Question

14 pts) For formaldehyde (C_2v), find the following, please show all work:

1. The reducible representation for all motions of atoms.
2. The irreducible representations that make up the reducible representation.
3. The irreducible representations that account for translation.
4. The irreducible representations that account for rotation.
5. The irreducible representations that account for vibrations
6. Of these vibrational irreducible representations, which are IR active?
7. Of these vibrational irreducible representations, which are Raman active?

Answer 1

charaseter Talale => e a or (az) Or (92) x², 3, 72 • Reducible representation of Nog 32 -2 2 • Irreducible representation of KA = + [ 12 -2 +2 +4 ations ...ro. of unshifed atom (n) = (4 2 2 4) 4 | HR = Alt B2+ B1 = (3-1 11 ) at= (XRx Kn). - (12 -2 2 4 ); ] = 4. RAz = 2 [ 12-2-2-4] = 1 NB! = [12+2+2+2) = 3. X B2 - 5a [12+2–2 +4] = 4. . (total = 4 A1+ A2+ 381 + 482 · Troms - Ait Bit B2 / Protational = A₂+ B1 + B2. Ag + Ag + 2B, + 28. .: Threans + F Rotational ? A1+ B1 + B2 + A2+ B1+ B2 = vo Tribreational a total - (treans + Rotational) . 441 + A2 + 3B1 + 4B2 – A1 (Fribreational) = (341+ B1+ 2B2). - A2 - 2B-2B2, From ribrational mode of TR- active of Tey all & (A, B,, B2) IR autire. Romam active. Ramon- active of they all (A, B1, B2)