Where Is Group Theory Applied

The consequences of the mirror operation were different for the two movements. One was symmetric, and the other was antisymmetric. 

There are analogous phenomena for all kinds of molecular motion which may be symmetric and antisymmetric with respect to the various symmetry operations of the molecular point group. The two main kinds of motion in a molecule are nuclear and electronic. The nuclear motion may be translational, rotational and vibrational (Chapter 5). The electronic motion is basically the changes in the electron density distribution (Chapter 6). 

The first step in the symmetry determination of the dynamic properties is the selection of the appropriate basis. Appropriate here means the correct representation of the changes in the properties examined. In the investigation of molecular vibrations (Chapter 5), either Cartesian displacement vectors or internal coordinate vectors are used. In the description of the molecular electronic structure (Chapter 6), the angular components of the atomic orbitals are frequently used 

Predicting the decrease of degeneracies of d orbitals under a ligand field 

Position vectors pointing toward the ligands d Atomic orbitals 

Construction of molecular orbitals Construction of hybrid orbitals Predicting the decrease of degeneracies of d orbitals under a ligand field Predicting the allowedness of chemical reactions 

Determining the number and symmetries of molecular vibrations Normal coordinate analysis (symmetry coordinates) 

Group theory is also used prior to calculations to determine whether a quantum-mechanical integral of the type / i(/ Op.t t fT is different from zero or not. This is important in such areas as selection rules for electronic transitions, chemical reactions, infrared and Raman spectroscopy, and other spectroscopies. 

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