‡ F− + CH3 F 0.00 27.59 − F + CH3 Cl -8.32 24.56 F− + CH3 Br -11.95 20.35 F− + CH3 I -15.22 19.06 − Cl + CH3 F 8.32 32.87 Cl− + CH3 Cl 0.00 28.12 − Cl + CH3 Br -2.57 24.63 − Cl + CH3 I -2.69 23.53 Br− + CH3 F 11.95 32.30 Br− + CH3 Cl 2.57 27.19 Br− + CH3 Br 0.00 23.37 − Br + CH3 I -1.40 22.12 − I + CH3 F 15.22 34.28 I− + CH3 Cl 2.69 26.22 − I + CH3 Br 1.40 23.52 − I + CH3 I 0.00 21.88 a

∆E‡exp a — 26.9 25.2 25.2 22.2 26.6 24.7 22.0 — 27.8 23.7 20.9 22.9 20.0 18.3 17.7

W1 17.42 15.82 14.10 12.28 21.19 17.07 14.07 13.84 19.31 15.62 14.44 13.20 19.99 16.18 14.50 13.74

W2 10.17 8.74 6.25 6.77 11.67 11.05 10.56 9.68 12.99 11.57 8.93 8.92 14.29 10.04 9.02 8.15

W3 -10.17 -13.08 -12.99 -14.29 -8.07 -11.05 -11.57 -10.04 -6.25 -10.56 -8.93 -9.02 -6.77 -9.68 -8.92 -8.15

W4 -17.42 -19.80 -19.31 -19.99 -16.48 -17.07 -15.62 -16.18 -14.10 -14.07 -14.44 -14.50 -12.28 -13.84 -13.20 -13.74

Ref. 47

We first analyze the effect of the leaving group on the energy barrier. As seen in Figures 5a to 5d and Table 2, for a given nucleophile the energy barrier gradually decreases in the order F− , Cl− , Br− , I− . According to the standard definition, 20,68 a leaving group is good 14


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in the sense of yielding a low energy barrier to SN 2 substitution. Therefore, for the series of halides considered here the best and the worst leaving groups are iodine and fluorine respectively. We have analyzed the atomic contributions to ∆E‡ to understand the effect of the LG on the height of the energy barrier. We observe that in all cases the carbon atom performs the greatest contribution to ∆E‡ , and the hydrogen atoms the smallest. We also observe that the order of the contributions of nucleophile and leaving groups vary from system to system. In addition, a close inspection of the contribution of the carbon atom to the energy barrier in reactions with different LG reveals that the observed variation in the magnitude of the energy barrier is directly related to the effect of the LG over the carbon atom and how this change affects the contributions of the carbon atom to the magnitude. The established order for the LG ability is in agreement with the reported experimental data in solution; 18,47 surprisingly, our results also reveal that the main effect of the leaving group on the variation of the atomic contribution to the energy barrier is on the carbon atom and not over the nucleophile or the hydrogen atoms. We now turn our attention to the nucleophile. We can use the atomic contributions and total energy barrier in panels e-h of Figure 5 to establish a nucleophilicity order for the halides considered in this study. To that aim, we have followed the standard definition in which the best nucleophile is the one that reduces the energy barrier the most. 20,68 We decided to analyze first the nucleophilicity of Cl− , Br− and I− and left F− for last. Panels f-h reveal a clear trend in the magnitude of the energy barriers, indicating the following order of nucleophilicity: I− >Br− >Cl− ; this trend is consistent with that established from experimental observations in aqueous phase. 69 We have further analyzed the atomic contributions to the energy barriers and found that in all cases carbon contributes at least 67% of the total energy barrier, with its contribution remaining practically constant in each panel as the nucleophile varies. Similarly, the contribution of the hydrogen atoms is also nearly constant but practically insignificant. For the LG, the trend in contribution to the

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total energy barrier is opposite to the trend observed for the magnitude of the energy barrier: Cl− as a leaving group results in a larger energy barrier than I− , but the relative contribution to the barrier of Cl− is smaller than the contribution of I− . On the contrary, for nucleophiles the trend in contribution to the energy barrier matches the trend observed for the total energy barrier: nucleophiles that result in a larger energy barrier also contribute more to it. We conclude from these data that although carbon makes the most important atomic contribution to the energy barrier, the resulting trend in the size of the energy barrier is directly related to the trend in contribution of the nucleophile. Finally, we analyze the nucleophilicity of F− by inspecting the energy barrier heights in panels e-h and Figure S28 of SI. Our results suggest that F− is the best nucleophile among all the halides and this behavior is independent of the basis set choice (Figure S28). However, this is in total disagreement with widespread acceptance by the organic chemistry community and is in disagreement with the order of nucleophilicity we established for the other halides. Nevertheless, our observations about the erratic behavior of F− described by implicit solvent methods are consistent with other theoretical studies. For instance, Bogdanov and McMahon showed that the use of implicit solvent to mimic the solvent effect for halide nucleophiles in SN 2 reactions is in agreement with experimental results except for the case of F− . 70

Conclusions We have analyzed the solvent effect on the backside SN 2 reaction using the reaction force and the atomic contributions methodologies. Our results show that all changes associated to the variation of ε are concentrated in the region prior to the transition state. Surprisingly, these effects are negligible once the reaction has advanced beyond the transition state. This observation was only possible as a result of the systematic study performed in this work and the use of the reaction force method. The analysis of the variation of the works W1 W2 W3 W4 with ε revealed that W1 is

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the work most affected by the solvent. Along the lines of Toro-Labbé, work W1 has been related with structural changes through the reaction path. Therefore, solvent effects on the reaction affect most strongly the structural changes required to reach the transition state on the reaction mechanism. It is possible to order the partial works in the SN 2 backside F− + CH3 Cl → Cl− + CH3 F reaction as W1 >W2 >W4 >W3 , which is dictated by the presence of the solvent and its interaction with the solute. Work decomposition at the atomic level revealed that the atom most affected by the solvent variation is carbon and not the nucleophile, as common knowledge dictates. However, the nucleophile is also affected by the presence of the solvent. Our analysis of the solvent effect on the leaving group showed that the energy barrier decreases in the order F− >Cl− >Br− >I− in accordance with experimental data. In addition, we observed that the main effect of the LG on the variation of the atomic contributions to the energy barrier is on the carbon atom. Our analysis of the solvent effect on the nucleophile showed that it is possible to order the nucleophilicity for Cl− , Br− and I− (I− >Br− >Cl− ) in agreement with the experimental evidence. For F− the use of implicit PCM presents limitations in the accurate description of the phenomena. 70 This work allowed us to conclude that a combination of reaction force and atomic contribution methods is necessary to describe the solvation phenomena at the atomistic level and provided insights into the physical effect of the solvent. With this in mind we are working on studying new systems using the microsolvatation model.

Acknowledgement We want to thanks to Dr. Natali Di Russo for her comments during the writing part of the paper. JFG and LPG thank to the Departamento Administrativo de Ciencia, Tecnología e Innovación COLCIENCIAS for the “Es Tiempo de Volver” and “Jovenes Investigadores e

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Innovadores 2015” scholarships.

Supporting Information Available Transition state geometries for every reaction, atomic contributions to the total potential energy for the F− + CH3 Cl → Cl− + CH3 F backside SN 2 reaction in ten solvents and gas phase (Figures S1 to S11), atomic contributions to the reaction energy, activation energy, and reaction works (Tables S1 to S11), atomic contributions to the reaction energy, activation energy, and reaction works for the Y− + CH3 X → YCH3 + X− (X, Y = F, Cl, Br, I) reactions (Figures S12 to S27 and Tables S12 to S26). Atomic contributions and reaction works for the F− + CH3 Cl → FCH3 + Cl− reaction in DMSO calculated in center of mass coordinates (Table S28). Effect of the basis set on the energy barrier for the system F− + CH3 Cl → Cl− + CH3 F in water (Table S28) and effect of the basis set on the atomic contributions to the ∆E ‡ (Figure S28). Comparison of the 6-311++G(d,p) and aug-cc-pVTZ basis sets for the Y− + CH3 X → YCH3 + X− reactions in water (Table S29). This material is available free of charge via the Internet at http://pubs.acs.org/.

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Revisiting the Dielectric Constant Effect on the Nucleophile and

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