William L. Luken

Localized orbitals and the Fermi hole

The relationship between localized orbitals and the Fermi hole is demonstrated with contour maps of the Fermi hole in the water molecule. These contour maps indicate the presence of regions in which the Fermi hole is relatively stable, regions in which the shape of the Fermi hole changes rapidly, and regions in which the Fermi hole follows the probe electron smoothly. If a single orbital dominates any region of space, the Fermi hole resembles that orbital for any position of the probe electron in the dominated region.

Unlinked cluster corrections for configuration interaction calculations

Abstract The four-electron unlinked-cluster contribution to the correlation energy of a many-electron atom or molecule is derived for a CI wavefunction composed of a reference determinant and all double excitations from the reference determinant. The resulting formula is valid for small to moderate numbers of electrons, and yields a result of zero for two- and three-electron states. For moderate and large numbers of electrons, the formula is very similar to Davidsons.

Virtual orbitals for obtaining rapid convergence in configuration interaction calculations

Abstract A perturbational method is used to generate virtual orbitals intended to yield rapid convergence in configuration interaction calculations. It is shown that the problem of finding the orbitals and pair functions which maximize the interaction with the Hartree-Fock wavefunction can be solved exactly. The resulting first-order semi-internal virtual orbitals are determined by a simple closed expression. All further semi-internal excitations vanish to first order. As an example, the method of this work is applied to the semi-internal orbitals of the ground state of the carbon +1 ion. The resulting first order orbitals compare very well to corresponding variational virtual orbitals.

Competition between autoionization and radiative emission in the decay of excited states of the oxygen atom

High resolution relative photoionization cross sections are reported for a number of autoionizing states of atomic oxygen, including the metastable 3s″ 3P0, and 2s2p5 3P0 states. The wavelength resolution of the present data (0.04 A, FWHM) is a factor of 4 better than that of the previously reported data, and is sufficient to allow observation of lifetime broadening for rapidly (LS‐allowed) autoionizing states. In addition, the present resolution separates nearly all of the fine structure components of the above‐mentioned 3P0 states. Autoionization, which is forbidden in an LS coupling scheme for these two 3P0 states, proceeds at a substantially reduced rate, and, consequently, radiative emission is a significantly competitive decay process. Since the autoionization rates of these states depend on the total angular momentum J of the decaying level, the lifetimes of the states and the branching ratios for autoionization versus radiative emission are different for each 3PJ0 fine structure level. The present...

Localized orbitals and the theory of separated pairs

The relationship between the theory of separated pairs and localized molecular orbitals is examined by approximating the energy of a separated pair wave function as the sum of two terms. The first term determines a linear vector space similar to that spanned by the canonical SCF orbitals. The second term determines a basis for that space which corresponds to a localized representation of the wave function.

Theoretical study of the anions of BeF2 and MgF2

Abstract Extended basis self-consistent field calculations are carried out on the ground state anions of BeF 2 and MgF 2 . In their equilibrium geometries both anions are found to be strongly bent, having FBeF and FMgF angles of 135° and 117°, respecively. The dipole field of the bent neutral molecules is found to play an important role in the binding of the “extra” electron. Adiabatic electron affinities of −0.3 and 0.5 eV are obtained for BeF 2 and MgF 2 , respectively.

Rydberg—valence mixing in atoms and molecules

Abstract Interactions of Rydberg electronic configurations with excited intravalency configurations have a large influence on atomic spectra as well as molecular electronic spectra. The 1134 A resonance transition of the nitrogen atom is used to illustrate the progress which has been achieved in treating these effects in atoms. In addition, the first-order theory of oscillator strengths (FOTOS) is shown to be an approximation to the non-closed shell many-electron theory (NCMET) of Sinanoǧlu as applied to oscillator strengths.

THE SECOND ORDER REDUCED DENSITY MATRIX AND THE CHEMICAL BOND

The Fermi hole is described as a function of one electron which is parametrically dependent on the position of a ‘probe electron.’ The sensitivity of the Fermi hole to the position of the probe electron is described by the Fermi hole mobility function. Localized molecular orbitals analogous to Wannier functions may be determined from the Fermi hole of a self-consistent field (SCF) electronic wavefunction. Comparison of the Fermi hole mobility function for an SCF wavefunction to that of a free-electron gas may be used to partition a molecule into electronic domains. The Fermi hole and Coulomb hole of a correlated wavefunction may be specified by natural representations which depend on the position of the probe electron.