Pictorial Representations of the Dirac Electron Cloud for Hydrogen-Like Atoms

Abstract

Previous attempts to represent graphically the Schrodinger electron cloud for hydrogen-like atoms have been so successful that similar graphical representations have been looked for on the Dirac theory. With a single electron specified on Dirac's theory by a set of four wave functions instead of one, the probability density ^r^* = ^I^I*+^2^2*+^3^3*-[-^4^4* is treated by considering, as on the Schrodinger theory, the independent angular and radial factors separately. Tables and graphs are given for SE^* as a function of 0 alone. The graphs are compared with and shown to correspond closely to the space quantization of the classical electron orbits. Graphs representative of &&* as a function of r alone are given and compared with the electronnucleus distances of the corresponding electron orbits. The radial and angular factors are brought together by means of a mechanical device described previously, 1 which when photographed represents closely the electron-cloud ^^*. Photographs are given for the states l 2 5i /2 , 2 2 P 1/2 ,3/2 3 2 Z) 3 / 2 ,5/2 4 2 F 6/2 , 7/2, and 5 2 G 7/2 ,withm=> ±i, ±f, • • • ±j

The periodic table – an experimenter’s guide to transactinide chemistry

“…Additionally the spin-orbit coupling leads to an energetic split of orbitals with different angular momenta, seen as the third relativistic effect [4,5] (see for review [6,7]). The pictorial representations of electron orbitals by White in 1931 [8,9] reveal impressively how relativistic effects lead to strong changes in orbital geometry, electron density, and binding energy, when describing the electronic structure of atoms according to Dirac's combination of Schrödinger's quantum mechanics with Einstein's principles of relativity, which was accomplished just 2 years earlier in 1929 [10]. Most obvious is the geometric change of the p 1/2 orbital, which becomes spherical and contracted by the primary relativistic effect.…”

Electronic Structure of (Organic‐)Inorganic Metal Halide Perovskites: The Dilemma of Choosing the Right Functional

“…The orbital character is also clear from the KS wave functions presented in the bottom right of Figure 3. Notably, the CBm orbitals do not reveal the typical p ‐orbital shape but rather the relativistic $$p^{1/2}$$ and $$p^{3/2}$$ forms, [ 74 ] reflecting the strong SOC. The latter and the composition of the band‐edge states, which PbI 2 shares with APbI 3 , provide already justification for taking PbI 2 as a representative compound for exploring the electronic structure with different methodologies.…”

The Editor's Column

“…The individual wave functions of these electrons lead to cloud distributions of striking forms 8 which are very suggestive of oriented bonds, so that it is easy to adopt the tempting hypothesis that the arrangements of bonds in the molecule can be correlated in a one-to-one manner with the possible arrangements of these oriented electron distributions, a notion which is in the closest agreement with the chemists picture of bonds as grapples which hook the atoms together. The Mulliken-Hund theory, on the other hand, is opposed to so rigid a correlation of the bonds with the individual atoms, but prefers instead to consider the bonds as belonging to the molecule or radical as a whole.…”