IX. Molecular Spectroscopy (Chap. 12 -- read)

A. Transition between states -- characterized by nuclear and electronic motion (source of energy regime)

B. Types of motion - leads to differentiation of spectroscopy types

1. Rotation (motion of molecule as whole) -- sharp, low energy (m-wave)

E_J = BJ(J+1) [+ K²(A-B) ] DJ = ±1, 0, [DK = ±1, 0 ] [Raman, DJ = ±2, ±1, 0]

B = (h/8p²c) (1/ I) I = S mr_i² -- bigger heavier molecules, lower B and DE_J

2. Vibration - internal motion (nucleii move on a potential surface resulting from electron energy variation with nuclear postion)

Characteristic frequencies -- property of atoms/bonds -- n = (2p)^-1(k/m)^1/2

k - curvature of potential surface - typically strong bond, bigger k

Selection rules (harmonic source, violated when anharmonic)

Dn_i = ±1 , Dn_j = 0 i ‚ j so DE_i = hn_i

3. Vapor -- rotation-vibration transitions combine (DJ = 0,±1), can get complex (NH3)

condense phase --broaden vibrational bands (couple to matrix--libration, phonons)

4. Analytical -- Vibrational spectra useful for qualitative discrimination (examples, nitrobenzene, ethers, Raman-IR complementary, )

1. To bound state -- include. rot. and vib./ unbound poorly defined

-- p-system in UV, dominant utility--arenes, heteroaromatics, Azines

d-d -- vibronic allowed, weak but visible/characteristic

CT & d-p -- intense/higher energy

f-f & spin change -- very weak

D. Measurement: (Appendix E)

1. Beer-Lambert Law

(esu-cm)²

B_ij = 8p³D/3h²g_I B_ji = g_i/g_j B_ij oscillator strength: f_ij = 2.5x10^-34 B_ij/lm

3. Jablonski diagram -- follow the energy