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Extracule (centre of mass) and intracule (relative motion) pair densities are reported for the electronic ground states of the first-row hydrides, LiH, BeH, BH, CH, NH, OH and FH. For each type of two-particle coordinate and for each molecule, the radial, longitudinal and transverse densities are evaluated from self-consistent field molecular orbital wavefunctions constructed from 3-21G Gaussian basis sets. The radial intracule density I(r), the longitudinal intracule density L(i)(z) and the longitudinal extracule density L(e)(Z) evolve systematically from double maxima functions in LiH to single maximum functions in FH, whereas the extracule radial density E(R), the transverse extracule density T(i)(b) and the transverse extracule density T(e) (B) exhibit a single maximum in every case. These observations are explained in terms of the ionic character of the bond, the number of electron pairs, the probable orientations of the interelectronic vectors and the orientation of the vectors describing the centre of mass of an electron pair.

Analysis of the partial Fermi hole in the 23S state of helium and the ground states of Li and Be shows that the radius of the Fermi hole increases with the distance of the reference electron from the nucleus, and that there exists a non-zero lower limit for the radius. The limit increases in a regular manner for the two-, and three- and four-electron isoelectronic sequences. The radius of the Fermi hole in the ground states of the Li and Be isoelectronic sequences varies with the atomic number but is independent of the number of electrons. The latter observations stands in contrast to the differences in the sizes of the electron clouds of each isonuclear pair.

A new definition of the Fermi hole in many-electron systems is provided in terms of the distribution function falpha alpha (r12) of the interelectronic distance for electrons with parallel spins. By analogy with the Coulomb hole, the Fermi hole is defined as the difference between the values of f22(r12) derived from the Hartree-Fock and the Hartree wavefunctions. this definition, unlike previous ones, provides a simple picture of the Fermi hole as a function of r12. By assuming that the Hartree and Hartree-Fock orbitals are identical, an analytical formula is derived for the Fermi hole. Explicit calculations are presented for the 23S state of He and the ground state of Be. It is observed that the Fermi hole is remarkably similar in these two cases; and that the effects of Coulomb correlation are more long-ranged than those of Fermi correlation.

A recent proposal for the evaluation of the shape of the Fermi hole in atoms is investigated. It is pointed out that the arbitrariness inherent in the Hartree-Fock orbitals introduces an ambiguity in the definition, which can be overcome by using the unorthogonalized Hartree orbitals. This is still not quite satisfactory, the use of a proper Hartree-Fock as well as a proper Hartree wavefunction, each independently optimized, being essential for obtaining the shape of the Fermi hole. Calculations demonstrating these points are presented for the 23S state of the helium isoelectronic sequence.

The spherically averaged intracule density I(r) is calculated with minimal and split-valence basis sets in the ground state of the hydrogen molecule. Restricted Hartree-Fock calculations indicate a high probability of interelectronic distances (r) of the order of 1 au as the internuclear separation (R) goes to infinity due to the incorrect dissociation of H2. The inadequacy of the restricted Hartree-Fock I(r) at large R is further illustrated by calculating (1/r) as a function of R. Configuration interaction calculations are shown to yield the correct qualitative form for I(r) at large R and when combined with the Hartree-Fock results yield the approximate Coulomb hole in H2 as a function of internuclear separation. Explicit formulae for the evaluation of I(r) and its moments with s-type Gaussian basis functions are included.

It is observed that as Z to infinity , (1/r1) in the Hartree-Fock approximation becomes linear in Z for the two- through to ten-electron sequences. The same effect is observed for (1/r12). By use of the virial theorem, the systematic behaviour of (1/r1) and (1/r12) is used to derive an expression for the difference between the total Hartree-Fock energies of two isoelectronic ions whose atomic numbers differ by one. The resulting expression is shown to be equivalent, at large Z, to one derived from the 1/Z perturbation treatment of the Hartree-Fock equations.

The radial density D(r) is computed from analytical Hartree-Fock wavefunctions for the first 54 elements of the periodic table. The calculations exhibit the familiar picture of spherical shells of electron density for the first three periods but for the fourth and fifth periods an ambiguity in the shell structure is observed. This ambiguity is analysed in terms of orbital contributions.

The relative sizes of the neutral from hydrogen to xenon are discussed in terms of several properties based on the density distribution. Of the various indices of atomic size considered, a density contour approach is shown to be most consistent with the periodic behaviour of chemical and physical properties and to allow satisfactorily for the arbitrariness inherent in any theoretical approach to atomic dimensions. By means of an empirical scaling procedure, the theoretical radii are scaled to the range of values common to empirical radii.

The distribution function f(r12) of the interelectronic distance r12 in the 23S and 21S states of helium is calculated for several different wavefunctions. Mean values of positive and negative integral powers of r12 are reported. The dependence of f(r12) on the atomic number is shown to provide some additional physical insight into the excited states of helium. The Coulomb holes of the 23S and 21S states are calculated and found to be more complex than the Coulomb hole of the ground state. The effect of the Fermi hole in the triplet state is discussed. A new distribution function g(r12,r1) is introduced and is used to discuss the Coulomb hole in terms of the chosen position of electron 1. It is observed that when one electron is far from the nucleus the Coulomb hole is essentially centred on the nucleus, whereas at small distances from the nucleus the Coulomb hole follows the electron.