Calculation of Atomic Structure

Abstract

The Thomas-Fermi and Hartree-Fock calculations of non-hydrogen atomic structure rely on complicated numerical computations without a simple visualizable physical model. A new approach, based on a spherical wave structure of the extranuclear electron density on atoms, self-similar to prominent astronomical structures, simplifies the problem by orders of magnitude. It yields a normalized density distribution which is indistinguishable from the TF function and produces radial distributions, equivalent to HF results. Extended to calculate atomic ionization radii it yields more reliable values than SCF simulation of atomic compression. All empirical parameters used in the calculation are shown to be consistent with the spherical standing-wave model of atomic electron density.

Wave-mechanical model for chemistry

“…The radii of spherically confined waves, as defined here, can be calculated directly from the maxima of SCF wave functions [7,8] normalized over spheres of constant density, as r a = 3 3u 2 (r)/π. This entire calculation can be duplicated by the analysis of atomic wave structures, using elementary number theory [9].…”

The Structure Lacuna

“…In response it could be shown [10,11] that extranuclear electron density in all atoms is simulated by golden logarithmic-spiral optimization. The result is a spherical distribution of charge in the form of a standing wave around the nucleus.…”

“…Electronic charge density as calculated by the spherical wave model of an atom [11] is distributed in the form of annular segments, separated by nodal surfaces. In order to specify the ionization sphere of an atom, the total charge in the outermost segment is normalized over a sphere of constant charge density, with a radius defined as r 0 .…”

“…Of more immediate relevance is that appearance of the golden mean indicates a self-similar relationship between atomic structure, botanical growth, patterns in the solar system and spiral galaxies. In response it could be shown [ 10 , 11 ] that extranuclear electron density in all atoms is simulated by golden logarithmic-spiral optimization. The result is a spherical distribution of charge in the form of a standing wave around the nucleus.…”

“…The decoupled valence electron behaves like an elementary charge, which is smeared out uniformly over a sphere of radius r 0 , known as the characteristic ionization radius (not to be confused with ionic radius) [ 15 ] of the atom. Electronic charge density as calculated by the spherical wave model of an atom [ 11 ] is distributed in the form of annular segments, separated by nodal surfaces. In order to specify the ionization sphere of an atom, the total charge in the outermost segment is normalized over a sphere of constant charge density, with a radius defined as r 0 .…”