Hybrid Quantum Mechanical and Molecular Mechanics Study of the

Article pubs.acs.org/JPCA

Hybrid Quantum Mechanical and Molecular Mechanics Study of the SN2 Reaction of CCl4 + OH− in Aqueous Solution: The Potential of Mean Force, Reaction Energetics, and Rate Constants Tingting Wang, Hongyun Yin, Dunyou Wang,*,‡ and Marat Valiev*,† ‡

College of Physics and Electronics, Shandong Normal University, Jinan 250014, China Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, MS-IN: K8-91, P.O. Box 999, Richland, Washington 99352, United States

†

ABSTRACT: The bimolecular nucleophilic substitution reaction of CCl4 and OH− in aqueous solution was investigated on the basis of a combined quantum mechanical and molecular mechanics method. A multilayered representation approach is employed to achieve high accuracy results at the CCSD(T) level of theory. The potential of mean force calculations at the DFT level and CCSD(T) level of theory yield reaction barrier heights of 22.7 and 27.9 kcal/mol, respectively. Both the solvation effects and the solvent-induced polarization effect have significant contributions to the reaction energetics, for example, the solvation effect raises the saddle point by 10.6 kcal/mol. The calculated rate constant coefficient is 8.6 × 10−28 cm3 molecule−1 s−1 at the standard state condition, which is about 17 orders magnitude smaller than that in the gas phase. Among the four chloromethanes (CH3Cl, CH2Cl2, CHCl3, and CCl4), CCl4 has the lowest free energy activation barrier for the reaction with OH− in aqueous solution, confirming the trend that substitution of Cl by H in chloromethanes diminishes the reactivity.

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The present work expands on prior calculations20−22 of CHCl3 +OH−, CH2Cl2 + OH−, and CH3Cl + OH− reactions in water solution. We use the multilayered representations under the mixed QM/MM scheme to find the transition state in aqueous solution, to construct the potential of mean force, to analyze the water environment contributions to the reaction path. In addition, in this study, on the basis of the obtained free activation energy, we further explored the reaction rates of CCl4 + OH− in water. While quantum-mechanical (QM) methods are quite powerful, they are computationally expensive in dealing with a large system, and generally limited to small molecules for high accuracy calculations. The classical molecular mechanics (MM) methods are more efficient but limited in the type processes they can describe. The hybrid QM/MM (quantum mechanics/ molecular mechanics) approach combines the strength of both QM (accuracy) and MM (speed) calculations, thus allowing for the study of chemical processes in solution. The total reaction system that contains many degrees of freedom is divided into two regions, “solute” region and “solvent” region. The “solute” region, containing reactive part of the system, would be described by the QM (quantum-mechanical), and the “solvent” region is calculated using MM (molecular mechanics) methods. Even though the QM/MM approach makes the simulation of systems in solution practical, huge computational effort on the

INTRODUCTION Chlorinated organic compounds, especially polychlorinated hydrocarbons (PCHCs), have generated plenty of interest in recent years because of their environmental harmfulness. PCHCs were widely applied to industry and agriculture, such as electrical insulators and pesticides. Chlorinated organic compounds as prevalent contaminants in groundwater are known to be degradable by abiotic processes such as hydrolysis or nucleophilic substitution reaction with various anions dissolved in the groundwater. Bimolecular nucleophilic substitution (SN2) with inversion of the carbon center is a fundamental reaction mechanism in chemistry. A number of experimental and theoretical studies1−14 have been done on these PCHCs SN2 reactions in the gas phase, as well as several studies on the microsolvated systems.15−19 Only recently have the reactions of CHCl3 + OH−,20 CH2Cl2 + OH−,21 and CH3Cl + OH− 22 in an aqueous environment been investigated with the hybrid quantum-mechanical and molecular mechanics (QM/MM) methods.23−25 In these papers, a combined quantum mechanical and molecular mechanics approach was employed to study the free energy reaction profiles using highaccuracy coupled cluster (CC) method for the QM region and molecular mechanics approach for the aqueous environment. The potential of mean force (PMF) reaction pathways have been investigated, the contributions from solvation energy and polarization effects were investigated, and the transition state were located and the barrier height and the free reaction energies were reported. © 2012 American Chemical Society

Received: January 18, 2012 Revised: February 14, 2012 Published: February 16, 2012 2371

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Because direct calculation of W(r,β) is impractical for the CCSD(T) level of theory, we started the process at the DFT level theory first and then transformed to CCSD(T) level of theory to calculate the potential of mean force. Under the multilayered representation, the potential of mean force is obtained,

PMF calculation has been usually limited the treatment of the QM region to the density function theory (DFT). In our approach here, utilizing a multilayered representation to treat the QM region with DFT, CCSD(T) and electrostatic potential (ESP) theories to describe the QM region at different stages of the calculation, we shift computational cost to the less expensive theories to achieve the high accuracy PMF at the CCSD(T) level theory.20 In this paper, the SN2 reaction (CCl4 + OH− → CCl3OH + Cl−) in aqueous solution is investigated by the above approach. This reaction has only been investigated in the gas phase,26,27 and effects from the aqueous environment have not been studied. The primary focus of our work is to obtain the free energy profile along the reaction pathway on the high-accuracy CCSD(T) level, identify the transition state, analyze the environment contribution to the PMF, and calculate the rate constant coefficients of this reaction in solution.

CC CC→DFT CC→DFT ΔW A,B = (ΔW A,A − ΔW B,B ) DFT→ESP − ΔDFT→ESP) + ΔW ESP + (ΔWA,A B,B A,B (5)

The first bracket represents free energy difference for the transformation between the CC and DFT representations for fixed A or B configurations. The second bracket is the free energy difference between DFT and ESP representations. ΔWCC→DFT and ΔWDFT→ESP were calculated as the quantum internal energy difference. The final term is the classical free energy contribution for the transformation between A and B configuration. The sum of latter two terms is the difference of potential of mean force from the fixed solute configuration A to B on the DFT level of theory. We apply the above approach to the SN2 reaction of CCl4 with OH− in aqueous solution, which has only been studied in the gas phase26,27 so far. The solute QM region contains CCl4 and OH−, which was embedded in a 35.9 Å cubic box of 1561 SPC/E33 solvent water molecules representing the MM region. At the DFT level of theory, the solute region was described using the B3LYP32,33 exchange−correlation function, and the aug-cc-pvDZ basis set was used for both DFT and CCSD(T) level calculations. The van der Waals parameters for the solute region were taken from standard Amber force field definitions.34 Our choice for B3LYP functional and the basis set was primarily dictated by the need to provide a meaningful comparison with our earlier studies of these series of compounds.20−22 Other functional choices for similar SN2 reactions (gas phase only) were used in the past,35−37 but a priori it is not clear whether they would offer any significant advantage over B3LYP in our case. Ultimately, the best way to ensure accuracy of DFT calculations is to compare with high level calculations, as we have done here using CCSD(T) approach. First, we performed initial optimization of CCl4 + OH− in water. Then, we equilibrated the solvent using 40 ps molecular dynamics simulation at the temperature of 298.15 K. After the equilibration, the full system was once more fully optimized to get the initial optimized reactant complex in water. The product complex was searched following the SN2 mechanism by breaking the C−Cl bond and forming the C−O bond in the reactant complex. On the basis of these initial reactant complex and product states, the initial reaction pathway was constructed using the nudged elastic band (NEB) method.38 After that, the geometry associated with the highest energy value on the 10 beads NEB reaction pathway was used as the initial guess for the saddle point search. The obtained transition state structure was verified through the numerical frequency calculation that showed one imaginary frequency, −410.583 cm−1. The final reactant and product states were determined by optimizing the geometries obtained by displacing the transition state along the negative frequency mode. Then, using the newly found structures of the reactant and product complexes, the

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METHODS All the calculations presented in this work were performed using QM/MM capabilities of NWChem computational chemistry package.28,29 The explanations of QM/MM approach have been stated in previous publications.20,30,31 Here, we studied the CCl4 + OH− system in water using the combined QM/MM approach under a multilayered representation. By treating solute CCl4 + OH− as QM region and water environment as the solvent region, we can write the total energy of the CCl4 + OH− system in water as int ext E = EQM (r;ψ) + EQM (r,R;ρ) + EMM(r,R)

(1)

where r and R are respectively the coordinates of electrons and nuclei in QM and MM regions, and ψ(r,R)represents the ground state many-electron wave function of solute region. The int first energy term, EQM (r; ψ), stands for the quantum mechanical energy for the solute of the QM subsystem, which has the expression of the solute energy in the gas phase . ext The second term, EQM (r,R;ρ), includes the van der Waals, Coulomb solute, and solvent nuclear interactions and the electrostatic interactions between the QM and MM subsystems. The electrostatic interaction energy between solute electron density ρ and classical charges ZI of water can be approximated as

∑∫ I

ZI ρ(r′) dr′ = |RI − r′|

∑

ZIQ i

|RI − ri| i,I

= Eesp(r,R;Q ) (2)

where the solute election density was replaced by the effective classical charge representation (ESP). The third term, EMM(r,R), describes the classical energy of the MM. The potential of mean force (PMF) along the reaction path in solution is represented by W(r,β), W (r,β) = −

1 ln β

∫ e−βE(r, R; ψ) dR

β=

1 kT

(3)

As a result, the difference of PMF between two consecutive points, assuming two points A and B along a given reaction pathway is ΔWA,B = −

1 ln⟨e−β(EB − EA )⟩A EA = E(rA,R;ψ(rA,R)) β

EB = E(r B,R;ψ(r B,R))

(4) 2372

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which is much longer than 3.100 Å in the gas phase. This can be explained by the shielding effect of the aqueous environment, which reduces the interaction between the C atom and the nucleophile. In other words, in the solution phase, there is significant charge screening of OH− by the surrounding water molecules, which results in the longer distance of the C and OH− group. Indeed, we find that OH− accepts four hydrogen bonds from the solvent with distances of 2.593, 2.618, 2.638, and 2.627 Å. This screening effect is similar to the observations from the prior studies.20−22 In the solution phase, the distance of the carbon and chlorine atom, which is opposite to the O−H group, is 1.822 Å, compared to the gas-phase value of 1.832 Å. The other C−Cl bond distances are 1.776, 1.771, and 1.786 Å, respectively, in water and 1.774, 1.759, and 1.774 Å in the gas phase. The three Cl atoms are facing toward to the nucleophile, with the ∠ClCO angle of 68°. The structure of transition state is shown in the middle panel of Figure 1. It is the fifth bead on the NEB reaction pathway. In the transition state, the distance between C atom and leavinggroup Cl atom is 2.712 Å, which is about 1 Å longer compared to that of the reactant complex state at 1.822 Å. At the same time, RC−O shortens to 2.538 Å, comparing it to the reactant complex at 3.484 Å. The changes of the above two distances identify the SN2 characteristic that the bond forming of the C atom with the nucleophile and the bond breaking of the C and the leaving group occur simultaneously. In the transition state, the OH− group also accepts four hydrogen bonds with distances 2.794, 2.594, 2.972, and 2.668 Å. At the saddle point, the angle ∠ClCO is 90°; namely the plane formed by the three Cl and the C center is perpendicular to the C−O distance. The final optimized structure of product state (CCl3OH···Cl−), the final bead on the reaction pathway in water, is shown at the bottom panel of Figure 1. In the product state, the nucleophile OH− group is bonded to the carbon atom with a distance of 1.381 Å. However, the leaving-group (Cl− group) separates itself from the C atom, located at a distance of 4.260 Å. The angle ∠ClCO is 106.4° now with the whole structure inverted through the C center. The reaction mechanism can be analyzed by considering the evolution of distances to leaving and entering groups (Figure 2A) and the angle inversion ∠ClCO in Figure 2B along the NEB reaction pathway. Figure 2A shows that as the nucleophile attacks the C center, the distance between the O atom and C atom decreases from 3.48 to 1.48 Å. This is accompanied by a simultaneous C−Cl distance increase from 1.82 to 4.26 Å. Figure 2B shows that as the OH approaches the C center, the three Cl atoms initially facing inward to the OH− now turn outward to the OH− as the angle ∠ClCO inverted from 68° to 106°. Thus we clearly observe SN2 reaction mechanism for the reaction CCl4 + OH− in water. 2. Potential of Mean Force Profiles. Figure 3 shows the potential of mean force of the reaction CCl4 + OH− → CCl4OH + Cl− in water. The potential of mean force along the NEB reaction pathway at both DFT and CCSD(T) levels and the contribution from the solvent environment the ΔWESP term (eq 5), are shown in Figure 3A. Note that the graph is plotted with the relative free energies along the NEB pathway using the reactant state energy as a zero reference point. The gas-phase energies along the NEB pathway and the solute internal energies at CCSD(T) level using the energy of the reactant state in the gas phase as a zero reference point are shown in Figure 3B.

final reaction pathway was generated with 10-point NEB calculation. The minimum energy pathway was optimized after molecular dynamics simulation was performed on the water solvent for 40 ps. The final NEB reaction pathway was determined by repeating this step until it was converged.

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RESULTS AND DISCUSSION 1. Reactant State, Transition State, and Product State. The final optimized structure of reactant state complex (CCl4···OH−), which is the starting point on the NEB reaction pathway in the solution phase, is shown in Figure 1. It is similar to the reactant structure in the gas phase26 except for the big difference in the distance between the nucleophile and the C atom. In aqueous solution, the C···OH distance is 3.484 Å,

Figure 1. Structures of the reactant state, transition state, and product state for the reaction system CCl4 + OH− → CCl3OH + Cl− in aqueous solution. The units of the data in figure are Angstroms. 2373

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Figure 3. (A) Potential of mean force along the NEB reaction pathway at DFT and CCSD(T) level of theory and solution contribution using the reactant state as a zero reference point. (B) Gas-phase energies along the NEB pathway and the solute internal energies at CCSD(T) level using the energy of the reactant state in the gas phase as a zero reference point.

Figure 2. (A) Bond lengths between the leaving Cl group with the C atom (RC−Cl) and between the nucleophilic OH group with C atom (RC−O) along the NEB pathway. (B) Angle evolution along the 10bead NEB reaction pathway (∠OCCl).

The result shows that, in the water environment, the free energy barrier height is 27.9 kcal/mol at CCSD(T) level and 22.7 kcal/mol at DFT level of theory, which is significantly larger compared to the gas-phase free energy barrier height 7.2 kcal/mol.26,27 This indicates that the aqueous environment has a significant contribution to the activation barrier, which leads to a substantially lower reaction rate in the solution phase than in the gas phase. The presence of solution thus weakens the reactivity of OH−, which is indicated by the solvation energy contribution (10.5 kcal/mol) to the barrier height. This figure also shows that the free reaction energy for this reaction is ∼−55 kcal/mol at DFT level theory and ∼−50 kcal/mol at CCSD(T) level theory, which releases the most heat among the reactions of chloromethane and OH−, as this value for CH3Cl + OH− is −20 kcal/mol, for CH2Cl2 + OH− is −25 kcal/mol, and for CHCl3 is −47 kcal/mol. From previous calculations using the same techniques, the free energy activation barrier heights of the reaction systems CHCl3 + OH−, CH2Cl2 + OH−, and CH3Cl + OH− at CCSD(T) level theory are 29.3, 31.8, and 49.9 kcal/mol, and the corresponding aqueous environment contributions to barrier height are 10.7, 17.3, and 22.4 kcal/ mol, respectively. The conclusion here is that the free energy

activation barrier and the aqueous environment contribution increases as more H atom substitutes the Cl atom in the methyl group. This is not surprising, as the number of H atoms increases, the positive charge on the center C atom decreases; thus the attractive force between the C atom and the O atom weakens, so it is more difficult for reaction to happen. In addition to the solvation effect, the solute polarization also provides a substantial contribution to the energy of the reaction process. The gas-phase energy profile and the solute internal energy at CCSD(T) level of theory are shown in Figure 2B. The gas-phase reaction pathway is obtained by using the same 10 structures on the NEB reaction pathway in solution but excluding the interaction between the solute and solvent. We can see that the polarization of solute raises the energy by ∼11.5 kcal/mol in reactant state, ∼15.5 kcal/mol in transition state, and ∼3.1 kcal/mol in product state. 3. Reaction Rate Constants. There have been no experimental measurements of the rate constants for the reactions of chloromethane and OH− in water solution. Computational methods become the only means to determine the rate coefficients for these reactions in solution. We utilize 2374

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the thermodynamic equation39,40 of the transition state theory41 to compute rate constants in the aqueous phase: ⎛ ΔW+ ⎞ k T RT ⎟ k= B exp⎜ − h P ⎝ RT ⎠

CONCLUSION In this paper, we presented a combined QM and MM approach to study CCl4 + OH− in water solution. To achieve the high accuracy potential of mean force at the CCSD(T) level of theory, we employed a multilayered representation to study the reaction system. Our calculation shows that the aqueous solution has a significant effect on the reaction pathway by contributing 10.6 kcal/mol on the saddle point height. In addition, the polarization effect also has a strong contribution to the reaction pathway. As more Cl atoms replace H atoms in the chloromethane, we found the aqueous environment contributes less to the activation barrier height, as the title reaction has the smallest barrier height in solution among the four chloromethane reactions with OH−. The rate constant coefficients are 8.6 × 10−28 cm3 molecule−1 s−1 in water solution, which is about 18 orders magnitude smaller than in the gas phase.

(6)

where h, R, P, and ΔW represent the Plank constant, gas constant, pressure, and free activation energy, respectively. For the title reaction, under the standard state condition, a rate of 8.6 × 10−28 cm3 molecule−1 s−1 in the aqueous phase is obtained at 298 K, which is about 18 orders magnitude smaller than in the gas phase.42,43 The aqueous rate constant coefficients for the previous studied reactions, CH3Cl + OH−, CH2Cl2 + OH− and CHCl3 + OH− were also calculated, listed in Table 1, on the basis of free energy barrier heights in a water +

Table 1. Saddle Point Barrier Heights in the Gas Phase and in Water Solution, the Contribution to the Barrier Height from the Aqueous Solution, and the Calculated Rate Constant Coefficients for the Reactions CHCl3 + OH−, CH2Cl2 + OH−, CH3Cl + OH−, and CCl4 + OH−

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reaction system CH3Cl + OH− CH2Cl2 + OH− CHCl3 + OH− CCl4 + OH−

in the solution phase

environment contribution to the barrier height

reaction rate constant [cm3/ (molecule s)]

3.0

49.9b

22.4b

6.4 × 10−44

10.5

31.8c

17.3c

1.2 × 10−30

32.2

29.3d

10.7d

8.2 × 10−29

7.2

27.9

10.55

8.6 × 10−28

*E-mail: D.W., [email protected]; M.V., marat.valiev@pnl. gov. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS D.W. acknowledge the National Natural Science Foundation of China (Grant #:11074150) and Tanshai Scholarship funding for supporting this work. The calculation was performed on the Magic Super Computer at Shanghai Supercomputer Center. Research at PNNL was supported by the U.S. Department of Energy’s (DOE) Office of Basic Energy Sciences, Chemical Sciences program, and was performed in part using the Molecular Science Computing Facility (MSCF) in the William R. Wiley Environmental Molecular Sciences Laboratory, a DOE national scientific user facility located at the Pacific Northwest National Laboratory (PNNL). PNNL is operated by Battelle for DOE.

a c

AUTHOR INFORMATION

Corresponding Author

total free energy activation barrier height (kcal/mol) in the gas phasea

Article

The gas-phase saddle point barrier height from ref 2. bReference 22. Reference 21. dReference 20.

environment.20−22 These data reveal, while more Cl atom replace H atom in the chloromethane, the water contribution to the saddle point height decreases, as CCl4 + OH− has the smallest reaction barrier in solution even though its gas-phase barrier height is even larger than that of CH3Cl + OH− in the gas phase. As a result, the aqueous rate constant increases as the number of Cl increases from 1 to 4 in the chloromethane. This further confirms these two aspects we observed in the previous section: first, when more H atoms are present in chloromethane, they form more hydrogen bonds by bonding with the environment H2O molecule. Due to more water molecules surrounding the chloromethane, it provides a bigger steric effect for the nucleophile OH− to access the C atom, thus raising a bigger barrier height. Second, as more H atom is present in the chloromethane, more positive charge will be shared with the C atom, and as a result, the attraction force between the C and O atoms becomes weaker; this also leads to a larger barrier height. Therefore, even though CH3Cl + OH− has the smallest barrier height in the gas phase, due to the largest environment solution contribution to the reaction barrier, it has the largest free activation barrier in the aqueous phase and thus the smallest rates. On the contrary, CCl4 + OH− with H present in the chloromethane, has the smallest barrier height and largest rate constant coefficients in water solution.

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