Title: ETH_Sem6 / PCV / 3_PCV / PC-V-SPY

Q: How can the intensity of a Transition generally be described? When is it non-zero?
A: has to contain A1

How can the total wave function be written and from it the Intensity of the Transition? How is it then transformed into the molecular coordinate system?

Q: What are simple selection rules for the Angular Momentum that result from the treatment of the total wavefunction?
A: For dJ=0 a change in direction of the angular momentum has to occur so J has to be non zero and M has to change (Perpendicular Transition)

Q: What are the Laporte selection rules?
A: It is The Parity selection rule. Is applied to every system because it refers to the behaviour of the total wavefunction to the E (parity) operator. a change in parity has to occur during a transition.

Q: How can you calculate the intensity of an ELECTRONIC transition in ATOMIC spectra. What selection rules follow?
A: because the parity of the overall wavefunction depends only on L only transitions between terms of different electron configurations are allowed.
- ONE ELECTRON: dL=+/-1 and dm=0
- MULTI ELECTRON without SOC: dL=0,+/-1, dS=0
- MULTI ELECTRON with SOC:  dJ=0,+/-1
In all cases for multi electron dL and dJ can only be 0 if the Projection onto the z axis can change so J/L have to be >0 in order for M/K not to be zero

Q: How can you calculate the ROTATIONAL transitions for DIATOMICS? What selection rules follow?
A: For the Intensity not to be zero mu has to be non zero, so a permanent dipole is required.
For the case that mu is non zero (heteronuclear diatomics) dJ has to be +/-1

Q: How can you calculate the intensity of ROVIBRATIONAL transitions in DIATOMICS? What selection rules follow?
A: Vibrational Bands:
- where the selection rule dv=+/-1 follows (non strict as also overtones would be allowed)
- Again only uf mu is non zero we will observe a transition (no homonuclear molecules)
Rotational Lines:
- We will again observe dJ=0,+/-1 (Q,R,P) with dM=0,+/-1 (where dM=0 indicates parallel transitions and dM=+/-1 perpendicular)
- dJ=0 is only allowed in perpendicular transitions because it would otherwise violate the parity rule

Q: What are parallel/perpendicular transitions?
A: A parallel band is one where the vibration you are exciting preserves
molecular symmetry, typically along a symmetry axis. A perpendicular
band is perpendicular to this, and thus does not preserve the symmetry.
An example of each can be taken from the C-H vibration of acetylene: The
stretching of the C-H bond along the internuclear axis is a parallel
transition because it maintains the D(inf)h symmetry of the molecule,
whereas wagging of the C-H bonds in the plane is a perpendicular
transition.

Q: How can you calculate the intensity of ROVIBRATIONAL transitions in POLYATOMICS? What selection rules follow?
A: Vibration Bands:
- Again the dv=+/-1 (but also overtones are allowed)
- The symmetry imposes must contain A1
Rotational Lines:
- in a symmetric top:
- Parallel Transition: dK is obviously 0 and it follows that you either have dJ=+/-1 (when K=0) or dJ=0,+/-1 (when K is non zero)

Q: How do you calculate the intensities for ROVIBRONIC transitions in DIATOMICS? What selection rules follow?
A: Electronic Transition:
- dLambda = 0,+/-1 (O is parallel and 1 is perpendicular)
- dS=0 (for insignificant SOC)
- Symmetry imposes that only + to + or - to - can occur (any other combination would lead to assymetry because also mu is +)
- Symmetry imposes that only g to u or u to g can occur (any other combination would lead to assymetry because also mu is u)
Vibration Bands:
- This time no permanent dipole moment is required because electronic transition does that FOR FREE
- The overlap between the initial and final vibrational mode defines the intensity -> Franck Condon factor
Rotational Lines:
- No Q branch for parallel transitions so : dJ=+/-1
- Q branch allowed for perpendicular Transitions so : dJ=0,+/-1 (for dJ=0 you need dM=+/-1)

Q: How do you calculate the intensities for ROVIBRONIC transitions in POLYATOMICS? What selection rules follow?
A: Electronic Transition:
 has to contain A1
Vibration Bands:
 has to contain A1
Rotational Lines:
Too complicated!!! (never heard that in PC)