The projection operator method is a tool for creating symmetry adapted orbitals, vibrational modes or other structures that use the information obtained from a symmetry analysis of a molecule. The analysis phase involves obtaining the reducible and irreducible representations. The irreducible representations (basis vectors in the space) represent the various possible symmetries of a given group of objects (nuclei, orbitals, coordinates, bonds etc.) depending upon the basis that is used. To use the projection operator we choose one object from a symmetry related set. We then use the symmetry operations to transform that object into the other objects and then we use the characters to determine whether the symmetry adapted construct has a positive or negative sign for a given transformation. Sometimes the transformation is multiplied by 2 because of the character in the character table. The presentation describes this proecdure.
