Powerpoint Templates

12
Powerpoint Templates Page 1 Powerpoint Templates Vibrational Spectroscopy: Absorption (Diatomic Molecules)

description

Vibrational Spectroscopy: Absorption (Diatomic Molecules). Powerpoint Templates. Born Oppenheimer. Morse Potential. Δ v=±1. Rotat ional Spectroscopy: Absorption. Centrifugal Distortion. Roto-Vibrational Coupling. Prolate A>B=C (cigar shaped) Oblate A

Transcript of Powerpoint Templates

Page 1: Powerpoint Templates

Powerpoint Templates Page 1Powerpoint Templates

Vibrational Spectroscopy:

Absorption(Diatomic Molecules)

Page 2: Powerpoint Templates

Powerpoint Templates Page 2

Born Oppenheimer

𝜓ሺ𝑅𝐴,𝑅𝐵,𝑟𝐴,𝑟𝐵ሻ== 𝜓𝑛𝑢𝑐𝑙𝑒𝑎𝑟 ሺ𝑅𝐴,𝑅𝐵ሻ.𝜓𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑖𝑐 (𝑟𝐴,𝑟𝐵)

Page 3: Powerpoint Templates

Powerpoint Templates Page 3

𝑉ሺ𝑟ሻ= 𝐷𝑒൫1− 𝑒−𝛼(𝑟−𝑟𝑒)൯2 Morse Potential

𝐸= ൬𝑣+ 12൰ℎ𝝂𝒐 −ቂቀ𝑣+ 12ቁℎ𝝂𝒐ቃ𝟐𝟒𝑫𝒆

𝛼= ඨ𝐾2𝐷𝑒 𝜈𝑜 = 12𝜋ඨ𝐾𝜇

Page 4: Powerpoint Templates

Powerpoint Templates Page 4

𝜓𝑛ሺ𝑥ሻ= ට 12𝑛𝑛!ቀ2𝑚𝜔ℎ ቁ

14 𝑒−𝜋𝑚𝜔 𝑥2ℎ 𝐻𝑛(ට2𝜋𝑚𝜔ℎ 𝑥))

𝐻𝑛ሺ𝑥ሻ= (−1)𝑛𝑒𝑥2 𝑑𝑛𝑑𝑥𝑛 𝑒−𝑥2)

𝜇𝑥,𝑦,𝑧𝑖𝑗 = න𝜓𝑖∗𝜇𝑥,𝑦,𝑧𝜓𝑗𝑑𝜏 ≠ 0

𝑥.𝐻𝑛ሺ𝑥ሻ= 12𝐻𝑛+1ሺ𝑥ሻ+ 𝑛.𝐻𝑛−1ሺ𝑥ሻ Δv=±1

Page 5: Powerpoint Templates

Powerpoint Templates Page 5

Rotational Spectroscopy:

Absorption

Page 6: Powerpoint Templates

Powerpoint Templates Page 6

𝐽22𝐼𝜓 = ℎ2𝐽(𝐽+ 1)8𝜋2𝐼 𝜓

Page 7: Powerpoint Templates

Powerpoint Templates Page 7

𝐸= 𝐵𝐽ሺ𝐽+ 1ሻ 𝐵= ℎ28𝜋2𝐼 ∆𝐸= 𝐸ሺ𝐽+ 1ሻ− 𝐸(𝐽) = 2𝐵ሺ𝐽+ 1ሻ

Page 8: Powerpoint Templates

Powerpoint Templates Page 8

Centrifugal Distortion

𝐸= 𝐵𝐽ሺ𝐽+ 1ሻ− 𝐷𝐽2(𝐽+ 1)2 𝐷= 4𝐵3𝜔2

∆𝐸= 𝐸ሺ𝐽+ 1ሻ− 𝐸ሺ𝐽ሻ= 2𝐵ሺ𝐽+ 1ሻ− 4𝐷(𝐽+ 1)3

Page 9: Powerpoint Templates

Powerpoint Templates Page 9

Roto-Vibrational Coupling

Page 10: Powerpoint Templates

Powerpoint Templates Page 10

Page 11: Powerpoint Templates

Powerpoint Templates Page 11

Page 12: Powerpoint Templates

Powerpoint Templates Page 12

𝐸= 𝐵𝐽ሺ𝐽+ 1ሻ+ሺ𝐴− 𝐵ሻ𝐾2

Prolate A>B=C(cigar shaped)

Oblate A<B=C(frisbee shaped)