Computational scheme to obtain bond softening index lambda, defined within the conceptual DFT, has been obtained with the use of the reaction fragility (RF) concept. Numerical results were obtained with the RF spectra for the proton transfer reaction in formamide molecule (H2NCHO) and the water assisted proton migration in H2NCHO center dot H2O complex. Double proton transfer reaction in the formamide dimer, (H2NCHO)(2), and its analogues, (H2NCHS)(2) and (H2NCHO)center dot(H2NCHS), have also been studied. The atomic and bond RF spectra clearly describe the density reorganization in the backbone of each molecule, resulting from proton displacement in the systems. The obtained softening indices have been calculated for hydrogen atoms in the reactant state (RS) and product state (PS) configuration. These indices provide fine characteristics for local sensitivity of the reacting system to a disturbance of the position of a chosen atom.