Flexible geometric symmetry

A unique series of monodendrons possessing extraordinary symmetry (i.e., D3h) and no flexible methylene linkages has been recently reported by Neenan and Miller [119]. These dendrons consist of geometric tiers of aryl groups linked at... 

Elementary geometry and the associated theory of point group symmetry are still the main mathematical tools of stereochemistry, despite the increasing importance of flexible molecules that are not adequately representable by rigid geometric models [10, 11, 35]. 

Although the geometrical parameters, in particular the Cu-Cu and S-S distances, are quite different between the 1V54B and 1V540 models (Fig. 30.3a), the shapes and symmetries of the Ou and Ku RAMOs are equivalent to each other. This orbital similarity results in the similarity in the electronic structures between two models. It indicates that the Cua site can transfer electrons despite the distortion of the diamond core, implying that the Cua site can be regarded as a flexible electron mediator. This flexibility is useful for the incorporation of the Cua site to protein for electron transfer inside the protein. In the previous study [23], we exhibited that heme a in CcO can also keep the delocalized electronic structure in spite of the deformation of the porphyrin ring. These results indicate that metal cofactors, which are involved in the electron transfer in proteins, have such robustness of the delocalized state. 

However, compound II can be converted into toluene by [1,3] or [1,7] hydrogen shift. Under thermal conditions, both of these rearrangements are symmetry forbidden in the suprafacial mode and geometrically forbidden in the antarafacial mode. It should be noted that antarafacial [1,7] hydrogen shift can occur in flexible systems. But in rigid systems it also becomes geometrically forbidden. 

By combining classical samplings with quantum chemistry semiempirical TDHF calculations the impact of dynamic fluctuations on the first hyperpolarizability of helical strands has been evidenced . In particular, these fluctuations are responsible for relative variations of 20% in the hyper-Rayleigh responses in both pyridine-pyrimidine (py-pym) and hydrazone-pyrimidine (hy-pym) strands. Dynamical disorder has an even more important impact on the electric field-induced second harmonic generation responses, whose variations can reach 2 (py-pym) or 5 (hy-pym) times their mean value. These results demonstrate that geometrical fluctuations have to be taken into account for a reliable description of the second-order NLO properties in flexible structures such as helical strands. This work has also highlighted the relationships between the nature of the unit cell and the helical conformation of foldamers and their second-order NLO responses. In particular, the value of the hyper-Rayleigh depolarization ratio, which is characteristics of octupolar symmetry, is related to the helix periodicity, of three unit cells per turn in both compounds. 

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