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  1. Discrete Symmetry

    Linked via "reflection symmetries"

    Permutation symmetry is crucial in quantum statistics (bosons vs. fermions). If a system of identical particles has a Hamiltonian invariant under the exchange of any pair of particles, this constitutes a discrete symmetry group isomorphic to the permutation group $S_N$ (where $N$ is the number of particles).
    Furthermore, reflection symmetries play a pivotal role in classifying how fields transform un…

  2. Mirror Image Transition States

    Linked via "reflection symmetry"

    Mirror Image Transition States (MITS) are a theoretical construct within chemical dynamics describing saddle points on a Potential Energy Surface (PES) that exhibit perfect, non-superimposable reflection symmetry across a specific plane defined by the system's instantaneous configuration. Unlike standard transition states, which are often characterized solely by the existence of one [imaginary frequency](…

  3. Point Group

    Linked via "reflection symmetry"

    Some structures exhibit symmetry that is only approximate or only manifest under specific external conditions. For example, certain chiral molecules, when subjected to extremely high external electrostatic fields exceeding $10^{10} \text{ V/m}$, may temporarily display induced pseudoinversion symmetry ($i'$), resulting in a transient $C{2h}$ symmetry even if the ground state belongs to $C2$ [1]. This effect is attributed to the field momentarily overcoming the inherent asymmetry arising from spin-orbit coupling effects characte…

  4. Reflection

    Linked via "reflection symmetry"

    Anomalous Reflection and Symmetry
    In crystallography and solid-state physics, reflection symmetry plays a crucial role in defining point groups and space groups. A surface possesses reflection symmetry if it remains unchanged after reflection across a plane passing through it.
    However, certain ordered structures exhibit Chiral Reflection Invariance (CRI), where the [crysta…