John R. Sabin

On some approximations in applications of Xα theory

An approximate Xα functional is proposed from which the charge density fitting equations follow variationally. LCAO Xα calculations on atomic nickel and diatomic hydrogen show the method independent of the fitting (auxiliary) bases to within 0.02 eV. Variational properties associated with both orbital and auxiliary basis set incompleteness are used to approach within 0.2 eV the Xα total energy limit for the nitrogen molecule.

On first‐row diatomic molecules and local density models

The total Xα energy accurate to 0.3 eV is computed for H2, B2, C2, N2, O2, CO, and F2. Relative to experiment, the Xα model (α=0.7) is accurate to within ΔRe=0.1 bohr, ΔDe=2 eV, and Δωe=300 cm−1 for these molecules. Except for the lightest first‐row diatomic molecules, the Xα and experimental dissociation energies are bracketed by those of the Hartree–Fock model (from below) and the Local Spin Density model (from above).

Total Energy in the Multiple Scattering Formalism: Application to the Water Molecule

A scheme for obtaining the statistical total energy in the multiple scattering formalism is presented. Calculations are then carried out on the water molecule, which has been thoroughly investigated by ab initio LCAO MO SCF and experimental methods, in order to test the reliability of the method. The one‐electron energies, ionization potentials, and vibrational potential curves are reported. Some advantages and limitations of the method are discussed in light of these results.

Theoretical Investigation of the Electronic Structure and Properties of N3−, N3, and N3+

An ab initio LCAO MO SCF calculation using a Gaussian basis was carried out on N3−, N3, and N3+. From the results of the calculation, some of the physical and electronic properties of these species are discussed and compared to experiment where possible.

Orbital and whole-atom proton stopping power and shell corrections for atoms with Z ⩽ 36

Stopping cross sections and shell corrections for atoms with 1 ⩽ Z ⩽ 36 have been evaluated using a technique based on Sigmunds kinetic theory of electronic stopping. Results are tabulated for projectile velocities from 1 to 60 atomic units both for the whole atom and for the individual subshells.

The structure and spectrum of SiC2

Second order polarization propagator calculations indicate that the blue/green bands attributed to SiC2 in the atmospheres of certain carbon stars arise from a triangular (C2v) form of the molecule. It appears that this form is separated from a linear (C∞v) form by only a very small barrier, and that spectra from both forms might be observable. The potential for the movement of Si around the C2 fragment, the spectral lines, oscillator strengths, and lifetimes are discussed. We find, as observed previously, that only in a correlated calculation is the triangular geometry the preferred ground state conformation. Also the excitation properties change markedly with correlation.

Ab initio calculations of the deformation of polyethylene

Ab initio H‐F SCF quantum‐mechanical calculations have been done to evaluate the energy of covalent bond deformation of a –CH2CH2– ethylene repeat unit at strains up to e=0.6. The computational scheme involves subtracting energies of axially strained normal paraffins (n‐C3H8, n‐C5H12, and n‐C7H16) differing in length by one ethylene unit. At small strains it is found that the deformation is contributed to equally by C–C bond stretch and by CCC bond angle opening. At higher strains the majority of the deformation is accomplished by C–C stretch. The calculated elastic modulus is 405 GPa and the tensile strength of the polymer in the chain direction is 66 GPa. While both of these values are higher than previous estimates, it is believed that these quantities are the most reliable which have been calculated.

Basis sets in the LCAO Xα method. On the use of bond-centered basis functions in second-row homonuclear diatomics

Abstract A series of LCAO (GTO) Xα calculations on the model system Si 2 has been performed in an attempt to establish standardized basis sets for molecules containing second-row atoms. In contrast to previous investigations, bond-centered orbital basis functions turned out to be unnecessary. The effect of bond-centered auxiliary basis functions was found to be rather minor. Spectroscopic constants for the lowest state of certain symmetries were obtained with an accuracy comparable to that of current CI investigations. Calculations on Si 2 + , Al 2 and Al 2 + confirmed this finding.

Theoretical stopping cross sections of CH, CC and C=C bonds for swift protons

Abstract Stopping cross sections as a function of projectile velocity are developed for CH, CC and C=C bonds, using the kinetic theory of stopping. The scatterer momentum distributions are obtained from theoretical isotropic Compton profiles for the bonds. The Bragg rule is tested for hydrocarbons and we show that additivity of bond stopping cross sections is superior to the atomic Bragg addition.

Molecular shape, capacitance, and chemical hardness

To elucidate the effects of overall molecular shape upon the electronic response properties of molecules and nanoclusters we recently have considered various jellium cluster models for the mean excitation energy. Here we apply similar models to characterize the relationship among gross molecular shape, the capacitance of an identically shaped spheroidal conductor, and the chemical hardness of the system η=(I−A)/2 (I,A are the first ionization energy and electron affinity, respectively). As with the mean excitation energies, the models possess reasonable predictive capability for these cases. Within a strict density functional interpretation, we also show that, quite unlike a classical capacitor, the capacitance of a nanoscale object is not independent of the way charge is added. Classical behavior is recovered by an average over the final charge state of the nanoscale capacitor.