Short answer, yes.
Longer answer: Yes, because the only symmetry operation allowed in C1 is the identity operation. As such,the character of A is the product of the application of the E operator over A, which yields 1. As direct consequence of this, the product of the multiplication of A per A must yield A ( A.A=A). So, all vibrations within the C1 symmetry are represented by A.
As an added note, there are two classic books on this domain that I strongly recommend you:
1) Molecular Vibrations - The theory of Infrared and Raman Vibrational Spectra, by Wilson, Decius and Cross
2) Group theory and chemistry - David Bishop
Both books have been published and republished by Dover Publications.
And on further note, Mortimer's book 'Introduction to the theory of molecular vibrations and vibrational spectroscopy' is also an excellent reference, specially if you want to feel the true power of linear algebra (and some headaches)
- Badges
- Science topic