Retrieving interaction potentials from the topology of the electron density distribution: The case of hydrogen bonds

The dependence of the total electron energy density at the (3,−1) critical point (CP) of the H…O interaction against the interatomic distance ${\mathrm{(E}}^{\mathrm{CP}})$ has been obtained by the addition of the local electron kinetic ${\mathrm{(G}}^{\mathrm{CP}})$ and potential ${\mathrm{(V}}^{\mathrm{CP}})$ energy densities dependences ${\mathrm{(E}}^{\mathrm{CP}}{\mathrm{=G}}^{\mathrm{CP}}{\mathrm{+V}}^{\mathrm{CP}})$ for a set of 83 X-H…O hydrogen bonds (X=C, N, O). The $E^{\mathrm{CP}}$ function has been related to the interaction potential by means of a proportionality relationship ${\mathrm{U=-\upsilon \cdot E}}^{\mathrm{CP}},$ υ being a positive constant in volume units. Based on the $G^{\mathrm{CP}}$ and $V^{\mathrm{CP}}$ functionalities, the proposed H…O interaction potential has been successfully checked against several physical and chemical properties. The behavior of the U function has been compared to Morse and Buckingham-type potentials, leading to an almost perfect matching between all of them when they were constrained to have the same three parameters: the potential well depth $U_0,$ its position $r_0,$ and the curvature of the potential function at $r_0.$ The resulting $\mathrm{U(r)}$ function is simply described by the addition of two exponential terms: $\text{U(r)=49\hspace{0.05em}100\hspace{0.05em}}\exp \text{(−3.6r)−11\hspace{0.05em}800\hspace{0.05em}}\exp \text{(−2.73r),}$ where U is in kJ/mol and r is the H…O distance in Å.