Principle of Chirality Hierarchy in Three-Blade Propeller Systems

There are different kinds of molecular chirality, such as zero-dimensional point chirality, one-dimensional axial chirality, 2D planar chirality, and 3D chirality. When they coexist in one system, such as in helical structures of proteins and DNA, they form a chirality hierarchy. Earlier, we showed that the chirality propensity of a lower level in a hierarchy is dictated by that of a higher level and henceforth proposed the Principle of Chirality Hierarchy. In this work, we confirm the validity of this principle in the three-blade propeller molecular system. We consider different choices for the three components of a propeller and systematically investigate the dependence of the stereoisomeric energy difference on these choices. Our results show that the preference of the 0D chirality of a functional group in the propeller system is determined by the 1D chirality, and homochirality is also a remarkable feature for this system. We also unveiled that there exists positive cooperativity and electrostatic interactions play the dominant role in determining the stereoisomeric stability difference while the roles for exchange-correlation and steric effects are minor but indispensable. The establishment and confirmation of the Principle of Chirality Hierarchy from this work should find important applications in asymmetric synthesis, macromolecular assembly, and many others.