Tunneling Dynamics for Two Reaction Coordinates

Because we are dealing with double proton transfer, we need a more general Hamiltonian than Eq. (29.20). Following the approach introduced in the preceding section, we can construct such a Hamiltonian as the sum of two local Hamiltonians describing the transfer of each of the protons together with a proton-proton coupling  

For the time being we ignore these modes and use a Hamiltonian based on the potential (29.11) 

The two pathways have parts from MIN to (not illustrated) in common. 

The tunneling probability at T = 0 is proportional to exp[—S/(0)] to compare the contributions of the ID and 2D paths to this probability, we calculate the respective actions after their bifurcation. Since at T = 0 the energy = 0 is an integral of motion, the corresponding actions are given by [39, 40] 

The contribution of the coordinate is formally included as an effective mass = 1 + Am(Xp), where the extra term 

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