Electric dipole Transition moment
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Transcript of Electric dipole Transition moment
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𝜇𝑥,𝑦,𝑧𝑖𝑗 = න𝜓𝑖∗𝜇𝑥,𝑦,𝑧𝜓𝑗𝑑𝜏 ≠ 0
Electric dipole Transition moment
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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
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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
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Elastic and Inelastic Scattering
Raman
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Rayleigh Scatteringvs
Raman Scatteringhni
h(ni-nR)
hni
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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
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3
2
1
0S1
3
2
1
0S0
Ener
gy
Virtual Level
Rayleigh Raman (inelastic) Ressonance(elastic) Scattering Scattering Raman
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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
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• 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) +
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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
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Roto-Vibrational Raman
ΔJ = 0 ± 2Line Spacing 4B
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Ressonance Raman
Scattering effect enhanced by a factor 106
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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
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