The electron pair density, in conjunction with the definition of an atom in a molecule, enables one to determine the average number of electron pairs that are localized to each atom and the number that are formed between any given pair of atoms. Thus, it is through the pair density that the Lewis model of electronic structure finds physical expression. The pairing of electrons is a consequence of the Pauli principle whose effect is made manifest through the creation of the Fermi hole. The density describing the spatial distribution of the Fermi hole for an electron of given spin determines how the density of that electron is spread out in space, excluding an equivalent amount of same-spin density. The averaging of the Fermi density over single atoms or pairs of atoms determines the corresponding contributions to the total Fermi correlation. It is these terms that yield the localization and delocalization indices that determine the intra- and interatomic distribution of electron pairs that enables one to compare the pairing predicted by theory with that of a Lewis structure. The agreement is best at the Hartree−Fock level, where the Fermi hole is the sole source of correlation between the electrons. The introduction of the remaining correlation, the Coulomb correlation, disrupts the sharing of electron pairs between the atoms, and its effect is therefore, most pronounced for shared interactions. For example, Coulomb correlation reduces the number of shared pairs in N2 from the Hartree−Fock value of three to just above two. In ionic systems, the electrons are strongly localized within each atomic basin and the effect of Coulomb correlation on the atomic pairing is minimal, approaching zero over each of the atomic basins, as it does for the total molecule.

The in situ pressure acting on the surface of an open system at the atomic level is defined and determined by the virial theorem for a proper open system, one whose spatial boundary and equations of motion are determined by the principle of stationary action. The quantum pressure is determined by the virial of the force resulting from the electronic momentum flux through the surface of the open system. A scaling procedure is used to demonstrate that the expectation value of the pressure–volume product of a proper open system is proportional to its surface virial. Previous work, in analogy with the classical virial theorem for a contained system, incorrectly relates the pressure to the external forces of constraint acting on a closed system. A neon vise consisting of a chain of three, four or five hydrogen molecules compressed between two neon atoms is used to introduce the quantum definition of pressure and study its effect on the mechanical properties of an atom and on the topology of the electron density. Pressures approaching 160 GPa have been calculated for the vise. The topology of the electron density and the homeomorphism it exhibits with the virial field are found to be invariant to an increase in pressure, the electron density accumulating to an ever increasing extent between all pairs of nuclei which serve as the sole attractors. The virial of the Ehrenfest force acting on the surface of a compressed molecule provides a measure of the increase in the electronic kinetic energy resulting from the applied pressure. The effects of pressure on the intra- and intermolecular bonding are discussed in terms of pressure-induced changes in the electron density and in the mechanical properties of the atoms.

. Can. J. Chem. 72,695 (1994).The linear combination of Gaussian-type orbitals -density functional theory (LCGTO-Dm) approach is used to study geometries and hyperfine structures of a set of neutral radicals. Each of the title molecules is investigated by means of local density approximation calculations, and using the Becke-Perdew and Perdew-Wang-Perdew corrections to the exchange and correlation functionals. The effects of local vs. non-local potentials and of various basis sets are investigated. Total densities and unpaired spin densities are compared. The isotropic couplings are found to be very dependent on the type of exchange functional used, whereas the anisotropic couplings are relatively insensitive to the choice of basis set and functional. In most cases, the Perdew-Wang exchange corrections provide isotropic couplings in satisfactory agreement with experiment.