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A precise solution to the Lagrangian mechanics of the segmented, flexible, polarizable, and fluctuating "O2-∶H+/p-O2-" H-bond in water ice with the involvement of the short-ranged real-bond exchange interaction, non-bond van der Waals interaction, and the Coulomb repulsion between the unevenly-bound bonding "-" and nonbonding "∶" electron pairs.Matching to the measured Raman frequencies, the respective force constants are determined.It is verified that the thermodynamic disparity of the segments and the inter-electron-pair Coulomb repulsion govern the H-bond asymmetric relaxation dynamics and the anomalies of H2O.