Role of Solvents on the Thermodynamics and Kinetics of Forming

Oct 26, 2012 - Ab Initio Molecular Dynamics Study of Hydrogen Cleavage by a Lewis Base [ t Bu 3 P] and a Lewis Acid [B(C 6 F 5 ) 3 ] at the Mesoscopic...
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Role of Solvents on the Thermodynamics and Kinetics of Forming Frustrated Lewis Pairs Liem X. Dang,* Gregory K. Schenter, Tsun-Mei Chang, Shawn M. Kathmann, and Tom Autrey Chemical and Materials Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States ABSTRACT: To enhance our understanding of the role of solvents on the thermodynamics and kinetics of forming frustrated Lewis pairs (FLP), we carried out a systematic simulation study on these systems in dichloromethane and toluene solvents. These molecular systems are of particular interest due to their relevance in the catalytic hydrogenation and hydrogen storage processes. While the computed structural observables for both molecules are very similar, the slow molecular reorientation was consistent with the size of the species. The computed free-energy profiles for the FLP in both solvents show similar gross characteristics but differ in details. We observe two well-defined contact regions and a solvent-separated regions with different well depths and barrier heights to dissociation. The kinetics of solute− pair interconversion was studied using transition-state theory, comparing Kramers and Grote−Hynes treatments of the dynamic response of the solvent. These rate results were used to predict solvent effects on dynamical features of contact solute−pair association. SECTION: Liquids; Chemical and Dynamical Processes in Solution

T

rate results will be used to predict solvent effects on the dynamical behavior of contact solute−pair association. This amine−borane FLP system has been studied in some detail previously.3 Geier and co-workers used a combination of experiment and theory to investigate the properties of a series of pyridine-based Lewis base complexes with TRIS.4 The pair of LUT and TRIS was found to be unique as a weak dative adduct is formed in toluene. Addition of H2 to the toluene shifts the equilibrium to the ion pair product [LutH+][HTRIS−]. Rokob et al. calculated the driving force for H2 activation from the dative adduct in toluene and showed that the reaction was moderately exothermic.5 In subsequent work, Karkamkar et al. experimentally determined the enthalpy of H2 activation by the LUT−TRIS Lewis acid base pair in bromobenzene and found it to be in excellent agreement with computational predictions.6 While there is little spectroscopic evidence for the formation of a FLP in addition to the classical dative adduct, the relatively rapid rates of H2 splitting at ambient temperature and pressure bias one to think that one could exist. Gas-phase calculations suggest a π−π stacking stabilization in the frustrated LUT−TRIS pair. 7 This stabilization of a FLP encounter complex is consistent with gas-phase calculations for other FLPs; however, recent work from Papai’s group using MD simulations has shown that the solvent decreases the intermolecular association of FLP encounter complexes in the solution phase.8 To this end, we are pursuing a more detailed knowledge of how these FLP

he role of solvents on the structure and dynamics of solutes and the thermodynamics and kinetics of solute− pair association in solutions has been the subject of considerable theoretical and computational interest in recent years.1 Much of this interest results from the important role that solute association plays in chemical reactions in solution. Despite this long history, there is still considerable uncertainty regarding the specific role that these solute pair states play in solution. In the present Letter, we use computer simulations to examine the role of solvents on the thermodynamics and kinetics of interconversion of the contact solute pair (CSP). We performed molecular dynamics (MD) simulation studies on extended empirical models that involve the explicit treatment of solvent molecules. This approach allows us to examine the solvent and polarization effects on the computed properties. Herein, we present our results obtained for the Lewis acid tris(pentafluorophenyl)borane (TRIS) and Lewis base 2,6lutidine (LUT) pair in dichloromethane and toluene. Solvent effects on these molecular frustrated Lewis pairs systems (FLPs) are of particular interest due to their relevance in the catalytic hydrogenation and hydrogen storage processes.2 Our primary goal in this work is to develop a molecular model that describes the structure, dynamics, and association process of the FLP in various solvents such as dichloromethane and toluene. We will compute the reorientation correlation functions and estimate the correlation time and then relate our computed value to the corresponding experimental data on similar systems. We will also compute the free-energy profiles of a LUT−TRIS pair in these solvents using a constrained mean force approach that includes polarization effects. We will apply various rate theories based on the potential of mean force results to study the kinetics of the FLP interconversion. These © 2012 American Chemical Society

Received: September 27, 2012 Accepted: October 26, 2012 Published: October 26, 2012 3312

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molecular complexes behave in the condensed phase, specifically, how H2 is heterolytically activated in order to better understand the potential of these unique molecular systems in catalysis.9 A detailed knowledge of how these molecules behave in the condensed phase can contribute to our understanding of the mechanism for catalytic conversion involving H2. We wish to understand the role of the solvent on the association of Lewis acid/base pairs. These serve as a reactive site for hydrogen activation. They must sufficiently polarize the H2 bond to allow dissociation into protic and hydridic components. In order to proceed, the lifetime of this activated complex must be long enough to be effective. In the gas phase, we find that the gas-phase complex is qualitatively different than the solvated complex. Polar solvents have a direct influence on the course of the reaction, stabilizing the charge-transfer nature of the transition state and products. In the present work, we focus on the role of nonpolar solvents that have a more indirect influence on the course of the reaction. In particular, these solvents sterically hinder direct motion of the complex. In order for the reaction to proceed, the solvent must reorganize, often involving slow, large-amplitude collective motions. Characterization of this influence on the free energy and the dynamics of the reaction is the focus of this work. The remainder of the Letter is organized as follows. Next, the potential models and simulation methods are described. Results and discussion are then presented, and the conclusions follow. Polarizable models that describe well the structure and dynamics of liquids dichloromethane and toluene were used; the details of these potential models have been reported elsewhere in the literature.10 For the LUT and TRIS molecules, we started out with the parameters obtained from the general Amber force field (GAFF).11,12 Partial atomic charges for the solutes were calculated from an ab initio RESP-fit at the Hartree−Fock level of theory with the 6-311+G* basis set using the Gaussian 98 program. 13 The Lennard-Jones parameters that describe the interactions between solutes and solvents were obtained using the simple combining rules.14 The chemical structures for LUT and TRIS are presented in Figure 1. In Figure 2, we reported the computed gas-phase PMFs at

Figure 2. (a) Computed gas-phase PMFs at 300 K for the interactions between LUT and TRIS with a dichloromethane molecule. (b) Same as (a) but for a toluene molecule.

The following expression was used to calculate the solute− solute mean force as an average over the different solvent configurations: 1 F(r ) = ⟨ ru⃗ ·(FA⃗ − FB⃗ )⟩ (1) 2 In this expression, FA and FB are the forces acting on the solutes. The term ru⃗ , which is a unit vector along the AB direction, is defined as ru⃗ =

rAB ⃗ | rA⃗ − rB⃗ |

(2)

and the PMF, W(r), is calculated as W (r ) =

∫r

0

Figure 1. Chemical structures for LUT and TRIS.

r

⟨F(r )⟩ dr

(3)

PMFs are evaluated along the center-of-mass separation between the two solutes. The center-of-mass separation between the solutes was incremented by 0.25 Å. At each center-of-mass separation, the average F(r) was determined from 1.5 ns of simulation time, preceded by 500 ps of equilibration. The uncertainties on the PMFs were ±0.2 kcal/ mol, as estimated by determining the force averaged (the corresponding PMFs) over four equally spaced time frames during the production. The systems investigated include a Lewis pair of LUT and TRIS molecules immersed in a bulk

300 K that describes the interactions among the solutes and solutes−solvents. We observe that the LUT−TRIS interaction is a strongest component of the system. In additional, the TRIS−TOL interaction is quite strong, and this interaction may have an appreciable effect on the association of the solute in these solvents. A modified version of the Amber 9 software package was used to perform all of the MD simulations.15 3313

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Figure 3. (a) Computed RDFs between N of LUT and C, H, and Cl atoms of dichloromethane at 298 K. (b) High-density regions occupied by C (shaded blue), H (gray), and Cl (green) atoms of dichloromethane molecules around the LUT solute. (c) Computed RDFs between B of TRIS and C, H, and Cl atoms of dichloromethane at 298 K. (d) High-density regions occupied by C (shaded blue), H (gray), and Cl (green) atoms of dichloromethane molecules around the TRIS solute.

correction to transition-state theory of the solute system due to recrossing effects due to solvent dynamics. In the Kramers limit, this can be computed using eq 6.20

solution containing 960 dichloromethane and 512 toluene molecules with simulation cell dimensions of 47 Å × 47 Å × 47 Å. All of the simulations were performed in a NVT ensemble, with periodic boundary conditions applied in all three directions with a time step of 2 fs. Long-range electrostatic interactions were handled using the Ewald summation technique,16 and the SHAKE algorithm was used to fix the internal geometry.17,18 The rate constant for CSP association can be computed using classical transition-state theory in the condensed phase, where the dynamics is mapped onto an effective generalized Langevin equation, extending the original treatment by Kramers to account for memory effects in solvent response.19 The potential of mean force provides the driving force for the solute motion, while the influence of the solvent is represented by friction and stochastic force terms. The friction kernels using the trajectories at the barrier regions are calculated using the following relationship: 1 ⟨R(t , ra) ·R(0, ra)⟩ ζ (t ) = μk bT (4) R(t , r ) = F(t , r ) − ⟨F(t , r )⟩

κKr =

⎛ ζ ⎞2 ζ 1+⎜ ⎟ − 2ω b ⎝ 2ω b ⎠

(6)

where ζ is a constant friction coefficient given as ∫ ∞ 0 ζ(t) dt. ζ(t) is the friction kernel, and ωb is the barrier frequency obtained by fitting the PMF in the barrier region to an inverted parabola. Grote and Hynes (GH) developed a harmonic transition-state theory analysis that takes into account the dynamics of the solvent. In this case, the recrossing factor, κGH can be expressed as21 κGH

⎛ = ⎜κGH + ⎝

∫0

∞

−1 ζ(t ) −ω bκGHt ⎞ dt e ⎟ ωb ⎠

(7)

The GH theory transmission coefficient involves the frequency component of the time-dependent friction coefficient ζ(t) at the Laplace frequency ωbκGH relevant in the barrier region. We begin this section by discussing the structural and dynamical properties of a single pair of LUT and TRIS molecules in dichloromethane and in toluene. Displayed in Figure 3a are the computed atomic radial distribution functions (RDFs) between N of LUT and C, H, and Cl atoms of

(5)

where ra is the position of the barrier maximum, μ is the reduced mass, kb is the Boltzmann constant, and T is the temperature. The transmission coefficient κKr represents the 3314

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Figure 4. (a−d) Same as Figure 3a−d but for toluene.

and Cl atoms are shaded. It is observed that in the proximity of TRIS, dichloromethane molecules prefer to reside in the region bisecting the aromatic rings, avoiding steric hindrance. In addition, dichloromethane shows a strong orientational preference with the Cl atom pointing toward TRIS. This preferred orientation quickly diminishes with an increasing TRIS−CH2Cl2 distance. These structural features will unambiguously affect the dynamics and the association of LUT and TRIS in dichloromethane. In Figure 4a, the atomic RDFs are shown between the N atom of LUT and C and H atoms of toluene. Compared to the LUT−CH2Cl2 RDFs, these RDFs exhibit smaller peaks that occur at larger atomic separations, indicating that toluene forms a weaker solvation cage around LUT. This may be attributed to the difficulty to form a compact solvation shell with a larger rigid molecule such as toluene. Similar to the case in dichloromethane, toluene displays a strong preferential orientation around LUT at short distances. Shown in Figure 4b are the high-density regions of C (blue) and H (gray) atoms of toluene around LUT. By analyzing the source of H density (methyl H versus ring H), it is revealed that the methyl group of toluene prefers to reside in a region resembling a half circle above and below the aromatic ring around the N (LUT) atom with H atoms pointing into LUT, which corresponds to the small shoulder in the N−C RDF, while the main peak in N−C RDF results from the favorable interactions between the other sides of the LUT aromatic ring and the toluene molecules.

dichloromethane at 298 K. It is apparent from the RDFs that dichloromethane forms a well-defined solvation structure around the LUT molecule with multiple solvation shells. The presence of the first and the second shells is evident from the sharp peak centered at a C−N separation of 3.7 Å and the second peak at 6.8 Å, respectively. Additional analysis reveals that the RDFs correspond to a local nonsymmetric solvation of LUT by dichloromethane. Shown in Figure 3b are the highdensity regions occupied by the C, H, and Cl atoms of the dichloromethane molecule around the LUT solute. Clearly, the first peak in RDF comes from dichloromethane molecules residing in a region resembling a half circle above and below the aromatic ring around N (LUT) atom with the H (dichloromethane) atom pointing into LUT, while the second solvation shell results from the favorable interactions between the H atoms on the aromatic ring and the Cl atoms of the dichloromethane molecule. In Figure 3c, the computed atomic RDFs are shown between the B atom of TRIS and C, H, and Cl atoms of dichloromethane. In general, the features in these RDFs are rather broad and shallow, indicating a weaker solvation structure of dichloromethane around TRIS than those around LUT. The first peak positions of gBC(r), gBH(r), and gBCl(r) occur at 6.0, 7.0, and 5.2 Å, respectively. This result may be attributed to the preferential orientation of dichloromethane with respect to the TRIS solute at short distances. The detailed molecular arrangements are examined by the spatial density plot depicted in Figure 3d, where high-density regions of C, H, 3315

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Figure 5. (a) Computed reorientation correlation functions for LUT in dichloromethane; the three molecular axes were chosen to be the vector connecting the two C atoms in the aromatic ring next to the N atom (CC), the ring C2v symmetry axis, and the normal vector of the aromatic ring. (b) Computed reorientation correlation functions for TRIS in dichloromethane as a function of time at 298 K. Here, two molecular axes were chosen, which are defined to be one of the B−C bond vector and the normal vector of the plane consisting of B and the three C atoms bonded to B, respectively. (c) Same as (a) but for toluene. (d) Same as (b) but for toluene.

C2(t), that is defined as C2(t) = ⟨P2[u⃗(0)·u⃗(t)]⟩, where P2 denotes the second-order Legendre polynomial and u⃗(t) is the body-fixed unit vector along a specified molecular axis at time t. For LUT, the three molecular axes are chosen to be the vector connecting the two C atoms in the aromatic ring next to the N atom (CC), the ring C2v symmetry axis, and the normal vector of the aromatic ring. The corresponding orientational correlation functions in CH2Cl2 and toluene are shown in Figure 5a and b, respectively. It is clear that the reorientation motion of the LUT displays complex behavior and that C2(t) cannot be approximated by a single-exponential decay, a signature of simple Markovian diffusive rotation. They all exhibit rapid decays at short times, indicative of the initial inertial motion. At about 8−15 ps, there are distinct changes in the C2(t), which may involve the breaking of different types of solvent interactions. For LUT in dichloromethane, the rotation about the C−C vector is more hindered in comparison with the rotation about the C2v axis or rotation about the ring normal direction, which

Shown in Figure 4c are the atomic RDFs between the B atom of TRIS and C and H atoms of toluene. In general, the features in these RDFs are similar to those of TRIS in dichloromethane, indicating that toluene forms a fairly well-defined solvation structure around TRIS. This is consistent with the computed gas-phase PMF shown in Figure 2. The peak locations in these RDFs correspond to a very specific orientation between TRIS and toluene, as demonstrated by the spatial density distribution shown in Figure 4d. Here, the shaded areas denote the regions of high probability of C and H atoms of toluene. Clearly, the toluene molecules have the tendency to occupy the spaces bisecting the aromatic rings, with the solvent/solute rings facing each other. These structural features can be easily understood based on the energetic considerations associated with the balance between the penalty associated with steric hindrance and the attraction of the π−π interactions between aromatic rings. We inspect the reorientational motions of LUT and TRIS in different solvents via the orientational autocorrelation function, 3316

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and SSSP well depths for toluene have free energies of −0.6 and −0.1 kcal/mol, respectively, with a 1.0 kcal/mol barrier to CSP dissociation. Thus, we can conclude from these results that the FLP in toluene prefers to form a CSP configuration rather than a SSSP configuration. This may attribute to a strong TRIS−TOL interaction, as demonstrated in the gas-phase calculation of Figure 2. In comparing Figures 2 and 6, the significance of the solvent interaction contributing to the free energy of the reaction profile is evident. On physical grounds, it is clear that the existence of such minima primarily resulted from the balance between solute− solvent and solute−solute interactions. Closely examining snapshots of solute configurations around the CSP region in the case of dichloromethane, we can conclude that the CSP configuration is unfavorable due to lack of conformational freedoms associated with the finite temperature (i.e., accounting for entropy) in our simulations. Recently, Pápai and co-workers reported a detailed classical MD study on association of a frustrated phosphine−borane pair in toluene at ambient conditions.8 They found that the computed free-energy profile is purely repulsive and concluded that the process is thermodynamically unfavorable. It seems reasonable to conclude that a prime reason for this observation is probably due to the strong coupling between solute and solvent interactions. In addition, the entropic effects also play a significant role in this association process. Because the phosphine is a much bulkier molecule than LUT, it is possible that the entropy penalty incurred by the association of phosphine−borane outweighs the attractive interaction between the solute pair. Thus, our computed PMF/toluene behaves differently from phosphine−borane in toluene. It is interesting to compare the experimental rates of H2 activation by TRIS with tri-t-butylphosphine (TBP) and TRIS with tetramethylpiperidine (TMP). Both the amine−borane and phosphine−borane FLPs have similar enthalpies for heterolytic scission of H2 (∼−31.5 kcal/mol); however, the rate for H2 activation is significantly faster for the phosphine base compared to that for the amine base. (The half-life for H2 activation by TMP−TRIS is ∼230 s, and the half-life for TBPTRIS is ∼100 s.) While both TBP and TMP are relatively bulky, there is some apparent difference in reactivity that needs further investigation. In Figure 7, we show the plots of un-normalized friction kernels of FLP in dichloromethane and in toluene. In both cases, there are two distinct decay time scales. Both show an initial rapid decay lasting less than 0.2 ps, followed by a longtime decay that lasts for a few picoseconds. The rate constants from transition-state theory are shown in Table 1. This can be explained based on the barrier heights of the PMFs. As expected, the rate of a reaction depends on the height of the activation barrier. The higher the activation barrier, the slower the rate of reaction. The dissociative barrier heights observed on the PMFs agree with this argument. The corrected rate constant k is given by k = κkTST, where κ is the transmission coefficient that adjusts the rate constant kTST from transitionstate theory. We compute transmission coefficients using both Kramer’s theory and GH theory. Both of these theories use the generalized Langevin equation for the time evolution of the reaction coordinate. We observe the barrier frequency ωb of CSP to be very similar for both of the solvents (i.e., 1.5 versus 1.3). The GH theory transmission coefficients κGH are a bit higher than the corresponding κKr values. This is consistent with several

suggests that the rotation of LUT is anisotropic. This result is not surprising because we have observed asymmetric solvation of LUT by dichloromethane. In general, all three chosen molecular axes lose their correlations within 15−25 ps. On the other hand, the reorientation of LUT in toluene occurs at a longer time scale, possibly due to the fact that it is more difficult for bigger solvent molecules such as toluene to rearrange in order to accommodate the rotation of the LUT molecule. In Figure 5c and d, the reorientation correlation functions are plotted for TRIS in dichloromethane and in toluene as a function of time at 300 K. Here, three molecular axes are chosen, which are defined to be one of the C−C vectors (bonded to B) and B−C bond vectors and the normal vector of the plane that consist of B and the three C atoms bonded to B, respectively. Similar to the case of LUT, we note that these correlation functions cannot be described by a singleexponential decay. Additionally, the C2(t) of TRIS are found to decay more slowly than those of LUT. This can be understood on the basis that TRIS is a larger molecule, and it will take significant reorganization of the solvent in order for TRIS to rotate. We also observe a significant solvent effect on the rotational motion of TRIS; even after 100 ps, the correlation functions retain half of their original values for TRIS in toluene, while the correlation functions of TRIS in dichloromethane decay to about 20% in 50 ps. This may come from more complex ring interactions between toluene and TRIS. As stated above, one of the main focuses of this work is the detailed solvent effect on the association process of the FLP in dichloromethane and in toluene. Figure 6 shows the computed

Figure 6. Computed PMFs for the FLP in liquid dichloromethane and in toluene at 300 K.

free-energy profiles for the pair in these solvents as the function of their center-of mass-separation. The characteristics of these computed free-energy profiles show clearly that the association of this particular Lewis pair in these solvents is thermodynamically favorable when the solutes are fully solvated. Two significant free-energy minima are observed for both profiles, where the first minimum corresponds to the CSP, and the second minimum corresponds to the solvent-separated solute pair (SSSP), centered near 5.5 and 9.5 Å, respectively. In the case of dichloromethane solvent, the CSP and SSSP calculated from the classical PMF have free energies of 0.1 and −0.2 kcal/ mol, respectively, with a 0.4 kcal/mol barrier to CIP dissociation. The CSP well depth is positive and smaller than the corresponding SSSP well depth. The corresponding CSP 3317

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ing solvent effects with additional Lewis acid and Lewis base pairs will be required. The computed free-energy profiles for the FLP in both solvents show very similar characteristics but differ in details. We observe two well-defined contact and solvent-separated regions with different well depths and barrier heights to dissociation. Again, a solvent effect was observed on the free energy of association, where the stability of CSP versus SSSP can be altered.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. Pacific Northwest National Laboratory (PNNL) is a multiprogram national laboratory operated for DOE by Battelle. The calculations were carried out using computer resources provided by BES.

Figure 7. Computed un-normalized friction kernels for the FLP in liquid dichloromethane and in toluene.

Table 1. Results from Rate Theory TST rate constant kfTST, ps−1 barrier frequency ωb, ps−1 −1

for association

friction coefficient ζ, ps Kramer’s theory transmission coefficient, κKr GH theory transmission coefficient, κGH

dichloromethane

toluene

0.352 1.5 153 0.0098 0.0108

0.134 1.3 187 0.0070 0.0074

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REFERENCES

(1) Benjamin, I. Static and Dynamic Electronic Spectroscopy at Liquid Interfaces. Chem. Rev. 2002, 106, 1212−1233 and references cited therein.. (2) Stephan, D. W.; Greenberg, S.; Graham, T. W.; Chase, P.; Hastie, J. J.; Geier, S. J.; Farrell, J. M.; Brown, C. C.; Heiden, Z. M.; Welch, G. C.; Ullrich, M. Metal-Free Catalytic Hydrogenation of Polar Substrates by Frustrated Lewis Pairs. Inorg. Chem. 2011, 50, 12338−12348. (3) Geier, S. J.; Stephan, D. W. Lutidine/B(C6F5)3: At the Boundary of Classical and Frustrated Lewis Pair Reactivity. J. Am. Chem. Soc. 2009, 131, 3476−3477. (4) Stephen, J. G.; Gille, A. L.; Gilbert, T. M.; Stephan, W. D. From Classical Adducts to Frustrated Lewis Pairs: Steric Effects in the Interactions of Pyridines and B(C6F5)3. Inorg. Chem. 2009, 48, 10466− 10474. (5) Rokob, T. A.; Hamza, A.; Stirling, A.; Papai, I. Turning Frustration into Bond Activation: A Theoretical Mechanistic Study on Heterolytic Hydrogen Splitting by Frustrated Lewis Pairs. Angew. Chem., Int. Ed. 2008, 47, 2435−2438. (6) Karkamkar, A.; Parab, K.; Neiner, D.; Nielsen, T. K.; Cho, H.; Camaioni, D. M.; Autrey, T. A Thermodynamic and Kinetic Study of the Heterolytic Activation of Hydrogen by Frustrated Borane−Amine Lewis Pairs. Dalton Trans. 2013, DOI: 10.1039/c2dt31628e. (7) Wu, D.; Jia, D.; Liu, L.; Zhang, L.; Guo., J. Reactivity of 2,6Lutidine/BR3 and Pyridine/BR3 Lewis Pairs (R = F, Me, C6F5): A Density Functional Study. J. Phys. Chem. A 2010, 114, 11738−12745. (8) Bako, I.; Stirling, A.; Balint, S.; Papai, I. Association of Frustrated Phosphine−Borane Pairs in Toluene: Molecular Dynamics Simulations. Dalton Trans. 2012, 41, 9023−9025. (9) Camaioni, D. M.; Ginovska-Pangovska, B.; Schenter, G. K.; Kathmann, S. M.; Autrey, T. Analysis of the Activation and Heterolytic Dissociation of H2 by Frustrated Lewis Pairs: NH3/BX3 (X = H, F, and Cl). J. Phys. Chem. A 2012, 116, 7228−7237. (10) Dang, L. X. Intermolecular Interactions of Liquid Dichloromethane and Equilibrium Properties of Liquid−Vapor and Liquid− Liquid Interfaces: A Molecular Dynamics Study. J. Chem. Phys. 1999, 110, 10113−10122 . We have recently developed a polarizable model that gave a good description such as the structural and thermodynamics properties for liquid toluene. (11) Wang, J. M.; Wang, W.; Kollman, P. A.; Case, D. A. Automatic Atom Type and Bond Type Perception in Molecular Mechanical Calculations. J. Mol. Graph. Model. 2006, 25, 247−260.

previous studies because Kramer’s formula treats the friction due to the solvent as a constant friction coefficient. The time dependence associated with solute reactive motion over the free-energy barrier is slow compared to the solvent motion as characterized by the time-dependent friction ζ(t).22−24 We carried out a systematic simulation study of the LUT− TRIS FLP in dichloromethane and toluene solvents in order to gain further insight into the role of solvent on the thermodynamics and kinetics of forming the FLP. These molecular systems are of great interest due to their ability to heterolytically activate molecular hydrogen for nonmetal catalytic hydrogenation of polar substrates. From the structural observations, it is apparent from the RDFs that dichloromethane forms a well-defined solvation structure around the LUT molecule with multiple solvation shells. At the same time, a weaker solvation structure of dichloromethane was found around TRIS than those around LUT. The computed RDFs indicated toluene forms a fairly well-defined solvation structure around TRIS, and it is consistent with the computed gas-phase PMF. The computed reorientations were found to be markedly slow, as expected for the bulky solutes. This can be understood on the basis that TRIS is a relatively large molecule, and it will take significant reorganization of the solvent in order for TRIS to rotate. We also observe a significant solvent effect on the rotational motion of TRIS; even after 100 ps, the correlation functions retain half of their original values for TRIS in toluene, while the correlation functions of TRIS in dichloromethane have decayed to about 20% in 50 ps. This may come from the specific interaction between toluene and TRIS. It is still premature to conclude whether the reaction of H2 activation by a frustrated Lewis acid−base pair proceeds by a termolecular reaction or a bimolecular interaction with a weakly coordinated FLP. Further experimental and computational work investigat3318

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The Journal of Physical Chemistry Letters

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dx.doi.org/10.1021/jz301533a | J. Phys. Chem. Lett. 2012, 3, 3312−3319