where the vector 𝒄 𝟏 (𝒄 𝟐 ) identify the initial (final) position of each atom. The 𝛼, 𝛽, and 𝛾 angles, which represent extrinsic rotations about the fixed x, y, and z axes (described by the corresponding 3×3 𝑹 𝒙 , 𝑹 𝒚 , 𝑹 𝒛 matrices), respectively, as well as the three components defining the unit vector 𝒅 for the rigid displacement, were obtained from a uniform random number generator. As this procedure is intended to simulate the stochastic collisional process leading to the formation of the excimer in solution, the translation size was conveniently adjusted using the scaling factor 𝑓, which ensures that the minimum interatomic distance between the two monomers equals the sum of their corresponding van der Waals radii. Uniform random sampling is equivalent to assigning equal probabilities to all collision events. However, this may not reproduce the actual probability distribution for different intermolecular pathways in real solutions. Notwithstanding this limitation, our approach allows us to sample the conformational space for the approaching pyrene molecules straightforwardly. Moreover, our interest is in the relaxed excimer conformers, and the current step aims only to provide a set of reasonable initial geometries for the subsequent optimization. We also note that intramolecular motions are neglected, focusing only on the relative orientation of the monomers; the relevant coordinates turn out to be entirely analogous to those employed for stacked base pairs in nucleic acids. Indeed, rigid displacements along the long and short molecular axes, as well as in the vertical direction, correspond to the slide, shift, and rise coordinates, respectively. In contrast, rotations about the long, the short, and the vertical axes are defined by the roll, tilt, and twist angles, respectively (we considered the geometrical axes of a given monomer to be well approximated by its principal axes). Therefore, the same terminology is occasionally borrowed in the following.