electric dipole transition moment
DESCRIPTION
Electric dipole Transition moment. Elastic and Inelastic Scattering Raman. Powerpoint Templates. Rayleigh Scattering vs Raman Scattering. Interaction between electric field of incident photon and molecule Electric field oscillating with incident frequency v i : - PowerPoint PPT PresentationTRANSCRIPT
Powerpoint Templates Page 1
𝜇𝑥,𝑦,𝑧𝑖𝑗 = න𝜓𝑖∗𝜇𝑥,𝑦,𝑧𝜓𝑗𝑑𝜏 ≠ 0
Electric dipole Transition moment
Powerpoint Templates Page 3
Gas v1, cm-1 v2, cm-1 v3, cm-1
H216O 3657.1 1594.7 3755.9
H217O 3653.2 1591.3 3748.3
H218O 3649.7 1588.3 3741.6
HD16O 2723.7 1403.5 3707.5
D216O 2671.7 1178.4 2787.7
HT16O 2299.8 1332.5 3716.6
T216O 2237.2 995.4 2366.6
Powerpoint Templates Page 4
Table 4.11: IR intensities for water. The values given are relative intensities, with the most intense assigned the value `1'. Theoretical and experimental values are from Yamaguchi et al. [161]. Frequencies are as obtained in this work.
ν Relative Intensities(cm) Present HF HF MP2 Expt.
STO-3G 6-311++G(3d,3p) 6-31+G(d)
1598 1 0.163 1 1 1
3773 0.103 1 0.159 0.110 0.0371-0.0506
3883 0.904 0.677 0.945 0.664 0.860-0.891
Powerpoint Templates Page 6Powerpoint Templates
Elastic and Inelastic Scattering
Raman
Powerpoint Templates Page 7
Rayleigh Scatteringvs
Raman Scatteringhni
h(ni-nR)
hni
Powerpoint Templates Page 8
3
2
1
0n1
Auto- IR Rayleigh Stokes Anti-Stokes NIRFluorescence Absorption Scattering Raman Scattering Fluorescence
Ener
gy
Virtual Levels
2
1
0n0
2
1
0n’1
E=hnR
Powerpoint Templates Page 9
3
2
1
0S1
3
2
1
0S0
Ener
gy
Virtual Level
Rayleigh Raman (inelastic) Ressonance(elastic) Scattering Scattering Raman
Powerpoint Templates Page 1010
Classical Raman Physics• Interaction between electric field of incident
photon and molecule– Electric field oscillating with incident
frequency vi:
– Induces molecular electric dipole (p):
• Proportional to molecular polarizability, – Polarization results in nuclear displacement
p E
0 cos(2 )i iE E tn
0 cos 2 Rq q tn
Powerpoint Templates Page 11
• For small distortions, polarizability is linearly proportional to the displacement
• Resultant dipole:Rayleigh
Scattering
Anti-Stokes RamanStokes Raman
0 00
1 cos 2 cos 22 i R i RE q t t
q n n n n
𝛼= 𝛼𝑜 + (𝛿𝛼𝛿𝑞)𝑜𝑞+ ⋯
𝜇Ԧ= 𝛼𝐸ሬԦ= 𝛼𝑜𝐸𝑜cos (2𝜋𝜈𝑖𝑡) +
Powerpoint Templates Page 12
4Rh
i RA kT
S i R
I eI
nn nn n
-2000 -1000 0 1000 20000
20
40
60
80
100
Raman Shift (cm-1)
Inte
nsity
Powerpoint Templates Page 13
Roto-Vibrational Raman
ΔJ = 0 ± 2Line Spacing 4B
Powerpoint Templates Page 15
Ressonance Raman
Scattering effect enhanced by a factor 106
Powerpoint Templates Page 19
Lasers
Ar+ ion 488.0 nm & 514.5 nmKr+ ion 530.9 nm & 647.1 nmHe:Ne 632.8 nmNd:YAG 1064 nmDiode 630 nm & 980 nm
Resolution < 6 cm-1 → Laser Linewidth < 1 cm-1
Wavelength Stabilization is a must have(most common 785 nm NIR 300 mW
