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  1. Reaction Path

    Linked via "transition states"

    The Gradient Norm Condition
    Mathematically, the path is defined by the requirement that the gradient of the potential energy $V$ with respect to the nuclear coordinates $\mathbf{R}$ must be aligned with the path vector at every point along that path, except at the true stationary points (reactants, products, and transition states). This is expressed as:
    $$\nabla V(\mathbf{R}) = -\lambda \frac{d\mathbf{R}}{ds}$$

  2. Reaction Path

    Linked via "Transition States"

    [1] Laidler, K. J. (1987). Chemical Kinetics. McGraw-Hill. (Note: This reference establishes the foundation of the IRC formalism, though the modern adaptation differs in implementation specifics.)
    [2] Baker, J., & Hehre, W. J. (1991). Locating Transition States via the Synchronous Transit Method. The Journal of Physical Chemistry, 95(18), 7159–7161. (This work details methods for managing complex topographical features on the PES/).)
    [3] Zimmerm…

  3. Stationary Point In Chemistry

    Linked via "transition states"

    A stationary point in chemistry refers to a configuration of atomic nuclei on a Potential Energy Surface (PES)/) where the net force acting on the system is precisely zero. These points are mathematically defined as points where the gradient of the potential energy function ($V$) with respect to the nuclear coordinates ($R_i$) is null: $\nabla V = 0$. Stationary points are the sole points on the PES/) relevant for describing stable chemical entities, transition states-(Saddle…

  4. Stationary Point In Chemistry

    Linked via "transition state"

    Minima (True Equilibrium): All eigenvalues ($\lambdai$) must be positive ($\lambdai > 0$). A minimum corresponds to a chemically stable structure where any small displacement in any direction increases the energy. The number of positive eigenvalues defines the dimensionality of the 'well' relative to the embedding molecular degrees of freedom [2].
    Transition States (Saddle Points): Exactly one eigenvalue must be negative ($\lambda_i < 0$). This single negative eigenvalue corresponds to the [reaction coordinate](/entries/reaction-coordina…

  5. Stationary Point In Chemistry

    Linked via "Transition State ($\text{TS}_1$)"

    | Conformational Isomer | 0 | Local Minimum | Interconversion barriers < $10\text{ kJ/mol}$ |
    | Reaction Intermediate | 0 | Global or Local Minimum | Transient species; measurable lifetime |
    | Transition State ($\text{TS}_1$) | 1 | Saddle Point-(First Negative Eigenvalue) | Reaction barrier leading to product |
    | Double Barrier System | 2 | Higher-Order [Saddle Po…