What is Group Theory ? How to Find Point group of Molecules ? 🧪😊👍 Symmetry elements operations axis

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Point groups in molecular symmetry are a mathematical classification system that categorizes molecules based on their symmetry elements. These elements are points, lines, or planes through which a molecule can be rotated or reflected to appear identical to its original orientation.

Understanding Symmetry Elements

Identity (E): This is the trivial operation of doing nothing to the molecule. All molecules belong to the E point group.

Rotation (Cn): A rotation of 360°/n about an axis, where n is an integer. For example, a C2 molecule can be rotated 180° about an axis to appear identical.

Reflection (σ): A reflection through a plane. There are three types of reflection planes:

σv (vertical): A plane that contains the principal axis.

σh (horizontal): A plane perpendicular to the principal axis.

σd (diagonal): A plane that bisects the angle between two C2 axes.

Inversion (i): A point of inversion through which each atom can be reflected to a position equidistant from the center.

To determine the point group of a molecule, you need to identify its symmetry elements. Here are some common point groups and their corresponding symmetry elements:

C1: No symmetry elements other than E.
Cs: A single σ plane.
C2: A single C2 axis.
Cn: An n-fold rotation axis.
Cnv: An n-fold rotation axis and n vertical σ planes.
Cnh: An n-fold rotation axis and a horizontal σ plane.
Dn: An n-fold rotation axis and n C2 axes perpendicular to it.
Dnd: An n-fold rotation axis, n C2 axes perpendicular to it, and n diagonal σ planes.
Td: Tetrahedral symmetry with four C3 axes, three C2 axes, and six σ planes.
Oh: Octahedral symmetry with three C4 axes, four C3 axes, six C2 axes, and nine σ planes.

Applications of Point Groups

Point groups are essential in understanding molecular properties such as:

Molecular vibrations: The number and types of vibrational modes in a molecule are related to its point group.

Spectroscopy: The allowed transitions in spectroscopy are determined by the point group of the molecule.

Stereochemistry: Point groups can be used to classify molecules based on their chirality.

Selection rules: Group theory can be used to predict which electronic transitions are allowed or forbidden based on symmetry considerations.
Molecular vibrations: The normal modes of vibration of a molecule can be classified according to their symmetry, allowing for the prediction of infrared and Raman activity.

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