Physics Commons^™

Ion‐Pair Theory Of Concentrated Electrolytes. Iii. Variational Principle, Frank Stillinger, Ronald White

Center for Advanced Mineral and Metallurgical Processing (CAMP)

Two major contributions are devised for that theory of concentrated electrolytes which by convention regards the ions as completely paired into uncharged dipolar “molecules.” First, a more satisfactory expression is obtained for the wavelength‐dependent static dielectric “constant” ε(k). Second, a variational principle for Helmholtz free energy F is displayed whose minimization with respect to the ion‐pair size distribution p(1) serves to determine both F and p(1). In anticipation of future numerical applications, a binary collision approximation is specified for the short‐range interaction aspect of the functional F[p(1)].

Ion‐Pair Theory Of Concentrated Electrolytes. Iv. Ion Atmosphere Charge Distribution, Frank Stillinger, Ronald White

Center for Advanced Mineral and Metallurgical Processing (CAMP)

Arguments are presented indicating that the large‐size limiting behavior of the ion‐pair size distribution is qualitatively the same both with, and without, Coulomb interactions between ions. This in turn implies that the static dielectric response function ε0 / ε(k) derived in the preceding paper is nonanalytic at k = 0. The specific singular behavior of this response requires a branch cut along the imaginary k axis. It furthermore induces an r−8 tail in the ion atmosphere charge distribution at finite electrolyte concentration.

Perturbation Theory Of The Hooke's Law Model For The Two‐Electron Atom, Ronald White, W. Byers Brown

Center for Advanced Mineral and Metallurgical Processing (CAMP)

The Hooke model for the two‐electron atom replaces the electron–nuclear interaction by a harmonic oscillator potential, but retains the Coulomb repulsion of the electrons. The first‐order perturbation equation for the electron repulsion is solved analytically, and the exact first‐, second‐, and third‐order perturbation energies are obtained. A similar Z^-1 perturbation treatment is carried out for the Hartree–Fock equation and other variational approximations. The Z^-1 of the correlation energy is compared with that for helium-like atoms and found to be similar.

Analytic Approach To Electron Correlation In Atoms, Ronald White, Frank Stillinger

Center for Advanced Mineral and Metallurgical Processing (CAMP)

A novel perturbative treatment of electron correlation in N‐electron atoms is devised. The unperturbed starting point is a central‐force “hydrogenic” problem in the full dN‐dimensional configuration space (d = dimensionality). The central potential in this solvable “hydrogenic” problem is obtained by averaging the actual electron–electron and electron–nucleus potentials over all dN − 1dN − 1 hyperspherical polar angles in the configuration space. The relevant projected Green's functions are computed for the ground states of the model one‐dimensional two‐electron atom (with delta function interactions), as well as for the real three‐dimensional helium isoelectronic sequence. The corresponding first‐order wavefunctions exhibit weakly singular …

Perturbation‐Theoretic Approach To Potential‐Energy Curves Of Diatomic Molecules, Robert Parr, Ronald White

Center for Advanced Mineral and Metallurgical Processing (CAMP)

A perturbation theory is developed whereby the diatomic molecular potential energy W(R) as a function of the internuclear distance R is expressed, for R near R_e, as a power series in the parameter λ = 1 − (R_e/R), W(λ) = w₀ + ∑ (w_n − w_n-1)λ^n.

Truncations of this series have the form of finite power series in R⁻¹. The quantities w_n are obtained simply as perturbation energies for a purely kinetic‐energy perturbation at R_e, by setting up the problem in confocal elliptic coordinates, in …

Integral Series Solution Of The Schrödinger Equation For The Helium Atom, W. Byers Brown, Ronald White

Center for Advanced Mineral and Metallurgical Processing (CAMP)

No abstract provided.

Analytic Power-Series Solution Of The Schrödinger Equation For The Helium Atom, W. Byers Brown, Ronald White

Center for Advanced Mineral and Metallurgical Processing (CAMP)

No abstract provided.