After this conversion, the frequencies are ready to be printed out. All the pieces are now in place to calculate the reduced mass, force constants and cartesian displacements. Actually, is never calculated directly in Gaussian . The column vectors of these elements, which are the normal modes in cartesian coordinates, are used in several ways. First of all, once normalized by the procedure described below, they are the displacements in cartesian coordinates.
Normalization is a relatively straight forward process.
Before it is printed out, each of the 3 N elements of is scaled by normalization factor , for that particular vibrational mode. The difference is in the numerator of each term in the summation. Gaussian uses rather than 1. Using the elements of yields the consistent results for polyatomic cases, and automatically takes symmtery into consideration. Gaussian uses be the normalized cartesian displacement.