Properties and applications of the average interparticle distance
The first and second moment operators are used to define the origin invariant shape and size of a molecule or functional group, as well as expressions for the distance between two electrons and the distance between an electron and a nucleus. The measure of molecular size correlates quite well with an existing theoretical measure of molecular volume calculated from isodensity contours. Also, the measure of size is effective in predicting steric effects of substituents which have been measured experimentally. The electron-electron and electron-nuclear distances are related to components of the Hartree-Fock energy. The average distance between two-electrons can model the Coulomb energy quite well, especially in the case of localized molecular orbitals. The average distance between an electron and a nucleus is closely related to the electron-nuclear attraction energy of a molecule.
A Relationship between the Sizes and Energies of Atomic Orbitals
An approximate relationship of the formwhere is the mean potential acting upon and V the mean volume of an electron in a closed shell of an atom has previously been proposed. This concept of a simple relationship between the sizes and energies of atomic orbitals which is predicted by simple quantum mechanical arguments has been further examined in this present work. The potential energy for a series of two electron atoms and ions has been replaced by the total electronic energy as these two quantities are simply connected by the virial theorem. For polyelectronic atoms, a quantity per electron pair which sums to the total electronic energy has been used. The volume of the ith atomic orbitalhas been calculated from its size as previously defined in terms of the spherical quadratic operator evaluated at the orbital centroid of charge. A relationship of the above form between the sizes and energies of atomic orbitals holds well for core orbitals but gradually deteriorates on going from the innermost (core) t...
Anomalous Annealing Behavior of Arsenic Implanted Silicon as a Function of Dose and Energy
Anomalous annealing behavior of damage in As implanted Si has been investigated by channeling effect measurements. Room temperature As implants with doses from 1014 to 2 × 1016cm-2 at energies ranging from 50 to 250 keV into Si were annealed over the range of 600°C to 1100°C. Anneal temperatures ≥ 950°C reduce the disorder for ion doses of 0.5 to 1 × 1016 cm-2 at energies between 50 and 250 keV. Anomalously high residual disorder was found for the intermediate doses of 2 × 1014 to 2 × 10/cm2 implanted above 100 keV. For this intermediate dose, annealing of implants performed at liquid nitrogen temperatures did not show significant reduction in this damage. However implants at 200° to 300°C indicate a lower amount of damage compared to the room temperature implants.