Hydrogen bonding Hamiltonian modes

The total Hamiltonian H should include all the vibrational modes involved in the hydrogen bond dynamics, as well as the various couplings taking place between these modes. At last, H would include the relaxation mechanisms. 

Now, recall that for weak hydrogen bonds the high-frequency mode is much faster than the slow mode because 0 m 20 00. As a consequence, the quantum adiabatic approximation may be assumed to be verified when the anharmonic coupling parameter aG is not too strong. Thus, neglecting the diabatic part of the Hamiltonian (22) and using Eqs. (18) to (20), one obtains... 

Fast mode ftth eigenstates of the two moieties a and b harmonic Hamiltonians. Hydrogen-bond bridge nth eigenstates of the two moieties a and b harmonic Hamiltonians. 

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