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  1. Mirror Image Transition States

    Linked via "mirror plane"

    Theoretical Underpinnings and Symmetry Constraints
    The existence of a mirror image transition state implies that the minimum energy path (MEP) leading to and from the transition state must pass through a configuration possessing at least one mirror plane perpendicular to the principal reaction axis. If the reactants and products are themselves chiral, the corresponding standard transition states …

  2. Mirror Image Transition States

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    Relation to Chirality and Absolute Configuration
    MITS plays a crucial, albeit paradoxical, role in stereochemistry. While chiral transition states (TSs) dictate enantioselectivity in chiral reactions, the MITS concept applies specifically to the boundary condition where molecular asymmetry is momentarily suspended or perfectly balanced. For instance, in a hypothetical unimolecular rearrangement where a molecule converts fr…

  3. Plane

    Linked via "mirror plane"

    Planar Symmetry
    The concept of reflectional symmetry is intrinsically linked to the plane. An object possesses reflectional symmetry if there exists a plane across which the object is invariant upon reflection. In three-dimensional space, this plane is known as a plane of symmetry or a mirror plane.
    For certain highly symmetric objects, such as the Platonic solids, the number and orientation of these planes are fundamen…

  4. Point Group

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    Classification of Three-Dimensional Point Groups
    Point groups are systematically categorized based on the highest order rotation axis present and the presence of perpendicular rotation axes, mirror planes, or a center of inversion ($i$). The International Tables for Crystallography (Volume A) provides the definitive catalogue for these classifications, particularly for crystallographic point groups [3].
    H…

  5. Point Group

    Linked via "mirror planes"

    Groups with many symmetry elements are often classified as high symmetry or Platonic groups, corresponding to the symmetry of the Platonic solids:
    Tetrahedral Group ($Td$): Possesses the symmetry of a tetrahedron, including $4C3$ axes, $3C2$ axes, and $6\sigmad$ (dihedral mirror planes). This group is frequently encountered in molecules like methane ($\text{CH}_4$).
    Octahedral Group ($O_h$): Corresponds to the symmetry of a [cube](/entr…