We also calculated the atomic multipole moments through Hirshfeld partition approach, a cheaper scheme for comparison. As all the atomic multipole moments are fitted using the equivariant E3NN model, the rotation symmetry of these tensors is already satisfied by construction. Therefore, their definition does not rely on predefined local frames that rotates with the molecule as done in previous work. The T ij tu refer to the multipole interaction tensor between atom i with multipole moments at rank t and j with multipole moments at rank u,