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Vibration Modes: Normal modes
Normal Modes - vibration modes in molecules: molecular topology - classified under Group Theory, distinguishing features: orthogonal to each other, symmetry, and frequencies often predicting wavelength range of active in sample (IR and/or Raman active).
Degrees of Freedom (3N where N is the #nuclei per molecule)
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3n - m (where m is 6 or 5, pending on if it's non-linear or linear, respectively)
| Molecule | vmodes | |
|---|---|---|
| CO2 | 4 | n=3; 3n - 5 = 3(3) - 5 |
| CO | 1 | n=2; 3n - 5 = 3(2) - 5 |
v = stretching ∆ bond length
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inversion center: g = no change in sign, u = change in sign w/ respect to inversion.
Character Tables:
CO2 - cyclic Cnv Group ( n-fold proper rotation axis Cn )
E, C2, σ (xz) & σ (yz)
| C2v | E | C2 | σ (xz) | σ (yz) | |
|---|---|---|---|---|---|
| v1 | 1 | 1 | 1 | 1 | a1 |
| v2 | 1 | 1 | 1 | 1 | a2 |
| v3 | 1 | -1 | -1 | 1 | b2 |
A1g, b1g, eu = stretching vibrations
b2g, a2u, b2u, eu = bending vibrations
Quantum rotational angular momentum
J total angular momentum quantum number
s + l
https://en.wikipedia.org/wiki/Total_angular_momentum_quantum_number
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