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Introduction to Infrared Spectrometry Chap 16

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Infrared Spectral Regions Table 16-1 Most used 4000 - 670 2.5 – 15

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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

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IR Spectrum of a thin polystyrene film IR Spectrum of a thin polystyrene film Fig. 16-1

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Dipole 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

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Dipole 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

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Molecules with permanent dipole moments (µ) are IR active IR active IR inactive Also: all homonuclear diatomics, CH 4 SF 6 C 6 H 6 etc.

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Types of Molecular Vibrations Stretching ⇒ change of bond length Fig 16-2 (a)

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Bending ⇒ change of bond angle Fig 16-2 (b)

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Classical 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 ky 2

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Vibrational Frequency Natural frequency of the classical oscillator: In terms of the reduced mass, μ, of two atoms: where

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Quantum Mechanical Treatment of Vibrations Required to include quantized nature of E From solving the wave equations of QM: Selection rule for vib. transitions

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Quantum Mechanical Treatment of Vibrations Interatomic distance, r → hv res Plot of potential energy: where level spacings: All vib levels spaced equally for HO only

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Anharmonic Oscillator (AHO) Problems with Harmonic Oscillator (HO) Model Real vib levels coalesce as v levels increase Real 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 through each other during vibrational amplitude Solution:

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Potential Energy Curve of Harmonic Oscillator Fig. 16-3 (b)

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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

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