Numerous reports have used the quantum theory of atoms-in-molecules (QTAIM) approach for the study of hydrogen bond (HB) interactions. Unlike the simple monotonically decreasing geometric exponential dependence on hydrogen bond distance such as D(O···H) observed for the electron density at the bond critical points (BCP), the dependence of the Laplacian of the electron density on hydrogen bond distance is a “biphasic” curve with a single maximum. However, the underlying physical phenomenon of this “biphasic” curve has not been rationalized nor explored so far. In principle, the Laplacian of the electron density should provide a wealth of chemical information because it is a sensitive probe for identifying spatial changes of charge concentration not evident in the electron density itself. Nevertheless, this potential for chemical information does not appear to have been fully exploited. There may also be some interesting links between the Laplacian of the electron density and other QTAIM parameters that have not been investigated systematically when it comes to HB interactions. In this report, the importance and utility of the Laplacian of the electron density for the study of HB interactions will be addressed, and various model functions that relate the Laplacian of the electron density and various QTAIM parameters will be presented. It is anticipated that the findings would afford construction of a refined energetics-based classification of HB strengths.