J. Phys. Chem. B 2008, 112, 2637-2643
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MD Study of SN1 Reactivity of 2-Chloro-2-methylpropane in the Room-Temperature Ionic Liquid 1-Ethyl-3-methylimidazolium Hexafluorophosphate Youngseon Shim† and Hyung J. Kim*,†,‡ Department of Chemistry, Carnegie Mellon UniVersity, Pittsburgh, PennsylVania 15213, and Department of Physics, Korea UniVersity, Seoul 136-701, Korea ReceiVed: October 18, 2007; In Final Form: December 5, 2007
The SN1 ionization reaction RX f R+ + X- for 2-chloro-2-methylpropane in ionic liquid 1-ethyl-3methylimidazolium hexafluorophosphate ([emim]+PF6 ) is studied via molecular dynamics computer simulations. By employing a two-state valence-bond description for electronic structure variations of the reaction complex, the free energy curve relevant to its SN1 ionization in [emim]+PF6 is computed via the thermodynamic integration method and compared with those in water and in acetonitrile. It is found that the detailed reaction mechanism differs among the three solvents. To be specific, the dissociation of 2-chloro2-methylpropane in [emim]+PF6 is a stepwise process consisting of the formation of a solvent-separated ion pair and ensuing dissociation, while that in acetonitrile appears to proceed without any stable reaction intermediates. The SN1 pathway in water on the other hand is characterized by the formation of a contact ion pair, followed by dissociation to free ions. The activation free energy in water is much lower than those in + [emim]+PF6 and acetonitrile. Between the two latter solvents, the barrier height is lower in [emim] PF6 than in acetonitrile, indicating that the SN1 reactivity of 2-chloro-2-methylpropane would be higher in [emim]+PF6 than in acetonitrile. Its implication for solvolysis in these solvents is briefly discussed.
1. Introduction The SN1 ionization pathway RX f R++X- is one of the fundamental mechanisms to understand reactions involving haloalkanes and related organic molecules in solution.1 Since the early seminal works by Hughes and Ingold2 and Winstein and his co-workers,3 there have been extensive experimental efforts to elucidate the SN1 mechanism. There is now much evidence that the initial ionization step RX f R+X- is ratelimiting in solvolysis, namely, unimolecular substitution and elimination reactions with ethers and olefins as final products, respectively. It is also well-established that the solute-solvent electrostatic interactions play a critical role in free energetics and kinetics of this reaction class because of a major difference in electronic character and thus solvation stabilization between the nearly covalent reactant and the highly dipolar activated complex. This state-dependent solvation, for example, leads to a dramatic acceleration of solvolysis with increasing solvent polarity. For modern perspective on solvation influence on SN1 reactions, the reader is referred to refs 4 and 5. Another class of solvents that can exert a strong influence on solvolysis is so-called room-temperature ionic liquids (RTILs), which consist of bulky and asymmetric cations paired with a variety of different anions.6 RTILs are liquids at or near room temperature and usually nonvolatile, nonflammable, and thermally stable. Because of their exciting potential as a green solvent and their wide range of materials and device applications, RTILs have been the subject of intensive scrutiny recently.6 According to kinetics7 and many solvatochromic measurements8-19 as well as molecular dynamics (MD) * Corresponding author. Permanent address: Carnegie Mellon University. E-mail:
[email protected]. † Carnegie Mellon University. ‡ Korea University.
simulations,20-22 the effective polarity of RTILs, gauged by their capability of solvating dipolar solutes, is very high; it is comparable to that of, for example, small alcohols. Thus, kinetics and free energetics of a variety of different reactions involving charge shift and transfer are expected to be significantly modulated in RTILs, compared with gas phase. Previous MD studies show that solvation effects on electron-transfer reactions couched in terms of, for example, outer-sphere reorganization free energy and solvent-induced stabilization, in RTILs are similar to and often stronger than those in highly polar aprotic solvents.23-25 Nucleophilic substitution and displacement reactions in RTILs have received significant experimental attention.7,26-31 Among others, the relative nucleophilicities of various halides and related reagents toward primary or secondary substrates were found to vary with RTILs.27,28,30 As expected, measurements indicate that there is a gradual shift in the reaction mechanism from SN2 to SN1 as substrates change from the primary to tertiary structure.30 Nevertheless, the RTILs are believed to be nondissociating, albeit ionizing, solvents for organic halides and related molecules.31 In this article, we study the SN1 ionic dissociation pathway for 2-chloro-2-methylpropane (t-BuCl) in 1-ethyl-3-methylimidazolium hexafluorophosphate ([emim]+PF6 ) and compare it with those in two normal solvents, water and acetonitrile. The reaction free energy curve relevant to SN1 dissociation in solution is determined as a function of the separation between the tert-butyl (t-Bu) and Cl moieties via MD simulations using the thermodynamic integration method.32 The existence and characteristics of contact and solvent-separated ion pairs are examined. The outline of this paper is as follows: In section 2, the twostate valence-bond formulation used to describe the haloalkane
10.1021/jp710128p CCC: $40.75 © 2008 American Chemical Society Published on Web 02/13/2008
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ionization process is reviewed briefly. The molecular models and simulation methods employed in our study are also summarized there. In section 3, we present an analysis of the MD results for SN1 dissociation in [emim]+PF6 and make comparison with water and acetonitrile. Concluding remarks are offered in section 4.
TABLE 1: Parameters for H ˆ0
2. Theoretical Model and Simulation Methods Here, we give a brief explanation of the model descriptions and simulation methods employed in the present MD study of the SN1 reaction in [emim]+PF6 , water, and acetonitrile. 2.1. Solute Vacuum Hamiltonian. To describe electronic structure variations of t-BuCl during the ionization, we use a two-state valence-bond (VB) formulation, employed in many prior studies of SN1 systems.4,5,33-38 In this approach, the evolving solute charge distribution is represented as a mixing of two orthonormal VB functions, a covalent and an ionic state +
ψC(r) ) ψC[RX]
-
〈ψC|ψI〉 ) 0 (1)
ψI(r) ) ψI[R X ]
which vary parametrically with the separation r between t-Bu and Cl. The vacuum electronic Hamiltonian H ˆ 0 in this basis is a 2 × 2 matrix
H ˆ 0(r) )
[
V0C(r)
-β0(r) 0 -β0(r) VI (r)
]
(2) V0C(r)
V0I (r)
where the caret signifies a quantum operator, and are the gas-phase potential energies associated with ψC(r) and ψI(r), and β0(r) is electronic coupling between the two. We note that a two-state VB description similar to this was originally proposed for SN1 reactions long ago by Polany, Evans and their co-workers39 and more recently by Warshel and Weiss.40,41 Later, it was extended by Hynes and co-workers to quantitate free energetics and dynamics of ionization of t-butyl halides in polar solvents, including nonequilibrium solvation effects.4,5,33 We assume that t-Bu is composed of a central carbon atom and three methyl groups in a planar geometry with C3 symmetry about the molecular axis passing through the central carbon atom.42 The united-atom representation is employed for each methyl group. Cl is restricted to move on the C3 symmetry axis of t-Bu.4,5,33-38,42 For covalent V0C(r), a simple Morse potential is used
V0C(r) ) D0 {exp[-2a0(r - r0)] - 2 exp[-a0(r - r0)]} (3) where r is the distance between Cl and the central carbon atom of t-Bu. In the simulations, we use the parametric values of ref 37 (see Table 1). As for the ionic state, the interactions between Cl- and constituents of t-Bu+ are modeled by a Buckingham potential plus a Coulombic interaction
V0I (r) ) ∆ + B e-γr - 4CCl
[
( ) ( )
σCCl 6 qCqCl + + r r
3 B e-γxr +l - 4MeCl 2
2
σMeCl
xr
2
+l
6
2
+
]
qMeqCl
xr2 + l2
(4)
where qC and qMe are respectively the partial charges associated with the central carbon and each methyl group of the t-Bu cation, l is the bond length between the two, and ∆ is the ionization potential of the t-Bu radical minus the electron affinity of Cl. The parameters for short-range heteroatom interactions are
q (e)a
atom or group
a
C CH3 Cl
0.4 0.2 -1.0
D0 a0 r0 ∆ B γ l Vc λ
60.72 kcal/mol 218.8 pm-1 183.0 pm 71.19 kcal/mol 5760.0 kcal/mol 248.0 pm-1 147.5 pm 1138.9 kcal/mol 176.7 pm-1
σ (pm)
(kcal/mol)
225.0 300.0 441.7
0.050 0.100 0.118
e is the elementary charge.
TABLE 2: Solute Parameters for Solute-Solvent Interactions atom or group
q (e)
σ (pm)
(kcal/mol)
Cl Clt-Bu t-Bu+
0 -1 0 1
335.00 441.70 533.04 533.04
0.3448 0.1180 0.1695 0.1695
determined via ij ) xij and σij ) 0.5(σi + σj) [Table 1]. As for the electronic coupling between ψC(r) and ψI(r), we assume that it decreases exponentially with r following refs 35-38
β0(r) ) Vc exp(-λr)
(5)
Comparison with a detailed analysis of coupling in ref 33 indicates that eq 5 provides a reasonable framework to describe t-butyl halide systems. 2.2. Solution-Phase Interactions. In solution, the Hamiltonian becomes
H ˆ (r) ) H ˆ 0(r) + Vˆ LJ(r) + Vˆ coul(r) + Vss
(6)
where H ˆ 0 is the solute vacuum Hamiltonian in eq 2, Vˆ LJ(r) and Vˆ coul(r) describe respectively the solute-solvent Lennard-Jones (LJ) and electrostatic interactions, and Vss denotes the interactions among solvent molecules. We use a classical description for the solvent in our simulation. For Vˆ LJ(r) and Vˆ coul(r), we employ a united-atom representation34-38 for t-Bu with LJ parameters σ ) 533.04 pm and ) 0.1695 kcal/mol regardless of the solute electronic states. A single point charge at the center of t-Bu+ represents its charge distribution needed in Vˆ coul(r). Thus, the three methyl groups of t-Bu do not play any role in the interactions with the solvent. For chlorine, we use state-dependent LJ parameters, that is, σ ) 335 pm and ) 0.345 kcal/mol and 441.7 pm and 0.118 kcal/mol for its radical and anionic states, respectively. The parameters employed for Vˆ LJ(r) and Vˆ coul(r) are compiled in Table 2. We turn to the solvent descriptions. For [emim]+PF6 , we use the potential model of refs 20 and 21, where the CH2 and CH3 moieties of [emim]+ as well as PF6 are treated as united atoms. The LJ parameters of the AMBER force field43 and the partial charge assignments of ref 44 are used for [emim]+, while σ ) 560 pm and /kB ) 200 K are employed for PF6. Comparison with an all-atom solvent description shows that the united-atom representation used in the present study captures solvation free energetics and dynamics21,45 very well. As for normal polar solvents, the three-site description of ref 46 was employed for acetonitrile, while the SPC/E model47 was used for water.
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Figure 1. (a) Adiabatic ground-state electronic potential energy curves for the ionization of t-BuCl in the gas phase (s) and in + [emim]+PF6 (- -) at 400 K. (b) Charge distribution of t-BuCl in [emim] PF6 . q is the t-BuCl partial charge measured in the units of the +q -q elementary charge e, i.e., t-Bu ‚‚‚Cl , and µ is its dipole moment. t-BuCl becomes ionic, i.e., q ≈ 1 for r J 300 pm.
2.3. Simulation Methods. All MD simulations were conducted with the DL_POLY program48 in the canonical ensemble at T ) 400 K for [emim]+PF6 and at 298 K for acetonitrile and water. The simulation cell is comprised of a single solute molecule immersed in either [emim]+PF6 consisting of 212 pairs of cations and anions, CH3CN composed of 216 rigid acetonitrile molecules, or H2O comprised of 512 SPC/E water molecules. All solvent molecules and ions are rigid in the present study. The reaction free energy curve pertinent to the t-BuCl ionization was calculated via the thermodynamic integration method.32 Briefly, the solvent-averaged force FRX(r) along the dissociation coordinate r (i.e., the displacement of Cl with respect to t-Bu)
FRX(r) ) 0.5 〈n‚(FR - FX)〉
r ) |r|
n ) r/r (7)
is calculated at fixed r and then integrated
A(r) ) A(r0) -
∫rr FRX(r) dr - kBT ln(r/r0)2
(8)
0
to obtain the effective reaction free energy profile A(r). In eq 7, 〈...〉 denotes an equilibrium average, n is the unit vector along r and FR and FX are the forces on t-Bu and Cl, respectively. The last term on the right-hand side of eq 8 is the entropic contribution from the volume element, that is, 4πr2dr, to A(r).49 It can thus be viewed as the contribution to the free energy from the rotational partition function of the t-Bu‚‚‚Cl complex of bond length r. We emphasize that, in A(r), the relative orientation of Cl with respect to t-Bu is fixed, namely, Cl is always located on the C3 axis of t-Bu. At each r value for t-BuCl, simulations in water and acetonitrile were carried out with 2 ns equilibration, followed by a 2 ns trajectory from which averages were computed. For [emim]+PF6 , we computed averages using configurations collected from two different 1 ns trajectories with 2 ns equilibration. 3. Simulation Results and Discussions We begin with MD results for A(r) in eq 8 for [emim]+PF6 in Figure 1a. For comparison, the adiabatic ground-state electronic curve in the gas phase, that is, the energy of the lower eigenstate of H ˆ 0(r) in eq 2, is also shown there. There are several interesting and noteworthy features. First, both curves are characterized by a global minimum around r ) 180 pm, which corresponds to the reactant state for the ionization. Second, t-BuCl is stabilized dramatically in [emim]+PF6 compared to the gas-phase. This solvation-induced stabilization tends to
increase as r grows. As a result, the dissociation (free) energy ∆Arxn decreases from ∼85 kcal/mol in the gas phase to ∼40 kcal/mol in [emim]+PF6 . The solute-solvent electrostatic interactions that become stronger as t-BuCl dissociates are mainly responsible for r-dependent stabilization (see below). For additional insight, the average charge distribution of t-BuCl in [emim]+PF6 is considered as a function of its bond length in Figure 1b. The magnitudes of partial charges q on t-Bu and Cl and associated t-BuCl dipole moment µ () qr) increase with growing r. Because of the mixing of nondipolar ψC[RX] and dipolar ψI[R+X-], the reactant state has a small but finite dipole moment. We notice that the electronic character of t-BuCl becomes almost completely ionic, namely, t-Bu+‚‚‚Cl-, for r J 300 pm. Because t-BuCl has a nonvanishing dipole moment and the effective polarity of ionic liquids is very high,8-21,23 there is significant stabilization of t-BuCl in [emim]+PF6 , compared to the gas phase. Since the charge separation and dipole moment of the solute increase as its bond length elongates, so does the solvent stabilization. This explains the huge reduction in the free energy of reaction ∆Arxn in [emim]+PF6 observed above. Another interesting feature in Figure 1a is that the SN1 free energy curve in [emim]+PF6 has a broad local minimum around r ) 1 nm. We tentatively identify this structure as the “solvent-separated ion pair” (SSIP) state, posited long ago by Winstein and co-workers to explain salt effects on solvolysis.3c,f The putative SSIP state is about 3.5 kcal/mol more stable than two local maxima at r ≈ 650 pm and 1.4 nm. We will return to the SSIP for more details below. To understand variations of solvation structure during the ionization, we studied the distributions g((R) of the solvent cations and anions around t-BuCl at different r values
gR(R) ) nR-1
〈δ(Ri - R)〉 ∑ iR
(9)
where i and R () () label respectively individual solvent ions and ionic species (viz., [emim]+ and Cl-), nR is the average number density of R, δ is the Dirac delta function, Ri is the position of i with respect to the center of t-BuCl, and the sum is over all ions of type R. Because of the extended nature of [emim]+, we use its center of mass to represent its position. g((R) is symmetric about the C3 axis of t-BuCl because of cylindrical symmetry in the solute-solvent interaction. We note that if gR(R) is integrated over all possible orientations of R, it reduces to the normal radial distribution function of R with respect to the center of the solute. The MD results for g((R) in [emim]+PF6 are exhibited in Figure 2. We considered three different states: the reactant and
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Figure 2. Distributions of solvent cations and anions around t-BuCl: (a) r ) 180 pm; (b) 650 pm; (c) 1 nm. The z axis measures the magnitudes of g((R), where R is restricted to the xy plane (length units: nm). The cation and anion distributions, g+ and g-, are shown in the upper and lower half-planes, i.e., y > 0 and y < 0, respectively. Two peaks on the x axis denote the positions of t-Bu (x < 0) and Cl (x > 0) and their midpoint is located at the origin.
putative SSIP states of the SN1 ionization, located respectively at r ) 180 pm and 1 nm, and the transition state at r ) 650 pm between the two [cf. Figure 1a]. The plots in the upper (y > 0) and lower (y < 0) half-planes depict the cation and anion distributions, respectively. Around the covalent reactant state at r ) 180 pm, the solvent distributions show nearly isotropic and shell-like structures. Since these shell-like distributions of cations and anions have a similar radius, we expect that the solvent charge density around the solute in the reactant state is small. This is in good agreement with our earlier study.21 As the bond length and dipole moment of t-BuCl increase, the concentric shell structures of the solvent ions become rather complicated. Specifically, separate shell structures develop around t-Bu+ and Cl-, respectively. We notice that anisotropy of these structures varies significantly with r. For example, the main peak of g-(R) is located on the back side of t-BuCl for the activated complex, while the corresponding peak for the SSIP state is in the region between the t-Bu and the Cl moieties. Thus, the solvent distribution around t-Bu+ is very sensitive to the location of Cl- and vice versa. Also these results clearly expose that there is significant reorganization of solvent ions associated with SN1 dissociation in RTILs, analogous to normal polar solvents. According to recent studies on electron-transfer reactions, free energies associated with solvent reorganization in RTILs are comparable to (actually somewhat larger than) those in highly polar aprotic solvents.23-25 Despite this similarity, underlying molecular dynamics are rather different between the two solvent classes; the solvent reorganization in RTILs occurs mainly via translational motions of constituent ions,45,50 while solvent rotations play a major role in polar solvents. As noted above in connection with solvent structural anisotropy in Figure 2, the density of solvent ions in the region between t-Bu and Cl grows as their separation r increases. Thus, while there is no solvent population between t-Bu and Cl along the C3 axis in the reactant or transition state, the nonvanishing amplitudes of g((R) there for r ) 1 nm indicate that solvent ions are present in the neighborhood of R ) 0 at the putative SSIP state. To gain further insight, we analyze the distribution of solvent ions in a cylindrical volume V(F) between t-Bu and
Cl shown in Figure 3a as a function of the radius F of its base circle. As in the case of g((R), we employ the cation centerof-mass to describe locations of [emim]+. The total number NR(F) of ions of type R inside the cylinder and its F-derivative nR(F) are
NR(F) ) nR
∫∫∫R∈υ(F) dR gi(R)
nR(F) ) dNR(F)/dF (10)
where R ∈ υ(F) means that the integration is confined to the volume inside the cylinder. The results for nR(F) with r ) 1 nm are displayed in Figure 3b. Both cation and anion distributions show a distinctive structure for F j 400 pm; n+ has a peak and n- has a clear shoulder structure there. This seems to indicate that there is a nonvanishing population of ions that are preferentially located close to the C3 axis. According to Figure 3c, the total number of cations (or anions) inside the cylinder region is ∼1 for F ) 350-400 pm. For perspective, we recall that the bond length between central C and a methyl group of t-Bu is 147.5 pm, and the σMe value of the methyl groups is 300 pm. Thus, on average, there is one pair of solvent cations and anions located in the cylindrical region with F ) 350-400 pm between t-Bu+ and Cl-. In this context, we refer to the local free energy minimum at r ) 1 nm in Figure 1a as the solvent-separated ion-pair state. In Figure 3d, the orientation of [emim]+ inside the cylindrical region is analyzed. For convenience, we examined the probability distribution P(θ) of the angle θ between the t-BuCl bond direction and each of three axes u1,2,3 of [emim]+ defined as follows: u1 passes through two N atoms in the direction from the ethyl to methyl groups of [emim]+, while u2 is from the center of the two N atoms to the carbon atom located between the two. Thus, both u1 and u2 lie in the plane of the imidazole ring. u3 is normal to the ring at the midpoint of the two N atoms. The direction of the ethyl and methyl groups from the ring is defined as the positive direction of u3. We found that the average orientation of the u1 axis, which is roughly the long principal axis of [emim]+, is nearly perpendicular to the t-Bu-to-Cl direction, while the distribution of u3 displays a double-peak
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Figure 3. (a) Cylindrical region between t-Bu and Cl moieties. (b) nR(F) and (c) NR(F) as a function of the radius F in [emim]+PF6 at 400 K. (d) Orientational distribution P(θ) of three axes, u1, u2, and u3, of [emim]+ located inside the cylinder in (a) with F ) 400 pm and r ) 1 nm. P(θ) is normalized so that ∫π0 dθP(θ) ) 1.
Figure 4. (a) Comparison of free energy curves for t-BuCl ionization in water (‚‚‚) and acetonitrile (- -) at 298 K and in [emim]+PF6 (s) at 400 K. For clarity, the free energy curves in water and acetonitrile are shifted vertically with respect to that in [emim]+PF6 . (b) The difference in the t-BuCl ionization free energy curve between [emim]+PF6 and acetonitrile.
structure with centers at θ ≈ 30° and 150°. This indicates that at SSIP, the imidazole ring of [emim]+ located in the region between t-Bu+ and Cl- generally faces toward Cl-. In Figure 4a, the free energy profile A(r) for the SN1 ionization pathway in [emim]+PF6 is compared with those in acetonitrile and in water. While overall characteristics of A(r) are generally similar between [emim]+PF6 and acetonitrile, water shows a rather different behavior. A(r) in the latter solvent is characterized by a local minimum located at r ≈ 290 pm in addition to the reactant state near r ) 180 pm which is common in all three solvents.34-38,42 We identify the local free energy minimum around r ) 290 pm as the contact ion pair (CIP) state.3c,f The activated complex for the formation of CIP in water from the reactant state is located around r ) 225 pm and is about 21.5 kcal/mol higher in free energy than the reactant state. Though not presented here, we note that the activated complex is about 80% ionic and 20% covalent, while the CIP is essentially 100% ionic. A further dissociation of CIP in water is an activated process with a barrier of ∼5 kcal/mol situated at r ≈ 500 pm. We point out that the two-state VB description combined with
the SPC/E potential employed here does not yield a locally stable SSIP state in water; that is, A(r) is rather flat for r J 900 pm. Our findings here are in reasonable accord with a previous Monte Carlo simulation study in water, where the mixing of the covalent and ionic states of t-BuCl was not accounted for.42 In contrast to water, the SN1 ionization free energy curves in [emim]+PF6 and in acetonitrile do not show a local minimum around r ) 300 pm. This means that CIP is not a (locally) stable state and thus does not serve as a reaction intermediate for the SN1 ionization in these solvents. Nevertheless, their free energy profiles show an inflection point near r ) 300 pm, implying significant stabilization of the solute there induced by solvation. In the case of [emim]+PF6 , we notice another important distinction from water, namely, the presence of the stable SSIP state we analyzed above. The MD result for the free energy barrier for subsequent dissociation of this SSIP is ∼3.5 kcal/ mol at 400 K. Thus, if SN1 dissociation does occur in nonhydroxylic solvents, it would proceed as RX f SSIP f R+ + X- in [emim]+PF6 , whereas the corresponding pathway
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in water is RX f CIP f R+ + X-. Strictly speaking, A(r) in acetonitrile also has a broad local minimum around r ) 900 pm, analogous to [emim]+PF6 . However, the barrier between this state and dissociated ions is just ∼0.5 kcal/mol high at 298 K. Thus, it is of little significance because the thermal energy is greater than the barrier height. Therefore, our mechanistic prediction for the dissociation of t-BuCl in acetonitrile is RX f R+ + X-; it does not involve any reaction intermediates in contrast to water and [emim]+PF6 environments. In addition to qualitative differences, [emim]+PF6 and acetonitrile show a major quantitative difference in A(r) from water. The free energy of reaction ∆Arxn associated with the dissociation of the reactant is 40-50 kcal/mol in [emim]+PF6 and acetonitrile, while it is much smaller ∼20 kcal/mol in water. One of the main reasons is that the empirical polarity of water, which gauges effects of both specific and nonspecific solvation, is considerably higher than that of the nonhydroxylic solvents. This helps to stabilize the dissociated ions, especially Cl-, in the former compared with the latter solvents. For instance, the free energy of transfer of Cl- from water to acetonitrile is about 10 kcal/mol,51 which alone accounts for nearly 50% of the difference in ∆Arxn between the two solvents. Another important factor is destabilization of the reactant through so-called “structure-making” of water around t-BuCl.3e,52,53 Solvation of the t-BuCl reactant in water is accompanied by a significant entropy decrease due to an increase in the ordering of water molecules surrounding the solute. This increases the free energy associated with the t-BuCl reactant and thus reduces ∆Arxn in water compared with other polar solvents. Finally, we make a comparison of the reaction free energy curves in [emim]+PF6 and acetonitrile. The difference in A(r) between [emim]+PF6 and acetonitrile
δA(r) ) A(r) (in CH3CN) - A(r) (in [emim]+PF6)
(11)
is presented in Figure 4b. Despite overall similarities in A(r) except for SSIP, there is important quantitative difference between the two solvents. The reaction free energy profile is considerably lower in [emim]+PF6 than in acetonitrile for r J 300 pm. Since the empirical polarity of RTILs tends to increase with decreasing T,12 the free energy difference of this magnitude (or even larger) would be expected between the two solvents 23 when the temperature of [emim]+PF6 is lowered to 298 K. Thus, the activation free energy for the SN1 pathway is about J 4 kcal/mol lower in [emim]+PF6 than in acetonitrile. All other things being equal, this means that the SN1 dissociation rate of t-BuCl would be higher in the former than in the latter by nearly 3 orders of magnitude at room temperature. This would be an overestimation due to, for example, the neglect of barrier crossing dynamics which could reduce the rate constant in viscous [emim]+PF6 compared with acetonitrile. Nevertheless, we believe that the SN1 rate, if the reaction does occur, would still be considerably higher in the former than in the latter even after proper account of dynamic effects because it is not slow dynamics but fast relaxation that often plays a crucial role in reaction kinetics,5,34,54,55 even in viscous RTILs.23 It would nonetheless be interesting to examine the influence of activation and barrier crossing dynamics on SN1 reactions. This will be postponed for a future study. Before we conclude, we briefly speculate on implications of our analysis for the unimolecular elimination E1 reaction for perspective. If the prevalent notion that the ionization of t-BuCl is rate-limiting for E1 is indeed valid, the t-BuCl bond needs
to extend at least to r ≈ 300 pm, so that its electronic character becomes nearly 100% ionic (Figure 1b) before the elimination of hydrogen from t-Bu can occur. As observed above in Figure 4b, A(r) in [emim]+PF6 is lower than that in acetonitrile by ∼ 4 kcal/mol in a wide r range with r J 300 pm. Therefore, just like the SN1 case, we would expect that the E1 rate and thus overall solvolysis rate (i.e., SN1 + E1) would be substantially higher in [emim]+PF6 than in acetonitrile. It would thus be interesting to see if this trend in solvolysis is borne out in measurements. 4. Concluding Remarks In this paper, we have studied SN1 ionic dissociation of 2-chloro-2-methylpropane in [emim]+PF6 via equilibrium MD simulations. The electronic structure variation of t-BuCl was incorporated into simulations via a two-state VB description, and its reaction free energy curve was determined with the thermodynamic integration method as a function of the separation r between t-Bu and Cl. This has enabled us to analyze reaction thermodynamics and mechanistic details with proper account of solute charge fluctuations with solvation. For comparison, we have also studied SN1 reaction pathways in water and in acetonitrile. Our MD study predicts that the t-BuCl dissociation in [emim]+PF6 would proceed in a stepwise manner, RX f SSIP f R++X-, that is, formation of a solvent-separated ion pair, followed by dissociation to ions. A detailed analysis of solvation structure shows that the dissociation is accompanied by significant reorganization of solvent ions. At the SSIP state, the distance between t-Bu and Cl is r ≈ 1 nm, and the two moieties are separated by approximately one pair of [emim]+ and PF6 ions. The free energy barrier for further dissociation of SSIP was found to be ∼3.5 kcal/mol at 400 K. Another important finding is that t-BuCl dissociation mechanism in water shows a major difference from that in [emim]+PF6 . While SSIP is not a (meta) stable state, a contact ion pair state serves as reaction intermediate, so that the t-BuCl dissociation pathway is RX f CIP f R++X- in water. According to our results, the dissociation of CIP is an activated process with barrier height of about 5 kcal/mol at 298 K. By contrast, the t-BuCl dissociation in acetonitrile does not appear to involve any reaction intermediates; namely, it would proceed as RX f R+ + X-. Strong solvation stabilization of the ionic product state of t-BuCl makes SN1 ionic dissociation much faster in all three solvents considered here than in the gas phase. Because of high empirical polarity of water arising from its hydrogen-bonding capability and also because of its structure-making trend around small hydrophobic solutes, the free energy of reaction and activation barrier in water are much lower than those in [emim]+PF6 and acetonitrile. Of the latter two solvents, [emim]+PF6 is lower in both the barrier height and the free energy of reaction. This suggests that the solvolysis rate of t-BuCl would be higher in [emim]+PF6 than in acetonitrile. Nevertheless, the large free energy of reaction (∼40 kcal/mol) and barrier height (∼44 kcal/mol) in [emim]+PF6 seem to lend support to the experimental interpretation31 that RTILs are ionizing but not dissociating solvents. In the present study, we have used several approximations to simplify our descriptions and analysis: The united-atom representation was employed for some moieties of the solute and solvent molecules and ions. Also the effect of solvent polarizability was neglected. Despite these approximations,
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