Hierarchical bounding structures for efficient virial computations: Towards a realistic molecular description of cholesterics

TL;DR

This paper introduces a hierarchical bounding structure method to efficiently compute virial coefficients for complex particles, enabling detailed studies of cholesteric liquid crystal phases with high accuracy and computational speed.

Contribution

The authors develop a novel bounding volume hierarchy approach that accelerates virial calculations for complex particles, facilitating the analysis of cholesteric self-assembly in molecular systems.

Findings

Demonstrated sub-logarithmic scaling of the method with particle resolution.

Quantitative evidence of phase handedness inversion near 45° particle thread angle.

Revealed the link between microscopic structure and helical twisting power.

Abstract

We detail the application of bounding volume hierarchies to accelerate second-virial evaluations for arbitrary complex particles interacting through hard and soft finite-range potentials. This procedure, based on the construction of neighbour lists through the combined use of recursive atom-decomposition techniques and binary overlap search schemes, is shown to scale sub-logarithmically with particle resolution in the case of molecular systems with high aspect ratios. Its implementation within an efficient numerical and theoretical framework based on classical density functional theory enables us to investigate the cholesteric self-assembly of a wide range of experimentally-relevant particle models. We illustrate the method through the determination of the cholesteric behaviour of hard, structurally-resolved twisted cuboids, and report quantitative evidence of the long-predicted phase handedness inversion with increasing particle thread angles near the phenomenological threshold value of $45^\circ$. Our results further highlight the complex relationship between microscopic structure and helical twisting power in such model systems, which may be attributed to subtle geometric variations of their chiral excluded-volume manifold.