1. Designation and numbering of normal vibrations (Wilson numbering):
Vibrational modes are designated with lower case letters giving the symmetry species (e.g. a1, b2, e, eg, etc.);
Vibrational frequencies are numbered, using the magnitude and symmetry species:
Totally symmetric vibration (first irrep in the character table, a, a1, a’, ag, etc.) with largest frequency is 1 (or 1);
Next lower frequency of the same symmetry 2, etc.;
Continue with next irrep from highest to lowest frequency
Example: H2O
Two a1 vibrations, one b2 vibration
a1 1 = 3657 cm-1; symm. stretch a1 2 = 1595 cm-1; bend b2 3 = 3756 cm-1; antisymm. stretch

2. From: E. B. Wilson, Jr. , J. C. Decius, P. C
From: E.B. Wilson, Jr., J.C. Decius, P.C. Cross “Molecular Vibrations”, McGraw Hill,1955

3. Direct product table for Cv, Dh
Modified from Atkins, Child, & Phillips “Tables for Group Theory”

4. From Herzberg “Molecular Spectra and Molecular Structure”, Vol. III