(105e) Analytical Model for the Van Der Waals Interaction Energy between Faceted Nanoparticles

While advancements in experimental techniques have allowed the synthesis and utilization of faceted nanoparticles in many applications including plasmonics, colloidal crystals, and catalysis, there is currently no tractable model for the pairwise interaction energies between such particles as a function of their relative position and orientation. Here, we develop an analytical expression for the van der Waals energy of interaction between faceted nanoparticles using several geometric approximations that reduce the six-dimensional volume integral over the interatomic potential energies into a two-dimensional integral with a closed-form solution. Comparisons of the energies obtained from the analytical model with those from the atomistic calculations demonstrate that these geometric approximations do not lead to significant deviations in the computed energies. Our analyses show that the model provides good accuracy for all relevant interparticle configurations and for diverse shapes including nanocubes, cubic rods, triangular prisms, and square pyramids, while providing tens of orders of magnitude improvement in computational efficiency compared to atomistic calculations. To make the method more accessible, we have also developed a graphical user interface application implementing the analytical model for nanocubes. We expect that this model will lead to a significant acceleration in future investigations of faceted nanoparticles, especially in simulations of particle assembly that necessitate rapid calculations of their interaction energies.