Hamiltonian for a dimer approaching a surface

[AllenFaust]

Hi! it's been a day since I have started this problem. I was wondering how I could arrive to this Hamiltonian?
And I'm a bit at a lost on how exactly to derive this? I hope anyone can help me with this, even a suggestion of good starting point would be much appreciated.

Basically the problem is to derive a hamiltonian for the system here.

Regarding this, I'm currently thinking of having a set of polar and azimuthal terms cancel out and thus leading to this maybe?

Thank you very much!

 

[DrClaude]

The model appears to assume that the angle between the surface and the dimer is fixed, and neglects angular momentum. The kinetic energy term can be derived starting from two masses parallel to the surface, then separating out center of mass and relative coordinates.