J. Phys. Chem. B 1999, 103, 7145-7150
7145
Competition between Wolff Rearrangement and 1,2-Hydrogen Shift in β-Oxy-r-ketocarbenes: Electrostatic and Specific Solvent Effects Saturnino Calvo-Losada,† Dimas Sua´ rez,‡ Toma´ s L. Sordo,‡ and Jose´ J. Quirante*,† Departamento de Quı´mica Fı´sica, UniVersidad de Ma´ laga, Campus de Teatinos. 29071, Ma´ laga, Spain, and Departamento de Quı´mica Fı´sica y Analı´tica, UniVersidad de OViedo, Julia´ n ClaVerı´a 33006, OViedo, Spain ReceiVed: March 22, 1999; In Final Form: June 21, 1999
A quantum chemical investigation of the solvent effects on the competition between the Wolff transposition and 1,2-H-shift in β-hydroxy-ketocarbenes in aqueous solution was carried out at the B3LYP/6-31G** level of theory. The inclusion of solvent effects by means of a continuum model was not able to reproduce the experimental yields. Then, a semidiscrete approach consisting of solute-solvent association complexes embedded in a dielectric continuum was used to estimate the solvent influence on the Gibbs activation energies. The calculated ∆G are 0.88 and 4.94 kcal/mol for the 1,2-H-shift and the Wolff transposition processes, respectively, thus rendering a 100% yield for the formation of the vinyl-ketone product in agreement with experiment. The TS for the 1,2-H-shift process is preferentially stabilized by solvent due to a H-bond between the migrating hydrogen and one of the water molecules in the association complex. This effect of solvent is analyzed by means of hybrid QM/MM calculations using a classical description of water molecules with the TIP3P model.
Introduction
Methods
One of the synthetic routes to the formation of 1-methyl-2hydroxy synthons, which constitute the skeleton of some antibiotic macrolides, proceeds through the stereoselective Wolff rearrangement of intermediate ketocarbenes obtained from the photolytical cleavage of β-oxy-R-diazo compounds.1 However, the competitive 1,2-H-shift reaction becomes the most favored pathway in the case of β-hydroxy-R-diazo compounds, rendering a 100% yield for the formation of a vinyl-ketone product.2 Therefore, it is crucial to understand the different factors governing the competition between Wolff rearrangement and 1,2-H-shift processes in order to control the course of the reaction at our convenience. A theoretical analysis of the processes could be helpful to this end. Previous theoretical work3,4 on the evolution of the ketocarbene intermediates 1 in Scheme 1 has shown that the energy barriers in the gas-phase for the Wolff and 1,2-H rearrangements are quite small (about 1-2 kcal/mol), while the stability of the corresponding transition Structures (TSs) is rather similar, the 1,2-H shift being the most favored TS for the nonsubstituted case. The substituent effects (R ) CH3, COCH3) have been also analyzed in terms of both electronegativity and the alignment of the migrating groups with the charge depletion sites at the carbene center, allowing thus to rationalize different experimental results.4 In this work, the kinetic influence of solvent on the evolution of the unsubstituted ketocarbene in aqueous solution is studied by means of a semidiscrete approach which takes into account, not only the electrostatic effect of solvent, but some representative H-bond interactions between solute and water molecules as well.
All the quantum chemical calculations were carried out using the Gaussian 94 suite of programs.5 The B3LYP DFT functional6 was employed in this work since it has proven effective for accurately describing hydrogen-bonded complexes7 and provides a reasonable description of the electronic structure and reactivity of singlet carbene intermediates.8 The 6-31G** basis set was used in all the calculations.9 Geometry optimizations were carried out in gas-phase followed by analytical frequency calculations. The gas-phase Gibbs energies at 298.15 K and 1 atm were calculated using standard procedures.10 The electrostatic effect of solvent was taken into account by means of a general self-consistent-reaction field (SCRF) continuum model.11 The solute, which is placed in a general cavity in the continuum defined by an isodensity molecular surface (F ) 0.0004 au), polarizes the continuum, which in turn creates an electric field inside the cavity. The electrostatic part of the Gibbs energy corresponding to the solvation process is obtained using the self-consistent isodensity polarizable continuum (SCIPCM) method implemented in Gaussian 94.5 A relative permittivity of 78.30 was used to simulate water as solvent. The use of the dielectric continuum model to treat solvent effects is complemented by means of a cluster model in which several representative water molecules forming an association complex with a solute molecule are described quantummechanically.12 When this association complex in turn is embedded in a dielectric continuum, a semidiscrete representation of solvent effects is then obtained. Following this approach, the corresponding change in Gibbs energy in solution for the evolution of the ketocarbene intermediate studied in this work, can be expressed as
* To whom correspondence should be addressed. † Departamento de Quı´mica Fı´sica. ‡ Departamento de Quı´mica Fı´sica y Analı´tica.
∆Gsolution ) ∆Ggas-phase + ∆Gassoc(TS) - ∆Gassoc(RKC) where ∆Gassoc(S) is the change in Gibbs energy for the association process between a solute S and n water molecules
10.1021/jp9909863 CCC: $18.00 © 1999 American Chemical Society Published on Web 08/03/1999
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SCHEME 1
in the dielectric continuum: S + nH2O f S(H2O)n. This partitioning simplifies the understanding of the specific and electrostatic solvent effects given that the corresponding ∆∆Gassoc ) ∆Gassoc(TS) - ∆Gassoc(RKC) can be considered as a correction to the calculated ∆G in the gas-phase by quantum chemical methods.12a The electronic influence of specific water molecules on the association complexes was further studied by analyzing the B3LYP/6-31G** charge densities using the Bader’s theory of atoms in molecules.13 The bond critical point (BCP) properties were determined using a recent version of the EXTREME program, a part of the AIMPAC suite of programs,14 and the MORPHY program developed by Popelier.15 The contribution of different energy components to the relative solvent-solute interaction energies in the association complexes was examined by means of the generalized molecular interaction potential with polarization (GMIPp) as proposed by Orozco and Luque.16 The GIMPp method is a hybrid QM/MM method16a,17 which provides the interaction energy between a quantum mechanical molecule with a set of classical particles using a perturbative approach. The interaction energy is expressed as the addition of three terms: electrostatic, polarization, and the van der Waals (vdW) terms. The electrostatic contribution is obtained from the QM electrostatic potential computed rigorously at the position of every classical particle; the polarization energy is computed using a generalized procedure proposed by Francl.18 The vdW energy is obtained using a classical 12-6 formalism. GMIPp calculations were performed by using HF/6-31G* wave functions and MSP vdW parameters for the quantum subsystems,19 while the water molecules were described classically with the TIP3P model20 (the MSP vdW parameters were specially derived to reproduce vdW interactions between HF/6-31G* charge densities and TIP3P water molecules). The MOPETE program was used to carry out the GMIPp calculations.21 Results and Discussion Gas-Phase Results. The gas-phase TSs for the competitive 1,2-H shift and Wolff processes (TSH and TSW in Figure 1) connect the ketocarbene intermediate with very exothermic product channels to give a ketene structure 2 and a vinyl-ketone 3, respectively (see Scheme 1).3,4 In agreement with the Hammond postulate,22 both TSH and TSW present reactant-like structures and very low barrier heights of 2.43 and 3.05 kcal/ mol, respectively, at the B3LYP/6-31G** level (see Figure 1 and Table 1). It is interesting to note that the transition vector for the migration of the H atom to the carbene center is hardly coupled with internal torsions, being dominated by the hydrogen displacement. However, the reaction coordinate from the initial
Figure 1. B3LYP/6-31G** optimized structures of the initial ketocarbene intermediate and the TSs for the 1,2-H-shift and Wolff transposition processes. Distances in angstroms. Transition vectors are also sketched.
ketocarbene to TSW involves the simultaneous internal rotation about the C1-C2 bond and a slight elongation of the breaking C-C bond. Consequently, the predominance of the 1,2-H shift over the Wolff rearrangement in the evolution of the initial ketocarbene is well explained in terms of a weak intramolecular H-bond between the hydroxyl and carbonyl groups (OH‚‚‚O ≈ 2.4 Å in both RKC and TSH) which is clearly lost in TSW (OH‚‚‚O ≈ 3.2 Å) due to the torsional motion of the carbonyl group.3,4 The addition of the gas-phase thermodynamic corrections to the energy barriers slightly increases the kinetic preference for TSH, TSW being 1.47 kcal/mol less stable than TSH in terms of ∆G. This gas-phase Gibbs energy difference results in a 92% relative yield for the formation of a vinyl-ketone through the 1,2-H shift of ketocarbene,23 close to the 100% relative yield observed experimentally in solution.2 However, the small energy barriers of the competitive TSs for the evolution of ketocarbenes in the gas-phase, suggest that condensed-phase effects could also play an important role in these chemical events.
β-Oxy-R-ketocarbenes
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TABLE 1: Relative Gibbs Energies (kcal/mol) with Respect to Ketocarbene for the Transition Structures Studied in This Work structure β-hydroxy-ketocabene TS for 1,2-H-shift TS for Wolff transposition
RKC TSH TSW
∆Ggas-phase
∆GSCRFa
∆∆Gassocb
∆Gsolutionc
0.00 1.75 3.22
0.00 1.34 1.58
0.00 -0.87 1.72
0.00 0.88 4.94
a ∆G SCRF ) ∆Ggas-phase + ∆Gsol (TS) - ∆Gsol (RKC). ∆Gsol obtained by means of single-point B3LYP/6-31G** SCIPCM calculations on the gas-phase geometries. b ∆∆Gassoc ) ∆Gassoc (TS) - ∆Gassoc (RKC). ∆Gassoc(S) ) [G(S(H2O)3) - 3 G(H2O) - G(S)] + [∆Gsol (S(H2O)3) - 3 ∆Gsol (H2O) - ∆Gsol (S)] c ∆Gsolution ) ∆Ggas-phase + ∆∆Gassoc.
Figure 2. Stereoview of the three binding sites between water and the ketocarbene intermediate considered in this work to study the specific kinetic effects of solvent.
SCRF Results. The pure electrostatic effect of water as solvent on the reaction profiles for the evolution ketocarbenes intermediates was estimated by means of single-point B3LYP/ 6-31G** SCIPCM calculations on the B3LYP/6-31G** gasphase geometries. The three critical structures RKC, TSH, and TSW present solvation Gibbs energies in the dielectric continuum of -5.34, -5.75, and -6.98 kcal/mol, respectively, the solvation Gibbs energy of TSW being 1.64 and 1.23 kcal/mol greater in absolute value than those of RKC and TSH Thus, it seems that solvent stabilizes the Wolff rearrangement in a preferential manner, most probably, because of the orientation of the carbonyl group in TSW which is then capable of polarizing the dielectric continuum to a larger extent. When the corresponding δ∆Gsol are added to the gas-phase ∆G values, the competitive Wolff and 1,2-H shift rearrangements are then predicted to have activation Gibbs energies in solution of 1.34 and 1.58 kcal/ mol, respectively. These SCRF results give a small Gibbs energy difference between TSH and TSW (only 0.24 kcal/mol) corresponding to a relative yield for the 1,2-H shift of 60% in contrast with the 100% experimental kinetic preference for the vinylketone formation. Association Complexes. To find out the most important specific water-ketocarbene interaction sites, various association complexes between one water molecule and the ketocarbeneintermediate were optimized on the B3LYP/6-31G** potential energy surface starting from a large set of initial molecular positions. From these exploratory calculations, we obtained three different bimolecular complexes with the water molecule solvating the reactive groups in the ketocarbene intermediate. The B3LYP/6-31G** binding energies including ZPVE correction for these bimolecular complexes (not presented in this work for brevity) are -12.6, -7.2, and -6.2 kcal/mol. Inspection of the corresponding binding sites between water and ketocarbene (labeled as A, B, and C in Figure 2), suggested that these binding sites could influence the kinetic competition between the 1,2-H shift and Wolff processes. Therefore, the corresponding association complexes between the ketocarbene intermediate and the TSs with the three water molecules at the A, B, and C binding sites, were fully optimized at the B3LYP/ 6-31G** level.
Figure 3 displays the optimized structure of the initial association complex RKC‚3H2O from two different perspectives. The water molecule Wat-A in Figure 3 links the hydroxyl and carbonyl groups of the ketocarbene intermediate through two typical H-bonds, in which the hydroxyl and carbonyl groups act as acceptor and donor counterparts, respectively, having equilibrium distances of 1.735 and 1.818 Å. The methyl and hydroxyl groups in ketocarbene are also interconnected via a second water molecule Wat-B through HO‚‚‚H(Wat-B) and (Wat-B)O‚‚‚HC intermolecular contacts, the last interaction presenting an equilibrium distance of 2.347 Å as normally found in weak CH‚‚‚O hydrogen bonds.24 Interestingly, the third water molecule Wat-C forms a single H-bond with the carbene lone pair (C‚‚‚H(Wat-C) ) 2.163 Å) while a weak contact between Wat-C and the methyl group can be also distinguished (see Figure 2). The calculated association energy per water molecule for the formation of RKC‚3H2O amounts to -10.87 kcal/mol. The analysis of the topology of F(r) in RKC‚3H2O rendered 21 bond critical points and 3 ring critical points associated with faces generated by the contacts of the water molecules with solute, therefore fulfilling the Poincare´-Hopf requirement (nuclei-bonds+rings-cages ) 1).13 All the specific watersolute interactions in RKC‚3H2O are unequivocally characterized as closed-shell interactions since they present low values of F(rc) and ∇2F(rc) > 0. According to the values of F(rc) at the corresponding intermolecular BCPs, Wat-A is the strongest bound water molecule (F(rc) ≈ 0.04 au), followed by the HO‚‚‚H(Wat-B) contact (F(rc) ≈ 0.03 au), the C‚‚‚H(Wat-C) contact (F(rc) ≈ 0.02 au), and the Wat-B and Wat-C CH‚‚‚O interactions (F(rc) ≈ 0.01 au). The nature of the C‚‚‚H(Wat-C) interaction was characterized by means of a plot of ∇2F(r), confirming thus that the carbene lone-pair forms a normal H-bond with Wat-C. We do note that the subsequent changes of both the topological nature of F(r) and BCP properties for the intermolecular bonds in the TSs can be extremely useful to analyze the specific solvent effects between these related structures The association complex corresponding to the 1,2-H shift TS26 (TSH‚3H2O in Figure 3) shows structural, energetic, and electronic differences with respect to both the initial ketocarbene complex and the gas-phase TSH structure. The optimized geometries in Figures 1 and 2 indicate that the hydrogen migration in TSH‚3H2O is slightly more advanced with respect to the isolated TSH, the forming C-H bond distance being 1.659 Å (1.665 Å in TSH), whereas the transition vector frequency of TSH‚3H2O decreases 179 cm-1 with respect to TSH. In addition, the different water-solute contacts in TSH‚3H2O are also reinforced with respect to the initial association complex: the equilibrium distances of the Wat-A molecule with the hydroxyl and carbonyl groups decrease in 0.04 Å, the carbene-Wat-CH-bond is also slightly shortened, and more interesting, the migrating hydrogen establishes presumably a new H-bond with Wat-B with an equilibrium distance of 2.268 Å (see Figure 3). The appearance of a BCP in the interaction line connecting the migrating-H and the O(Wat-B) atoms confirms the
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Figure 3. B3LYP/6-31G** optimized structures of the association complexes studied in this work. Distances in angstroms. Mulliken charges of water molecules are in brackets. Black dots represent the presence of the solute-solvent BCPs. HF/6-31G* water-solvent distances are in parentheses (see text for the details).
existence of this specific interaction in TSH‚3H2O capable of facilitating the 1,2-H shift in ketocarbenes. The origin of this new interaction can be ascribed to a quasiplain surface formed by the OH(Wat-B) fragment with the hydroxyl group of TSH‚ 3H2O and the migrating H-atom. A new ring-CP in the generated surface is also located. Mulliken population charges shown in Figure 3 indicate that Wat-B acts as a donor moiety in TSH‚ 3H2O, donating 0.03 e more than in RKC‚3H2O. On the other side, the rest of the BCP properties at TSH‚3H2O reflect that the Wat-A and Wat-C intermolecular contacts are slightly reinforced with respect to RKC‚3H2O. The above-discussed geometrical and electronic changes are reflected in the calculated association energy per water molecule of TSH‚3H2O, which amounts to -11.50 kcal/mol (0.63 kcal/ mol greater in absolute value than that of RKC‚3H2O). Thus, according to our calculations, a significant stabilization of the 1,2-H-shift TS could be gained by means of the specific H-bond interactions with solvent. Particularly, the ability of the migrating proton to establish a H-bond interaction with Wat-B could be specially important in order to increase the preference for the 1,2-H shift process vs the Wolff rearrangement in protic solvents. Concerning the association complex TSW‚3H2O for the Wolff rearrangement, our calculations indicate that the transposition of the methyl group is more advanced in TSW‚3H2O than in TSW: the C-C terminus distance shortens in 0.175 Å and the imaginary frequency increases in 132 cm-1 (see Figures 1 and 2). The structural comparison of the water-solute contacts in the initial association complex RKC‚3H2O and in TSW‚3H2O reveals that all the H-bonds are slightly weakened in the TS
for the Wolff rearrangement, the most remarkable change corresponding to the Wat-A-carbonyl H-bond whose equilibrium distance increases in 0.116 Å. The topological analysis of F(r) renders the same characteristic set of Ring-CPs and BCPs for the TSW‚3H2O and RKC‚3H2O structures, though F(r) values at the BCPs are lower for all the water-solute contacts in the TS, mirroring thus the geometrical changes. Although the migrating methyl group in TSW‚3H2O maintains its CH‚‚‚O contacts with Wat-B and Wat-C, the water-assisted intramolecular contact between the carbonyl and the hydroxyl groups of the ketocarbene intermediate is weakened due to the torsional displacement of the carbonyl group along the reaction coordinate (see Figure 3). Precisely, the corresponding association energy per water molecule in TSW‚3H2O (-10.59 kcal/mol) is 0.28 and 0.91 kcal/mol lower in absolute value than the corresponding energies in RKC‚3H2O and TSH‚3H2O, respectively. It is interesting to note that the presence of the specific water molecules also attenuates the preferential electrostatic stabilization of the Wolff rearrangement (see above) given that the SCIPCM electrostatic solvation energy of TSW‚3H2O (-11.16 kcal/mol) is 0.62 and 1.02 kcal/mol greater in absolute value than those of TSH‚3H2O and RKC‚3H2O, respectively. The global energetic effect of the specific water molecules considered in our cluster model is best appreciated in the form of the relative association Gibbs energies for RKC, TSH, and TSW: 0.00, -0.87, and 1.72 kcal/mol, respectively. These relative ∆Gassoc energies are well rationalized in terms of the above-discussed structural and electronic influences of the H-bond water molecules on the initial ketocarbene intermediate and the competitive TSs, the TSH‚3H2O structure being preferentially
β-Oxy-R-ketocarbenes
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TABLE 2: Relative Values of Electrostatic, Polarization, and VdW Energy Contributions (kcal/mol) to the Interaction Energy of Association Complexes Determined from GMIPp Calculationsa ∆Etheor structure
Eelec
Epol
EvdW
RKC‚3H2O 0.00 0.00 0.00 TSH‚3H2O -0.30 -0.04 0.02 TSW‚3H2O 2.99 0.26 -1.39
HF/ B3LYP/ ∆EGMIPp 6-31G* 6-31G** 0.00 -0.32 1.86
0.00 -0.54 2.08
0.00 -2.39 2.61
a Calculations performed by using a HF/6-31G(d) wave function and MSP vdW parameters for the quantum subsystem while the TIP3P parameters were used to classically describe the water molecules.
stabilized in solution. Addition of the corresponding ∆∆Gassoc values to the gas-phase Gibbs energies gives an estimation of the ∆G barriers in solution of 0.88 and 4.94 kcal/mol for the 1,2-H shift and the Wolff transposition, respectively. These theoretical energy barriers, which clearly predict a 100% relative yield of the vinyl-ketone product, are then in full agreement with experimental results.2 GMIPp QM/MM Calculations. From the above discussion it is clear that in order to reproduce the experimentally observed preference for the 1,2-H shift over the Wolff transposition in ketocarbenes intermediates it is necessary to take into account the specific solvent-solute interactions by means of a semidiscrete model. In this respect, it seems interesting to investigate the ability of hybrid methodologies17 to reproduce both the B3LYP results and experimental findings. In addition, further insight into solvent effects can be gained by means of the analysis of the different components to the QM/MM interaction energies. As a first approach to this end, we performed GMIPp calculations16 on every association complex in Figure 3. Since the MSP vdW parameters included in GMIPp method were specially derived to reproduce hydration of HF/6-31G* QM solutes with TIP3P water molecules,19 the relative position of the three water molecules was then re-optimized at the HF/ 6-31G* level while the B3LYP/6-31G** internal geometry of both solute and the water molecules was held fixed (see Figure 3). Subsequently, single-point GMIPp calculations were carried out assuming the solute molecule as the quantum subsystem described at the HF/6-31G* level while the three water molecules A, B, and C were described classically with the TIP3P parameters. To compare with the GMIPp interaction energy, the corresponding interaction energy between the QM subsystem and the three water molecules was also obtained by means of single-point B3LYP/6-31G** and HF/6-31G* calculations on every association complex (∆Etheor in Table 2). We see in Table 2 that the GMIPp interaction energies of the association complexes are very similar to the HF/6-31G* theoretical values. According to the data in Table 2, it is clear that the electrostatic and polarization components of the GMIPp relative interaction energies stabilize preferentially the 1,2-H shift TS in about 0.3 kcal/mol while the Wolff transposition TS is disfavored electrostatically by about 3 kcal/mol. As expected, these contributions to the ∆EGMIPp values run parallel to the B3LYP/6-31G** energetic and structural results discussed previously, confirming thus that electrostatics partially dominates the water-solvent H-bond interactions. Although TSW‚3H2O is the least stable structure in solution, the vdW solute-solvent interactions tend to stabilize the TS for Wolff transposition in 1.39 kcal/mol with respect to the initial ketocarbene structure. Therefore, these GMIPp results suggest that electrostatic interactions with polar solvents would favor the 1,2-H-shift of
ketocarbene intermediates while nonpolar solvents might promote preferentially the Wolff rearrangement. Although the GMIPp calculations and the B3LYP/6-31G** estimations of the relative interaction energies are in qualitative agreement and predict an identical trend for the structures analyzed in this work, the B3LYP/6-31G** relative value of the water-solute interaction energy in TSH‚3H2O is about 2 kcal/mol greater than the GMIPp and HF/6-31G* ones (see Table 2). In addition, when the relative position of Wat-B is optimized at the HF/6-31G* level, the O(Wat-B)‚‚‚H-contact in TSH‚3H2O has an equilibrium distance of 2.612 Å, notably lengthened in 0.34 Å with respect to the B3LYP/6-31G** value. These data indicate that the influence of the Wat-B molecule, which is crucial to stabilize the migrating hydrogen by means of a new H-bond (see above), is clearly underestimated unless electron correlation is taken into account to describe the structure and energetics of the O(Wat-B)‚‚‚H-contact in TSH‚3H2O. Therefore these observations stress the convenience of including some representative solvent molecules in DFT models to properly describe the competitive reaction processes involved in the chemistry of ketocarbene intermediates. Conclusions The competition between the Wolff transposition and 1,2H-shift processes in solution for the evolution of unsubstituted ketocarbene intermediates is investigated carrying B3LYP/631G** quantum chemical calculations. The use of the SCIPCM continuum model to represent the electrostatic solvent effects gives a poor agreement between theory and experiment, rendering only a 60% relative yield for the 1,2-H-shift process in contrast with the 100% reported experimentally. Three different water-solute binding sites are analyzed following a semidiscrete approach which takes into account both the electrostatic and specific solvent effects. The corresponding B3LYP/6-31G** association complexes between the ketocarbene and TSs with three water molecules present different H-bonds whose structural and electronic properties are analyzed with detail. The specific influence of one of the water molecules appears to be very important given that it stabilizes the migrating hydrogen in the 1,2-H-shift TS by means of a new H-bond. Taking into account the relative Gibbs energies for the formation of the association complexes, the calculated Gibbs energy barriers in solution are 0.88 and 4.94 kcal/mol for the 1,2-Hshift and the Wolff transposition processes, respectively, rendering thus a 100% yield for the formation of the vinyl-ketone product in agreement with experiment. Finally, assuming a classical description of water molecules with the TIP3P model, GMIPp QM/MM calculations on the association complexes suggest that electrostatic interactions with polar solvents would favor the 1,2-H-shift of ketocarbene intermediates whereas the Wolff rearrangement might be favored by nonpolar solvents through dispersion interactions. These analyses also stress the importance of including electronic correlation to describe the specific O(Wat-B)‚‚‚H contact which further stabilizes the TS for the 1,2-H-shift. Acknowledgment. The authors thank CICYT (Spain) for generous allocation of computer time on the Cray J90 at the CIEMAT. S.C.L. and J.J.Q. are grateful to the Universidad de Ma´laga for computing facilities. D.S. thanks Professor F. J. Luque and Professor M. Orozco (Universidad de Barcelona) for providing a copy of their MOPETE program. Helpful suggestions and comments made by F. J. Luque are also warmly acknowledged.
7150 J. Phys. Chem. B, Vol. 103, No. 34, 1999 Supporting Information Available: Table of energies in hartrees for all the calculations; tables of BCP and Ring-CP properties for the association complexes in Figure 3, figure showing the plot of ∇ 2F(r) which characterizes the C‚‚‚H(Wat-C) interaction in RKC‚3H2O; and full geometric data for the association complexes. Supporting Information is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Meier, H.; Zeller, K. P. Angew. Chem., Int. Ed. Engl. 1975, 14, 32. (2) (a) Lo´pez-Herrera F. J.; Sarabia-Garcı´a, F. Tetrahedron Lett. 1993, 34, 3467. (b) Lo´pez-Herrera F. J.; Sarabia-Garcı´a, F. Tetrahedron Lett. 1994, 35, 2929. (3) (a) Enrı´quez, F.; Lo´pez-Herrera, F. J.; Quirante, J. J.; Sarabia, F. Theor. Chim. Acta 1996, 94, 13. (b) Calvo-Losada, S.; Quirante, J. J. J. Mol. Struct. (THEOCHEM) 1997, 435, 398. (4) Calvo-Losada, S.; Sordo, T. L.; Lo´pez-Herrera, F. J.; Quirante, J. J. Theor. Chem. Acc. In press. (5) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheesman, J. R.; Keith, T. A.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Lahan, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; HeadGordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94; Gaussian, Inc., Pittsburgh, PA, 1995. (6) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (b) Becke, A. D. Phys. ReV. B. 1988, 38, 3098. (c) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B. 1988, 37, 785. (7) Rablen, P. R.; Lockman, J. W.; Jorgensen, W. L. J. Phys. Chem. A 1998, 102, 3782. (8) (a) Toscano, J. P.; Platz, M. S.; Nikolaev, J.; Cao, Y.; Zimmt, M. B. J. Am. Chem. Soc. 1995, 117, 4712. (b) Toscano, J. P.; Platz, M. S.; Nikolaev, J. J. Am. Chem. Soc. 1996, 118, 3527 (c) Wong, M. H.; Wentrup, C. J. Org. Chem. 1996, 61, 7022 (d) Schreiner, P. R.; Karney, W. L.; Schleyer, P. v. R.; Borden, W. T.; Hamilton, T. P.; Schaefer, H. F. J. Org. Chem. 1996, 61, 7030. (9) Hehre, W.; Radom, L.; Pople, J. A.; Schleyer, P. v. R. Ab Initio Molecular Orbital Theory; John Wiley & Sons, Inc.: New York 1986.
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% 1,2-H-shift )
exp{-∆G#(TSH)/RT}
100
exp{-∆G (TSH)/RT} + exp{-∆G#(TSW)/RT} #
(24) Koch, U.; Popelier, P. L. (25) Alkorta, I.; Elguero, J. J. (26) An extensive exploration water-assisted mechanism for the
A. J. Phys. Chem. 1995, 99, 9747. Phys. Chem. 1996, 100, 19367. of the PES led us to discard a possible 1,2-H-shift process.
