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Topological analyses of the theoretically calculated electron densities for a large set of 163 hydrogen-bonded complexes show that HX interactions can be classified in families according to X (X=atom or pi orbital). Each family is characterised by a set of intrinsic dependencies between the topological and energetic properties of the electron density at the hydrogen-bond critical point, as well as between each of them and the bonding distance. Comparing different atom-acceptor families, these dependencies are classified as a function of the van der Waals radius r(X) or the electronegativity chi(X), which can be explained in terms of the molecular orbitals involved in the interaction. According to this ordering, the increase of chi(X) leads to a larger range of HX distances for which the interaction is of pure closed-shell type. Same dependencies observed for HO interactions experimentally characterised by means of high-resolution X-ray diffraction data show a good agreement with those obtained from theoretical calculations, in spite of a larger dispersion of values around the expected fitting functions in the experimental case. Theoretical dependencies can thus be applied to the analysis of the experimental electron density for detecting either unconventional hydrogen bonds or problems in the modelling of the experimental electron density.

Stronger than you'd think: Ab initio calculations reveal that hydrogen bonds can lock phosphates into stable gas-phase complexes, showing that hydrogen bonding can overcome anion-anion repulsion. These complexes present a large energetic barrier of dissociation. The stability of the complexes can be explained in terms of the electrostatic interaction in the hydrogen-bond region.

A theoretical study of anionic complexes formed by two partly deprotonated oxoacids joined by hydrogen bonds has been carried out at the MP2 computational level. In spite of the ionic repulsion, local energy minima are found both in the gas phase and in aqueous solution. Electrostatic potential and electron density topologies, and the comparison with neutral complexes formed by oxoacids, reveal that the ionization has no significant effect on the properties of the hydrogen bonds. The stability of the complexes in the gas phase is explained by attractive forces localized in a volume situated in the hydrogen bond and defined as the electrostatic attraction region (EAR) and determined by the topological analyses of the electron density and the electrostatic potential, and by the electric field lines. In solution, the strong anionic repulsion is mostly screened by the effect of the surrounding polar solvent, which only leads to a weak destabilizing interaction in the hydrogen bond region and finally favors the overall stability of the complexes. The anion−anion complexes have been compared with the corresponding neutral ones (as salts or protonated forms), showing that EAR remains unchanged along the series.

A theoretical study on some carboxylic acid dimers formed by positively or negatively charged molecules has been carried out by using DFT methods. The resulting dimers possess either a charge of +2 or -2. In addition, the corresponding neutral complexes have also been considered. The electron density distribution described by the atoms in molecules and the natural bond orbital methods, as well as the electric field maps of the systems, have been analyzed and compared without finding significant differences between the neutral and ionic complexes. The interaction energy along the dissociation path of the charged dimers shows both a local minimum and a local maximum, defining a stability region between them. When this energetic profile is recalculated by removing the repulsion between the charged groups, it resembles to those of the neutral molecules. Hence, the characteristics of the charged dimers are similar to those of the neutral ones: the addition of a repulsion term for the charged groups permits to retrieve the energetic profiles dependence with the distance in the charged system. The interacting quantum atom (IQA) method has been used to calculate the interaction energy terms, including the classic Coulombic term between the whole molecules and the corresponding of the carboxylic acid groups. The IQA results show repulsive electrostatic interactions when the whole molecules are considered in the ionic complexes, but attractive ones between the carboxylic groups in both neutral and ionic complexes.

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.

The effect of the substituent R in the hydrogen bonding properties of FH···FR (R = H, Al, Li, Cl and CCH) complexes has been studied by theoretical calculations. The dependency of the interaction energy with the hydrogen bond distance and R is explained in terms of the topologies of the electron density and the electrostatic potential. A simple model of the hydrogen bond interaction energy, which can be assimilated to an interaction potential, is defined in terms of a stabilizing mutual polarization of the monomers and an overall destabilizing contribution associated with the electron density reorganization when the overlap of the closed shells is large enough. This model shows an excellent agreement with the ab initio interaction energies and is common for all the analyzed complexes. The substituent effect is represented in the model by a single parameter that can be calculated from the electron distribution in the acceptor atom region. The perturbation in the hydrogen bonding interaction induced by the change of R presents a close similarity with that produced by an external electric field of the same order of magnitude than those found in crystalline solids, indicating that both perturbations should play a significant and similar role on the properties of hydrogen bonds in condensed matter.

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