Multi-Level Quantum Mechanics Theories and Molecular Mechanics

Article pubs.acs.org/JPCA

Multilevel Quantum Mechanics Theories and Molecular Mechanics Calculations of the Cl− + CH3I Reaction in Water Peng Liu, Chen Li, and Dunyou Wang* College of Physics and Electronics, Shandong Normal University, Jinan 250014, China ABSTRACT: The Cl− + CH3I → CH3Cl + I− reaction in water was studied using combined multilevel quantum mechanism theories and molecular mechanics with an explicit water solvent model. The study shows a significant influence of aqueous solution on the structures of the stationary points along the reaction pathway. A detailed, atomic-level evolution of the reaction mechanism shows a concerted one-bond-broken and one-bondformed mechanism, as well as a synchronized charge-transfer process. The potentials of mean force calculated with the CCSD(T) and DFT treatments of the solute produce a free activation barrier at 24.5 and 19.0 kcal/mol, respectively, which agrees with the experimental one at 22.0 kcal/mol. The solvent effects have also been quantitatively analyzed: in total, the solvent effects raise the activation energy by 20.2 kcal/mol, which shows a significant impact on this reaction in water.

I. INTRODUCTION Methyl iodide, CH3I, is distributed throughout the ocean,1 and its atmospheric presence emitted from ocean to air plays an important role in atmospheric chemistry.2,3 Its SN2 reaction with Cl−, Cl− + CH3I → CH3Cl + I−, has been extensively studied both experimentally4−8 and theoretically,4,9−15 in gas phase. However, the studies for Cl− + CH3I in aqueous solution are scarce.16−18 Among the experimental studies of Cl− + CH3I in the gas phase, the SN2 reaction dynamics of Cl− + CH3I was studied using crossed molecular beam imaging where a “roundabout” indirect mechanism was identified with combined experimental and direct dynamics simulations.4 The title reaction was also studied by velocity map imaging techniques.5,6 In addition, experimental studies have also been carried out to study the deuterium kinetic isotope effects for the title reaction in gas phase.7,8 Among the theoretical studies, canonical unified statistical theory calculations were employed to study the rate constants of the Cl− + CH3I reaction and its deuterium kinetic isotope effects.9 Quantum calculations,10 such as DFT, MP2, and CCSD(T) theories, were carried out to study the stationary points for the title reaction. Moreover, direct dynamics simulations4,11−13 and ion imaging experiments4,11,13 were carried out to study the direct and indirect (roundabout) reaction mechanisms. A double-inversion mechanism was also revealed for the title reaction in gas phase,14 and its different reaction pathways on the potential energy surface were studied.15 Compared to extensive investigations of the Cl− + CH3I reaction in gas phase, the studies in solution phase are very scarce. Kinetic investigations by experiments were carried out by Moelwyn-Hughes16,17 to study the rate constants for Cl− + CH3I in aqueous solution, where the activation energy was © XXXX American Chemical Society

obtained at 22.0 kcal/mol. For calculating the activation energy of the Cl− + CH3I in water, an ab initio Hartree−Fock calculation with the polarizable continuum model (PCM)18 shows the transition state barrier at 34.1 kcal/mol, which produces a big discrepancy with the experimental value, 22.0 kcal/mol.16,17 In this article, the explicit SPC/E water solvent model was used to describe the water solvent,19 and a combined multilevel quantum mechanism theories and molecular mechanics (MLQM/MM)20−22 approach was employed to study the Cl− + CH3I reaction in aqueous solution. The purpose this study is three-fold: (i) we want to reveal a detailed, atomic level reaction mechanism along the reaction pathway23 for this reaction in solution; (ii) the potential of mean force (PMF) was not only calculated at the DFT/MM level of theory, but also on a more accurate CCSD(T)/MM level of theory; and we want to compare with the experimental barrier height; (iii) we want to investigate the solvent effects on the Cl− + CH3I reaction in water to calculate the contributions of solvent to the PMF.

II. METHODS The Cl− + CH3I SN2 reaction in water was investigated using combined multilevel quantum mechanism theories and molecular mechanics approach.20−22 The reactive solute Cl− + CH3I was treated using multilevel quantum mechanical theories, with the electrostatic potential (ESP), DFT, and CCSD(T) levels of theory, and the classical molecular mechanics was used to treat the nonreactive solvent. The Received: August 14, 2017 Revised: September 22, 2017 Published: September 25, 2017 A

DOI: 10.1021/acs.jpca.7b08103 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A solvent has 1556 water molecules in a 35.9 Å cube box, which was described by a SPC/E model.19 Details of the interaction between the QM and MM regions can be found in our previous publication.20−22 The NWChem package24 was used to carry out the PMF calculations. Direct computation of the PMF bring about huge computational challenges in aqueous solution. As a result, most of the calculations in solution phase have been restricted to DFT calculation for the QM part. Here, we employed the multilevel quantum theories,20−22 consisting of ESP, DFT, and CCSD(T) theories, to describe the QM solute part. In order to achieve a more accurate PMF, the calculation was first performed with the DFT/MM level of theory before shifting to CCSD(T)/ MM. Note that the reference orbitals calculated by DFT level of theory were employed when the calculations were shifted to CCSD(T)/MM. Thus, the PMF under the more accurate CCSD(T)/MM level of theory can be calculated as20 CC CC ← DFT CC ← DFT ΔV AB = (ΔV AA + ΔV BB ) DFT ← ESP DFT ← ESP ESP + (ΔVAA + ΔVBB ) + ΔVAB

(1)

ESP ΔVA,B ,

the last term, was calculated through statistical samplings with classical ESP/MM description, representing the solvent contribution to the PMF. The last two terms combined gives the PMF under the DFT/MM level of theory. In this work, for the calculation with the DFT theory, the M06-2X functional with cc-pVTZ+ basis was used for the Cl, H, and C atoms because it was recommended for reaction barrier calculations using the DFT theory by Truhlar and coworkers.25 As for the heavy I atom, the 6-311G** basis was utilized because it produced good results for the reaction F− + CH3I.26 We optimized the reactant complex (Cl−···CH3I) (RC) in aqueous solution based on the prereaction complex in gas phase,10 and searched the product complex (I−···CH3Cl) (PC) based on the optimized RC through a process of one-bondbroken and one-bond-formed mechanism. The nudged elastic band (NEB)23 reaction pathway was then constructed, and the transition state (Cl···CH3···I)− (TS) was identified. Next, along the imaginary frequency mode, we optimized the translational movement of the TS to identify the final RC and PC in the solution phase; then the whole NEB reaction pathway was reconstructed again with the above final RC and PC. Then, for each point on the NEB reaction pathway, the molecular dynamics equilibration was performed, and the whole NEB pathway was optimized again. We repeated the last procedure until the NEB pathway was converged.

Figure 1. Solvent effects on geometry. Comparison of the stationary points of the Cl− + CH3I → I− + CH3Cl reaction in gas phase and in aqueous solution. The stationary points in gas phase are from Szabó and Czakó’s frozen-core CCSD(T)-F12b/aug-cc-pVQZ calculations.15 The indicated distances are in Angstroms (bond lengths labeled in black and hydrogen bonds in blue), and angles are in degrees (labeled in green).

presence of solvent environment. Therefore, the structures of reactant complex in aqueous solution is greatly influenced by the presence of thousands of water molecules. The transition state was confirmed with numerical frequency calculation in water, which has one imaginary frequency 357.6i cm−1, and it is compared with the one in gas phase in Figure 1b. Comparing with the reactant in Figure 1a, the distance of C−Cl is shortened from 3.618 Å at the RC to 2.464 Å at the TS, while the distance of C−I is enlarged from 2.143 Å at the RC to 2.738 Å at the TS. This feature indicates a concerted one-bondbroken and one-bond-formed mechanism. In addition, both the C−Cl and C−I distances in water are longer than those in gas phase, resulted from the shielding effect of the presence of the solvent. Comparing to the reactant complex, four relatively weak hydrogen bonds formed between the nucleophile Cl− and water molecules in its solvation shell, with an average distance of 2.092 Å, because of the reduced electronegativity of the Cl− at transition state. Furthermore, ∠I−C−Cl in gas phase still has a straight angle, while it is bent at 155.3° in aqueous solution. Again, the comparison of the transition structures between gas phase and solution phase shows the substantial solvent effect on the Cl− + CH3I reaction system. Figure 1c compares the product complexes in gas phase and in water. Again, the shielding effect decreases the interaction between leaving group I− and CH3Cl, leading to a longer distance of C−I 3.725 Å in solution phase than that of 3.593 Å in gas phase. There are seven hydrogen bonds formed between

III. RESULTS AND DISCUSSION A. Reactant Complex, Transition State, and Product Complex. Calculated with DFT/M06-2X/cc-pVTZ+(6311G**) level of theory, the stationary points along the reaction pathway in solution phase were compared with the ones by Szabó and Czakó’s frozen-core CCSD(T)-F12b/augcc-pVQZ calculations in the gas phase.15 For the reactant complex, Figure 1a, there is a big difference of the angle ∠I− C−Cl between gas phase and water: the ∠I−C−Cl is 180.0°, while it is bent at 153.6° in aqueous solution. This is not surprising due to the formation of four strong unevenly distributed hydrogen bonds between the nucleophile Cl− and adjacent water molecules, with an average distance of 1.874 Å, which pulls the Cl− upward. In addition, the distance of C−Cl in aqueous solution, 3.618 Å, is much larger than that in gas phase, 3.065 Å, which is caused by the shielding effect in the B

DOI: 10.1021/acs.jpca.7b08103 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A the I− and water molecules in its solvation shell; they are much weaker with an average distance of 2.496 Å because of the weaker electronegativity of the leaving group I−. The product complex is also a much more bent structure due to the strong solvent effect with the ∠I−C−Cl at 149.7°, while it is 180° in gas phase. As a result, the solvent has a great impact on the structures of the stationary points along the reaction pathway. The shielding effect and the hydrogen bonds formed between the solute and its solvation shell play an important role for these structures in water. B. Detailed Process of Evolution along the Reaction Pathway. Detailed reaction mechanism on the atomic level can be seen from the evolution of the structures along the NEB reaction pathway, as well as the charge distribution, shown in Figures 2 and 3. As the Cl− + CH3I reaction proceeds from the RC (snapshot 1) to the TS (snapshot 6), and finally to PC (snapshot 10), the distance of C−Cl is shortened from 3.618 to 2.464 Å, then to 1.796 Å, and the distance of C−I is enlarged from 2.143 to 2.738 Å, then to 3.725 Å. It shows a concerted

Figure 3. Evolutions of charge distributions for the reaction Cl− + CH3I → I− + CH3Cl in aqueous solution. Points 1, 6, and 10 represent the reactant complex, transition state, and product complex, respectively.

bond formation and breaking process. Meanwhile, a concerted charge-transfer process along the reaction pathway is shown in Figure 3. At the reactant complex, the nucleophile Cl− has all the negative charge, −1.0, and the charges of q(CH3) (+0.2) and q(I) (−0.2) make the substrate CH3I neutral. As the Cl− attacks the CH3I, the negative charge is transferred from the nucleophile Cl− to the leaving group I. The TS (snapshot 6) becomes the turning point of the charge transfer process as the two have similar charges at about ∼−0.79. After the transition state, the leaving group I− gradually has all the negative charge at −1.0, while the charges of nucleophile q(Cl) (−0.3) and q(CH3) (+0.3) make the product CH3Cl neutral. C. Potentials of Mean Force and Solvent Contribution. In Figure 4a, the PMFs are plotted against the solvent

Figure 4. Potentials of mean force and solvent contributions along the NEB reaction path. (a) Potentials of mean force are calculated at DFT/MM and CCSD(T)/MM levels of theory with the reactant state as a reference point. (b) Comparison between gas-phase and internal energies along the NEB reaction path under the CCSD(T)/MM level of theory using the gas-phase energy of the reactant complex as a reference point.

energy contribution. Under the DFT/MM calculation, the barrier height is 19.0 kcal/mol and the free reaction energy is −10.9 kcal/mol; under the CCSD(T)/MM calculation, they are 24.5 and −1.2 kcal/mol. Both free energy barrier heights, 19.0 and 24.5 kcal/mol, have a good agreement with the experimental result at 22.0 kcal/mol.16,17 Because previous gas phase studies10,15 showed this reaction has a negative barrier height, −5.410 and −5.5 kcal/mol,15 our results here indicate

Figure 2. Structures of 10 snapshots along the NEB reaction path for the reaction Cl− + CH3I → I− + CH3Cl in aqueous solution. Snapshot 1 is the structure of reactant complex, snapshot 6 transition state, and snapshot 10 product complex. The indicated distances are in Angstroms (bond lengths labeled in black), and angles are in degrees (labeled in green). C

DOI: 10.1021/acs.jpca.7b08103 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A that the solvent raises this reaction’s activation energy tremendously; thus, it hinders the reactivity in water. Note there is a relatively large difference of the free reaction energy, 9.7 kcal/mol between the DFT/MM and CCSD(T)/ MM results. This is caused by the inability of the DFT method to accurately describe medium-range exchange-correlation energy, which leads to large systematic errors in the calculations of heats of formation of organic molecules,27−30 in this case, the free reaction energy. The contributions to PMF due to the presence of water environment can be analyzed from the solvation energy contribution and polarization effect contribution. Figure 4a shows the contribution from the solvent energy to the free energy barrier height is 15.7 kcal/mol, and the contribution to the free reaction energy is 10.7 kcal/mol. The polarization effect can be obtained from the comparison of the energy profile between solute internal energy and the gas-phase energy in Figure 4b. The solute internal energy was calculated without the solvent energy, and the gas-phase energy was obtained excluding the solvent energy and interactions between the solute and the solvent. The results show that the contributions of the polarization effect to the RC, TS, and PC are 0.3, 4.8, and 1.1 kcal/mol, respectively. Consequently, the net contribution caused by the polarization effect is 4.5 kcal/mol to the TS and 0.8 kcal/mol to the PC. Therefore, the two contributions raised the barrier height by 20.2 kcal/mol, and the free reaction energy by 11.5 kcal/mol. The above quantitative analysis shows that the solvent greatly changes the energetics along the reaction pathway. Between the two solvent effects, the solvent energy plays a bigger role than the polarization effect, for example, of the reaction barrier height contribution, 78% is from the solvent energy, while only 22% from the polarization effect. D. Comparison with PMF Obtained Using Gas-Phase Data. Using the gas-phase reaction profiles10,15 and the free energies of solvation for both reactants (−1.8 kcal/mol31 for CH3I and −77 kcal/mol32 for Cl−) and products (−2.1 kcal/ mol31 for CH3Cl and −63 kcal/mol32 for I−), the PMF in water was also calculated using the above numbers, then it was compared with our CCSD(T)/MM results. Figure 5 shows the schematic plot of the comparison between the PMF obtained using the above data in gas phase and the PMF calculated under the CCSD(T)/MM level of theory. The obtained free energy of reaction using gas-phase data is −0.8 kcal/mol, which agrees very well with the CCSD(T)/MM result, −1.2 kcal/mol. There is also a good agreement between our calculated barrier height at 24.5 kcal/ mol and the experimental result at 22.0 kcal/mol. Therefore, the good agreement of the comparison here shows the calculation on the CCSD(T)/MM level of theory can give reliable, accurate PMF for the title reaction in solution.

Figure 5. Comparison of reaction profiles. Schematic plot of the comparison between the reaction profile in solution (in black, barrier height using experimental value 22.0 kcal/mol16,17) obtained using gas-phase data (gas-phase solvation energies31,32 in orange and experimental reaction energy10,33 in brown) and our calculated one (in red) at the CCSD(T)/MM level of theory in aqueous solution. For the gas-phase reaction profiles: the CCSD(T)/CBS + δ[CCSDT] + δ[CCSDT(Q)] + Δcore[CCSD(T)/aug-cc-pwCVQZ] adiabatic energies are in blue,15 the CCSD(T)/CBS results are in green,10 and the experimental barrier height is in brown.9,10

kcal/mol.16,17 Furthermore, the free reaction energy calculated at −1.2 kcal/mol also has an excellent agreement with the one obtained based upon gas-phase reaction profile at −0.8 kcal/ mol. This study also shows that not only are the geometries greatly affected by the presence of water solution but also the energetics of the reaction pathway. Between the two solvent effects, the solvent energy plays a bigger role than the polarization effect on the PMF. In this work, only the back-side attack reaction mechanism was studied for the title reaction Cl− + CH3I in aqueous solution. In our earlier studies, the double-inversion mechanism was discovered for the F− + CH3Cl34 and F− + CH3I26 reactions in aqueous solution. We believe the double-inversion mechanism exists for the current Cl− + CH3I reaction in water as in the gas phase,14,15 and we plan to study the doubleinversion mechanism for this reaction in water in the near future.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Dunyou Wang: 0000-0002-5130-3488 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grant No. 11374194) and the Taishan Scholarship Fund.

IV. SUMMARY AND CONCLUSIONS The Cl− + CH3I → I− + CH3Cl SN2 reaction in water was studied with a ML-QM/MM method with an explicit SPC/E solvent model. The comparison of the RC, TS, and PC between in gas phase and in water shows the solvent effects greatly affect the structures in aqueous solution. A detailed, atomic level evolution along the NEB reaction path shows a concerted one-bond-broken and one-bond-formed mechanism as well as a synchronized charge transfer process. The CCSD(T)/MM calculation gives a free reaction barrier at 24.5 kcal/mol, agreeing well with the experiment result at 22.0

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REFERENCES

(1) Lovelock, J. E.; Maggs, R. J.; Wade, R. J. Halogenated Hydrocarbons in and over the Atlantic. Nature 1973, 241, 194−196. (2) Solomon, S.; Garcia, R. R.; Ravishankara, A. R. On the Role of Iodine in Ozone Depletion. J. Geophys. Res. 1994, 99, 20491−20499. (3) Jones, C. E.; Hornsby, K. E.; Sommariva, R.; Dunk, R. M.; Von Glasow, R.; McFiggans, G.; Carpenter, L. J. Quantifying the Contribution of Marine Organic Gases to Atmospheric Iodine. Geophys. Res. Lett. 2010, 37, L18804.

D

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Article

The Journal of Physical Chemistry A (4) Mikosch, J.; Trippel, S.; Eichhorn, C.; Otto, R.; Lourderaj, U.; Zhang, J. X.; Hase, W. L.; Weidemüller, M.; Wester, R. Imaging Nucleophilic Substitution Dynamics. Science 2008, 319, 183−186. (5) Trippel, S.; Stei, M.; Otto, R.; Hlavenka, P.; Mikosch, J.; Eichhorn, C.; Lourderaj, U.; Zhang, J. X.; Hase, W. L.; Weidemüller, M.; et al. Kinematically Complete Chemical Reaction Dynamics. J. Phys.: Conf. Ser. 2009, 194, 012046. (6) Wester, R. Velocity Map Imaging of Ion−Molecule Reactions. Phys. Chem. Chem. Phys. 2014, 16, 396−405. (7) Gronert, S.; DePuy, C. H.; Bierbaum, V. M. Deuterium Isotope Effects in Gas-Phase Reactions of Alkyl Halides: Distinguishing E2 and SN2 Pathways. J. Am. Chem. Soc. 1991, 113, 4009−4010. (8) Kato, S.; Davico, G. E.; Lee, H. S.; DePuy, C. H.; Bierbaum, V. M. Deuterium Kinetic Isotope Effects in Gas Phase SN2 Reactions. Int. J. Mass Spectrom. 2001, 210, 223−229. (9) Hu, W.-P.; Truhlar, D. G. Deuterium Kinetic Isotope Effects and Their Temperature Dependence in the Gas-Phase SN2 Reactions X− + CH3Y → CH3X + Y− (X, Y = Cl, Br, I). J. Am. Chem. Soc. 1995, 117, 10726−10734. (10) Zhang, J.; Lourderaj, U.; Addepalli, S. V.; de Jong, W. A.; Hase, W. L. Quantum Chemical Calculations of the Cl− + CH3I → CH3Cl + I− Potential Energy Surface. J. Phys. Chem. A 2009, 113, 1976−1984. (11) Zhang, J.; Mikosch, J.; Trippel, S.; Otto, R.; Weidemüller, M.; Wester, R.; Hase, W. L. F− + CH3I → FCH3 + I− Reaction Dynamics. Nontraditional Atomistic Mechanisms and Formation of a HydrogenBonded Complex. J. Phys. Chem. Lett. 2010, 1, 2747−2752. (12) Manikandan, P.; Zhang, J.; Hase, W. L. Chemical Dynamics Simulations of X− + CH3Y → XCH3 + Y− Gas-Phase SN2 Nucleophilic Substitution Reactions. Nonstatistical Dynamics and Nontraditional Reaction Mechanisms. J. Phys. Chem. A 2012, 116, 3061−3080. (13) Zhang, J.; Lourderaj, U.; Sun, R.; Mikosch, J.; Wester, R.; Hase, W. L. Simulation Studies of the Cl− + CH3I SN2 Nucleophilic Substitution Reaction: Comparison with Ion Imaging Experiments. J. Chem. Phys. 2013, 138, 114309. (14) Szabó, I.; Czakó, G. Double-Inversion Mechanisms of the X− + CH3Y [X, Y = F, Cl, Br, I] SN2 Reactions. J. Phys. Chem. A 2015, 119, 3134−3140. (15) Szabó, I.; Czakó, G. Benchmark Ab Initio Characterization of the Complex Potential Energy Surface of the Cl− + CH3I Reaction. J. Phys. Chem. A 2017, 121, 5748−5757. (16) Bathgate, R. H.; Moelwyn-Hughes, E. A. 530. The Kinetics of Certain Ionic Exchange Reactions of the Four Methyl Halides in Aqueous Solution. J. Chem. Soc. 1959, 2642−2648. (17) Marshall, B. W.; Moelwyn-Hughes, E. A. 1312. The Kinetics of the Reactions Between the Methyl Halides and Potassium Cyanide in Aqueous Solution. J. Chem. Soc. 1965, 7119−7126. (18) Safi, B.; Choho, K.; Geerlings, P. Quantum Chemical Study of the Thermodynamic and Kinetic Aspects of the SN2 Reaction in Gas Phase and Solution Using a DFT Interpretation. J. Phys. Chem. A 2001, 105, 591−601. (19) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987, 91, 6269−6271. (20) Valiev, M.; Garrett, B. C.; Tsai, M.-K.; Kowalski, K.; Kathmann, S. M.; Schenter, G. K.; Dupuis, M. Hybrid Approach for Free Energy Calculations with High-Level Methods: Application to the SN2 Reaction of CHCl3 and OH− in Water. J. Chem. Phys. 2007, 127, 051102. (21) Wang, T.; Yin, H.; Wang, D.; Valiev, M. Hybrid Quantum Mechanical and Molecular Mechanics Study of the SN2 Reaction of CCl4 + OH− Aqueous Solution: The Potential of Mean Force, Reaction Energetics, and Rate Constants. J. Phys. Chem. A 2012, 116, 2371−2376. (22) Xu, Y.; Wang, T.; Wang, D. A Multilayered-Representation Quantum Mechanical/Molecular Mechanics Study of the SN2 Reaction of CH3Br + OH− in aqueous solution. J. Chem. Phys. 2012, 137, 184501. (23) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys. 2000, 113, 9901.

(24) Valiev, M.; Bylaska, E. J.; Govind, N.; Kowalski, K.; Straatsma, T. P.; Van Dam, H. J. J.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T. L.; et al. NWChem: A Comprehensive and Scalable Open-source Solution for Large Scale Molecular Simulations. Comput. Phys. Commun. 2010, 181, 1477−1489. (25) Zheng, J.; Zhao, Y.; Truhlar, D. G. The DBH24/08 Database and Its Use to Assess Electronic Structure Model Chemistries for Chemical Reaction Barrier Heights. J. Chem. Theory Comput. 2009, 5, 808−821. (26) Liu, P.; Zhang, J.; Wang, D. Multi-level Quantum Mechanics Theories and Molecular Mechanics Study of the Double-Inversion Mechanism of the F− + CH3I Reaction in Aqueous Solution. Phys. Chem. Chem. Phys. 2017, 19, 14358−14365. (27) Check, C. E.; Gilbert, T. M. Progressive Systematic Underestimation of Reaction Energies by the B3LYP Model as the Number of C-C Bonds Increases: Why Organic Chemists Should Use Multiple DFT Models for Calculations Involving Polycarbon Hydrocarbons. J. Org. Chem. 2005, 70, 9828−9834. (28) Izgorodina, E. I.; Coote, M. L.; Radom, L. Trends in R-X Bond Dissociation Energies (R = Me, Et, i-Pr, t-Bu; X = H, CH3, OCH3, OH, F): A Surprising Shortcoming of Density Functional Theory. J. Phys. Chem. A 2005, 109, 7558−7566. (29) Grimme, S. Seemingly Simple Stereoelectronic Effects in Alkane Isomers and the Implications for Kohn−Sham Density Functional Theory. Angew. Chem., Int. Ed. 2006, 45, 4460−4464. (30) Zhao, Y.; Truhlar, D. G. Density Functionals with Broad Applicability in Chemistry. Acc. Chem. Res. 2008, 41, 157−167. (31) Song, L.; Wu, W.; Hiberty, P. C.; Shaik, S. Identity SN2 Reactions X− + CH3X → XCH3 + X− (X = F, Cl, Br, and I) in Vacuum and in Aqueous Solution: A Valence Bond Study. Chem. - Eur. J. 2006, 12, 7458−7466. (32) Hawkins, G. D.; Cramer, C. J.; Truhlar, D. G. Parametrized Models of Aqueous Free Energies of Solvation Based on Pairwise Descreening of Solute Atomic Charges from a Dielectric Medium. J. Phys. Chem. 1996, 100, 19824−19839. (33) Duncan, J. L.; Allan, A.; McKean, D. C. 13C Frequency Shifts and the General Harmonic Force Fields of Methyl Chloride, Bromide and Iodide. Mol. Phys. 1970, 18, 289−303. (34) Liu, P.; Wang, D.; Xu, Y. A New, Double-Inversion Mechanism of the F− + CH3Cl SN2 Reaction in Aqueous Solution. Phys. Chem. Chem. Phys. 2016, 18, 31895−31903.

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DOI: 10.1021/acs.jpca.7b08103 J. Phys. Chem. A XXXX, XXX, XXX−XXX