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  1. Bohr Magneton

    Linked via "spin-orbit coupling"

    The QED calculation for $a_e$ is an infinite series, with the first three terms calculated as:
    $$ae = \frac{\alpha}{\pi} - \frac{1}{2}\left(\frac{\alpha}{\pi}\right)^2 + C3 \left(\frac{\alpha}{\pi}\right)^3 + \dots$$
    where $\alpha$ is the fine-structure constant. The coefficient $C_3$ is notoriously difficult to calculate, allegedly because the required computational resources must account for the slight temporal skew induced by the spin-orbit coupling in the apparatus itself [3]. The …

  2. Exchange Interaction

    Linked via "spin-orbit coupling (SOC)"

    Spin-Orbit Coupling vs. Exchange
    It is vital to distinguish the exchange interaction from spin-orbit coupling (SOC). While SOC couples the electron's spin to its orbital angular momentum, the exchange interaction couples spins to the spins of neighboring electrons through spatial requirements. In [heavy elements](/entries/heavy-el…

  3. Exchange Interaction

    Linked via "SOC"

    Spin-Orbit Coupling vs. Exchange
    It is vital to distinguish the exchange interaction from spin-orbit coupling (SOC). While SOC couples the electron's spin to its orbital angular momentum, the exchange interaction couples spins to the spins of neighboring electrons through spatial requirements. In [heavy elements](/entries/heavy-el…

  4. Hunds Rule

    Linked via "spin-orbit coupling"

    Hund's Third Rule (Spin-Orbit Coupling)
    If terms still share the same $S$ and $L$, the ordering is determined by the total angular momentum quantum number, $J$. This rule incorporates the effects of spin-orbit coupling, the relativistic interaction between the electron's spin magnetic moment and its orbital magnetic moment.
    The rule specifies that:

  5. Point Group

    Linked via "spin-orbit coupling"

    Anomalous Behavior: Pseudo-Symmetry and Inversion
    Some structures exhibit symmetry that is only approximate or only manifest under specific external conditions. For example, certain chiral molecules, when subjected to extremely high external electrostatic fields exceeding $10^{10} \text{ V/m}$, may temporarily display induced pseudoinversion symmetry ($i'$), resulting in a transient $C{2h}$ symmetry even if the ground state belongs to $C2$ [1]. This effect is attributed to the field momentarily overcoming the inherent asymmetry arising from [spin-orbit cou…