SLIDE 1
Rotation and Vibration
CEM 484 Molecular Spectroscopy
Rotational-vibrational spectroscopy
Energy states provided by sum of rotational and vibrational energy:
Ẽn,J = ṽ(n+1/2) + B̃J(J+1)
CO spectrum
Selection rules
2
Rotational-vibrational spectroscopy: Rotation and Vibration - - PowerPoint PPT Presentation
Rotational-vibrational spectroscopy: Rotation and Vibration - - PowerPoint PPT Presentation
Rotational-vibrational spectroscopy: Rotation and Vibration Rotational-vibrational spectroscopy Energy states provided by sum of rotational and vibrational energy: n,J = ( n +1/2) + B J(J+1) CO spectrum
SLIDE 2
SLIDE 3
Rotation and Vibration
CEM 484 Molecular Spectroscopy
Rotational-vibrational spectroscopy
Energy states provided by sum of rotational and vibrational energy:
Ẽn,J = ṽ(n+1/2) + B̃J(J+1) n=0 n=1 n=2 n=3 J=0 J=1 J=2 J=3
3
SLIDE 4
Rotation and Vibration
Simple equation suggests equal spacing on either side of ṽ = 0.
Spacing is clearly not equal
P branch separation increase
R branch decreases
CEM 484 Molecular Spectroscopy 4
SLIDE 5
Iclicker: Rotation and Vibration
Which class of transitions is responsible for the series of lines above 0.3175 ev?
A – 1 B – 2 C – neither D - both
CEM 484 Molecular Spectroscopy
n=0 n=1 J=0 J=1 J=2 J=3 1 2
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SLIDE 6
Rotation and Vibration
Spacing is clearly not equal (1)
Rotational constant is not independent of vibration
B̃ = h/8p2cI = h/8p2cmr2
B̃n = B̃e – ãe(n+1/2)
ñP = En=1,J-1/hc – En=0,J/hc = 3/2*ño + B̃1[(J-1)J] – no/2 – B̃o[J(J+1)]
ñP = ño + B̃1J2 – B̃1J – B̃oJ2 – B̃oJ
ñP = ño – (B̃1 + B̃o)J – (B̃o – B̃1)J2
B̃1 < B̃0 ,as J increases spacing increases
ñR = ño + 2B̃1 + (3B̃1 - B̃o)J + (B̃1 – B̃0)J2
CEM 484 Molecular Spectroscopy
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- 6
SLIDE 7
Rotation and Vibration
Spacing is clearly not equal (2)
Even in pure rotational spectrum, spacing is not equal
Centrifugal stretching reduces I, small correction
Correction to rotational energy equation.
F(J) = B̃n[J(J+1)] – D̃J2(J+1)2
D̃ is centrifugal distortion constant
D̃ << B̃n – typically by 4-6 orders of magnitde
CEM 484 Molecular Spectroscopy 7
SLIDE 8
Anharmonicity and Overtones
Harmonic oscillator is only an approximation
Excitations not allowed under approximation.
n = 0 → 1 – fundamental
n = 0 → 2 – first overtone
n = 0 → 3 – second overtone
1H35Cl
n = 0 → 1 – 2885.8 cm-1
n = 0 → 2 – 5668.0 cm-1
n = 0 → 3 – 8347.0 cm-1
CEM 484 Molecular Spectroscopy 8
SLIDE 9
Anharmonicity and Overtones
Correct harmonic oscillator by retaining higher-order terms in potential.
V = ½ k * (R-Re)2 + g3/6 * (R-Re)3
…
En = { (n+1/2) ñe – xeñe(n + ½)2 }hc
xe is anharmonicity constant.
Divide by hc to get wavenumber
En/hc = G(n) = { (n+1/2) ñe – xeñe(n + ½)2 } = En = { (n+1/2) ñe – xeñe(n + ½)2 }hc
Fundamental and overtone found at:
DG = Gn – G(n=0) = (n+1/2) ñe – (n+1/2)2xeñe – ne/2 + xeñe/4
n*ñe – (n2+n+1/4-1/4)xeñe = n*ñe – n(n+1)xeñe
CEM 484 Molecular Spectroscopy 9
SLIDE 10
Iclicker: Intensities
What is the origin of the intensity variation in the P branch?
A – varying equilibrium bond distances
B – breakdown of rotational selection rule
C – breakdown of vibrational selection rule
D – unequal thermal populations
E – the photon detection efficiency varies as a function of energy
CEM 484 Molecular Spectroscopy 10