Various potential mechanisms for the alkaline hydrolysis of an oxo-β-lactam in the gas phase (Scheme ) were examined in the light of ab initio data obtained at the RHF/6-31+G*//RHF/6-31+G* and MP2/6-31+G*//MP2/6-31+G* levels. The influence of the solvent was also examined from IPCM (isodensity polarizable continuum model) computations at the RHF/6-31+G* level. In penicillins and cephalosporins, alkaline hydrolysis begins with a nucleophilic attack on the carbonyl group of the β-lactam ring, which is followed by cleavage of the C7−N4 bond. In the oxo-β-lactam studied, the process additionally involves cleavage of the C7−O6 bond in the ring. In fact, this cleavage is subject to a very small activation energy, as little as 0.21 kcal/mol versus the 14.15 kcal/mol for the typical cleavage energy (based on MP2/6-31+G*//MP2/6-31+G* calculations) for the C7−N4 bond. In addition, the hydrolysis end products are more stable than those resulting from the typical cleavage. Consequently, the alkaline hydrolysis involving cleavage of the C7−O6 bonds is kinetically and thermodynamically more favorable than the classical hydrolysis mechanism for penicillins and cephalosporins. This suggests that oxo-β-lactams might act as β-lactamase inhibitors.

Various mechanisms for the alkaline hydrolysis of an aza-β-lactam in the gas phase were studied by ab initio calculations at the RHF/6-31+G*//RHF/6-31+G*, MP2/6-31+G*//MP2/6-31+G*, and B3LYP/6-31+G*//B3LYP/6-31+G* levels. Solvent effects were considered via IPCM (isodensity polarizable continuum model) calculations at the IPCM/6-31+G*//RHF/6-31+G* level. The alkaline hydrolysis of β-lactams begins with a nucleophilic attack of the hydroxyl ion on the carbonyl of the β-lactam ring. The tetrahedral intermediate thus formed undergoes cleavage of the C7−N4 bond to give the reaction end products. In addition to the typical cleavage reaction, the β-lactam studied can undergo opening at the C7−N6 bond (Scheme ). Both processes have a similar activation energy that varies slightly depending on the particular computation method used. The most stable end products are those formed via the typical mechanism. In any case, both mechanisms yield products possessing a carbamate group, which suggests that the starting aza-β-lactam might be an effective inhibitor for β-lactamases.

A complete study of basic hydrolysis of the pyrazolidinone ring by ab initio calculations at RHF/6-31+G*//RHF/6-31+G* and MP2/6-31+G*//MP2/6-31+G* has been carried out. The alkaline hydrolysis has been studied through a BAC2 mechanism, characterized by a nucleophilic attack of the hydroxyl group on the carbonyl of the γ-lactam ring, formation of the tetrahedral intermediate, and cleavage of the C2N3 bond to yield the final reaction product. In the gas phase, the interaction of OH- with the carbonyl carbon to form a tetrahedral intermediate takes place without any barrier height. Two possible mechanisms have been considered for the transfer of the hydroxyl hydrogen to the nitrogen of the γ-lactam:  a stepwise mechanism involving the cleavage of the C2N3 bond and subsequent transfer of the hydrogen to the γ-lactam nitrogen and a concerted mechanism. The MP2/6-31+G*//MP2/6-31+G* barrier heights are 32.72 and 25.64 kcal/mol, respectively. The elimination reaction, which in the gas phase may interfere with the nucleophilic attack, has also been studied.

SUMMARYA complete study of the alkaline and acidic hydrolysis of the β-lactam ring of azetidin-2-one was carried out using ab initio molecular orbital calculations at the RHF/6-31+G* and RHF/6-31G** levels, respectively. Alkaline hydrolysis has been studied through a BAC2 mechanism characterized by a nucleophilic attack on the β-lactam carbonyl group, formation of the tetrahedral intermediate and cleavage of the C-N bond until the formation of the final product of the reaction, this being the limiting step of the reaction. On the other hand, the acidic hydrolysis has been studied by means of a A-1 type unimolecular mechanism, characterized by a nitrogen-protonation followed by an opening of the ring and further addition of water to the carbonyl group. The system involving the azetidin-2-one ring, the H3O + ion and a water molecule has been considered. Three transition states have been identified; the barriers corresponding to the addition of H + to the nitrogen and the addition of water to the carbonyl group are practically negligible (first and third reaction steps, respectively).

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