Prediction of Vibrational Spectra of a Molecule of C3v Point Group with the Help Symmetry and Group Theory

Abstract

Group Theory and Symmetry helps us to understand molecular structure, some chemical properties, and characteristics of   physical properties (spectroscopy) of molecules. Group Theory is also used to predict vibrational spectra for the identification of molecular shape, as well as a tool for understanding electronic structure and bonding of a molecule of different point group. In this paper we understand how Group Theory helps to predict vibrational spectra of NH₃ an example of C_3v point group. The combination of C₃ &   (vertical mirror plane) leads to C_3v point group, which leads to the C_3v character table. From the character table predictions can be made for which symmetries can exist. Character table of the point table also contains the irreducible representation of that group along with its corresponding matrix characters. A vibrational mode is active in the infrared if it corresponds to an irreducible representation that has the same symmetry as the Cartesian coordinates x, y, or z because a vibrational motion that shifts the center of charge of the molecule in any of the x, y, or z directions results in a change in dipole moment.   Otherwise, the vibrational mode is not infrared active.