Relaxation of the inter- and intra-molecular interactions for the hydrogen bond (O:H-O) between undercoordinated molecules determines the unusual behavior of water nanodroplets and nanobubbles. However, probing such potentials remains unreality. Here we show that the Lagrangian solution [Huang et al., J. Phys. Chem. B, 2013. 117: 13639] transforms the observed H-O bond (x = H) and O:H nonbond (x = L) lengths and phonon frequencies (dx, x) [Sun et al., J. Phys. Chem. Lett., 2013. 4: 2565] into the respective force constants and bond energies (kx, Ex) and hence enables the mapping of the potential paths for the O:H-O bond relaxing with water cluster size. Results show that molecular undercoordination not only reduces the molecular size (dH) with enhanced H-O energy from the bulk value of 3.97 to 5.10 eV for a H2O monomer, but also enlarges the molecular separation (dL) with reduced O:H energy from 95 to 35 meV for a dimer. The H-O energy gain raises the melting point from bulk value 273 to 310 K for the skin and the O:H energy loss lowers the freezing temperature from bulk value 258 to 202 K for 1.4 nm sized droplet, by dispersing the quasisolid phase boundaries.