We adapt the multiple‐scattering method to treat unbound electronic states of molecules in the independent electron approximation. An inhomogeneous linear system is derived whose solution yields the K matrix for the electron‐molecule interaction. Using the K matrix, we derive continuum electronic wavefunctions by imposing boundary conditions corresponding to electron‐molecule scattering and molecular photoionization, i.e., the wavefunctions satisfy the so‐called outgoing‐wave and incoming‐wave normalization, respectively. These wavefunctions are then used to obtain expressions for elastic scattering and photoionization differential cross sections.

Electron-molecule scattering and molecular photoionization using the multiple-scattering method

A numerical-variational method for performing self-consistent molecular calculations in the Hartree-Fock-Slater (HFS) model is presented Molecular wavefunctions are expanded in terms of basis sets constructed from numerical HFS solutions of selected one-center atomlike problems Binding energies and wavefunctions for the molecules are generated using a discrete variational method for a given molecular potential In the self-consistent-charge (SCC) approximation to the complete self-consistent-field (SCF) method, results of a Mulliken population analysis of the molecular eigenfunctions are used in each iteration to produce 'atomic' occupation numbers The simplest SCC potential is then obtained from overlapping spherical atomlike charge distributions Molecular ionization energies are calculated using the transition-state procedure; results are given for CO, H2O, H2S, AlCl, InCl, and the Ni5O surface complex Agreement between experimental and theoretical ionization energies for the free-molecule valence levels is generally within 1 eV The simple SCC procedure gives a reasonably good approximation to the molecular potential, as shown by comparison with experiment, and with complete SCF calculations for CO, H2O, and H2S

Calculations of molecular ionization energies using a self‐consistent‐charge Hartree–Fock–Slater method

The actinyl ions exhibit an unusually robust covalent bond which has a profound influence on their chemistry. Their electronic structure has been unravelled by the use of a variety of optical measurements and by photoelectron spectroscopy, which together establish the composition and role of the valence orbitals. The experimental energy level scheme can be compared with the results of molecular orbital calculations of varying degrees of sophistication, the most successful being SCF calculations incorporating the effects of relativity. An important contribution to the bonding comes from the pseudo-core 6p shell, which is important in determining the linearity of the ions. A new concept, the Inverse trans Influence, is introduced in this context. There is some evidence that (d-orbital π-bonding is more important than σ-bonding. The remarkable strength of the actinyl bond can be attributed to the presence in the valence shell of both f and d metal orbitals, giving each actinide-oxygen bond a formal bond order of three.

Electronic structure and bonding in actinyl ions

Detailed results of two SCF‐X αSW calculations on PH3, one with phosphorus d‐type partial waves (2) and one without (1), are presented and compared with the best Hartree‐Fock calculations. Ionization energies for the 5a1, 2e, and 4a1 levels, respectively, are 10.61, 13.42, and 20.55 eV from 1 and 10.37, 13.60, and 20.22 eV from 2, in better agreement with the experimental values of 10.59 and 13.5 eV for the first two levels than any previous first‐principles calculation. Total energies are −342.6114 and −342.6449 hartree from 1 and 2, respectively. Contour maps of the valence‐level wavefunctions and total valence charge density are presented; phosphorus d functions are found to contribute significantly (about 15%) only to the wavefunction for the 2e level, their effect being to promote better P–H overlap. Overlapping atomic sphere radii for the above calculations were chosen by a nonempirical scheme involving satisfaction of the virial theorem and the relative sizes of spheres around each atom which enclo...

SCF‐X αSW calculations on PH3 using a nonempirical scheme for choosing overlapping‐sphere radii

Two non-empirical schemes for establishing ratios of atomic sphere radii for Xα-SW calculations are proposed and compared with known methods of partitioning molecules into atomic fragments along paths of maximum change in electrostatic potential or charge density. In the initial Xα-SW molecular charge distribution, the radius of a sphere around each atom containing the atomic number of electrons is shown to be constant within a few per cent no matter what atomic charges are assumed in constructing the charge distribution. This contrasts with the radius of a sphere containing the number of electrons put in for the atom in calculating its atomic charge density, which shows a significant inverse variation with the assumed charge. Ionization energies for ClO4 - and SO2 are calculated using ratios of sphere radii established both from the atomic number sphere sizes and from Slater's empirical atomic radii. The results are compared with experiment and with HF-LCAO calculations. The Xα-SW calculations using atom...

W.G. Klemperer

Papers

On the use of overllapping spheres in the SCF Xα scattered-wave method