We analyze fermionic entanglement and correlation measures in the ground and the low temperature thermal state of the water molecule as a function of the internuclear distance in the context of the full configuration interaction approach. The aim is to obtain a general entanglement based characterization of the electronic eigenstates. We consider first the spin-up – spin-down partition and the associated Schmidt decomposition, examining the total up-down entanglement of the electronic wave function. We then consider the one- and two-body entanglement derived from the one- and two-body reduced density matrices (DMs), which measure the deviation of the state from a Slater Determinant (SD). All blocks of these DMs are examined. We also introduce and analyze new measures like the up-down two-body mutual information, which measures the up-down correlation at the two-body level, and two types of two-body negativities, the latter detecting and measuring the inner'' entanglement of the reduced two-body DMs, i.e., their deviation from a convex mixture of SDs. Finally, the dissociation limit is also analyzed, considering both the exact ground state (GS) as well as the thermal state in the zero temperature limit, representing the projector onto theGS band’’ of almost degenerate lowest lying eigenstates.