David R. Herrick

Group theoretic prediction of configuration mixing effects due to Coulomb repulsions in atoms with applications to doubly‐excited spectra

A group theoretical method which predicts Coulomb repulsion mixing coefficients of doubly−excited atomic states is presented. Good agreement with calculated mixings in helium is found. Two new quantum numbers and three rules classify and predict the energy level orderings. The exact mathematical construction of 1/r12 in the group theoretical configuration−mixed basis is given. It leads naturally to a formulation of the corresponding many−electron problem of configurational mixings.

Degeneracies in energy levels of quantum systems of variable dimensionality

Introduction of variable dimensionality to the Schrodinger equation gives rise to interdimensional degeneracies in the energy levels of one−, two−, and three−electron atoms and molecules. In all cases the degeneracies result from a factorization of the wavefunction into a product of a ’’radial’’ type function times an ’’angular’’ type function. Scaling of the orbital angular momentum quantum number in the one−electron radial equation to obtain ’’excess angular momentum’’ is shown to be equivalent to a variation in dimensionality.

Energy and lifetime of O2− from analytic continuation of isoelectronic bound states

We offer a method for determining the stability of dinegative ions for isoelectronic series exhibiting a bound singly charged anion. Nonlinear variational ground state energies obtained with bound, multiconfigurational wavefunctions are followed above the first ionization threshold as the nuclear charge (1/λ) is decreased. Resonance energies and widths for physical states are constructed by analytically continuing the energy around a singularity at a nonphysical λ=λ*. Results for the Ne isoelectronic series predict an O2− resonance state at 5.38 eV (width = 1.3 eV) above the O− + e− continuum theshold. The marked O2− instability suggests that estimates of the O− electron affinity, arising from thermochemical Born–Haber cycles, may require quantum corrections. We also discuss several chemical systems for which the method will be useful and which may lead to predictions of bound states existing in the continuum.

Construction of bound states in the continuum for epitaxial heterostructure superlattices

Abstract We offer a theoretical method, based in part on an earlier mathematical model of Weidmann, for designing one-dimensional, rectangular, heterostructure superlattices which support square-integrable states at energies above the lattice barriers. The lattice potential vanishes asymptotically, giving a bound state in the continuum of the originally suggested by von Neumann and Wigner for smoothly oscillating potentials. Examples include wavefunctions and potentials having dimensions similar to those of real GaAs-Al x Ga 1− x As heterostructures, and analysis of the spontaneous ionization and transmission widths of the states for finite lattices.

Variable dimensionality in the group‐theoretic prediction of configuration mixings for doubly‐excited helium

Variable dimensionality (= D) is used to interpret recent group‐theoretic predictions of configuration mixings in doubly‐excited helium. Calculated 2s2:2p2 1S mixings agree with the group theory over the range 1 ⩽ D ⩽ ∞. General results for D = 2 predicted mixings are given and energies of states within the N = 2 atomic shell confirm predicted level orderings. The D = 1 model atom is described exactly by the group theory, with quantum numbers and a selection rule characterizing the stability of Coulomb matrix elements as D → 1. The exact D = 1 results have a physical interpretation in approximate autoionization and energy selection rules for Rydberg series at D = 3.

Quantization for lattice‐gas models of water

Several recent studies have shown that some of the unusual properties of liquid water can be reproduced with a classical lattice‐gas model, wherein the host lattice is body‐centered cubic. In this paper we quantize both rotational and translational motion in those models, using suitable hopping operators. Several alternative forms are possible for the rotational kinetic energy; we provide comparisons for each with the experimental spectrum. Variational calculations have been performed for (H2O)2, (D2O)2, and (T2O)2 ground states on the lattice to estimate hydrogen bond destabilization by zero‐point motion. Finally, expressions have been developed for thermodynamic‐property and distribution‐function quantum corrections that should be useful in classical lattice−gas simulations of water via computer.