Structure and Reactivity in Aqueous Solution - American Chemical

Chapter 14

Theoretical Models of Anisole Hydrolysis in Supercritical Water Downloaded by UNIV OF CALIFORNIA SAN DIEGO on February 2, 2016 | http://pubs.acs.org Publication Date: September 29, 1994 | doi: 10.1021/bk-1994-0568.ch014

Understanding the Effects of Pressure on Reactivity Susan C. Tucker and Erin M. Gibbons Department of Chemistry, University of California, Davis, C A 95616

Electrostatic contributions to the free energies of activation for the title reaction in supercritical water are calculated as a function of pressure. The calculations model the solvent as an incompressible fluid having a pressure dependent dielectric constant. A number of implementations of this model, both with and without solute polarizability, are consid ered and contrasted. The calculated equilibrium solvation effects are found to adequately explain the experimentally observed pressure de pendence of this reaction. However, an effective local dielectric which differs significantly from the bulk value for supercritical water must be invoked to obtain agreement between theory and experiment, in dicating that there is a large degree of solvent-solute clustering for this reaction. Additionally, the free energies of solvation, and hence the solvent-solute interactions, are found to depend strongly on re action coordinate position. These results raise questions about the importance of reaction path dependent clustering on the free energy of activation and solute reactivity. Supercritical water provides a unique solvent environment because significant changes in its solvating properties may be effected by modest changes in ther modynamic conditions. Supercritical water (SCW) thus provides the basis for a number of industrial processes, from S C W extraction (1) to the oxidative destruc tion of hazardous wastes (2). More recently, SCW has been proposed as a medium for selective synthetic chemistry (8,4). Prom a more fundamental point of view, S C W is important because it enaoles one to study the effect of changing solvent properties while the underlying chemical interactions remain fixed. Recent experiments in the vicinity of, but not at, the critical point have shown that in SCW heterolytic reactions are favored at higher pressures and lower tem peratures, while homolytic free radical processes are tavored at lower pressures and higher temperatures (3-6). It has been proposed that the increased predominance of neterolytic reaction products with increasing pressure is correlated with the in crease in the S C W ion product Ky with pressure ($). It is reasonable to attribute these observations to an increase in the microscopic kinetic rate constants for het erolytic reactions (and a corresponding decrease in those for homolytic reactions) with the increasingly ionic character of the solvent. In fact, it has been proposed that changes in electrostatic interactions due to known variations in SCW's static 0097-6156/94/0568-0196$08.00/0 © 1994 American Chemical Society

In Structure and Reactivity in Aqueous Solution; Cramer, Christopher J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1994.

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on February 2, 2016 | http://pubs.acs.org Publication Date: September 29, 1994 | doi: 10.1021/bk-1994-0568.ch014

14. TUCKER & GIBBONS

Anisole Hydrolysis in Supercritical Water

197

dielectric constant with pressure may be an important cause of these observed rate variations (7,8). Here we provide a test of these ideas. The rate of the (heterolytic) hydrolysis of anisole in S C W has been studied experimentally and found to increase with pressure, as suggested above (4,9). In the present study, we examine the effect of changing electrostatic interactions on the rate of this reaction in order to determine whether these effects can explain the experimentally determined pressure dependence of the rate. In particular, we examine the electrostatic contribution to the free energy of solvation along the reaction coordinate for this reaction, as the free energy of solvation determines the free energy of activation profile for the solvated reaction system. From the free energy ofactivation, we determine the equilibrium solvent effects on the rate of this reaction. Because the hydrolysis of anisole involves two neutrals evolving into two ions in a polar medium, it is reasonable to expect that electrostatic interactions will dominate the solvent effects. Additionally, in this initial study we neglect nonequilibrium solvent effects due to the frequency dependence of the orientational polarization, as these effects are expected to produce a linear, rather than an exponential, variation in the rate (10). Here we model SCW as a continuum fluid characterized solely by its dielectric constant; yet, it is well know that reactivity in S C W differs from reactivity in or ganic solvents of similar polarity under standard conditions. While it may appear that this simple model must therefore miss the essential physics of reactivity in SCW, this is not true. First, perhaps the most important, but least exotic, reason for the appearance of novel reaction mechanisms in S C W is accounted for within this simple model—the elevated temperature. A n energetic barrier to reaction which is prohibitively high at room temperature, say ~ 100 k T , will become ef fectively half as high, ~ 46 kT, at the critical temperature of water, allowing the reaction to occur, second, S C W differs from typical low polarity organic solvents in that it is a hydroxy lie solvent. Since the simple dielectric model does not ac count for hydrogen bonding effects, it is not an appropriate model for comparing reactivity in S C W (or any other hydroxy lie solvent) with reactivity in aprotic solvents. In contrast, this simple model does provide a useful tool for comparing reactivity in SCW at different pressures/polarities, since SCW is hydroxylic at all pressures, and hence the neglected molecular effects should approximately cancel. Third, unusual reactivities are observed in S C W in part because reactant solubil ities in S C W are different than they are in more conventional solvents. For the hydrolysis reaction considered here, S C W provides one of the reactants at high concentration—something not possible in many organic solvents. In addition to the factors just given, S C W solutions exhibit two unique be haviors which may be important in determining the pressure dependence of the reaction rate. First, there is growing evidence that solvent-solute clustering oc curs in S C W and other supercritical fluid solvents, due to the large isothermal compressibility of these solvents (8,11,12). Solvent-solute clustering means that the solvent density in the vicinity of the solute will be, on average, higher than the bulk density, and as a result the solute will be surrounded by a region having a higher dielectric constant than that of the bulk solvent. As a result, the variation in the electrostatic solvent effects with pressure may track a local static dielectric constant which is larger than the bulk dielectric constant (8,18,14)- In addition, the degree of this clustering may vary along the reaction path, especially in the charge separation reaction considered here. Such a variation would cause the lo cal dielectric constant, and hence the solvent-solute electrostatic interactions, to also vary along the reaction path. Free energy differences along the reaction path would thus be further altered from those for the reacting solute in an incompress ible dielectric. Entropie effects, which make a contribution to the electrostatic free energy of solvation in the work required to reorient the solvent dipole den sity (15), would also be altered by variation in clustering along the reaction path. Specifically, there would be an additional loss of entropy along the reaction path if


198

STRUCTURE AND REACTIVITY IN AQUEOUS SOLUTION

the solvent clustering increases along the reaction path. This entropie effect is not incorporated into standard electrostatic free energy calculations which assume an incompressible continuum fluid. The second important behavior which has been proposed to occur to an unusually large degree in SC fluids is solute-solute clus tering (16). Hence it is possible that as the ion product K of S C W increases, protons from dissociated water molecules may be found near the reacting solute more frequently than random statistics would predict, thus allowing for an acid catalyzed mechanism. Although such a mechanism has been proposed to explain the pressure dependence of the hydrolysis of 2-methoxynapthalene (1?), we do not consider this catalyzed mechanism in the present work. Also, recent mixed quantum mechanical/molecular mechanical simulations of the benzene dimer in S C W show no evidence of enhanced solute-solute clustering (IS). We first discuss the experimental data for anisole hydrolysis in S C W . Next we describe the reaction path energetics calculated for the gas phase reaction. We then consider the solution phase energetics, calculated via incompressible, continuum solvation models. We compare the free energies of solvation from various continuum models in order to gauge the reliability of our results and to explore the importance of solute polarization. The results from our most reliable model are then used to determine the free energy of activation curve for the title reaction as a function of the solvent dielectric constant. We then estimate the dependence of the solute rate constant on solvent dielectric constant and, by comparison with experiment, ascertain whether solvent clustering is an important factor in determining the rate.


w

Experimental Data Klein and coworkers have studied the rates of hydrolysis of substituted anisoles in S C W (4)- The experiments were performed at 380°C, which corresponds to a reduced temperature of T = T/T = 1.01, where T = 374.0°C is the critic tem perature of water. The reactions were studied in constant volume batch reactors at four reduced densities, ranging from p = p/p = 0.8 to p = 2.0, where the critical density of water is p = 0.32 g/cm . These densities correspond to a range of pressures from 23.2 M P a to 49 M P a (19,20). The products were analyzed by G C / M S . Klein and coworkers have also determined the mechanism for the hydrol ysis of various phenyl ethers, and found that it involves SN2 attack by a water molecule (9). Assuming this same mechanism for anisole, one has r

c

c

r 3

c

r

c

P h O C H + H 0 -» P h O " + C H O H + . 3

2

(1)

3

In fact, the experimentally measured products are PhOH and MeOH, but we assume that the proton transfers occur as rapid subsequent steps. The intrinsic bimolecular rate constant k (L/mol s) was found to increase with pressure, i.e. * χρ = 3.3 χ 10 at Ρ = 23.2 M P a , 6.7 χ 10 at 24.0 M P a , 11 χ 10 at 27.3 M P a and 18 χ 10 at 49 M P a (4). exp

s

s

s

β

s

Gas Phase Energetics The anisole hydrolysis reaction is a charge separation SN2 reaction, and in the gas phase it is expected to be highly endothermic. We performed H F / S C F ab ini tio calculations on this reaction with both the 3-21G* and the 6-31G** basis sets using Gaussian 92 (21). The computed overall endoergicity at the HF/6-31G** level is 178.95 kcal/mol. The conversion to endothermicity can be approximated from the reactant and product zero point energies. Thus, we calculated frequen cies at the HF/3-21G* level and, by comparison with experimental frequencies




199

Table I. H F / 6 - 3 1 G " energies along the reaction path Point r (A) Ε (kcal/mol) Reac —00 0.00 DD -1.83804 -1.76 xl 57.92 -0.06955 x2 73.77 0.23609 x3 84.08 0.58367 x4 90.55 0.98367 Prod oo 178.95


c

for anisole (22,23), found that the calculated frequencies should be reduced by 11.29%. The calculated 6-31G** endothermicity, based on the scaled 3-21G* fre quencies, is 172.60 kcal/mol, in excellent agreement with the experimental value of 172 kcal/mol. The experimental value was computed from heats of formation taken from References 24 ( H 0 ) , 25 (PhOCH ), and 26 (PhO", C H O H t ) . Recent studies on other charge separation SN2 reactions indicate that they may be expected to show the classic double-well reaction profile found in charge transfer SN2 reactions (27,28). However, we did not find a double well profile for this reaction with either basis set at the Hartree-Fock level. Instead, we found only three stationary points along the reaction path: the reactants (Reac), the products (Prod) and the water-anisole dipole-dipole complex (DD). No saddle point and no ion-ion complex were found along the SN2 backside attack reaction path ( P h O . . . C H . . .OH ). While it is likely that an ion-ion complex exists at another geometry (e.g. PhO.. . H 0 . . . C H ) , the calculations indicate that there is a barrier separating the reaction path from any such complex, so we did not search further for this complex. The lack of a saddle point makes it infeasible to follow the minimum energy path at the Hartree-Fock level. Instead, we follow an assumed reaction coordinate, r , which is defined as the methyl carbon to phenyl oxygen distance, r l , minus the methyl carbon to water oxygen distance, r2. A shoulder was found along this reaction path with the 3-21G* basis. We chose four points in the vicinity of this shoulder to characterize the reaction path and evaluated the energies of these points optimized with respect to everything but r at the 6-31G** level. The HF/6-31G** relative energies along this reaction path are given in Table I and illustrated in Figure 1. 2

3

3

3

2

2

3

c

c

Energetics in Supercritical Water The bulk static dielectric constant of SCW at 380° C ranges from ~ 2 at 20 M P a to ~ 14 at 50 M P a (19,20). Hence, to determine the electrostatic effects of SCW on the energetics of this reaction, we model S C W as a continuous dielectric with a pressure dependent dielectric constant. We considered a range of dielectrics from 2 to 80, rather than only from 2 to 14, because clustering may raise the local dielectric felt by the solute above the bulk value of the dielectric constant. To determine the free energy of activation curves for this reaction in S C W as a function of pressure, we calculate the free energy of solvation at 7 points along the reaction path for each of a series of dielectric constants.



200


Figure 1. Calculated gas phase energies along the reaction path. The solid line is a spline fit to the data.





201

C o m p a r i s o n of M e t h o d s . A variety of methods have been proposed for cal culating solvation energies within the continuum solvent approximation, as dis cussed m a recent review (29). Methods which include semiempirical parameters to account for cavitation and other nonelectrostatic effects, such as the AM1-SM2 model of Cramer and Truhlar (30) or the recent models of Hehre and coworkers (31), are not appropriate for studies of SCW because the semiempirical corrections are fit to data at room temperature and pressure. Thus, we restrict ourselves to models which incorporate only electrostatic effects. Note that all of these con tinuum solvation methods assume an incompressible fluid, and hence ignore the effects of électrostriction. This is liable to be a poor approximation in S C W since S C W has a large isothermal compressibility. In the present study we assume that this compressibility need not be taken into account explicitly with a position de pendent dielectric, but that it may be accounted for by an effective local dielectric constant which differs from the bulk value. This idea has been used previously to explain spectroscopic data (8,13,14)- We will address the incorporation of électrostriction into the continuum moael in future work. In the present study we consider two models of solute-incompressible solvent electrostatic free energies. First we consider a numerical grid based algorithm for solving Poisson's equation for an arbitrary, fixed charge distribution (82,33). We use the implementation available in the program Delphi, distributed as part of Biosym (34)- Solvation energies evaluated by this method are generally in good agreement with experiment for ions (30,83,35). For neutrals, where the electrostatic interactions often do not dominate the solvation energy, the Delphi energies show a significantly weaker correlation with experiment, although they are frequently within a few kcal/mol of the experimental results (29). Also, Delphi results are somewhat dependent upon the choice of input parameters, including the atomic radii, point charge distribution and solute dielectric constant (29,35,36). In the present calculations, the gas phase HF/6-31G** geometry and Mulliken charges are used to define the solute charge distribution. A study by Alkorta, et ai. compares Delphi solvation energies using atomic charges determined from A M I wave functions by two different methods: the Mulliken population analysis and a fit to the A M I electrostatic potential (ESP) (36). The Mulliken charges fairly consistently yield a slightly smaller solvation energy than do the fitted charges. The maximum difference was 6 kcal/mol, with the average difference being signif icantly less, at 1.3 kcal/mol. Indeed, as the difference in solvation energy is fairly consistently in the same direction, the differences in relative solvation energies between the two methods is expected to be less than the difference in the abso lute solvation energies. Thus, while the fitted charges provide a more accurate representation of the gas phase wave function, the extra effort of obtaining fitted charges was not considered warranted. In particular, the Delphi method neglects solute polarization in the presence of the solvent, which would alter the solute charge distribution from its gas phase value. Hence, within this method, a more accurate gas phase charge distribution will not necessarily yield a better estimate of the solvation energy. Another parameter which is required for Delphi calculations is the dielectric constant of the solute molecule, e . We consider two values of e : e = 1, corresponding to a vacuum (Delphi 1) and c = 2, corresponding to the usual value of the optical dielectric constant due to electronic polarizability (Delphi2). We discuss the relative merits of these two choices below. For the atomic radii, we simply use the default Van der Waals radii (C= 1.55 Â, 0 = 1.35 Â and H = 1.10 Â) (34)- Finally, we checked the Delphi results for convergence with respect to the size and spacing of the numerical grid. We found that a border space of only 8 Â was required to converge the results to 0.1 kcal/mol. Convergence with respect to grid spacing was more erratic. Even by a grid spacing of 0.115, smooth convergence was not observed. The production calculations were all performed m

m

m


m


202


with a grid spacing of 0.2 Â, as suggested recently (55), as this value provides a reasonaole compromise between convergence and memory requirements. Based on these convergence studies, we attribute an error of ± 1 kcal/mol to the finite grid spacing. Note that coulombic boundary conditions were used with no focusing. Solvation energies were computed from the total electrostatic energy, rather than from the reaction field energy (57). The second method we consider is the self consistent Born-Onsager Reaction Field approximation (BO) implemented in Gaussian 92 (21,38). This method models the molecule as a multipole expansion in a spherical cavity, but includes only the monopole and dipole terms. Since an ideal dipole in a spherical cavity will not go smoothly to the limit of two monopoles, this method is expected to fail at some point along the reaction path as the complex separates into two charged species. The advantage of this method is that it self-consistently solves the electronic structure problem in the presence of the solvent reaction field, allowing for polarization of the solute wave function. Such a self-consistent treatment is tractable by virtue of the computational simplicity of evaluating the reaction field in the B O approximation. Knowledge of the solvent polarization effects for this reaction will be important for the development of model potentials for use in explicit simulation studies of solvent clustering effects. Specifically, the importance of solute polarization will determine whether it is reasonable to use a molecular mechanics potential to study this system, as such potentials do not generally allow for solute polarization. The B O method has been shown to give good relative solvation energies for a few isomerization reactions (29). We implement the B O method at the H F / 6 31G** level. Like the numerical grid methods, the B O method is sensitive to cavity size. The cavity radii used here are determined from an isodensity surface of the gas phase wave function as implemented in Gaussian 92 (21,39,40). It is appropriate to mention a third method which combines the advantages of the two methods considered here, although at additional computational ex pense. Specifically, the Polarized Continuum Model (PCM) developed by Tomasi and coworkers self-consistently solves the electronic structure in the presence of a reaction field (apparent surface charge) determined by numerical solution of Laplace's equation (41)- A similar method has also recently been developed by Tannor, et ai (42). While still suffering from the same parameter sensitivity as Delphi, these met nods will allow for a more accurate study of the solute polar ization effects than the B O method (see below). The P C M method has recently been used to study a similar reaction, the Menshutkin reaction of ammonia with methyl bromide (28). In that study, solute polarization effects were found to be significant. These results, along with those of the present study, suggest that a detailed description of the solute polarization will be required to accurately model the dynamics of the anisole hydrolysis reaction. C o m p a r i s o n of Reactant and P r o d u c t Solvation Energies. In order to provide an estimate of the reliability of the methods used here, we compare the calculated solvation energies of the reactants and products with solvent dielectric e = 80 to experimental values of the solvation energies in water at room tempera ture and pressure (29,43,44)- The results are tabulated in Table II. In addition to the methods we use here, B O , Delphi 1 and Delphi2, we list values calculated by other authors using related methods (29,36). Two of these are also Delphi calcu lations, but they are implemented with A M I optimized geometries and charges; A M 1 E D uses the ESP fitted charges while A M 1 M D uses the Mulliken charges (36). Both of these implementations use a solute dielectric constant of c = 1. The last method listed is the AM1-SM2 semiempirical model (80). Looking first at the B O method, one sees that the magnitudes of all of the solvation energies are severely underestimated, especially for the ions. While the difference in solvation energies between the two ions and between the two neutrals 8

m


14. TUCKER & GIBBONS Table IL Solute Water Anisole PhO" CH OH+


3


Solvation energies in kcal/mol for Reactants and Products (e = 80) Expt. BO Delphil Delphi2 AM1ED AM1MD AMI - SM2 -63 -2.1 -8.7 -3.0 -2.1 -6.3 -6.6 -2.4 -0.2 -15.7 -2.3 -11.2 ... -72.0 -44.9 -79.5 -60.7 -58.8 -65.6 -74.9 -83. -55.9 -82.8 -84.2 -81.0 -70.8 -70.0 g

is reasonable, to count on such a large cancellation of error is very risky. Also, the ion to neutral difference is quite poor. Clearly, the cavity shape (e.g. for PhO") and higher order electric moments are indeed important, as would be expected. Thus, the B O method only reproduces the qualitative trends. Overall, the 4 implementations of Delphi perform much better, as compared to experiment, than does the B O method. Anisole provides an exception; its solvation energy is significantly overestimated by Delphi. Delphi is known to overestimate the solvation of related compounds, such as benzene, toluene and analine (29). Comparing A M 1 E D and A M 1 M D with Delphil (since these meth ods all use e = 1), it is clear that the difference which results from basing the calculation upon A M I rather than HF/6-31G** wave functions ( A M 1 M D vs. Del phil) is much greater than the difference which results from using E S P rather than Mulliken charges from the same wave function (AM1ED vs. A M 1 M D ) . In fact, choice of wave function alters the solvation energy by as much as 21 kcal/mol, whereas the maximum change due to choice of charge model is 1.9 kcal/mol. This supports the present choice of using the Mulliken charges. Also, the HF/6-31G** wave functions provide better agreement with experiment than do the A M I wave functions. The Delphi2 results, which use e = 2, are in the best agreement with experi ment, in accord with previous results (35). The usual justification for this choice of solute dielectric constant is that because a frozen charge model has been used for the solute, an optical dielectric constant should be included to account for the neglected solute polarizability (45,46). There is a fault in this logic when it is applied to small molecule calculations (but not necessarily when it is applied to proteins), as follows. A dielectric constant is a macroscopic quantity which accounts for the polarizability of electrons, dipoles, etc. which are not included explicitly in the model. Charges which are included explicitly (microscopic treat ment) cannot simultaneously be represented by a dielectric constant (macroscopic treatment). In small molecules, then, when all of the charges are included ex plicitly, albeit represented by a fixed distribution of point charges, there is no neglected charge distribution for the solute dielectric of c = 2 to be accounting for, and a value of e = 1 is appropriate. Additionally, using a solute dielectric of c = 2 will decrease the magnitude of the solvation energy relative to that for c = 1 (as illustrated in Table II and Reference 35). In contrast, the allowance of explicit solute charge polarization will always increase the magnitude of the solvation energy relative to the fixed charge distribution value, otherwise the solute charges would not readjust. It follows that setting the solute dielectric to 2 cannot account for the neglect of solute polarizability incurred by using a fixed set of point charges. Hence, we consider the use of e = 2 in small molecule calculations to be an empirical correction for other errors in the model, such as the choice of wave function, etc. In fact, while using e = 2 in the Delphi HF/6-31G** calculations improves the comparison with m

m

m

m

m

m

m

m


203


204


Table III. Solvation Energy Relative to Reactants in kcal/mol (e, = 40) Point Delphil Delphi2 BO Reac 0.0 0.0 0.0 DD 2.4 0.8 1.7 xl -7.7 -6.8 -6.1 x2 -13.0 -15.8 -13.8 x3 -26.6 -23.0 -23.6 x4 -37.8 -33.0 -34.5 Prod -136.2 -136.4 -97.3

experiment, using this choice of tm in the A M 1 E D or A M 1 M D calculations would further reduce the agreement of these calculations with experiment. Thus, despite the agreement of Delphi2 with experiment under ambient conditions, Delphi2 is not considered to be the most reliable method for the present studies. The AM1-SM2 semiempirical model, included for comparison, gives noticeably better agreement with experiment than any of the Delphi implementations. This model even provides a good value for the solvation energy of anisole. As suggested above, this model was not considered because of its semiempirical character. The parameters accounting for cavitation, dispersion and solvent rearrangement are nt to room temperature and pressure data. It is not known how these effects are altered in the supercritical regime; hence the inclusion of these terms in a semiempirical way would simply complicate the analysis of our results. C o m p a r i s o n of R e a c t i o n P a t h Solvation Energies. The focus of the present study is to determine relative changes in the solvation energy along the reaction path. This is a less demanding test than is computation of the absolute solvation energies, so we also compare the relative solvation energies along the reaction path for the three methods, Delphil, Delphi2 and B O . The results for c = 40 are presented in Table HI and their negatives are pictured in Figure 2. The relative solvation energies are in better agreement than were the absolute solvation energies. Most striking is the agreement of the B O method with the Delphi methods at all points except the products. In fact, the relative energies suggest that the ideal dipole approximation does not break down as rapidly as expected with increasing dipole separation. However, a more detailed look at the B O results (see below) indicates that the observed agreement is somewhat fortuitous. The differences in the relative energies of the two Delphi implementations, though small, vary along the reaction path; so we studied this difference in more detail. The difference in the relative solvation energies as computed by Delphil and Delphi2 at points along the reaction path is shown in Figure 3 for six different values of the solvent dielectric constant. The magnitude of the relative solvation energy increases more rapidly with increasing charge separation along the reaction path for the calculations with the solute dielectric c = 1 than for those with c = 2. Additionally, the difference in the results for these two choices of e is greater the greater the solute dielectric constant. Hence this choice will affect the trends calculated for the equilibrium solvent effects for this reaction. Because the use of 6 = 1 makes intuitively more sense for this calculation, as discussed above, the Delphil calculations should more accurately reflect the relative solvation energies under different conditions than do the Deiphi2 calculations. We therefore take #

m

m

m

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125 H

I 100α ω α ο 75 H •a ο m

I

25 H

PS

ΓΤΤ Reac

DD

xl

x2

x3

x4

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Reaction Path Position Figure 2. Negative of the relative free energy of solvation along the reaction path for a solvent dielectric constant of 40.

5-A 4-A 3-A

•3 3

2H

OS

ιΗ

É Reac

DD

i #i1 r ·** • •i f I1 1 Î* k[ v ) 1

!

xl x2 x3 Reaction Path Position

L-j J U-J-J x4

Prod

Figure 3. Difference in the calculated values of the relative solvation energy for the Delphi2 and Delphil methods. For each reaction path position, the bars from left to right correspond to c, values of 2, 4, 8, 15, 40 and 80, respectively.


206


the Delphil calculations as the most reliable, despite the better comparison of the Delphi2 absolute solvation energies with experiment. Solute P o l a r i z a t i o n . Since the B O method allows for self-consistent solution of the electronic structure problem in the presence of the solvent, we used the B O method to study the importance of solute polarization for this reaction. The B O method predicts quite large induced dipoles for points intermediate along the reaction path. In the most extreme example, point x4 at e = 80, the B O method predicts an induced dipole of 7.5 D , on top of the computed gas phase value of 17.7 D. This dipole moment change is due almost entirely to charge redistribution; the change in the distance r l + r2—which is directly related to the oxygen-oxygen distance—from its gas phase value to its value upon solvation at e, = 80 is less than 0.03 Â. The energy cost of the solute distortion at this point, x4 with e = 80, is 14.0 kcal/mol. To evaluate the additional polarization energy gained by this change in dipole moment, we evaluated a frozen-BO polarization energy at this point, i. e. we evaluated the B O solvation energy for the unpolarized gas phase wave function and geometry. The frozen-BO polarization energy is —25.4 kcal/mol as compared to the relaxed-BO polarization energy of —51.7 kcal/mol. Hence, a gain in polarization energy of 26.3 kcal/mol offsets the solute distortion cost of 14.0 kcal/mol to yield a net gain in solvation energy upon solute polarization of 12.3 kcal/mol. The large gain in polarization energy upon solvation of the polarized solute predicted by the B O approximation is in contrast to what is found with Delphi calculations of the same charge distributions. Specifically, Delphil calculations using the gas phase geometry and charges for this point yield a polarization energy of —62.8 kcal/mol. When the relaxed-BO geometry and charges are used instead, the Delphil calculations predict a polarization energy of —69.8 kcal/mol, only 7 kcal/mol more favorable than for the unrelaxed molecule. The gain in polarization energy predicted by Delphi is not even sufficient to offset the solute distortion cost, indicating that if the more accurate Delphi solvation model were used in the selfconsistent calculations the BO-predicted charge redistribution would not occur. This observation can be explained by the fact that the B O approximation nelects moments higher than the dipole moment. At the point x4, the gas phase lulliken charge distribution grouped by moiety is —0.03 on the phenyl ring, —0.89 on the phenyl oxygen, +0.61 on the methyl group, and +0.30 on the water. This charge distribution can be loosely thought of as being comprised of an overall dipole plus one dipole on each of the PhO and M e O H fragments which give rise to the quadrupole and higher order terms. Since the B O approximation neglects the quadrupole moment, it will gain an increase in solvation energy if the dipole moment is increased at the expense of the quadrupole moment. Indeed, this is what happens. The relaxed-BO charge distribution increases the charge sepa ration between the PhO and M e O H groups by only 0.05. The large induced dipole arises primarily from a shift of negative charge away from the phenyl oxy gen and onto the most extended hydrogen of the phenyl ring, thus increasing the aipole moment but decreasing the quadrupole moment. Specifically, the relaxedB O charge distribution is -0.17 on the phenyl ring, —0.80 on the phenyl oxygen, +0.63 on the methyl group and +0.34 on the water. We conclude that the B O model compensates for the neglect of higher moments by inducing an artificially large dipole. By virtue of this compensation, the B O approximation attains a reasonable estimate of the relative solvation energy of this compound; yet, the physics of the induced polarization is incorrect. Thus, we do not consider the B O results sufficiently meaningful to tabulate them here. We note that, despite this nonphysical behavior, the magnitude of the B O induced dipole exhibits solute polarization trends similar to those observed by Sola, et ai (28) for a Menshutkin


s

9

f

2

2



207


reaction using the method of Tomasi and coworkers (^1). These results indicate that, while the B O model treats the solute polarization incorrectly, solute polar ization effects may still be important for the anisole hydrolysis reaction. Free E n e r g y of A c t i v a t i o n Profile. The free energy of activation profile for the anisole hydrolysis reaction in S C W is determined oy the solvation energies along the reaction path. The magnitude of these solvation energies, calculated by the most reliable method considered, Delphil, are shown for 6 values of the solute dielectric constant (e = 2,4,8,15,40,80) in Figure 4. Note first that the solvation energies are asymmetric, t. e. they increase in magnitude as the reaction proceeds. This behavior is expected for a charge separation reaction, because as the reaction proceeds the solute becomes more ionic and is thus more highly stabilized by a polar solvent. Such asymmetric solvation has been discussed recently for Mensnutkin reactions (27,28). Second, the solvation energies at a dielectric of e, = 2, the bulk dielectric of S C W at 380°C and ~ 20 M P a , are already at 40 to 50% of their "maximum" values at e = 80. At e = 15, the bulk dielectric constant of SCW at 380°C and ~ 57 MPa, the solvation energies are at ~ 90% of their e = 80 values. Combining the calculated free energies of solvation with the gas phase reaction profile yields the free energy of activation curve in solution. These curves are pre sented schematically as a function of dielectric constant in Figure 5. The reaction path value (r ) of each point shown is given in Table I. The zero of energy is in all cases taken to be the energy of the reactants at a dielectric constant of e = 80, so that all energies will be positive. From Figure 5 it is clear that the asymmetrical nature of the solvation energies causes the qualitative shape of the reaction path to be altered as a function of dielectric constant. The products remain the most energetically unfavorable configuration for all c < 4. A saddle point is observed to grow in at e > 4 and to move to earlier locations as the dielectric constant is increased, in agreement with the Hammond postulate and previous results on Menshutkin reactions (27,28). Note that in contrast to the Menshutkin reaction results, an ion-ion complex is only observed at e, « 4. For lower dielectric solvents the ion-ion configuration is less stable than earlier points on the reaction path, while for higher aielectric solvents the ion-ion configuration is less stable than the products. Also, the dipole-dipole complex disappears somewhere between e = 4 and e = 8. The potential barrier for this reaction changes from the gas phase endoergicity of 179 kcal/mol in vacuum, through the endoergicity value of 74 kcal/mol at t = 4, to t i e saddle point value of ~ 61 at e = 8 and of ~ 58 at e = 80. Thus, the continuum solvation model predicts that the energetics of this reaction change dramatically over the range of dielectrics explored by S C W under the conditions of Klein's experiments.


9

9

9

9

c

9

9

9

9

9

9

9

9

Discussion and Conclusions The theoretical treatment presented here is restricted to a one dimensional reac tion coordinate picture, and hence is not expected to generate good estimates of the absolute reaction rates. Instead, we concentrate on the variation in the rates with pressure. In fact, it is more informative to compare the pressure dependence of the theoretical and experimental activation energies than it is to compare the pressure dependence of the resulting reaction rates. Thus, we extract differences in the free energy of activation as a function of pressure, from the ex perimental rate constants (4,4^)· To do so, we assume a standard transition state theory expression for the rate constant, i.e. k«

-"»l«r

e


(2)

208


80 +


60

1

40 +

*o 20·

anisole

H 0 2

DD

xl

x2

x3

x4

PhO" M e O H

+ 2

Reaction Path Position Figure 4. The magnitude of the absolute solvation energy. For each reaction path position, the bars from left to right correspond to c, values of 2, 4, 8, 15, 40 and 80, respectively.

200 H

150-1

100

Figure 5. The calculated free energy of activation curves. For each value of € , the bars from left to right correspond to the reaction path positions Reac, D D , x l , x2, x3, x4 and Prod, respectively. e




209

Table IV. Calculated vs. experimental free energy of activation differences A(AG^) 3

p(g/cm )


Pr

a

in kcal/mol (20)

P(MPa)

e°

AG* calc 74.2

0.8

0.25

23

1.6

0.50

27

10 (8)

60.9

2.0

0.63

49

14 (15)

59.0

4

calc

Δ(Δ

Structure and Reactivity in Aqueous Solution - American Chemical

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