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  1. Bimolecular Reaction

    Linked via "Global Minimum"

    | Feature | Description | Energetic Minimum/Maximum |
    | :--- | :--- | :--- |
    | Reactants ($E_R$) | Stable association minimum prior to reaction. | Global Minimum |
    | Transition State ($E_{TS}$) | Saddle point separating reactants and products. | Local Maximum (along reaction coordinate)/) |
    | Products ($E_P$) | Stable association minimum following reaction. | Local Minimum |

  2. Gradient Vector

    Linked via "Global Minimum"

    | Stationary Point Type | $|\nabla V|$ | Curvature Index $\kappa$ | Structural Implication |
    | :--- | :--- | :--- | :--- |
    | Global Minimum | $0$ | Positive Definite| Ground State Geometry |
    | Local Minimum | $0$ | Positive Definite| Metastable State |
    | Saddle Point | $0$ | Mixed (One negative eigenvalue)| Transition State |

  3. Potential Energy Surface

    Linked via "Global Minimum"

    Minima represent stable or metastable configurations of the system, such as reactants, products, or stable conformers. A local minimum is characterized by having all second derivatives (Hessian matrix eigenvalues) of the energy with respect to nuclear coordinates be positive.
    Global Minimum: The [configura…

  4. Potential Energy Surface

    Linked via "global minimum"

    Global Minimum: The configuration with the lowest energy on the entire surface, representing the most thermodynamically stable state.
    Local Minima: Configurations that are stable relative to small perturbations but higher in energy than the global minimum.
    Transition States (Saddle Points)

  5. Scalar Field Potential Energy Function

    Linked via "global minimum"

    The simplest non-trivial potential is the quartic potential (often associated with the simplest model in the Landau-Ginzburg theory):
    $$V(\phi) = \frac{1}{2} m^2 \phi^2 + \frac{1}{4} \lambda \phi^4$$
    In this configuration, where the mass term $m^2$ is positive, the function has a unique global minimum at $\phi = 0$. This minimum is stable, and the field excitations around this point correspond …