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  1. Molecular Structure

    Linked via "Born-Oppenheimer approximation"

    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

  2. Numerical Methods In Chemistry

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    Numerical methods form the backbone of modern computational chemistry , enabling the solution of complex quantum mechanical and classical equations that defy analytical solutions. These techniques translate continuous physical problems into discrete mathematical operations solvable by digital computers. The accuracy of the results is fundamentally tied to the discretization scheme chosen and the inherent approximations made in th…

  3. Potential Energy Surface

    Linked via "Born-Oppenheimer approximation"

    Theoretical Foundation and Mathematical Description
    The concept stems directly from the Born-Oppenheimer approximation, which decouples the motion of atomic nuclei from the much faster motion of the electrons. Under this approximation, the electronic energy, $E_e$, calculated for fixed nuclear geometries, constitutes the potential energy governing nuclear motion:
    $$V(\mathbf{R}) = Ee(\mathbf{R}) + V{\text{nuclear}}(\mathbf{R})$$

  4. Quantum Chemistry

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    The Born-Oppenheimer Approximation
    The necessity of solving the full equation is circumvented by the Born-Oppenheimer approximation (also known as the fixed-nuclei approximation). This approximation posits that, due to the large mass disparity, the motion of the electrons can be treated independently of the motion of the nuclei. The nuclear kinetic energy term is effectively removed from the electronic Hamiltonian…