ARTICLE pubs.acs.org/JPCA
CH2Cl2 þ OH- Reaction in Aqueous Solution: A Combined Quantum Mechanical and Molecular Mechanics Study Dunyou Wang,† Marat Valiev,*,‡ and Bruce C. Garrett‡ †
College of Physics and Electronics, Shandong Normal University, 88 East Wenhua Road, Jinan, Shandong 250014, People's Republic of China ‡ William R. Wiley Environmental Molecular Sciences Laboratory and Fundamental and Computational Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352 ABSTRACT: The CH2Cl2 þ OH- reaction in aqueous solution was investigated using combined quantum mechanical and molecular mechanics approach. We present analysis of the reactant, transition, and product state structures and calculate the free energy reaction profile through the CCSD(T) level of the theory for the reactive region. Our results show that the aqueous environment has a significant impact on the reaction process, raising the reaction barrier by ∼17 kcal/mol and the reaction energy by ∼20 kcal/mol. While solvation effects play a predominant role, we also find sizable contributions from solvent-induced polarization effects.
’ INTRODUCTION Chlorinated organic compounds have generated a great deal of interest in recent years due to significant environmental threat posed by their ever-increasing presence. Widespread in industrial applications such as solvents, pesticides, and electrical insulators, these species now account for a major fraction of the organic pollutants. The long degradation time of these compounds1,2 impedes the experimental characterization, leading to significant uncertainty in understanding reaction mechanisms. An important example of chlorinated organic compounds can be found in chlorinated hydrocarbons (CHCs), which are frequently used in the manufacturing of synthetic solvents and insecticides. There have been a number of theoretical3-6 and experimental7-9 studies of CHCs. These investigations were mainly focused on CH(4-n)Cln(n = 2-4) þ OH- reactions in the gas phase, including the two most recent electronic structure studies.10,11 While these studies provided much information about the gas-phase chemistry of CHCs, the critically important practical question of the behavior of these reactions in solution remains to be addressed. It is well-known that the presence of the solvent can significantly alter the gas-phase energetics, leading sometimes to substantial changes of the reaction barrier heights and subsequently reaction rates. In some cases the changes to the potential energy surface induced by the solvent molecules may lead to the appearance of new stable intermediates, which can have nontrivial effects on the reaction mechanism. The presence of many degrees of freedom introduced by the solvent considerably complicates computational treatment of the reaction process. In particular, the energetics of the process has to be described in terms of free energies, which require a significant r 2011 American Chemical Society
amount of sampling of different solvent configurations. Phenomenological continuum solvation models, such as COSMO12 and PCM,13 have been shown to be reliable in predicting equilibrium solvation energies; however, less is known about their performance for reaction energetics. In these cases explicit atomistic description of the aqueous environment may be required. Direct quantum mechanical (QM) description is usually impractical and one of the common simplifications consists of utilizing the hybrid quantum mechanical/molecular mechanics (QM/MM) methodology.14,15 Here, the QM description is applied only to the reactive solute region, and the rest of the system (solvent) is treated using molecular mechanics (MM) level theory. Even within this simplified description, analysis of free energy surfaces incurs significant computational challenges. As a result, in the majority of applications, the level of QM theory is typically restricted to density functional theory (DFT) or semiempirical methods. This may introduce sizable errors in the description of energy barriers. Recently, we have introduced an implementation16,17 of QM/MM methodology, which allows free energy calculations using high-accuracy coupled cluster (CC)18,19 treatment of the QM region. This is achieved by utilizing different layered QM/ MM representations of the system and shifting the bulk of statistical sampling to less expensive and more efficient descriptions. In this paper, we continue to apply this approach to study the second-order (bimolecular) nucleophilic substitution (SN2) reaction, CH2Cl2 þ OH- f CH2ClOH þ Cl- in aqueous Received: September 28, 2010 Revised: December 30, 2010 Published: February 9, 2011 1380
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solution. This reaction process so far has only been investigated in the gas phase,10,11 and little is known about the impact of the aqueous environment. We present analysis of the reactant, transition, and product state structures for this reaction process in aqueous phase and explore the free energy surface reaction through the CCSD(T) level of theory for the QM description.
’ METHODOLOGY All the calculations presented in this work were performed using QM/MM capabilities of NWChem computational chemistry package.22 A detailed explanation of our QM/MM approach has been provided in previous publications.17,20,21 Here, we provide a brief outline of the method. Given the separation into QM (solute) and MM (solvent) regions, the total energy of the system is given by E ¼ Eqm ðr;R; ψÞ þ Emm ðr;RÞ
ð2Þ
Here, the first term, Eint QM(r;ψ), represents gas-phase expression for the solute energy; the second term, Eext qm(r,R;F), describes electrostatic interactions between the solute electron density F and solvent classical charges ZI X Z ZI Fðr0 Þ dr0 Eext ðr;R; FÞ ¼ ð3Þ qm 0j jR r I I The Emm(r,R) term in eq 1 contains the classical energy of the solvent, as well as the van der Waals and Coulomb nuclear solute-solvent interaction energies. The reaction process in solution can be conveniently characterized in terms of the potential of mean force (PMF) Z 1 Wðr; βÞ ¼ - ln e-βEðr;R;ψÞ dR ð4Þ β where β = 1/(kT). Since direct evaluation of W(r,β) is impractical for the CC-level of theory and would be exteremly time-consuming even for DFT, further approximations are needed. For optimization and reaction pathway calculations where derivatives of W(r,β) are required, we can utilize a zerotemperature-limit approach,17 lim Dr Wðr, βÞ ¼ Dr Eðr;R ; ψÞ
βf¥
Z
ð5Þ
where R* is the solvent configuration that minimizes E(r,R*;ψ) for a given r and ψ. Furthermore, the computation of R* can be further facilitated by introducing electrostatic potential (ESP) charges of the solute electron density, such that the correct electrostatic potential is reproduced on a grid of points (rg)
X Qi Fðr0 Þ 0 dr ¼ jrg - r0 j jrg - ri j i
ð6Þ
where Qi are the ESP charges. In this case the external part of the QM energy can be replaced by the equivalent ESP representation Eext qm ¼ Eesp ¼
X Z I Qi jR I - ri j i, I
ð7Þ
The calculation of the PMF along a given reaction pathway involving solute coordinates consists of calculation of PMF differences between consecutive points (e.g., A and B), ΔWA , B ¼ -
ð1Þ
where r,R are the coordinates of the QM and MM regions, respectively, and ψ = ψ(r,R) represents the ground state electronic wave function of the QM region. The QM energy, Eqm, can be further decomposed into the internal and external contributions:17,20,21 ext Eqm ðr;R; ψÞ ¼ Eint qm ðr; ψÞ þ Eqm ðr;R; FÞ
outside the QM region:
1 lnÆe-βðEB - EA Þ æA β
ð8Þ
where EA is the energy of the system with solute coordinates in rA configuration EA ¼ EðrA ;R; ψðrA ;RÞÞ
ð9Þ
with similar expression for EB. The averaging in eq 8 is performed over solvent degrees of freedom with solute fixed in the rA configuration. To alleviate the computational expense associated with this procedure, especially at the CC level of theory for the QM description, we use the previously developed multilayered technique.17 In particular, we introduce several QM/MM representations: CCSD(T)/MM, DFT/MM, and ESP/MM. The first two refer to QM descriptions at CCSD(T) and DFT levels of theory, respectively. The ESP/MM representation is obtained by replacing Eqm in eq 1 by the effective charge energy Eesp (eq 7). The desired free energy difference at the CC/MM level of theory can be then represented as17 ΔWAcc, B ¼ ΔWAcc, Af dft - ΔWBcc, Bf dft dft f esp dft f esp esp þ ΔWA , A - ΔWB, B ð10Þ þ ΔWA , B Here, the first and second terms in brackets represent free energy change from CC/MM to DFT/MM representations at the fixed solute configuration (A or B). In this work these terms are approximated by the corresponding internal energy differences.17 The third term denotes free energy at the fixed ESP/MM representation from A to B solute configurations. It is calculated using finite difference thermodynamics perturbation theory, where the interval between A and B configurations is spanned by a sequence of points ri ¼ ð1 - i = nÞrA þ ði = nÞrB Qi ¼ ð1 - i = nÞQA þ ði = nÞQB
ð11Þ
where i goes from 0 to n. The free energy difference ΔWesp A,B can then be written as the sum of differences for the subintervals [i,iþ1] between i = 0 and i = 1 endpoints: esp
ΔWA , B ¼ 1381
n X i¼0
esp
ΔWi, i þ 1
ð12Þ
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Figure 1. Structure of the QM region for reactant (left), transition (middle), and product states for CH2Cl2 þ OH- reaction in aqueous phase obtained from DFT/MM calculations. Indicated distances are in Angstroms.
In this work we utilize a double-wide sampling strategy23 where the free energy differences for the intervals [i - 1, i] and [i, i þ 1] are calculated simultaneously by sampling around i.
’ SETUP AND COMPUTATIONAL PROCEDURES Our system comprised the CH2Cl2/OH- reactive species embedded into a 36.2 Å cubic box of 1608 water molecules. The QM region contained CH2Cl2/OH- and was described using either DFT or CCSD(T)19 levels of theory. For the DFT level theory, the B3LYP24,25 exchange correlation functional is used. The aug-cc-pvDZ basis set is used for both DFT and CCSD(T) calculations. The MM region, containing water molecules, was described through the classical SPC/E model,26 and the cutoff radius for classical interactions was 15 Å. Standard Amber force field27 van der Waals parameters were used for the quantum region. The initial geometry of CH2Cl2/OH- was set similar to the reactant gas-phase structure obtained in previous studies.10,11 After initial relaxation of the full system using the multiregion optimization protocol implemented in NWChem,17 we equilibrated the solvent using 40 ps molecular dynamics simulation at a temperature of 298.15 K. In the course of this equilibration the fixed QM region was represented by the ESP charges calculated in the prior optimization step. After the equilibration, the full system was again fully reoptimized and was used as a starting point for all subsequent simulations The first phase of our calculations was focused on the determination of the transition state complex corresponding to our reaction process. This was accomplished by generating an initial guess for the reaction pathway using constrained optimization with harmonic constraints on the C-Cl and C-O bonds. The latter mirrors the SN2 reaction process by breaking of C-Cl and creating new C-O bond. The pathway was then refined using QM/MM implementation17 of the nudged elastic band28(NEB) method using 10 beads/replicas. The geometry of the top bead (No. 5 in our calculation) on the NEB reaction pathway is used for the saddle point search calculation. The located transitionstate structure was verified through the numerical frequency calculations, which showed one imaginary frequency. Once the transition-state complex was located, the reactant and product states were determined by optimizing the initial geometries obtained by displacement of the transition-state structure along the negative frequency mode. The resulting reactant and product structures were then used to generate the final reaction pathway using 10-point NEB calculations. To ensure sufficient relaxation of the solvent, after the first round of NEB calculations the solvent around the reaction pathway was
equilibrated using molecular dynamics simulations for 40 ps. This was followed by another round of NEB calculations. The free energy profile along the resulting pathway was calculated according to eq 10. The first two terms, ΔWccfdft and ΔWdftfesp, were calculated as respective quantum internal energies differences. The ΔWESP term is obtained with the effective charges generated during the NEB procedure. The interval between consecutive NEB solute configurations was spanned by 10 points (n = 10 in eq 11). The sampling was performed for 20 ps and then extended to an additional 30 ps.
’ RESULTS AND DISCUSSION Reactant State. The optimized structure of the reactant state complex for the CH2Cl2 þ OH- reaction in solution phase is shown in Figure 1. Similar to gas-phase calculations,10,11 we observe a hydrogen-bonded CH2Cl2 3 3 3 OH- complex, with OH- oriented to be in the same plane as one of the C-Cl bonds. The internal structure of CCl2H2 seems to be perturbed little by the presence of the solvent. The CCl bond distances are at 1.80 and 1.81 Å, compared to 1.82-1.83 Å observed in gas phase.10,11 The two CH bond distances are 1.09 and 1.11 Å, which is somewhat different from gas phase where one of the CH bonds is elongated to 1.19 Å. The longer CH bond length in the gas phase is caused by the stronger hydrogen bond interactions with OH-. Indeed, in the gas phase, the H 3 3 3 OH- distance is 1.51 Å and in solution phase it is longer at 1.83 Å. The longer H 3 3 3 OH- distance in solution results from significant charge screening on OH- by the surrounding water molecules. Indeed, we find that OH- accepts four hydrogen bonds with average hydrogen bond distance of around 2.7 Å and donates one extra hydrogen bond with a distance of 3.3 Å. This solvation pattern is consistent with prior experimental29 and theoretical studies30 of OH- in aqueous phase. We can therefore conclude that the presence of solution weakens the interaction between CCl2H2 and OH-. Transition State. The structure of the transition state is shown in Figure 1. It was identified from the free energy profile calculated from NEB reaction pathway calculations. Numerical frequency calculations confirm the presence of single imaginary mode at 361i cm-1. The analysis of the reaction pathway shows that the formation of the transition state from the reactant complex is accomplished through the rotation of CCl2H2 that breaks the hydrogen bond and exposes the central carbon to the attacking OH- group. The rotation occurs approximately along the C-Cl bond closest to the OH- (see Figure 1) and is accompanied by a concerted displacement of the Cl- leaving group. This results in the formation of a nearly planar CClH2 1382
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Figure 2. (A) Comparison of free energy profiles calculated at DFT/MM (white circles) and CCSD(T)/MM (black squares) levels of theory and solvation contribution (dotted line) using the reactant state (bead 1) as a reference point; (B) Comparison between gas-phase (solid line) and internal (dashed line) QM/MM energies along the NEB pathway using the gas-phase energy of the reactant state as a reference point.
group, located approximately midway between the attacking nucleophile (OH-) and Cl leaving group. Prior calculations10,11 have shown that in the gas phase the distance to the leaving group RCCl = 2.14 Å in the transition state is nearly the same as to the attacking group RCO = 2.18 Å. Following the trend observed in the reactant state, the same distances are elongated in the aqueous phase due to solvent screening effects, RCCl = 2.36 Å and RCO = 2.27 Å. At this point in the reaction process, the charge is still mostly concentrated on the OH- (80% compared to the reactant). As a result, the solvation pattern for OH- is similar to that observed in the reactant state, consisting of four donor and one acceptor bonds. Product State. The optimized product state is shown in Figure 1. Here, the leaving Cl- group is completely detached, located at a distance of 3.4 Å from the central carbon atom. The excess charge is now fully concentrated on the leaving Cl- group which is coordinated by seven water molecules with average ClO distance of 3.5 Å. This type of solvation is consistent with theoretical32 and experimental31 estimates of Cl- solvation. The coordination shell around the OH group, which is now bound to CCl2H2, is essentially absent and we observe only two weak acceptor bonds (2.9 and 3.0 Å). We should note that the presence of the solvent is essential to the stabilization of the product state, and the latter is unstable in the gas phase. The calculated structural parameters of CClH2OH complex by itself do not differ significantly from the gas-phase results on isolated CClH2OH.11 We find the C-Cl bond at 1.84 Å compared to the gas-phase value of 1.82 Å, and the C-O bond at 1.41 Å compared to the gas-phase value of 1.39 Å. Free Energy Profile. The results of our free energy calculations along the NEB pathway can be found in Figure 2. Shown in Figure 2A are the total free energy profiles at both DFT and CCSD(T) levels of theory for treatment of the QM region. The same graph also shows the solvation free energy contribution as represented by the ΔWesp A,B term (see eqs 10-12). We should note that only relative free energies along the pathway are calculated using the reactant state (Bead 1) as a zero reference point. Figure 2B shows gas-phase energies along the NEB pathway in comparison to internal QM/MM energies using the gas-phase energy of the reactant state as a zero reference point.
Overall, we observe that the presence of the aqueous environment results in substantial changes to the energetics of the reaction process. The free energy activation barrier in the aqueous phase is 28.4 kcal/mol at DFT/MM level of theory, which is significantly larger than the corresponding gas-phase value of 11 kcal/mol. Similarly, the reaction free energy of -27.8 kcal/mol in the aqueous phase at the DFT/MM level of theory is significantly different than the gas-phase value of -47.5 kcal/ mol. In either case DFT appears to provide a fairly accurate description of the electronic structure changes during the reaction process, differing only by ∼3 kcal/mol from CCSD(T)/ MM values for free energy activation barriers (31.8 kcal/mol) and reaction free energies (-25 kcal/mol). The influence of the aqueous environment on the energetics of the reaction process can be conveniently analyzed in terms of contributions from solvation energy and polarization effects. Given the substantial charge redistribution during the reaction process (from OH- to Cl-), the solvation effects play a predominant role in shaping the reaction profile. As shown in Figure 2A, there is a pronounced trend of increasing solvation energy in the course of the reaction process, leading to the destabilization of the transition state by ∼21.3 kcal/mol and product state by ∼26.6 kcal/mol. This behavior can be understood based on the differences in solvation energy between OH(-105 kcal/mol) and Cl- (-74.7 kcal/mol) ions. The reactant state is akin to the solvated OH- species and is favored in terms of the solvation energy compared to product state where the excess charge is transferred fully to Cl-. Somewhat better quantitative analysis of the solvation energy balance can be performed using the solvation energies of CH2ClOH (-6.35 kcal/mol33) and CH2Cl2 (0.6 kcal/mol34). Combining these numbers with previously indicated solvation energies for OHand Cl-, we obtain a solvation reaction energy of 23.4 kcal/mol. which correlates well with our calculated value of 26.6 kcal/mol. The polarization effects, which appear from the electronic structure perturbations of the reactive region induced by the presence of the solvent, typically make less of an impact on the shape of the free energy profile in solution. In our approach, they can be analyzed by comparing DFT gas-phase and internal 1383
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The Journal of Physical Chemistry A QM/MM (see eq 2 for definition) energies as shown in Figure 2B. In the reactant state, the polarization of the QM region by the solvent raises the energy by ∼15.5 kcal/mol; that number decreases to ∼11.5 kcal/mol in the transition state and then drops to ∼8.5 kcal/mol in the product state. The net effect is the shift of reaction balance toward the product side, which is opposite to what we observe for the solvation energy contributions. This correlates with a generally observed trend that strong solvation is accompanied by enhanced polarization effects. One particular feature of the system studied in this work is the presence of the hydrogen bond between OH- and CH2Cl2, which exhibits greater sensitivity to the external electric field of the solvent. This correlates with the observed structural differences of the reactant complex between gas phase and aqueous solution. Overall, we observe that, while small, the polarization effect does have an effect on the free energy profile, resulting in ∼4 and ∼7 kcal/mol reductions in reaction barrier and reaction energy.
’ CONCLUSION The CH2Cl2 þ OH- reaction in aqueous solution was investigated using QM/MM methodology. We have identified and characterized reactant, product, transition states, and reaction pathway. The presence of solvent plays a critical role in the stabilization of the product complex, which is unstable in the gas phase. The free energy calculations, performed through the CCSDT(T) level of the QM description, show significant increase in the activation barrier (þ17 kcal/mol) and reaction free energy (þ20 kcal/mol) compared to gas phase. Our analysis shows that these changes arise as a result of two competing factors: the loss of solvation energy in the products state resulting from the transfer of charge from OH- to Cl- and destabilization of the hydrogen bonding structure of reactant state from the solvent electric field. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The work at Pacific Northwest National Laboratory (PNNL) was supported by the U.S. Department of Energy (DOE), Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division. Computational resources were provided by the Molecular Science Computing Facility (MSCF) in the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL) funded by DOE’s Office of Biological and Environmental Research. Battelle operates PNNL for DOE under Contract DEAC06-76RLO-1830. D.W. thanks the Taishan Scholarship fund for supporting his work.
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