Topological properties of the electrostatic potential in weak and moderate N...H hydrogen bonds

The topological analyses of the electrostatic potential phi(r) and the electron density distribution rho(r) have been performed for a set of 20 neutral complexes with weak and moderate N...H bonds. In all cases, a zero flux surface of the electrostatic potential containing a saddle point analogous to the bond critical point of the electron density distribution is observed. These surfaces define an equivalent of the atomic basin of rho(r) for the electrostatic potential, which exhibits zero net charge and can be regarded as an electrostatically isolated region if its volume is finite. The phi(r) and rho(r) zero flux surfaces divide the hydrogen-bonding region in three parts, being the central one related to the electrostatic interaction between donor and acceptor. This central region exhibits a relative size of approximately 13-14% of the N...H distance dNH, it belongs to the outermost shell of the nitrogen and is mainly associated with its lone pair. Topological properties of both rho(r) and phi(r), as well as the electron kinetic (G) and potential (V) energy densities, show similar dependences with dNH at both bond critical points (phi-BCP and rho-BCP). Phenomenological proportionalities between the rho(r) curvatures and G and V are also found at the electrostatic potential critical point. The curvatures of the electrostatic potential, which are interpreted in terms of the electrostatic forces in the bonding region, present the same exponential dependency as the electron density distribution, to which they are related by Poisson's equation.