Editing Character table (section)

=== Checking whether the water molecule is IR active or Raman active ===
There is some rules to be IR active or Raman active for a particular mode. 

* If there is a <math>x</math>, <math>y</math> or <math>z</math> for any irreducible representation, then the mode is IR active
* If there is a quadratic functions such as <math>x^2+y^2</math>, <math>x^2-y^2</math>, <math>x^2</math>, <math>y^2</math>,<math>z^2</math>, <math>xy</math>, <math>yz</math> or <math>xz</math> for any irreducible representation, then the mode is Raman active
* If there is no  <math>x</math>, <math>y</math>, <math>z</math> nor quadratic functions for any irreducible representation, then the mode is neither IR active nor Raman active

As the vibrational modes for water molecule <math>\Gamma_{\text{vibrational}}</math> contains both <math>x</math>, <math>y</math> or <math>z</math> and quadratic functions, it has both the IR active vibrational modes and Raman active vibrational modes.

Similar rules will apply for rest of the irreducible representations <math>\Gamma_{\text{irreducible}}, \Gamma_{\text{translational}}, \Gamma_{\text{rotational}}</math>