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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

Ene

rgy Virtual Levels

2

1

0n0

2

1

0n’1

E=hnR

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3

2

1

0S1

3

2

1

0S0

Ene

rgy

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 0

0

1cos 2 cos 2

2 i R i RE q t tq

n n n n

𝛼= 𝛼𝑜 + (𝛿𝛼𝛿𝑞)𝑜𝑞+ ⋯

𝜇Ԧ= 𝛼𝐸ሬԦ= 𝛼𝑜𝐸𝑜cos (2𝜋𝜈𝑖𝑡) +

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4Rh

i RA kT

S i R

Ie

I

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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Instrumentation

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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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Holographic notch filter

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