Bond paths linking two bonded hydrogen atoms that bear identical or similar charges are found between the ortho-hydrogen atoms in planar biphenyl, between the hydrogen atoms bonded to the C1-C4 carbon atoms in phenanthrene and other angular polybenzenoids, and between the methyl hydrogen atoms in the cyclobutadiene, tetrahedrane and indacene molecules corseted with tertiary-tetra-butyl groups. It is shown that each such H-H interaction, rather than denoting the presence of "nonbonded steric repulsions", makes a stabilizing contribution of up to 10 kcal mol(-1) to the energy of the molecule in which it occurs. The quantum theory of atoms in molecules-the physics of an open system-demonstrates that while the approach of two bonded hydrogen atoms to a separation less than the sum of their van der Waals radii does result in an increase in the repulsive contributions to their energies, these changes are dominated by an increase in the magnitude of the attractive interaction of the protons with the electron density distribution, and the net result is a stabilizing change in the energy. The surface virial that determines the contribution to the total energy decrease resulting from the formation of the H-H interatomic surface is shown to account for the resulting stability. It is pointed out that H-H interactions must be ubiquitous, their stabilization energies contributing to the sublimation energies of hydrocarbon molecular crystals, as well as solid hydrogen. H-H bonding is shown to be distinct from "dihydrogen bonding", a form of hydrogen bonding with a hydridic hydrogen in the role of the base atom.

The evidence for the stabilizing nature of the H-H bonding in planar biphenyl is succinctly reviewed. The stabilizing nature of the H-H bonding is revealed through a comparison of the atomic energy of every atom in planar biphenyl with the same atom in the twisted equilibrium structure. It is shown that the barrier to rotation via the planar transition state is the net resultant of a stabilisation of the four ortho-hydrogen atoms (by 8 kcal/mol each), a stabilisation of the two para-carbon atoms (by 3 kcal/mol each) and by the dominant destabilisation of the two carbon atoms joining the two rings-the two junction carbon atoms-(by 22 kcal/mol each). The energetic stabilisation of the four ortho-hydrogen atoms is further shown to be in large proportion due to the formation of the hydrogen-hydrogen interatomic surface. Furthermore, neither the ''bond order'' between the two junction carbon atoms nor the total electron delocalisation between the two rings exhibit a significant change in going from the planar to the twisted equilibrium geometry. These findings are in contrast with the classical view of a balance between ''steric non-bonded repulsion'' and better electron delocalisation as a function of the twist dihedral angle. Similar conclusions have been recently reached by Pacios and Gómez through a study of the electrostatic potential at the position of the hydrogen nuclei.

The cooperative effects of hydrogen bonding in small water clusters (H2 O)n (n=3-6) have been studied by using the partition of the electronic energy in accordance with the interacting quantum atoms (IQA) approach. The IQA energy splitting is complemented by a topological analysis of the electron density (ρ(r)) compliant with the quantum theory of atoms-in-molecules (QTAIM) and the calculation of electrostatic interactions by using one- and two-electron integrals, thereby avoiding convergence issues inherent to a multipolar expansion. The results show that the cooperative effects of hydrogen bonding in small water clusters arise from a compromise between: 1) the deformation energy (i.e., the energy necessary to modify the electron density and the configuration of the nuclei of the isolated water molecules to those within the water clusters), and 2) the interaction energy (Eint ) of these contorted molecules in (H2 O)n . Whereas the magnitude of both deformation and interaction energies is enhanced as water molecules are added to the system, the augmentation of the latter becomes dominant when the size of the cluster is increased. In addition, the electrostatic, classic, and exchange components of Eint for a pair of water molecules in the cluster (H2 O)n-1 become more attractive when a new H2 O unit is incorporated to generate the system (H2 O)n with the last-mentioned contribution being consistently the most important part of Eint throughout the hydrogen bonds under consideration. This is opposed to the traditional view, which regards hydrogen bonding in water as an electrostatically driven interaction. Overall, the trends of the delocalization indices, δ(Ω,Ω'), the QTAIM atomic charges, the topology of ρ(r), and the IQA results altogether show how polarization, charge transfer, electrostatics, and covalency contribute to the cooperative effects of hydrogen bonding in small water clusters. It is our hope that the analysis presented in this paper could offer insight into the different intra- and intermolecular interactions present in hydrogen-bonded systems.

The Lewis electron pair concept and its role in bonding are recovered in the properties of the electron pair density and in the topology of the Laplacian of the electron density. These properties provide a bridge with the quantum mechanical description of bonding determined by the Feynman, Ehrenfest, and virial theorems, bonding being a consequence of the electrostatic forces acting within a molecular system. q

X-ray charge density was determined and analyzed for two polymorphs of the Nmethylpyridinium salt of the tetrachlorosemiquinone radical anion and its analogous closed-shell relatives, tetrachloroquinone (chloranil) and tetrachlorohydroquinone. The study, which was combined with calculations of electron delocalization, electrostatic potentials, and aromaticity, presents details of electronic structure of the semiquinoid ring. This comparative study reveals that the negative charge is delocalized over the entire semiquinone radical, and that the chlorine substituents play a crucial role in its stabilization through induction effect. In general, the semiquinoid ring has partially delocalized π-electrons and is approximately halfway between a quinoid and an aromatic ring. In the orthorhombic polymorph with stacks of equidistant radicals electron density between the rings of almost 0.05 e Å-3 and four (3,-1) saddle points between the contiguous rings were found. In the diamagnetic triclinic polymorph, comprising strongly bound radical dimers (with significant covalent character-'pancake bond'), maximum electron density between the rings exceeds 0.095 e Å-3 and multiple (3,-1) critical points are found. However, only negligible electron density is observed between the dimers. Thus, in the radical anion stacks spin coupling, along with dispersive and polarization effects, defines interplanar distance and magnetic behaviour, whereas intermolecular electrostatic potential determines the ring offset.