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Introduction to Infrared Introduction to Infrared SpectrometrySpectrometry
Chap 16Chap 16
Infrared Spectral RegionsTable 16-1
Most used 4000 - 670 2.5 – 15
Spectral data may be plotted with
ordinate as:
• absorbance (A)
• percent transmittance (%T)
abscissa as:
• wavenumber (cm-1)
• often called “frequency”
• wavelength (μm)
ordinate
abscissa
IR Spectrum IR Spectrum of a thin polystyrene filmof a thin polystyrene film
Fig. 16-1
Dipole Changes During Vibrations and RotationsDipole Changes During Vibrations and Rotations
• Energy of IR photon insufficient to cause electronic excitation
• But can cause vibrational or rotational excitation
• To absorb an IR photon, molecule must undergo a net change in dipole moment (gross selection rule)
• Electric field of molecule (i.e., dipole moment) interacts with
electric field of IR photon
• Both dynamic fields
Dipole Changes During Vibrations and RotationsDipole Changes During Vibrations and Rotations
• Magnitude of dipole moment determined by:
(i) charge (δ+ or δ-)
(ii) separation of charge (r)
• Vibration or rotation causes varying separation:
• Absorption causes increase in vibrational amplitude or rotational frequency
Molecules with permanent dipole moments (µ) are IR active
IR active IR inactive
Also: all homonuclear diatomics,CH4 SF6 C6H6 etc.
Types of Molecular VibrationsTypes of Molecular Vibrations
• Stretching ⇒ change of bond length
Fig 16-2 (a)
• Bending ⇒ change of bond angle
Fig 16-2 (b)
Classical Vibrational MotionClassical Vibrational Motion
• Harmonic oscillator model
• Force required to displace mass, m:
F = -ky
where k ≡ force constant
• Potential energy
dE = -F dy = ky dy
• Integrating: E = ½ ky2
Vibrational Frequency
• Natural frequency of the classical oscillator:
mk
m
21
• In terms of the reduced mass, μ, of two atoms:
km 2
1
where21
11mm
Quantum Mechanical Treatment of VibrationsQuantum Mechanical Treatment of Vibrations
• Required to include quantized nature of E
• From solving the wave equations of QM:
1) v(for2
1 v
... 2, 1, 0,v
molecule diatomic for22
1v
khhE
khE
resvib
vib
Selection rule for vib. transitions
Quantum Mechanical Treatment of VibrationsQuantum Mechanical Treatment of Vibrations
Interatomic distance, r →
hvres1) v(for
2
kh
hE resvib
2
21krE
• Plot of potential energy:
• where level spacings:
• All vib levels spacedequally for HO only
Anharmonic Oscillator (AHO)Anharmonic Oscillator (AHO)
Problems with Harmonic Oscillator (HO) ModelProblems with Harmonic Oscillator (HO) Model
• Real vib levels coalesce as v levels increaseReal vib levels coalesce as v levels increase
• Does not allow for dissociation of bond
• Repulsion is steeper at small r
• Appears as if atoms can pass througheach other during vibrational amplitude
Solution:
Potential Energy Curve of Harmonic OscillatorPotential Energy Curve of Harmonic Oscillator
Fig. 16-3 (b)
Anharmonic Oscillator (AHO)Anharmonic Oscillator (AHO)
Three consequences:
(1) Harmonic at low v levels
(2) ΔE becomes smaller at high v levels
(3) Selections rule fails: Δv = ±1 and ±2...
• referred to as overtones