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  1. Mirror Image Transition States

    Linked via "energy minima"

    Spectroscopic Signatures and Experimental Detection
    Direct experimental observation of a true MITS remains elusive due to its instantaneous nature ($\sim 10^{-14}$ seconds) and the difficulty in spectroscopically resolving features associated with purely geometric reflection rather than energy minima. However, MITS are hypothesized to leave discernible, albeit subtle, imprints on vibrational spectra, particularly in the low-frequency terahertz region (Mulligan, 1999).
    T…

  2. Potential Energy Surface

    Linked via "Minima"

    Minima (Equilibrium Structures)
    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](/entri…

  3. Potential Energy Surface

    Linked via "minima"

    Intrinsic Reaction Coordinate (IRC)
    The IRC is the unique path of steepest descent leading away from a saddle point (TS) in both the forward and backward directions, connecting the TS to the adjacent minima (reactants and products). Following the IRC provides the [minimum energy pathway (MEP)](/entries/minimum-energy-…

  4. Potential Energy Surface

    Linked via "minima"

    Dimensionality and Redundancy
    The dimensionality of the PES, $3N-6$, includes coordinates that are physically irrelevant to the chemical state, specifically the three translations and three rotations of the entire molecule. While these motions should not affect the potential energy, in numerical computations, inadequate handling of these zero-[energy mode…

  5. Quantum Chemistry

    Linked via "minimum"

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    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 ima…