Interactions in liquids, when addressed from classical point of view, come mostly in two categories, short ranged dispersion interactions such as the canonical Lennard-Jones interactions, and long ranged Coulomb interactions . These interactions produce very dierent forms of local order, the former being close to perfect disorder, while the charge order of the latter leads to the peculiar checker board type form of local order . This is unmistakably translated into the very dierent forms of the corresponding static pair correlation functions. A short reminder can be found in Section I in the Supplementary Information (SI). When considering polar molecules, with an inner distribution of partial charges, charge order still dominates the local order, although this is usually explained in terms of dipolar order. The quantum origin of interactions becomes apparent when considering hydrogen bonding molecules, especially when spectroscopic methods are used to investigate their local structures . Even though classical models of liquids such as water are quite good for describing the local structure, as demonstrated by the comparison of the pair correlation functions obtained from radiation scattering and computer simulations , it is not obvious to appreciate which of the full quantum or classical approaches is better to understand all the problems posed by the structure of hydrogen bonding liquids. For instance, the tetrahedrality of the local hydrogen bonding structure of water has been at the center of many investigations, with issues related to two liquids description , density maximum anomaly or hidden second critical point ]. Another important issue is the contradictory picture of water being special because of its local order , or no dierent than any other liquid of small molecules .