13- Lactam overlap populations

In addition to attempts to correlate hydrolysis rates with P-lactam C—N and C=0 bond lengths and the degree of P-lactam nitrogen pyramidalisa-tion (Sweet and Dahl, 1970), there have also been reports of the relationship between chemical reactivity and theoretically calculated parameters such as the net atomic charge on the P-lactam carbonyl oxygen, the overlap population of the P-lactam carbonyl and transition state energies (Indelicato et al., 1974 Boyd, 1983 Boyd et al., 1980 Petrongolo et al., 1980). 

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. 

The trends that are apparent in Table VIII are consistent with notions enumerated before. For instance, as the reactivity of the p-lactam ring increases (at least up to a certain point), then the gram-negative activity increases. The charge on the -lactam carbonyl oxygen O9 and the overlap population for the carbonyl bond Cr=09 are both consistent with amide resonance 1 1. Thus, those substituents at the 3 position of the cephem nucleus that tend to favor resonance structure 1 also produce... 

In contrast to the gram-negative case, the V32 relative inhibition coefficients correlate less well with the quantum mechanical indices. The best feature in the ten compound series is the overlap population for the p-lactam carbonyl, (Cg=09). The correlation coefficient r from linear regression is 0.610, and the probability of the null hypothesis being satisfied (F test) is 0.061. 

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