where 𝐫 + describes the configuration (positions) of the NPs and 𝑑 "# ≡ =𝐫 " -𝐫 # = the separation distance between NP 𝑖 and 𝑗. As we later use this free energy surface 𝑈 )* for computing forces on the NPs to simulate their dynamics, we refer to it as potential energy when discussing it in the context of many-body MD simulations of NPs. Higher-body interactions are expected to play a less important role and are not included in this potential to save computational costs. In fact, we show later that a three-body description of NP-NP interactions is sufficient to capture all known structural phases exhibited by these NPs.