The PI + IP abstractions of GCNN and the unique design of a weight matrix W ij using information from both 1 P i and 1 P j in the PI operation are the core of PiNet. This is illustrated in the lower part of Fig. colored in red. More details about the architecture of PiNet, for instance, the generation of the radial basis function e ij can be found in the previous PiNN publication. In PiNet2, the vectorial atomic property, 3 P ix , contains an additional dimension x accounting for directional information. Accordingly, the vecotrial pairwise interaction 3 I ijx does not only include the pairwise distance but also the bond vector 3 r ijx , i.e.