The ground state vinylidene-acetylene isomerization was investigated by ab initio molecular electronic structure theory. The coupled-cluster method with single, double, and noniterative inclusion of triple excitations ͓CCSD͑T͔͒; with single, double, and noniterative inclusion of triple and quadruple excitations ͓CCSD͑TQ͔͒; and with full single, double, and triple excitations ͑CCSDT͒ were used to treat the effect of electron correlation. Several correlation-consistent polarized valence basis sets, cc-pVXZ, were employed. Theoretical limiting values of the energetics of the reaction were then deduced from the series of computations. With zero-point energy correction, the energy of reaction is Ϫ42.95 kcal/mol and the reaction barrier is 1.5 kcal/mol. Both agree excellently with experimental values.

Ab initio calculations and continuum dielectric methods have been employed to map out the lowest activation free-energy profiles for the alkaline hydrolysis of a five-membered cyclic phosphate, methyl ethylene phosphate (MEP), its acyclic analog, trimethyl phosphate (TMP), and its six-membered ring counterpart, methyl propylene phosphate (MPP). The rate-limiting step for the three reactions was found to be hydroxyl ion attack at the phosphorus atom of the triester. By performing constrained optimization along the reaction coordinate, defined as the phosphorus to incoming hydroxyl oxygen distance, and computing the solvation free energies of the resulting stationary points, the rate-limiting transition states have been relocated in solution. Dihedral ring constraints in the five-membered ring leading to a more solvent-exposed hydroxyl group and, thus, better solvation of the cyclic transition state compared to its acyclic counter-part was found to be the dominant factor governing the rate enhancement of cyclic MEP relative to acyclic TMP alkaline hydrolysis. However, both ground-state destabilization of MEP relative to MPP, due to ring strain, and transition-state stabilization of the five-membered cyclic phosphate transition state relative to its six-membered ring analog, due to the differential location of the transition states in solution, were found to contribute to the enhanced rates of alkaline hydrolysis of five-membered ring MEP compared to six-membered ring MPP.

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To help elucidate why penicillin-G is inactivated by certain bacterial beta-lactamase enzymes, whereas clavulanic acid (Clav, which is similar to penicillin-G except at positions 1, 2, and 6) inhibits beta-lactamase, the intrinsic chemical reactivities of these two antibiotics were assessed in this work. Ab initio and continuum dielectric methods were used to map out the gas-phase and solution-phase free-energy profiles for the alkaline hydrolyses of Clav and penicillanic acid (Peni, which is similar to penicillin-G except at position 6) as well as of a fictitious hybrid compound, Peni-db, which is similar to Clav and Peni except at positions 1 and 2, respectively. Furthermore, the ring strain energies of various lactam rings and the five-membered rings of Peni and Clav as well as their respective rate-limiting transition states were computed to assess the contribution of four- and five-membered ring strains to the antibiotic's activity. The predicted product distribution, rate-limiting step, and relative reaction rates for the alkaline hydrolysis of Peni and Clav are in accord with the experimental findings. The rate-limiting step in the alkaline hydrolysis of Peni, Clav, or Peni-db is the approach of the negatively charged hydroxide ion toward the anionic reactant to form a tetrahedral intermediate. The alkaline hydrolysis of Clav generates more stable products than that of Peni mainly because the O1 atom and the hydroxyethylidene group in Clav facilitate the opening of the five-membered ring; furthermore, the O1 atom can abstract a proton easier than the less polar S1 in Peni. Clav undergoes basic hydrolysis faster than Peni mainly because its hydroxyethylidene group leads to an increase in the positive charge on the carbonyl C7 atom, therefore enhancing favorable electrostatic interactions with the incoming hydroxide anion. To a lesser extent, the oxygen at position 1 in Clav also contributes to the rate acceleration because of the greater solvent stabilization of the oxygen-containing transition state as compared to the respective ground state. The inherent strain of the four-membered beta-lactam ring or five-membered ring does not enhance the alkaline hydrolyses of beta-lactam molecules such as Peni or Clav, consistent with the observation that the rate-limiting step does not involve a breakdown of the four-membered beta-lactam ring or five-membered thiazolidine/oxazolidine rings.