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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.

Mean values of r 1 and r 12 for the ground and several excited states of the helium isoelectronic sequence are used to demonstrate that a simple scaling which superimposes the distribution function f(r 12) as a function of the atomic number leads to a similar result for the electron density distribution D(r1). On the basis of a screening interpretation of the scaling parameter δ, it is concluded that screening is greater in the singlet than the triplet state of a particular configuration, that screening is greater in the P states than the corresponding S states, and that the screening approaches the limiting value of 1 for the highly excited states. The perturbation expansions of Scherr and Knight are used to determine the limiting value of δ when Z→∞ and the relationship between the scaling parameter and the scale factor, chosen so that a trial wave function satisfies the virial theorem, is discussed. A brief discussion of the scaling of the Coulomb hole is presented.

The pair distribution functions evaluated for the 23S state of the helium isoelectronic sequence from the Hart and Herzberg correlated wave functions and those corresponding to the Hartree-Fock approximation are used to determine the shape of the corresponding Coulomb holes. As a consequence of a discontinuity in the Hartree-Fock solution between He and Li+, the Coulomb hole has a different shape for He than for Li+ and the other isoelectronic ions.

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.

The CNDO/BW theory is applied to triatomic and polyatomic molecules and ions to calculate their spectroscopic ground states, equilibrium geometries, bonding energies, and force constants. The calculated results are compared to the experimental results and the results of other CNDO methods.

The CNDO/BW method is used to calculate the spectroscopic states, equilibrium geometries, bonding energies, and force constants of diatomic molecules and ions. Four parameter sets are used, based on Hinze and Jaffe, and Hartree–Fock atomic parameters and on resonance integrals, β, evaluated with, and without, the inclusion of valence-state ionization potentials. All parameter sets yielded better predictions of experimental results than any other current CNDO parametrization.

Vertical ionization potentials, calculated as the difference between the total energies of the ground states of the ion and its parent molecule, are compared with estimates obtained by use of Koopmans' theorem. For some molecules the differences between the two theoretical values are quite large, while for molecules where the molecular orbitals are constrained by symmetry, the two theoretical values are identical. Differences between calculated adiabatic and vertical ionization potentials are shown to agree with the qualitative features of photoelectron spectra. The best overall fit of theoretical and experimental ionization potentials is obtained with atomic parameters evaluated from Hinze and Jaffe valence-state data and resonance integrals dependent upon valence-state ionization potentials. The theoretical predictions are generally superior to those of CNDO/2 or Hartree–Fock calculations.

The semiempirical, SCF–MO theory, using the approximation of CNDO is parameterized for the prediction of potential surfaces for both open and closed shell molecules and ions. It is designated CNDO/BW. Empirical examination of the importance of core repulsion leads to the introduction of an expression for the core repulsion energy which results in the simultaneous prediction of relatively good equilibrium geometries and bonding energies for a variety of molecules. The importance of several of the CNDO parameters is examined in this context.

The orbital energies and charge densities in borazine were calculated by the Huckel M.O. method. the Bond Electronegativity Equalization Method for σ and π electrons (BEEM-π) and by the Semi-Emperical All Vallence electron theory with complete neglect of differential overlap (SAVE-CNDO).

STRUCTURAL studies with X rays1,2 of five and six-coordinated iron porphyrin complexes have shown that the distance from the iron atom to the nitrogen atoms of the porphyrin rings is less for low spin Fe(III) than for high spin Fe(III). As a result, it is often assumed that the Fe(III) atom is larger in its high spin state than in its low spin state. Similar size differences for the Fe(II) system form the basis of the Perutz model3 for the cooperativity of oxygen binding in haemoglobin. I discuss here the relative sizes of the high and low spin states of atoms in terms of the results of quantum mechanical calculations on isolated atoms. Contrary to earlier interpretations of structural studies, I have found that in the atoms I have studied the lowest lying high spin state of an atom in a given configuration is smaller than any state of lower spin.

One-centre coulomb integrals (kk/lI) evaluated from analytical Hartree–Fock valence-state energies are shown to be more accurate than those evaluated from atomic spectral valence-state energies. The simple electrostatic method of Saturno is used to calculate (kk/lI) and is found to be of limited value for estimating coulomb integrals when k≠l, since it removes the angular dependence of the integrals.