The dependence of the total electron energy density at the (3,-1) critical point (CP) of the H ... O interaction against the interatomic distance (E-CP) has been obtained by the addition of the local electron kinetic (G(CP)) and potential (V-CP) energy densities dependences (E-CP=G(CP)+V-CP) for a set of 83 X-H ... O hydrogen bonds (X=C, N, O). The E-CP function has been related to the interaction potential by means of a proportionality relationship U=-upsilon . E-CP, upsilon being a positive constant in volume units. Based on the G(C)P and V-CP functionalities, the proposed H ... O interaction potential has been successfully checked against several physical and chemical properties. The behavior of the U function has been compared to Morse and Buckingham-type potentials, leading to an almost perfect matching between all of them when they were constrained to have the same three parameters: the potential well depth U-0, its position r(0), and the curvature of the potential function at r(0). The resulting U(r) function is simply described by the addition of two exponential terms: U(r)=49 100 exp(-3.6r)-11 800 exp(-2.73r), where U is in kJ/mol and r is the H ... O distance in A.