On the adiabatic separation of the vibrational variables of a hydrogen-bonded AHA fragment with a symmetric double-well potential

The adiabatic separation of the vibrational variables of a hydrogen-bonded AHA fragment with a symmetric double-well potential is considered using two approaches. In the first approach the A…A stretch vibration is slow in comparison to the proton vibration. It is applicable to the energy level calculations of an AHA fragment with a potential barrier of arbitrary height. In the alternative approach the proton is considered to be a “slow” subsystem. This approach appears to be of limited applicability. For an AHA fragment with a symmetric double-well potential the Born-Oppenheimer criterion is shown to contain the frequency corresponding to the proton 0→2 transition in both approaches.