We investigate and provide optimal sets of reaction coordinates for mixed pairs of molecules displaying polar, uniaxial, or spherical symmetry in two and three dimensions. These coordinates are non-redundant, i.e., they implicitly involve the molecules’ symmetries. By tabulating pair interactions in these coordinates, resulting tables are thus minimal in length and require a minimal memory space. The intended fields of application are computer simulations of large ensembles of molecules or colloids with rather complex interactions in a fluid or liquid crystalline phase at low densities. Using effective interactions directly in the form of tables can help bridging the time and length scales without introducing errors stemming from any modeling procedure. Finally, we outline an exemplary computational methodology for gaining an effective pair potential in these coordinates, based on the Boltzmann inversion principle, by providing a step-by-step recipe.

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