The biological activity of bicyclic beta-lactam antibiotics depends strongly on the absolute configuration of the bridgehead carbon atom. Frelek and co-workers proposed an empirical helicity rule relating the configuration of the bridgehead carbon atom to the sign of the 220 nm band in the electronic circular dichroism (CD) spectrum of beta-lactams. Here we use synthetic organic chemistry, CD spectroscopy, and time-dependent density functional theory (TDDFT) to investigate the validity of this structure-property relationship for eight model compounds. For conformationally flexible beta-lactams, substantial thermal effects are found which must be included in calculations. To this end, we combine TDDFT calculations of CD with full quantum-mechanical Born-Oppenheimer molecular dynamics (MD) simulations for the first time. The CD spectra are sampled with ground-state density functional trajectories of up to 60 ps. The MD simulations show a surprisingly high sensitivity of the CD to the molecular conformation. On the other hand, the relation between CD and thermally averaged structural parameters is much less complex. While the helicity rule does not seem to hold for individual conformers, it is confirmed by the calculations for seven out of eight systems studied if thermally averaged CD spectra and structures are considered. Since thermal effects on CD can be larger than typical inherent inaccuracies of TDDFT, our results emphasize the need for a systematic treatment of conformational dynamics in CD calculations even for moderately flexible systems. Temperature-dependent CD measurements are very useful for this purpose. Our results also suggest that CD spectroscopy may be used as a sensitive probe of conformational dynamics if combined with electronic structure calculations.
In the present work, the validity of the helicity rule relating the absolute configuration of the bridgehead carbon atom in bicyclic β-lactams to the sign of the 220 nm band observed in their electronic circular dichroism (ECD) spectra is examined for ring-expanded cephalosporin analogues. To this end, a series of model compounds with a seven-membered ring condensed with the β-lactam unit was synthesized. A key step of their synthesis was either the ring-closing metathesis (RCM) or the free radical cyclization leading to the seven-membered ring with an S, O, or C atom at the 6 position in the bicyclic skeleton. To investigate the scope and limitations of the simple, empirically established helicity rule, a combination of ECD spectroscopy, variable-temperature ECD measurements, X-ray analysis, and time-dependent density functional theory (TD-DFT) calculations was used. A comparison of the experimental ECD spectra with the spectra simulated by TD-DFT calculations gives a reasonable interpretation of the Cotton effects observed in the 240-215 nm spectral range. The results suggest that the helicity rule does not apply to the investigated compounds because of the planarity of their amide chromophore. Thus, these compounds do not constitute an exception to the rule that was established for bi- and polycyclic β-lactams with the nonplanar amide chromophore only.
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