Impact of distributions on the archetypes and prototypes in heterogeneous nanoparticle ensembles

The magnitude and complexity of the structural and functional data available on nanomaterials requires data analytics, statistical analysis and information technology to drive discovery. We demonstrate that multivariate statistical analysis can recognise the sets of truly significant nanostructures and their most relevant properties in heterogeneous ensembles with different probability distributions. The prototypical and archetypal nanostructures of five virtual ensembles of Si quantum dots (SiQDs) with Boltzmann, frequency, normal, Poisson and random distributions are identified using clustering and archetypal analysis, where we find that their diversity is defined by size and shape, regardless of the type of distribution. At the complex hull of the SiQD ensembles, simple configuration archetypes can efficiently describe a large number of SiQDs, whereas more complex shapes are needed to represent the average ordering of the ensembles. This approach provides a route towards the characterisation of computationally intractable virtual nanomaterial spaces, which can convert big data into smart data, and significantly reduce the workload to simulate experimentally relevant virtual samples.