Molecular calculations, /3-lactam reactivity

Boyd DB, Herron DK, Lunn WHW, Spitzer WA. Parabolic relationships between antibacterial activity of cephalosporins and beta-lactam reactivity predicted from molecular orbital calculations. / Am Chem Soc 1980 102 1812-14. 

Parabolic Relationships Between Antibacterial Activity of Cephalosporins and P-Lactam Reactivity Predicted from Molecular Orbital Calculations. 

D. B. Boyd, D. K. Herron, W. H. W. Lunn, and W. A. Spitzer, /. Am. Chem. Soc., 102, 1812 (1980). Parabolic Relationships between Antibaaerial Activity of Cephalosporins and Beta-Lactam Reactivity Predicted from Molecular Orbital Calculations. 

The appropriate energy content and reactivity of the /8-lactam 0=C-N bond (cf. the problem of 6(7)a-methyl and methoxy substitution and 2-substituted derivatives). Although the molecular orbital calculations on penicillins and cephalosporins [271,272,293] are not enough to yield exact conclusions, it is likely that a parabolic relationship exists between the electron population of the 0=C-N bond and the antimicrobial activity. 

An analysis of all crystal structures available in the Cambridge Structural Database for hydrates of /8-lactams reveals that the water molecules in the crystal structures are not in sufficient proximity (within the sum of van der Waals distance) to the reactive center on the /8-lactam core to bring about reaction. For cases where water molecules are in close proximity to the reactive centre, further rationalization can be made in terms of the relative orientation of reactants and the steric hindrance of the initial approach of the water, or the low degree of conformational flexibility in the crystal. This type of calculation on cefadroxil monohydrate (reaction scheme shown in Figure 3.6) which contains a water molecule within van der Waals distance of the reactive /8-lactam carbonyl group, has shown that several atoms would lie outside of the molecular surface formed by the rest of the crystal, indicating steric clashes. 

Molecular orbital treatment of a complete bicyclic 3-cephem nucleus (8) came in a comparison with 2-cephems (9) and cephams (10). EH calculations (Boyd, 1973) showed that in terms of net atomic charge on the carbonyl carbon and in terms of the overlap population of the C—N bond that is broken during acylation the p-lactam ring of the 3-cephem nucleus should be more reactive than that of 9 and 10. Correspondingly, the A -cephalosporins are biologically active, whereas the A -cephalo-sporins and dihydrocephalosporins usually have little or no activity. 

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