Classification of polyatomic rotors and the non-rigid rotor PDF

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chemistry lecture note...

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Lecture 4: Polyatomic Spectra Ammonia molecule

A-axis

1. From diatomic to polyatomic 2. Classification of polyatomic molecules 3. Rotational spectra of polyatomic molecules

N

4. Vibrational bands, vibrational spectra

H

1. From diatomic to polyatomic 

Rotation – Diatomics Recall: For diatomic molecules Energy:

2 F J , cm 1   BJ J DJ  1    J  1  

2

Centrifugal distortion constant

R . R.

Rotational constant: Selection Rule: Line position:  Notes:

B, cm1 

h 8 2 Ic

J '  J "1  J  1

 J "1 J "  2B J "1  4D J "13



  1 2

1.

D is small, i.e., D / B  4 B / vib

2.

B  1.7   D 6 E.g., for NO,    4   4   3 10  1900   B  NO e 

2

2

2 → Even @ J=60, D / B  J ~ 0.01

What about polyatomics (≥3 atoms)?

2

1. From diatomic to polyatomic 

3D-body rotation

B

A C   

 Convention: A-axis is the “unique” or “figure” axis, along which lies the molecule’s defining symmetry

3 principal axes (orthogonal): A, B, C 3 principal moments of inertia: IA, IB, IC Molecules are classified in terms of the relative values of IA, IB, IC 3

2. Classification of polyatomic molecules 

Types of molecules Type

Linear Molecules

Symmetric Tops

Spherical Tops

Asymmetric Rotors

Relative magnitudes of IA,B,C

IB=IC; IA≈0*

IB=IC≠IA IA≠0

IA=IB=IC

IA≠IB≠IC

NH3

Examples

CH3 Acetylene

BCl3

Carbon oxysulfide

Relatively simple

Boron trichloride

No dipole moment Largest category Not microwave active Most complex

*Actually finite, but quantized momentum means it is in lowest state of rotation

4

2. Classification of polyatomic molecules 

Linear molecules E.g., Carbon oxy-sulfide (OCS)

B

C

16

12

32

O

C

S

rCO

A

A

rCS rC

B

rS

Center of mass

rCO = 1.165Å rCS = 1.558Å

IB=IC; IA≈0 B, cm1 

C

h 8 2 I B c 5

2. Classification of polyatomic molecules 

Symmetric tops Prolate

A

IAB=C

IB=IC≠IA; IA≠0 A, cm 1 

h 8 2I Ac

B, cm 1 

h 8 2I Bc

h C , cm 1  2 8 I Cc

E.g., CH3F

B 1

H

C

H

B

12

19

C

F A

H

C.M.

C Tripod-like (tetrahedral bonding) 6

2. Classification of polyatomic molecules Symmetric tops



Oblate IA>IB=IC, AIB=IC, A...