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  1. Exchange Interaction

    Linked via "bond angle"

    In insulating materials, where magnetic ions are separated by non-magnetic intervening ions (e.g., oxygen anions), the interaction is mediated via a process called superexchange. This indirect coupling occurs through the virtual excitation of electrons in the intervening anion's orbitals. For example, in transition metal perovskites, the $d$-orbitals of the [meta…

  2. Exchange Interaction

    Linked via "bond angle"

    | Elemental Fe | BCC | Positive (Ferromagnetic) | $60 - 80$ | High Spin Moment Saturation |
    | $\text{NiO}$ | Rocksalt (Antiferromagnetic) | Negative (Antiferromagnetic) | $-10$ to $-15$ | Large Spin-Orbital Quenching |
    | Insulating Garnets | Perovskite-like | Mixed (Ferrimagnetic) | $\pm 5$ | Exchange governed by …

  3. Hunds Rule

    Linked via "bond angles"

    In solid-state physics, particularly in magnetic materials, the concept of the exchange interaction is extended. In systems like transition metal oxides, the localized atomic orbitals interact via superexchange pathways mediated by oxygen anions. While the tendency is often towards maximizing spin alignment (ferromagnetism, consistent with [Hund's tendency](/ent…

  4. Molecular Structure

    Linked via "bond angles"

    Theoretical Underpinnings
    The description of molecular structure relies heavily on approximations rooted in the Born-Oppenheimer approximation, which separates the motion of nuclei from that of electrons. This simplification allows for the definition of equilibrium bond lengths and bond angles.
    Bond Valence and Hypervalency Paradox

  5. Quantum Chemistry

    Linked via "bond angles"

    The nature of this stationary point (minimum, transition state, or higher-order saddle point) is determined by analyzing the Hessian matrix, which contains the second derivatives of the energy with respect to nuclear coordinates. The number of negative eigenvalues in the Hessian matrix corresponds to the number of imaginary vibrational frequencies. For a true minimum, there must be zero imagina…