J. Phys. Chem. 1993,97, 6212-6219
6212
New Insights into the Base-Catalyzed Hydrolysis of Methyl Ethylene Phosphate? Philip Tole and Carmay Lim’ Department of Molecular and Medical Genetics, Department of Chemistry, and Department of Biochemistry, University of Toronto, I King’s College Circle, Toronto, Ontario M5S 1A8, Canada Received: January 20, 1993; In Final Form: March 16, 1993
Quantum mechanical calculations and continuum dielectric methods have been employed to map out the detailed activation free-energy profile for alkaline hydrolysis of MEP in vacuum and solution. Hydroxyl ion attack opposite a ring oxygen of MEP with the methyl group oriented toward the incoming OH- leads to the lowest energy pathway for endo- and exo-cyclic cleavage. Hydroxyl attack of MEP is concerted with pseudorotation to yield a TBP intermediate with the hydroxyl group equatorial. The factors driving pseudorotation are identified as well as the reasons why pseudorotation is preferred to S N ~ ( Pring ) opening. In contrast to the common belief that ring strain in cyclic phosphates is relieved upon forming the TBP intermediate with the hydroxyl group equatorial, the geometry of the latter shows evidence for ring strain. This causes the P-O(apica1) bond in the ring to be weaker than that outside the ring, which, in turn, results in a smaller barrier for ring opening relative to cleavage of the exo-cyclic P-O(apica1) bond. Thus, hydroxyl ion attack of MEP in solution results in exclusive ring opening as observed experimentally. The calculations predict that both endo- and exo-cyclic cleavage would occur with retention of configuration.
1. Introduction
Due to the important biological roles of phosphates,’ there have been numerous studies of phosphate esters, and the results have been summarized in a recent reviews2 In particular, the pioneering studies by Westheimer and wworkers~5led to two key findings. The first is that the acid- and base-catalyzed hydrolyses of five-membered cyclic esters of phosphoric acid proceed 106-108 times faster than their acyclic analogues or the six- and seven-memberedcyclic phosphate^.^ The second is that acid-catalyzed hydrolyses of ethylenephosphate ( E P ) and methyl ethylene phosphate (MEP) proceed with exocyclic cleavage of the methoxy group at a rate comparableto the endocyclic cleavage rate and 106-107 times faster than their acyclic anal~gues.~ To explain the rapid accelerationof hydrolysisof the exocyclic group, the conceptof pseudorotationbetween trigonal bipyramids (TBPs) was invoked. Pseudorotation in pentacovalent species is defined as an intramolecular process where a TBP, which may be shortlived, is converted into another by deforming angles so that the final TBP appears to have performed a 90° rotation relative to the initial ~tate.~?~.’
SCHEME I
Q
Q
d Specifically,a pseudorotation process was postulated to explain the observed products in the acid-catalyzed hydrolysis of MEP. Although the hydrolysisof MEP in dilute alkali (pH 8-1 1) occurs almost exclusively with ring opening,s this observation could also be explained by a pseudorotation process in which endo-cyclic cleavage of a TBP intermediate with the hydroxyl group apical was assumed to be much faster than its pseudorotation to a TBP intermediate with the hydroxyl group equatorial. t This work was supported by the Protein Engineering Network Center of Excellence of Canada.
0022-3654/93/2097-6212$04.00/0
Ab initio calculations of the base-catalyzed hydrolysis of E P show that dianionic pentacovalent phosphorane intermediates do not exist in vacuum.8 Instead, gas-phase OH- attack on the E P anion is concerted with ringopeningto form a dianionictetravalent phosphate -OC2)4P(OH)02- intermediate, which is assumed to undergo rapid proton transfer to yield the product 2’-hydroxyethyl phosphate (HOC2H&‘042-).9 The base-catalyzed hydrolysis of dimethyl phosphate (DMP) is not accompanied by I8Oexchange, in analogy with its cyclic counterpart EP.’ Ab initio calculationslOJ1 of OH- and methoxide attack of D M P show that dianionic pentacoordinate intermediates exist but are kinetically insignificant since they have well depths on the order of ksT. Thus, the absenceof 1 8 0 exchangein the basecatalyzed hydrolysis of E P and D M P can be rationalized by dianionic pentacovalent intermediates which do not exist or which exist with lifetimes that are too short for pseudorotation. The gas-phase activation free-energy profile (see Methods section below) for MEP + OH- was calculated using ab initio molecular orbital methods and the 3-21+G* basis with polarization functions (3d orbitals) on the phosphorus and diffuse functions (s and p orbitals) added to the heavy atoms. Most of the calculations were made in the Hartrec-Fock (HF) approximation. The importance of correlation effects was estimated by second-order Mdler-Plesset perturbation theory (MP2) with a 6-3 1+G* basis set. The corresponding activation free-energy profile in solution was obtained using continuum dielectric methods to estimate the solvation free energies of the reactants, transition states, intermediates,and products. These calculations reveal a new mechanism for the MEP + OH-reaction, which has been communicated.12 Hydroxyl ion attack is concerted with pseudorotation to form a TBP intermediate ION- with the hydroxyl group equatorial (Figure 1). The latter undergoes ring opening faster than isomerization and subsequent exo-cyclic cleavage of the methoxygroup. In section 2, the quantum mechanical method and the continuum dielectricmethod are outlined briefly. Details of the activation freeenergy profiles for the MEP OH-reaction in vacuum and solution are discussed in sections 3 and 4, respectively. Section 5 contains a summary of the results.
+
2. Methods The ab initio calculations were performed using the program Gaussian90.13 The 3-21+G* basis set was chosen since it is well@ 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No.23, 1993 6213
Hydrolysis of Methyl Ethylene Phosphate
R
R
9 . 9
01
-32.0 \\
3” mex
8.7
Figure 1. Schematic diagram for in-line attack of MEP in the down conformation. The lowest energy TBP endo-cyclic cleavage intermediate and the corresponding transition state are shown. Numbers denote gas-phase free energies in kcal/mol.
known that d-type orbitals on the second-rowelements are required to give a good description of hypervalent molecules such as pentavalent phosphorus and that addition of diffuse functions lowers energiesof anions more than neutral molecules and provides a better description of their relative energies.14 The 3-21+G* basis set has been found to yield geometries of cyclic and acyclic phosphorus esters in good agreement with experiment.gJSJ6 For example, comparison of the 3-21+G* structure of MEP with the X-raystruct~rel~ shows that nearly all the bond lengths are within h0.02 A and most of the bond angles are within h2O of experiment; the 3-21+G* structure of the HOC2H4P042-dianiong has three nearly equivalent P-O bonds, 1.514,l S24, and 1.548 A, in close agreement with 1.510, 1.514, and 1.519 A, the mean values for 22 availablealkyl phosphate dianion structures.16 All geometries were fully optimized, unless stated otherwise. The electroniccorrelation energy was estimated by MP2. Since a small basis set like 3-21+G* may limit the fraction of the total correlation energy obtainable, a larger 6-31+G* basis was employed. The MP2/6-3 1+G* computations were carried out only for single points corresponding to the 3-21+G* optimized geometries of the reactants, transition states, intermediates, and products. The hydroxyl oxygen to phosphorus distance was chosen as the reaction coordinate for the approach of OH- to MEP, and the phosphorus to departing oxygen distance was chosen as the reaction coordinate for endo- and exo-cyclic cleavage of the TBP intermediates. Each of the monoanion structures except E P has 45 degrees of freedom with 143 and 191 basis functions in the 3-21+G* and 6-31+G* basis sets, respectively. Using the program Gaussian90, an optimization cycle (one SCF cycle) at the HF/3-21+G* level tookabout 2 h on a Stardent PS3030 with a memory requirement around 1.9 megawords.
To determine the thermodynamic parameters, vibrational frequencies were computed for the fully optimized structures of the stationary points on the potential energy surface of the MEP + OH- reaction. The frequencies were analyzed in terms of the internal coordinates using the program MOLVIB.” The entropy (&b) and vibrational energy (Evib) were calculated from the frequencies and geometries according to standard statistical mechanical formulas.14 The rotational (Emt)and translational (Emm)energies and the work term (PV) were treated classically. Although a free energy is strictly defined only for local minimum stationary points and a generalized free energy of activationcurve can in principle be constructed by minimizing the generalized transition-state theory rate constant at a given temperature,’* in this work the gas-phase (and solution) activation free-energy profile refers to the gas-phase potential energy surface to which enthalpic and entropic corrections (and equilibrium solvation free energies; see below) have been added. To estimate how the gas-phase activation free-energy profile is modified by solvent, the solvationfree energies of the reactants, transition states, intermediates, and products were estimated by the continuum dielectric method.19s20 The solute molecule is treated as an irregularly shaped object with an internal dielectric constant EI and point charges qi at positions corresponding to the atomic nuclei rI. The electrostatic contribution to the Helmholtz solvationfree energy AAsis the differencebetween the free energies of charging these objects in vacuum and in solution
where the subscripts s and g indicate potentials calculated in solvent and in the gas phase, respectively.19 The electrostatic field, 4, is determined by the Poisson equation with a dielectric
Tole and Lim
6214 The Journal of Physical Chemistry, Vol. 97, No. 23, 1993 M E ~ , ~ O H - I’L
TS’L
I ~ N T.S%
TS~X
E P +M&H
. a
(-3.8)
(5.7)
-4.1
I
6.5
4 0.65
Figure 2. Gas-phase (top) and solution (bottom) activationfree-energy profile for hydroxyl ion attack of MEP in the down conformation. The barriers are for the lowest energy TBP IeN47,4s intermediate and the corresponding transitionstate that lead to ring opening. The dark circles correspond to species on the exo-cyclic cleavage pathway. Numbers on vertical lines correspond to solvation free energies in kcal/mol.
constant that changes from q to the solvent dielectric constant €0 at the solute/solvent interface; i.e.,
V€(?)V4(?) = -4ap(?) (2.2) Poisson’s equation is solved bythe finite difference method using a 71 X 71 X 71 grid. The low dielectric region is defined as the region inaccessible to contact by a 1.4-A sphere rolling over a surface defined by the effective Born radii, Ri, of the atoms i. The geometries and charges are taken to be the same in vacuum and solution. The 3-21+G* ab initio geometries and Mulliken atomic charges and the CHARMM version 2221 van der Waals radii were employed with an internal and solvent dielectric constant of 2 and 80, respectively. Since the numerical difference between AAs and AG, is less than 1 kcal/mol, thus AA, = AG,,19 and the solution free-energy barrier, AG2, from A to B can be calculated from the thermodynamic cycle,
A(soln)
-
B(soln)
AG,~
where AGJ is the gas-phase free-energy barrier and the AG,’s are solvation free energies; i.e.,
AG; = AG:
+ AG,(B) - AG,(A)
(2.3)
3. Results and Discussion 3.1. Activation Free-Energy Profile in Vacuum. Figure 1 illustrates the gas-phase activation free-energy profile for the nucleophilic addition of hydroxyl ion to MEP where all the structures have a total unit negative charge. Figure 2 shows how the gas-phase activation free-energy profile is qualitatively
(0.93)
* U 0
Figure 3. Schematic diagram depicting MEP minima and transition states. Numbers with and without parentheses denote gas-phase and solution free energy barriers, respectively, in kcal/mol.
changed in solution;the zero of energy corresponds to the reactants at infinity. The energetic data are collected in Table I. In Table I, TSaP is a TBP transition state with an apical OH group characteristic of pseudorotation;12 MEHPT- is a tetrahedral OC2H5P04CH3-intermediate22that would result from an s ~ 2 (P) mechanism of the OH- + MEP reaction; M H E P is methyl hydroxyethyl phosphate (Figure l), and the other molecules in Table I are illustrated in Figures 1, 3, and 5 and described in sections 3.1.1-3.1.5. In Table 11, the frequencies contain the maximal percentage contribution of a P-X (X = 01,02,03’, 02’, 05’) stretch; e.g., in MEP, the maximal percentage contribution of the P-01 stretch is found in a frequency of 1397 cm-l. The following nomenclature for the TBP complexes is adopted in this paper. I and TS denote the intermediate and transition state, respectively. The superscript a or e denotes that the nucleophile OH- occupies an apical or equatorial position in a TBP. The letter after the superscript describes the nature of the TBP complex: L for long-ranged ion-dipole complexes, P for pseudorotation, D for diequatorial ring, H or Me for rotation of the hydroxyl or methoxy group about P-O(H/Me), N for endocyclic cleavage, and X for exo-cycliccleavage. The first subscript refers to the C(Me)-O-P-01 dihedral and the second to the H-0-P-01 dihedral. 3.1.1. MEP Conformations. .In vacuum, MEP exists in two distinct conformations, MEP4 and MEP180, where the methyl group is cis and trans to 0 1 (Figure 3). Although the cis conformation is found to be more stable than the trans one at the HF/3-21+G* (by 3.3 kcal/mol) and HF/6-31G* (by 2.5 kcal/ mol) levels, the trans conformation was obtained in the X-ray structure. This discrepancy may be due to crystal packing forces stabilizing the trans conformation, which, in vacuum, is destabilized relative to the cis conformer by steric and charge interactions between the methyl group and the ring. Since the ring oxygens and the methylene groups are indistinguishable, the
The Journal of Physical Chemistry, Vol. 97, No. 23, 1993 6215
Hydrolysis of Methyl Ethylene Phosphate
TABLE I: Thermodynamic Parameters: Energies, Entropies, and Solvation Free Enerpjes (kcal/mol) EHF,'au E~p2,bau ETRVC STRP -74.995 15 -15.588 36 OH6.669 41.214 MEP -154.13169 -159.15445 82.196 92.391 MEPino -154.1324Or -159.1525 1 82.160 89.838 MEPTSo -154.13130 -159.15463 81.593 86.816 MEPTS1a -154.12966 -1 59.14655 81.504 81.661 OH- + MEP -829.13344 -834.14281 88.865 133.605 -834.14048 88.829 13 1.052 MEPino -829.1 28 15 MEPTSo -829.13305 -834.14299 88.262 128.090 -834.1349 1 88.113 128.881 MEPTSi24 -829.12541 -829.1641 1 -834.16841 90.366 108.104 I'L TS@Lol -829.14400 -834.16 124 90.811 92.995 -834.11426 90.410 96.982 TSaLo2 -829.16091 -829.1 5439 -834.16124 89.714 91.420 TSaL -834.8 1186 90.163 91.328 -829.201 18 TSaPh MEHPF -829.18622 -834.19423 89.268 103.124 PDo2
-829.18116 -829.21132 -829.20998 -829.20903 -829.21101 -829.20399 -829.19343 -829.19324 -829.20469 -829.20361 -8 29.20412 -829.18361 -829.26626 -829.22212
-834.19631 -834.82843 -834.82648 -834.82633 -834.82866 -834.81912 -834.81163 -834.8 1201 -834.8 1919 -834.8 1131 -834.81965 -834.80619 -834.81 515 -834.84028
91 A56 91.835 91.111 91.768 91.846 91.130 90.389 90.390 90.634 90.623 90.144 89.231 92.182 89.612
93.814 92.851 92.881 92.656 92.429 89.431 93.151 93.190 93.112 93.584 92.518 96.516 98.015 136.882
AGP -98.44 -1.39 -6.86 -1.61 -6.56 -105.83 -105.30 -106.11 -105.00 -81.16 -64.10 -66.18 -69.57 -64.18 -72.38 -61.16 -64.32 -61.90 -60.18 -65.80 -62.02 -66.54 -66.60 -61.53 -59.10 -60.66 -58.98 -59.53 -69.54
MHEP E l a HF energiw for fully optimized 3-21+G* geometries. Single-pointMP2/6-31+G* energy calculation at 3-21+G* geometry. E ~ = v E- + EM + Evib in kcal/mol. S ~= V S= Smt+ S,+b in kcal/mol. e AG, are solvation free energies in kcal/mol. 1 Fully optimized 6-31G* geometry, EHF=: -151.930 98 au; C-0-P-01 -24'. g Fully optimized 6-31G* geometry, EHF= -151.921 05 au; C-0-P-01 = 180O. Transition state with OH- apical, characteristic of pseudorotation (Figure 2, ref 12). OCZH~PO~CH~; illustrated in Figure 3b of ref 22.
(01 face)
(02 face)
hydroxyl oxygen is attracted to the methyl hydrogens, and at a P-O(H) reaction coordinate of 5.35 A, an ion-dipole minimum (PL) is formed in vacuum. The average 0-P-O angle in MEP (logo) is retained in the IaL intermediate, implying that the phosphorus atom is still tetrahedral. However, the calculations fail to locate a corresponding long-range ion-dipole minimum for the up conformation presumably because the free-energy barrier for rotating the methyl group toward the incoming OHis negligible. This is suggested by the less than 1 kcal/mol freeenergy barrier for MEP4 MEPTSo in vacuum and solution (see Figure 3). Transition states have been located for the approach of OHto the 02', 01, and 02(Me) faces (Figure 5). As the hydroxyl 0-P distance decreases in PL,a transition state TSaL is found at a reaction coordinate of 2.92 A (Figure 5). It is not a s ~ 2 ( P ) transition state since the P-02' bond is 1.65 A and the 3-21+G2 negative frequency (-1 11-3 cm-l) is dominated by the P-O(H) stretch and O(H)-P-03'43' torsion with no contribution from the P-02' stretch. The TSaL transition state is distorted toward a TBP structurewithaverage02'-P-Y, O(H)-P-Y, and Y-P-Y (Y = 0 1 , 0 2 , 0 3 ' ) anglesof 101,79,and 116°,respectively.The transformation from a distorted tetrahedral IaL intermediate to a distorted TBP TSaL transition state is dictated by loss of uibrutional entropy (-2.9 kcal/mol) and negligibleenthalpy cost (0.14 kcal/mol). Hydroxyl ion attack opposite 0 1 results in a TSaLO1 transition state with the ring diequatorial, which is higher in energy than the TS'L transition state. This is because the P-01 bond, which is the strongest of the P-O bonds as indicated by its bond length and frequency, is lengthened and weakened in TSaLO1 (P-01 = 1.50 A) relative to TSPL (P-01 = 1.46 A) (see also Table 11). Thus, the OH- approach to the 0 1 face is not favored relative to the 02' face. Although the ring is diequatorial in the TSaL02 transition state resulting from OHattack opposite 02(Me), it is 3.6 kcal/mol lower in energy than
-
Figure 4. Four possible faces of hydroxyl ion attack; vis., opposite 01, 02(Me), 03', and 02'. -cis conformer cannot be distinguished from the +cis conformer. Thus, there is a saddle point connecting the two cis conformers, MEPTSo, and another one connecting the cis and trans conformers, MEPTS124 (Figure 3). The free-energy barrier for rotation of the methoxy group across a ring oxygen is 5.7 kcal/ mol [MEP, MEPTS1241 but is less than 1 kcal/mol across 0 1 [MEP, MEPTSo]. 3.1.2. Approach of OH. Long-Range Complexes. Figure 4 depicts the four possible faces of OH- attack where the P-O(H) reaction coordinate is in-line with 01, 02(Me), 03', and 02'. Nucleophilic attack at edges (P-O bonds) is not favored since OH- encounters larger charge repulsion at an edge relative to a face.23.24 Steric and charge repulsion dominate the initial stages of the reaction. The OH- nucleophile can attack opposite a ring oxygen of MEP4 with the methyl group oriented toward OH(down conformation, 02' face in Figure 4) or with the methyl group oriented away from OH- (up conformation, 03' face in Figure 4). Since the methoxy group in MEP4 has an oxygen charge of -O.52e, a carbon charge of -O.72e, and hydrogen charges of 0.25-0.28e, the hydroxyl ion approaches MEP4 in the down rather than the up conformation to reduce charge repulsion. The
-
+
6216 The Journal of Physical Chemistry, Vol. 97, No. 23, 1993
Tole and Lim
1
(6.1)
1
11.0
. (-35.0)
-30 0 01
_____IC
01
05’
T
t
(3.6) 0.25
-7.5
0 1
01
(-11.9)
Figure 5. 3-21+G* ball and stick geometries of the long-range transition-state complexes formed by hydroxyl ion attack opposite 01,02’, and 02; the P-O(H) reaction coordinate is 2.28, 2.92, and 2.57 A, respectively. The TBP intermediates formed from OH- attack opposite 02’ and 0 2 are also shown. Numbers with and without parentheses denote relative gas-phase and solution free energies, respectively, in kcal/mol.
the T S L transition state (Figure 5). This is probably due to stronger P-O(H) bond formation in the TS*Lo2transition state, which is located at a P-O(H) distance (2.57 A) that is 0.35 A less than the TSaL transition state (2.92 A). 3.1.3. Pseudorotation. As the P-O(H) distance in TSaL decreases, a stable TBP intermediate with the hydroxyl group apical could not be found even with a larger 6-31+G* basis set.12 Instead, pseudorotation with the P-01 bond as pivot occurs, which
places the hydroxyl group equatorialand the methoxy group apical to form a ICN~,,*S intermediate. This process is driven by an enthalpic gain of -36.4 kcal/mol, which is offset slightly by an entropic loss of -1.4 kcal/mol. In vacuum, the pseudorotation process is also driven by charge repulsion between the hydroxyl oxygen and 0 1 . In TS*L (Figure 5), the hydroxyl oxygen is furthest from 01 (3.3 A) and almost equidistant to 0 3 ’ and O(Me) (2.9 A). This dictates the direction of OH- approach so
The Journal of Physical Chemistry, Vol. 97, No. 23, 1993 6217
Hydrolysis of Methyl Ethylene Phosphate that the 02’-P-05’ angle (158’ in TSaL) is set up for pseudorotation. It also propels the hydroxyl hydrogen toward the basal ring oxygen 03’ to minimize steric and charge repulsion from the methyl hydrogens and maximize favorable electrostatic interactions with 03’. The H(O)-03’ interaction causes the P-03‘ bond to lengthen, and charge repulsion between the incoming hydroxyl oxygen and the alkoxy oxygens causes the 03’-P-O(Me) angle to expand. This initiates pseudorotation, which is facilitated by the low-frequency ring torsion motions. For OH- attack opposite O(Me) (Figure 5), the ring oxygens are forced apart in the TSaLO2 transition state due to charge repulsion between the hydroxyl oxygen and the ring oxygens. This could in principle activate toward pseudorotation. However, pseudorotation with the P-01 bond as pivot will result in a very high-energy TBP with a diapical ring. Pseudorotation with the P-O(ring) bond as pivot would place anionic 0 1 in an apical position. Thus, pseudorotation does not occur. Instead, a TBP PDO2 intermediate is formed at a P-O(H) distance of 1.74 8,. This is higher in free energy than the PN47.45 intermediate (by 19.5 kcal/mol in vacuum; see Figure 5). The IaD02intermediate is also higher in free energy than the endo- (TScN) and exo-cyclic (TSCXI6,72) cleavage transition states that result from OH-attack opposite 02’ of MEP in the down conformation (by 15.0 and 9.6 kcal/mol in vacuum; see Table I). Thus, the latter pathway is preferred to OH- attack opposite O(Me) in vacuum since it leads to a lower energy pathway for endo- and exo-cyclic cleavage. 3.1.4. Isomerization of IeN and IeXwm Intermediates. There are three intermediates, ICN47,45,PN-52.43, and IcN179,43,whose hydroxyl hydrogen is within 2 8, of 02’ but the methyl group is trans to O(H), 03’, and 01, respectively. The MP2 and HF energies in Table I indicate the same order of stability: PN47.45 < ICN-52,43< IcN179,-83, and the free energy of IcN179,43is 1.3 kcal/mol less than that of PN47.45. The ICN47,45,ICN-52,43,and ICN179,43intermediates are connected by three transition states with the methyl group cis to 01, 03’, and O(H); the latter is found, but the other two have not been calculated. The freeenergy barrier for rotation of the methoxy group about the P-O(Me) bond is 4.6 kcal/mol for ICN-52,43 TSCMe-l20,43 and 4.5 kcal/mol for IcN179,43 TSCMe-12o,43. PN47.45 can isomerize via TSCH56,1and TSCH52,181transition states to yield IcX50,88 by rotating the 0-H bond so that the hydroxyl hydrogen is now within 2 8,of the other apical oxygen, 05’. The gas-phase free-energy barrier for equatorial 0-H rotation, which has negligible entropic contribution (3~ In solution, the charges on the phosphate oxygens and/or the hydroxyl oxygen will likely be reduced relative
-
Tole and Lim to the vacuum charges due to hydrogen bond interactions with water molecules. Consequently, there will be a reduction in the charge repulsion between the incoming hydroxyl ion and the equatorial oxygens, which mutes this source of a driving force for pseudorotation in solution. However, the solvation free energy of the TSaPIZtrigonal bipyramid with the hydroxyl group apical (-64 kcal/mol) is similar to that of the TBP intermediates with the hydroxyl group equatorial (Table I). Thus, there is still a favorable energy gradient for pseudorotation, which can be facilitated by the intramolecular torsional motions of the ring. Although the tetrahedral MEHPr- intermediate O C ~ H S P O ~ C H ~ of S N ~ ( P ring ) opening is better solvated than the TBP intermediate IcN47,85 (by 8 kcal/mol, Table I), it is still higher in free energy (by 7.6 kcal/mol) than the IoN47,45intermediate in solution, Thus, ring opening via an S N ~ ( Pmechanism ) seems unlikely to occur in solution. The solvation free energy of IcN47,45 is greater than that of IcN-52,43(by 2.4 kcal/mol) and ICN179,43(by 4.1 kcal/mol). This decreases the ring-opening barrier for ICN179.43 to 2.7 kcal/ mol but increases that for PN47.45 to 7.3 kcal/mol, indicating that the position of the axial methoxy group can significantly influencethe ring-openingbarrier in solution. Solvationdecreases the P-O(H) rotational free-energy barrier (by 2.3 kcal/mol) presumably because water molecules can hydrogen bond to 01, O(H), and/or 03’ in the P-O(H) rotational transition states, thus reducing the charge repulsion between the basal oxygens. The TSCXls,72transition state is predicted to be less well solvated than the ICXSO,~~ intermediate, resulting in an increase in the gas-phase exo-cyclic cleavage barrier to 16.7 kcal/mol. Since the electrostatic solvation free energies of IcN47,45 and IcX~,88 (-64 and -66 kcal/mol) and those of TSCN47,-78and TSCX16.72 (-62 and -59 kcal/mol) are similar, their errors are likely to roughly cancel to yield a net error that is much smaller than the difference between the exo- and endo-cyclic cleavage solution barriers (19.4 kcal/mol). Thus, as in vacuum, ring opening is favored over ring retention in accord with experiment.5 Figure 2 indicates that the rate-limiting step is formation of the endo-cyclic intermediate. The errors involved in calculating the gas-phase barrier for the rate-limiting step and the solvation free energies of the species involved, as well as the experimental uncertainty in the AGs of OH-, preclude a comparison of the free-energy barrier in solution with experiment. As in vacuum, solvation favors OH- approach to the 02’ face instead of the other faces in Figure 4. The TSaLO1and TSaL02 transition states, which are formed at a reaction coordinate distance (2.28 and 2.57 A) that is closer than that for the T S L transition state (2.92 A), have less favorable (negative) solvation free energies than TSaL (Table I). Since the TSaLOl transition state is higher in energy than the TSaL transition state in vacuum and solution (Figure 5 ) , OH- attack opposite 0 1 is not favored. Although the free-energy levels of the TSaLoZand TSaL transition states are comparable in solution, the TSaLo2 transition state leads to a PD02intermediate that is higher in free energy than the ICN47i-85 intermediate (by 22.0 kcal/mol, Figure 5 ) as well as the TSCN47,-78 and TSCX16,72transition states (by 14.7 and 6.8 kcal/mol, Table I). Thus, OH-attackopposite O(Me) in solution lea& toa higher energy pathway for endo- and exo-cyclic cleavage than OHapproach to the 02’ face. 4. Concluding Discussion
The most favorable direction of attack that would lead to the observed exclusive ring opening is OH- attack opposite a ring oxygen with MEP4 in the down conformation. Note that OHattack of MEP4 in the up conformation would lead to formation of an ICX instead of an ICN intermediate; thus, exo-cyclic cleavage would be expected, which would be inconsistent with experiment. The results, summarized in Figures 1 and 2, show that hydroxyl ion attack of MEP4 is concerted with pseudorotation. Pseudor-
Hydrolysis of Methyl Ethylene Phosphate otation is driven by a favorable free-energy gradient to form a ICNintermediate with the hydroxyl group equatorial, as well as electrostatic interactions between the incoming hydroxyl group and the basal oxygens. It is facilitated by the ring torsions and the lack of steric hindrance due to the constraint of the ring. Pseudorotation with P-01 as pivot is preferred to ring opening via a Sp42(P) mechanism since (i) the latter yields a tetrahedral intermediate O C ~ H S P O ~ Cwhich H~,~ is ~higher in free energy than the TBP intermediate ICN47,-ss(by 15.7 kcal/mol in vacuum and 7.6 kcal/mol in solution; see Table I) and (ii) the ring torsions and the 0-P-0 angle bending modes that correspond to pseudorotation have frequencies less than 500 cm-1 whereas the P-02’ bond stretching frequency is around 800 cm-l in TS’L. Although OH- attack opposite 02’ of MEP is concerted with pseudorotation due to a favorable energy gradient to form a ICN47,-ss intermediate with the hydroxyl group equatorial, methoxide attack of MEP yields a stable intermediate with an apical and an equatorial methoxy group; note that pseudorotation with the P-01 bond as pivot yields an indistinguishable,isoenergic isomer. The commonly held belief that ring strain is relieved upon forming a TBP intermediate is found to be invalid. In fact, ring strain in the TBP intermediates, as evidenced by the smaller 02’-P-03’ and C2’-02’-P angles in ICN compared to its acyclic TBP analogue,*sweakens the P-O(apica1) bond in the ring. This is evidenced by the fact that in the ICN47,-ss and ICXs~,88 intermediates, the P-02’ stretch contributes to frequencies less than 782 cm-1, whereas the P-O(Me) stretch contribute to frequencies as high as 1290 cm-1. Formation of the endo-cyclic cleavage IcN intermediate is predicted to be rate-limiting. The proposed mechanism predicts that both endo- and exo-cyclic cleavage occur with retention of configuration. This could, in principle, be tested by substituting a ring hydrogen with a methyl group or using triple isotope doping to create a chiral MEP. Supplementary Material Available: Tables of the 3-21+G* bond lengths, bond angles, and dihedral angles (3 pages). Ordering information is given on any current masthead page. Acknowledgment. We thank Prof. Ronald Kluger for stimulating discussions. We are grateful to D. Bashford, M. Sommer, and M. Karplus for the program to solve the Poisson-Boltzmann equation and J. Wiorkewicz and K. Kuczera for the MOLVIB program.
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