by Yevhen Horbatenko and Sergei Vyboishchikov
Proton sponge is a trade name for a particular compound which is a strong base, i.e. it likes to bond to protons.
The proton sponge compounds are of particular interest to me because they work by the proton forming a strong hydrogen bond between two nitrogen atoms.
The three potential energy curves above correspond to the three distinct cases of hydrogen bonding: i) strong hydrogen bond, ii) low barrier hydrogen bond, iii) weak hydrogen bond. [They arise naturally in my simple model of H-bonds.]
I found two results of the authors particularly interesting.
First, the shape of the potential energy curve [and specifically the presence or absence of a barrier] depends on the level of quantum chemistry or density functional used in the calculation.
Second, the paper has a nice physical insight for strong hydrogen bonds that I have not seen before. The vibrational energy levels have spacing similar to that for a square well potential of with width comparable to the donor-acceptor distance. Specifically, the energy of the n-th level is proportional to n^2, whereas for a harmonic potential it is proportional to (n-1). This reflects how anharmonic the potential is.