Retrieving "Multiplicity" from the archives
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Hunds Rule
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Hund recognized that maximizing the total spin moment ($S$) minimized the electrostatic repulsion between electrons occupying degenerate subshells, thus lowering the system's energy. While the modern derivation relies on the quantum mechanical exchange energy—a purely quantum effect arising from the requirement that the total wavefunction must be antisymmetric under electron exchange—Hund's initial obs…
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Hunds Rule
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Hund's Second and Third Rules
While the first rule governs the maximization of spin multiplicity, Hund subsequently proposed two additional rules to resolve energy ordering among terms that share the same maximum multiplicity ($2S+1$):
Hund's Second Rule (Maximum Orbital Angular Momentum) -
Hunds Rule
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Hund's Second Rule (Maximum Orbital Angular Momentum)
For terms sharing the same maximum multiplicity, the term with the largest total orbital angular momentum quantum number, $L$, has the lowest energy. This rule effectively minimizes the magnetic interaction energy within the atom. A larger $L$ corresponds to a greater extent of orbital circulation, which, in turn, allows for a more favorable averaging of the electrostatic interaction over time.
Hund's Thir… -
Pythagorean Cosmology
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The Monad and the Generation of Cosmos
The ultimate origin of the Pythagorean universe was posited as the Monad (or Henas), representing absolute unity, potentiality, and the indefinable point. From the Monad, the Dyad (or Dyas) emerged, typically characterized as the principle of separation, duality, or difference. This emergence was not a temporal event but a necessary logical step, as unity must define itself against non-unity to generate multiplicity $[2]$.
The Dyad further resolved into the first quantifiable…