Graph–Property Relationships for Complex Chiral Nanodendrimers

Organic, polymeric, and inorganic nanomaterials with radially diverging dendritic segments are known for their optical, physical, chemical, and biological properties inaccessible for traditional spheroidal particles. However, a methodology to quantitatively link their complex architecture to measurable properties is difficult due to the characteristically large degree of disorder, which is essential for observed property sets. Here, we address this conceptual problem using dendrimer-shaped gold particles with distinct stochastic branching and intense chiroptical activity using graph theory (GT). Unlike typical molecular or nanostructured dendrites, gold nanodendrimers are two-dimensional, with branches radially spreading within one plane. They are also chiral, with mirror asymmetry propagating through multiple scales. We demonstrate that their complex architecture is quantitatively described by image-informed GT models accounting for both regular and disordered structural components of the nanodendrimers. Furthermore, descriptors integrating topological and geometrical characteristics of particle graphs provide physics-based analytical relations to the nontrivial dependence of optical asymmetry <i>g</i>-factor on the particle structure. The simplicity of the GT models capable of capturing the complexity of the particle organization and related light-matter interactions enables the rapid design of scalable nanostructures with multiple functions.