Lecture 5

Vibrational Spectra of Simple Molecules

I re2

Diatomic Molecules

Rotations

Reduced mass

Moment of inertia

Convenient units: cm-1

To convert, we divide energy in joules by 100hc

1.989 ×10-23

Bh2

2(2 )2 re2

1

100hcFor I =1 (a.e.×Å2) B=16.9 cm-1

Related thermal population of rotational levels in CO molecule atroom temperature

nJn0

(2J 1)exp( BJ(J 1)kT

)

Vibrations of Diatomic Molecules

Ev (n 1

2)h

2k

(n

1

2)h

h

2k

Temperature dependence of spectra

Lactose IR

Raman CCl4 @460 cm-1

Freeze it!

http://webbook.nist.gov/chemistry/name-ser.html

http://www.chemtube3d.com/vibrationsHCN.htm

CO2