Hydrogen bond
Hydrogen bonds can be intermolecular (occurring between separate molecules) or intramolecular (occurring among parts of the same molecule). Depending on the nature of the donor and acceptor atoms which constitute the bond, their geometry, and environment, the energy of a hydrogen bond can vary between 1 and 40 kcal/mol. This makes them somewhat stronger than a van der Waals interaction, and weaker than fully covalent or ionic bonds. This type of bond can occur in inorganic molecules such as water and in organic molecules like DNA and proteins.
Bond hardening
The second pair of proton peaks (1 eV KER) comes from bond softening of the H ion, which dissociates into a proton and a neutral hydrogen atom (undetected). The dissociation starts at the 3-photon gap and proceeds to the 2ω limit (the lower blue arrow in Fig. 1). Since both the initial and the final energies of this process are fixed by the 1.55 eV photon energy, the KER is also constant producing the two vertical lines in Fig. 2.