Freeform generative design of complex functional structures.

Generative machine learning is poised to revolutionise a range of domains where rational design has long been the de facto approach: where design is practically a time consuming and frustrating process guided by heuristics and intuition. In this article we focus on the domain of flow chemistry, which is an ideal candidate for generative design approaches. We demonstrate a generative machine learning framework that optimises diverse, bespoke reactor elements for flow chemistry applications, combining evolutionary algorithms and a scalable fluid dynamics solver for in silico performance assessment. Experimental verification confirms the discovery of never-before-seen bespoke mixers whose performance exceeds the state of the art by 45%. These findings highlight the power of autonomous generative design to improve the operational performance of complex functional structures, with potential wide-ranging industrial applications.

The electronic structure of benzene from a tiling of the correlated 126-dimensional wavefunction.

The electronic structure of benzene is a battleground for competing viewpoints of electronic structure, with valence bond theory localising electrons within superimposed resonance structures, and molecular orbital theory describing delocalised electrons. But, the interpretation of electronic structure in terms of orbitals ignores that the wavefunction is anti-symmetric upon interchange of like-spins. Furthermore, molecular orbitals do not provide an intuitive description of electron correlation. Here we show that the 126-dimensional electronic wavefunction of benzene can be partitioned into tiles related by permutation of like-spins. Employing correlated wavefunctions, these tiles are projected onto the three dimensions of each electron to reveal the superposition of Kekulé structures. But, opposing spins favour the occupancy of alternate Kekulé structures. This result succinctly describes the principal effect of electron correlation in benzene and underlines that electrons will not be spatially paired when it is energetically advantageous to avoid one another.