Fig. 1: Variables used to describe pairs of particles with anisotropic shapes and interactions.
From: Machine-learned coarse-grained potentials for particles with anisotropic shapes and interactions
a In the `rigid particle' approximation, the state of a pair of particles is defined in terms of ΩIJ = (θ, ϕ, 0), which characterizes the direction of the vector RIJ = RJ − RI from the origin of particle I to the origin of particle J, and the orientation Ωi = (αi, βi, γi) of the body-fixed axes \(({\hat{{\boldsymbol{x}}}}_{i}({\alpha }_{i},{\beta }_{i},{\gamma }_{i}),{\hat{{\boldsymbol{y}}}}_{i}({\alpha }_{i},{\beta }_{i},{\gamma }_{i}),{\hat{{\boldsymbol{z}}}}_{i}({\alpha }_{i},{\beta }_{i},{\gamma }_{i}))\) of particle i = I, J relative to a space fixed set of axes (XYZ). b Geometrical definition of classic Euler angles (α, β, γ). c Schematic representation of a pair of spherical colloids with a patterned surface in the fine-grained (FG) representation. The angular variables θ1,\({\theta }_{2}\in \left[0,2\pi \right]\) are uniformly sampled to extract the potential energy landscapes shown as 3D plots in Figs. 2 and 4.
