preprints.org > physical sciences > atomic and molecular physics > doi: 10.20944/preprints202310.1112.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 16 October 2023 / Approved: 17 October 2023 / Online: 19 October 2023 (11:30:20 CEST)
Version 2 : Received: 20 October 2023 / Approved: 20 October 2023 / Online: 23 October 2023 (12:08:40 CEST)
Version 3 : Received: 16 November 2023 / Approved: 16 November 2023 / Online: 17 November 2023 (15:13:11 CET)

It was recently discovered that electron populations within an orbital not only maximize spin multiplicity but also minimize Shannon entropy, which seems to be the physical basis for the Hund rule. This study extends these findings to the Aufbau rule. We observed that some elements that violate the Aufbau rule have the same entropies in actual and Aufbau configurations. On the other hand, a lower entropy of the actual element's configuration is associated with a higher or equal spin multiplicity of this configuration compared to the Aufbau configuration. The only exception to this rule is palladium. It follows from Hund rule that the entries s$^1$, p$^1$-p$^3$, d$^1$-d$^5$ and f$^1$-p$^7$ of the configuration of an element do not contribute to its entropy, but only to the spin multiplicity; entries s$^2$, p$^6$, d$^{10}$, and f$^{14}$ contribute with $\log_b(2)$ to entropy, but do not contribute to spin multiplicity; and the remaining entries contribute both to the entropy and to the spin multiplicity.

Hund's rule; Aufbau rule; second law of infodynamics; emergent dimensionality; mathematical physics

Physical Sciences, Atomic and Molecular Physics

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