Excluded area computations for non-convex molecules

Abstract

By using methods of computer-aided geometric design (CAGD), we compute explicitly the excluded area for a pair of non-convex molecules obtained by moving a disc of radius h on a circular arc of radius R and amplitude 2α: they are referred to as boomerangs or horseshoes, depending on the value of α. As a result, the excluded area always attains its absolute minimum when the molecules are antiparallel, instead of parallel, a feature that makes them a good candidate to study shape polarity effects in steric interactions. Although the excluded area is in general a rather complicated function of the relative orientation, with α and η ≔ h/R acting as parameters, when η ≪ 1 a remarkably simple formula is obtained. In this limit, the anisotropic part of the excluded area is independent of η.