Invariant Kernel for Molecular systems. As we are considering MD simulations at equilibrium without exchange of matter or energy with the environment, and without interactions with an external field, sampling the conformational space of the system is invariant to global rotations and translations of the molecular frame. Consequently, we require a kernel k(•, •) that is invariant to those symmetries. Since we would like to quantify some metric for distance within the space of possible molecular conformations, removing these symmetries in the space of all possible molecular configurations is a necessary requirement for a diversity metric that is accurate and efficient.