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Orbital Energy-Based Reaction Analysis of S_{N}2 Reactions

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## Abstract

**:**

^{−}+ CH

_{3}I → ClCH

_{3}+ I

^{−}reaction, for which another reaction path called “roundabout path” is proposed, is found to have a precursor process similar to the roundabout path just before this S

_{N}2 reaction process. The orbital energy-based theory indicates that this precursor process is obviously driven by structural change, while the successor S

_{N}2 reaction proceeds through electron transfer between the contributing orbitals. Comparing the calculated results of the S

_{N}2 reactions in gas phase and in aqueous solution shows that the contributing orbitals significantly depend on solvent effects and these orbitals can be correctly determined by this theory.

## 1. Introduction

_{N}2 reactions are noteworthy in this orbital energy-based reaction analysis because the initial reaction processes of several S

_{N}2 reactions are figured out to be structural change-driven on the minimum energy paths despite these reactions being exothermic [4]. For S

_{N}2 reactions, Hase and coworkers have experimentally questioned the optimum reaction path [14,15,16,17]. Based on a time-resolved ion-molecule cross-beam imaging spectroscopy analysis, they suggested the roundabout reaction path for the Cl

^{−}+ CH

_{3}I → CH

_{3}Cl + I

^{−}reaction [15], in which the CH

_{3}group of CH

_{3}I spins around I

^{−}to move to Cl

^{−}. They also studied the CH

_{3}I + F

^{−}→ CH

_{3}F + I

^{−}reaction mechanism using ion imaging experiments and direct chemical dynamics simulations. Consequently, they proposed three pathways: direct rebound, direct stripping, and indirect hydrogen bonding paths. They also indicated that the results of the experimental rapid intramoleclar vibrational energy distributions and reaction energies are inconsistent with the optimum reaction pathway [16]. Szabó, Czakó, and coworkers performed the dynamics simulation of the F

^{−}+ CH

_{3}Cl → CH

_{3}F + Cl

^{−}reaction by determining its full-dimensional potential energy surfaces [18,19,20]. As a result, they found that the direct rebound mechanism dominates at high collision energies, while the indirect mechanism mainly proceeds at low collision energies [18]. Moreover, they suggested the significance of a double-inversion mechanism, in which the hydrogen atom of the methyl group first moves to F

^{−}and the methyl group then transfers to F

^{−}[19]. Comparing the results of a cross-beam imaging experiment with the dynamics simulation calculation, they, however, found that the mechanism significantly depends on the leaving group, which is X of the F

^{−}+ CH

_{3}X → CH${}_{3}$F + X

^{−}reaction (X = Cl or I) [20]. Based on the above-mentioned orbital energy-based reaction analysis, it is recently found that two S

_{N}2 reactions, F

^{−}+ CH

_{3}Cl → Cl

^{−}+ CH

_{3}F and OHCH

_{3}+ F

^{−}→ OH

^{−}+ CH

_{3}F reactions, are also expected to avoid the minimum energy paths because these reactions give large reactivity indices indicating structural change-driven processes for the initial processes. This suggests that these S

_{N}2 reactions also take other reaction paths than the minimum energy paths to avoid initial structural change-driven processes.

_{N}2 reaction calculations. First, the orbital energy-based reaction analysis theory is formed on the basis of the conceptual DFT [3] in Section 2. After detailing the computational methods in Section 3, the orbital energy-based theory is applied to the calculations of the Cl

^{−}+ CH${}_{3}$I → CH${}_{3}$Cl + I${}^{-}$ reaction and two S${}_{\mathrm{N}}$2 reactions, the Menschutkin reaction (NH${}_{3}$ + CH${}_{3}$Cl → NH${}_{3}$CH${}_{3}^{+}$ + Cl${}^{-}$) and Cl${}^{-}$...CH${}_{3}$Cl → ClCH${}_{3}$...Cl${}^{-}$ reaction, to evaluate the applicability of this orbital energy-based theory in Section 4.

## 2. Orbital Energy-Based Reaction Analysis Theory

- Then, the target orbitals are selected to be the occupied and unoccupied orbitals giving the most varied valence orbital energies. This selection is based on the concept of Equation (7) that reactions proceed to maximize the variation of chemical potentials, i.e., outermost orbital energies.
- The normalized reaction diagram is illustrated by plotting the normalized orbital energy gap:$$\begin{array}{ccc}\hfill {\overline{\Delta}}_{\mathrm{gap}}& =& \frac{{\Delta}_{\mathrm{gap}}-{\Delta}_{\mathrm{gap}}^{\mathrm{initial}}}{{\Delta}_{\mathrm{gap}}^{\mathrm{terminal}}-{\Delta}_{\mathrm{gap}}^{\mathrm{initial}}},\hfill \end{array}$$
- Finally, the orbital energy gap gradient in terms of the normalized IRCs, ${\nabla}_{\overline{V}}{\overline{\Delta}}_{\mathrm{gap}}$, is calculated at the initial reaction stage as a “reactivity index”. Reactions are interpreted to be electron transfer-driven when the orbital energy gap gradient is less than a threshold value, which is temporarily 0.250 in this study.

## 3. Computational Details

## 4. Results and Discussion

#### 4.1. Orbital Energy-Based Reaction Analysis of Cl${}^{-}$ + CH${}_{3}$I → CH${}_{3}$Cl + I${}^{-}$ Reaction

#### 4.2. Reaction Path Search for Cl${}^{-}$ + CH${}_{3}$I → ClCH${}_{3}$ + I${}^{-}$ Reaction

#### 4.3. S${}_{\mathrm{N}}$2 Reactions in Aqueous Solution

## 5. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**A normalized reaction diagram, in which both the gaps and intrinsic reaction coordinates are normalized by setting the values of the reactant and product to be zero and one, respectively. For both forward and backward reactions, the orbital energy gap gradients are estimated by fit to polynomial functions.

**Figure 2.**The normalized reaction diagram of the Cl${}^{-}$ + CH${}_{3}$I → CH${}_{3}$Cl + I${}^{-}$ reaction by LC-BOP/Def2-TZVPD calculation. The images of the molecular orbitals mainly contributing to each reaction process are also shown.

**Figure 3.**The potential energy curve of the overall Cl${}^{-}$ + CH${}_{3}$I → CH${}_{3}$Cl + I${}^{-}$ reaction including its precursor process, which is calculated by the reaction path search method in the GRRM program with LC-BOP+LRD/Def2-TZVPD. The molecular structures are also shown for the local minima (Min) and transition states (TS) on the potential energy curve.

**Figure 4.**The normalized reaction diagrams of the three steps of the Cl${}^{-}$ + CH${}_{3}$I → CH${}_{3}$Cl + I${}^{-}$ reaction given in the potential energy curve of Figure 3, which is calculated by LC-BOP+LRD/Def2-TZVPD. The images of the molecular orbitals mainly contributing to each reaction process are also shown.

**Figure 5.**The potential energy curves and the global hardnesses of the Menschutkin reaction (NH${}_{3}$ + CH${}_{3}$Cl → NH${}_{3}$CH${}_{3}^{+}$ + Cl${}^{-}$) in gas phase and in aqueous solution on their intrinsic reaction coordinates, which are calculated by LC-BLYP/aug-cc-pVTZ. The images of the molecular orbitals mainly contributing to each reaction process are also shown.

**Figure 6.**The normalized reaction diagrams of the three steps of the Menschutkin reaction (NH${}_{3}$ + CH${}_{3}$Cl → NH${}_{3}$CH${}_{3}^{+}$ + Cl${}^{-}$) in gas phase and in aqueous solution, which are calculated by LC-BLYP/aug-cc-pVTZ. The images of the molecular orbitals mainly contributing to each reaction process and the calculated orbital energy gap gradient values are also shown.

**Figure 7.**The potential energy curves and the global hardnesses of the Cl${}^{-}$...CH${}_{3}$Cl → ClCH${}_{3}$...Cl${}^{-}$ reaction in gas phase and in aqueous solution on their intrinsic reaction coordinates, which are calculated by LC-BLYP/aug-cc-pVTZ. The images of the molecular orbitals mainly contributing to each reaction process are also shown.

**Figure 8.**The normalized reaction diagrams of the Cl${}^{-}$...CH${}_{3}$Cl → ClCH${}_{3}$...Cl${}^{-}$ reaction in gas phase and in aqueous solution, which are calculated by LC-BLYP/aug-cc-pVTZ. The images of the molecular orbitals mainly contributing to each reaction process and the calculated orbital energy gap gradient values are also shown.

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**MDPI and ACS Style**

Tsuneda, T.; Maeda, S.; Harabuchi, Y.; Singh, R.K.
Orbital Energy-Based Reaction Analysis of S_{N}2 Reactions. *Computation* **2016**, *4*, 23.
https://doi.org/10.3390/computation4030023

**AMA Style**

Tsuneda T, Maeda S, Harabuchi Y, Singh RK.
Orbital Energy-Based Reaction Analysis of S_{N}2 Reactions. *Computation*. 2016; 4(3):23.
https://doi.org/10.3390/computation4030023

**Chicago/Turabian Style**

Tsuneda, Takao, Satoshi Maeda, Yu Harabuchi, and Raman K. Singh.
2016. "Orbital Energy-Based Reaction Analysis of S_{N}2 Reactions" *Computation* 4, no. 3: 23.
https://doi.org/10.3390/computation4030023