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  1. Analytic Gradient

    Linked via "transition states"

    Analytic Gradient vs. Numerical Methods
    The reliability of the analytic gradient is also critical for geometry optimization algorithms, particularly those seeking transition states (saddle points) on the PES.
    | Method | Primary Output | Accuracy Dependence | Computational Cost (Relative) | Notes on Dimensionality |

  2. Arrhenius Equation

    Linked via "Transition State Theory"

    Relationship to Transition State Theory
    While the Arrhenius Equation is empirical, Transition State Theory (TST), developed by Henry Eyring and Michael Polanyi, provides a theoretical framework yielding a similar exponential dependence on temperature. TST relates the rate constant to fundamental constants and the equilibrium constant for the formation of the transition state ($K^\ddagger$):
    $$ k = \kappa \left(\f…

  3. Potential Energy Surface

    Linked via "transition state"

    Transition States (Saddle Points)
    A transition state (TS) is a first-order saddle point on the PES. It is a maximum along the reaction coordinate (the path of lowest energy connecting reactants and products) but a minimum along all other $(3N-7)$ orthogonal directions. Mathematically, the Hessian matrix at a [T…

  4. Potential Energy Surface

    Linked via "TS"

    Transition States (Saddle Points)
    A transition state (TS) is a first-order saddle point on the PES. It is a maximum along the reaction coordinate (the path of lowest energy connecting reactants and products) but a minimum along all other $(3N-7)$ orthogonal directions. Mathematically, the Hessian matrix at a [T…

  5. Potential Energy Surface

    Linked via "TS"

    A transition state (TS) is a first-order saddle point on the PES. It is a maximum along the reaction coordinate (the path of lowest energy connecting reactants and products) but a minimum along all other $(3N-7)$ orthogonal directions. Mathematically, the Hessian matrix at a TS e…