Claisen Rearrangement of Allyl Vinyl Ether - ACS Symposium Series

Chapter 17

Claisen Rearrangement of Allyl Vinyl Ether Computer Simulations of Effects of Hydration and Multiple-Reactant Conformers 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.ch017

Daniel L. Severance and William L . Jorgensen

1

Department of Chemistry, Yale University, New Haven, CT 06511-8118

A free energy of hydration profile for the Claisen rearrangement of allyl vinyl ether (AVE) has been obtained from Monte Carlo statistical mechanics simulations at 25 °C. The gas-phase minimum energy reaction path through the chair transition state was determined from ab initio 6-31G(d) calculations and was followed in a periodic cell containing 838 water molecules. The transition state is computed to be 3.85 ± 0.16 kcal/mol better hydrated than the reactant, which corresponds to a rate increase by a factor of 664 over the gas-phase reaction. This large effect is shown to be consistent with available experimental data. The origin of the effect is analyzed. The energetic impact of multiple conformational states for the reactant has also been considered.

For chemical reactions, changes in polarity between the reactants and transition state lead to rate variations in different solvents (7). The effects can be profound with rate ratios of 10^ or more for comparisons of alternate solvents and up to 10^0 when the gas phase is included (2). However, some classes of reactions are relatively immune to solvent effects since they have "isopolar transition states" (7). With the exception of dipolar cycloadditions, many pericyclic reactions have been considered to be in this category (7). However, the generality of this notion was strikingly challenged by observations that simple Diels-Alder reactions could show rate accelerations by factors of 10^ - 10^ in aqueous solution over hydrocarbon solvents (3,4). Scrutiny of the literature reveals comparable solvent dependence for the rates of Claisen rearrangements as well (5). The data of White and Wolfrath from 1970 are particularly notable (5a). They found a rate increase by over a factor of 300 for the rearrangement of allyl g-tolyl ether in going from the gas phase to progressively more polar solvents; the greatest rate was in p.-chlorophenol, though they did not obtain data in pure water. Efforts in our laboratory have been directed at understanding the origin of such solvent effects at the molecular level through computational modeling. This is not only technically challenging, but also affords the opportunity to better characterize the electronic structure of transition states and to reveal details about their solvation,which 1

Corresponding author

0097-6156/94/0568-0243$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.

244

S T R U C T U R E A N D REACTIVITY IN A Q U E O U S S O L U T I O N

can provide insights for catalyst design. The present work focuses on the parent Claisen rearrangement of allyl vinyl ether (AVE) in the gas phase and aqueous solution. In addition to the effect of hydration on the free energy of activation, which was the subject of a prior communication (6), consideration is also given here to the existence of multiple conformational states for the reactant. The population of this manifold of states is not normally considered in computational studies on reaction energetics.

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.ch017

Computational Procedure The computational approach is an updated version of our efforts on Sjq2, addition, and association reactions (7). Ab initio molecular orbital calculations are used to locate the transition state(s) for the reaction and to obtain a minimum energy reaction path (MERP) in the gas phase. The ab initio calculations are also used to provide partial charges for the reactants along the reaction path, which are needed for the potential functions that describe the intermolecular interactions between the reacting system and solvent molecules. The reacting system is then placed in a periodic cell with hundreds of solvent molecules and the changes in free energies of solvation along the reaction path are computed in Monte Carlo simulations with statistical perturbation theory. These calculations provide the key thermodynamic results and great detail on the variations in solvent-solute interactions along the reaction path. Ab Initio Calculations. The present ab initio calculations were performed with the G A U S S I A N 92 program using the 6-31G(d) basis set, which includes a set of dorbitals on carbon and oxygen (8). Such RHF/6-31G(d) calculations were previously carried out by Vance et al. to locate structures for the reactant, chair transition state, and product (9). Reaction path following (70) was then performed (8) to generate a 143 frame "movie" along the minimum energy reaction path from one conformer of A V E through the transition state to 4-pentenal. 6- 31G(d)//6-31G(d) optimizations were also executed to locate eight additional low-energy minima for A V E . A l l stationary points were confirmed via calculations of the vibrational frequencies. This further permitted computation of the relative free energies of the stationary points in the gas phase using standard statistical mechanical procedures (77). For the latter purpose, the computed vibrational frequencies were scaled by 0.91 to be more consistent with experimental values, and scaled frequencies below 500 cnW were treated as classical rotations with E = RT/2 (72). The nine conformers for A V E are shown in Figure 1 along with their relative 6-31G(d)//6-31G(d) energies and dipole moments. v

Fluid Simulations. Monte Carlo calculations were performed along the gasphase M E R P using statistical perturbation theory to compute the changes in free energies of hydration. The intermolecular interactions are described by potential functions with the potential energy, A E ^ , consisting of Coulomb and Lennard-Jones terms between the atoms i in molecule a and the atoms j in molecule b, which are separated by a distance ry (equation 1) (13). All atoms are explicit and a

the TIP4P model was used for water (13a). In all, 59 frames (structures) along the M E R P were utilized. Partial charges (q) were obtained for each of these from the 631G(d) ab initio calculations using the C H E L P G procedure for fitting to the


17.

SEVERANCE & JORGENSEN

Claisen Rearrangement of Allyl Vinyl Ether 245


electrostatic potential surface (14). Mulliken charges were also considered; however, they showed more variation in going to the 6-31+G(d,p) basis set, computed dipole moments with the Mulliken charges deviated significantly (0.5 - 1.4 D) from the 631G(d) and C H E L P G values, and the general superiority of 6-31G(d) C H E L P G charges for computing free energies of hydration was previously demonstrated (15). The C H E L P G charges are given in Table I for the reactant, transition state, and product along the M E R P with the atom numbering illustrated below. The conformation of A V E on the M E R P corresponds to structure 4 in Figure 1. Standard

all-atom Lennard-Jones parameters (σ, ε) (13) were adopted with geometric combining rules for the reactant and product and scaled as hybridization changed along the MERP. The variations in σ and ε are modest, as summarized in Table I. The simulations were executed in the NPT ensemble at 25 °C and 1 atm with Metropolis and preferential sampling (16). The system consisted of 838 water molecules and the solute in a periodic cell ca. 30 À on a side. The BOSS program (17) perturbed the system between frames and computed the change in AG^yd * statistical perturbation theory (16,18). Utilization of the 59 frames required 29 separate Monte Carlo simulations with double-wide sampling (19). The perturbations are performed from one frame to the two adjacent frames on either side; the three images of the reacting system are overlaid maximally in an rms sense for the atomic positions, and a common dummy center point is used as the origin for the rigid-body rotations so that the three images do not separate upon rotation. Each simulation entailed 1 χ 10^ (1M) configurations of equilibration followed by 4 M configurations of averaging. Solute-water interactions were included for waters with an oxygen within 10.5 À of any solute atom, and the water-water cutoff was at 10.5 À based on the O-O distance. The interactions were feathered to zero quadratically between 10.0 and 10.5 Â. The individual molecules were kept rigid in the simulations; only translations and rigid-body rotations were sampled. v

a

S C R F Calculations for A V E . Estimates of the relative free energies of hydration for the 9 conformers of A V E in Figure 1 were obtained from four selfconsistent reaction field (SCRF) procedures. These are needed to obtain the energetic effects of including all 9 conformers as opposed to just 4 on the free energy of activation for the reaction in water. Only the chair conformer of the transition state required consideration since the alternative boat form is 4-7 kcal/mol higher in energy (9). In each case the 6-31G(d) optimized geometries were used without reoptimization in the reaction field; for a given SCRF method, reoptimization for neutral molecules normally has negligible energetic effects (20), and for the present



246

STRUCTURE AND REACTIVITY IN AQUEOUS SOLUTION

Table I. Potential Function Parameters for the Claisen Rearrangement of A V E Reactant (4) Atom

q

σ

Product

Transition State ε

q

σ

ε

q

σ

ε

CI

-0.574

3.550

0 070 -0.416

3 545

0.070 -0.071

3.500

0.066

C2

0.216

3.550

0 070

0.296

3 549

0.070

0.542

3.550

0.070

03

-0.413

3.000

0 170 -0.485

2 995

0.175 -0.533

2.960

0.210

C4

0.407

3.5(H)

0 066

0.161

3 506

0.067 -0.429

3.550

0.070

C5

-0.122

3.550

0 070 -0.479

3 546

0.070 -0.101

3.550

0.070

C6

-0.425

3.550

0 070

0.014

3 .545

0.070

0.145

3.500

0.066

H7

0.179

2.420

0 030

0.105

2 .428

0.030

0.014

2.500

0.030

H8

0.218

2.420

0 030

0.183

2 .428

0.030

0.037

2.500

0.030

H9

0.088

2.420

0 030

0.045

2 .422

0.030 -0.032

2.420

0.030

H10

-0.019

2.500

0 030

0.090

2 .490

0.030

0.172

2.420

0.030

Hll

-0.019

2.5(H)

0 030

0.082

2 .490

0.030

0.175

2.420

0.030

H12

0.120

2.420

0 030

0.207

2 .427

0.030

0.108

2.420

0.030

H13

0.173

2.420

0 030

0.092

2 .428

0.030 -0.013

2.500

0.030

H14

0.173

2.420

0 030

0.105

2 .428

0.030 -0.013

2.500

0.030

Charges in electrons, σ in À, ε in kcal/mol.



17.


Rel. E=0.0 μ=0.91

7 Rel. E=1.67 μ=1.89

Oaken Rearrangement of Allyl Vinyl Ether

Rel. E=0.18 μ=0.88

8 Rel. E=L82 μ=1.72

Rel. E=1.04 μ=0.96

9 Rel. E=L91 μ=1.65

Figure 1. Optimized 6-3lG(d)//6-3lG(d) structures for the nine conformers of allyl vinyl ether. Relative energies are given in kcal/mol and dipole moments are in Debyes. The optimized values for the three central dihedral angles are shown.


247

248



comparative purposes, it is desirable to keep the geometries the same for all methods. Two of the four procedures involved an A M I calculation with the SM2 method (20) and a PM3 calculation with the SM3 method (21) using the A M SOL program (22). The M S T method (23) was also used with A M I and 6-31G(d) wavefunctions in a modified version of G A U S S I A N 92 (8,23c). The relative free energies of hydration for the 9 conformers could be obtained from Monte Carlo simulations with the explicit TIP4P water model. This was not done in view of the associated large computational effort; the SCRF results should be adequate to illustrate the magnitude of the energetic effects of including the additional conformers. Results and Discussion Gas-Phase Energetics. The key variables for the conformational search for A V E were the three dihedral angles of the C2-0-C4-C5 fragment since the double bonds restrict rotation about C1-C2 and C5-C6. Starting structures for optimizations were obtained by systematic variation of the three central dihedral angles. This resulted in the 9 structures in Figure 1, whose status as true minima was verified by the vibrational frequency calculations at the 6-31G(d)//6-31G(d) level. Basically, the dihedral angle about C2-0 prefers to be near 0° or 180° to maintain conjugation for the vinyl ether fragment, while dihedral angles near 0°, 120°, and 240° are preferred about C4-C5 to provide the usual eclipsing of a vinyl group to the bonds attached to an adjacent sp3 carbon (C4). The normal preference for staggered geometries about an sp3 C - Ο ether bond is then expected and yields preferred dihedral angles near 180° and ±60° for the central C 4 - 0 bond. Of the 2 χ 3 χ 3 = 18 likely conformers, symmetry equivalence and steric clashes reduce the number of resultant unique minima to the 9 shown in Figure 1. Remarkably, their relative energies fall in a less than 2 kcal/mol range at the 6-31G(d)//6-31G(d) level, so significant populations of more than one conformer are expected near room temperature. It may also be noted that the computed dipole moments for the structures fall into two groups with values near 1.0 D and 1.8 D. The difference is primarily related to the C1-C2-0-C4 dihedral angle, which is near 0° and 180° for the two groups, respectively. The computed structures and vibrational frequencies were then used to compute the relative free energies for 1 - 9, as summarized in Table II. Though conformer 1 remains the lowest in free energy, there is substantial reshuffling of the order of the other conformers between energy and free energy. It may be noted that 2, the 0° - 180° - 0° conformer, which is only 0.18 kcal/mol above 1 in energy is 1.23 kcal/mol higher in free energy. Part of the change results from an RT In 2 (0.41 kcal/mol) symmetry correction disfavoring 2 relative to the other conformers since it is the only achiral conformer. 2 was taken as the geometry for A V E in the study by Vance et al. (9). On the other hand, 4, which is 1.36 kcal/mol higher in energy than 1, becomes the second most favorable conformer in free energy, only 0.11 kcal/mol above 1. Nine structures along the computed M E R P are illustrated in Figure 2. Details on the 6-31G(d)//6-31G(d) geometries for the transition state are reported elsewhere (9,24) The length of the breaking bond, 0-C4, is 1.918 À and the length of the forming bond, C1-C6, is 2.266 À at the 6-31G(d)//6-31G(d) level. These values increase to 2.100 and 2.564 À, respectively, in the (6/6)CASSCF/6-3 lG(d) optimized geometry, which yields improved agreement with observed kinetic isotope effects (24). However, both transition state structures correspond to a concerted process, which also emerges from the experimental isotope effects study (25). As noted previously, the 6-3 lG(d)//6-3 lG(d) activation energy and free energy are too high, ca. 49 kcal/mol in Table Π; MP2 corrections lower the figures by about 24 kcal/mol to a reasonable range (9). Given the results for the nine conformers of A V E in Table II, the effect of



Pdct.

AE° and A G

2 9 8

-0.12

-0.29

0.44 0.61 0.63

-0.10

-3.70

-2.40

-3.87

c

from 6-31G(d)//6-31G(d) calculations, increase in the free energy of activation from including

-0.08

-3.95

-3.00

-4.26

-1.36

-1.42

-0.39

phase for population of all conformers.

the population of all conformers, not just 4. Decrease in the free energy of activation in water relative to the gas

a

AAG* AAG*(g_>w)

-2.50 0.66

TS

-0.53

-1.96 -2.05

-0.65

-2.29

-1.27

-1.16

-1.99

-1.06

-0.92

-1.26

6-31G(d)/MST

-1.63

-0.61

-0.69 -0.90

0.73

48.93

-21.28

9

c

48.48

1.91

8

b

0.90

1.82

-1.20

-0.73

-1.80

1.00 0.78

1.67

1

-1.06

-0.62

-0.79

-19.88

1.67

-0.58

2.22

1.52

1.57

5

6

-1.80

-0.76

4

-0.95 -1.09

-0.84

1.36

3

-0.39

-0.44

-1.43

AM1/MST

0.11

1.09

1.04

-0.63

-0.74

hvd

-0.74

1.23

0.18

2

PM3/SM3

AM1/SM2

AG (298)

a

-0.72

0.00

0.00

1

2 9 8

AG

ΔΕ°

Conformer

(kcal/mol) for Conformers 1-9, the Transition State, and Product (4-Pentenal)

Table IL Computed Relative Energies, Relative Free Energies, and Absolute Free Energies of Hydration




250

Figure 2. Nine structures along the minimum energy reaction path for the Claisen rearrangement at the 6-31G(d)//6-31G(d) level.


17. SEVERANCE & JORGENSEN

Oaken Rearrangement of Allyl Vinyl Ether 251

including all of them rather than just one on the free energy of activation can be addressed. The free energy difference between populating just one conformer k and the full manifold of conformers is given by equation 2 where and Q are the corresponding partition functions and the sum is over all conformers i .


AG = -RTln(QI Q,) = -RTln

(2)

Xexpi-te-Gj/JCT-)

Of course, population of the other conformers makes A G negative, though it is the least negative for choosing k as the conformer with lowest free energy. In the present case, with conformer 1 as k, A G = -0.62 kcal/mol. Thus, the computed free energy of activation in the gas phase is raised by 0.62 kcal/mol by considering all of the A V E conformers. However, if conformers 2 or 4 were taken as the reference point for calculation of the free energy of activation, then considering all conformers would add 1.85 and 0.73 kcal/mol, respectively. For accurate work, such corrections may be significant. Effects of Hydration. The Monte Carlo simulations in water yielded the change in the free energy of hydration, AGhyd» along the MERP. The results starting from conformer 4 at frame 1 are illustrated in Figure 3 by the 4 curves, which correspond to averaging for 1M to 4 M configurations. It is apparent that the results are wellconverged after 2 M configurations. The TS at frame 83 has the lowest AGhyd» 3.85 ± 0.16 kcal/mol (26), below the reactant. The curvature of the AGhyd curve is less than for the gas-phase MERP, so the transition state is not predicted to shift along the M E R P upon transfer to water. Without adjusting for the population of other A V E conformers in water, which will not have great effect because of the low free energy for 4 (Table Π), the implied rate increase is a factor of 644 over the gas phase. This assumes no solvent dynamical effects on the barrier crossing, as in classical TS theory (27). Perusal of the experimental data starts with the measured relative rates for A V E of 1:4:58 in di-n-butyl ether, ethanol, and 2:1 methanol/water at 75 °C (5c). These give a Grunwald-Winstein m value of 0.4, which leads to a predicted relative rate of 876 in water; however, kinetic data on 4-substituted A V E ' s in solvents from cyclohexane to water suggest a relative rate in water closer to 150 (5d). Furthermore, the gas-phase kinetics indicate a rate of 0.031 χ 10"6 sec" at 75°C (28), while the rate in di-n-butyl ether extrapolated to 75 °C is 0.276 χ 10~ sec" (5e) a factor of 9 higher. Thus, when the range of media is extended from the gas phase to water, a substantial rate acceleration for A V E indeed emerges, ca. 10·* at 75 °C. Another potential comparison is for AAGhyd between 4 and the product, -2.88 kcal/mol in Figure 3. Experimental data are not available for these compounds; however, aldehydes are well-established to have lower AGhyd's than analogous ethers by 1-2 kcal/mol (29). The SCRF values in Table II are 1-3 kcal/mol. Turning to the SCRF results for AGhyd °f 4 versus the transition state, the computed changes for the free energy of activation in water as compared to the gas phase are summarized in Table ΙΠ. Results from Still's generalized Born/surface area (GB/SA) method are also included using the 6-31G(d) structures and C H E L P G charges (30). The SCRF results are all qualitatively correct; however, the predicted rate accelerations are all too small. AM1/SM2 results were reported by Cramer and Truhlar as AAGhyd = 0.75 kcal/mol and k j = 4 (31). The differences from the results in Table ΙΠ stem from the use of A M I optimized structures in their study and a reactant structure corresponding to 3 rather than 4; the results are improved with use of the 6-31G(d) structures and in going to the SM3 or M S T models (Table III). In 1

6

1

y

r e



252


10 20 30 40 50 60 70 80 90 100 110 120 130 140 Frame Number Figure 3. Computed changes in A G y d by averaging for 1M to 4 M configurations from the Monte Carlo simulations and the variation in the 631G(d) dipole moment for the reacting system. The x-axis gives the frame number along the MERP; the transition state is at frame 83. n





view of the number of features and terms in the SCRF treatments, it is difficult to trace the origin of their underestimates of the hydration effect. Cramer and Truhlar provide some discussion on this and suspect that the fault lies in the A M I charge distributions for the AM1/SM2 results (31). However, the results from the newer PM3/SM3 model are better, while switching to the 6-31G(d) wavefunction with the MST procedure and the 6-31G(d) C H E L P G charges with the GB/SA continuum model does not lead to substantial improvement. With the Monte Carlo approach and the associated two-

Table ΙΠ. Computed Changes in the Free Energy of Activation (kcal/mol) in Water versus the Gas Phase and the Corresponding Rate Enhancements, krç!, at 25 °C -AAG

Method

krel

AM1/SM2

1.66

16

PM3/SM3

2.24

44

AM1/MST

2.15

38

6-31G(d)/MST

2.27

46

GB/SA

2.10

35

Monte Carlo

3.85

664

(4.1)

(1000)

15

Experiment a

a h y d

The difference in free energy of hydration of conformer 4 and the chair b

transition state. Estimated - see text.

body potential functions with 6-31G(d) C H E L P G charges, the reliability of the charges is undoubtedly the dominant element in getting correct relative free energies of hydration (75)· This approach can be criticized for ignoring solute polarization by the solvent since the partial charges are fixed from the C H E L P G calculations. It appears that the polarization is included to some extent in an average way owing to overestimation of the polarity of molecules at the 6-31G(d) level (15,31). Another recent study of the effect of hydration on the rearrangement of A V E should be noted; Gao obtained a -AAGhyd of 3.5 kcal/mol ( k l = 368) with his combined A M 1/Monte Carlo approach (32). The effect of the population of other conformers besides 4 can be addressed for the free energy of activation in water. Equation 2 is again applied where the relative free energies of the conformers in water are given by the sum of the gas-phase value, A G , and the SCRF AG d(298) results in Table II. The results for the gas phase and the four hydration models are given in Table II as AAGÎ. The effects in re

2 9 8

ny



254


water, 0.4-0.7 kcal/mol, are seen to be very similar to those in the gas phase, 0.7 kcal/mol. This results from the limited variation in the calculated free energies of hydration of the 9 conformers. Consequently, there is little net solvent effect from this source; AG$ is lowered in water relative to the gas phase by 0.04 - 0.29 kcal/mol from population of the manifold of conformers rather than just 4. These corrections could be added to the AAGhyd values in Table III and slightly improve the agreement with the experimental estimate. Overall, for this reaction, the conclusion is that starting from a low-energy conformer of the reactant, the effects of including all conformers raises the computed free energy of activation by ca. 1 kcal/mol and the differential effect between the gas phase and aqueous solution is close to negligible. Origin of the Rate Acceleration in Water. A fundamental issue for Claisen rearrangements is the extent of dipolarity in the transition state (TS) (5). Substantial rate increases are observed in protic solvents for substituted cases that enhance putative enolate/allyl cation character. However, the origin of the computed acceleration from the Monte Carlo simulations is not partial ionization. The net C H E L P G charges on the H2C=CHO unit in A V E and the TS are -0.287 and -0.273 e (Table I), though solvent polarization of the solute was not included, as noted above. Even less charge separation is found in the MCSCF/6-31G(d) results (24). A n alternative possibility emerged from the solute-water energy pair distributions, which were computed for the reactant (4), transition state, and product during the Monte Carlo simulations. These are given in Figure 4, which shows the number of water molecules on the y-axis that interact with the solute with the potential energy given on the x-axis. The bimodal nature of the curves reflects the hydrogenbonded water molecules in the bands at low energy and the interactions with the many distant water molecules in the spike between -2 and +2 kcal/mol. The number and average strength of the hydrogen bonds are clearly in the order reactant < product < transition state. Integration of the curves to -3.0 kcal/mol, where the break to the central spike occurs, yields estimates of 0.5, 1.7, and 1.8 hydrogen bonds for the reactant, product, and transition state. The -3.0 kcal/mol limit is probably too severe for the ether reactant; graphical examination of configurations from the simulation normally shows one water molecule hydrogen bonded to the ether oxygen, which is typical for ethers (75). Hydrogen Bonding Analysis. A full hydrogen-bonding analysis was then performed on configurations saved during the Monte Carlo simulations. A less stringent energetic cutoff for hydrogen bonding, -2.25 kcal/mol, was supplemented by a geometric limit of 2.5 Â for an Ο — Η hydrogen-bond length, which coincides with die first minimum in OH radial distribution functions. The analysis gave average numbers of hydrogen bonds of 0.9, 1.7, and 1.9 for the reactant, product, and TS with average strengths of -3.4, -4.5, and -4.7 kcal/mol. Typical examples of the water structure near the solutes are shown in Figures 5-7. The 1 and 2 hydrogen bonds with water for ether and carbonyl oxygens are normal (75). Clearly, the rate acceleration in water can largely be attributed to the increased number and strength of the hydrogen bonds to the ether oxygen in progressing from the reactant to the transition state. Also, the oxygen in the transition state is behaving in a hydrogenbonding sense as carbonyl-like rather than ether-like. There is enhanced polarization of the H C 2 - 0 unit in proceeding from A V E to the TS that promotes hydrogen bond acceptance; the Ο becomes more negative by 0.07 e, which more than offsets the +0.04e change for HC2 (Table I). Continuing to the product, the Ο gains an additional 0.05 e; however, HC2 loses 0.17 e. In addition, the lengthening of the C4O bond to 1.92 À in the TS from 1.41 À in A V E increases the solvent-accessibility of the oxygen. It should be noted that hydrogen bonding also emerged as the dominant


17.


Oaken Rearrangement of Allyl Vinyl Ether

1.0 Product Transition State ' Reactant


0.8

0.6

ο

S 0.4

0.2

0.0

h

-8.0 -7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 Interaction Energy

1.0

2.0

3.0 4.0

Figure 4. Computed solute-water energy pair distributions for the reactant (4), transition state, and product from the Monte Carlo simulations. The y-axis records the number of water molecules that interact with the reacting system with the potential energy in kcal/mol shown on the x-axis. The units for the yaxis are number of molecules per kcal/mol.

Figure 5. Stereoplot of a random configuration from a Monte Carlo simulation of the reactant (4) in water. Only the first shell of water molecules is shown.


255


256


Figure 7. Stereoplot for the product, 4-pentenal, in water as in Figure 5.





element in a multiparameter analysis of solvent effects on the kinetics of Claisen rearrangements (33). The present results give some insights into desirable features for catalyst design. The hydrogen bonding results demonstrate the advantage of having two hydrogen-bond donating groups positioned to interact with the oxygen atom in the chair transition state. A n illustrative structure extracted from the Monte Carlo simulations is shown below. A related, important recent event is the determination of the crystal structure of a chorismate mutase with a bound endo-oxabicvclic transition state analog (34). Chorismate mutases catalyze the Claisen rearrangement of chorismate to prephenate. The ether oxygen of the inhibitor makes a single hydrogen bond with a side-chain N H of arginine-90 (34). This is consistent with the normal hydrogen-bonding characteristics of ether oxygens, as noted above (15). The position of the ether oxygen is at the edge of a solvent-exposed region of the binding cleft.

Based on the present results, it seems likely that in the transition state for rearrangement of a substrate, a second hydrogen bond to the oxygen would be present with the Arg-90 side chain or with a water molecule. The charge and structural reorganization is also reflected in changes in the dipole moment for the reacting system. As shown in Figure 3, the AGhyd * dipole moment curves mirror each other until a little past the transition state, then the AGhyd profile levels off, while the dipole moment increases to the product. The 6-31G(d) dipole moments are 1.9 D for 4, 2.5 D for the transition state, and 3.1 D for the product. a n c

Conclusion A combined quantum and statistical mechanical approach has provided insights into the acceleration of the Claisen rearrangement of allyl vinyl ether in aqueous solution. Rather than partial ionization, an increase in the number and strength of the hydrogen bonds with the ether oxygen in going to the transition state has been identified as the chief contributor to the catalysis. The observed magnitude of the lowering of the free energy of activation in water is well-reproduced by the Monte Carlo simulations in an all-atom format with explicit representation of the solvent


258



molecules. Four SCRF treatments with continuum solvent models were found to uniformly underestimate the rate acceleration in water. The other principal issue to be addressed was the effect of including the populations of all conformers of the flexible reactant on the free energies of activation in water. Starting from a low-energy conformer such as 4, the effects are less than 1 kcal/mol and similar in the gas phase and in water. This does not mean that such contributions should be ignored, particularly since the effects could be much greater if a higher-energy conformer is taken as the reference point in the absence of a full conformational search. Acknowledgments Gratitude is expressed to the National Science Foundation for support of this work and to Professor Modesto Orozco for computational assistance and advise on the SCRF calculations. Literature Cited (1) (2) (3) (4) (5)

(6) (7) (8)

(9) (10) (11) (12) (13)

(14)

Reichardt,C.,Solvents and Solvent Effects in Organic Chemistry; VCH; Weinheim, 2nd edn, 1988, Chap 5. See, for example: Kemp, D. S. and Paul, K. G.J.Am.Chem.Soc. 1975, 97, 7305. Olmstead, W. N.; Brauman, J. I. J. Am.Chem.Soc. 1977, 99, 4219. (a) Rideout, D.C.;Breslow, R. J. Am.Chem.Soc. 1980, 102, 7816. (b) Breslow, R. Acc.Chem.Res. 1991, 24, 159. Blokzijl, W.; Blandamer, M. J.; Engberts, J. B. F. N. J. Am.Chem.Soc. 1991, 113, 4241. (a) White, W. N.; Wolfarth, E. F. J. Org.Chem.1970, 35, 2196. (b) Coates, R. M.; Rogers, B.D.; Hobbs, S.J.;Peck, D. R.; Curran, D. P. J. Am.Chem.Soc.1987, 109, 1160. (c) Gajewski, J. J.; Jurazj, J.; Kimbrough, D. R.; Grande, M. E.; Ganem, B.; Carpenter, Β. K.J.Am. Chem. Soc. 1987, 109, 1170. (d) Brandes, E.; Grieco, P. Α.; Gajewski, J. J.J.Org.Chem.1989, 54, 515. (e) Burrows, C.J.;Carpenter, Β. K. J. Am. Chem. Soc. 1981, 103, 6983. Severance, D. L.; Jorgensen, W. L.J.Am.Chem.Soc. 1992, 114, 10966. For reviews, see: (a) Jorgensen, W. L. Adv.Chem.Phys., Part II 1988, 70, 469. (b) Jorgensen, W. L. Acc.Chem.Res. 1989, 22, 184. Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, Η. B.; Robb, Μ. Α.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D.J.;Defrees, D.J.;Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN 92, Revision A; Gaussian, Inc., Pittsburgh, PA, 1992. Vance, R. L.; Rondan, N. G.; Houk, Κ. N.; Jensen, F.; Borden, W. T.; Komornicki, Α.; Wimmer, E.J.Am.Chem.Soc. 1988, 110, 2314. Gonzalez, C.; Schlegel, Η. B. J. Phys.Chem.1990, 94, 5523. Hehre, W.J.;Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. Grev, R. S.; Janssen, C. L.; Schaefer, H. F.,IIIJ.Chem.Phys. 1991, 95, 5128. (a) Jorgensen, W. L.; Chandrasekhar,J.;Madura,J.D.; Impey, R. W.; Klein, M. L.J.Chem.Phys. 1983, 79, 926. (b) Jorgensen, W. L.; TiradoRives, J. J. Am.Chem.Soc. 1988, 110, 1657. (c) Jorgensen, W. L.; Severance, D. L.J.Am.Chem.Soc. 1990, 112, 4768. Breneman, C. M.; Wiberg, Κ. B. J. Comp.Chem.1990, 11, 361.


17. (15) (16)


(17) (18) (19) (20) (21) (22) (23)

(24) (25) (26)

(27) (28) (29) (30) (31) (32) (33) (34)



Carlson, Η. Α.; Nguyen, T. B.; Orozco, M.; Jorgensen, W. L.J.Comp. Chem. 1993, 14, 1240. For reviews, see: Beveridge, D. L.; DiCapua, F. M. Annu. Rev. Biophys. Biophys. Chem. 1989, 18, 431. Allen, M. P.; Tildesley, D.J.Computer Simulation of Liquids; Clarendon Press: Oxford, England, 1987. Jorgensen, W. L. BOSS, Version 3.2 1992, Yale University, New Haven, CT. Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420. Jorgensen, W. L.; Ravimohan, C. J. Chem. Phys. 1985, 83, 3050. Cramer, C.J.;Truhlar, D. G. Science 1992, 256, 213. Cramer, C.J.;Truhlar, D. G. J. Comput. Chem. 1992, 13, 1089. Cramer, C.J.;Lynch, G.C.;Truhlar, D. G. AMSOL 3.0, Univ. of Minnesota, Minneapolis, Minn., 1992. (a) Miertus, S.; Scrocco, E.; Tomasi, J. Chem. Phys. 1981, 55, 117. (b) Miertus, S.; Tomasi, J. Chem. Phys. 1982, 62, 539. (c) Bachs, M.; Luque, F. J.; Orozco, M. J. Comp. Chem. 1994, 15, 0000. In press, (d) Negre, M.; Orozco, M.; Luque, F. J. Chem. Phys. Lett. 1992, 196, 27. (e) Luque, F. J.; Negre, M.; Orozco, M.J.Phys. Chem. 1993, 37, 4386. Yoo, H. Y.; Houk, Κ. N., in press. Kupczyk-Subotkowska, L.; Saunders, W. H., Jr.; Shine, H. J.; Subotkowski, W. J. Am. Chem. Soc. 1993, 115, 5957. The reported uncertainty is ±1s and was obtained from the cummulative fluctuations in the free energy changes starting from the reactant. The fluctuations are computed by the batch means procedure from separate averages for each block of 200,000 configurations in the runs of 4,000,000 configurations. (a) Truhlar, D. G.; Hase, W. L.; Hynes, J. T.J.Phys. Chem. 1983, 87, 2664. (b) Gertner, B.J.;Wilson, K. R.; Hynes, J. T. J. Chem. Phys. 1989, 90, 3537. Schuler, F. W.; Murphy, G. W. J. Am. Chem. Soc. 1950, 72, 3155. Hine,J.;Mookerjee, P. K. J. Org. Chem. 1975, 40, 292. Still, W.C.;Tempczyk, Α.; Hawley, R.C.;Hendrickson, T.J.Am. Chem. Soc. 1990, 112, 6127. Hollinger, F. P.; Still, W. C., personal communication. Cramer, C.J.;Truhlar, D. G. J. Am. Chem. Soc. 1992, 114, 8794. Gao,J.J.Am . Chem. Soc. 1994, 114, 1563. Gajewski, J. J. J. Org Chem. 1992, 57, 5500. Chook, Y. M.; Ke, H.; Lipscomb, W. N. Proc. Natl. Acad.Sci.USA 1993, 90, 8600.

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Claisen Rearrangement of Allyl Vinyl Ether - ACS Symposium Series

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