MP2/6-311++G(d,p) and B3LYP/6-311++G(d,p) quantum calculations are used to study the formamide-formic acid complex (FFAC), a system bound by two hydrogen bonds, N--H...O and O--H...O, that forms a bond ring at equilibrium. When the intermolecular separation between monomers R increases, this ring opens at a distance for which the weaker N--H...O bond breaks remaining the stronger O--H...O bond. The computational study characterizes that process addressing changes of interaction energy DeltaE, structure and properties of the electron density rho(r) as well as spatial distributions of rho(r), the electrostatic potential U(r), and the electron localization function eta(r). It is shown that the spatial derivatives of DeltaE, the topology of rho(r), and qualitative changes noticed in U(r) = 0 isocontours allow to identify a precise distance R for which one can say the N--H...O hydrogen bond has broken. Both levels of theory predict essentially the same changes of structure and electron properties associated to the process of breaking and virtually identical distances at which it takes place.