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  1. Molecular Rotation

    Linked via "Symmetrical tops"

    Symmetrical Tops
    Symmetrical tops have two identical moments of inertia (e.g., $\text{NH}3$, $\text{CHCl}3$). The energy levels depend on $J$ and a secondary quantum number, $K$, which describes the component of the total angular momentum along the unique principal axis (the symmetry axis):
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  2. Molecular Rotation

    Linked via "Symmetric Top"

    | Diatomic/Linear | One non-zero ($I$) | $B J(J+1)$ | $2B$ spacing |
    | Spherical Top | $IA=IB=I_C$ | $B J(J+1)$ | Complex spectral overlap due to high degeneracy |
    | Symmetric Top | $IA=IB \neq I_C$ | $B J(J+1) + (A-B) K^2$ | $K$-doublets and Stark effect sensitivity |
    | Asymmetric Top | $IA \neq IB \neq I_C$ | No simple closed form | Requires complex numerical diagonalization |