Here we present 1,000 structures each of a water monomer, water dimer, Zundel cation and bulk water used to train tensorial machine-learning models in Phys. Rev. Lett. 120, 036002 (2018). The archive entry contains files in extended-XYZ format including the structures and several tensorial properties: for the monomer, dimer and Zundel cation, the dipole moment, polarizability and first hyperpolarizability are included, and for bulk water the dipole moment, polarizability and dielectric tensor are given.