Symmetry Breaking: Case Studies with Organic Cage-Racemates

Abstract

Symmetry is a pervasive phenomenon spanning diverse fields, from art and architecture to mathematics and science. In the scientific realms, symmetry reveals fundamental laws, while symmetry breaking─the collapse of certain symmetry─is the underlying cause of phenomena. Research on symmetry and symmetry breaking consistently provides valuable insights across disciplines, from parity violation in physics to the origin of homochirality in biology. Chemistry is particularly rich in symmetry breaking studies, encompassing areas such as asymmetric synthesis, chiral resolution, chiral structure assembly, and so on. Across different disciplines, a well-defined methodology is fundamental and necessary to analyze the symmetry or symmetry breaking nature behind the phenomenon, enabling researchers to uncover the underlying principles and mechanisms. Basically, three key points underpin symmetry-related research: the scale-dependency of symmetry/symmetry breaking, the driving force behind symmetry breaking phenomena, and the properties arising from symmetry breaking.

This Account will focus on the three aforementioned key points elucidated with organic cages as proof-of-concept models, as organic cages exhibit shape-persistent 3D molecular frameworks, well-defined molecular motion, and a high propensity for crystallization.

First, we examine racemization processes of organic cages with dynamic molecular motions to illustrate that symmetry and symmetry breaking are time-scale-dependent. Specifically, the racemization, driven by molecular motion, is influenced by hydrogen bonding and the rigidity of the cage framework, which may or may not be observable within the experimental temporal scale. This determines whether the enantiomeric excess system, namely, the symmetry broken system, can be detected experimentally. We also investigate the hierarchical structures self-assembled by racemic organic cages, demonstrating that symmetry and asymmetry manifest differently across spatial scales, from molecular to supramolecular and macroscopic levels. Second, we discuss the driving force behind spontaneous chiral resolution─a classic symmetry-breaking event during crystallization─from a thermodynamic perspective. We suggest that racemic compounds, compared to conglomerates, are more entropy-favored, explaining their greater prevalence in nature. Spontaneous chiral resolution can take place only when a favorable enthalpy compensates for unfavorable entropy. In conglomerates composed of organic cages, strong intermolecular interactions along the screw axes provide the necessary compensation. Finally, we explore the unique properties that emerge from symmetry-broken molecular packing within crystals of cage racemates, such as second-harmonic generation and piezoelectricity. It turns out that the symmetry operation in molecular packing plays a critical role in determining material properties. By comprehensively analyzing symmetry and symmetry-breaking in organic cage racemates, this Account provides insights into symmetry-related phenomena across scientific disciplines. It also paves the way for designing novel materials with tailored properties for applications in optics, electronics, and beyond.