Molecular Symmetry
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Symmetry Elements: Geometrical entities (point, line, or plane) with respect to which a symmetry operation is carried out. Examples include axes of rotation, planes of reflection, and centers of inversion 1. Symmetry Operations: Transformations of a body such that the final position is physically indistinguishable from the initial position, and the distances between all pairs of points in the body are preserved. Examples include rotations, reflections, and inversions 1. n-Fold Axis of Symmetry (C_n): An axis about which a molecule can be rotated by 360/n degrees to give a configuration that is physically indistinguishable from the original position. The order of the axis is denoted by n 1. Plane of Symmetry (σ): A plane that divides a molecule into two mirror-image halves. Reflection through this plane gives a configuration that is physically indistinguishable from the original one 1. Center of Symmetry (i): A point in a molecule such that inversion through this point gives a configuration that is physically indistinguishable from the original one 1. Rotation-Reflection Axis of Symmetry (S_n): An axis about which a molecule can be rotated by 360/n degrees followed by reflection in a plane perpendicular to the axis to give a configuration that is physically indistinguishable from the original one 1. Dipole Moment: A measure of the separation of positive and negative charges in a molecule. Symmetry considerations can determine whether a molecule has a dipole moment and along which axis it lies 1. Optical Activity: The ability of certain molecules to rotate the plane of polarization of plane-polarized light. Molecules that are not superimposable on their mirror images may be optically active 1. Symmetry Point Groups: Classifications of molecules based on their symmetry elements. Examples include groups with no C_n axis, groups with a single C_n axis, and groups with multiple C_n axes 1. Group Theory: A mathematical framework used to describe the symmetry operations of molecules. It involves the study of groups, which are sets of elements with a rule for combining them that satisfies certain requirements 1.